The perimeter of the trapezoid-shaped window frame is 23.59 feet. Write and solve an equation to find the unknown side length x (in
feet).

Answer:

[tex]m\angle 3=30^\circ,~m\angle 8=150^\circ[/tex]

Step-by-step explanation:

Angles and Lines

We must recall some properties of angles and lines:

Linear pair of angles: Two angles are linear if they are adjacent angles formed by two intersecting lines. They must add up to 180°.

Corresponding angles: They are angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are congruent, i.e., they have the same measure.

The figure shows two parallel lines a and b, crossed by the line m. These conditions make the following relations be true:

Angles 3 and 4 are linear pair

Angles 8 and 4 are corresponding.

The first relation leads to:

[tex]m\angle 3+m\angle 4 = 180^\circ[/tex]

The second relation leads to:

[tex]m\angle 4 = m\angle 8[/tex]

Since:

[tex]m\angle 3=x[/tex]

[tex]m\angle 8=5x[/tex]

Substituting:

[tex]x + 5x = 180^\circ[/tex]

Simplifying:

[tex]6x = 180^\circ[/tex]

Solving for x:

[tex]x = 180^\circ/6[/tex]

[tex]x = 30^\circ[/tex]

Now,

[tex]m\angle 3=x=30^\circ[/tex]

[tex]m\angle 8=5x=150^\circ[/tex]

[tex]m\angle 3=30^\circ,~m\angle 8=150^\circ[/tex]

Answer:

63

Step-by-step explanation:

36 is approximately 30% of 124 and 42 is approximately 33% of 124, so 30 + 33 = 63

Answer:

Answer, B

Step-by-step explanation:

add the odes and sonnets, and find the percentage of 78/124 which is 62.9% rounded to 63%.

Answer:

Midpoint (xM, yM)  =  (4, 5)

Hope it helps if it does pls give me brainly :)

Answer:  An estimate done quickly: The circumference is about 75 ft.

Step-by-step explanation:

Round π to 3, and 24 to 25.  3 times 25 is 75

A more exact value would be 75.36

3.14 × 24 = 75.36

Answer:

hope this helps 3,160 tons of water flows over Niagara Falls every second. This accounts for 75,750 gallons of water per second over the American and Bridal Veil Falls and 681,750 gallons per second over the Horseshoe Falls.

Step-by-step explanation:

brainlist would help thx

Answer:

88

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7

2x - 10 = 9 - 3x + 6 + 8 + 3x + 7

2x = 10 + 6 + 8 + 7 + 9

2x = 40

x = 40 ÷ 2

x = 20

Thus, x = 20

-TheUnknownScientist

Answer:

3 seconds

Step-by-step explanation:

Answer:

they have to pay for school supplies

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: So if you do 50 dollars - 70% you get, 15 U.S. dollars

Hope this helps :)

Complete question is;

The diameter of bushings turned out by a manufacturing process is a normally distributed random variable with a mean of 4.035 mm and a standard deviation of 0.005 mm. A sample of 25 bushings is taken once an hour.

a. Within what range should 95 percent of the bushing diameters fall?

b. Within what range should 95 percent of the sample means fall?

c. What conclusion would you reach if you saw a sample mean of 4.020?

Answer:

A) (4.0252, 4.0448).

B) (4.0331, 4.0369).

C) If i saw a sample mean of 4.020, i would conclude that the sample came from a population that did not have a population mean equal to 4.035

Step-by-step explanation:

A) We know that an approximate 95% confidence interval for the item in question has a range of diameter given by the equation;

Range = x¯ ± 1.96σ

Now, since we have a mean of 4.035 mm and a standard deviation of 0.005 mm, we can solve;

Range of bushing diameter = 4.035 ± (1.96 × 0.005) = 4.035 ± (0.0098)

= 4.0252 or 4.0448 and it can be written as;(4.0252, 4.0448).

B) We also know that In the large-sample case, a 95% confidence interval estimate for the population mean is given by the formula;

CI = x¯ ± (1.96s/√n))

Thus, if we solve, we get;

CI = 4.035 ± (1.96 × 0.005 )/√25

CI = 4.035 ± 0.0019

or (4.0331, 4.0369).

c. If i saw a sample mean of 4.020, i would conclude that the sample came from a population that did not have a population mean equal to 4.035 because it doesn't fall into the range of confidence intervals we got earlier.

Answer:

free 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

QR = 27 ÷ 2 = 13.5

Answer:

the answer is 4(5c-2d)

Answer:

20c-8d

Step-by-step explanation:

As long as you weren't any values for c or d, this expression cannot be simplified any further.

HTH :)

Answer:

Step-by-step explanation:

-3

perpendicular slope is the negative of the reciprocal

the reciprocal of 1/3 is 3

the opposite of 3 = -3

Answer:

not multiplying 3 by 5 it should be 15 over 10 and not 3 over 30

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Put in Parentheses.

(5 + 1) x 10 =

Solve numbers inside parentheses.

5 + 1 = 6

Now we have 6 x 10.

6 x 10 = 60

Answer:

if you ment to say 2 is 12.5% of what number the answer would be 16

Step-by-step explanation:

Write down what you know with x as the number you need to find.

Of is always "multiply"

Choose another way to write 12.5%

2 =12.5% of x

So 2 = 0.125xx

x= 2 *over*0.125

x=16

Answer:

x=16

Step-by-step explanation:

Let the number be x.

if they say 12.5% of a number, this means that 12.5/100 *x which will be :

12.5/100x

make it an equation (a true one)

12.5/100x=2

divide.

2 divided by 12.5/100x would be

x=16!

Cheers, I hope you can understand it well!

Answer:

2,000 is the value of the digit 2 in the thousands place

Answer:

2139 with a remainder of 1

Step-by-step explanation:

hope this helps :))) have a great day!

Answer:

-2.5

Step-by-step explanation:

Your want to isolate the x. This is a multiplication problem, so use the inverse operation, which is division. Divide both sides of the equation by

1/4 by multiplying by the reciprocal, 4. (− 5

8)(4) is − 5/2. Use substitution to check the answer. x = − 5/2 :)

Answer: First, you isolate x by dividing 1/4 on both sides.  

1/4x divided by 1/4 equals zero, which just leaves x, and -5/8 divided by 1/4 equals -5/2, so x = -5/2. -5/2 can be simplified to -2.5,  

To check the answer, substitute x for -5/2:

* 1/4 multiplied by -5/2 equals -5/8

* 5/8 = 5/8, so this proves that my answer is correct.

Answer:

Step-by-step explanation:

Given:

AB ≅ BC

AK ≅ KC

∠AKE ≅ ∠CKP

To Prove:

ΔAKE ≅ ΔCKP

         Statements                               Reasons

1). AB ≅ BC                                          1). Given

2). ∠BAC ≅ ∠BCA                              2). Property of Isosceles triangles

3). ∠EKA ≅ ∠PKC                               3). Given

4). ΔAKE ≅ ΔCKP                               4). ASA Postulate of congruence

Hence ΔAKE ≅ ΔCKP.

Answer:

Step-by-step explanation:

Given the equation

[tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]

putting y=15

[tex]\frac{1}{5}x-\frac{2}{3}\left(15\right)=30[/tex]

[tex]\frac{1}{5}x-10=30[/tex]

add 10 to both sides

[tex]\frac{1}{5}x-10+10=30+10[/tex]

[tex]\frac{1}{5}x=40[/tex]

[tex]x=200[/tex]

Therefore, the value of x:

Answer:

13/12

Step-by-step explanation:

2(5/3+3/4)_4/3

2(20+9/12)_4/3

2(29/12)_4/3

58/24_4/3

58_32/24

26/24

13/12

Answer:

1/5                                5

Step-by-step explanation:

Answer: The scale factor for the reduction is 1/5. B= 5 feet

Step-by-step explanation:

The scale factor for the reduction is 1/5.

The length of A=20 (1/5)= 4 feet

What is the length of B?

B= 5 feet

Answer:

Following are the solution to the given point:

Step-by-step explanation:

In point a:

[tex]\to 2ty'=8y\to \frac{1}{y} dy = 4 \frac{1}{t} dt\\\\\to \int \frac{1}{y} dy = 4 \int \frac{1}{t} dt \\\\\to \log y = 4 \log t + \log C\\\\\to \log y = \log ct^4\\\\\to y=ct^4 \\\\\to y(-2)=16 \\\\\to 16= c(-2)^4\\\\\to 16= 16c\\\\\to c= \frac{16}{16}\\\\\to c=1\\\\\to r=4[/tex]

In point b:

[tex]\to 2ty' = 8y \\\\\to y'- \frac{4}{t} y=0 \\\\here \ p(t) = \frac{1}{t}[/tex] it's a discontinuous point at t=0, and the largest internal containing -2 since [tex]y=(-2) = 16 \ is\ (-\infty, 0)[/tex]

In point c:

[tex](-\infty,0 ) \cup (0, \infty)[/tex]