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2 years ago

Please help! Thank you.

Mathematics

1 answer:

I am Lyosha [343]2 years ago

5 0

Answer:

Step-by-step explanation:

x((7/2)-(7/3))=y+x

x(7/6)=y+x

7x=6y+6x, x=6y. y/x=1/6

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Emily's piggy bank contains twice as many dimes as nickels. It contains two more quarters than nickels. Emily calculates that if

ANTONII [103]

Answer:

Emily has 10 nickels, 20 dimes and 12 quarters in her piggy bank

Step-by-step explanation:

The number of dimes in Emily's piggy bank = 2 × The number of nickels

The number of quarters in it = 2 + The number of nickels

Whereby;

The number of quarters = The number nickels

The number of dimes = The number of quarters

The number of nickels = The number of dimes

The total amount = Current amount - $150

Let 'x' represent the number of dimes, let 'y' represent the number nickels, and let 'z' represent the number quarters in Emily's piggy bank, we have;

x = 2 × y

z = 2 + y

The total amount in the piggy bank is therefore;

Total = C = x×0.1 + y×0.05 + z×0.25 = 2·y×0.1 + y × 0.05 + (2 + y) × 0.25 = 0.5·y + 0.5

C = 0.5·y + 0.5

With the second condition, we have;

z = y

x = z

y = x

We get

x × 0.1 + y × 0.05 + z × 0.25 = y ×0.1 + y×0.05 + y×0.25 = 0.4·y = C - 1.5

∴ C = 0.4·y + 1.5

Which gives;

0.5·y + 0.5 = 0.4·y + 1.5

0.1·y = 1.5 - 0.5 = 1

y = 1/0.1 = 10

y = 10

Therefore;

x = 2×y = 2 × 10 = 20

z = 2 + y = 2 + 10 = 12

Therefore;

The number number of nickels in her piggy bank, y = 10

The number of dimes in her piggy bank, x = 20

The number of quarters in her piggy bank, z = 12

3 0

2 years ago

Read 2 more answers

Which parabola will have a minimum value vertex?

emmasim [6.3K]

Answer:

What functions?

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please

Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

$S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx$

We let the substitution take place.

Therefore, we let $u = 1 + 4x^{2}$

Thus, $du = 8dx.$

So,

$xdx = \frac{1}{8}du$

Also, the interval of the integration changes to [ 37, 65]

Thus,

$S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx$

= $\frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} } }$

= 156.5 units²

8 0

3 years ago

∠K and ∠L are complementary angles. If m∠K = 3x + 3 and m∠L = 10x – 4, find the measures of both angles.

Oduvanchick [21]

Answer:

∠K =24

∠L =66

Step-by-step explanation:

first you need to find X in order to solve.

since they are Complementary they add together to equal 90 degrees

so we can set them equal to 90

13x-1=90

13x=91

x=7

now we can plug them in!

---

∠K = 3(7)+3 = 24

∠L =10(7)-4=66

4 0

3 years ago

Allison invested $70,000 in an account paying an interest rate of 6.2%

jeka94

Answer and Step-by-step explanation:

First, you need to make the function to represent the information given.

We start with 70,000 in the account, and have an interest rate of 6.2%.

We want to know how long it will take to get $223,200.

The equation for simple interest is:

A = $P(1 + rt)$

Where A is the total amount, P is the principle amount of money, r is the rate, and t is the time.

Now, we plug in the values and solve for t.

$223,200 = 70,000(1+6.2t)$

$\frac{\frac{223,200}{70,000} -1}{6.2} = t$

t = 0.353

Multiply by 100 to get the years.

t = 35.3

So, it will take Allison 35.3 years to get 70,000 dollars to 223,200 dollar with an interest rate of 6.2%

#teamtrees #PAW (Plant And Water)

I hope this helps!

5 0

2 years ago

Read 2 more answers