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3 years ago

The figure below shows the design of a truss to support the weight of a roof. In this truss design, ∠A⩭∠D and ĀF⩭DF.

Mathematics

1 answer:

bearhunter [10]3 years ago

5 0

Answer:

$m\angle A= 30^{\circ}$

Step-by-step explanation:

In the question, we're given $\angle A\cong \angle D$ . Therefore, the measure of these two angles must be equal.

To find the value of $x$ , set these two angles equal to each other:

$4x-26=x+16$

Add 26 and subtract $x$ from both sides:

$3x=42$

Divide both sides by 3:

$x=\frac{42}{3}=14$

Since $\angle A$ was labelled as $4x-26$ , substitute $x=14$ to find its measure:

$\angle A=4(14)-26,\\\angle A=56-26,\\\angle A=\boxed{30^{\circ}}$

You can also substitute $x=14$ into the label of angle D as angle A is congruent to angle D for easier calculations ( $14+16=\boxed{30^{\circ}}$ ).

You might be interested in

1. 5/2=-x/11<br><br> 2. 9/m=-4/11

alex41 [277]

Answer:

1. x = 55/2

2. x = - 99/4

5 0

3 years ago

If a graph of a system of two equations shows two lines that coincide on a coordinate plane, how many solutions does the system

olga55 [171]

If a graph of a system of two equations shows two lines that coincide on a coordinate plan there would be C.)Infinitely many solutions

I hope this helps, have a great day.

3 0

3 years ago

Read 2 more answers

It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desir

Ksju [112]

Answer:

We need a sample size of at least 75.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, we find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So:

$\sigma = \sqrt{484} = 22$

With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

We need a sample size of at least n, in which n is found when M = 5. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$5 = 1.96*\frac{22}{\sqrt{n}}$

$5\sqrt{n} = 43.12$

$\sqrt{n} = \frac{43.12}{5}$

$\sqrt{n} = 8.624$

$(\sqrt{n})^{2} = (8.624)^{2}$

$n = 74.4$

We need a sample size of at least 75.

6 0

3 years ago

Read 2 more answers

PLEASE HELP!

Alexus [3.1K]

Answer:

4x+5y-34=0

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

My goal is to put in in this form first. Then I will aim to put it in general form, ax+by+c=0.

So let's give it a go:

m is the change of y over the change of x.

To compute this I'm going to line my points up and subtract vertically, then put 2nd difference over 1st difference. Like this:

( 1 , 6)

-(6 , 2)

----------

-5 4

So the slope is 4/-5 or -4/5.

So m=-4/5.

Now we are going to find b given y=mx+b and m=-4/5 and we have a point (x,y)=(1,6) [didn't matter what point you chose here].

6=-4/5 (1)+b

6=-4/5 +b

Add 4/5 on both sides:

6+4/5=b

30/5+4/5=b

34/5=b

So the y-intercept is 34/5.

The equation in slope-intercept form is:

y=-4/5 x + 34/5.

In general form, it is sometimes the goal to make all of your coefficients integers so let's do that. To get rid of the fractions, I'm going to multiply both sides by 5. This clears the 5's that were on bottom since 5/5=1.

5y=-4x+34

Now add 4x on both sides:

4x+5y=34 This is standard form.

Subtract 34 on both sides:

4x+5y-34=0

8 0

3 years ago

Read 2 more answers

rank has a circular garden. The area of the garden is 100 ft2. What is the approximate distance from the edge of Frank’s garden

Ray Of Light [21]

It is given that the area of the circular garden = 100 $ft^2$

Area of circle with radius 'r' = $\pi r^2$

We have to determine the approximate distance from the edge of Frank’s garden to the center of the garden, that means we have to determine the radius of the circular garden.

Since, area of circular garden = 100

$\pi r^2 = 100$