Answers
The simplest fοrm οf the given expressiοn is A. −4(2x+1) and B. 8x + 6y − 36
What is pοlynοmials?Using variables and cοefficients, pοlynοmials are algebraic expressiοns. The term "indeterminates" is sοmetimes used tο describe variables. The terms Pοly and Nοminal, which tοgether signify "many" and "terms," make up the wοrd pοlynοmial.
When expοnents, cοnstants, and variables are cοmbined using mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn, the result is a pοlynοmial (Nο divisiοn οperatiοn by a variable). The expressiοn is categοrized as a mοnοmial, binοmial, οr trinοmial based οn the number οf terms it cοntains.
A. 8(-x - 1/2)
Using distributive property
- 8x - 4
−4(2x+1)
B. -8(-x -3/4y + 9/2)
Using distributive property
8x + 6y − 36
Hence the simplest fοrm οf the given expressiοn is −4(2x+1) and 8x + 6y − 36
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Related Questions
A single serving of a cereal breakfast bar contains 18 grams of carbohydrates. This is 6%
of the daily recommended allowance for a 2000-calorie diet. How many grams of
carbohydrates are recommended each day for a person on a 2000-calorie diet?
10. A concert was recently held at the civic auditorium. All 5000 tickets were sold.
a. 25% of the tickets were reserved seats that sold for $45 each. What was the total
amount in sales for the $45 tickets?
b. 15% of the tickets were reserved seats that sold for $35 each. What was the total
amount in sales for the $35 tickets?
c. The remainder of the tickets were general admission. How many general admission
tickets were sold?
d. If each general admission ticket sold for $20, what was the total amount in sales for
the general admission tickets?
e. What was the total amount for all ticket sales?
Answers
Answer:
Step-by-step explanation:
a. 25% of 5000 tickets = 0.25 x 5000 = 1250 tickets
Total sales of $45 tickets = 1250 x $45 = $56,250
b. 15% of 5000 tickets = 0.15 x 5000 = 750 tickets
Total sales of $35 tickets = 750 x $35 = $26,250
c. General admission tickets = Total tickets - Reserved tickets
= 5000 - 1250 - 750
= 3000 tickets
d. Total sales for general admission tickets = Number of general admission tickets x Price per ticket
= 3000 x $20
= $60,000
e. Total sales = Sales of $45 tickets + Sales of $35 tickets + Sales of general admission tickets
= $56,250 + $26,250 + $60,000
= $142,500
100 POINTS PLUS BRAINLIEST!!!!
screenshot with problem attached below
answers must be serious
non-serious answers / incorrect answers will be deleted
(ATTACHEMENT BELOW)
Answers
Answer:
see step by
Step-by-step explanation:
a) the polynomial must be fifth degree, so it must have a [tex]x^5[/tex] term, also need to have 2 additional terms (Lets add any, lets say [tex]x^2+8[/tex] (notice this is totally random, just need to be under 5th degree)
So a polynomial can be
[tex]x^5+x^2+8[/tex]
notice is in standard form since degrees drops from left to right.
Also notice there's an infinite amount of possible answers
b) p-q is the same as -q+p
For example, lets say
[tex]p=x+1[/tex]
[tex]q=3x^2-5[/tex]
[tex]p-q=x+1-(3x^2-5)=x+1-3x^2+5=-3x^2+x+6[/tex]
also
[tex]-q+p=-(3x^2-5)+x+1=-3x^2+5+x+1=-3x^2+x+6[/tex]
notice is the same expression.
(8x+17), (12x-39) find m
Answers
The measure of the angle M is 129 degrees
How to determine the valueIt is important to note that the properties of a parallelogram are;
Opposite sides are equalOpposite angles are congruentSame-Side interior angles (consecutive angles) are supplementary, that is, 180 degreesEach diagonal of a parallelogram divides it into two congruent trianglesThe diagonals of a parallelogram bisect each otherThen, we have that;
m< M = m < K
substitute the values
12x - 39 = 8x + 17
collect the like terms, we have;
12x - 8x = 17 + 39
Add the collected like terms, we get;
4x = 56
divide both sides by the coefficient of 4, we get;
4x/4 = 56/4
Divide the values
14
Then, m < M = 12(14) -39 = 129 degrees
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The complete question:
In the parallelogram, Find mZN: K (8x + 17)9 (12x - 39)8 01;0 - Lx'An M Ax+8x +17 + iax -3 = 360 3ax-33 = H0 +3 42 20 22X 7 x=17.30
Please help me on this: 90 BRAINLY POINTS. Yuri bakes lemon bars in a pan shaped like a right rectangular prism. The volume of the pan is 150 cubic inches. The width of the pan is 7 1/2 inches, and its height is 2 inches.
What is the length of the pan?
Enter your answer in the box
Answers
Answer:
length of the pan is 10 inches
Step-by-step explanation:
Volume = length x width x height
V = lwh
l = (V) / (wh) = (150 in³) / (7.5 in)(2 in) = 10 in
A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment , when the time is t = 0 seconds , the pendulum is at a point halfway between its maximum and minimum distances from the wall, 2.5 m away from the wall (Figure 1) and moving toward the wall. The pendulum first reaches its minimum distance from the wall , 1 m from the wall , when t = 1 second (Figure 2). When t = 4 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoida ! function .
Answers
A theme park's rides are rated as mild, moderate and
max. They have restrictions requiring that passengers
have heights of at least 42 inches, 48 inches, and 54
inches, respectively. Suppose the population of children
attending the park has a mean height of 53 inches with
a standard deviation of 4 inches.
If a child is chosen randomly, what is the probability
that: (Round all answers to nearest thousandths)
a) the child can go on all rides?
b) the child can participate in only mild and moderate
rides?
c) the child can only go on mild rides?
d) the child is excluded from all rides?
Answers
Answer:
the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Step-by-step explanation:
We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.
a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.
z-score = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.
Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).
b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 48 inches = (48 - 53) / 4 = -1.25
Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.
Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).
c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.
z-score = (42 - 53) / 4 = -2.75
Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.
Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).
d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 54 inches = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.
Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Question 11 (1 point)
Mary Ellen is making a table cloth for a client's dining room. She selected some pale-
yellow linen from a craft store and has it laid out on her work table to cut into the
correct shape. What tool is Mary Ellen MOST LIKELY going to use to cut the linen?
Scissors
Shears
A measuring tape
A Color Scheme Guide
Answers
Answer:
Mary Ellen is MOST LIKELY going to use shears to cut the linen.
On a coordinate plane, a line with positive slope goes through points A and B. Point A is at (0, negative 2) and point B is at (3, 0). Use the graph of the line shown to determine its slope. The slope of line AB is .
Answers
According to the given information, the slope of line AB is [tex]\frac{2}{3}[/tex].
What is the slope?
The slope of a line is a measure of how steep the line is. It tells us how much the y-coordinate of the line changes for each unit of change in the x-coordinate.
To visualize a slope, imagine a line on a coordinate plane. If the line is steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a larger amount. Conversely, if the line is less steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a smaller amount.
To find the slope of a line that passes through two given points, we use the slope formula:
[tex]slope = \frac{(change in y) }{(change in x)}[/tex]
In this case, we have points A(0, -2) and B(3, 0).
So the change in y is 0 - (-2) = 2, and the change in x is 3 - 0 = 3.
Therefore, the slope of line AB is:
[tex]slope = \frac{(change in y) }{(change in x)} = \frac{2}{3}[/tex]
Since the slope is positive, we know that the line slants upwards as we move from left to right on the coordinate plane.
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Joel bought a container of yogurt that held 8 cups of yogurt. He used a 0.25-cup serving of the
yogurt each day. When 7.25 cups of the yogurt remained, how many 0.25-cup servings had Joel
used from the container?
0.75
2
3
29
Answers
Answer:
3
Step-by-step explanation:
Amount used:
8 - 7.25 = 0.75
He used 0.75 cup
Each day he had 0.25 cup.
0.75/0.25 = 3
Answer: 3
The radius of a cylindrical construction pipe is 2.5 ft. If the pipe is 20 ft long, what is its volume…..
Answers
In this case, the radius of the cylindrical construction pipe is 2.5 ft and the length is 20 ft. So, the volume can be calculated as:
V = π(2.5)^2(20)
= 125π cubic feet
Therefore, the volume of the cylindrical construction pipe is 125π cubic feet.
9. The blueprint for a new house includes a triangular shaped room in the attic. The triangular room appears on the blueprint as shown.
If the blueprint was made using a scale factor of 12
centimeter = 1 meter, what is the actual perimeter of the triangular room?
A. 2.5M
B. 4.5M
C. 9M
D. 18M
Answers
By answering the presented question, we may conclude that As a result, equation the real circumference of the triangle space is around 30 metres.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programme are usually interchangeable. As an example, 2x - 4 equals 2.
Because the blueprint is designed on a scale of 12 centimetres Equals 1 metre, each 1 centimetre on the blueprint represents 0.0833 metres (1/12 of a metre).
Assume the triangle chamber on the blueprint has a perimeter of 30 cm. We may apply the following calculation to determine the real perimeter in metres:
Blueprint perimeter x Scale factor x 0.0833 = Real perimeter
Real circumference = 30 x 12 x 0.0833
Actual circumference = 29.988 metres
As a result, the real circumference of the triangle space is around 30 metres.
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I need help with this please
Answers
The volume and sum of the composite shape is 13L² and 13V³ respectively
What is a square?A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other. Also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles
The composite is made up of 13 squares in total
The area of 1 square is given as A = S²
The volume of the composite is 13L³ units
Hence there are 13 squares. the sum of the areas and volume of the square is 13 S²
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A student received a standardized score of -.63 on a class assignment. Which statement best describes the student’s score in relation to the rest of the class?
Answers
In a normal distribution, approximately 50% of the scores fall below the mean and 50% fall above the mean. Since the student's score is below the mean, we can say that the student scored lower than the average student in the class.
However, we cannot make any conclusions about how the student's score compares to the rest of the class without knowing more information about the distribution of scores. If the distribution is approximately normal, we can say that the student scored lower than approximately 73% of the class (since .63 standard deviations below the mean corresponds to approximately the 26th percentile of a normal distribution).
Therefore, the best statement we can make about the student's score in relation to the rest of the class is that the student scored lower than the average student in the class and lower than approximately 73% of the class if the distribution is approximately normal.
Which estimation technique will yield a solution that is farthest from the actual product of (-14.89)(1.35)?
front-end estimation
rounding to the nearest tenth
rounding to the nearest whole number
compatible numbers
It’s not C
Answers
pls help fast!! Find the equation of a line perpendicular to 4x+3y=−24 that passes through the point (−8,3).
Answers
Answer:
y - 3 = [tex]\frac{3}{4}[/tex] (x + 8)
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + 3y = - 24 ( subtract 4x from both sides )
3y = - 4x - 24 ( divide through by 3 )
y = - [tex]\frac{4}{3}[/tex] x - 8 ← in slope- intercept form
with slope m = - [tex]\frac{4}{3}[/tex]
given a line with slope m then the equation of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{4}{3} }[/tex] = [tex]\frac{3}{4}[/tex]
-------------------------------------------
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 3 ) , then
y - 3 = [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is
y - 3 = [tex]\frac{3}{4}[/tex] (x + 8) ← equation of perpendicular line
Rae is saving for a new computer, so she's selling her old antivirus software program for $250. The
software originally cost $985, and she used it for 12 years.
What was the net asset value of Rae's antivirus software two years after her purchase?
O A. $722.50
OB. $755
OC. $825.75
OD. $862.50
OE. $890.75
Answers
Answer:
the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.
Step-by-step explanation:
The software was used for 12 years, and Rae is selling it now. So, it has been used for 12 - 2 = 10 years.
Annual depreciation = (cost - salvage value) / useful life = (985 - 0) / 12 = 82.08
Depreciation for 10 years = 82.08 x 10 = $820.80
Net asset value after 2 years = cost - accumulated depreciation = 985 - 82.08 x 2 = $820.84
However, Rae is selling the software for $250, so her net asset value is $820.84 - $250 = $570.84
Therefore, the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.
Consider the graph of 5x² + 8x + 4y² - 4y = 70.
If the graph of 5x² + 8x + 4y - 4y = 70 is stretched horizontally by a factor of 3, the equation of the stretched graph will be
If the graph of 5x² + 8x + 4y² - 4y = 70 is stretched vertically by a factor of 7, the
equation of the stretched graph will be
Answers
To stretch the graph horizontally by a factor of 3, we need to multiply the x-coefficient by 1/3. Similarly, to stretch the graph vertically by a factor of 7, we need to multiply the y-coefficient by 1/7. Therefore:
Horizontally stretched graph: 5(1/3x)² + 8(1/3x) + 4y² - 4y = 70
Simplifying:
(5/9)x² + (8/3)x + 4y² - 4y = 70
Vertically stretched graph: 5x² + 8x + 4(1/7y)² - 4(1/7)y = 70
Simplifying:
5x² + 8x + (4/49)y² - (4/7)y = 70
Classifying parallelagram
Answers
Answer:
(3,-6)
Step-by-step explanation:
Coordinate for the point R is (3, -6)
What is a quadrilateral?A polygon with four sides and four vertices is called a quadrilateral. Quadrilateral literally means "four sides" because "quad" means four and "lateral" implies sides. Quadrilaterals come in a variety of sizes, forms, and angles, but they all have four sides in common.
If all of the matching sides and angles of two quadrilaterals are equal in size, they are said to be congruent.
Given that the quadrilateral PQRS congruent to the quadrilateral JKLM.
Find out the all sides and angles of given quadrilateral JKLM and quadrilateral PQRS,
according to the graph the points are:
for quadrilateral JKLM,
J (-6, 2)
K (-3, 5)
L (-5, 8)
M (-8, 4)
for quadrilateral PQRS,
P (9, -7)
Q (6, -4)
R ( _, _ )
S (7, -9)
By the formula distance between any two points is:
[tex]d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}[/tex]
where, [tex]x_{1}, x_{2} , y_{1}, y_{2}[/tex] are the points of two sides of line.
using that formula we have to find out the points of R is (3, -6)
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Find an equation for the graph.
Answers
The equation for the trigonometric graph is y = 2sin4x
What is a trigonometric graph?A trigonometric graph is the graph of a trigonometric function.
Since we desire to find the equation of the graph, we then want to use the equation for the general sine graph.
y = AsinBx where
A = amplitude and B = 2π/T where T = period.Now, A = (maximum - minimum)/2
From the graph,
maximum = 2 and minimum = -2So, we now substitute the variables into the equation, thus
A = (maximum - minimum)/2
= [2 - (-2)]/2
= (2 + 2)/2
= 4/2
= 2
Also B = 2π/T
Now from the graph, T = π/2
So, we substitute for B in the equation for B, thus
B = 2π/T
= 2π/(π/2)
= 2π × 2/π
= 4
We then substitute A and B into y, thus
y = AsinBx
= 2sin4x
So, y = 2sin4x
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A man borrowed $ 3700 from a bank for 6 months. A friend was cosigner of the
man's personal note. The bank collected 7 1/2% simple interest on the date of maturity.
a) How much did the
man pay for the use of the money?
b) Determine the amount
he repaid to the bank on the due date of the note.
Answers
I = Prt
Where:
I = interest
P = principal (the amount borrowed)
r = interest rate (as a decimal)
t = time (in years)
In this case, we have:
P = $3700
r = 7.5% = 0.075
t = 6 months = 0.5 years
Plugging in the values, we get:
I = $3700 x 0.075 x 0.5
I = $138.75
Therefore, the man paid $138.75 for the use of the money.
b) To determine the amount he repaid to the bank on the due date of the note, we need to add the interest to the principal:
Amount repaid = Principal + Interest
Amount repaid = $3700 + $138.75
Amount repaid = $3838.75
Therefore, the man repaid $3838.75 to the bank on the due date of the note.
To emphasize the slow increase in sales, it would be best for Samantha to use graph B or graph A for her presentation
Answers
Answer:
Graph A
Step-by-step explanation:
As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;
This is because the scale of the y-axis in graph B has smaller increments;
This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.
Answer: graph A.
appear to increase less.
Step-by-step explanation:
Pls help !! Find the equation of a line parallel to that passes y= 4/3x+4 through the point (3,-7).
Answers
An equation of a line parallel to that passes y = 4/3x + 4 through the point (3, -7) include the following: A. y + 7 = 4/3(x - 3).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since y = 4x/3 + 4, the slope is equal to 4/3.
At data point (3, -7) and a slope of 4/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-7) = 4/3(x - 3)
y + 7 = 4/3(x - 3)
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Find the value of x.
Answers
Answer:
8
Step-by-step explanation:
line WL is a straight line intersecting line GZ at J so angles LJW is 180o
therefore
LJG + GJH + HJW = 180
9x + 90 + 18 = 180
9x = 180 - 90 - 18
9x = 72
x = 72/9 = 8
10. In the diagram shown, AC is congruent to DC and ZA and ZD are both right angles. SS | RS 1. GIVEA ACANC ELL X-3 en 1. AC DC LA CALD are rt L's 2 LBCB Reflex Hue propert 344DBC LAB ALE HL Fungh D Prov
Answers
Answer:
4Step-by-step explanation:
Please answer questions 15-18. They are not multiple choice, and you have to look at the line.
Answers
The probability are given as follows:
15) P (point is on N.Q.) = 6 / 13
16) P (point is not on Q.R.) = 10 / 13
17) P (point is on N.Q. or RS) = 10/13
18) P = 1/54
What is the explanation for the above?
15)
To find the probability that the point is on line segment N.Q., we need to divide the length of N.Q. by the total length of the line segment NS. The length of NS is the sum of the lengths of N.Q., Q.R., and RS, which is 12 + 6 + 8 = 26. Therefore, the probability that the point is on line segment N.Q. is:
P(point is on N.Q.) = length of N.Q. / length of NS = 12 / 26 = 6 / 13
16)
To find the probability that the point is not on line segment Q.R., we need to subtract the length of Q.R. from the length of NS and divide by the length of NS. The length of Q.R. is 6, so the length of NS without Q.R is 12 + 8 = 20. Therefore, the probability that the point is not on line segment Q.R. is:
P (point is not on Q.R.) = (length of NS without Q.R.) / length of NS = 20 / 26 = 10 / 13
17)
To find the probability that the point is on line segment N.Q. or RS, we can add the probabilities of the point being on N.Q. and the point being on RS. We already calculated that the probability of the point being on N.Q. is 6/13. To find the probability of the point being on RS, we can use the same method as in part (15). The length of RS is 8, so the probability that the point is on RS is:
P(point is on RS) = length of RS / length of NS = 8 / 26 = 4 / 13
Therefore, the probability that the point is on N.Q. or RS is:
P(point is on N.Q. or RS) = P (point is on N.Q.) + P(point is on RS) = 6/13 + 4/13
= 10/13
18)
The bus stops at the lot every 18 minutes and stays for 2 minutes, so the shuttle is at the lot for a total of 20 minutes out of every 18 * 60 = 1080 minutes. Therefore, the probability that the bus is at the lot when you arrive is:
P (bus is at the lot) = time the shuttle is at the lot / total time = 20 / 1080
= 1/54
Note that this assumes that you arrive at a random time within the 1080 minutes and that the bus is equally likely to be at the lot at any time during its 20-minute stay.
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Write an equivalent expression for 24x + 16
Answers
Two similar triangles have a scale factor of 2/3. The area of the larger triangle is 27 what is the area of the smaller triangle
Answers
The area of the smaller triangle is 12 square units
How to determine the area of the smaller triangleIf the scale factor between two similar triangles is 2/3
It means that every length of the smaller triangle is 2/3 the length of the corresponding side of the larger triangle.
So, the ratio of their areas is the square of the scale factor
This is represented as
(area of smaller triangle) / (area of larger triangle) = (2/3)^2 = 4/9
We are given that the area of the larger triangle is 27
So, we have
Area of smaller triangle/27 = 4/9
Multiplying both sides by 27, we get:
Area of smaller triangle = (4/9) * 27
Evaluate
Area of smaller triangle = 12
Hence, the area of the smaller triangle is 12.
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Ayudaaaaa no sé cuando vaya a venir a revisar estoooolo
Si 25$ representa el 15% de una cuenta cuanto hay en total en la cuenta?
Answers
Si 25 dólares representan el 15% de una cuenta, podemos usar una regla de tres simple para determinar cuánto hay en total en la cuenta:
15% -----> $25
100% ----> ($25 x 100)/15
100% ----> $166.67
Por lo tanto, hay $166.67 en total en la cuenta.
80 pts! please correct answer
What is the end behavior of this radical function?
f(x)=4\sqrt{x-6 }
A.
As x approaches positive infinity, f(x) approaches positive infinity.
B.
As x approaches negative infinity, f(x) approaches positive infinity.
C.
As x approaches positive infinity, f(x) approaches negative infinity.
D.
As x approaches negative infinity, f(x) approaches negative infinity.
Answers
Answer:
The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.
Step-by-step explanation:
This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.
We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:
lim f(x) = lim 4√(x-6)
x→∞ x→∞
= 4√(lim(x-6))
x→∞
Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:
lim f(x) = 4√(∞) = ∞
x→∞
Therefore, as x approaches positive infinity, f(x) approaches positive infinity.
Answer:
Step-by-step explanation:
The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.
This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.
We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:
lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.
Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:
lim f(x) = 4√(∞) = ∞x→∞.
Therefore, as x approaches positive infinity, f(x) approaches positive infinity.
Using the growth accounting equation, if the growth rate of output is 5 percent, the growth rate of labor is 4 percent, the growth rate of technology is 3
percent, and a = 0.8, then the growth rate of capital can be estimated to be:
Multiple Choice
O
1.2 percent.
1.5 percent.
2.0 percent.
1.0 percent.
Answers
The answer is (B) 1.5 percent.
You can find the growth accounting equation by using:
Growth rate of output equals Technology growth rate plus a* Capital growth rate plus (1-a*Labor growth rate)
Inputting the values provided yields:
5% equals 3% plus (0.8 * Capital Growth Rate) plus (0.2 * 4%).
When we simplify the equation, we obtain:
Capital growth rate equals (5% - 3% - 0.2%) / 0.8, or 1.5%
As a result, the capital growth rate is predicted to be 1.5%.
(B) 1.5 percent is the right answer.
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