The diagram below shows part of the graph of the equation y= the graph intersects the x-axis at the points. Find the value of a and the value of b. I'm not allowed to use the calculator and I need the process

The Diagram Below Shows Part Of The Graph Of The Equation Y= The Graph Intersects The X-axis At The Points.

Answers

Answer 1

The value of a and b are 11 and 14.

What is an equation on a graph?

The equation on a graph shows the point where the equation intersects

on the x-axis and the y-axis.

We have,

The function as y = 2x² + ax + b

Where it intersects on the x-axis at the points (-7/2, 0) and (2, 0).

Now we can write it as:

At point (-7/2, 0).

0 = 2 (-7/2)² + a(-7/2) + b

0 = 49 / 2 - 7a/2 + b

7a/2 - b = 49/2 _____(1)

At point (2, 0)

0 = 2(2)² + 2a + b

0 = 8 + 2a + b

2a + b = -8 _____(2)

From (1) and (2) we can find a and b.

From (1)

7a/2 - 49/2 = b

b = (7a - 49) / 2 ______(3)

putting in (2)

2a + (7a - 49) / 2 = -8

4a + 7a - 49 = -16

3a - 49 = -16

3a = -16 + 49

3a = 33

a = 11

putting in (3)

b = (7x11 - 49) / 2

b = (77 - 49) / 2

b = 28 / 2 = 14

Thus the value of a and b are 11 and 14.

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Answer 2

The value of a and b for the given equation is 3 and -14 respectively.

The given equation is y=2x²+ax+b, (-7/2, 0) and (2, 0).

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now put (-7/2, 0) and (2, 0) in the given equation and find a and b value.

That is, 0=2 (-7/2)²+a(-7/2)+b

⇒ 49/2 -7a/2+b=0 ----(I)

0=2(2)²+a(2)+b

⇒ 8+2a+b=0

⇒ b=-2a-8 -----(II)

Put b=-2a-8 in equation (I) and simplify.

That is, 49/2 - 7a/2 -2a-8=0

⇒ 49/2 - 11a/2 - 8 =0

⇒ 49 - 11a=16

⇒ 11a=33

⇒ a=3

Put a=3 in equation (II) and simplify.

That is, b=-2(3)-8=-14

Therefore, the value of a and b for the given equation is 3 and -14 respectively.

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Related Questions

In a high school, 28% of the school’s population is seventeen years old. Of the students who are seventeen years old, 44% play a sport. One student at the high school is chosen at random to represent the school at a community event. What is the probability that the selected student will be seventeen years old and not play a sport?

Answers

Answer:

15.68%

Step-by-step

Since 44% of the 28% play sport subtract 44 from 100 to see how many of the 28% do not play sports and you get 56%. So multiply 56% and 28% and you get 15.68%.

y=-0.72x + 7.7
Find y when x = 3.5.

Answers

Answer:

y = 5.18

Step-by-step explanation:

replace x in the equation with 3.5

y = -0.72x + 7.7

y = -0.72(3.5) + 7.7

y = -2.52 + 7.7

y = 5.18

Answer:

5.18

Step-by-step explanation:

Does anyone know the answer?

Answers

Answer:

cos57° = x/51

General Formulas and Concepts:

Trigonometry

[Right Triangles Only] sin∅ = opposite over hypotenuse [Right Triangles Only] cos∅ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to solve for the missing side length.

Step 2: Set up ratios

We can choose between the 2 angles and have multiple ratios to solve for x.

sin33° = x/51

cos57° = x/51

Hence, we see that the 1st option would be the correct answer.

Find the selling price of a suit if a store
paid $140 for it, and it was marked up 80%
over the cost.

Answers

I think you multiply 140 and 80% and then add thst to the 140

Answer:

$252

Step-by-step explanation:

The store paid $140 for the suit. Let's first find the 80% of $140.

$140 x 80% = $112

So now we just need to add $112 to $140.

$140 + $112 = $252

The endpoints of a diameter of a circle are (7,-4) and (-3,2).
What is the equation of the circle in standard form?

Answers

Answer:

Step-by-step explanation:

-21x - 8y = 0

URGENT!! Please i need to be done with this class by midnight!!
Pablo is riding his bike. The number of revolutions (turns) his wheels make varies directly with the distance he travels. See the graph below.(a) How many revolutions does Pablo make per foot of distance traveled? (b) What is the slope of the graph?

Answers

Answer:

A general line can be written as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

if we know that the line passes through the points (x1, y1) and (x2, y2), the slope will be:

a = (y2 - y1)/(x2 - x1)

In this case, we can see that the line passes through the points (0,0) and (4,2) then the slope will be:

a = (2 - 0)/(4 - 0) = 2

Then the equation is:

y = 2*x + b

And because we have the point (0, 0), we know that the y-intercept is equal to zero, then the equation is:

y = 2*x

This means that Pablo does 2 revolutions per feet, and we already found that the slope of the equation is 2.

5. Which image in the collage to the right is an
example of an object not doing work?
O A. climbing a rock wall
B. a water wheel in a dry river
C. kicking a soccer ball
D. carrying a bicycle down the stairs

Answers

Answer:

B. A water wheel in a dry river

Step-by-step explanation:

Work is said to be done when a force moves a body or an object through a certain distance in the direction of the force. Thus for work to be done, force and distance are required.

i.e Work done = Force x distance

It is measured in Joules.

Also, the work done by an object could be a measured of potential energy.

So that,

Work done = potential energy = mass x gravitational force x height

Considering the collage in the question, since the water wheel is in a dry river no work is done. Water wheel is a device that functions through the flow of water body, thus causing its rotation.

vegetable ghee is stored in the cylindrical vessel of internal radius 1.4m height 1.5m. if it is transferred into the rectangular tin cans 33cm * 10cm*5cm how many cans are required to empty the vessel

Answers

Answer:

5,598 cans are required to empty the vessel

Step-by-step explanation:

The volume of a cylinder of radius r and height h is:

[tex]V = \pi r^2h[/tex]

The volume of a box of dimensions X, Y, and Z is:

V=X.Y.Z

A cylinder of r=1.4 m and height h=1.5 is used to store vegetable ghee. It contains a volume of:

[tex]V_1 = \pi 1.4^2*1.5[/tex]

[tex]V_1=9.236\ m^3[/tex]

Converting to cubic cm:

[tex]V_1=9.236*1,000,000\ cm^3[/tex]

[tex]V_1=9,236,282\ cm^3[/tex]

The volume of each rectangular tin can is:

[tex]V_2=33*10*5=1,650\ cm^3[/tex]

[tex]V_2=1,650\ cm^3[/tex]

The number of cans required to empty the vessel is:

[tex]V_1/V_2=9,236,282/1,650 = 5,598[/tex]

5,598 cans are required to empty the vessel

PLEASE HELP FAST ILL GIVE BRAINLIST

At 10 m tall farmhouse is located 28.0 metres away from a tree with a an Eagles nest. The angle of the elevation from the roof of the farmhouse to the Eagles nest is 30
What is the height of the Eagles nest?

A 16m
B 24m
C 26m
D 48m

Answers

Answer:

26m

Step-by-step explanation:

opp represents the height of the nest from the angle of elevation,adj represents the distance of the farmhouse from the building . Therefore,according to Tan rule (TOA)

Tan30° = opp/adj

opp= tan30° x adj

opp= tan30° x adj

opp = 0.5774 x 28

0pp= 16.12m

the height of the eagle's nest from the ground = 16m + 10m(since the farm house is 10m tall)

the height ...= 26m

Is y=3 proportional?

Answers

Yes it is proportional

wait it is proportional

g(x)=−4x−4, find g(-2)g(−2)

Answers

Answer:

g(-2) = 4

Step-by-step explanation:

g(x)=−4x−4

Find g(-2)

This means let x = -2

g(-2)=−4(-2)−4

       = 8 -4

       = 4

Keenan hiked 15 times as far as Margot. How far did Keenan hike? Let m = the total number of miles

Answers

Keenan hiked 15 times as far as Margot. How far did Keenan hike? the total number of miles be m

The Keenan hike is measured in m is [tex]\frac{15m}{16}[/tex]miles.

The given parameters;

Keenan and Margot hiked m miles altogether.

Let the distance Margot hiked = n

Then, the distance Keenan hiked = 15n

The combined distance both hiked: m = n + 15n

Calculating Margot's hiked distance in terms of m is as follows:

m = n + 15n

m = 16n

n=[tex]\frac{m}{16}[/tex]

The calculation for Keenan's hike in terms of miles is

= 15(n)

=15[tex]\frac{m}{16}[/tex]

=[tex]\frac{15m}{16}[/tex]

Thus, the  distance hiked by Keenan in terms of m is [tex]\frac{15m}{16}[/tex]miles.

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If ray DB If ray DB is an angle bisector of

Answers

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

[tex]m∠ADB = \frac{1}{2} m∠ADC [/tex]

⟹[tex]8x - 3 = \frac{1}{2} \times 74[/tex]

[tex]8x - 3 = 37 ⟹8x = 37 + 3[/tex]

Divide both sides by 8 to find the value of x

[tex]x = \frac{40}{8} [/tex]

Therefore:

[tex]x = 5[/tex]

WILL MARK BRAINLIST ASAP Write an equation passing through the point and perpendicular to the given line (-2,-2); y= - 1/5x+9

Answers

Answer:

A line that is perpendicular to the x-axis is a vertical like with a slope equal to infinity. A line parallel to it would have the same slope and will also be a vertical line perpendicular to the x-axis. As the line passes through the point (2, -1) its equation is x = 2.

Step-by-step explanation:

please give brianliest

help!! A group of friends receives a dinner bill for $87.50. The sales tax rate is 5%.
How much is the bill with tax? Round to the nearest dollar. *

Answers

Answer:

$91.88

Step-by-step explanation:

$87.50 x 1.05 = $91.88

Answer:

87.50*1.05=91.875 simplify to nearest dollar. The answer is $92

Step-by-step explanation:

The cost y (in dollars) to rent a pickup truck is proportional to the number x of hours that the pickup truck is rented. It costs $100 to rent the truck for 4 hours. Write an equation that represents the cost to rent a pickup truck for x hours?

Answers

Answer:

Step-by-step explanation:D∧M a\\

* 16 points *. can somebody help me thanks

Answers

Answer:

b) [tex]\sqrt{10\\}[/tex]

Step-by-step explanation:

use law of sines to find all the sides and angles

If 3/4 pound of sugar makes 10 cakes, how much sugar, in pounds, is needed to make 1 cake?

Answers

Answer:

3/40 or 0.075 pounds

Step-by-step explanation:

If v 1 =(-2,5) and v 2 =(4,-3) , then the angle between the two vectors is Round your answer to two decimal places.

Answers

Answer:

-2.5, 4.-3

Step-by-step explanation:

I'm trying I hope this help's??

Find the angle between the vectors (5,-4) and (-7,3).
Round final answer to the nearest whole degree.
Angle =

Answers

Answer:

α = 164.5387822595581°

Step-by-step explanation:

Calculate dot product:

a · b = ax · bx + ay · by = 5 · (-7) + (-4) · 3 = - 35 - 12 = -47

Calculate magnitude of a vector:

|a| = ax2 + ay2 = 52 + (-4)2 = 25 + 16 = 41

|b| = bx2 + by2 = (-7)2 + 32 = 49 + 9 = 58

Calculate angle between vectors:

cos α =   a · b

|a|·|b|

cos α =   -47

41 · 58

 = -  47

2378

√2378 ≈ -0.9638111202541978

α = 164.5387822595581°

If you take a number multiply by 7 then takeaway 1. You get the same as if you took the number multiply by 5 then takeaway 8. What is the number?

Answers

7x - 1 = 5x - 8
Minus 5x on each side
2x -1 = -8
Plus 1 on each side
2x = -7
Divide by 2 on each side
x = -7/2

The number is most likely -7/2

Answer:

x = -3.5

Step-by-step explanation:

First we create the equation.

Let x = the unknown number

7x-1 = 5x - 8

Add 8 to both sides

7x + 7 = 5x

Subtract 7x

7 = -2x

Divide by 2

-7/2 = x

-3.5 = x

C
f
33 mi
44 mi
What is the length of the hypotenuse?
C =
miles

Answers

Answer:

The hypotenuse is 55 miles

Step-by-step explanation:

Given the sides of a right angle triangle as 33 and 44 miles, we want to get the hypotenuse

Mathematically, by Pythagoras’ theorem, the hypotenuse square is the sum of the squares of the other two sides

So we have;

h^2 = 33^2 + 44^2

h^2 = 3025

h = √3025

h =55 miles

pls help :( i’ll give brainliest

Answers

Answer:

x=12; Converse of conrresponding angles postulate

Step-by-step explanation:

On parrallel lines the corresponding angles are equal. To find x we can set up the equation up like this:

8x-17=5x+19

Solve

X=12

The converse used was the Converse of Corresponding Angles Postulate

solve by factoring

[tex]x^{4}+x^{3}-6x^{2}[/tex]

Answers

Think the answer is...

Lin and Han's families provide money for their school lunch accounts.
• Han starts with $100 in his account. He spends $15 each week on lunches.
• Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each
week to her account.
1. At the end of 4 weeks, who has more money in their account?
2. After how many weeks will Han and Lin have the same amount of money in their lunch
accounts?

Answers

Answer:

1. Lin

2. 3 weeks

Step-by-step explanation:

Lin has more money in his account, and after 3 weeks Han and Lin will have the same amount of money in their lunch accounts.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Han starts with $100 in his account. He spends $15 each week on lunches.

Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each week to her account.

For hen:

x be the number of weeks

Total amount left = 100 - 15x

Plug x = 4

Total amount left = $40

For Lin:

y be the number of weeks.

Total amount = 25 + 10y

Plug y = 4

Total amount = 25+40 = $65

Lin has more money in his account.

To have the same amount:

100 - 15x = 25 + 10y

x = y

100 - 15x = 25 + 10x

x = 3 weeks

Thus, Lin has more money in his account, and after 3 weeks Han and Lin will have the same amount of money in their lunch accounts.

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Find the total cost of a pair of shoes for $57 with a sales tax of 2%

Answers

Answer:

58.14

Step-by-step explanation:

57x.02=1.14

add that to 57 and get 58.14

Input Output
6 11
8 13
10 15
If the same rule is used, what is the output for the input of 20?
A. 12
B. 17
C. 25
D. 30

Answers

C.25 because 11-6 is five 13-8 is five and 15-10 is five so 25-20 is five

Please help! Almost done! thx

Answers

Answer:

c^2 = a^2 + b^2 - 2ab cos(C)

Step-by-step explanation:

The angle at A is named A, the angle at B is named B, and the angle at C is named C

The amount of calories you consume after eating x pieces of candy is represented by the function. y=135x. Find the domain of the function and determine whether it is discrete or continuous.

Answers

Answer:

The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

Step-by-step explanation:

Helppppppppppppppppppppppppppppppppppp

Answers

Answer:

the answer its 7^2 +7^3x5 its d hope helps you

Step-by-step explanation:

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