Question 12
Using the equations Soda = 12.5-0.2475t and Water=8.2+0.56t, if sales of
bottled water continue to increase at this rate and sales of carbonated soft drinks
continue to decline, during what year will the amount sold be the same?
I don't know
You answered 7 out of 11 correctly. Asking up to 12.
2 attempts
Answers
The sales of bottled water and carbonated soft drinks will be the same in the year 2028 (in 5.323 years).
How to find the amount sold will be sameTo find the year when the sales of soda and water will be equal, we need to solve the equation:
Soda = Water
12.5 - 0.2475t = 8.2 + 0.56t
where
t = time
collecting like terms
12.5 - 8.2 = 0.2475t + 0.56t
4.3 = 0.8075t
Then we can solve for t by dividing both sides by 0.8075:
t ≈ 5.323
If t is in years, this tells us that the sales of soda and water will be equal in approximately 5.323 years.
To find the year when this will happen, we need to add 5.323 to the current year.
Assuming the current year is 2023, we get:
2023 + 5.323 ≈ 2028.323
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Related Questions
Oak Creek Company is preparing its master budget for 2020. Relevant data pertaining to its sales, production, and direct materials budget are as follows.
Sales: Sales for the year are expected to total 1 million units. Quarterly sales are 20%, 25%, 25% and 30% respectively. The price is expected to be at $40 per unit for the first three quarters and $45 per unit beginning in the fourth quarter. Sales in the first quarter of 2021 are expected to be at 10% higher than the budgeted sales for the first quarter of 2020.
Production: Management desires to maintain the ending finishing goods inventories at 20% of the next quarter’s budgeted sales volume.
Direct materials: Each unit requires 2kg of raw materials at a cost of $10 per kilogram, Management desires to maintain raw materials inventories at 10% of the next quarter’s production requirement for the first quarter of 2020 are 500,000kg.
Prepare the sales, production, and direct materials budgets by quarters for 2020.
Answers
Q1:
Sales = 1,000,000 x 20% = 200,000 units
Revenue = 200,000 x $40 = $8,000,000
Q2:
Sales = 1,000,000 x 25% = 250,000 units
Revenue = 250,000 x $40 = $10,000,000
Q3:
Sales = 1,000,000 x 25% = 250,000 units
Revenue = 250,000 x $40 = $10,000,000
Q4:
Sales = 1,000,000 x 30% = 300,000 units
Revenue = (250,000 x $40) + (50,000 x $45) = $10,750,000
Total Revenue = $38,750,000
Production Budget:
Q1:
Production = 200,000 / (1 - 0.2) = 250,000 units
Raw Materials Required = 250,000 x 2 kg = 500,000 kg
Q2:
Production = 250,000 / (1 - 0.2) = 312,500 units
Raw Materials Required = 312,500 x 2 kg = 625,000 kg
Q3:
Production = 250,000 / (1 - 0.2) = 312,500 units
Raw Materials Required = 312,500 x 2 kg = 625,000 kg
Q4:
Production = 300,000 / (1 - 0.2) = 375,000 units
Raw Materials Required = 375,000 x 2 kg = 750,000 kg
Raw Materials Budget:
Q1:
Raw Materials Required = 500,000 kg
Add: Desired ending inventory = 10% x 625,000 kg = 62,500 kg
Total Raw Materials Required = 562,500 kg
Less: Beginning inventory = 10% x 500,000 kg = 50,000 kg
Raw Materials to be Purchased = 512,500 kg x $10/kg = $5,125,000
Q2:
Raw Materials Required = 625,000 kg
Add: Desired ending inventory = 10% x 625,000 kg = 62,500 kg
Total Raw Materials Required = 687,500 kg
Less: Beginning inventory = 10% x 562,500 kg = 56,250 kg
Raw Materials to be Purchased = 631,250 kg x $10/kg = $6,312,500
Q3:
Raw Materials Required = 625,000 kg
Add: Desired ending inventory = 10% x 625,000 kg = 62,500 kg
Total Raw Materials Required = 687,500 kg
Less: Beginning inventory = 10% x 687,500 kg = 68,750 kg
Raw Materials to be Purchased = 618,750 kg x $10/kg = $6,187,500
Q4:
Raw Materials Required = 750,000 kg
Add: Desired ending inventory = 10% x 750,000 kg = 75,000 kg
Total Raw Materials Required = 825,000 kg
Less: Beginning inventory = 10% x 687,500 kg = 68,750 kg
Raw Materials to be Purchased = 756,250 kg x $10/kg = $7,562,500
Therefore, the sales, production, and direct materials budgets by quarters for 2020 are as follows:
Sales Budget:
Q1: $8,000,000
Q2: $10,000,000
Q3: $10,000,000
Q4: $10,750,000
Production Budget:
Q1: 250,000 units
Q2: 312,500 units
Q3: 312,500 units
Q4: 375,000 units
Raw Materials Budget:
Q1: $5,125,000
Q2: $6,312,500
Q3: $6,187,500
Q4: $7,562,500
Please help will mark Brainly
Answers
Answer:
A. x < 0
Step-by-step explanation:
function y is increasing from -8 to 0 as x is increasing from -4 to 0. Therefore the answer is A
The list below shows the scores for each of Sarah’s homework assignments.
100, 95, 47, 83, 87, 89, 89
If the score 47 is removed from the list, which of the following statements is true
Answers
The correct statement regarding the mean of the data-set when the score of 47 is removed is given as follows:
The mean increased by about 6.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The observations for this problem are given as follows:
100, 95, 47, 83, 87, 89, 89.
There are 7 observations, and their sum is given as follows:
100 + 95 + 47 + 83 + 87 + 89 + 89 = 590.
Hence the mean is of:
590/7 = 84.29.
Removing the observation of 47, there will be 6 observations, with a sum of 590 - 47 = 543, hence the mean is of:
543/6 = 90.5.
Meaning that the mean increases by about 6.
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The Director of Nursing (DON) in a long-term care facility receives a gross yearly salary of $67,000. The DON is married with three dependents and has enrolled in the company's insurance family plan. The long-term care facility employees receive paychecks every other week. a. Calculate the gross salary per pay period. b. Compute the net salary per pay period.
Answers
a. To calculate the gross salary per pay period, we need to divide the yearly salary by the number of pay periods in a year:
Gross salary per pay period = Yearly salary / Number of pay periods per year
Since there are 26 pay periods in a year (bi-weekly paychecks), we have:
Gross salary per pay period = $67,000 / 26 = $2,576.92
Therefore, the DON's gross salary per pay period is $2,576.92.
b. To compute the net salary per pay period, we need to take into account federal and state taxes, Social Security, and Medicare deductions, as well as any other pre-tax or post-tax deductions, such as health insurance premiums or retirement contributions.
Assuming a standard tax withholding rate of 20%, Social Security and Medicare deductions of 7.65%, and health insurance premiums of $200 per pay period, we can calculate the net salary per pay period as follows:
Net salary per pay period = Gross salary per pay period - Taxes - Social Security and Medicare - Health insurance
Net salary per pay period = $2,576.92 - ($2,576.92 x 0.20) - ($2,576.92 x 0.0765) - $200
Net salary per pay period = $2,576.92 - $515.38 - $197.02 - $200
Net salary per pay period = $1,664.52
Therefore, the DON's net salary per pay period is $1,664.52.
Answer this question please
Answers
Shape P could have been transformed using a translation, rotation, reflection or a combination of these transformations.
What is tranformations?Transformation in maths is a way of changing the position, size or shape of a given object. It involves moving the object from one position to another. This can be done using a combination of translation, rotation, reflection and enlargement.
A translation is when a shape is moved in a straight line and all points are moved the same distance in the same direction. A rotation is when a shape is rotated around a fixed point and all points are moved the same angle. A reflection is when a shape is flipped over a line and all points are reversed on the other side of the line.
In the case of Shape P, since one point was invariant, the transformation must have been either a translation, rotation or a combination of both. A translation would have been impossible as all points are moved the same amount and direction, hence, the invariant point would have been moved. A rotation is possible as all points are moved the same angle, and the angle of rotation could be adjusted to keep the invariant point in the same place. A combination of both of these transformations could also have been used to keep one point invariant.
Overall, Shape P could have been transformed using a translation, rotation, reflection or a combination of these transformations. In this case, the transformation must have been either rotation or a combination of both translation and rotation. The angle of rotation or the combination of translation and rotation would have been adjusted to keep the invariant point in the same place.
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Complete the ratio table.
8
40
48
56
3
15
18
36
Answers
Answer:
52 : 39 56 : 42 60 : 45
64 : 48 68 : 51
Step-by-step explanation:
find the exact value of x.
Answers
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{6}{x}=\cfrac{x}{8}\implies 48=x^2\implies \sqrt{48}=x\implies \sqrt{4^2\cdot 3}=x\implies 4\sqrt{3}=x[/tex]
Can you help me solve this
Answers
We can see that linear function B has a greater rate of change than function A.
Which function has the greater rate of change?The general linear function is written as:
y = a*x +b
Where a is the rate of change.
If we know two points on the linear function, (x₁,y₁) and (x₂, y₂), then the rate of change is given by:
a = (y₂ -y₁)/(x₂ - x₁)
For function A we use the first two on the table (1, 5) and (2, 7)
a = (7 - 5)/(2 - 1) = 2
For the function B we willuse (1, 1) and (2, 4), then:
a = (4 - 1)/(2 - 1) = 3
Function B has a greater rate of change.
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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores 75 are normally distributed with a mean of 100 and a standard deviation of 15.
Answers
Answer:
the area of the shaded region is 0.9525 (rounded to four decimal places).
Step-by-step explanation:
Since IQ scores above 75 are shaded, we need to find the area to the right of 75 on the normal distribution curve with mean 100 and standard deviation 15.
Using a standard normal table or calculator, we can find the z-score corresponding to 75 as follows:
z-score = (75 - 100) / 15 = -1.67
The area to the right of this z-score is the probability that an IQ score is above 75, which is the shaded area in the graph.
Using a standard normal table or calculator, we find that the area to the right of a z-score of -1.67 is 0.9525 (rounded to four decimal places).
Therefore, the area of the shaded region is 0.9525 (rounded to four decimal places).
The population of a country has been decreasing for several decades. In 1990, the population was about 122 million people. In 2010, the population was about 113million people. Determine the percent decrease in the country's population during this time period.
Answers
Answer:
About a 7.3 percent Decrease
Step-by-step explanation:
First, calculate the diffrence between the two numbers:
122-113=9
Then, divide this number by the original number, it being 122, and then multiply that number by 100.
the simplified version of this number to the tenths place is 7.38%
Write an equation that expresses the following relationship.
d varies directly with the square of w
In your equation, use k as the constant of proportionality.
Answers
Answer:
d = kw²
Step-by-step explanation:
The equation that expresses the relationship "d varies directly with the square of w" is:
d = kw² (or kw^2 if you prefer to write it that way!)
where k is the constant of proportionality.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
Question
The average daily balance of a credit card for the month of December was $5600, and the unpaid balance at the end of the
month was $6900. If the monthly interest rate is 2.5% of the average daily balance, what is the total balance on the next
billing date January 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs. For
example, $5, 678.00 should be entered as 5678.00.
Answers
Answer:
The first step is to determine the amount of interest charged for the month of December based on the average daily balance:
Average Daily Balance = $5600
Monthly Interest Rate = 2.5%
Interest Charged for December = Average Daily Balance * Monthly Interest Rate * Number of Days in December
Number of days in December is 31.
Interest Charged for December = $5600 * 0.025 * 31 = $4340.00
The total balance on the credit card on January 1 will be the sum of the unpaid balance at the end of December and the interest charged for December:
Total Balance on January 1 = Unpaid Balance at End of December + Interest Charged for December
Total Balance on January 1 = $6900 + $4340.00
Total Balance on January 1 = $11240.00
Rounded to the nearest cent, the total balance on the next billing date January 1 is $11,240.00.
The nearest cent, the total balance on the next billing date, January 1, is $12640.00.
To calculate the total balance on the next billing date, we need to consider the average daily balance for December, the unpaid balance at the end of December, and the monthly interest rate.
The monthly interest rate is 2.5% of the average daily balance. Let's calculate the interest charged for the month of December:
Interest charged = (2.5/100) * Average daily balance
= (2.5/100) * $5600
= $140
Next, let's calculate the total balance on the next billing date, January 1:
Total balance = Average daily balance + Interest charged + Unpaid balance
= $5600 + $140 + $6900
= $12640
Rounded to the nearest cent, the total balance on the next billing date, January 1, is $12640.00.
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How many times more powerful were the seismic waves of the Belair earthquake than standard seismic waves?
Answers
The seismic waves from the earthquake in Caracas were 12589.25 times stronger than typical seismic waves.
How do seismic waves work?Seismic waves are acoustic energy waves that passes through the Earth. It can be brought on by massive landslides, volcanic eruptions, magma movement, earthquakes, and artificial explosions that discharge a lot of low-frequency acoustic energy.
By using formula for, M= log(w/w_0), we can find:
10^M= w/w_0, it means 10^M.w_0, = w
but M=4.1, so 10^4.1 = 12589.25
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Bruce won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Bruce a bucket of fish to divide evenly among 5 dolphins. Each dolphin gets 4 fish
Answers
The equation which can be use to find the number of fish f in the bucket before Brooke feeds the dolphins is [tex]4 * 3 = f[/tex].
Which equation can you use to find the number of fish?An equation refers to a mathematical statement that is made up of two expressions connected by an equal sign.
Let f be the number of fish in the bucket before Brooke feeds the dolphins. The equation that can be used to find the value of f is: [tex]4 * 3 = f[/tex]
This equation represents the fact that there are 4 dolphins and each dolphin receives 3 fish, so the total number of fish in the bucket must be equal to 4 times 3. Solving this equation, we get:
f = 12
Therefore, there were 12 fish in the bucket before Brooke fed the dolphins.
Full question "Brooke won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Brooke a bucket of fish to divide evenly among 4 dolphins. Each dolphin gets 3 fish. Which equation can you use to find the number of fish f in the bucket before Brooke feeds the dolphins"
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Brainliest!! Pls help!! Find the equation of a line parallel to y = -x+6 that passes through the point (-5,-9).
Answers
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6
Equation Q: 5y + 9z = 1
Which of the following is a possible step used in eliminating the y-term?
Please help
Answers
Answer:
Leaving equation Q the same, multiply both sides of equation P by -5.
(y + z = 6) × -5
What is the missing measure of the missing angle 59 86?
Answers
The missing measure of the angle on the triangle will be 45°.
How to calculate the angleAn angle is the measure of the space between two intersecting lines or planes. It is usually measured in degrees or radians. A degree is a unit of measurement for angles, where a full circle is 360 degrees, while a radian is a unit of measurement for angles defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (more than 90 degrees and less than 180 degrees), or straight (exactly 180 degrees).
The missing angle will be:
= 180° - (76° + 59°)
= 180° - 145°
= 35°
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need help with This Math
Answers
The number of intersection points is (a) 1 point or 2 points.
How to determine the number of intersection pointsGiven that
Line AB and circle P lie on the same plane.
And, we have
AP = 6 mm
BP = 8 mm
The intersection points can be 0, 1, or 2.
Since the radius of circle P is 6mm, any intersection point must also be 6mm away from P.
Next, we have the following test cases
If line AB intersects circle P at one point, then that point must be on the circle centered at P and have a radius of 6mm. If line AB intersects circle P at two points, then both points must be on the same circle centered at P with a radius of 6mm.Hence, the answer is (A) 1 point or 2 points.
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A car is traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 34 minutes ? In 1 hour ?
Answers
let's firstly convert the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{ccll} miles&minutes\\ \cline{1-2} \frac{3}{2}&\frac{9}{4}\\[1em] x&34 \end{array}\implies \cfrac{~~ \frac{3 }{2 } ~~}{x}~~ = ~~\cfrac{~~ \frac{9}{ 4} ~~}{34}\implies \cfrac{3}{2x}=\cfrac{9}{(4)(34)}\implies \cfrac{3}{2x}=\cfrac{9}{136} \\\\\\ (3)(136)=18x\implies \cfrac{(3)(136)}{18}=x\implies \cfrac{68}{3}\implies \stackrel{ miles }{x=22\frac{2}{3}}[/tex]
Step-by-step explanation:
11/2 is equivalent to 21/4 is
equivalent to 9/4
The unit rate will be:
3/2 miles= x
9/4 min 1 min
Now use this unit to find how far the car will travel in 26 minutes
2/3 mile •26 min= 52/3 miles or 17 and 1/3
miles
1 min
Since 1 hour is equal to 60 minutes, we can
multiply the unit rate by 60 to find the distance traveled in 1 hour.
2/3 mile• 60 min = 120/3 = 40 miles
traveled in 1 hour
1 min
solve this proof? flow chart proof
Answers
Since HM = NK and ∠FGH = ∠KGH = 45°, we have FG = KH by the hypοtenuse-leg (HL) cοngruence theοrem.
What is Triangles?A triangle is geοmetric shape that is fοrmed by the three straight line segments that cοnnect tο fοrm the three sides. These sides enclοse regiοn in plane, and three pοints where line segments intersect are called vertices.
We are given that HF GK, and ZF and ZK are right angles.
Tο prοve: FG KH
We will use the fοllοwing steps tο prοve the statement:
Draw perpendiculars frοm F and G tο HK, and label the pοints οf intersectiοn as M and N, respectively.
Since ZF is a right angle, we have ∠FMH = 90°.
Similarly, since ZK is a right angle, we have ∠GNK = 90°.
We are alsο given that HF GK, sο triangle HFG is cοngruent tο triangle KFG by the hypοtenuse-leg (HL) cοngruence theοrem.
Therefοre, FH = GK and ∠HFG = ∠KFG.
Since ∠FMH = 90° and FH = GK, we have HM = NK.
Alsο, since ∠HFG = ∠KFG, we have ∠FGH = ∠KGH.
Using angle additiοn pοstulate, we have ∠FGH + ∠KGH = ∠FGK = 90°.
Thus, ∠FGH = ∠KGH = 45°.
Finally, since HM = NK and ∠FGH = ∠KGH = 45°, we have FG = KH by the hypοtenuse-leg (HL) cοngruence theοrem.
Therefοre, FG KH, which cοmpletes the prοοf.
Hence, we have prοved that FG KH.
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Carmen is planning rail lines for a new train station. Help her find m z1. Explain how you found that solution.
Answers
In summary, to find m z1, we need to know the relationship between the rail lines and the angles formed by their intersection.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.
Here,
In order to help Carmen find m z1, we need some additional information about the rail lines and the angles involved.
Assuming that z1 is an angle formed by the intersection of two rail lines, we can use the following steps to find its measure:
Identify the other angles formed by the two rail lines. If the rail lines are perpendicular, then z1 is a right angle and has a measure of 90 degrees. If the rail lines are not perpendicular, then they form two pairs of opposite angles, each with a measure of x degrees.
Use the fact that the sum of the measures of all angles formed by the intersection of two rail lines is 360 degrees. This means that the sum of the measures of the two pairs of opposite angles is 360 degrees.
Solve for x by setting the sum of the measures of the two pairs of opposite angles equal to 360 degrees and then solving for x. Once you have x, you can find the measure of any of the angles formed by the intersection of the rail lines, including z1.
For example, let's say that the two rail lines form two pairs of opposite angles, each with a measure of x degrees. Then, we have:
2x + 2z1 = 360 (since the sum of the measures of all angles formed by the intersection of two rail lines is 360 degrees)
Simplifying this equation, we get:
2z1 = 360 - 2x
z1 = (360 - 2x)/2
Now we need more information to find x, such as the measure of one of the opposite angles or the relationship between x and another angle in the figure. Once we know x, we can substitute it into the equation for z1 to find its measure.
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Consider the system of equations and the partial solution below.
6x+3y=9
5x+4y=10
Multiply the first equation by -4.
Multiply the second equation by 3.
Add the resulting system of equations.
Which terms will cancel when you add the resulting system of equations?
-36 and 36
-24x and 24x
O-15x and 15x
-12y and 12y
Answers
-15x and 15x is the answer
Answer:
-12y and 12y
Step-by-step explanation:
lets do the multiplication to each equation
[tex]\left \{ {{(6x+3y)(-4)=9(-4)} \atop {(5x+4y)3=10(3)}} \right.[/tex]
this is
[tex]\left \{ {{-24x-12y=-36} \atop {15x+12y=30}} \right.[/tex]
if we add the systems notice the values that do cancel are -12y and 12y
and the results of the adition is
[tex]-9x=-6[/tex]
from this
[tex]x=\frac{-6}{-9} =\frac{2}{3}[/tex]
and you can find y from any of the first equation.
[tex]y=3-2x=3-\frac{4}{3} =\frac{5}3}[/tex]
Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,10)
, (2,6)
, (3,3)
, (4,10)
, (5,4)
, (6,3)
, (7,2)
Answers
The linear regression equation for the data-set in this problem is given as follows:
y = -1.04x + 9.57.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.
The seven points that represent the data-set for this problem are given as follows:
(1, 10), (2,6), (3, 3), (4,10), (5, 4), (6, 3), (7, 2).
Inserting these points into the linear regression calculator, the linear regression equation for the data-set in this problem is given as follows:
y = -1.04x + 9.57.
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Can anyone help me with this question?
Answers
The two points of tangency are (-1,3) and (1,-3).
What is the equation of a tangent to the circle?
The equation of a tangent to a circle is a linear equation that describes a line that touches the circle at exactly one point, without crossing it. A tangent line is perpendicular to the radius of the circle at the point of contact.
Since the line T is tangent to the circle, the radius of the circle drawn to the point of tangency (-1,3) is perpendicular to the line T. Therefore, the center of the circle must lie on the line perpendicular to T at (-1,3).
The equation of the tangent line T can be found by taking the derivative of the equation of the circle and evaluating it at the point of tangency (-1,3):
2x + 2y(dy/dx) = 0
dy/dx = -x/y
At the point (-1,3), dy/dx = -(-1)/3 = 1/3. Therefore, the equation of the tangent line T is:
y - 3 = (1/3)(x + 1)
y = (1/3)x + 10/3
The slope of any line perpendicular to T is -3 (the negative reciprocal of 1/3). The point-slope form of the equation of a line with slope -3 passing through (-1,3) is:
y - 3 = -3(x + 1)
y = -3x
To find the points of tangency, we need to solve the system of equations consisting of the equation of the circle and the equation of the tangent line:
x² + y² = 10
y = -3x
Substituting y = -3x into the first equation, we get:
x² + (9x²) = 10
10x² = 10
x² = 1
x = ±1
Substituting these values of x into y = -3x, we get:
(-1,3) and (1,-3)
Therefore, the two points of tangency are (-1,3) and (1,-3).
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10.3 Surface Area of Triangular Prisms.
Please help with these 6 answers in photo
Answers
The letter of the 3D figure which matches the statement of the student with regards to the surface areas of the figures are;
The net of this triangular prism covers the smallest total surface area; B
The lateral surface area is 96.6 unit²; C
The total surface area is 111.6 units²; C
The lateral surface area is 85.56 unit²; A
The total surface area is 103.96 unit²; A
The net of this triangular prism covers the largest lateral surface area; C
What is the surface area of a 3D figure?
The surface area of a three dimensional, (3D), figure is the area of the boundary surface that surrounds the space occupied by the figure.
The surface areas and the lateral surface areas of the nets and the prisms are presented as follows;
Figure A;
Surface area = 2×(1/2)×4.6×4 + 3×6.2×4.6 = 103.96
The lateral surface area = 3×6.2×4.6 = 85.56
Figure B;
Surface area = 2×(1/2)×4×3.8 + 2×4.3×6 + 4×6 = 90.8
The lateral surface area = 2×4.3×6 + 4×6 = 75.6
Figure C;
Surface area = 2×(1/2)×5×3 + 5×7 + 3×7 + 5.8×7 = 111.6
The lateral surface area = 5×7 + 3×7 + 5.8×7 = 96.6
Therefore;
The net of the triangular prism in Figure B covers the smallest surface areaFigure C has a lateral surface area of 96.6The total surface area of Figure C is 111.6 unit²The lateral surface area of Figure A is 85.56 unit²The total surface area of Figure A is 103.96 unit²The triangular prism with the largest surface area is Figure C with a surface area of 111.6 unit²Learn more on the surface area of a prism here: https://brainly.com/question/16421693
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please help solve this question
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Answer: B and C
Step-by-step explanation:
Find the linear function with the following properties
f(0)=1 slope of f=3
F(x)=
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Therefore , the solution of the given problem of function comes out to be f(x) = 3x + 1 is the linear function with the specified properties.
Describe function.Numerous subjects, including mathematics, numbers, and their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between various variable elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.
Here,
The slope-intercept form of the linear function f(x) is written as
=> f(x) = mx + b,
where m is the slope and b is the y-intercept.
We can infer from the listed characteristics that f(0) = 1 and f's slope is 3.
We have the following equation for a line in the point-slope form:
=> f - 1 = 3(x - 0) (x - 0)
When we simplify this solution, we obtain:
=> f = 3x + 1
Consequently, f(x) = 3x + 1 is the linear function with the specified properties.
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Volume of rectangular prism
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Answer:104
Step-by-step explanation:
solve the system of equations graphed on the coordinate axes below
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Answer (0,0)
Step-by-step explanation:
Method 1)
look at the graph to see where the two lines intersect, which is at (0,0).
Method 2)
[tex]\frac{4}{3} x[/tex] = -2x ............................set the 2 equations equal
[tex]\frac{10}{3} x[/tex] = 0.................................set the equation to 0 (by adding 2x to both sides)
x = 0.....................................solve for x (by dividing both sides by [tex]\frac{10}{3}[/tex]
Note: you can use y = [tex]\frac{4}{3} x[/tex] OR y = -2x
y= -2x
y = -2(0)...............................plug in the x
y = 0.....................................solve
(x,y)
(0,0)......................................plug in x and y value
[tex]|x| - 5 |x + 6 = 0[/tex]
Where [x] the greatest integer function then the solution for X is
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The greatest integer value for x is -8
How to determine the greatest integer value for xFrom the question, we have the following parameters that can be used in our computation:
|x| - 5|x + 6 = 0
Express properly
So, we have
|x| - 5|x + 6| = 0
This gives
|x| = 5|x + 6|
When both sides of the equation are compared, we have
x = 5x + 30
So, we have
4x = -30
Divide by 4
x = -7.5
Approximate to an integer
x = -8
Hence, the value of x is -8
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