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3 years ago

Maria has $1.25 in nickels and dimes. She has a total of 16 coins. How many of each coin does he have?

1 answer:

7 0

Q=quarters, d=dimes

q+d=8
.25q+.1d=1.25

Let's set the first equation to equal d.

d=8-q

.25q+.1(8-q)=1.25

Distribute.

.25q+.8-.1q=1.25

Combine Like Terms

.15q+.8=1.25

Subtract .8

.15q=.45

Divide by .15

q=3

Now, let's solve for d in the first equation.

d+3=8

Subtract 3, and you get d=5

So, there are 5 dimes and 3 quarters in Maribel's pocket.

Check: .25(3)+.1(5)=1.25

.75+.5=1.25
1.25=1.25 which is true.

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3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

100 POINTS! I WILL GIVE BRAINLIEST! SHOW ALL WORK PLEASE!

pishuonlain [190]

Answer:

1. 2(3x−2)(2x−3)

2. 3(3x+1)(2x+5)

3. 2(4x+1)(2x−5)

4. 4(2x+1)(2x+7)

5. 5(3x+1)(2x−5)

6. 3(3x−7)(2x+1)

7. 3(5x+3)(3x−2)

8. 2(7x−2)(2x−5)

9. 2(7x−3)(2x−3)

10. 4(5x−11)(2x+1)

11. 5(x−2)(x+12)

12. (x−1)(x−8)

15. x=1 or x=4

Step-by-step explanation:

1. Factor 12x2−26x+12

12x2−26x+12

=2(3x−2)(2x−3)

2. 3(3x+1)(2x+5)

3. Factor 16x2−36x−10

16x2−36x−10

=2(4x+1)(2x−5)

4. Factor 16x2+64x+28

16x2+64x+28

=4(2x+1)(2x+7)

5. Factor 30x2−65x−25

30x2−65x−25

=5(3x+1)(2x−5)

6. Factor 18x2−33x−21

18x2−33x−21

=3(3x−7)(2x+1)

7. Factor 45x2−3x−18

45x2−3x−18

=3(5x+3)(3x−2)

8. Factor 28x2−78x+20

28x2−78x+20

=2(7x−2)(2x−5)

9. Factor 28x2−54x+18

28x2−54x+18

=2(7x−3)(2x−3)

10. Factor 40x2−68x−44

40x2−68x−44

=4(5x−11)(2x+1)

11. Factor 5x2+50x−120

5x2+50x−120

=5(x−2)(x+12)

12. Let's factor x2−9x+8

x2−9x+8

The middle number is -9 and the last number is 8.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -9

Multiply together to get 8

Can you think of the two numbers?

Try -1 and -8:

-1+-8 = -9

-1*-8 = 8

Fill in the blanks in

(x+_)(x+_)

with -1 and -8 to get...

(x-1)(x-8)

15. Let's solve your equation step-by-step.

(x−2)(x−3)=2

Step 1: Simplify both sides of the equation.

x2−5x+6=2

Step 2: Subtract 2 from both sides.

x2−5x+6−2=2−2

x2−5x+4=0

Step 3: Factor left side of equation.

(x−1)(x−4)=0

Step 4: Set factors equal to 0.

x−1=0 or x−4=0

x=1 or x=4

Sorry I wasn't able to do 13 and 14 but hope this helps! :)

8 0

3 years ago

How much would it be $55 for every 15 shirts?

notsponge [240]

Answer:

<h3>$825 it would be that</h3>

Step-by-step explanation:

<h3>it would be that all you have to do is multiple 55×15=825</h3><h3>5×5</h3><h3> $55 \times 15 = 825$ </h3>

8 0

3 years ago