Factor the expression below.
x^2 – 6x + 9
A.
(x - 3)(x - 3)
B.
3(x2 - 2x + 3)
C.
(x - 3)(x + 3)
D. (x + 3)(x + 3)​

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have the equation:}\\\\-3y=15-4x\\\\-3y=-4x+15\qquad\text{ivide both sides by (-3)}\\\\\boxed{y=\dfrac{4}{3}x-5}\\\\\boxed{slope=\dfrac{4}{3}}\\\boxed{y-intercept=-5}[/tex]

[tex]\text{To draw a graph we need only two points.}\\\text{We choose any value of x, put it to the equation of the line}\\\text{and calculate the value of y:}\\\\for\ x=0\\\\y=\dfrac{4}{3}(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=3\\\\y=\dfrac{4}{3}(3)-5=4-5=-1\to(3,\ -1)\\\\\text{The graph is in attachment}.[/tex]

Answer:

answer in picture

Step-by-step explanation:

Answer: Blueberry = $6, Pumpkin = $17

Step-by-step explanation:

Let B represent blueberry pie and P represent pumpkin pie.

      Kim: 12B + 8P = 208

- Krystal: 10B + 8P = 196

                2B         =   12

                  B         =    6

Input B = 6 into either of the equations to solve for P

10B + 8P = 196

10(6) + 8P = 196

 60  + 8P = 196

           8P = 136

             P = 17

Answer:

To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.

On both sides, powers have the same base, so their exponents must be equal.

Step-by-step explanation:

Write the missing exponent:

25=5^x

Let x be the missing exponent.

To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.

That is,

25=5*5 or 5^2

Now,

5^2=5^x

Powers have the same base so their exponent must be equal.

Hence the missing exponent is 2

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\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=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=9\\ r=3.8\\ \stackrel{S_n}{S_9}=44240 \end{cases}[/tex]

[tex]\bf 44240=a_1\left( \cfrac{1-3.8^9}{1-3.8} \right)\implies 44240\approx a_1\left( \cfrac{-165215.101}{-2.8} \right) \\\\\\ 44240\approx a_1(59005.393)\implies \cfrac{44240}{59005.393}\approx a_1\implies \stackrel{\textit{rounded up}}{0.75=a_1}[/tex]

When all the terms of a geometric sequence are added, then that expression is called geometric series. The first term of the given geometric series is 0.75.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

Let's suppose its initial term is, the multiplication factor is  r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

Given the sum of the geometric series is 44,240, while the number of terms is 9. Also, the common ratio of the series is 3.8. Thus, we can write,

Sₙ = a(rⁿ-1)/(r-1)

44240 = a(3.8⁹ - 1)/(3.8 - 1)

44240 = a 59005.3933

a = 0.75

Hence, the first term of the given geometric series is 0.75.

Learn more about the Sum of terms of geometric sequence:

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Answer:

[tex]\large\boxed{D.\ (x-3)^2+(y+2)^2=81}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center at (3, -2) and the radius r = 9. Substitute:

[tex](x-3)^2+(y-(-2))^2=9^2\\\\(x-3)^2+(y+2)^2=81[/tex]

Answer:  b. 6

Step-by-step explanation:

The maximum value is the y-value of the vertex.

Step 1: Find the x-value (aka Axis Of Symmetry) using the formula: [tex]x=\dfrac{-b}{2a}[/tex]

[tex]x=\dfrac{-(2)}{2(-1)}=\dfrac{-2}{-2}=1[/tex]

Step 2: input the x-value (above) into the given equation to solve for y:

[tex]y=-x^2+2x+5\\y=-(1)^2+2(1)+5\\y=-1 + 2 + 5\\y = 6[/tex]

Answer:

C. 0.36

Step-by-step explanation:

There is already a 45% chance of having oil on the land.

The oil kit has an 80% accuracy rate.

Therefore the kit has an 80% chance, of that 45% chance, of detecting oil. (Assume the owners in the area are correct in their 45% assumption)

This can be expressed as 80%*40% or 0.8*0.45

= 0.36 or 36%

Hope this helps!

Answer:

C. 0.36

Step-by-step explanation:

Answer:

the answer would be d

Step-by-step explanation:

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6) is: A. [tex]\frac{3(6) - 1}{2(6)+1}[/tex]

In Mathematics, an algebraic expression is a type of mathematical equation which is typically used for showing the relationship existing between two (2) or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.

Based on the information provided, the quotient of the two expressions can be computed as follows;

[tex]\frac{r(x)}{s(x)} =\frac{3x - 1}{2x+1} \\\\[/tex]

When the value of x is 6, the output value of the expression

[tex]\frac{r}{s}(6) =\frac{3(6) - 1}{2(6)+1}[/tex]

Complete Question;

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6)?

Answer:

C. [tex]\{y|y\ge 1\}.[/tex]

Step-by-step explanation:

Consider the parent function [tex]f(x)=\sqrt{x}.[/tex]

Now consider given function [tex]h(x)=\sqrt{x+4}+1[/tex] (translated 4 units left and 1 unit up.)

Answer:

The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]

Step-by-step explanation:

Given : The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left and 1 unit up to create the function h(x).

To find : What is the range of h(x)?

Solution :

When the graph f(x) is translated then

1) f(x)+b shifts the function b units upward.

2) f(x + b) shifts the function b units to the left.

The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left.

i.e. [tex]y=\sqrt{x+4}[/tex]

The graph of [tex]y=\sqrt{x}[/tex] is translated 1 unit up.

i.e. [tex]y=\sqrt{x+4}+1[/tex]

So, The required function h(x) is [tex]h(x)=\sqrt{x+4}+1[/tex]

The range of a function is set of output values produce by a function.

In the given graph, y value is always greater than and equal to 1.

So, The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]

Y1=2/3x , Y2=2/3x-2

those are the graph of the functions

[tex]f(n+1)=f(n)-8\\f(1)=100\\\\f(2)=100-8=92\\f(3)=92-8=84\\f(4)=84-8=76\\f(5)=76-8=68\\f(6)=68-8=60[/tex]

Answer:

The answer is option D.

Step-by-step explanation:

Answer:

D: Answer:(x-9)(x-3)

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

(-4) -6? well it equals 24 because a negative plus a negative equals a positive.

Hope my answer has helped you! If not i'm sorry.

Answer:

The correct answer is -10. 24 isn't correct ^^^^.

Step-by-step explanation:

The water weight of a 125lb person is 75lbs.

Answer:

[tex]\large\boxed{y=\dfrac{32}{9}}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}x+3y=1\\2x-3y=-30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=-29\qquad\text{divide both sides by 3}\\.\qquad x=-\dfrac{29}{3}\\\\\text{put the value of x to the first equation}\\\\-\dfrac{29}{3}+3y=1\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\left(-\dfrac{29}{3\!\!\!\!\diagup_1}\right)+(3)(3y)=(3)(1)\\\\-29+9y=3\qquad\text{add 29 to both sides}\\\\9y=32\qquad\text{divide both sides by 9}\\\\y=\dfrac{32}{9}[/tex]

By adding the system of equations and solving for x, then substantifying back into the first equation, we find that y in this system of equations is approximately 3.5556.

To find the value of y in the given system of equations, you can add the two equations together. The first equation is x+3y=1 and the second equation is 2x – 3y = -30. Here are the steps:

This value, 3.5556, is the value of y in the solution for the system of equations.

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Answer:

x = 30

Step-by-step explanation:

The sum of the 3 interior angles of a triangle = 180°, hence

x + x + 10 + 3x + 20 = 180

5x + 30 = 180 ( subtract 30 from both sides )

5x = 150 ( divide both sides by 5 )

x = 30

Step-by-step explanation:

When the object hits the ground, h = 0.

0 = -21.962x + 114.655

x = 5.2

From the table, the object landed at x = 4.6 seconds.  So the line of best fit predicts a time 0.6 seconds greater than actual.

The original height is when x = 0.

h = -21.962(0) + 114.655

h = 114.7

So the line of best fit predicts the object was dropped from a height of 114.7 meters.  This is higher than the actual 100 meters.

At x = 3.5:

h = -21.962(3.5) + 114.655

h = 37.8

So the line of best fit estimates the object reached a height of 37.8 meters after 3.5 seconds.

We know that at x = 0, h = 114.7.  This is more than 4 meters from the actual initial height of 100 m.

Therefore, the answer must be A.

Answer:

A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Angle 9 = 85 degrees

Angle 9 and < 11 are vertical angles

Vertical angles are equal

<11 = 85 degrees

Answer:

B.

The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.

Answer:

B.

The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.

Answer:

[tex]1\frac{1}{2}[/tex]

Step-by-step explanation:

If there is 1500 cellular phones per 1000 people, then the number of phones per person is:

[tex]\frac{1500}{1000} = \frac{15}{10} = \frac{3}{2}[/tex]

Now we know that [tex]\frac{3}{2} = 1 + \frac{1}{2} = 1\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

the slope is 4

y int is 1

Answer:

x < -1

Step-by-step explanation:

5 - 3 = 2

-2x < 2

x < -1

Answer:

Answer is x > -1

Step-by-step explanation:

Because -2x + 3 < 5

                       -3   -3 minus 3 on both sides

Then:        -2x  <  5

                  -2      -2 divide negative 2 on both sides

And get  x > -1, Because if you divide by negative numbers the sign always flips.

Sorry i had to reedit it's -1 because you divide my bad.

Hope my answer has helped you and if not i'm sorry.

Answer:

C 340 square units

Step-by-step explanation:

Divide it into smallest pieces.

I see two rectangles that I'm going to do.

The long rectangle reading the paper from bottom to top is a 4 by (4+11+4) rectangle.

The wide rectangle reading the paper from left to right is a 24 by 11 rectangle.

We need to find the area of both of these rectangles and then just add them together to get the total area.

So first rectangle has area 4(19)=76 and the second rectangle has area 264.  The sum of these two numbers are 340 square units.

Hello There!

The answer would be 340 square units

First, let's find the area of our small rectangle located to the left. The formula for a rectangle is width*height so we would multiply19 because we know that on our right rectangle the height is 11 and we would add 4 to that and add another 4 to that to get our length of our rectangle on the left.

Next, we multiply 24 by 11 because we are using our same formula for the rectangle on the right and once we multiply, we get a product of 264.

Finally, we add 264 and our area of the rectangle on the right together and get a sum of 340 square units.

Have A Great Day!

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1250\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years\dotfill &5 \end{cases} \\\\\\ I=(1250)(0.0725)(5)\implies 453.125 \\\\\\ \stackrel{\textit{he'll have to repay}}{1250+453.125}\implies 1703.125[/tex]

Answer:

  x^4 +8/7x^3  + 6x +1

Step-by-step explanation:

8/7x^3 + x^4 + 6x +1

Standard from is from the largest power to the smallest power

  x^4 +8/7x^3  + 6x +1

Answer:

what is the period after the 9?

Answer:

50

Step-by-step explanation:

Evaluate the products before addition

18 - (9 × - [tex]\frac{4}{3}[/tex] ) + (10 × 2)

= 18 - (- 12) + 20

= 18 + 12 + 20

= 50

Answer:area is 84

Step-by-step explanation:

6*14

Answer:

its c 42 square feet

Step-by-step explanation:

Answer:

all work is shown and pictured