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3 years ago

A square-shaped painting has an area of 120 square inches. What is the length of each of its sides?

Mathematics

1 answer:

lutik1710 [3]3 years ago

5 0

Answer:

Step-by-step explanation:

120÷4=30 (4 because a square has 4 sides)

and you can check it by doing 4×30=120

hope this helped

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Tickets for the school concert were 3$ and 2$. If 245 tickets were sold for a total of $630, how much of each kind were sold?

Hatshy [7]

2x + 3y = 630
x + y = 245 then you want to get rid of x so in the second equation × by -2 and get -2x -2y =-490 subtract this equation from the first to get y=$140 substitute 140 in for y and get x= $105 and 2x=210 and 3y=420 210 +420=630

7 0

4 years ago

What’s the length of three pipes, when combined they equal 72m, how do I find the answer

allochka39001 [22]

Answer:

Each pipe is 24m

Step-by-step explanation:

Given:

three pipes
combined equal 72m
let the variable x represent the length of 1 pipe

Algebraic Expression:

3 pipes times length equals 72m (the total length)

3x = 72, we want x to be alone so divided both sides by 3

3x / 3 = 72 / 3

x = 24

Learn more about Algebraic Expression here: brainly.com/question/4344214

7 0

2 years ago

Given: EM, EQ-secants Prove: MP·EW=WQ·EP

Dennis_Churaev [7]

Answer:

Step-by-step explanation:

A secant is a straight line from a point outside a given circle that passes through two points on its circumference.

From the given diagram, EM and EQ are secants.

Thus,

<PEW ≅ <WEP (common angles)

<EMP ≅ <EQW (secant-chord theorem)

<WMP ≅ <PQM (inscribed angles of arc WP)

Therefore,

$\frac{EW}{WM}$ = $\frac{EP}{PQ}$ (corresponding sides of a triangle)

This implies that,

EW*PQ = EP*WM

Therefore,

MP*EW = WQ*EP (properties of a similar triangle)

7 0

3 years ago

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare y

DiKsa [7]

The area of the surface is given exactly by the integral,

$\displaystyle\pi\int_0^5\sqrt{1+(y'(x))^2}\,\mathrm dx$

We have

$y(x)=\dfrac15x^5\implies y'(x)=x^4$

so the area is

$\displaystyle\pi\int_0^5\sqrt{1+x^8}\,\mathrm dx$

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the $i$ -th subinterval are, respectively,

$\ell_i=\dfrac{5-0}{10}(i-1)=\dfrac{i-1}2$

$r_i=\dfrac{5-0}{10}i=\dfrac i2$

with midpoint

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

with $1\le i\le10$ .

Over each subinterval, we interpolate $f(x)=\sqrt{1+x^8}$ with the quadratic polynomial,

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

Then

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that the latter integral reduces significantly to

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\frac56\left(f(0)+4f\left(\frac{0+5}2\right)+f(5)\right)=\frac56\left(1+\sqrt{390,626}+\dfrac{\sqrt{390,881}}4\right)$

which is about 651.918, so that the area is approximately $651.918\pi\approx\boxed{2048}$ .

Compare this to actual value of the integral, which is closer to 1967.

4 0

3 years ago

Do all composite numbers have a 2 in the ones place?

marshall27 [118]

Answer:

No!

Step-by-step explanation:

Prime is anything that cannot be divided into but by one and itself, therefore all even numbers are Composite.

8 0

3 years ago