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Romashka-Z-Leto [24]

3 years ago

12

Which expressions are equivalent to x+x+x+2 Choose 2 answers: Choose 2 answers: (Choice A) A 3x + 23x+23, (Choice B) B 3 + 2x3+2

x3, (Choice C) C 3(x+2)3(x+2)3, (Choice D) D 2(x+1)+x2(x+1)+x2 (Choice E) E 5x5x

1 answer:

OlgaM077 [116]3 years ago

3 0

Answer:

A and D

Step-by-step explanation:

3x + 2 = x + x + x + 2

2(x+1)+x = 2x + 2 + x = 3x+2

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A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shif

omeli [17]

We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is $\frac{7\pi}{12}$ . The graph of the function does not show a phase shift. We are asked to write the equation of our function.

We know that general form a cosine function is $y=A\cos(b(x-c))-d$ , where,

A = Amplitude,

$\frac{2\pi}{b}$ = Period,

c = Horizontal shift,

d = Vertical shift.

The equation of parent cosine function is $y=\cos(x)$ . Since function is reflected about x-axis, so our function will be $y=-\cos(x)$ .

Let us find the value of b.

$\frac{2\pi}{b}=\frac{7\pi}{12}$

$7\pi\cdot b=24\pi$

$\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}$

$b=\frac{24}{7}$

Upon substituting our given values in general cosine function, we will get:

$f(x)=-11\cos(\frac{24}{7}x)-9$

Therefore, our required function would be $f(x)=-11\cos(\frac{24}{7}x)-9$ .

7 0

2 years ago

How are the 4s related in 44,268

Ahat [919]

Well they are close to eachother and are both have a thousand. Such as the 1st 4 is 10 thousand but the 2nd 4 us in the thousands.

6 0

3 years ago

kari74 [83]

Answer:

The area of the triangular section is 12 square units. The area of the entire figure is 60 square units.

Step-by-step explanation:

4 0

2 years ago

The temperature, H, in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation. H = 70 + 1

Alex73 [517]

Answer:

The temperature a t = 0 is 190 °F

The temperature a t = 1 is 100 °F

The temperature a t = 2 is 77.5 °F

It takes 1.5 hours to take the coffee to cool down to 85°F

It takes 2.293 hours to take the coffee to cool down to 75°F

Step-by-step explanation:

We know that the temperature in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation:

$H(t)=70+120(\frac{1}{4})^t$

a) To find the temperature a t = 0 you need to replace the time in the equation:

$H(0)=70+120(\frac{1}{4})^0\\H(0)=70+120\cdot 1\\H(0) = 70+120\\H(0)=190 \:\°F$

b) To find the temperature after 1 hour you need to:

$H(1)=70+120(\frac{1}{4})^1\\H(1)=70+120(\frac{1}{4})\\H(1) = 70+30\\H(1)=100 \:\°F$

c) To find the temperature after 2 hours you need to:

$H(2)=70+120(\frac{1}{4})^2\\H(2)=70+120(\frac{1}{16})\\H(2) = 70+\frac{15}{2} \\H(2)=77.5 \:\°F$

d) To find the time to take the coffee to cool down $85 \:\°F$ , you need to:

$85 = 70+120(\frac{1}{4})^t\\70+120\left(\frac{1}{4}\right)^t=85\\70+120\left(\frac{1}{4}\right)^t-70=85-70\\120\left(\frac{1}{4}\right)^t=15\\\frac{120\left(\frac{1}{4}\right)^t}{120}=\frac{15}{120}\\\left(\frac{1}{4}\right)^t=\frac{1}{8}$

$\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)$

$\ln \left(\left(\frac{1}{4}\right)^t\right)=\ln \left(\frac{1}{8}\right)$

$\mathrm{Apply\:log\:rule}=\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$t\ln \left(\frac{1}{4}\right)=\ln \left(\frac{1}{8}\right)$

$t=\frac{\ln \left(\frac{1}{8}\right)}{\ln \left(\frac{1}{4}\right)}\\t=\frac{3}{2} = 1.5 \:hours$

e) To find the time to take the coffee to cool down $75 \:\°F$ , you need to:

$75=70+120\left(\frac{1}{4}\right)^t\\70+120\left(\frac{1}{4}\right)^t=75\\70+120\left(\frac{1}{4}\right)^t-70=75-70\\120\left(\frac{1}{4}\right)^t=5\\\left(\frac{1}{4}\right)^t=\frac{1}{24}$

$\ln \left(\left(\frac{1}{4}\right)^t\right)=\ln \left(\frac{1}{24}\right)\\t\ln \left(\frac{1}{4}\right)=\ln \left(\frac{1}{24}\right)\\t=\frac{\ln \left(24\right)}{2\ln \left(2\right)} \approx = 2.293 \:hours$

3 0

3 years ago

the average adult horse needs 2/5 bale of hay each day to meet dietary requirements. A horse farm has 44 bales of hay?

Serhud [2]

How many 2/5's fit into 44
2/5 times x=44
multiply both sides by 5/2 to clea fraciton (5/2 times 2/5=10/10=1)
x=220/2
x=110
will support for 110 days

6 0

2 years ago