Solve the following system of equations and show all work.

y=-x^2 + 4
y=2x+1

Answers

Answer 1

Answer:

Step-by-step explanation:

y = -x²+4 and y = 2x+1

Therefore,  -x²+4 = 2x+1

x²+2x-3 = 0

x = 1,-3

There are two solutions:

(1,3) and (-3,-5)

Solve The Following System Of Equations And Show All Work.y=-x^2 + 4y=2x+1
Answer 2

The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).

We have,

To solve the system of equations:

Set the expressions for y equal to each other:

-x² + 4 = 2x + 1

Rearrange the equation to bring all terms to one side:

-x² - 2x + 3 = 0

Solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we will use factoring.

Factor the quadratic equation:

(-x - 3)(x - 1) = 0

Set each factor equal to zero and solve for x:

-x - 3 = 0 or x - 1 = 0

Solve the first equation:

-x = 3

x = -3

Solve the second equation:

x = 1

Substitute the values of x back into one of the original equations to find the corresponding values of y.

For x = -3:

y = 2(-3) + 1

y = -6 + 1

y = -5

For x = 1:

y = 2(1) + 1

y = 2 + 1

y = 3

Therefore,

The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).

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Related Questions

1. Daniel rolls a 6-sided number cube 36 times. How many times should he expect to roll a 4?

A 9

B 4

C 6

D 10​

Answers

Im not sure but I think probably like 9 sorry if it’s wrong!
I think it’s 9 , correct me if I’m wrong

$750 loan 7% a year three years of no payments how much interest are you paying?

Answers

Answer:

$157.50

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year,

then, solving our equation

I = 750 × 0.07 × 3 = 157.5

I = $ 157.50

The simple interest accumulated

on a principal of $ 750.00

at a rate of 7% per year

for 3 years is $ 157.50.

(T & G) -> (E v D) what does this mean

Answers

Answer:

The work done by the electric field in Figure 1 to move a positive charge q from A, the positive plate, higher potential, to B, the negative plate, lower potential, is

W = −ΔPE = −qΔV.

The potential difference between points A and B is

−ΔV = −(VB − VA) = VA − VB = VAB.

Entering this into the expression for work yields W = qVAB.

Work is W = Fd cos θ; here cos θ = 1, since the path is parallel to the field, and so W = Fd. Since F = qE, we see that W = qEd. Substituting this expression for work into the previous equation gives qEd = qVAB.

The charge cancels, and so the voltage between points A and B is seen to be

{

V

AB

=

E

d

E

=

V

AB

d

(uniform E − field only)

Step-by-step explanation:

The relationship between V and E for parallel conducting plates is E=Vd E = V d. From a physicist's point of view, either ΔV or E can be used to describe any charge distribution

7.5 - 3.2 + 4³ ÷ 2

I NEED HELP PLIS :(​

Answers

Answer:

36.3

Step-by-step explanation:

Answer:

36.3

Step-by-step explanation:

Step 1: 7.5-3.2+2⁶÷2

Step 2: 7.5-3.2+2⁵

Step 3: 7.5-3.2+32

Step 4: 7.5-3.2+32

I need help please. Show your steps

Answers

Answer:

i dont know how anyone could answer this lol you're f u ck ed

Step-by-step explanation:

The fractions and decimals in order from least to greatest 7/48 0.5 0.75 9/16

Answers

Answer:

7/48,0.5,9/16,0.75

Step-by-step explanation:

Hope this helps

Help plz fast anyone‍help mee plzzzzzzzzzzzzzz

Answers

Answer:

It would take them 5 minutes

Step-by-step explanation:

640/4= 160 (this is how many words they can read per minute)

800/160=5 (doing this helps us figure out how long it would take them to read 800 words)

Answer:

I think its 5 I'm not sure tho.....

Step-by-step explanation:

640 Divide By 4 = 160

so 800 Divided By 160 = 5  

A letter home to the parents of seniors at Westgate High School says, "a simple random sample of 30 Westgate seniors that took the SAT-M test this year produced a mean of 512 and a standard deviation of 95. A confidence interval for the true mean for all WHS seniors is 512.00 ± 47.8." The confidence level for this interval is Group of answer choices

Answers

Answer:

It's 99%

Step-by-step explanation:

It just is.

A confidence interval for the true mean for all WHS seniors is 512.00 ± 47.8." The confidence level for this interval is 99%. The correct option is D.

What is the percentage?

The percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Divide the amount by the total value to get the percentage, then multiply the resulting number by 100.

Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Therefore, the correct option is D, 99%.

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The question is incomplete. Your most probably complete question is given below:

90%

92%

95%

99%

over 99.9%

PLEASE TELL ME HOW YOU DID IT I HAVE TO SHOW WORK !!!Jeans are on sale for 40% off. The jeans Justin wants to buy are marked with an original price of $80. What is the
total cost, in dollars, for a pair of jeans at the sale price, including a 7% tax?

Answers

Lamoooo

Step-by-step explanation:

Answer:

40% x $80.00 = $32.00

$32.00 x 7% = $2.24

Step-by-step explanation:

$2.24

How is the graph solution of 2x>10 different from the graph of the solution of 2x=10 ?

Answers

Answer:

the first one means that any number bigger than 5 whereas 2x=10 means that x can either be a positive or a negative value

Step-by-step explanation:

What is the equation of the given line? (-4,3) (2,-3)

Answers

Answer:

y=-x-1

Step-by-step explanation:

Y = -4x + 3
Y = 2x -3

Of people who died in the United States in recent years, 86% were white, 12% were black, and 2% were Asian. (This ignores a small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death is a white person who died of diabetes is about:____

Answers

Answer:

The probability that a randomly chosen death is a white person who died of diabetes is of 0.0241 = 2.41%.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: The person is white

Event B: Died of diabeters.

Of people who died in the United States in recent years, 86% were white

This means that [tex]P(A) = 0.86[/tex]

Diabetes caused 2.8% of deaths among whites

This means that [tex]P(B|A) = 0.028[/tex]

The probability that a randomly chosen death is a white person who died of diabetes is about:

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)*P(A) = 0.028*0.86 = 0.0241[/tex]

The probability that a randomly chosen death is a white person who died of diabetes is of 0.0241 = 2.41%.

What is x when 44x=78

Answers

X= 1.77
Hope this helps :)

Answer:

≈ 1.77

Step-by-step explanation:

So we are looking for x in 44(x) = 78.

All we have to do is isolate the variable, get x by itself.

Divide 44 by both sides :

[tex]\frac{44x}{44} = \frac{78}{44}[/tex]

[tex]x = 1.772727272723[/tex]

Which can be rounded to 1.77

What is the side of the square garden that has an area of 100
square feet?

Answers

I think it’s 10 I don’t know for sure


(3 + 2) (5-v2)
Expand and simplify

Answers

Answer:

25−5v2

oof oof oof oof oof oof oof oof

Please best awnswer gets brainliest

Answers

Answer: he was a stranger or a hunter

Step-by-step explanation: I think this because it says that they covered him with their muskets and muskets are obviously kind of gun, so it had to be a stranger or hunter.    hope this helped if not sorry

A triangle has sides with lengths of 7 yards, 8 yards, and 9 yards. Is it a
right triangle?

Answers

Answer:

No, it is not a right triangle.

Step-by-step explanation:

A right triangle will follow the Pythagorean Theorem: a² + b² = c²

c is the hypotenuse, or the longest side. In this case, it is 9.

That means a and b are 7 and 8.

Now let's plug in the values to see if they simplify correctly.

(7)² + (8)² = (9)²

Simplify the exponents.

49 + 64 = 81

Add the left side.

113 = 81

The above expression is not true; therefore, this triangle is not a right triangle.

Help me i will give best answer to correct answer.

Answers

Answer:

x=3 and y=3

Step-by-step explanation:

albert needs to make a grade of more than 90 to get an a in his math class

Answers

Yeah I’m just like Albert

Help please! Thank you!!

Answers

Answer:

alternate exterior angle is answer

Answer:

Angle 2 and angle 8 are alternative exterior angles

Mr. Kershner is a school nurse. He uses, on average, 24 self-adhesive bandages during each spring month: March, April, and May. He also knows that in June there are several field days and he will need 4 times the number of bandages for that month.

If the bandages cost 3 cents each, what is his total cost for March through June?

Answers

If the bandages cost 3 cents each,  Mr. Kershner's total cost for bandages from March through June is $5.04.

What is an arithmetic operation?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

The number of bandages used by Mr. Kershner in March, April, and May is 24 bandages each month, for a total of 24 x 3 = 72 bandages for those three months.

In June, he will need four times as many bandages as in the other months, for a total of 4 x 24 = 96 bandages.

The total number of bandages used from March through June is 72 + 96 = 168 bandages.

The cost of each bandage is 3 cents, so the total cost for 168 bandages is 168 x 3 = 504 cents, or $5.04.

Therefore, Mr. Kershner's total cost for bandages from March through June is $5.04.

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In horse racing, a trifecta is a type of bet. To win a trifecta bet, you need to specify the horses that finish in the top three spots in the exact order in which they finish. If eight horses enter the race, how many different ways can they finish in the top three spots

Answers

Answer: 336 different ways

Step-by-step explanation:

Ok, we have a total of 8 horses, and we have 3 places.

First, second, third.

The total number of combinations will be equal to the product of the number of possible options that we have in each place.

For the first place, we could have any of the 8 horses, so there are 8 possible options.

For the second place, we will have 7 horses (because one is already in the first place) then here we have 7 options.

For the third place, we will have 6 horses (because one is in the first place and another is in second place) then here we have 6 options.

The total number of different ways in which the horses can finish is:

C = 8*7*6 = 336 different ways

Find the values of x and y.

Answers

Answer:

x = 67

y = 169

Step-by-step explanation:

We know that (x-1) + 52 + (y-7) = 180 because they're all on the same straight line. We also know that x-1 = 66, because they are alternate interior angles.

Solve for x:

x-1 = 66

x = 67

Now solve for y:

(67-1) + 52 + (y-7) = 180

y = 169

A circus show started at 6:15 p.m and ended at 9:30 p.m. What was the duration of the show?

Answers

The duration of the show was 3 hours and 15 minutes.

I’m so confused, how do I do this?

Answers

Answer:

x = 14

Step-by-step explanation:

These angles are vertical each other, another way of saying they are opposite each other in an X. Since these angles are vertical, they are equal!

60 = 5x - 10 | Given, from here on is basic algebra

70 = 5x | Add 10 to both sides

14 = x | Divide both sides by 5

Can you help me on question nine?!

Answers

Answer:

B

Step-by-step explanation:

Unit rate means out of 1.

The one with 1 on the bottom is the unit rate

B

how do you expand (8+x) (9+x)

Answers

Answer:

x²+17x+72

Have a great day :)

a square flower garden in Samantha's backyard has an area of 100 square feet how much fencing will she need to enclose the flower garden​

Answers

Answer:

perimeter = 40 feet

Step-by-step explanation:

side^2 = 100

side = 10

perimeter = 10 x 4 =40

the value of a certain car after r years is modeled by the expression 150000.7t. What are the initial cost, I, and the rate of deprecation, r, of this car?

Answers

Answer:

74037.7t

Step-by-step explanation:

Pls help extra points and mark brainlist

Answers

Answer:

2 terms

8 and 4c

Step-by-step explanation:

Answer:

2 terms

Step-by-step explanation:

8 & 4c

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