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2 years ago

Dimes and quarters. Total coins = 44 Total value = $9.20 Show work.

Mathematics

1 answer:

lilavasa [31]2 years ago

8 0

D+q=44
.1d+.25q=9.20
10d+25q=920
-10d-10q=-440
15q=480
q=32
44-32=d
d=12
q=32

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Select the situation that describes the following expression.<br>co<br>alယ

Mazyrski [523]

Answer:

what are the things at the end.

Step-by-step explanation:

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2 years ago

Solve each system using elimination. 3x+3y=27 x-3y=-11

Natalija [7]

Answer:

x=4

y=10

Step-by-step explanation:

3x +3y = 27

x - 3y = -11 (add these up so 3y will be eliminated and you'll have x only)

4x = 16

now let's eliminate x (you can put 4 instead of x though)

3x + 3y = 27

-3/ x -3y= -11 (multiple the the 2nd equation with -3 to eliminate x )

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3 years ago

Solve the equation for principal values of x. Express solutions in degrees.

Hitman42 [59]

Option C:

x = 90°

Solution:

Given equation:

$\sin x=1+\cos ^{2} x$

<u>To find the degree:</u>

$\sin x=1+\cos ^{2} x$

Subtract 1 + cos²x from both sides.

$\sin x-1-\cos ^{2} x=0$

Using the trigonometric identity: $\cos ^{2}(x)=1-\sin ^{2}(x)$

$\sin x-1-\left(1-\sin ^{2}x\right)=0$

$\sin x-1-1+\sin ^{2}x=0$

$\sin x-2+\sin ^{2}x=0$

$\sin ^{2}x+\sin x-2=0$

Let sin x = u

$u^2+u-2=0$

Factor the quadratic equation.

$(u+2)(u-1)=0$

u + 2 = 0, u – 1 = 0

u = –2, u = 1

That is sin x = –2, sin x = 1

sin x can't be smaller than –1 for real solutions. So ignore sin x = –2.

sin x = 1

The value of sin is 1 for 90°.

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Option C is the correct answer.

3 0

2 years ago

Read 2 more answers

Write this statement as a conditional statement in the form “if p, then q.”

ss7ja [257]

Answer:

if the measure of an angle is 90°, then the angle is a right angle.

Step-by-step explanation:

p=the measure of an angle is 90°

q=the angle is a right angle

p is the hypothesis of the conditional statement

q is the conclusion of the conditional statement

5 0

2 years ago

What is −13+2z=−56 Thanks

Zinaida [17]

<h3>Original Equation:</h3>

$-\frac{1}{3}+2z=-\frac{5}{6}$

<h3>Steps:</h3>

<em>*To solve for a variable, isolate the desired variable onto one side.</em>

Firstly, we want to add 1/3 to each side however -5/6 and 1/3 do not share the same denominator, and we want them to have that and we can do that by finding the LCD, or lowest common denominator. To find the LCD, list the multiples of 6 and 3 and the lowest multiple that they share is their LCD. In this case, their LCD is 6. Multiply -1/3 by 2/2:

$-\frac{1}{3}\times \frac{2}{2}=-\frac{2}{6}\\\\-\frac{2}{6}+2z=-\frac{5}{6}$

Now that we have common denominators, add both sides by 2/6:

$2z=-\frac{3}{6}\\\\2z=-\frac{1}{2}$

Next, you want to cancel out 2 to isolate z. Usually, one would divide both sides by 2, however remember that <u>dividing by a number is the same as multiplying by it's reciprocal.</u> To find a number's reciprocal, flip the numerator and denominator around. In this case, since 2 is a <em>whole number</em> this means that the denominator is 1. In this case: 2/1 would become 1/2. Multiply both sides by 1/2:

$\frac{1}{2}\times 2z= -\frac{1}{2}\times \frac{1}{2}\\\\z=-\frac{1}{4}$

<h3>Final Answer:</h3>

<u>Your final answer is z = -1/4.</u>

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2 years ago