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I am Lyosha [343]

3 years ago

12

a circular garden has an area of 64

ign="absmiddle" class="latex-formula"> square yards. What is the circumference of the garden? Give your answer in terms of $\pi$

2 answers:

SpyIntel [72]3 years ago

7 0

4.51 is the correct answer

timama [110]3 years ago

6 0

I hope this helps you

Area =pi.r^2

64.pi=pi.r^2

r=8

Circumference =2pir

Circumference =2.pi.8

Circumference =16.pi

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Vilka [71]

Answer: B

Step-by-step explanation: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.

The final answer is B.

4 0

3 years ago

Read 2 more answers

Consider the quadratic function f(x) = -x^2 + 1x + 12. Determine the following: (enter all numerical answers as integers, fracti

vovikov84 [41]

Answer and Explanation:

Given : The quadratic function $f(x)=-x^2+x+12$

To find : Determine the following ?

Solution :

The x -intercept are where f(x)=0,

So, $-x^2+x+12=0$

Applying middle term split,

$-x^2+4x-3x+12=0$

$-x(x-4)-3(x-4)=0$

$(x-4)(-x-3)=0$

$x=4,-3$

The x-intercepts are (4,0) and (-3,0).

The smallest x-intercept is x=-3

The largest x-intercept is x=4

The y -intercept are where x=0,

So, $f(0)=-(0)^2+0+12$

$f(0)=12$

The y-intercept is y=12.

The quadratic function is in the form, $y=ax^2+bx+c$

On comparing, a=-1 , b=1 and c=1 2

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

$h=-\frac{b}{2a}$

$h=-\frac{1}{2(-1)}$

$h=\frac{1}{2}$

For k, The y-coordinate of the vertex is given by,

$k=f(h)$

$k=-h^2+h+12$

$k=-(\frac{1}{2})^2+\frac{1}{2}+12$

$k=-\frac{1}{4}+\frac{1}{2}+12$

$k=\frac{-1+2+48}{4}$

$k=\frac{49}{4}$

The vertex of the function is $(h,k)=(\frac{1}{2},\frac{49}{4})$

The x-coordinate of the vertex i.e. $x=-\frac{b}{2a}$ is the axis of symmetry,

So, $x=-\frac{b}{2a}=\frac{1}{2}$ (solved above)

The axis of symmetry is $x=\frac{1}{2}$ .

4 0

4 years ago

A case of grapefruit weighs 35 3/4 pounds. of this weight, 1/8 is not ripe. What is the weight of the grapefruit that are ripe?

Irina18 [472]

Turn those 2 fractions into a improper fraction and do keep change flip and then turn it back into a mixed number

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3 years ago

Assume each figure shown has the same orientation. Which figure is the image of square LMNP after a translation of

umka21 [38]

Figure 4 is the image of the square LMNP after the translation.

<u>Step-by-step explanation:</u>

Let us see the coordinates of the pre image LMNP as,

L (-3,1)

M(-1,1)

N(-1,-1)

P(-3,-1)

after translation of (x,y) → (x+5, y -3) the coordinates of the image obtained as,

L'(2,-2)

M'(4,-2)

N'(4,-4)

P'(2,-4) which matches the image 4.

8 0

4 years ago

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(4^7/5^2)^3 i Don't get it

jenyasd209 [6]

Answer:

$\sf \dfrac{4^{21}}{5^6}$

Step-by-step explanation:

Exponent Law:

$\sf \boxed{\left(\dfrac{a^m}{b^n}\right)^{x}=\dfrac{a^{m*x}}{b^{n*x}}}$

When any base is being multiplied by an exponent, distribute the exponent to each part of the base.

$\sf \left(\dfrac{4^7}{5^2}\right)^{3}=\dfrac{4^{7*3}}{5^{2*3}}$

$\sf =\dfrac{4^{21}}{5^6}$

7 0

1 year ago