If triangle QRS is dilated by a scale factor of 1/5 through the origin, which of the following points represents the coordinates of R’?

The Value at the end will be \(-2\).

The initial value is defined as 3.

In the second line, the multiply operation executed primarily followed by subtraction.

\(i.e, \text{value} = 3 - (2 \times 3) = 3 - 6\)

\(\therefore \text{value} = - 3\) in the second line.

Incrementing the value in the last line results in \(-2\).

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Solution

Step 1:

The driver will first notice a decrease in gasoline mileage at 30mph.

Step 2

The Compact car showed the decrease

Final answer

The driver will first notice a decrease in gasoline mileage at 20mph.

The Compact car showed the decrease

The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.

The ratio refers to the relative size of one quantity compared to another.

The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction.  We can also express the ratio in its standard form (:).

Given   Sum of     Equivalent

Ratio     Ratios          Ratios

5/36        36         13.89% or 0.1389

2:9           11          18.18% or 0.1818

3 to 18     21          14.28% or 0.14.28

1:3            4           25% or 0.25

Thus, we can conclude that 1:3 is the largest ratio amont the others.

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Answer: 224 boxes of paper

Step-by-step explanation: The key to this problem is to first find the volume of Nico's truck and divide it by the volume of one paper box.

To find the size (volume) of Nico's truck, first multiply the dimensions (length, width and height) given.

7x4x8 would be 224 cube feet.

Now, what's the volume of each box containing paper? In the question it said that the boxes are shaped like a cube and the length to each side (edge) is 1 foot.

Volume of cube= edge x edge x edge

In this case, the edge is one so the volume would be 1 cube foot.

Finally, divide the volume of the truck (amount of space) by the volume of each cube (the size of each box): 224÷1= 224

224 is the number of boxes of papers Nico can pack into the back of this truck.

and that's the answer to this problem.

Below is the illustration (note mine is only an rough drawing, you can draw a better scale if you would like to)

Answer: 3.55, 6.187, 9.312, 27.132

Step-by-step explanation:

The easiest way I do this is by rounding all the numbers to the nearest hundredths, tenths, or whole numbers.

3.55 = 4
6.187 = 6
9.312 = 9
27.132 = 27

Answer: 10x-6

Step-by-step explanation:

we know that perimeter P is 2L+2W

2L= 2(3x+2)=6x+4

2W=2(2x-5)=4x-10

P=6x+4+4x-10=10x-6

Answer:

\(x=2$\pm$\sqrt{42}\)

Step-by-step explanation:

The given equation is:

\(x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0\)

Formula:

A quadratic equation \(ax^{2} +bx+c=0\) has the following roots:

\(x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}\)

Where \(D= b^{2} -4ac\)

Comparing the equation with \(ax^{2} +bx+c=0\)

a = 1

b = -4

c= -38

Calculating D,

\(D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168\)

Now, finding the roots:

\(x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}\)

So, the solution is:

\(x=2$\pm$\sqrt{42}\)

Answer is A or the first one

Answer:

12 people are need to walk 24 dogs

Step-by-step explanation:

12/2=6

24/2=12

Answer:

12 people can walk 24 dogs.

Step-by-step explanation:

Given information,

→ 6 people can walk 12 dogs.

→ People required for 24 dogs = ?

Let us assume that,

→ Missing value = p

Forming the equation,

→ 6/12 = p/24

Then the value of p will be,

→ 6/12 = p/24

→ p/24 = 6/12

→ p × 12 = 6 × 24

→ 12p = 144

→ p = 144/12

→ [ p = 12 ]

Hence, the value of p is 12.

Note that the answers to the above question are given as follows;

Question 1: The measure of the third angle is 60°.

Question 2: No triangles can be constructed with two angles measuring 80° and 100°.

Question 3: The circumference of the circle is approximately 28.5 cm.

Question 4: The best approximation of the area of the circle is 28.26 square inches.

Question 5: The area of the bottom of the circular tent is approximately 153.86 square meters.

Question 1:

“The measure of the third angle is 20° False

The measure of the third angle is 40° False

The measure of the third angle is 60° True (Sum of angles in a triangle)

Question 2:

Two angles measuring 80° and 100° cannot form a triangle because the sum of the angles in any triangle must be 180°. Therefore, no triangles can be constructed with two angles measuring 80° and 100°.

Question 3:

The formula for the circumference of a circle is C = 2πr, where r is the radius and π is approximately 3.14. Therefore, the circumference of a circle with a radius of 4.53 cm is:

C = 2 x 3.14 x 4.53 ≈ 28.47 cm

Rounding to the nearest tenth, the circumference is approximately 28.5 cm.

Question 4:

The formula for the area of a circle is A = πr^2, where r is the radius and π is approximately 3.14. Since the diameter of the circle is 6 inches, the radius is half of that, or 3 inches. Therefore, the area of the circle is:

A = 3.14 x 3^2 = 28.26 square inches

Therefore, the best approximation of the area is 28.26 square inches.

Question 5:

The formula for the area of a circle is A = πr^2, where r is the radius and π is approximately 3.14. Therefore, the area of a circular tent with a radius of 7 meters is:

A = 3.14 x 7^2 ≈ 153.86 square meters

Therefore, the area of the bottom of the tent is approximately 153.86 square meters.

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Answer:

5/8

Step-by-step explanation:

The answer should match the image below.

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

\( \sqrt[4]{ {x}^{3} } \)

Step-by-step explanation:

\( \sqrt{x} \times \sqrt[4]{x} \\ = {x}^{ \frac{1}{2} } \times {x}^{ \frac{1}{4} } \\ = {x}^{ \frac{1}{2} + \frac{1}{4} } \\ = {x}^{ \frac{3}{4} } \\ = \sqrt[4]{ {x}^{3} } \)

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

Answer:

12/5 gallons/minute, or 2 2/5 gallons/minute

Step-by-step explanation:

Find the unit rate with time as the independent variable:

2 gallons

---------------- = 12 gallons / 5 minutes = 12/5 gallons/minute

5/6 minute

Answer:

.41666 or 5/12 Gallons per minute

Step-by-step explanation:

5/6 divided by 2

9514 1404 393

Answer:

  45 ft

Step-by-step explanation:

The fence is shown as 18 cm, which is 9 times 2 cm. If 2 cm represents 5 ft, then the actual fence will be 9 times 5 ft = 45 ft.

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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Answer:

x=14

Step-by-step explanation:

two named angles are equal because they are known as corresponding angles; therefore, set them equal to each other

6x+3=87

6x=84

x=14

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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14 is the asnwer because sqaure root of 200 is 14.14213562 and if you round that it is 14

A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

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A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.

We have,

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

The probability that a particular song is played is 0.23,

As can be seen that the problem is of combination, so we have to choose 5 out of 7,

Calculate the combination as shown below,

⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2

⁷C₅ = 7 × 6 / 2

⁷C₅ = 21

Calculate the probability as shown below,

P = ⁷C₅  × (0.23)⁵ × (0.77)²

P = 0.008

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complete question;

During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.

Answer:

Answer choices: 1/2, 7/8, 19/24, 6/8.

Step-by-step explanation:

The number of songs written by the guitarist and by the drummer is given as follows:

The number of songs written by each is obtained using a system of equations, for which the variables are given as follows:

The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote, hence:

x = 2y - 8.

They wrote a total of 46 songs, hence:

x + y = 46.

Replacing the first equation into the second, the number of songs written by the drummer is of:

2y - 8 + y = 46

3y = 54

y = 18.

Hence the number of songs written by the guitarist is given as follows:

x = 46 - 18

x = 28.

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Answer:

If y= 2x + 7 were changed to y = 1/2x+7, It would be less steep.

Step-by-step explanation:

A. It would be less steep.

Answer:

the answer is A

Step-by-step explanation:

This is because the slope of the original function (gradient = 2) is greater than that of the other line which has a slope of 0.5

The volume of the cube-shaped box is 56 cubic inches larger than the volume of the rectangular box.

Volume and capacity are two crucial ideas that are both fundamental and among those fundamental ideas that need to be thoroughly grasped. These ideas are a few that every youngster needs to comprehend from an early age. Different items will be displayed, especially when it comes to geometry in math, for which the volume and capacity must be computed. With a few practize problems, this will also enable the pupils to successfully solve bigger and more difficult problems. We come across a great deal of three-dimensional objects in our daily lives that take up a certain amount of space. The total amount of space that a material occupies is referred to as its volume.

Given

In the figures below the cube shaped box is 6 in wide and the rectangular box is 10 inches Long 4 inches wide and 4 inches high

Volume of cube box

= 6³

= 216

Volume of rectangular box

= 10 ×4×4

= 160

Difference

= 216 - 160

= 56

The volume of the cube-shaped box is 56 cubic inches larger than the volume of the rectangular box.

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