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madam [21]
3 years ago
10

Rectangle ABCD has m∠BAC=4x+5and m∠ACD=5x−4. Find m∠CAD m∠CAD =

Mathematics
1 answer:
Natalija [7]3 years ago
6 0

Answer:

m∠CAD = 49degrees

Step-by-step explanation:

For a rectangle ABCD if m∠BAC=4x+5and m∠ACD=5x−4, then;

m∠BAC = m∠ACD (alternate angles)

4x+5 = 5x - 4

4x-5x  = -4-5

-x = -9

x = 9

Also

m∠BAC+m∠CAD = 90

4x+5+m∠CAD = 90

4(9)+5+m∠CAD = 90

36+5+m∠CAD = 90

41+m∠CAD = 90

m∠CAD = 90-41

m∠CAD = 49degrees

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Which inequality represents the statement below?
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Answer:

B. X+6.4<9.9

Step-by-step explanation:

The sum of a number is represented by X. So X and 6.4 is X+6.4. Is less than 9.9, so <9.9. You get X+6.4<9.9.

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3 years ago
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Tamika makes a 5.5% commission selling electronics. How much commission does she make if she sells a flat-screen TV for $10,000?
strojnjashka [21]

Answer: She makes $550

Step-by-step explanation:

This is because to find the answer you do 10000t imes 5.5%

And 5.5% is 0.055

So you do 10000 times 0.055

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3 years ago
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F(x)=-9x^2-2x and g(x)=-3x^2+6x-9, find (f-g)(x) and (f-g)(-4)
Alona [7]

Answer:

(f - g)(x)= - 6 {x}^{2} - 8x + 9

(f - g)(-4!)= - 55

Step-by-step explanation:

f(x) =  - 9 {x}^{2}  - 2x,  \:  \: g(x) =  - 3 {x}^{2}  + 6x - 9 \\ (f - g)(x) = f(x)  - g(x) \\  = - 9 {x}^{2}  - 2x - (- 3 {x}^{2}  + 6x - 9) \\  =  - 9 {x}^{2}  - 2x  + 3 {x}^{2}   -  6x  +  9 \\    \purple{ \boxed{ \bold{(f - g)(x)= - 6 {x}^{2}  - 8x + 9}}} \\ (f - g)( - 4)= - 6 {( -4 )}^{2}  - 8( - 4) + 9 \\  =  - 6 \times 16 + 32 + 9 \\  =  - 96 + 41 \\ \red{ \boxed{ \bold{(f - g)( - 4)= - 55}}}

6 0
3 years ago
John took all his money from his savings account. He spent $88 on a radio and 1/4 of what was left on presents for his friends.
gayaneshka [121]

Answer:

$968

Step-by-step explanation:

x= the money John originally had in his savings account

The statement says that John spent $88 on a radio and 1/4 of what was left on presents for his friends. This means that the remaining money is 3/4 of the total amount minus the money spent on the radio:

3/4(x-88)

Then, it says that of the money remaining, John put 4/11 into a checking account and the last remaining $420 was left to charity. Since, he spent 4/11 of the remining 3/4(x-88), the remaining is 7/11 of that and that remaining is equal to $420 that was the money left at the end:

7/11(3/4(x-88))= 420

21/44(x-88)=420

21/44x-42=420

21/44x=462

x=968

According to this, the money that John originally had in his savings account was $968.

He spent $88 on a radio: 968-88= 880

1/4 of what was left on presents for his friends: 880/4= 220

880-220=660

Of the money remaining, John put 4/11 into a checking account: 660*(4/11)=240

the last remaining $420 was left to charity: 660-240= 420

6 0
3 years ago
A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. Wha
enot [183]

Answer:

the correct option is E. d is biased.

Step-by-step explanation:

As given,

The expected value of d hat is not equal to D.

We know that,

The unbiased-ness is the property that tells the expected value of d is equal to D

So, the correct option is E. d is biased.

5 0
3 years ago
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