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2 years ago

A problem in a test given to small children asks them to match each of three pictures

Mathematics

1 answer:

Lelechka [254]2 years ago

5 0

Answer:

Step-by-step explanation:

because there are only three pictures

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(06.04 MC)

Andru [333]

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

◉ $\large\bm{ -4}$

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

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

WILL GIVE BRAINLIEST need help asap

olganol [36]

Answer:

(-13, -10)

Step-by-step explanation:

Your original point is (-17, -13) The instruct tell you to move the point 4 units to the right and down 7 units.

-17 + 4 = -13

-3 - 7 = -10

8 0

1 year ago

Read 2 more answers

Factor completely 81x4 − 16.

STALIN [3.7K]

$(9x^{2} +4)(3x+2)(3x-2)$

Option C

Step-by-step explanation:

Given,

$81x^{4} -16$

To find the factors.

Formula:

$a^{2} -b^{2}= (a+b)(a-b)$

Now,

$81x^{4} -16$

= $(9x^{2} )^{2}-4^{2}$

= $(9x^{2}+4)(9x^{2}-4)$

= $(9x^{2}+4) ((3x)^{2} -2^{2} )$

= $(9x^{2} +4)(3x+2)(3x-2)$

8 0

3 years ago

Read 2 more answers

On a roulette wheel, half of the slots numbered 1 through 36 are red and half are black. Two slots numbered 0 and 00, are green.

Mrac [35]

Answer:

Two slots, numbered 0 and 00, are green.

What are the odds against a red slot's coming up on any spin of the wheel?

Step-by-step explanation:

3 0

3 years ago

What is the ratio of 4/9 and 5/9 in simplest form

a_sh-v [17]

$\dfrac{4}{9}:\dfrac{5}{9}=\dfrac{4}{9}\cdot\dfrac{9}{5}=\dfrac{4}{5}$

3 0

3 years ago