Answer:
$35 for 12 slices
Monthly cost for x slices of pizza = 20 + 1.25x
Step-by-step explanation:
Monthly Membership cost = $20
Discounted cost per slice of pizza = $1.25
Discounted total cost for 12 slices = $1.25 x 12 = $15
Total cost = 20 + 15 = $35 this momth
For x slices of pizza, monthly cost = 20 + 1.25x
Solve the following inequality algebraically. |x−5∣>10
Answer:
The answer to the inequality is
x < -5
x > 15
A rental car company charges $53.46 per day to rent a car and $0.13 for every mile driven. Mei Mei wants to rent a car, knowing that:
She plans to drive 350 miles.
She has at most $260 to spend.
Which inequality can be used to determine dd, the maximum number of days Mei Mei can afford to rent for while staying within her budget?
The correct inequality will be 53.46d + 45.5 ≤ 260
What does a math inequality look like?
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Given That:
She plan to drive 350 miles and each mile cost $0.13 which is total $45.5
and she have to pay $53.46 for each day
So the correct inequality will be 53.46d + 45.5 ≤ 260
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Please help me it’s due tonight!
Help me find the y intership form (y=mx+B)
13.parallel to 2x - 3y = through point (-1, 2)
14. perpendicular to 1/3X+4
through point (0, 5)
15. perpendicular to 3x - y =-4 through point (0, -2)
16. perpendicular to 4x + 5y = 20
through point (1, 1)
17. perpendicular to 4x +7y = 13
through point (-2, 6)
The linear functions for this problem are given as follows:
13. y = 2x/3 + 8/3.
14. y = -3x + 5.
15. y = -1/3x - 2.
16. y = 5/4x - 1/4.
17. y = 7/4x + 19/2.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.The slope is also related with parallel and perpendicular lines, as follows:
If the lines are parallel, they have the same slope.If the lines are perpendicular, the multiplication of their slopes is of -1.In item 13, the line in slope-intercept form is:
y = 2x/3.
The line we want to find is parallel, hence it has the same slope, that is:
y = 2x/3 + b.
When x = -1, y = 2, hence:
2 = -2/3 + b
b = 8/3.
Hence the line is:
y = 2x/3 + 8/3.
For item 14, the line is perpendicular to:
y = 1/3x + 4.
Hence the slope is found as follows:
1/3m = -1
m = -3.
Then:
y = -3x + b.
When x = 0, y = 5, hence b = 5 and the line is:
y = -3x + 5.
For item 15, the line is perpendicular to:
y = 3x + 4.
Then the slope is found as follows:
3m = -1
m = -1/3.
Then:
y = -1/3x + b.
When x = 0, y = -2, hence b = -2 and the line is:
y = -1/3x - 2.
For item 16, the line is perpendicular to:
y = 4 - 4/5x.
Then the slope is found as follows:
-4m/5 = -1
m = 5/4.
Hence:
y = 5/4x + b.
When x = 1, y = 1, hence:
1 = 5/4 + b
b = -1/4.
Then the line is:
y = 5/4x - 1/4.
For item 17, the line is perpendicular to:
y = 13/7 - 4/7x
Then the slope is found as follows:
-4m/7 = -1
m = 7/4.
Hence:
y = 7/4x + b.
When x = -2, y = 6, hence:
6 = -14/4 + b
b = 19/2.
Hence the line is given by:
y = 7/4x + 19/2.
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The length of a rectangle is 2 times its width.
The area of the rectangle is 32 in.². What is
the length of the rectangle?
The point (-3,-5) is on the graph of a function. Which equation mus O f(-3) -5 f(-3,-5) = -8 O f(-5) = -3 f(-5, -3) = -2
So the correct answer is a. f(-3)=-5.
Solution :
Cartesian coordinate system
A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
Cartesian Plane:
A plane consists of axes and quadrants. Thus, we call the plane the Cartesian Plane, or the Coordinate Plane, or the x-y plane. The axes are called the coordinate axes.
Abscissa and Ordinate
The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis and it is known as Abscissa.
The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis and it is known as the Ordinate.
So,
the point (-3, -5) corresponds to the graph of the function.
A point on a graph in the Cartesian coordinate system then that point consists of coordinates (x, y).
In, y=f(x) and x so (x, f(x))
x is a x-coordinate and y=f(x) is y-coordinate.
So if we have a point (-3, -5) the corresponding coordinates are x=-3 and
y=f(x)=-5. So it must be true that y=f(-3)=-5.
So the correct answer is a. f(-3)=-5.
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Tv sells at 60 percent off retail what percent is wholesale price
The wholesale price of the TV will be 0.40 x where x represents the retail price.
Percentage :
In mathematics, it is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Let the retail price of TV be x
Now, we are given that it is sold off at 60 percent discount.
Whole sale price = x - 60 % of x
Whole sale price = x - 60 / 100 x
Whole sale price = x - 0.60 x
Whole sale price = 0.40 x.
Therefore, the wholesale price of the TV will be 0.40 x where x represents the retail price of the TV.
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Please Help Me, I’d Really Appreciate It.
Write the following fraction as a decimal: 2/5
0.25
2.5
0.4
4.0
Answer:
It's 0.4
Step-by-step explanation:
2/5 = 40/100 = 4/10 = 0.4
Hope that helps :)
1. Find the value of Y
2. Find angle 1
3. Find angle 2
4. Find the value of X
Could someone please lend me a hand with this?
Find the (perpendicular) distance from the line given by the parametric equations
x(t)= -2-6t
y(t)= 1-3t
z(t)= -5+7t
to the point (-8,9,8)
Answer:
[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex] Whatever this number may be
Step-by-step explanation:
The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus
[tex]6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0[/tex]
We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:
[tex]6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94[/tex]
Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:
[tex](-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})[/tex]
At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual [tex]\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}[/tex], whatever abomination of a number it might become:
[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex]
At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.
10. Alice bought 2.3
pounds of apples for $2.99
per pound. How much did
she spend on apples?
Answer:
2.3(2.99)=$6.877
Step-by-step explanation:
Multiply the pounds (2.3) by the price of apples per pound.
Hope this helps! :)
Answer:
2.3(2.99)=$6.877
Step-by-step explanation:
Hope this helps!
Multiply (4.12 × 10−9)(8.3 × 1015). Write the final answer in scientific notation.
34.196 × 10−134
3.4196 × 107
3.4196 × 10−135
34.196 × 106
Omg, I'm just stuck on this question, please help loves
Answer:
[tex]3.4196 \times 10^{7}[/tex]
Step-by-step explanation:
Given expression:
[tex](4.12 \times 10^{-9})(8.3 \times 10^{15})[/tex]
Remove the parentheses:
[tex]\implies 4.12\times 10^{-9} \times 8.3 \times 10^{15}[/tex]
Collect like terms:
[tex]\implies 4.12 \times 8.3 \times 10^{-9} \times 10^{15}[/tex]
Multiply the numbers 4.12 and 8.3:
[tex]\implies 34.196 \times 10^{-9} \times 10^{15}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 34.196 \times 10^{(-9+15)}[/tex]
[tex]\implies 34.196 \times 10^{6}[/tex]
Scientific notation is written in the form [tex]\boxed{a \times 10^n}[/tex]
where [tex]1\leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.
To convert 34.196 × 10⁶ into scientific notation, move the decimal point to the left by one place and increase the power of 10 by 1:
[tex]\implies 34.196 \times 10^{6}=3.4196 \times 10^{7}[/tex]
0.000345 standard form
Answer:
0.000345 in standard form would be:
3.45 times 10 to the -4 power
Step-by-step explanation:
The number tells use that we have to divide by 10 and we are working with a negativenumber equal to the power of 4.
Answer:
3.45 × 10^-4
Step-by-step explanation:
Move from the decimal point till you you get to after the first number.
Then you put the decimal point there and because it's starts with 0. i.e it is not up to one
You put minus in front of it when raising it to the power of 10
Solve the formula for the variable c.
x/a=b/c
Answer:
(d) c = ab/x
Step-by-step explanation:
You want to solve the proportion x/a = b/c for the variable c.
SolutionThe usual method recommended for solving almost any kind of proportion is to first clear the fractions. You do this by multiplying both sides by the product of the denominators. This has the appearance of "cross multiplication."
[tex]\dfrac{x}{a}=\dfrac{b}{c}\qquad\text{given}\\\\\\\dfrac{x}{a}\cdot ac=\dfrac{b}{c}\cdot ac\qquad\text{multiply by $ac$}\\\\xc=ba\qquad\text{simplify; each numerator times the opposite denominator}[/tex]
At this point, it is a "one-step" linear equation in c, so is solved by dividing by the coefficient of c, which is x.
[tex]\dfrac{xc}{x}=\dfrac{ab}{x}\\\\\boxed{c=\dfrac{ab}{x}}[/tex]
A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
The number of students who will be going on the trip is B. 40 students.
What is a mathematical expression?A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.
The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.
Data and Calculations:The total of the weekend trip = $4,030
The cost of cleaning for the bus = $30
The cost of food and lodging per student = $60
The bus charge per student = $40
Total cost per student = $100 ($60 + $40)
The total cost, y = 4,030 - 30 - 100x
The number of students = x
x= (4,030 - 30)/100
= (4,000/100)
= 40.
Thus, the number of students who will be going on the trip is B. 40 students.
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Which expression is equivalent to the given expression? 3 x 2 + 5 x − 7 ( x 2 + 4 ) A. - 4 x 2 + 5 x − 4 B. x 2 + 4 C. x 2 + 28 D. - 4 x 2 + 5 x − 28
According to the solving the non of the quadratic equations equivalent.
4X² + 5x - 3.
What is a quadratic equation and how does it work?A quadratic equation seems to be a second-order polynomial equation in a variable, x ax2+bx+c=0, with a 0 as the coefficient. The fundamental theorem of algebra ensures that it has at least one solution as it is a second-order polynomial problem. The solution could be straightforward or difficult.
What exactly is the equivalent formula?Equivalent equations are those that have the same solutions or roots. An equivalent equation is produced by adding or subtracting the identical number or expression from both sides of an equation. Equivalent equations are produced by multiplying and dividing both sides of such an equation by the same non-zero value.
According to the given equation:3 X² + 5 x − 7 + ( X² + 4 ).
Simplifying this equation:
3 X² + 5 x − 7 + X² + 4
= 4X² + 5x - 3
According to the solving the non of the quadratic equations equivalent.
4X² + 5x - 3.
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I understand that the question you are looking for is:
Which expression is equivalent to the given expression?
3 X² + 5 x − 7 + ( X² + 4 ).
A. - 4X² + 5X − 4
B. X² + 4
C. X² + 28
D. - 4 X² + 5x − 28
Which model shows the sum of 0.19 and 0.8?
Eve bought 28.37 pounds of peanuts and 30.36 pounds of raisins. How many pounds of snacks did she buy in all?
Answer:58.73
Step-by-step explanation:
28.37+30.36=58.73
From the top of abuilding, Cecilia finds that the angle of depression of a table on the ground is 30 degrees. If the table is 40 m from the base of the building, find the height of the building
The height of the building is 23.09m.
Let the height of the building be "h".The distance between the table and the base of the building is 40 m.From the top of the building, the angle of depression of the table on the ground is 30°.The angle of depression is the angle formed by the horizontal line and the item as seen from the horizontal line. It is mostly used to calculate the distance between two objects where the angles and distance from the ground are known.We can also say that, from the table, the angle of elevation of the top of the building is 30°.For a better visualization of the problem, see the image attached below.Apply trigonometry.Tan(30°) = h/401/√3 = h/40h = 40/√3h = 23.09mTo learn more about angles, visit :
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At a bakery, one customer pays $5.67 for 3 bagels and 4 muffins. Another customer pays $6.70 for 5 bagels and 3 muffins. Which system of equations can be used to determine the cost x (in dollars) of one bagel and the cost y (in dollars) of one muffin at the bakery?
The bagel costs $0.89 and a muffin costs $0.75
How to create a system of equations?Let B = Bagel cost
Let M = Muffin cost
Thus, from the given question parameters, the system of equations that can be used to determine the cost x is;
3B + 4M = 5.67 ------(1)
5B + 3M = 6.70 ------(2)
Multiply the 1st equation by 3 and the 2nd equation by (-4) to get;
9B +12M = 17.01 ------(3)
-20B - 12M = -26.80 ------(3)
Add equations 3 and 4 together to get;
-11B = -9.79
B = 0.89
Plug this value for B in to the 1st equation and solve for M to get;
3(0.89) + 4M = 5.67
2.67 + 4M = 5.67
4M = 3.00
M = 0.75
Thus, a bagel costs $0.89 and a muffin costs $0.75
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Jen and her friends have a half-day at school, so they plan to spend the afternoon
paddleboarding at Lake Evergreen. They want to spend the rest of the day on the water, but
it starts to rain after paddleboarding for only of an hour! Jen is disappointed when she
realizes the sun doesn't go down for another 4
hours.
Use an equation to find the amount of time Jen planned to spend paddleboarding.
To write a fraction, use a slash (/) to separate the numerator and denominator.
Using proportions, it is found that Jen planned to spend 19/4 hours paddleboarding.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
In this problem, we have that:
She spent 3/4 of an hour paddleboarding.The sun doesn't go down for another 4 hours.4 + 3/4 = 4.75 hours = 19/4.
Jen planned to spent 19/4 hours paddleboarding.
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Locate the value of the constant π on a number line using rational numbers.
The value of the constant π is located between 3 and 4 on a number line
How to locate the value of the constant π on a number line using rational numbers?The value is given as
Value = π
As a general rule, the value of π is
π = 22/7
So, we have
Value = 22/7
Evaluate the quotient of 22/7
So, we have
Value = 3.143
The number 3.143 is greater than 3 but less than 4
This means that, 3.143 is between 3 and 4
In other words, the value of the constant π is located between 3 and 4 on a number line
Hence, the value of the constant π is located between 3 and 4 on a number line
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4 more than 3 times a number is equal to 6 more than 2 times the number
Answer:
x=2
Step-by-step explanation:
3x+4=2x+6
3x=2x+2
x=2
is the value of the digit 5 in 0.5is 1/10 times as much as the value in 0.05
Answer:
No
Step-by-step explanation:
1/10 = 0.1
0.05 x 0.1 = 0.005
Hands-On Activity 2
Maria is also collecting books. She wants to make packages that have 3 fiction
books and 4 nonfiction books. She already has 9 fiction books. How many
nonfiction books will she need?
q
Use a multiplication table to compare the numbers.
Step 1 Complete the rows for 3 and 4 on a multiplication table. non a cas
9 12 15 18 21 24 27 30.
8 12 16 20 24 28
24 28 32 36 40
fiction
nonfiction
Sten 2
136
4
Road across the top until you reach 9. Find the corresponding number.
what is the pattern being used in the table?
Maria need 12 fiction books.
Multiplication table: A multiplication chart is a table that shows the products of two numbers. Usually, one set of numbers is written on the left column and another set is written as the top row. The products are listed as a rectangular array of numbers.
Given that She wants to make packages that have 3 fiction books and 4 nonfiction books. She already has 9 fiction books
Step 1
Complete the rows for 3 and 4 on multiplication table
Fraction : 3,6,9,12, 15, 18, 21, 24,27,30.
Notification : 4,8,12,16,20,24,28,32,36,40.
Step 2
Read across the top until you reach 9. The corresponding number bottom row.
The top untill you reach 9 the corresponding number bottom row is 12
Maria need 12 fiction books.
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To charter a bus to carry students to New York City, the cost is $100 to make the booking , plus $25 for each student who is a passenger on the bus. Then, the cost function C(x) giving the cost if x students are ( what is m and b) mxtb
The value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.
As per the given relation in the question, we see that b is calculated once and m is calculated based on the variable value x, which is the number of students. Hence, for correct calculation, value of m is $25 and value of b is $100.
The cost if 8 students are passengers will be calculated by keeping the value of x and other constants as per the above answer.
Cost = 25×8 + 100
Cost = 200 + 100
Cost = $300
Number of students will again be found as the value of x, by keeping the values as specified above.
400 = 25x + 100
25x = 400 - 100
25x = 300
x = 300 ÷ 25
x = 12
Hence, value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.
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The complete question is attached in figure.
Simon says that 7 x 2 is equal to 8 x 1 because both sets of factors add to 9. Do you agree with Simon's reasoning? Explain why or why not.
Answer:
No, I do not agree with Simon's reasoning.
Step-by-step explanation:
7*2=14
8*1=8
BUT
7+2=9
8+1=9
YET
Simon isn't properly solving the equation with the right basic operation of arithmetic. He must multiply, not use addition.
Hope this helps.
A health food store was charging $4.10 for a small salad but raised the price 8%. The new price after the increase is $4.43.Enter an expression to show how the new price was calculated.
Answer: $4.10*0.08%=0.33
Step-by-step explanation:
solve the expression when k=6 and c=2
5 x k - 10c + 8
Answer:
18
Step-by-step explanation:
5*(6)-10(2)+8 = 18
Substitute k = 6 and c = 2 into the equation and solve it.
Solve for y.
d = 5x + 5y
d=5x
5
O y = 5(d - 5x)
Oy =
0y = d-Sx
X
Oy=
5x-d
5
The cost of 6 gallons of gas at one gas station costs Julian $13.50. The cost of 8 gallons of gas at a different gas station cost Dorian
$18.80.
Answer:
$5.30 for two gallons
Step-by-step explanation: