work out the coordinates of the points of intersection of the graphs
y= 4x^2+8x+3 and y=x+5
Answer (_____,_____) and (______,______)

Answers

Answer 1

Step-by-step explanation:

The point of intersection occurs when the two graphs have equal values of  x and  y at the same time. There is only one solution, because two straight lines can only intersect once.

[tex]y =4x^2 + 8x + 3 , y = x + 5\\\\4x^2 + 8x + 3 = x +5\\\\4x^2 + 8x + 3 -x -5 = 0\\\\4x^2 +7x -2 =0\\\\4x^2 + 8x -x - 2 = 0\\\\4x(x + 2) -1(x+2) = 0\\\\(4x - 1)(x+2) =0\\\\4x -1 = 0 , x+2 =0\\\\x = \frac{1}{4}, -2[/tex]

[tex]x_1 = \frac{1}{4}, x_2 =-2[/tex]

[tex]y_1 = 4x^2 + 8x + 3 \\\\x_1 = \frac{1}{4}\\\\y_1 = 4(\frac{1}{4})^2 + 8(\frac{1}{4}) + 3 = \frac{1}{4} + 2 + 3 = \frac{1}{4} +5 = \frac{21}{4}\\\\y_2 = x+ 5\\x_2 = -2\\y_2 = -2 + 5 =3[/tex]

Answer :

[tex](x_1, y_1) = (\frac{1}{4} , \frac{21}{4})\\\\(x_2,y_2) = (-2, 3)[/tex]

Answer 2

Answer:

(- 2, 3 ) and ([tex]\frac{1}{4}[/tex], [tex]\frac{21}{4}[/tex] )

Step-by-step explanation:

Given the 2 equations

y = 4x² + 8x + 3 → (1)

y = x + 5 → (2)

Substitute y = 4x² + 8x + 3 into (2)

4x² + 8x + 3 = x + 5 ( subtract x + 5 from both sides )

4x² + 7x - 2 = 0 ← in standard form

(x + 2)(4x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

4x - 1 = 0 ⇒ 4x = 1 ⇒ x = [tex]\frac{1}{4}[/tex]

Substitute these values into (2) for corresponding values of y

x = - 2 : y = - 2 + 5 = 3 ⇒ (- 2, 3 )

x = [tex]\frac{1}{4}[/tex] : y = [tex]\frac{1}{4}[/tex] + 5 = [tex]\frac{21}{4}[/tex] ⇒ ([tex]\frac{1}{4}[/tex], [tex]\frac{21}{4}[/tex] )


Related Questions

On a hike, Oscar's elevation change after 12 minutes was-84 feet. Assuming his elevation was changing at a constant rate, what integer represents his elevation change per minute?​

Answers

Answer: -7

Step-by-step explanation:

From the information given, we are.l told that Oscar's elevation change after 12 minutes was -84 feet.

Since his elevation was changing at a constant rate, his elevation change per minute will be:

= -84 feet / 12

= -7feet/minutes

Therefore, the integer is -7.

Marty and Ethan both wrote a function, but in different ways.

Answers

Answer:

what did their functions look like?

Step-by-step explanation:

Answer:

Marty and Ethan both wrote a function in a different way.

Step-by-step explanation:

They both wrote a function.

A farmer is fencing off his field. A diagram is given and shows how the field has been divided into two regions. Find the perimeter of the entire field. Reaction 1 has length 530 feet and width 526 feet. Region 2 has length 974 feet and width 526 feet. a. 2556 ft c. 4052 ft b. 4060 ft d. 5112 ft

Answers

Answer:

the answer is B 4060 ft

Step-by-step explanation:

the answer is B have a nice day

Angle J and angle M are base angles of isosceles trapezoid JKLM. If angle J= 15x+9 and angle M=9x+15 find K

Answers

Answer:

156°

Step-by-step explanation:

To solve this problem, we first use the relation

15x + 9 = 9x + 15, on collecting like terms, we have

15x - 9x = 15 - 9

6x = 6

x = 1

And if x is equal to 1, then the base angles are 15 + 9 which is 24°.

And finally, to find k, we subtract the calculated angle from 180 and thus

180 - 24 = 156°

What is the volume of the rectangular prism?

Answers

V=whl which mean length,weight,height


In 3 hours, Fast Eddy performed 21 663 loops with his yo-yo. How manyloops could he do in 8 hours at this rate?
57 768
58 738
59 348
56 588

Answers

Answer:

58 738

Step-by-step explanation:

Hope this helps!

Answer: 57 768

Step-by-step explanation:

None needed you'll thank me later

Which describes the number and type of roots of the equation x^3 + 121x = 0?
a. 2 real roots, 1 imaginary root
b. 1 real root, 2 imaginary roots
c. 3 real roots
d. 3 imaginary roots

Answers

Answer:

b; 1 real root and 2 imaginary roots

Step-by-step explanation:

From here, we have

x(x^2 + 121) = 0

x = 0 (1 real root)

or

x^2 + 121 = 0

x^2 = -121

x = √(-121) (2 imaginary roots)

so is would be two complex numbers from above

Factorise the following:
a) x – 5x - 6
b) x + 3x – 40
C) - 7x - 30

Answers

Answer:

-4x-6

4x-40

-7x-30

Step-by-step explanation:

Evaluate 2^5 divides 4^2

Please answer ASAP. 50 points. No files/doc

Just explanation and answer

Answers

i have no idea i’m sorry

Answer:

2

Step-by-step explanation:

2^5/4^2

32/4^2

32/16

2

I did bad but what's the answer for this?

Answers

Answer:

28 degrees

Step-by-step explanation:

A triangle is always equal to 180 degrees so add the degrees together

40+2x+3x=180

40+5x=180

5x/5=140/5

x=28

David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

Answers

Answer:

Step-by-step explanation:

The function for this problem is: h(t) = -16(t)^2 + vt + s h= the height t= time v= velocity s= starting height With the information given, we know that the starting height is 0, since it was from the ground, and the velocity of the ball is 35 feet per second. Inserting the these information into the equation, we get: h(t) = -16(t)^2 + 35t Now the question asks to find the maximum height. It can be done by using a grapher to graph the maximum of the parabola. It could also be done by finding the vertex, which would be the maximum, of the graph by using x= -b/(2a), where b is equal to 35 and a is equal to -16. We get x=35/32, the x-value of where the vertex lies. You can use this value as the t-value in the previous equation to find the h-value of the vertex. When you do, you get h= 19.1 feet, or answer D.

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Answers

Answer:B hope this helps! :D

Step-by-step explanation:

help me please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

?

Step-by-step explanation:

with what

Answer:

120

Step-by-step explanation:

I got 120 because the width of the diamonds are 30. (180 - 150)

We can make sure that is correct by checking all the other pyramids.

anyways, we have 30 60 90 120 150 for all our pyramids. So the answer is indeed

120

Gia wants to go skating and needs to figure out which place offers a better deal. Roller haven charges a one-time rental free of $10 and charges $3 per hour to skate. Paradise skate charges a one-time rental free of $5 and charges $4 hour per to stake. Write a system of equations that describes the situation.

Answers

The system of equations would be:

3x+10
4x+5


Is this the right answer?

Answers

Answer:

yes

Step-by-step explanation:

10 is half of 20 but the equation is 11/20 therefore 11/20 is greater than 10/20=1/2

help will give brainlist if right!!!!

Answers

Are you taking the state test-

What is the volume of this rectangular prism? 1/2, 4, 3/2

Answers

I’m guessing that the answer is 3
( I don’t see anything)

1. Determine the value of x.
Please help

Answers

Answer:

55..........................

7. James has a bag of 200 candies. Suppose he chooses without looking. There is a 25% chance that he will get a jolly rancher. How many jolly ranchers are in the bag. Explain your thinking.

Answers

Answer:

50 candies

Step-by-step explanation:

since there are 200 in total and there is a 25% chance of getting one, I multiplied 0.25×200.

Hope this helps

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Answers

Answer:

Step-by-step explanation: Finding the height can be solved using a simple formula using the length of the base and the area. You should multiply length times area! hope this helps.

Karina’s paycheck stub had several items listed on it. Which of these items listed on her paycheck is not a deduction?

federal taxes
Social Security
tuition reimbursement
Medicare tax

Answers

Answer:I believe it’s tuition reimbursement edge 21

Step-by-step explanation:

The length of three sides of a triangle are 12, 35 and 37 centimeters. Determine whether the triangle is a right triangle. Show your calculations to support your answer.

Answers

Answer:

it is a right triangle

Step-by-step explanation:

confirm if it is a right triangle using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

12² + 35²

144 + 1225 = 1369

square toot of 1369 is 37

so

12² + 35² = 37²

ILL BRAINLIEST YOU AND GIVE YOU 20 EXTRA POINTS IF YOU GET IT RIGHT PLEASE HELP ME

Answers

Answer:

A=(0,2)

B=(2,0)

C=(0,-2)

D=(-2,0)

Step-by-step explanation:

tbh I think iw

Slide left or right first, then go up and down

horizontal then vertical

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which of these expression is equivalent to -2(3-y)​

Answers

[tex]( - 6 + 2y)[/tex]

answer the question

1

Which descriptions apply to a coordinate plane? Choose more

than one answer.


Cartesian plane


Two-dimensional


Three-dimensional


Extends forever


Perpendicular axes


Parallel axes

Answers

The descriptions that apply to a coordinate plane are:

a) Cartesian plane

b) Two-dimensional

d) Extends forever

e) Perpendicular axes.

The descriptions that apply to a coordinate plane are:

Cartesian plane: A coordinate plane is often referred to as a Cartesian plane, named after the mathematician René Descartes, who introduced the concept of using coordinates to represent points in space.

Two-dimensional: A coordinate plane is a two-dimensional space where points are represented using two perpendicular axes (usually labeled as x-axis and y-axis).

Extends forever: The coordinate plane extends infinitely in all directions along the x-axis and y-axis, allowing representation of points with arbitrary coordinates.

Perpendicular axes: The two axes in a coordinate plane are perpendicular to each other, intersecting at the origin (0, 0). The x-axis is horizontal, and the y-axis is vertical.

The description "Three-dimensional" does not apply to a coordinate plane. A coordinate plane is a two-dimensional space, and it does not have a third axis to represent points in three dimensions.

In a three-dimensional space, you would need an additional axis (usually labeled as z-axis) perpendicular to the x-axis and y-axis to represent points in three dimensions.

Hence, The descriptions that apply to a coordinate plane are:

a) Cartesian plane

b) Two-dimensional

d) Extends forever

e) Perpendicular axes.

learn more on coordinate plane :

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Answers

Answer:

MEAN 5.8 add all the points up then divide by the number of dots

MEDIAN 5 the middle of the data

MODE 5 most accruing one

RANGE 7 maximum minus minimum

Given sin= 3/5 find cos

Answers

Answer:

Step-by-step explanation: you have to use a caculator this is very similar to log you type in Sin as 3/5 then you will divide by cos then you have your answer

Select the ordered pairs that are part of the
solution set of this system of inequalities.

Answers

Answer:

ye boy

Step-by-step explanation:

Answer:

the second one, I asked my Kids.


ASAP!!!!!!!!!!!!!!!

Answers

Answer:

A, or 33,439.99

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 15,600.00(1 + 0.1/1)(1)(8)

A = 15,600.00(1 + 0.1)(8)

A = $33,439.99

16 x -4 =
(need process)

Answers

Answer:

-64

Step-by-step explanation:

-16+-16+-16+-16=-64

Answer:

[tex] - 64[/tex]

Step-by-step explanation:

Ignore any negative sign for now.

[tex]16 \times 4[/tex]

Use the algorithm method.

1 6

× 4

______

6² 4

Now consider the signs. One number is positive, and the other number is negative. Therefore, the result will be negative.

[tex]16. \: - 4 = > negative[/tex]

Therefor, 16 × -4 = -64

[tex] - 64[/tex]

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