what's the volume of the figure​

Answer:

The volume of the triangular prism is 4 times smaller than the original triangular prism

Step-by-step explanation:

we know that

The volume of of the triangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the triangular base

h is the height of the prism

If the height is divided by 4

then

The new volume is equal to

[tex]V=Bh/4[/tex]

therefore

The volume of the triangular prism is 4 times smaller than the original triangular prism

Answer:

Step-by-step explanation:

Step 1:  rewrite the equation of the given line in to slope-intercept form by solving for y

  3y + 5x = 6    

     3y = -5x + 6               (subtract 5x from both sides)

        y = -(5/3)x + 2           (divide both sides by 3)

Step 2:  Our line is parallel to this line, so it has the same slope, and a

y-intercept of 4, so we have...

  y = -(5/3)x + 4      

*slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept,

Answer:

D. 10

Step-by-step explanation:

Answer:

If a polygon does not have five angles, then it is not a pentagon.

Step-by-step explanation:

The conditional statement is : if a polygon has five angles, then it is a pentagon.

The conditional statement is in the form of :

"If p, then q", then its inverse statement is in the form "If not p, then not q".

So, answer will be : If a polygon does not have five angles, then it is not a pentagon.

Answer:

A

Step-by-step explanation:

The area of a square is A = s². So the area of this square is A = (2x+2)² = 4x² + 8x + 4.

The perimeter of the triangle is 4/3x + 4/3x+4/3x = 12/3x = 4x.

The difference between the two values is subtraction. Subtract the expressions and simplify.

4x² + 8x + 4 -4x = 4x² + 4x + 4

This expression is also equal to 3. Set it equal to 3 and solve for x.

4x² + 4x + 4 = 3

4x² + 4x + 1 = 0

Substitute a = 4, b = 4 and c = 1 into the quadratic formula.

The quadratic formula is [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex].

Substitute and you'll have:

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-4+/-\sqrt{4^2-4(4)(1)} }{2(4)}=\frac{-4+/-\sqrt{16-16} }{8)}[/tex]

[tex]\frac{-4+/-\sqrt{0} }{8} = \frac{-4}{8}=\frac{-1}{2}[/tex]

Answer:

1.0

Step-by-step explanation:

the 9 would round up because the number to its right is 5 or more but since 9 rounds to 10, the one would carry over to the ones place

Place value can be defined as the value of a digit in a given number. Examples of place value are : Ten Thousand, Thousands, Hundreds, Tens, Ones, Tenth, Hundredth, Thousandth, Ten Thousandth e.t.c

0.955 rounded to the nearest tenth of an inch is 1.0.

Rounding up 0.955 to the nearest tenth:

Therefore, 0.955 rounded to the nearest tenth of an inch is 1.0.

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Answer: mental maths

Step-by-step explanation:

The sum or the addition of the numbers 193 and  564 will be 757.

In mathematics, addition is defined as the summing up the two quantities or adding the two numbers it is denoted by + sign.

It is given that there are two numbers 193 and 564 so the sum will be calculated as:-

Addition = 193+564

Addition =757

Hence sum or the addition of the numbers 193 and  564 will be 757.

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Answer:

x = 15

Step-by-step explanation:

OP and PQ intersect at right angles since PQ is tangent to the circle. This implies that OQ will be the hypotenuse in the right angled triangle OPQ.

Applying Pythagoras theorem;

17^2 - 8^2 = x^2

x = 15

are there any options?????

Answer:

where are the Answers to choose from?

Step-by-step explanation:

Final answer:

To calculate the radius of the cylindrical can, we use the volume of a cylinder formula, V = πr²h. After substituting the given values and solving for r, the radius of the can is found to be approximately 5.64 cm.

Explanation:

To find the radius of the cylindrical can that contains 1500 cm³ of coconut milk with a height of 15 cm, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height.

Given V = 1500 cm³ and h = 15 cm, we can rearrange the formula to solve for r (radius).

The rearranged formula is r = √(V/(πh))

Plug the values into the formula:

r = √(1500 cm³/(3.142 × 15 cm))

r = √(1500/47.13)

r = √(31.83)

r ≈ 5.64 cm

Therefore, the radius of the can is approximately 5.64 cm.

Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing calculator -----> solve the quadratic equation

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5 ----> x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

B

Explanation:

Solve for n:

Subtract 8 on both sides.

5n + 8 = 30

       -8    -8

Divide by 5 on both sides.

5n = 22

---     ----

5        5

Getting a solution of 4 2/5.

n = 4 2/5

Check:

5(4 2/5) + 8 = 30

22 + 8 = 30

30 = 30

Answer:

0.63

Step-by-step explanation:

63 divided by 100 on a calculator would get you the answer.

63 divide bye 100 will give you 0.63

63/100=0.63

For this case, we convert the mixed numbers into fractions:

[tex]5 \frac {50} {100} = \frac {100 * 5 + 50} {100} = \frac {550} {100} = \frac {55} {10} = 5.5[/tex]

[tex]2 \frac {72} {100} = \frac {100 * 2 + 72} {100} = \frac {272} {100} = 2.72[/tex]

Now, rewriting the expression in three equivalent forms we have:

[tex]\frac {550} {100} - \frac {272} {100} = \frac {278} {100}[/tex]

[tex]5.5-2.72 = 2.78\\2 \frac {78} {100}[/tex]

Answer:

[tex]2 \frac {78} {100}[/tex]

Answer:

D  550 ft²

Step-by-step explanation:

5.5 x 5 = 27.5

4 x 5 = 20

A = LW

27.5 x 20 = 550

Scaling is the process in which the dimension of an object is multiplied or increased by the same ratio.  The actual area of the rectangular patio is 550 feet².

Scaling is the process in which the dimension of an object is multiplied or increased by the same ratio.

As it is given that the ratio by which the patio is scaled is 1 inch = 5 feet. Therefore, a single inch on the drawing is 5 feet in the real world.

Now, the dimensions of the patio on the scale drawing are 5.5 inches by inches, therefore, each of the dimensions will be scaled.

[tex]\text{Length of the Patio}= 5.5\rm \times 5 = 27.5\ feet[/tex]

[tex]\text{Width of the Patio} = 4 \times 5 = 20\rm\ feet[/tex]

Further, the area of the rectangle is the product of its length and its breadth, therefore, the area of the rectangular patio is

[tex]\text{Area of the Patio} = Length \times Breadth\\[/tex]

                           [tex]= 27.5 \times 20\\\\= 550\rm\ feet^2[/tex]

Hence, the actual area of the rectangular patio is 550 feet².

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Answer:

65.5 m

Step-by-step explanation:

Step 1. Find the width of the rectangle.

The formula for the area of a rectangle is

A = lw

Data:

A = 265.5 m²

l =     18    m

Calculation:

265.5 = 18w

w = 265.5/18 = 14.75 m

Step 2. Calculate the perimeter

The perimeter (P) of a rectangle is the sum of the lengths of its sides.

P = 2(l + w) = 2(18 + 14.75) = 2 × 32.75 = 65.5 m

The perimeter of the rectangle is 65.5 m.

The  experimental probability of spinning a number greater than 3 is 2/5

It is a branch of mathematics that deals with the occurrence of a random event.

The total times spun is 14+12+16+15+13

We get 70

Add all of the times spun to get 70. To get 16/70 then divide by 2 to get 8/35.

The spun greater than three are 15+13

which is 28

Now Probability of an Event P(E) = Number of times an event occurs / Total number of trials.

=28/70

=14/35

=2/5

Hence, the  experimental probability of spinning a number greater than 3 is 2/5

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Answer:

Final answer is slope [tex]m=\frac{5}{2}[/tex]

Step-by-step explanation:

Given equation is [tex]5x-2y=7[/tex]

Now question says to find the slope.

Since given equation [tex]5x-2y=7[/tex] is a linear equation so we need to compare [tex]5x-2y=7[/tex] with slope intercept formula [tex]y=mx+b[/tex] to get the value of slope m.

Since [tex]5x-2y=7[/tex] is not in that form so first let's rewrite it in y=mx+b form

[tex]5x-2y=7[/tex]

[tex]-2y=-5x+7[/tex]

[tex]y=\frac{-5x+7}{-2}[/tex]

[tex]y=\frac{5}{2}x-\frac{7}{2}[/tex]

Now comparing with y=mx+b, we get [tex]m=\frac{5}{2}[/tex]

Hence final answer is slope [tex]m=\frac{5}{2}[/tex]

Answer:

Slope = 5/2

Step-by-step explanation:

It is given an equation of line  5x – 2y = 7

To find the slope of equation we have to rewrite this equation in y = mx + c form

To convert the given equation to y = mx + c

The given equation is

 5x – 2y = 7

⇒ 5x + 7 = 2y

⇒ 2y = 5x + 7

⇒ y = (5x + 7)/2

y = 5x/2 + 7/2

The above equation is of the form y = mx + c

Here slope = m = 5/2

Answer:

[tex]A= (-1,0)\\B=(1,0)[/tex]

Step-by-step explanation:

The transformation of the segment AB is:

[tex](x+4,\ y-3)[/tex]

Given the points of the line segment A'B':

[tex]A'=(3,-3)[/tex] and  [tex]B'=(5,-3)[/tex]

The coordinates of the points A and B in the line segment AB,can be calculated through this procedure:

For A:

x-coordinate:

Substitute the x-coordinate of A' (we can represent it with[tex]x_{(A')}[/tex]) into [tex]x_{(A')}=x_A+4[/tex] and solve for [tex]x_{A}[/tex], which is the x-coordinate of A:

[tex]x_{(A')}=x_A+4\\\\3=x_A+4\\\\3-4=x_A\\\\x_A=-1[/tex]

y-coordinate:

Substitute the y-coordinate of A' (we can represent it with[tex]y_{(A')}[/tex]) into [tex]y_{(A')}=y_A-3[/tex] and solve for [tex]y_{A}[/tex], which is the y-coordinate of A:

[tex]y_{(A')}=y_A-3\\\\-3=y_A-3\\\\-3+3=y_A\\\\y_A=0[/tex]

The point of A is: (-1,0)

For B:

x-coordinate:

Substitute the x-coordinate of B' (we can represent it with[tex]x_{(B')}[/tex]) into [tex]x_{(B')}=x_B+4[/tex] and solve for [tex]x_{B}[/tex], which is the x-coordinate of B:

[tex]x_{(B')}=x_B+4\\\\5=x_B+4\\\\5-4=x_B\\\\x_B=1[/tex]

y-coordinate:

Substitute the y-coordinate of B' (we can represent it with[tex]y_{(B')}[/tex]) into [tex]y_{(B')}=y_B-3[/tex] and solve for [tex]y_{B}[/tex], which is the y-coordinate of B:

[tex]y_{(B')}=y_B-3\\\\-3=y_B-3\\\\-3+3=y_B\\\\y_B=0[/tex]

The point of B is: (1,0)

The original coordinates of points A and B on the line segment AB, before the transformation, are (-1, 0) and (1, 0), respectively, as found by applying the inverse of the transformation to the coordinates of A' and B'.

To find the original coordinates of the line segment AB before the transformation, we need to apply the inverse of the given transformation to the new coordinates of A' and B'. The transformation is given by (x, y) → (x+4, y-3), so the inverse would be (x', y') → (x'-4, y'+3).

For point A' with coordinates (3, -3), applying the inverse transformation gives us:
A = (3-4, -3+3) = (-1, 0)

For point B' with coordinates (5, -3), applying the inverse transformation gives us:
B = (5-4, -3+3) = (1, 0)

Therefore, the original coordinates of points A and B on the line segment AB are (-1, 0) and (1, 0), respectively.

Answer:

28 units

Step-by-step explanation:

The volume of the rectangular prism is 28 cubic units.

To find the volume of a rectangular prism, we use the formula:

Volume = Base Area * Height

The Base Area is 21/2 (21/2 = 10.5) and the Height is 8/3, we can calculate the volume as follows:

Volume = 10.5 * (8/3)

To multiply fractions, we simply multiply the numerators together and the denominators together:

Volume = (10.5 * 8) / 3

Volume = 84 / 3

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:

Volume = 28

So, the volume of the rectangular prism is 28 cubic units.

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Answer:

rate of flow of hot water = 480 L/hour

and rate of flow of cold water = 720 L/hour

Step-by-step explanation:

Suppose rate of flow of hot water = x

and rate of flow of cold water = y

Given that,

Twice the water flow in the hot water pipe is equal to three times the water flow from the cold pipe.

Combined it equals 1200 L/hour.

According to the question

2x = 3y

x + y = 1200

x = 1200 - y

put this value of x in equation1

2(1200-y) = 3y

2400 - 2y = 3y

2400 = 5y

y = 480

x = 3(480)/2

x = 720

The flow rate in the hot water pipe is 720 L/hour, and the flow rate in the cold water pipe is 480 L/hour, solved through a system of linear equations.

The student's question involves solving a system of linear equations to find the flow rate in each pipe. The problem states that twice the flow in the hot water pipe is equal to three times the flow in the cold water pipe, and that combined, the flow is 1200 L/hour.

Let's define the flow in the hot water pipe as H liters per hour and the flow in the cold water pipe as C liters per hour. The two given conditions can be translated into the following equations:

To solve for H and C, we can use substitution or elimination method. First, we can solve Equation 1 for H to get:

H = 1.5C

Now, we substitute H in Equation 2 with 1.5C:

1.5C + C = 1200

Combining like terms, we get:

2.5C = 1200

Dividing both sides by 2.5, we find the flow rate of the cold pipe:

C = 1200 / 2.5

C = 480 L/hour

Now we can substitute C back into the equation for H to find the hot water flow:

H = 1.5 * 480

H = 720 L/hour

Therefore, the flow rate in the hot water pipe is 720 L/hour, and the flow rate in the cold pipe is 480 L/hour.

Answer:

8 more glasses

Step-by-step explanation:

12-4=8

Final answer:

After serving 4 glasses of the original 12 glasses of lemonade, Jasmine can serve 8 more glasses. We calculate this by subtracting the number of glasses already served from the total number of glasses the pitcher contains.

Explanation:

Jasmine made a pitcher of lemonade that contains 12 glasses. After she serves 4 glasses of lemonade, we can calculate how many more glasses, g, she can serve by subtracting the number of glasses served from the total number of glasses that the pitcher initially had. The equation then becomes: 12 glasses - 4 glasses = g.

To find the value of g, we subtract 4 from 12, which gives us:

g = 12 - 4 = 8

Therefore, Jasmine can serve 8 more glasses of lemonade from the pitcher.

she could be any age from 1-19

Answer:

Step-by-step explanation:

The age is = (20) - (Annette Age)

Answer:

The function is [tex]f(x) = 27(\frac{1}{3})^x[/tex]

Step-by-step explanation:

Compare the y values. Notice that the y values are all multiples of 3 and they decrease by dividing by 3 each time. This suggests the base is 1/3.

Now check when x = 0. This is the initial value since the zero exponent gives an output of 1. So the only way for (0,27) to be a point is for 27 to e multiplied as the initial value. The function is [tex]f(x) = 27(\frac{1}{3})^x[/tex]

Answer:

C

Step-by-step explanation:

The scale is on 2 inches represents 30 feet that means for every 30 feet it's to inches on the scale and the stadium is 180 feet

180/30 to get 6 then times 6 by 2 to get 12. Because there 6 sets of 30 in 180. That's 12 on the scale because there 2 inches for every 30 feet that why you time the 6 by 2 to get 12 inches

I hope this helps you

The range is the difference between the largest number and the smallest number.

The largest number given is 21, the smallest number given is 12.

21 - 12 = 9

The range is 9.

Answer: 9

Step-by-step explanation:

Range = subtract the highest number by the lowest number

Put the numbers in order from least to greatest.

12, 14, 15, 16, 17, 17, 21

21 - 12 = 9

612 inches is the answer to your question

To convert 51 inches to feet and inches, divide by 12 to get 4 feet with a remainder of 3 inches, making the final measurement 4 feet 3 inches.

To convert 51 inches to feet and inches, we need to know that there are 12 inches in a foot.

Therefore, we can divide 51 by 12 to find out how many full feet we have and then take the remainder as the leftover inches.

To perform the calculation:

This conversion from inches to feet and inches is commonly used in various measurements such as personal height, the length of materials, or dimensions for construction.

See in the explanation

Recall that you have to write complete question in order to get good and precise answers. I found a similar question and attached the options below. However, the question has missing graph, too. So let's face this problem in a general way.

1. It must be proportional because the points lie on the same line.

The points not not only must lie on the same line, but that line must pass through the origin because two quantities x and y are directly proportional if we can write an expression:

[tex]y=kx \\ \\ Being \ k \ the \ constant \ of \ proportionality[/tex]

That is, if x increases, y also increases at the same rate.

2. It must be proportional because each time x increases by 2, y stays the same.

In this case as x increases by 2, y stays the same, meaning that this relationship is constant. So in this case they aren't proportional, but we can write:

[tex]y=c \\ \\ Being \ a \ real \ constant[/tex]

3. It cannot be proportional because the y-values are not whole numbers:

This doesn't make sense. The only condition for a direct proportion is that the line must pass through the origin and for any constant of proportionality [tex]k[/tex]

4. It cannot be proportional because a straight line through the points does not go through the origin:

This is is true because the definition of direct proportion is that the line passes through the origin for some constant k:

[tex]y=kx[/tex]

So if I could see the graph, I'd choose the fourth option.

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Answer:

it cannot be proportional because a straight line through the point does not go through the origin

Step-by-step explanation:

Answer:

8 oz bottle

Step-by-step explanation:

1.36/8 = .17

3.20/16 = .20

Answer:

Product A

Step-by-step explanation:

You're going to use the sell price divided by bottle size.

Product A, $1.36/8, $0.17  per oz.

Product B, $3.2/16, $0.2 per oz.

therefore A is cheaper

Inequality shows a relationship between two numbers or two expressions.

The number is between -7 and -2.

i.e

-7 < M < -2

Inequalities show a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

2x > 4

3x < 7

We have,

Let the number be = M

If the product of -5 and a number is greater than 35 or less than 10.

The product of -5 and a number greater than 35 can be written as

-5M > 35 _____(1)

The product of -5 and a number less than 10 can be written as

-5M < 10 _____(2)

From (1) we get,

M > 35/-5

M > -7 _____(3)

From (2) we get,

M < 10/-5

M < -2 ______(4)

From (3) and (4) we get,

-7 < M < -2

Thus

The number is between -7 and -2.

i.e

-7 < M < -2

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Final answer:

The question asks to solve two inequalities resulting from the product of -5 and a number being greater than 35 or less than 10. The solution reveals the number must be either smaller than -7 or greater than -2.

Explanation:

The student's question relates to an inequality involving multiplication with a negative number. The statement 'the product of -5 and a number is greater than 35 or less than 10' can be translated into two separate inequalities because of the 'or.' They are as follows:

-5x > 35

-5x < 10

To solve these inequalities, you would divide each side by -5. Remember the rule: when you divide or multiply an inequality by a negative number, you must flip the inequality sign.

For -5x > 35:

x < -7

For -5x < 10:

x > -2

Therefore, the number must be either smaller than -7 or greater than -2.