Mathematics High School

Given ​ f(x)=x2+14x+40 ​.


Enter the quadratic function in vertex form in the box.

Answers

Answer 1
Please indicate exponentiation using " ^ "   Thanks.

f(x)=x2+14x+40 => f(x)=x^2+14x+40

Next, complete the square:

f(x)=x^2+14x+ 49 - 49 +40 = (x+7)^2 - 9 

Write this in the form y = (x+7)^2 - 9  or y + 9 = (x+7)^2
Comparing this result to y = a(x-h)^2 + k, we see that h = -7 and k=-9

In vertex form, the equation is y + 9 = (x+7)^2 and the vertex is at (-7, -9).

Related Questions

L'shanda can choose between 3 sweaters and 4 skirts. if she selects 1 sweater and 1 skirt, how many possible outcomes are in the sample space answer

Answers

Nuber of outcomes = 3 * 4  = 12 Answer

We have been given that L'shanda can choose between 3 sweaters and 4 skirts.

We need to figure out the number of ways in which L'shanda can pick 1 sweater and 1 skirt out of the available items.

We need to use combinations here. First of all, we will figure out the number of ways of choosing 1 sweater out of 3 available sweaters. And then we will determine the number of ways of choosing 1 skirt out of 4 available skirts.

Number of ways of choosing 1 sweater = [tex]_{1}^{3}\textrm{C}=\frac{3!}{2!1!}=\frac{3\cdot 2!}{2!} = 3[/tex]

Number of ways of choosing 1 skirt = [tex]_{1}^{4}\textrm{C}=\frac{4!}{3!1!}=\frac{4\cdot 3!}{3!} = 4[/tex]

Therefore, total number of ways to select 1 sweater and 1 skirt are [tex]3\cdot 4 = 12[/tex]


Mike is going to a ball game on saturday. he will pay $8.00 admission, plus $1.50 per item he buys at the concession stand. which of the equations represents this information?

Answers

The first thing you should do for this case is to define a variable:
 x: number of items that he buys at the concession stand
 y: total payment
 We now write the equation that represents this problem.
 We have then:
 y = 1.50x + 8
 Answer:
 An equation that represents this information is:
 y = 1.50x + 8

The equation that represents this information will be y = 1.5x + 8.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mike is going to a ball game on Saturday.

He will pay $8.00 for admission, plus $1.50 per item he buys at the concession stand.

Let x be the number of items and y be the total cost.

Then we have

y = 1.5x + 8

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-2x+4y=-8 which graph models the equation

Answers

Hello!

First you have to get the equation into slope-intercept form

Slope-intercept form is y = mx + b

-2x + 4y = -8

Add 2x to both sides

4y = 2x - 8

Divide both sides by 4

y = 1/2 x - 2

The graph is a line that goes through the points (0, -2), (-2, -3), (2, -1) and
(4, 0)

Hope this helps!

1. Point B lies on line AC. AC = 127, AB is represented by the expression -12x + 11, and BC is represented by the expression -8x - 4. What is the length of AB?

2. Point E lies on line DF. DE is represented by the expression 2x - 8. EF is represented by the expression 2x - 4. If DF = 36 inches, what is the length of DE? What is the length of EF?

Answers

For number 1.
Since AB + BC = AC
Then
-12x + 11 - 8x -4 = 127
-20x + 7 = 127
X = -6

Ab would then equal 83

Solve the polynomial equation. state the multiplicity of each root. 8x3 - 12x2 + 6x - 1 = 0

Answers

Factorise to get (x - 0.5)^3 = 0
The equation has root 1/2 with multiplicity 3.

A researcher reports that mean ratings of liking for some food are m = 0.8, sd = 2.4. if the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated cohen's d?

Answers

cohen's d is a rathe rwrong way to word things so i suggest you rerun your Claulctaion

find the surface area of a sphere with a radius of 0.8 ft

Answers

Sphere Surface Area     =     4 • π • r²
Sphere Surface Area     = 4 * PI * .8^2
Sphere Surface Area     = 8.0424771932 square feet
 

Write the equation for a parabola that has x− intercepts (−1.6,0) and (−3.2,0) and y−intercept (0,25.6).

Answers

x-intercepts are zeroes of the parabola.
(x-x1)(x-x2)=(x+1.6)(x+3.2)=x² +1.6x+3.2x+5.12=x²+4.8x+5.12
 
y=x²+4.8x+5.12, but the y-int. is (0, 25.6),

So, our parabola should look like
y=5(x²+4.8x+5.12)
y=5x²+24x+25.6
 Answer: y = 5(x + 1.6)(x + 3.2)

∞∞∞∞∞∞∞∞
Explanation:
∞∞∞∞∞∞∞∞

x-intercept = (-1.6, 0) and (-3.2, 0)

=====>   y = a(x + 1.6)(x + 3.2)

Given y-intercept = (0, 25.6)

=====>  25.6 = a( 0 + 1.6)(0 + 3.2) 
=====>  25.6 = 5.12a
=====>  a = 5

Plug in a = 5 into the equation

=====>  y = 5(x + 1.6)(x + 3.2)

I am having a bit of a hard time solving this problem, it would be a pleasure if some one were to help me!

Answers

I got 42.5 cuz 4x+10=180 then take away 10 from both sides so 4x=170 and you divide each side by 4
Supplementary; they equal 180 degrees when added.

Also, 4x + 10 + x =180
Combine like terms; 5x + 10 = 180

Here, x=34

34 degrees is the answer!



The scatterplot shows a linear relationship between the distance traveled and the time elapsed. What is the rate of change of the linear relationship?
For every increase in time by 1 hour, the distance increases
36 miles.
54 miles.
72 miles.
90 miles.

Answers

To solve the question we get the slope for the given  graph. This is given by:
slope,m=(change in y-values)/(change in x-values)
taking 2 points (1.25, 90) and (0.75,54) we get:
slope,m=(90-54)/(1.25-0.75)=36/0.5=72
The answer is:
72 miles

Answer:

The answer is C. 72 miles.

Step-by-step explanation:

Hadmids will start at 11:00A.M., but the players must arrive at the field three-quarters of an hour early to warm up. The game must end by 1:15 P.M. Hadmid say he has to be at the field at 9:45 A.M is hadmid correct? Explain your answer.

Answers

"Three quarters of an hour early" would imply "3/4 hour before 11:00 a.m., which would be 10:15 a.m.  So Hadmid would be 30 minutes PLUS 45 minutes too early if he were to arrive at 9:45 a.m.

the perimeter of a rectangular parking lot is 190 meters. the width is one fourth the length. write a system of equation for this scenario

Answers

Hello!

You can make 2 equations based on what you know

2l + 2w = 190

w = 0.25l

Put w into the first equation

2l + 2(0.25l) = 190

Distribute the 2

2l + 0.5l = 190

Combine like terms

2.5l = 190

Divide both sides by 2.5

l = 76

Put l into the second equation

w = 0.25(76)

Multiply

w = 19

The length is 76 and the width is 19

The answer is

2l + 2w =190
w = 0.25l

Hope this helps!

Final answer:

To write a system of equations for the scenario, assign variables to the length and width of the rectangular parking lot. Use the information given to create two equations.

Explanation:

To write a system of equations for this scenario, let's start by assigning variables to the length and width of the rectangular parking lot. Let's say the length is represented by 'L' and the width is represented by 'W'. According to the given information, the width is one fourth the length, so we can write the equation:

W = (1/4)L

The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter is given as 190 meters, so we can write the equation:

2L + 2W = 190

Now we have a system of equations:

W = (1/4)L

2L + 2W = 190

These are the equations that represent the given scenario.

Two ships leave a harbor at the same time. one ship travels on a bearing upper s 12 degrees upper w at 18 miles per hour. the other ship travels on a bearing upper n 75 degrees upper e at 12 miles per hour. how far apart will the ships be after 2 ​hours?

Answers

Between N75E and E there are (90-75)=15°
Between E and S there are 90°
Between South and S12°W there 12°
Applying cosine rule 
Another way is to measure all angles clockwise from north (called azimuth) The ship at S12°W is at 180+12 = 192° 
The ship at N75°E is at 75° 
Angle between them is 192-75 = 117°

Applying cosine rule:
c=√(36²+24²-2×36×24cos117)
c=√2656.496
c=51.54 mi


Use the following graph of the function f(x) = 2x3 + x2 − 3x + 1 to answer this question:

(graph of 2x cubed plus x squared minus 3x plus 1)

What is the average rate of change from x = −1 to x = 1?
−1
1
2
4

Answers

the answer to the question is 2


We have been given a polynomial [tex]f(x)=2x^{3} +x^{2}-3x+1[/tex] and we are asked to find average rate of  change from x = −1 to x = 1.

First of all we will find f(-1) and f(1).

[tex]f(-1)=2\cdot (-1)^{3} +(-1)^{2}-3(-1)+1[/tex]

[tex]f(-1)=2\cdot (-1) +1+3+1[/tex]

[tex]f(-1)=-2 +5=3[/tex]

Let us find f(1),

[tex]f(1)=2\cdot (1)^{3} +(1)^{2}-3(1)+1[/tex]

[tex]f(1)=2\cdot 1 +1-3+1[/tex]

[tex]f(1)=2+1-3+1[/tex]

[tex]f(1)=4-3=1[/tex]

Now let us find slope for our values.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{f(1)-f(-1)}{1-(-1)}[/tex]

[tex]m=\frac{1-3}{1--1}[/tex]    

[tex]m=\frac{-2}{1+1}[/tex]

[tex]m=\frac{-2}{2}=-1[/tex]

Therefore, average rate of change from our given x values will be -1.


write the standard form of the line that passes through the given point. include your work in your final answer. (-8,0) and (1,5)

Answers

We are given two points on the line. Using these points first we need to find the slope of the line.

The points are (-8,0) and (1,5). The slope(m) of the line will be:

[tex]m= \frac{5-0}{1+8} = \frac{5}{9} [/tex]

Using the slope and a point (-8,0) we can write the equation in point slope form as:

[tex]y-0= \frac{5}{9}(x+8) \\ \\ y= \frac{5x}{9} + \frac{40}{9} \\ \\ 9y=5x+40[/tex]

In standard form, the equation will be:

5x - 9y = - 40

The perimeter of a rectangle is 22 ft and the area is 24 ft what is the length and width

Answers

Length:8
Width:3
This is middle school not high school

The center of a circle is at (2, −5) and its radius is 12.

What is the equation of the circle?

(x−2)2+(y+5)2=144
(x+2)2+(y−5)2=144
(x+2)2+(y−5)2=24
(x−2)2+(y+5)2=24

Answers

The equation of the circle is given by (x-h)^2 + (y-k)^2 = r^2 where (h,k) represent the center of the circle and r represents the radius

From the question , we have been given (h,k) = (2,-5) and r =12

(x-2)^2 + (y-(-5))^2 = 12^2

The two minuses in the second term cancel out and give a plus. (-*- = +)

(x-2)^2 + (y+5)^2 = 144

So, the equation of the circle is:

(x-2)^2 + (y+5)^2 = 144 (Option A)


Could someone please help with this question!

Answers

I added a screenshot of the question

Part (A):
Since the two figure are similar, therefore, we will use the similarity proportionality to get the unknown side as follows:
[tex] \frac{16}{8} = \frac{x}{2} [/tex]

x = [tex] \frac{2*16}{8} = 4 units[/tex]

Part (B):
Since the two figures are similar, therefore, we will use similarity proportionality to get the unknown sides as follows:
[tex] \frac{y}{8} = \frac{12}{4} = \frac{18}{x} [/tex]

x = [tex] \frac{18*4}{12} = 6 units[/tex]

y = [tex] \frac{12*8}{4} = 24 units[/tex]

Hope this helps :)

Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?

Answers

147 candies -----70%
x candies     -----100%

x=(147*100)/70= 210
Total were sold 210 candies.

Emily sold 147 candles for a fundraiser. If she sold 70% of the total number of candles sold for the fundraiser, what is the total number of candles sold for the fundraiser?

Solution:

Candles Emily sold=70% of Total Number of Candles

Emily sold 147 candles.

So, We have,

147=70% of Total Number Of Candles

Let, Total Number Of Candles=x

147=70% of x

147=[tex] \frac{70}{100} [/tex] *x

147=[tex] \frac{70x}{100} [/tex]

Let us multiply by 100 on both sides

147*100=[tex] \frac{70x*100}{100} [/tex]

14700=[tex] \frac{70x*1}{1} [/tex]

14700=70x

To solve for x, Let us divide by 70 on both sides

[tex] \frac{70x}{70}=\frac{14700}{70} [/tex]

x=14700/70

x=210

Total Number of Candles=210

In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 3x – 1, and HE = 5y + 4. Find the values of x and y.

Answers

The diagonals of a parallelogram bisect each other.

DH = HF and GH = HE

x + 5 = 2y
3x - 1 = 5y + 4

Solve the first equation for x.
x = 2y - 5

Now substitute 2y - 5 for x in the second equation.

3(2y - 5) - 1 = 5y + 4

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute 20 for y in the first original equation.

x + 5 = 2y

x + 5 = 2(20)

x + 5 = 40

x = 35

Answer: x = 35 and y = 20

The values of x and y in parallelogram DEFG are:

x = 35y = 20

Given:

DH = HF and GH = HE

We have the following equations according to the given condition.

x + 5 = 2y ...(1)

3x - 1 = 5y + 4 ...(2)

From equation (1), we can express x in terms of y:

x = 2y - 5 ...(3)

Substitute this value of x in equation (2):

3(2y - 5) - 1 = 5y + 4

Simplify and solve for y:

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute y = 20 in equation (3) to find x:

x = 2(20) - 5

x = 40 - 5

x = 35

Therefore, the values of x and y in parallelogram DEFG are:

x = 35

y = 20

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The cost of gasoline is expected to increase by 2.5% next year. If p represents the current cost of gasoline, which experession represents the expected gasoline price next year?

Answers


[tex]y = x \times 0.025[/tex]

The perimeter of a rectangle is 108 inches. the rectangle is 34 inches long. how wide is it?

Answers


[tex] \frac{108 - 34 - 34}{2} [/tex]
= 20 inches

In a rectangle, there are 2 similar length measurements & 2 similar width measurements

Jason eats 10 ounces of candy in 5 days. a. How many pounds does he eat per day?
b. How long will it take Jason to eat 1 pound of candy?

Answers

A. He eats 1/8 a pound of candy each day.
B. It would take him a total of 8 days to eat a pound of candy.

A. Since he ate 10 ounces in 5 days, you divide 10 by 5 to find he ate 2 ounces per day. Since there are 16 ounces in a pound that would be your denominator (bottom of fraction) and 2 would be the numerator (top of your fraction). You will get 2/16 which if you simplify (divide by 2) you get 1/8.

B. Knowing that there are 16 ounces per pound and he ate 1/8 pound ( 2/16 pound or 2 ounces) a day, you can either look at the simplified denominator to get the answer, or, divide 16 by 2 to get your answer.

I hope this helps!

Two jets leave Dallas at the same time and fly in opposite directions one is flying west 50 mph faster than the other another two hours the Jets are 2500 miles apart find the speed of the jet

Answers

hope this helps............

Use the difference of squares theorem to find the solution of the following equation:

v^2 = 252

Answers

v^2 = 252
v^2 - 252 = 0
(v - sqrt252)(v + sqrt252) = 0

so the 2 solutions are sqrt252 and - sqrt252

=  15.87 and -15.87   to nearest hundredth.

please help but only answer if you're going to show work please!!!!

Answers

input h = - 2 into the expression

4[3(-2)  - 6]
---------------
  1 + (-2)

     4[-6  - 6]
= ---------------
      -1

     4[-12]
= ---------------
      -1

     -48
= ----------
      -1
= 48
To solve this problem you must apply the proccedure shown below:

 1. You have the following expression given in the problem above:

 4(3h-6)/(1+h)

 2. Then, if h is h=-2, you have to substitute this value into the expression given above, as below:

 4(3h-6)/(1+h)
 4(3(-2)-6)/(1+(-2))

 3. Then, you have
 4(-6-6)/(1-2)
 4(-12)/-1
 -48/-1
 48

write this as an equation in point-slope form Please answer as quickly as possible. 50 pts!!!!!


m=-3, (-2,1)

Answers


The answer is:   "  y − 1  =  - 3(x + 2) " .
__________________________________________________________

Explanations: 
__________________________________________________________

Note:  The "point-slope form" of the equation of a line is:

                  →     " y − y₁ = m(x −x₁) " . 

We are given the slope,  m" , is:  " - 3 " ;  

We are given a point on the line [on the graph that is represented by this equation];  with the coordinates:  " (-2 , 1) " ;  

                          →   which is in the format: " (x₁ , y₁) " ;
                                      
                          →   As such:  " x₁  = -2 "  ;   " y₁  =  1 " ; 
_____________________________________________________
As aforementioned, the equation of a line in "point-slope form" ;  is:  
_________________________________________________________
                          →    " y − y₁ = m(x − x₁) " ;  

in which:
 
 →  "(x₁ , y₁) " represents the coordinates of a given point on the [line of the graph represented by the equation] ;  AND: 

 →   " m "  =   the slope of the line [represented by the equation] " ; 

We proceed by substituting our known values for "m" ;  "y₁" ; and "x₁" :
 
 →       " y − 1  =  - 3(x − (-2) ) "  ;   
_______________________________________________________                                                        
 →   Rewrite as:
_______________________________________________________
 →      "  y − 1  =  - 3(x + 2) "  ;  

 →    which is our answer;  since it is written in "point-slope form" .
_______________________________________________________

20 POINTS!
Find P(4).
I don't know or understand how to do this.

Answers

its a 1 out of 8 chance to get 4 or a 0.125 chance in landing on it

The calculated value of the probability of 4

How to determine the probability of 4

From the question, we have the following parameters that can be used in our computation:

The spinner

Where, we have

Sections = 8

Also, we have

Sections that read 4 = 1

Using the above as a guide, we have the following:

P(4) = 1/8

Hence, the probability of 4 is 1/8

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A , O and B lie on a straight line segment

Evaluate x the diagram is not drawn to scale

Answers

we know that
if A , O and B lie on a straight line segment
then
∡AOY+∡YOZ+∡ZOB=180°
so
3x+x+x=180-----> 5x=180--------> x=180/5--------> x=36°

the answer is
x=36°

The value of x from the given diagram is; 36°

Sum of angles on a straight line.

The sum of angles on a straight line is 180°.

In this scenario, the sum of angles on the straight line: AOB is 180°.

Therefore, we have

3x + x + x = 180°

5x = 180

x = 36°

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A circle with the equation (x + 4)2 + (y - 3)2 = 9 is reflected over the line y = -1. What is the equation of the image?

(x - 2)2 + (y - 3)2 = 9
(x + 4)2 + (y - 5)2 = 9
(x + 4)2 + (y + 5)2 = 9
(x - 2)2 + (y + 5)2 = 9

Answers

The center of the given circle  = (-4, 3)
So the center of the image  = (-4, 3 -2(4)  =  (-4, -5)

So the equation of the image  is
(x + 4)^2 + (y + 5)^2 = 9

Its  choice 3.

The equation of the image circle is,

(x + 4)² + (y + 5)² = 9.

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Since, We know that;

After reflect a point over the line y = -1, we need to use the formula ;

(x,y) → (x, -y - 2).

Hence, We can apply this formula to each point on the circle and simplify to get the equation of the image circle:

(x + 4)² + (y - 3)²= 9

(x + 4)² + (-y - 2 - 3)² = 9

(x + 4)² + (y + 5)² = 9

So, the equation of the image circle is,

(x + 4)² + (y + 5)² = 9.

Therefore, the correct option is,

(C) (x + 4)² + (y + 5)² = 9.

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