Solve each equation by completing the square 6x2+12x-27=-9

Answer:

16

Step-by-step explanation:

Given

f(x)=5x^2+9x-2

Remainder theorem states that when f(x) is divided by x-a then the remainder can be calculated by calculating f(a).

Now Using the remainder theorem to divide 5x^2+9x-2 by x+3 to find the remainder:

f(x)=5x^2+9x-2

f(-3) = 5(-3)^2 +9(-3) -2

       =5(9) - 27 -2

       = 45-29

        = 16 !

Answer:

16

Step-by-step explanation:

apexs

Answer:

-25%

20 characters

so the difference is 84 - 63 = 21.

if we take 84 to be the 100%, what is 21 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 84&100\\ 21&x \end{array}\implies \cfrac{84}{21}=\cfrac{100}{x}\implies 4=\cfrac{100}{x}\implies 4x=100 \\\\\\ x=\cfrac{100}{4}\implies x=25[/tex]

Answer:

Step-by-step explanation:

A direct variation suggest that the value of x in the equation would greatly affect the value of y such that when x is increasing, y also increases and the other way around. The equation for a direct variation is that,

                              y  = kx

Substituting the given values in the ordered pair,

                          5 = k(4)   ; k = 5/4

answer: y = kx hope this helps

Answer:

Option A. is the correct option.

Step-by-step explanation:

As per table given in this question values of the function has been given as

f(x) = -3 for x = -2

We can rewrite the function as f(-2) = -3

As we know inverse of the function means [tex]-2 = f^{-1}(-3)[/tex]

or inverse function g(-3) = -2

and the ordered pair for the inverse function will be (-3, -2)

Similarly other ordered pairs for the inverse function given will be

(3, -1), (9, 0), (15, 1), (21, 2)

Therefore, the ordered pairs will be (-3, -2), (3, -1), (9, 0), (15, 1), (21, 2)

Option A is the right option.

Nicole has 25 ten-dollar bills.

To find out how many ten-dollar bills Nicole has, we can divide the total amount of money she has by the value of each bill.

$250 / $10 = 25

Therefore, Nicole has 25 ten-dollar bills.

Answer in detail:

Nicole has $250 in ten-dollar bills. This means that she has 25 groups of $10.

We can divide $250 by $10 to find out how many groups of $10 she has.

$250 / $10 = 25

Therefore, Nicole has 25 ten-dollar bills.

Another way to look at it is this way:

If Nicole has 1 ten-dollar bill, then she has $10.

If Nicole has 2 ten-dollar bills, then she has $20.

If Nicole has 3 ten-dollar bills, then she has $30.

And so on.

So, to find out how many ten-dollar bills Nicole has, we can simply divide the total amount of money she has by the value of each bill.

Answer:

50 Students

You can find the number of boys and girls by dividing the total, so there are a total of 20 boys and 30 girls in the choir of 50. The ratio 2 boys : 3 girls means we can divide the chorus into groups.

ANSWER

See attachment.

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x + 1} - 2[/tex]

The parent function is

[tex]y = \sqrt[3]{x} [/tex]

When we shift the parent graph to the left one unit, and down 2 units, we obtain the graph of the given function.

The graph of this function is shown in the attachment.

The mean would be the best! The mean is when you add up all of those grades and divide by the amount of exams.

If you're solving it,

504 is the total divided by 6 tests would be 84.

The answer is 84 I’m glad i could help you

Answer:

Step-by-step explanation:

Unsure of what you're asking here.  What's "dias?"

I do see that the longer arrow has length 5 (there are 5 squares along this arrow from bottom to top) and that the shorter one has length 2.

If we add these two vectors together, we get a vector of length 5 + 2, or 7, that points upward just as these two original vectors do.

yes that would work but just keep that in mind that 1+1=2

Answer:

The average rate of change is 3

Step-by-step explanation:

0 to 5 is 5 in difference then the change on the next one: 1 to 9 the difference is 8 so the change is 3 and it increases by three on the rest of them.

I'm pretty sure the average rate of change would be 3

The equivalent expression of the expression P (z ≥ 1.7) is,

⇒ 1 - P (z ≥ - 1.7)

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

The expression is,

⇒ P (z ≥ 1.7)

Now, By definition of Probability of z - score we get;

⇒ P (z ≥ 1.7) = 1 - P (z ≥ - 1.7)

Thus, The equivalent expression of the expression P (z ≥ 1.7) is,

⇒ 1 - P (z ≥ - 1.7)

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Answer:

-7, -2, 4, 5

Step-by-step explanation:

Integers with a dash in the front of them signify a negative. With negative numbers, the higher the value of the accompanying number, the lower value it has as a negative number, so, of course the negative integers would go from the "least" end of the spectrum. Because 7 has a higher positive value than 2, it has a lower negative value, putting -7 on the lower end, following it with the -2. As 5 has a higher positive value than 4, 5 is put on the highest end on the spectrum, with 4 right behind it. With all of these integers settled, we can organize the numbers in the order of -7, then -2, then 4, then 5.

Step-by-step explanation: To write these integers from least to greatest, first draw a number line and graph each of the integers

In the image provided, notice that I've only labeled every other unit on the number line. This  is a labeling technique that we can use to keep things from getting too crowded on the number line.

Now, let's graph our integers.

Integers to the left are always less than integers to to the right. So in this problem, we can see that -7 < -2 < 4 < 5.

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\displaystyle\sum \limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf S_{20}=\displaystyle\sum \limits_{n=1}^{\stackrel{\stackrel{n}{\downarrow }}{20}}~\stackrel{\stackrel{a_1}{\downarrow }}{3}(\stackrel{\stackrel{r}{\downarrow }}{1.5})^{n-1}\implies S_{20}=3\left(\cfrac{1-1.5^{20}}{1-1.5} \right)\implies S_{20}=3\left(\cfrac{1-\stackrel{\approx}{3325.3}}{-0.5} \right) \\\\\\ S_{20}=3\left(\cfrac{-3324.3}{-0.5} \right)\implies S_{20}=3(6648.6)\implies S_{20}=19945.8[/tex]

19945.8 to simplify, the answer is

Answer:

for 4x = 20 you have to use the division property of equality divide 20 by 4

for x - 11 = 9 you have to use the addition property of equality add 9 to 11

for 5x + 6x = 22 you have to combine like terms add 5x and 6x to make 11x

for 5(x – 2) = 30 you have to use the distributive property multiply 5 and x; 5 and -2

4x = 20; x = 5

x - 11 = 9; x = 20

5x + 6x = 22; 11x = 22; x = 2

5(x – 2) = 30; 5x - 10 = 30; x = 8

Answer:

1. B

2. A

3. A

4. B

Step-by-step explanation:

Answer:

Y = W = 15 ft.

X= L = 60 ft.

So width is 15 and the length is 60.

Answer: A. 15 feet

Step-by-step explanation:

The formula used to calculate the perimeter of a rectangle is:

[tex]P=2l+2w[/tex]

Where "l" is the lenght of the rectangle and "w" is the width.

You know that the length of this rectangle is 4 times its width. This means that:

[tex]l=4w[/tex]

And you know that the perimeter is 150 feet.

Then, you need to substitute  [tex]l=4w[/tex] and the value of the perimeter into the formula and solve for "w":

[tex]150=2(4w)+2w\\\\150=10w\\\\w=\frac{150}{10}\\\\w=15feet[/tex]

so we know the terminal point is at (9, -3), now, let's notice that's the IV Quadrant

[tex]\bf (\stackrel{x}{9}~~,~~\stackrel{y}{-3})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{9^2+(-3)^2}\implies c=\sqrt{81+9}\implies c=\sqrt{90} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf cos(\theta )=\cfrac{\stackrel{adjacent}{9}}{\stackrel{hypotenuse}{\sqrt{90}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{9}{\sqrt{90}}\cdot \cfrac{\sqrt{90}}{\sqrt{90}}\implies \cfrac{9\sqrt{90}}{90}}\implies \cfrac{\sqrt{90}}{10}\implies \cfrac{3\sqrt{10}}{10}[/tex]

Answer

b

Step-by-step explanation:

Answer:

− -10x^2-33x+1

Step-by-step explanation:

Answer:

I believe A, C, and D are Coplanar and i think B. is non-collinear.

Step-by-step explanation:

A, C and D are coplanar because they lie on the same line.

B is non-collinear, because it don't lie on the same line as A, C, and D.

Hope my answer has helped you!

The greatest common factor is 2x

2 can go into both 10 and 12

and so can x

i think it is m because it simply the vertex

Answer: (12)(8)-6

Step-by-step explanation: Product indicates you are going to multiply the numbers. When you see the phrase "less than" you want to flip the numbers.

Use the Pythagorean theorem:

30^2 + 40^2 = X^2

900+ 1600 = x^2

X^2 = 2500

x = √2500

x = 50

The answer is 50 feet.

Answer:

y=9

Step-by-step explanation:

(9,-1) is the answer.

Answer:

The distance reduces to 0 as you go from 0° to 90°

Step-by-step explanation:

The question requires you to find the distance using different values of L and check the trend of the values.

Given C=2×pi×r×cos L where L is the latitude  in ° and r is the radius in miles then;

Taking r=3960 and L=0° ,

C=2×[tex]\pi[/tex]×3960×cos 0°

C=2×[tex]\pi[/tex]×3960×1

C=7380[tex]\pi[/tex]

Taking L=45° and r=3960 then;

C= 2×[tex]\pi[/tex]×3960×cos 45°

C=5600.28[tex]\pi[/tex]

Taking L=60° and r=3960 then;

C=2×[tex]\pi[/tex]×3960×cos 60°

C=3960[tex]\pi[/tex]

Taking L=90° and r=3960 then;

C=2×[tex]\pi[/tex]×3960×cos 90°

C=2×[tex]\pi[/tex]×3960×0

C=0

Conclusion

The values of the distance from around the Earth along a given latitude decreases with increase in the value of L when r is constant

Answer:

1. 4; 2. 32; 3. 9; 4. 8; 5. 12; 6. 16; 7. 6; 8. 8; 9. 8; 10. 8

The probability of obtaining at random without replacement two gum balls is 3/11.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A gumball machine contains six yellow gumballs and five orange gumballs.

So, N(Y) = 6 and N(O) = 5 and the number of sample space N(S) = 11.

Therefore, The probability of obtaining at random without replacement two gum balls is,

P(YY) = (6/11)×(6 - 1)/(11 - 1).

P(YY) = (6/11)×(5/10).

P(YY) = 30/110.

P(YY) = 3/11.

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Answer:

[tex]\large\boxed{A==\dfrac{3-\sqrt6}{12}\ cm^2}[/tex]

Step-by-step explanation:

The shaded region is the triangle with base b and height h.

[tex]b=BD-CD\to b=\dfrac{\sqrt2}{2}-\dfrac{\sqrt3}{3}=\dfrac{3\sqrt2}{(2)(3)}-\dfrac{2\sqrt3}{(2)(3)}=\dfrac{3\sqrt2-2\sqrt3}{6}\\\\h=AD\to h=\dfrac{\sqrt2}{2}[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A=\dfrac{\frac{3\sqrt2-2\sqrt3}{6}\cdot\frac{\sqrt2}{2}}{2}=\left(\dfrac{3\sqrt2-2\sqrt3}{6}\right)\left(\dfrac{\sqrt2}{2}\right)\left(\dfrac{1}{2}\right)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\dfrac{(3\sqrt2-2\sqrt3)(\sqrt2)}{(6)(2)(2)}=\dfrac{(3\sqrt2)(\sqrt2)-(2\sqrt3)(\sqrt2)}{24}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{(3)(2)-2\sqrt6}{24}=\dfrac{2(3-\sqrt6)}{24}=\dfrac{3-\sqrt6}{12}[/tex]

Answer:

see explanation

Step-by-step explanation:

The area of the shaded triangle = area of ΔABD - area of ΔADC

A of ΔABD = [tex]\frac{1}{2}[/tex] × AD × BD

A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex]

   = [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex]

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

A of ΔACD = [tex]\frac{1}{2}[/tex] × AD × DC

A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{3}[/tex]

A = [tex]\frac{\sqrt{6} }{12}[/tex]

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

shaded area = [tex]\frac{1}{4}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex]

= [tex]\frac{3}{12}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex] = [tex]\frac{3-\sqrt{6} }{12}[/tex]

I believe the correct answer from the choices listed above is option D. The expression that could be used to determine the average rate at which the object falls during the first 3 seconds of its fall would be  (h(3)-h(0))/3. Average rate can be calculated by the general formula:

Average rate = (change in y-axis) / (change in x-axis)

In this case,

Average rate = (change in height) / (change in time)

The average rate at which the object falls during the first 3 seconds can be calculated using the equation for average rate of change (h(3) - h(0))/3. Using the given function h(t) = 300 - 16t, this comes out to be -16 feet per second.

In this problem, we are given a mathematical model of a falling object, as follows: h(t) = 300 - 16t. Here, the function h(t) represents the height of the object t seconds after it is dropped from a platform 300 feet above the ground.

To determine the average rate at which the object falls during the first 3 seconds, we should use the equation for average rate of change in functions. That is, the change in height divided by the change in time, or (h(3) - h(0))/3.

Let's calculate: h(3) = 300 - 16*3 = 252, and h(0) = 300. Then, the average rate = (252 - 300) / 3 = -48/3 = -16 ft/sec. This indicates that the object falls at an average rate of 16 feet per second during the first three seconds.

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Answer:

So we already knew all three sides, there are more than one way to do it, for example:

sin∠F = HG/HF = 12/13

cos∠F = GF/HF = 5/13

tan∠F = HG/GF = 12/5

ctg∠F = GF/HG = 5/12

All of them will give you the result which is approximately 67°.

Answer:

The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²

Step-by-step explanation:

* Lets revise how to multiply two brackets with three terms

∵ (a + b - c)(a + b + c)

- Multiply the first term of the first bracket by the three terms of the

 second bracket

∵ a × a = a²

∵ a × b = ab

∵ a × c = ac

- Then multiply the second term in the first bracket by the three terms

 of the second bracket

∵ b × a = ba

∵ b × b = b²

∴ b × c = bc

- Then multiply the third term term in the first bracket by the three terms

 of the second bracket

∵ -c × a = -ca

∵ -c × b = -cb

∵ -c × c = -c²

- Now add all these terms together

∴ a² + ab + ac + ba + b² + bc + -ca + -cb + -c²

- We have like terms lets add them

∵ ab = ba  , ac = ca , bc = cb

∴ a² + (ab + ba) + (ac + -ca) + (bc + -cb) + b² + -c²

∴ a² + 2ab + 0 + 0 + b² - c²

∴ a² + 2ab + b² - c²

∴ The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²

The answer is:

[tex]a^{2} +b^{2} -c^{2} +2ab[/tex]

To solve the problem, we need to remember the distributive property.

The distributive property is defined by the following way:

[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]

Also, we need to remember how to add like terms. The like terms are the terms that share the same variable and the same exponent, for example:

[tex]x+x^{2}+x=x^{2} +2x[/tex]

We were able to add the first and the third term because they share the same variable and the same exponent.

Now, we are given the following expression to simplify:

[tex](a+b-c)(a+b+c)[/tex]

So, applying the distributive property and adding like terms, we have:

[tex](a+b-c)(a+b+c)=(a*a)+(a*b)+(a*c)+(b*a)+(b*b)+(b*c)-(c*a)-(c*b)-(c*c)\\\\(a+b-c)(a+b+c)=a^{2}+ab+ac+ba+b^{2} +bc-ac-bc-c^{2}\\\\(a+b-c)(a+b+c)=a^{2} +b^{2} -c^{2} +2ab[/tex]

Hence, we have that the given expression is equal to:

[tex]a^{2} +b^{2} -c^{2} +2ab[/tex]

Have a nice day!