The equations y= x^2/2 - 8 and y=2x−2 are graphed below. What are the solutions to the equation x^2/2−8=2x−2

graph is attached


Please choose one answer below
x=−6 and x=10
x=−4 and x=4
x=−2 and x=6
x=−8 and x=−2

First, to get applied by the fraction rule: [tex]\displaystyle\frac{3^4}{1}[/tex], then, the applied rule [tex]\displaystyle\frac{a}{1}=a[/tex]. Finally, simplify to find the answer. [tex]\displaystyle3^4=3*3*3*3=81[/tex], the correct answer is 81. I hope this will help you. Have a wonderful day!

[tex]\left(\dfrac{1}{3}\right)^{-4}=3^4=81[/tex]

Answer:

4.44 hours

Step-by-step explanation:

One pump can fill a swimming pool in 8 hours.

In 1 hour pump can fill the pool = [tex]\frac{1}{8}[/tex]

another pump can fill the swimming pool in 10 hours.

in 1 hour another pump can fill the pool = [tex]\frac{1}{10}[/tex]

Let the total time will it take together to fill the pool = x

[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{x}[/tex]

[tex]\frac{5+4}{40}[/tex] = [tex]\frac{1}{x}[/tex]

[tex]\frac{9}{40}[/tex] = [tex]\frac{1}{x}[/tex]

9x = 40

x = [tex]\frac{40}{9}[/tex]

x = 4.44 hours

It will take 4.44 hours to fill the pool if both pumps are open.

Answer:

15 scarfs.

Step-by-step explanation:

The cost of 10 scarfs in Store A = 12 * 10 = $120.

The number of scarfs  that can be bought in Store A for $120

= 120 / 8 = 15.

15 scarfs

The cost of 10 scarfs in Store

A = 12 * 10 = $120

The number of scarfs  that can be bought in Store A for $120

= 120 / 8 = 15.

How to determine a price for your product?

To do so, you’ve got to be clear on:

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Answer:

its D

Step-by-step explanation:

Answer:

D, The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

[tex]\frac{\pi }{4}[/tex]

Step-by-step explanation:

To convert from degrees to radians

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

given degree measure = 45°, then

radian = 45 × [tex]\frac{\pi }{180}[/tex] ( divide 45 and 180 by 45 )

           = [tex]\frac{\pi }{4}[/tex]

Answer:

π/4 radians.

Step-by-step explanation:

To convert to radians we multiply degrees by π/180.

So 45 degrees = 45 * π / 180

= π/4 radians.

Answer:

In the given   Δ ABC

the height will be CD

sin (A) = [tex]\dfrac{P}{H}[/tex]

sin (A) = [tex]\dfrac{CD}{b}[/tex]................(1)

now to find area of the ΔABC

area of the ΔABC  = [tex]\dfrac{1}{2}\times Base \times Height[/tex]

                                =[tex]\dfrac{1}{2}\times c \times CD[/tex]

from equation (1) we can substitute of the value of CD.

                               =[tex]\dfrac{1}{2}\times c \times b sin(A)[/tex]  

The base of ΔABC is c then the height is CD and the area of triangle is given by:   [tex]\rm \dfrac{1}{2}\times c \times b\times sin(A)[/tex]

Given :

AC = b

BC = a

c is the base of triangle ABC.

Solution :

In the given triangle ABC

[tex]\rm sin(A) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

the height will be CD,

[tex]\rm sin (A) = \dfrac{CD}{b}[/tex]   ----- (1)

Area of the triangle ABC

[tex]\rm = \dfrac{1}{2}\times base\times height[/tex]

[tex]\rm =\dfrac{1}{2}\times c \times CD[/tex]   --- (2)

Now from equation (1) and (2) we get

[tex]\rm Area\;of\;\Delta ABC = \dfrac{1}{2}\times c \times b\times sin(A)[/tex]

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Answer with step-by-step explanation:

We are to write nine proper fractions (where the numerator is smaller than the denominator) and nine improper fractions (where the denominator is bigger than the numerator) using the number 3, 5 and 8.

Proper fractions:

[tex] \frac { 3 } { 5 },\frac { 3 } { 8 } \frac { 5 } { 8 }, \frac { 3 }{ 5 . 8 },\frac{5}{3.8}, \frac{8}{5.3},\frac{3}{5+8},\frac{5}{3+8}, \frac{5-3}{8} \imples\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{40},\frac{5}{24}, \frac{8}{15},\frac{3}{13},\frac{5}{11}, \frac{1}{4}[/tex]

Improper fractions:

[tex]\frac{5}{3},\frac{8}{3} \frac{8}{5},\frac{40}{3},\frac{24}{5}, \frac{15}{8},\frac{13}{3},\frac{11}{5}, \frac{19}{3}[/tex]

Answer: Yes, you can write nine Proper Fractions and nine Improper Fractions  using the numbers 3,5,and 8.

Step-by-step explanation:

You need to remember that a fraction is Proper when the numerator is less than the denominator and it is Improper fraction when the numerator is greater than the denominator.

Knowing this, you can write the following nine Proper Fractions and nine Improper Fractions, using the numbers 3,5 and 8:

Proper Fractions:

[tex]\frac{3}{5},\frac{3}{8},\frac{3}{5+8},\frac{3}{8*5},\frac{5}{8},\frac{5}{3+8},\frac{5}{8*3},\frac{5-3}{8},\frac{8}{5*3}\\\\\\\frac{3}{5},\frac{3}{8},\frac{3}{13},\frac{3}{40},\frac{5}{8},\frac{5}{11},\frac{5}{24},\frac{1}{4},\frac{8}{15}[/tex]

Improper Fractions:

[tex]\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{8+3}{8},\frac{5+8}{3},\frac{3*5}{8},\frac{8*5}{3},\frac{3+8}{5},\frac{8*3}{5}\\\\\\\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{11}{8},\frac{13}{3},\frac{15}{8},\frac{40}{3},\frac{11}{5},\frac{24}{5}[/tex]

Answer:

[tex]x = \frac{8}{23} \: \: \: \\ y = \frac{292}{23} [/tex]

Answer:

-5, 2

Step-by-step explanation:

Answer:

The probability that the proportion of Grammy award winners will be less than 47% is 0.6915

Step-by-step explanation:

* Lets explain how to solve the problem

- Suppose 46% of American singers are Grammy award winners.

- In a random sample of size 622 is selected

- We want to find the probability that the proportion of Grammy award

 winners will be less than 47%

* At first we must to calculate z

∵ [tex]z=\frac{P^{'}-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex], where

# P' is the sample proportion

# n is the sample size

# P is probability of success

∵ The sample proportion is 47% = 47/100 = 0.47

∴ P' = 0.47

∵ The sample size is 622

∴ n = 622

∵ The probability of success is 46% = 46/100 = 0.46

∴ P = 0.46

∴ [tex]z=\frac{0.47-0.46}{\sqrt{\frac{0.46(1-0.46)}{622}}}=0.5004[/tex]

- P(P' < 0.47) = P(z < 0.5004)

∵ P(z < 0.5004) = 0.6915

∴ P(P' < 0.47) = 0.6915

* The probability that the proportion of Grammy award winners will

 be less than 47% is 0.6915

Answer:

x=5

Step-by-step explanation:

If the equation is:

3(x+1)=7(x-2) -3

Solution:

Multiply (x+1) by 3 and (x-2) by 7

3x+3 = 7x-14 -3

3x+3 = 7x -17

Now combine the like terms:

3+17 = 7x-3x

20 = 4x

Now divide both the terms by 4

20/4 = 4x/4

5 = x

You can write it as x=5

Thus the value of x is 5 ....

Answer:

Option B. [tex]YV=5\ units[/tex]

Step-by-step explanation:

we know that

The Intersecting Secant-Tangent Theorem, states that If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

In this problem

[tex]WZ^{2}=WV*WY[/tex]

substitute and solve for WV

[tex]6^{2}=WV*4[/tex]

[tex]WV=36/4=9\ units[/tex]

we have that

[tex]WV=WY+YV[/tex]

substitute

[tex]9=4+YV[/tex]

[tex]YV=9-4=5\ units[/tex]

In a scenario where 'u' varies directly with 'v', the constant of variation, k is found by: k=u/v. Here, k becomes 6/-7. If we want to know the value for 'u' when v=4, we use the calculated k in our formula, resulting in u=4*(6/-7) which equals -24/7.

The question is about the direct variation between two quantities 'u' and 'v'. If 'u' varies directly with 'v', it means that multiplying or dividing one quantity will have the same effect on the other. We use the mathematical formula for direct variation to find the values: 'u' = kv, where k is the constant of variation.

So, we first find 'k' when u = 6 and v = -7. From our formula, k = u/v = 6/-7.

When we know the k, we can find u' when v = 4. Using the formula, 'u' = kv = 4 * (6/-7) = -24/7.

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Answer:

4p(2-3q)

Step-by-step explanation:

Factor out 4 first:

8p-12pq​

4(2p-3pq) Next, factor out p like you would any other number.

4p(2-3q)

Answer:

4p (2-3q)

Step-by-step explanation:

Break each term into its prime factors

8p = 4*2p = 2*2*2p

12pq = 4*3pq = 2*2*3*p*q

The common factors are 2*2*p

That is the greatest common factor.  Take that outside the parentheses.  Leave what is left inside the parentheses

2*2*p( 2-3q)

4p (2-3q)

Answer:

B.

Step-by-step explanation:

To simplify something that looks like [tex]\frac{\text{whatever}}{\sqrt{a}-\sqrt{b}}[/tex] you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:

[tex]\sqrt{a}+\sqrt{b}[/tex].

If you had  [tex]\frac{\text{whatever}}{\sqrt{a}+\sqrt{b}}[/tex], then you would multiply top and bottom the conjugate of [tex]\sqrt{a}+\sqrt{b}[/tex] which is [tex]\sqrt{a}-\sqrt{b}[/tex].

The conjugate of a+b is a-b.

These have a term for it because when you multiply them something special happens.  The middle terms cancel so you only have to really multiply the first terms and the last terms.

Let's see:

(a+b)(a-b)

I'm going to use foil:

First:  a(a)=a^2

Outer: a(-b)=-ab

Inner:  b(a)=ab

Last:    b(-b)=-b^2

--------------------------Adding.

a^2-b^2

See -ab+ab canceled so all you had to do was the "first" and "last" of foil.

This would get rid of square roots if a and b had them because they are being squared.

Anyways the conjugate of [tex]\sqrt{17}-\sqrt{2}[/tex] is

[tex]\sqrt{17}+\sqrt{2}[/tex].

This is the thing we are multiplying and top and bottom.

For this case we have the following expression:

[tex]\frac {3} {\sqrt {17} - \sqrt {2}}[/tex]

We must rationalize the expression, so we multiply by:

[tex]\frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}}[/tex]

So, we have:

[tex]\frac {3} {\sqrt {17} - \sqrt {2}} * \frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {17- \sqrt {17} * \sqrt {2} + \sqrt {17} * \sqrt {2} -2} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {15}[/tex]

Thus, the correct option is option B.

Answer:

OPTION B

Answer:

6 which is none of your answers.

Are you sure your function is right?

Is value to plug in x=-8?

Step-by-step explanation:

To find the value of the function at x=-8, you replace x with -8 in the function.

g(x)=3(x+10)

g(-8)=3(-8+10)

g(-8)=3(2)

g(-8)=6

g(-8) = 6.

The value of g(x) = 3(x + 10) when x = -8 is:

Substituting x = -8 in the function g(x)

g(-8) = 3 (-8+ 10)

Solving the operation in the  parenthesis

g(-8) = 3 (-8 + 10)

g(-8) = 3 (2)

Solving the multiplication

g(-8) = 6

Answer:

Option C is correct.

Step-by-step explanation:

The rate of change can be found by finding the slope of given ordered pairs.

y₂=12, y₁=7,x₂=1,x₁=0

rate of change = y₂-y₁/x₂-x₁

rate of change = 12-7/1-0

rate of change = 5/1 = 5

Now considering next two points,

y₂=17, y₁=7,x₂=2,x₁=1

rate of change = y₂-y₁/x₂-x₁

rate of change = 17-12/2-1

rate of change = 5/1 = 5

So, the rate of change for this set of ordered pairs is 5.

Option C is correct.

Answer:

= 52°

Step-by-step explanation:

The obtuse angle at O is twice the angle made at the circumference /by the same segment b.

=52×2=104°

The base angles that are made by isosceles triangle that has the apex with angle 104° equal to (180-104)/2=38°

The radii of a circle are equal and meet tangents at right angles.

Angle a= 90-38= 52°

Answer:

x^2+11x+10

or

(x+1)(x+10) since you can factor x^2+11x+10

Step-by-step explanation:

Let's do synthetic division.

We are dividing by x+2, so -2 will be on the outside. Like this:

-2 |         1          13          32         20

   |                     -2        -22         -20

   |___________________________

             1          11           10            0

The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.

The other factor we found by doing this is (x^2+11x+10).

You can find more factors by factoring x^2+11x+10.

Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).

Answer:

16

Step-by-step explanation:

8 / 2  * (2 + 2)

4 * (2 + 2)

4 * 4

16

Step-by-step explanation:

PEMDAS is ( Thank you google )

" PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete."

First, 2 + 2 = 4

Second, 8 divided by 2 is 4.

Third, 4x4= 16

Therefore, the answer is 16.

Answer:

i believe the answer is 9.5

Step-by-step explanation:

cos60 = c / 19 = 9.5

Answer:

see explanation

Step-by-step explanation:

Calculate the slope m of the line using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, 3) and (x₂, y₂ ) = (1, - 97)

m = [tex]\frac{-97-3}{1+7}[/tex] = [tex]\frac{-100}{8}[/tex] = - [tex]\frac{25}{2}[/tex]

Answer:

Road A

Step-by-step explanation:

The slope of road A is:

154 / 2200 = 0.07

The slope of road B is:

153 / 3400 = 0.045

Road A has the larger slope, and is therefore steeper.

The steepness of a road is determined by the ratio of the vertical climb to the horizontal distance. By calculating this ratio for both Road A and Road B, we find that Road A, with a ratio of 0.07, is steeper than Road B, which has a ratio of 0.045.

The steepness of a road is determined by the ratio of the vertical climb to the horizontal distance. This is equivalent to finding the slope in mathematics. We can calculate this for both Road A and Road B:

For Road A, the slope can be calculated as rise over run, or 154 feet over 2200 feet, yielding approximately 0.07. For Road B, applying the same formula gives 153 feet over 3400 feet, resulting in a slope of about 0.045.

Comparing these two results, it is clear that Road A, with a slope of 0.07, is steeper than Road B, which has a slope of 0.045.

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Answer:

y-3=2(x-1)

Step-by-step explanation:

So it looks like your line goes through (2,5) and (1,3) based on what you have said.

Looking at 5 to 3, that is down 2.

Locking at 2 to 1, that is left 1.

So the slope is -2/-1 =2/1=2.

Plug in the (x1,y1)=(1,3) and slope=m=2.

So using point slope form we have y-3=2(x-1).

Answer:

Step 3

Step-by-step explanation:

Just did the test

Answer:

Option D. 4:1

Step-by-step explanation:

we know that

If two solids are similar, then the ratio of the lengths of corresponding parts is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared

In this problem

The scale factor is equal to  [tex]\frac{2}{1}[/tex] (ratio of corresponding lengths)

therefore

The ratio of their surface areas is equal to

[tex](\frac{2}{1})^{2}=\frac{4}{1}[/tex]

Answer:

-6

Step-by-step explanation:

The average rate of a function f(x) on the interval from x=a to x=b is [tex]\frac{f(b)-f(a)}{b-a}[/tex].

So in the problem you have from [tex]x=2[/tex] to [tex]x=4[/tex].

The average rate of the function from x=2 to x=4 is

[tex]\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}[/tex].

Now we need to find f(4) and f(2).

f(4) means what is the y-coordinate that corresponds to x=4 on the curve.

f(4)=-15 since the ordered pair at x=4 is (4,-15).

f(2) means what is the y-coordinate that corresponds to x=2 on the curve.

f(2)=-3 since the ordered pair at x=2 is (2,-3).

So let's plug in those values:

[tex]\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}[/tex].

Now we just simplify:

[tex]\frac{-15+3}{2}[/tex]

[tex]\frac{-12}{2}[/tex]

[tex]-6[/tex]

Answer:

No correct answer.

Step-by-step explanation:

C: 2 or 3 is  1/2 the probability. The expectation is that you should get about 250 readings that are either 2 or 3.

A is not correct. It will land on an even number about 250 times. What should happen in theory is far different than what will happen when you try it. Exactly is too confining a word.

B: It will land on 1 about 1 out of every 4 times. 1/4 * 500 = 125. So B is not right.

D: Same as B. There is no answer.  

Answer:

A. exactly $9.54

Step-by-step explanation:

First add up how much he bought

Sandwich    5.98

drink            2.99

apple            1.49

                    ---------

                     10.46

Then subtract this from 20

20.00

-10.46

--------------

 9. 54

When you get money back, you get exact change.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-9-0)^2+(1-10)^2}\implies d=\sqrt{(-9)^2+(-9)^2} \\\\\\ d=\sqrt{81+81}\implies d=\sqrt{162}\implies d\approx 12.73[/tex]

A perfect square trinomial can be factored using the pattern x²+2ab+b²=(x+a)² or x²-2ab+b²=(x-a)². The term 'a' is the square root of the last term, and 'b' is half of the second term's coefficient.

In mathematics, a perfect square trinomial is a type of second-order polynomial or quadratic function with a specific form. It is used in the factorization process, particularly when solving quadratic equations of the form ax² + bx + c.

A perfect square trinomial is a trinomial in the form x²+2ab+b² or x²-2ab+b². To factor such a trinomial, the pattern (x+a)² or (x-a)² is used where 'x' is the variable, 'a' is the square root of the third term, and 'b' is half of the coefficient of the second term. Hence, x²+2ab+b² factors to (x+a)², whereas x²-2ab+b² factors to (x-a)².

Take for example, the trinomial x²+6x+9. Here, 'a' is 3 (as √9=3) and 'b' is 3 (as half of 6 is 3). Both 'a' and 'b' are equal so we know the trinomial is perfect square and it factors to (x+3)².

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The factor a perfect square trinomial, use the pattern [tex](a+b)^2[/tex] = [tex]a^2[/tex]  +2ab+  [tex]b ^{2}[/tex] and simplify .

The pattern for a perfect square trinomial is a helpful algebraic expression that represents the square of a binomial.

It takes the form [tex](a+b)^2[/tex] = [tex]a^2[/tex] +2ab+[tex]b ^{2}[/tex]  

where a and b are variables. When faced with a trinomial that fits this pattern, you can use it to factor the trinomial efficiently.

To factor a perfect square trinomial, compare it with the pattern. If the trinomial can be expressed in the form [tex](a+b)^2[/tex] =[tex]a^2[/tex]+2ab+ [tex]b ^{2}[/tex] , then it is a perfect square trinomial.

Identify [tex]a^2[/tex]  ,2ab and [tex]b ^{2}[/tex] terms in the trinomial.

Once identified, you can write the factored form as [tex](a+b)^2[/tex].  This means the trinomial can be factored as  [tex](a+b)^2[/tex] where a is the square root of the first term, and b is the square root of the last term.

This process is essentially reverse-engineering the expansion of the perfect square trinomial pattern.

Factoring using the perfect square trinomial pattern can save time compared to other methods, making it a valuable tool in algebraic manipulations and simplifying expressions.