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3 years ago

The measure of ∠A is 12° greater than the measure of ∠B. The two angles are complementary. Find the measure of each angle.

Mathematics

2 answers:

denis-greek [22]3 years ago

6 0

Answer:

m<A = 51, m<B = 39

Step-by-step explanation:

x+x+12=90

2x+12=90

2x=78

x=39

m<A = 51, m<B = 39

Vikentia [17]3 years ago

3 0

Answer:

39° = m∠A

51° = m∠B

Step-by-step explanation:

Complementary angles have a sum of their measures = 90

Let x = m∠B

then x + 12 = ∠A

m∠A + m∠B = 90

x + 12 + x = 90

2x + 12 = 90

2x = 78

x = 39° = m∠A

x + 12 = 39 + 12 = 51° = m∠B

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Find the distance between the lines Y=3x+10 Y=3x-20 AND Y=3/2x+3/2 Y=3/2x-5

rosijanka [135]

At first we need to know how to find the distance between two parallel lines
The parallel lines which have the same slope
If we have two parallel lines ⇒ y₁ = mx + c₁ and y₂ = mx + c₂
So, the distance between y₁ and y₂ = d = $\frac{|c_{1} - c_{2}|}{\sqrt{1 + m^{2}}}$
========================================================

Part (1):
=======

The distance between the lines

 Y₁ = 3x + 10 and Y₂ = 3x - 20
∴ m = 3 , c₁ = 10 and c₂ = -20
∴ d = $\frac{| 10 - (-20)|}{\sqrt{1 + 3^{2}}}= \framebox{9.5}$

========================================================

Part (2):
=======

The distance between the lines

Y₁ = 3/2 x + 3/2 and Y₂ = 3/2 x - 5
∴ m = 3/2 = 1.5 , c₁ = 3/2 = 1.5 and c₂ = -5
∴ d = $\frac{| 1.5- (-5)|}{\sqrt{1 + 1.5^{2}}}= \framebox{3.6}$

6 0

3 years ago

The scatter plot and table show the number of grapes and blueberries in 10 fruit baskets.

balu736 [363]

c is the correct answer i believe

4 0

3 years ago

In a survey of 1000 eligible voters selected at random, it was found that 100 had a college degree. Additionally, it was found t

o-na [289]

Answer:

A. 8%

B. 39.6%

C. 58.4%

D. 41.6%

Step-by-step explanation:

Computation to determine the probability of eligible voter selected at random

First step is to Draw up a contingincy table which will include Rows = Degree/No degree

and Columns= Vote/Not vote

..............Vote..No vote

Degree 80...20...100

(80%*100=80)

(100-80=20)

No Degree 504..396..900

(1000-100=900)

(56%*900=504)

(504-900=396

Totals 584..416...1000

(80+504=584)

(20+396=416)

(900+100=1,000)

Summary

..............Vote..No vote

Degree 80...20...100

No Degree 504..396..900

Total Totals 584..416...1000

A. Calculation to determine the probability of The voter had a college degree and voted in the last presidential election.

P = 80/1,000

P=0.08*100

P=8%

Therefore the probability of The voter had a college degree and voted in the last presidential election will be 8%

B. Calculation to determine the probability of The voter did not have a college degree and did not vote in the last presidential election.

P =396/1000

P=0.396*100

P=39.6%

Therefore the probability of The voter did not have a college degree and did not vote in the last presidential election will be 39.6%

C. Calculation to determine the probability if The voter voted in the last presidential election.

P = 584/1,000

P=0.584*100

P=58.4%

Therefore the probability if The voter voted in the last presidential election will be 58.4%

D. Calculation to determine the probability if The voter did not vote in the last presidential election.

P = 416/1000

P=0.416*100

P=41.6%

Therefore the probability if The voter did not vote in the last presidential election will be 41.6%

8 0

2 years ago

Lucy used 3 gal of paint to cover 900 ft. She needs to cover a total of 1,100 ft?.

insens350 [35]

Step-by-step explanation:

3 gal = 900 ft

... gal = 1100 ft

So, each gal is used for cover 300 ft,

Then,

$\sf \frac{1100}{900} \times 3 = \frac{11}{3} = \boxed{ \bold{ \red{3 \frac{2}{3} \: gal}}}$

We need 3 2/3 gal to cover 1100 ft.

Hope it helps!

7 0

2 years ago

1 question need help thank you!!

inn [45]

The correct answer is: [D]: " x² – 5x – 24 " .
____________________________________________________
Explanation:
_____________________________________
Given: " (x + 3)(x – 8) " ; expand :
______________________________________
Note: (a + b) (c + d) = ac + ad + bc + bd .
_____________________________________
a = x ;

b = 3 ;

c = x

d = 8
_______________________________________

" (x + 3)(x – 8) " ;

= (x * x) + ( -8 * x) + ( 3 * x ) + (3 * -8) ;

= x² + (-8x) + 3x + (-24) ;

= x² – 8x + 3x – 24 ;

→ Combine the "like terms" :

– 8x + 3x = – 5x ;

And simplify the expression;

to get:

→ " x² – 5x – 24 " ; which is: Answer choice: [D]: " x² – 5x – 24 " .
________________________________________________________

7 0

3 years ago