All categories

2 years ago

How do you solve this problem??

Mathematics

1 answer:

Ad libitum [116K]2 years ago

5 0

Answer: x = 64

Step-by-step explanation:

First, order each of the three right triangles by the lengths of the sides. Each triangle has a small (s) leg, a medium (m) leg, and a hypotenuse (h). You can determine their order visually.

Left Δ: s = 36 m = unknown h = 60

Right Δ: s = unknown m = x h = unknown

Big Δ: s = 60 m = unknown h = 36 + x

Next, notice that you can set up a proportion with the Left and Big triangles using the s and h. We can't use m because it has two unknowns.

$\dfrac{s}{h}:\quad \dfrac{36}{60}=\dfrac{60}{36+x}$

Cross multiply and solve for x:

36(36 + x) = 60(60)

1296 + 36x = 3600

36x = 2304

x = 64

You might be interested in

3х – 12 = 5х – 31 How do I solve this

yaroslaw [1]

Answer: x = 9.5

Step-by-step explanation:

3x - 12 = 5x - 31

First, add 31 to each side.

We get:

3x + 19 = 5x

Subtract 3x from each side.

We get:

19 = 2x

Divide both side by 2

9.5 = x

8 0

3 years ago

A carton has a length of 2 1/4 feet, width of 1 3/5 feet, and height of 2 1/3 feet. What is the volume of the carton?

Alik [6]

Multiply 2 1/4, 1 3/5 and 2 1/3 together! It would be easier to turn these mixed fractions into improper fractions.

5 0

3 years ago

In triangle abc, angle A is the right angle. What is the value of y?

Natalka [10]

Answer:

Step-by-step explanation:

In a right triangle, the side opposite to the 90 degree angle (here, side opposite to angle A) is known as the hypotenuse.

Also, the side that is "opposite" to the angle given (here side opposite is y to angle given 30 degrees) is the opposite side.

Since we want to find "opposite" and have "hypotenuse" , recalling trig ratios, we can say opposite/hypotenuse is the ratio SINE, so we can write:

$Sin(30)=\frac{y}{7}$

We solve for y:

$Sin(30)=\frac{y}{7}\\y = 7 Sin(30)$

Since the answer choice has angles in radians, we recall 30 degrees is $\frac{\pi}{6}$ radians.

Thus, the correct answer is $7Sin(\frac{\pi}{6})$ , or option A

3 0

3 years ago

Read 2 more answers

Determine the equation of each line

katovenus [111]

Answer:

see explanation

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 )

(a)

here m = - $\frac{3}{4}$ and c = 6, hence

y = - $\frac{3}{4}$ x + 6 ← equation of line

(b)

here m = 6, hence

y = 6x + c ← is the partial equation

to find c substitute (2, - 6 ) into the partial equation

- 6 = 12 + c ⇒ c = - 6 - 12 = - 18

y = 6x - 18 ← equation of line

(c)

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (4, 7)

m = $\frac{7-3}{4+1}$ = $\frac{4}{5}$ , hence

y = $\frac{4}{5}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 3 ), then

3 = - $\frac{4}{5}$ + c → c = 3 + $\frac{4}{5}$ = $\frac{19}{5}$

y = $\frac{4}{5}$ x + $\frac{19}{5}$ ← equation of line

3 0

3 years ago

Please help with 6 and 7

Ilya [14]

Answer:

6. The number is $-5$

7. The two numbers are $10$ and $11$

Step-by-step explanation:

Question six can be re-worded to create the following expression:

$-2=\frac{4x+10}{5}$

Solve for x to find the number:

$-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x$

Question seven can be solved by first listing the constraints (assuming x is smaller than y):

x and y are less than 20
$x + 1 = y$
$3x - 8 = 2y$

To get the numbers, we can create a system of linear equations. First, solve for $y$ in each expression:

$y = x+1$

$2y = 3x-8\\y = \frac{3}{2}x - 4$

Solve for $x$ :

$x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x$

Solve for $y$ :

$y = x + 1\\y = 10 + 1\\y= 11$

4 0

1 year ago

Read 2 more answers

How do you solve this problem??​

How do you solve this problem??