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3 years ago

Which choice describes the translation represented by the translation rule (x,y) -->(x+4, y-1)?

Mathematics

1 answer:

Brrunno [24]3 years ago

7 0

$x+4\to4\ units\ to\ the\ left\\\\y-1\to1\ unit\ down$

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The ratio of tulips to roses is 17/11. If there are 3444 tulips and roses in the garden, how many are tulips?

irga5000 [103]

You can also approach it this way:

28 flowers times n = 3444

so n = 123

11 x 123 = roses, 17 x 123 = tulips.

Those 2 products should add up to 3444. They do. :-)

gotchaaaaaa

ahhh

thanxxx

5 0

2 years ago

What are two numbers that add to make 36 with one of the numbers be exactly twice the other

Tema [17]

To solve, set an equation:
First Number: x
Second Number: 2x

x+2x=36
3x=36
divide both sides by 3
x=13

First Number: (x) 12
Second Number: (2x) 24

Answers: 12 and 24

3 0

3 years ago

Read 2 more answers

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

What is 1.28 as a fraction. Simplify

attashe74 [19]

128/100=32/25
..................

8 0

3 years ago

Read 2 more answers

Step by step workout of ;<br> log x^3+log 5x=5 log 2-log 2/5

Charra [1.4K]

Answer:

x = 2

Step-by-step explanation:

$log \: {x}^{3} + log \: 5x = 5log \: 2 - log \: \frac{2}{5} \\ \\ \therefore \: log( {x}^{3} \times 5x) = log {2}^{5} - log \: \frac{2}{5} \\ \\ \therefore \: log( 5{x}^{4}) = log 32 - log \: \frac{2}{5} \\ \\ \therefore \: log( 5{x}^{4}) = log \bigg(32 \times \frac{5}{2} \bigg) \\ \\ \therefore \: log( 5{x}^{4}) = log \bigg(16 \times 5) \\ \\ \therefore \: 5{x}^{4}= 16 \times 5 \\ \\ \therefore \: {x}^{4}= {2}^{4} \\ \\ \huge \purple{ \boxed{\therefore \: {x} = 2}}$

4 0

2 years ago