The graph of $y=ax^2+bx+c$ passes through points $(0,5)$, $(1,10)$, and $(2,19)$. Find $a+b+c$.

Answers

Answer 1

Answer:

[tex]a+b+c=10[/tex]

Step-by-step explanation:

We are given that the graph of the equation:

[tex]y=ax^2+bx+c[/tex]

Passes through the three points (0, 5), (1, 10), and (2, 19).

And we want to find the value of (a + b + c).

First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:

[tex]y=ax^2+bx+5[/tex]

Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:

[tex](10)=a(1)^2+b(1)+5[/tex]

Simplify:

[tex]5=a+b[/tex]

The point (2, 19) tells us that when x = 2, y = 19. Substitute:

[tex](19)=a(2)^2+b(2)+5[/tex]

Simplify:

[tex]14=4a+2b[/tex]

This yields a system of equations:

[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]

Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:

[tex]-10=-2a-2b[/tex]

Add the two equations together:

[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]

Combine like terms:

[tex]4 = 2a[/tex]

Hence:

[tex]a=2[/tex]

Using the first equation:

[tex]5=(2)+b\Rightarrow b=3[/tex]

Therefore, our equation is:

[tex]y=2x^2+3x+5[/tex]

Thus, the value of (a + b + c) will be:

[tex]a+b+c = (2) + (3) + (5) = 10[/tex]


Related Questions

Given m
II
n, find the value of x.
m
n
20
119°
Please help

Answers

x=119

hope it doesn't help you!!

Which table shows a proportional relationship between a and b?

Answers

Answer:

It is c

Step-by-step explanation:

Please help, explain too and I will give brainliest :)

Answers

Answer:

c

Step-by-step explanation:

Answer:

C. 37 degrees

Step-by-step explanation:

27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.

I'm sure you can do it with an actual formula, but i can't recall. Cheers

Which equation represents a line that passes through ( -2 , 4 ) and has the slope of 2/5

Answers

Answer:

y = 2/5x +24/5

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 2/5 x +b

Substitute the point into the equation and solve for b

4 = 2/5(-2)+b

4 = -4/5 +b

Add 4/5 to each side

20/5 +4/5 = b

24/5 = b

y = 2/5x +24/5

A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. By how much % more is the marked price above the cost price? ​
Give full explanation

Answers

Answer:

Let the MP of 1 article = Rs 1

MP of 15 article = Rs 15

SP of (15+1) articles = 15 x 96/100

= Rs 14.40

CP of 16 article = 14.40/135 x 100

= Rs 32/3

CP of 1 article = 32/3x16

= Rs 2/3

Required % = 1/3 x 3/2 x 100

= 50

Part B
Question
Type the correct answer in the box.
The y-intercept of the parent function, f(x), is
I
The y-intercept of the child function, g(x), is

Answers

Answer:

The y-intercept of the parent function, f(x), is 0

The y-intercept of the child function, g(x), is  7

Step-by-step explanation:

Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.

The solution is :

Vertex is (-2, 0)

y-intercept is 4.

What is vertex?

In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

here, we have,

to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':

f(x) = (x+2)^2 = x2 + 4x + 4

Then, to find the vertex, we can use the formula:

x_v = -b / 2a

x_v = -4 / 2 = -2

Now, finding the y_vertex, we have:

f(x_v) = (-2)^2 + 4*(-2) + 4 = 0

So the vertex is (-2, 0)

To find the y-intercept, we make x = 0 and then find f(x):

f(0) = 0 + 0 + 4 = 4

So the y-intercept is 4.

To learn more on vertex click:

brainly.com/question/12563262

#SPJ2

complete question:

Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².

vertex: ( ? , ? )

y-intercept: ?

Can someone please help, I'll give out 20 points !

Question - Where is the blue point on the number line?

Answers

I believe it would be negative three (-4) since the lines are thinner however; there is a chance they are skip counting by 2. In that case the answer would be negative six (-6).

Answer:

-6

Step-by-step explanation:

The number line is created by skip counting of 2.

So, -2 ,  then -4 and then -6.

So,  blue dotted point is (-6)

Graph the following equations by plotting 3 points and then connecting the points to form a line. Show your work to find the 3 points and then list the ordered pairs you used as part of your answer.

Answers

Answer:

The way I would tackle these types of problems would be to make a table, then graph the points using the results I get.

Step-by-step explanation:

So explaining the table is kinda hard since I suck at explaining, so I've attached a file showing the table I've made for number 1.

First Step:

Make the table. Make it a 3x4 table. For the top row, put y, the equation (I put 'y=2x' as shown in number 1), then x. Then for the left column, go down by one box, then put: -1, 0, 1. Really, you can put any numbers, but to make it easy for yourself, just write the numbers I've listed. These will be your y-values you'll be substituting.

Second Step:

a.) Plugging in the numbers. For the middle column, I've put down y=2x in each box, as shown in my table. Then for each of those boxes, plug in the numbers to the left of them and substitute them for the y-value. For example, look at the second row. The left box has '-1', so I replaced the 'y' in the equation and got '(-1)=2x'.

b.) After substituting the y-values, solve for x. For this case, you'll need to divide both sides by 2. If it doesn't make much sense, think about a seesaw. If you have 5 pounds on both sides, the seesaw will stay balanced. Add an additional 5 pounds to one side, then the seesaw will start tipping towards the heavier sides. So in order to keep an equation balanced, you must do any action to both sides of the equation. After diving both sides by 2, you'll get the value for x.

Final Step:

After finding the x-values for each of the y-values, it's time to graph the equations. Remember, x is left to right and y is down to up. To graph them, let's use the second row for example. y=-1 and x=-0.5. So all you need to do is to start from the origin (0,0), then go half a unit to the left, as x is negative, then go a unit down, as y is negative, then make a point. The rest should be pretty straight forward.

After making all three points, just get a ruler or any straight edge, then align it along those three points, then just make a line, and boom! You've solved number 1! For the purpose of saving my time, I'm pretty sure you can solve the rest using what I've just told you. Good luck!

Solve 7x + 1 < 4(x - 2).

A. {x | x > 3}
B. {x | x > -3}
C. {x | x < -3}
D. {x | x < 3}

Answers

SoLuTiOn☞

Given:- 7x + 1 < 4(x - 2)

Solving It:-

7x + 1 < 4(x - 2)

7x + 1 < 4x - 8

7x - 4x < -8 -1

3x < -9

x < -9/3

x < -3

So Correct Solution Set Will Be

C. {x | x < -3}

Hope This Helps You
So your answer is C hope this help

Given sin
=
=
V23 and tan o
find cos 0.
23
11 )
12
?
COS 0 =
TO

Answers

Answer: [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Use trigonometry (shown in image below) to find the 3 side-lengths:

The side opposite of θ = [tex]\sqrt{23}[/tex]The base side adjacent to θ = 11The hypotenuse = 12

According to right triangle trigonometry:

cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Substitute in the values:

cos θ = [tex]\frac{11}{12}[/tex]


Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If x+2 is a factor of x^3-6x^2-11x+k then k=

Answers

Answer:

k=10

Step-by-step explanation:

Brainliest please~

Answer:

K=10

Step-by-step explanation:

Correct on Plato

i will brainliest
avoid spam

Express each of the following percentages as a fraction and simplify it.

(i) 25% (ii) 40% (iii) 16% (iv) 150%

(v) 120% (vi) 58% (vii) 32% (viii) 175%

Answers

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]\sf{25\%=\dfrac{25}{100}=\dfrac{1}{4} }[/tex]

[tex]\sf{ 40\%=\dfrac{40}{100}=\dfrac{2}{5} }[/tex]

[tex]\sf{16\%=\dfrac{16}{100}=\dfrac{4}{25} }[/tex]

[tex]\sf{150\%=\dfrac{150}{100}=\dfrac{3}{2} }[/tex]

[tex]\sf{120\%=\dfrac{120}{100}=\dfrac{6}{5} }[/tex]

[tex]\sf{58\%=\dfrac{58}{100}=\dfrac{29}{50} }[/tex]

[tex]\sf{32\%=\dfrac{32}{100}=\dfrac{8}{25} }[/tex]

[tex]\sf{175\%=\dfrac{175}{100}=\dfrac{7}{4} }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\sf{ }[/tex]

[tex]\hookrightarrow\sf{ 25\% =\dfrac{25}{100}=\boxed{\bf \dfrac{1}{4} }} \\\hookrightarrow\sf{ 40\% =\dfrac{40}{100}=\boxed{\bf \dfrac{2}{5} }} \\\hookrightarrow \sf{16\%=\dfrac{16}{100}=\boxed{\bf\dfrac{4}{25}} } \\ \hookrightarrow\sf{150\%=\dfrac{150}{100}=\boxed{\bf\dfrac{3}{2} }} \\ \hookrightarrow\sf{120\%=\dfrac{120}{100}=\boxed{\bf\dfrac{6}{5} }} \\\hookrightarrow \sf{58\%=\dfrac{58}{100}=\boxed{\bf\dfrac{29}{50}} } \\\hookrightarrow \sf{32\%=\dfrac{32}{100}=\boxed{\bf\dfrac{8}{25} }} \\ \hookrightarrow\sf{175\%=\dfrac{175}{100}=\boxed{\bf\dfrac{7}{4}} } \\ [/tex]

Whats his mistake and the correct awnser

Answers

Answer:

θ ≈ 35.7°

Step-by-step explanation:

His mistake was in using the wrong trig. ratio

Instead of using cosine he should have used the sine ratio

sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then

θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )

what is the solution to this equation?
5x-4+3x=36

A. x=16
B. x=5
C. x=20
D. x=4

Answers

B. x = 5

tip : if in a rush just plug in the number and see if its true

8x - 4 = 36

x = 5

Which of the following represents x = 1/3y written in general form?
3x - y = 0
X-1/3y=0
1/3x-y=0

Answers

Answer:

x-⅓y=0

Step-by-step explanation:

thats the answer

brainly please

Answer: 3x-y=0

Step-by-step explanation:

X = 1/3y

X × 3 = 1/3 y × 3

3x = y

3x - y = y- y

3x- y = 0

PLEASE HELP URGENTLY!!

Answers

Answer:

x = 69

Step-by-step explanation:

since AB is parallel to CD we can find the value of y with the following equation :

2y - 40 = 66 add 40 to both sides

2y = 110 divide both sides by 2

y = 55

from supplementary angles, we know that the exterior angle's measure is 124

since the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle

y + x = 124 we found value of y earlier

55 + x = 124 subtract 55 from both sides

x = 69

4. (03.05)
The graph shows the production of cars per day at a factory during a certain period of time. What is the domain of this function during this period? (1 point)



The domain is all real numbers o through 9.
The domain is all integers o through 9.
The domain is positive real numbers.
The domain is all positive integers.

Answers

Answer:

B. domain is all integers 0 through 9

Step-by-step explanation:

Domain values area usually plotted along the horizontal axis. In this case, the number of days is the domain of the of the function.

The domain of the function that is plotted on the graph ranges from 0, 1, 2 to 9.

1, 2, 3 to 9 are all integers. Therefore, we can conclude that the "domain is all integers 0 through 9."

The slope of a line is 5/9 and the slope of another line is -975. The two lines
are

Answers

Answer:

the third option - they are perpendicular to each other.

Step-by-step explanation:

for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.

and that is exactly what happened here.

What is value of x if 20x-10*110=50

Answers

Answer:

57.5

Step-by-step explanation:

20x - (10 x 110) = 50

=> 20x - 1100 = 50

=> 20x = 1150

=> x = 1150/20

=> x = 115/2

=> x = 57.5

No idea how to do

[tex]\frac{4r + 20}{r + 5}[/tex]

when r ≠ 5 ?

Answers

Factorize the numerator:

4r + 20 = 4r + 4×5 = 4 (r + 5)

I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:

(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4

Diego's family truck holds 21 gallons of fuel. Each day the car uses 1.5 gallons of fuel. A warning light comes on when the remaining fuel is 2.5 gallons or less. Starting from a full tank, can Diego's family drive the car for 10 days without the warning light coming on? Explain or show your reasoning. Starting from a full tank, can Diego's family drive the car for 15 days without the warning light coming on? Explain or show your reasoning. Diego says the expression 21 - 1.5t helps him understand this situation. In this situation, what does this expression represent, and what does the variable t stand for? Write and solve an equation to determine the number of days Diego's father can drive the car without the warning light coming on. Write and solve an inequality that represents the number of days driven without the warning light coming on. Explain clearly what the solution to the inequality means in the context of this situation

Answers

Answer:

The inequality is 0.6x < 12.5

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Step-by-step explanation:

14 gallons-1.5 gallons=12.5 gallons    

we know that  

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on    

so  

Let  

x ----> the number of days

0.6x < 12.5 inequality that represent the situation  

Solve for x

x < 12.5/0.6

x < 20.8 days

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Does this graph show a function? Explain how you know.

Answers

Answer:

A is the correct one

cause according to function rule the vertical line should cut only on a one point to be function

as here we can see that vertical line cuts here at two point



A house has increased in value by 28% since it was purchased. If the current value is $288,000, what was the value when it
was purchased?

Answers

Answer:

$368,640

Step-by-step explanation:

288,000 * .28 = 80640

288,000 + 80640 = 368640

Can Anyone please tell me How to Multiply 18√2×18√2...
Please show steps aslo..​

Answers

Answer:

648

Step-by-step explanation:

18√2×18√2= (18√2)²

                  = (18)²×(√2)²

                  = 324×2

                  = 648

Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?

1/9
9
-9
-1/9

Pls answer​

Answers

Answer:

[tex]\boxed{\sf a = 9 }[/tex]

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

[tex]\sf\longrightarrow 3x - 2y +7=0 [/tex]

[tex]\sf\longrightarrow 6x +ay -18 = 0 [/tex]

Step 1 : Convert the equations in slope intercept form of the line .

[tex]\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}[/tex]

and ,

[tex]\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a} [/tex]

Step 2: Find the slope of the lines :-

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

[tex]\sf\longrightarrow Slope_1 = \dfrac{3}{2} [/tex]

And the slope of the second line is ,

[tex]\sf\longrightarrow Slope_2 =\dfrac{-6}{a} [/tex]

Step 3: Multiply the slopes :-

[tex]\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1 [/tex]

Multiply ,

[tex]\sf\longrightarrow \dfrac{-9}{a}= -1[/tex]

Multiply both sides by a ,

[tex]\sf\longrightarrow (-1)a = -9 [/tex]

Divide both sides by -1 ,

[tex]\sf\longrightarrow \boxed{\blue{\sf a = 9 }} [/tex]

Hence the value of a is 9 .

pls help me solve this multiplication fractions. (show work)​

Answers

Answer:

32:3/4

33:4/3

34:40

35:48

Answer:

32. 3/4
33. 4/3
34. 40
35. 384/7

Step-by-step explanation:

32. 9/10 • 5/6

Multiply 9 x 5/10 x 6

9 x 5/10 x 6 = 45/60

Then simplify 45/60 “by factoring out 45 and 60 and finding the Greatest Common Factor (GCF)”

45/60 = 3/4

•••••••••••••••••••••••••••••••••••••••••••••••••••

33. 16/21 • 7/4

Multiply 16 x 7/21 x 4

16 x 7/21 x 4 = 112/84

Then simplify 112/84 “by factoring out 112 and 84 and finding the Greatest Common Factor (GCF)”

112/84 = 4/3

•••••••••••••••••••••••••••••••••••••••••••••••••••

34. 8 4/7 • 4 4/6

Multiply 7 by 8 and add 4

7 x 8 + 4 = 60

Then add the denominator back

60/7

Multiply 6 x 4 and add 4

6 x 4 + 4 = 28

Then add the denominator back

28/6

We’re left with 60/7 • 28/6

Multiply 60 x 28/7 x 6

60 x 28/7 x 6 = 1680/42

Then simplify 1680/42 “by factoring out 1680 and 42 and finding the Greatest Common Factor (GCF)”

1680/42 = 40

••••••••••••••••••••••••••••••••••••••••••••••••

35. 7 4/8 • 6 2/5

Multiply 8 by 7 and add 4

8 x 7 + 4 = 60

Then add the denominator back

60/7

Multiply 5 x 6 and add 2

5 x 6 + 2 = 32

Then add the denominator back

32/5

We’re left with 60/7 and 32/5

Multiply 60 x 32/7 x 5

60 x 32/7 x 5 = 1920/35

Then simplify 1920/35 “by factoring out 1920 and 35 and finding the Greatest Common Factor (GCF)”

1920/35 = 384/7

••••••••••••••••••••••••••••••••••••••••••••••••

please mark me as brainliest! This took me effort

what would be the u to usub and what would be the steps to solving this integral?

Answers

Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).

Then substituting u = ln(x) and du = dx/x gives

[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]

63.89 X n = .6389 Solve for n *
A. 10
B. 100
C. .01
D. .1

Answers

Answer:

c. .01

Step-by-step explanation:

.6389 divided by 63.89

(C)
63.89*n=.6389

.6389/63.89=n
0.01=n

Work out the circumference of this circle 7.5

Answers

Answer:

47.12

Step-by-step explanation:

C=2πr=2·π·7.5≈47.12389

Sameera purchased 3 (1/2) kg of apples and 4 (3/4) kg of oranges. What is the total weight of fruits purchased by her ?

Answers

Answer:

8 1/4 kg

Step-by-step explanation:

Add the weight of the fruits together

3 1/2 + 4 3/4

Get a common denominator of 4

3 2/4 + 4 3/4

7 5/4

7 4/4 + 1/4

8 1/4 kg

Other Questions
a concave mirror has a radius of curvature of 60cm. How close to the mirror should an object be placed so that the rays travel parallel to each other after reflection How do you reach enlightenment in Buddhism?A. Through reincarnationB. Through warC. Through tradeD. Through meditation a letter about the good result of truthfulness How would you describe the narrator, Junior Polatkin? (Choose all answers that apply)DynamicFlatStaticRound Can someone please help solve this equation thank you PLZ HELP!! ASAP PLZ!! NO FILES. InstructionsCreate a multimedia project that contains the text element and all the contents that you have studied about that element Solve for p.19p2p+16p+12=18p= in 16 years, Marissa will be five times older than she is today. How old is she? What is | 34 | ?-------l l-------l l-------- Damaged items are marked down 25% to 40%. A newspaper coupon holder; to an additional 10% markdown of the new price due to the damage. What is the lowest price of a damaged item that was originally marked GHC100? A GHC 35.60 B GH 5000 C. GHC 18.00 D. GHC 40.80 E GHC 23.40 An individual taxpayer reports the following items for the current year: Ordinary income from Partnership A, operating a movie theater in which the taxpayer materially participates $70,000 Net loss from Partnership B, operating an equipment rental business in which the taxpayer does not materially participate (9,000) Rental income from building rented to a third party 7,000 Short-term capital gain from sale of stock 4,000 What is the taxpayers adjusted gross income for the year? NEED HALP!!! Find the ordered pair $(s,t)$ that satisfies the system The midpoint of has coordinates of (4, -9). The endpoint A has coordinates (-3, -5). What are the coordinates of B? The majority of immigrants that entered the United States during the industrial age came from Most of the heat loss for outdoor swimming pools is due to surfaceevaporation. So, the greater the area of the surface of the pool, the greaterthe heat loss. For a given perimeter, which surface shape would be moreefficient at retaining heat: a circle or a rectangle? Justify your answer. Please whoever knows they can solve this, help!I have attached the question down below. Please explain in detail and diagrams if the question permits you to do so. Thank you. I will also be marking the brainiest. Write 5 examples of Declarative sentences, exclamatory, interrogative, and imperative sentences. Which of the following statements is true?a. Overhead can be applied slowly as a job is worked on.b. Overhead can be applied when the job is completed.c. Overhead should be applied to any job not completed at year-end in order to properly value the work in process inventory. A project has an expected risky cash flow of $500 in year 3. The risk-free rate is 4%, the expected market rate of return is 14%, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 3, CEQ3. (Assume CAPM holds.)