An architect is planning to make two triangular prisms out of iron. The architect will use ∆ABC for the bases of one prism and ∆DEF for the bases of the other prism.
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(a) What is the scale factor from ∆ABC to ∆DEF?

(b) Suppose the height of the prism made by ∆ABC is 15 centimeters. What is the volume of the prism made by ∆ABC? Remember to show your work.

(c) Suppose the volume of the prism made by ∆ABC is 4459 cm^3. What is the volume of the prism made by ∆DEF? Remember to show your work.

Answer:

p=12

Step-by-step explanation:

936=78p

divide 78 from both sides.

12=p

Answer:

12

Step-by-step explanation:

you have to get the variable by itself. so you would divide by 78. taking 936/78=12

Answer:

41/6

Step-by-step explanation:

-12+81=-1+6(2a-2)

first distribute:

-12+81=-1+12a-12

combine like terms:

-12+81= -1+12a-12

69=-13+12a

add -13 with 69:

82=12a

divide 82 and 12:

82/12= 41/6

Answer:

a = 0

Step-by-step explanation:

given

-12 + 8a =-a + 6(2a -2)

Distribute the righ side

-12 + 8a = -a +6x2a -6x2

-12 + 8a = -a +12a - 12

-12 + 8a = 11a -12

Collect like terms

-12 + 12 = 11a - 8a

0 = 3a

Divide both sides by 3

0/3 = 3a/3

0 = a

a = 0

Answer:

(a) 4x=5(x-18)

(b) ∠A=∠B=360°

Step-by-step explanation:

Corresponding angles : when two lines are crossed by a transversal , the angle in matching corners are called corresponding angles.

Since the corresponding are congruent.

Therefore,

∠A=∠B

⇔4x=5(x-18)

⇔4x=5x-90

⇔4x-5x=-90

⇔-x=-90

⇔x=90

Therefore ∠A=∠B= 4×90°=360°

Answer:

13

Step-by-step explanation:

Circumference=2πr

2πr=26π

2r=26

r=13

Final answer:

The radius of a bicycle wheel that travels 26π inches per revolution is found using the circumference formula. By solving 26π = 2πr, the radius is determined to be 13 inches.

Explanation:

The question asks to determine the radius of a bicycle wheel that travels 26π inches per revolution. To find the radius, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we know the wheel travels 26π inches for each revolution, this distance is the circumference of the wheel.

Setting up the equation 26π = 2πr, we can solve for the radius r by dividing both sides of the equation by 2π:

The radius of the bicycle wheel is 13 inches.

Answer:

Option C) [tex]x^{\frac{5}{9}}[/tex] is correct

Therefore [tex](x^5)^{\frac{1}{9}}=x^{\frac{5}{9}}[/tex]

Step-by-step explanation:

Given expression is

To simplify the given expression :

[tex](x^5)^{\frac{1}{9}}[/tex]

[tex]=(x)^{5\times \frac{1}{9}}[/tex] ( using the property [tex](a^m)^n=a^{mn}[/tex] )

[tex]=x^{\frac{5}{9}}[/tex]

Therefore [tex](x^5)^{\frac{1}{9}}=x^{\frac{5}{9}}[/tex]

Therefore option C) [tex]x^{\frac{5}{9}}[/tex] is correct

Therefore the simplified expression is [tex]x^{\frac{5}{9}}[/tex]

Answer:

4³

Step-by-step explanation:

2 / 2 = 1

4 raised to the power of one is 4

4 raised to the power of 3 is 4³

Answer:

The numbers are 15 and 6.

Step-by-step explanation:

We can solve the problem algebraically (using equations). First, write equations that represent the situation.

Choose variables to represent the numbers:

let the numbers be "x" and "y"

Take apart each section of the problem and make an equation.

"The sum of two numbers is 21"

x + y = 21             Sum means the answer when you add numbers

"Their difference is 9"

x - y = 9               Difference means the answer when you subtract numbers

Using the two equations, you can solve using elimination. With this method, you get rid of one of the variables, so you can easily solve for the other one. You can use elimination when one of your variables have the same variable number. Both equations have "1x" and "1y" ("1" is never written).

Add the equations together by adding normally, with each of the terms with the same variable.

.     x + y = 21             Add each term

+     x - y = 9            (x + x = 2x)     (y + (-y) = 0)     (21 + 9 = 30)

.   2x + 0 = 30         "y" variable cancelled out

.          2x = 30        

.       2x/2 = 30/2         Divide both sides by "2" to isolate "x"

.            x = 15         Answer for one number

To find the other number, substitute 'x' for 15 into one of the equations.

x + y = 21

15 + y = 21         Isolate "y" now

15 - 15 + y = 21 - 15         Subtract 15 from both sides

y = 21 - 15         15-15 cancelled out on the left side. Solve right side.

y = 6       Answer for second number

Therefore the two numbers are 15 and 6.

Answer:

x = m+-4

Step-by-step explanation:

We are trying to figure out the slope and the slope equals m, Then we have the y-intercept which that equals -4

Answer:

length of longer piece = 18 m

Step-by-step explanation:

Timothy had 24 meters of ribbon

shorter piece is 6 meters

longer piece = actual piece - shorter piece

                      = 24 - 6

                      = 18 m

Final answer:

The longer piece of ribbon is 18 meters long, which is obtained by subtracting the length of the shorter piece from the total length of the ribbon.

Explanation:

Timothy started with a 24-meter long ribbon and cut it into two pieces, with the shorter piece being 6 meters in length. To find the length of the longer piece, we subtract the length of the shorter piece from the total length of the ribbon.

Length of the longer piece = Total length of the ribbon - Length of the shorter piece

Length of the longer piece = 24 meters - 6 meters = 18 meters.

Therefore, the longer piece of ribbon is 18 meters long.

Answer:

The actual area of the page will be 120 square inches.

Step-by-step explanation:

Janice is creating a page of scrapbook having vertices (2,1), (7,1), (7,7), and (2,7).

If we plot the points on the coordinate plane then we will see that the page is of a rectangular shape with length (7 - 1) = 6 units which is parallel to the y-axis and width (7 - 2) = 5 units which is parallel to the x-axis.

So, the area of the page is (6 × 5) = 30 square units.

Now, given that 1 square unit is equivalent to 4 square inches.

Therefore, the actual area of the page will be (30 × 4) = 120 square inches. (Answer)

The total amount that Karen will be for the sweatshirt including tax will be $32.10.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Karen buys a sweatshirt for $30. The sales sold be tax in her state is 7%.

The total amount that Karen will be for the sweatshirt including tax will be calculated as,

Total cost = $30 x (1 + 7%)

Total cost = $30 x (1 + 0.07)

Total cost = $30 x (1.07)

Total cost = $32.10

The total amount that Karen will be for the sweatshirt including tax will be $32.10.

More about the percentage link is given below.

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Answer:

x = 6

Step-by-step explanation:

x = 3 is the equation of a vertical line parallel to the y- axis.

The equation of a parallel line will therefore be a vertical line.

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (6, 1) with x- coordinate 6, thus

x = 6 ← equation of parallel line

Final answer:

The equation of the line that is parallel to x = 3 and passes through (6, 1) is x = 6.

Explanation:

The question relates to finding the equation of a line that is parallel to another line, specifically the line x = 3, and that also passes through a given point, namely (6, 1). Since the line x = 3 is a vertical line, any line parallel to it will also be vertical and have an equation of the form x = k, where 'k' is a constant.

In this case, the line we are looking for must go through the point (6, 1), which means it will have the same x-coordinate as this point. Therefore, the equation of the line is simply x = 6.

What have you done?

on observing the conversions we get that

triangle GHI is congruent to triangle G''H''I''

Hope this helps.

Answer:

c?

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

30 divided by 5 x what is left over from the whole.

Answer:

3/5 left or 10$

Answer: 10-6x

Step-by-step explanation:

Answer:

Step-by-step explanation:

10-6x

Answer:

[tex]y=-6[/tex]

Step-by-step explanation:

we know that

A line parallel to the x-axis is a horizontal line

The equation of a horizontal line is equal to the y-coordinate of the point that passes through it

In this problem the line passes through the point (6,-6)

so

The y-coordinate is -6

therefore

The equation of the line is

[tex]y=-6[/tex]

Answer:

By bike= 4 hours

By walk= 3 hours

Step-by-step explanation:

Given: Sydney travel by bike at 9 mph

           Sydney travel by walk at 7 mph.

           Total trip time= 7 hours

           Distance to bookstore= 57 miles.

Lets assume the time spent travelling by bike be "x".

∴ Time spent travelling by walk is [tex](7-x)[/tex]

Now, lets find the distance travelled on bike and by walk.

we know, [tex]Distance= speed\times time[/tex]

∴ Distance by bike= [tex]9\times x= 9x[/tex]

   Distance by walk= [tex]7\times (7-x)[/tex]

Using distributive property of multiplication.

∴ Distance by walk= [tex]49-7x[/tex]

Next, forming an equation for total distance travelled to find x.

⇒ [tex]9x+ (49-7x)= 57\ miles[/tex]

Opening parenthesis

⇒ [tex]9x+49-7x= 57[/tex]

⇒[tex]2x+49= 57[/tex]

Subtracting both side by 49

⇒[tex]2x= 8[/tex]

dividing both side by 2

⇒[tex]x= \frac{8}{2}[/tex]

∴[tex]x= 4\ hours[/tex]

Hence, time spent travelling on bike is 4 hours.

Subtituting the value x to find the time spent travelling by walk.

Times spent travelling by walk= [tex]7-4= 3\ hours[/tex]

hence, time spent travelling by walk= 3 hours

Answer:

B

Step-by-step explanation:

r = 14/2 = 7units

[tex]Volume of sphere=\frac{4}{3}*\pi*r^{3}\\\\=\frac{4}{3}*3.14*7*7*7\\\\=1436.03cubic units\\\\Volume of cylinder=\pi*r^{2}*h\\\\=3.14*7*7*14\\\\=2154.04 cubic units[/tex]

Answer:

B

Step-by-step explanation:

r = 14/2 = 7units

Answer:

The value is always 0.

plz mark me as brainliest :)

hope this helped Peppa Pig

Answer:

The solution for x is (-∞, 3).

Step-by-step explanation:

The provided inequality is: [tex]4x-2<10[/tex]

Solve for x a follows:

[tex]4x-2<10\\\\Add\ 2\ to\ both\ sides\\\\4x-2+2<10+2\\\\4x<12\\\\Divide\ both\ sides\ by\ 4\\\\\frac{4x}{4}<\frac{12}{4}\\\\x<3[/tex]

The range of the values of x is

[tex]x<3\\This\ implies\ that\ x\ belongs\ to\ the\ interval\ (-\infty, 3)[/tex]

Thus, the range of the values of x is (-∞, 3).

Answer:

4+7=11

7-4=3

So the numbers must be 4, and 7.

Using the Segment Addition Postulate, we determined that the length of segment EH is 20 units, given the lengths of segments EG, FG, and FH in the figure.

In the given figure, we have three points E, F, G, and H, with F being between E and G, and G being between F and H. We are given the lengths of line segments EG, FG, and FH, and we need to find the length of segment EH.

To find EH, we can use the Segment Addition Postulate, which states that for three collinear points, if one point is between the other two, then the sum of the lengths of the two smaller segments is equal to the length of the larger segment.

In this case, we have:

EG + GF = EF

Given that EG is 10 and GF is 2:

10 + 2 = EF

12 = EF

Now, we know the length of segment EF is 12. Next, we can apply the same principle to segments EF and FH:

EF + FH = EH

Substituting the values:

12 + 8 = EH

20 = EH

So, the length of segment EH is 20 units.

For more such information on: Segment Addition Postulate

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Answer:

102

Step-by-step explanation:

Nat had a total of 102 stamps which he divided into 17 sets. Each set contained six stamps.

To find out how many stamps Nat had, we need to multiply the number of sets by the number of stamps per set. Nat divided his stamps into sets of six. He made 17 sets. To calculate the total number of stamps, we perform the multiplication:

Multiply the number of stamps in each set (6) by the number of sets (17).

6 stamps/set × 17 sets = 102 stamps
Hence, Nat had 102 stamps in total.

3.5 inches

Step-by-step explanation:

128 feet : 16 inches

28 feet : x inches

Then,

128 / 16 = 28 / x

8 = 28 / x

x = 28 / 8

Therefore,

x = 3.5 inches

Answer:

B= 3.5 in.

Step-by-step explanation:

Answer:

27.83

Step-by-step explanation:.15(24.20)=3.63

3.63+24.20+27.83

To calculate a 15% tip on a $24.20 bill, convert 15% to a decimal (0.15), and multiply this by the total bill. The tip should be $3.63.

The concept behind leaving a tip is to provide payment that is a certain percentage of the total bill. In your query, you want to leave a 15% tip on a bill of $24.20. To figure out how much the tip would be, you would multiply the total bill by the tip percentage.

First, you need to convert the tip percentage into a decimal form. To do that, you divide the percentage by 100. So 15 divided by 100 is 0.15.

Next, you multiply the total bill by this decimal. In this case, 24.2 (the total bill) multiplied by 0.15 equals 3.63. Thus, the tip they should leave is $3.63.

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Answer:

171

Step-by-step explanation:

(133+206+x)/3 = 170

133+206+x = 510

339 + x = 510

x = 171

(133+206+171)/3 =

Final answer:

When 2 pizzas, each cut into 8 slices, are equally shared among 3 friends, each person would eat 5 and 1/3 slices of pizza.

Explanation:

The question involves dividing a certain number of pizza slices equally among friends. Initially, we have 2 pizzas and each pizza is cut into 8 slices, making a total of 16 slices. To find out how many slices each person ate when the amount is the same for everyone, we simply divide the total number of slices by the number of friends.

Since a pizza slice cannot be split into a third naturally, practically, each friend would eat 5 slices and a little bit more from another slice.

Answer:

X =71. The reason is because the interior angles of a triangle add up to 180. 180-38=142. It is an isosceles triangle so the bottom two angles are equal. Divide 142/2 to get 71. ;)

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

make the mixed numbers improper fractions: 13/4-11/4

13/4-11/4 = 2/4

2/4 = 1/2

Answer:

1/2

Step-by-step explanation: