All categories

3 years ago

The figures in the picture are similar to each other find the value of x

Mathematics

1 answer:

alisha [4.7K]3 years ago

6 0

Answer:

x = 7

Step-by-step explanation:

Similar figures have sides that are proportional. Setting up a proportion for the sides of the figures will help solve for 'x':

$\frac{small}{large}=\frac{3}{6}=\frac{(x-3)}{(x+1)}$

Cross-multiply: 3(x + 1) = 6(x - 3)

Distribute: 3x + 3 = 6x - 18

Combine like terms: 21 = 3x

Solve for 'x': x = 7

You might be interested in

Please help me (It's for a really important grade)

Sholpan [36]

Answer:

4/5

Step-by-step explanation:

Sin = Opposite / Hypotenuse

Note that hypotenuse = longest side

We want to find sinФ

The opposite side length of angle "Ф" has a length of 8 and the longest side or hypotenuse has a length of 10

So sinФ would equal 8/10 which can be simplified to 4/5

7 0

2 years ago

A recipe uses 1 1/4 cups of milk to make 10 servings if the same amount of milk is used for each serving how many servings can b

aev [14]

Answer:

128 servings

Step-by-step explanation:

5/4 cups of milk for 10 servings is equal to 1/8 cup per 1 serving

there are 16 cups in a gallon

let 'n' = # servings in a gallon

so 1/8 : 1 is 16 : n

1/8n = 16

n = 16(8)

n = 128

3 0

3 years ago

Solve the equation:

adelina 88 [10]

Answer:

x=1 is the correct answer

7 0

3 years ago

Read 2 more answers

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$