Determine the unknown side of the similar triangle. A) 2 B) 3 C) 4 D) 5

If ∠G is supplementary to ∠H and the measure of ∠G is 65° what is the measure of ∠H?

Elina [12.6K]

Solution:

Given:

∠G = 65°

Supplementary angles are a pair of angles that sum up to 180°.

It should be noted:

If ∠G and ∠H are a pair of supplementary angles, they both sum up to 180°.

Equation formed: ∠G + ∠H = 180

Substitute the values into the equation.

∠G + ∠H = 180
=> 65 + ∠H = 180

Subtract 65 both sides.

=> 65 - 65 + ∠H = 180 - 65
=> ∠H = 180 - 65 = 115°

7 0

1 year ago

Ughh i suck at dilation

Ivenika [448]

Look at!!:
Pre image A(3,4), B(1,5) C(6,6);
If you multiply these coordinates by 3/2, you get its images:

A(3,4) ⇒ A`(3*3/2, 4*3/2)=(4.5, 6)
B(1,5) ⇒B`(1.*3/2, 5*3/2)=(1.5, 7.5)
C(6,6) ⇒C`(6*3/2, 6*3/2)=(9,9)

Therefore the scale factor is 3/2.
When the scale factor of a dilation is >1, then we have an enlargement, an expansion.
In this case 3/2=1.5>1

Answer:

The dilation is expansion.
The scale factor is 3/2.

7 0

2 years ago

Intellectual development (Perry) scores were determined for 21 students in a first-year, project-based design course. (Recall th

Anit [1.1K]

Answer:

The 99% confidence interval is (3.0493, 3.4907).

We are 99% sure that the true mean of the students Perry score is in the above interval.

Step-by-step explanation:

Our sample size is 21.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 21-1 = 20$ .

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.99}{2} = \frac{0.01}{2} = 0.005$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 20 and 0.005 in the two-sided t-distribution table, we have $T = 2.528$

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{0.40}{\sqrt{21}} = 0.0873$

Now, we multiply T and s

$M = 2.528*0.0873 = 0.2207$

Then

The lower end of the interval is the mean subtracted by M. So:

$L = 3.27 - 0.2207 = 3.0493$

The upper end of the interval is the mean added to M. So:

$LCL = 3.27 + 0.2207 = 3.4907$

The 99% confidence interval is (3.0493, 3.4907).

Interpretation:

We are 99% sure that the true mean of the students Perry score is in the above interval.

7 0

2 years ago

Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?

BlackZzzverrR [31]

Answer:

$\boxed{\sf a = 9 }$

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

$\sf\longrightarrow 3x - 2y +7=0$

$\sf\longrightarrow 6x +ay -18 = 0$

Step 1 : Convert the equations in slope intercept form of the line .

$\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}$

and ,

$\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a}$

Step 2: Find the slope of the lines :-

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

$\sf\longrightarrow Slope_1 = \dfrac{3}{2}$