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3 years ago

14

Jasmine has a bag of 48 peanuts. She eats 3/4 of the bag during the baseball game. How many peanuts does she have left? Explain

and show how you got the answer.

1 answer:

rosijanka [135]3 years ago

7 0

Answer:

12

Step-by-step explanation:

If she eats 3/4 of the bag, that means she has 1-3/4 = 4/4 -3/4 = 1/4 of the bag left

The bag has 48 nuts. Take the number of nuts times the 1/4 she has left

48 * 1/4 = 12

She has 12 nuts left

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A group of students are planning a mural at a wall the rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning

zvonat [6]

Answer: $46x^2+73x+15$

Step-by-step explanation:

The area of a rectangle can be calculated with the formula:

$A=lw$

l: the length of the rectangle.

w: the width of the rectangle.

The area of the remaning wall after the mural has been painted, will be the difference of the area of the wall and the area of the mural.

Knowing that the dimensions of the wall are $(6x+7)$ by $(8x+5)$ , its area is:

$A_w=(6x+7)(8x+5)\\\\A_w=48x^2+30x+56x+35\\\\A_w=48x^2+86x+35$

As they are planning that the dimensions of the mural be $(x+4)$ by $(2x+5)$ , its area is:

$A_m=(x+4)(2x+5)\\\\A_m=2x^2+5x+8x+20\\\\A_m=2x^2+13x+20$

Then the area of the remaining wall after the mural has been painted is:

$A_{(remaining)}=A_w-A_m\\\\A_{(remaining)}=48x^2+86x+35-(2x^2+13x+20)\\\\A_{(remaining)}=48x^2+86x+35-2x^2-13x-20\\\\A_{(remaining)}=46x^2+73x+15$

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3 years ago

Which word could describe the relationship of the lines containing the points (1, 6) and (1, 3)?

Elan Coil [88]

Answer:

Coincidental

Step-by-step explanation:

<em>If the two lines have the same two points, they must also have the same slope </em><em>and</em><em> the same y intercept. From this we can deduct that they are actually the same line. Two lines that are directly on top of each other are considered coincidental lines.</em>

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3 years ago

If a^ 1/n = n What is an equivalent form of 7? Show steps plz!

Scrat [10]

Answer:

7⁷

Step-by-step explanation:

a^(1/7) = 7

a = 7⁷

6 0

3 years ago

At what rate per annum ci will RS 2000 amount to RS 2315.35 in 3 years

Mashutka [201]

<u>ANSWER: </u>

Rate per annum at which CI will amount from RS 2000 to RS 2315.35 in 3 years is 5%

<u>SOLUTION: </u>

Given,

P = RS 2000

C.I = RS 2315.35

T = 3 years

We need to find the rate per annum. i.e. R = ?

We know that,

When interest is compound Annually:

$Amount $=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{n}$$

Where p = principal amount

r = rate of interest

n = number of years

$2315.35=2000 \times\left(1+\frac{R}{100}\right)^{3}$

$\left(1+\frac{R}{100}\right)^{3}=\frac{2315.35}{2000}$

$\left(1+\frac{R}{100}\right)^{3}=1.157$

$1+\frac{R}{100}=\sqrt[3]{1.157}$

$1+\frac{R}{100}=1.0500$

$\frac{R}{100}=1.05-1$

$\frac{R}{100}=0.05$

R = 5%

Hence, rate per annum is 5 percent.

3 0

3 years ago

Integrate x+1/sqrt(x). I know that the answer is 2/3 • sqrt(x) • (x+3) + C, but I don't know how it is simplified from 2/3 • x^3

Andreas93 [3]

$\displaystyle\int\frac{x+1}{\sqrt x}\,\mathrm dx=\int\frac x{x^{1/2}}+\frac1{x^{1/2}}\,\mathrm dx$

$=\displaystyle\int x^{1/2}+x^{-1/2}\,\mathrm dx$

By the power rule,

$=\dfrac{x^{3/2}}{\frac32}+\dfrac{x^{1/2}}{\frac12}+C$

(this seems to be the step you're not getting?)

$=\dfrac23x^{3/2}+2x^{1/2}+C$

The next step is to pull out a common factor of $x^{1/2}$ from the antiderivative:

$x^{3/2}=x^{1/2+1}=x^{1/2}\cdot x^1$

so that the final result is

$\dfrac23x^{3/2}+2x^{1/2}+C=\dfrac23x^{1/2}(x+3)+C$

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3 years ago