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3 years ago

A piano, which normally sells for $800, is marked

Mathematics

1 answer:

belka [17]3 years ago

8 0

Answer

700 is 87.5% of 800

Step-by-step explanation:

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12 points

Charra [1.4K]

Parallel = same slope
Y = 5x + b
8 = 5(5) + b
8 = 25 + b
b = -17
Equation: y = 5x - 17

5 0

3 years ago

I NEED HELP ASAP!<br> What is the scale factor?

Mama L [17]

Answer:

x=10 and scale factor is 15/9 or 1 2/3

Step-by-step explanation:

FIrst, find scale factor. 9 to 15. Times by 15/9 or 1 2/3.

Find x. 6*1 2/3 = 10

6 0

3 years ago

Read 2 more answers

(06.04 MC)

Andru [333]

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◉ $\large\bm{ -4}$

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Before performing any calculation it's good to recall a few properties of integrals:

$\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}$

$\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }$

So we apply the first property in the first expression given by the question:

$\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}$

And we solve the second integral:

$\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }$

Then we take the last equation and we subtract 10 from both sides:

$\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}$

And we divide both sides by 2:

$\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }$

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}$

Then we apply the second property to this integral:

$\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}$

Then we use the other equality in the question and we get:

$\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}$

$\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}$

We substract 8 from both sides:

$\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}$

• $\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}$

7 0

2 years ago

Theodore invests a total of $17,500 in two accounts paying 2% and 12% annual interest, respectively. How much was invested in ea

iVinArrow [24]

Answer:

11,500 at 2% and $6,000 at 12%.

Step-by-step explanation:

Let x represent amount invested at 2% and y represent amount invested at 12%.

We have been given that Theodore invests a total of $17,500 in two accounts. We can represent this information in an equation as:

$x+y=17500...(1)$

$x=17500-y...(1)$

We are also told that he invested $17,500 in two accounts paying 2% and 12% annual interest, respectively. After one year, the total interest was $950.00.

Interest earned at 2% in one year would be $0.02x$ .

Interest earned at 12% in one year would be $0.12y$

$0.02x+0.12y=950...(1)$

Upon substituting equation (1) in equation (2), we will get:

$0.02(17500-y)+0.12y=950$

$350-0.02y+0.12y=950$

$350+0.10y=950$

$350-350+0.10y=950-350$

$0.10y=600$

$\frac{0.10y}{0.10}=\frac{600}{0.10}$

$y=6000$

Therefore, Theodore invested $6,000 at 12%.

Upon substituting $y=6000$ in equation (1), we will get:

$x=17500-6000$

$x=11500$

Therefore, Theodore invested $11,500 at 2%.

5 0

3 years ago

What type of object is generated when you rotate a 2-dimensional object about an axis?

dalvyx [7]

A three-dimensional object

6 0

3 years ago