How many solutions does y=-x^2-4x+7 have

Answers

Answer 1

Answer:

x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Step-by-step explanation:

Solve for x:

y = -x^2 - 4 x + 7

y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:

-x^2 - 4 x + 7 = y

Multiply both sides by -1:

x^2 + 4 x - 7 = -y

Add 7 to both sides:

x^2 + 4 x = 7 - y

Add 4 to both sides:

x^2 + 4 x + 4 = 11 - y

Write the left hand side as a square:

(x + 2)^2 = 11 - y

Take the square root of both sides:

x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2


Related Questions

Mr Cole made this diagram of his bedroom. Which is the area of Mr. Cole's bedroom?
10 ft
5 ft
4 ft
8 ft
A 90 square feet
B 82 square feet
c 72 square feet
D 36 square feet

Answers

The answer is 72 square feet

Answer:

B

Step-by-step explanation:

area =area of full shape - area of B

=10×9-4×2

=90-8

=82

What is the volume of this rectangular prism?

Answers

Answer:  5/8 cm^3

Step-by-step explanation:

V = l x w x h

l = 3/4 cm

w = 1/3 cm

h = 5/2 cm

V = (3/4 cm) x (1/3 cm) x (5/2 cm) = 15/24 cm^3 = 5/8 cm^3

Harry and Jenny are going to the movies. They each bought a medium popcorn, and Harry got a small soft drink. Jenny had a $4 coupon as a discount, and Harry paid the rest, which came to $23. A movie ticket costs $8, and a medium popcorn costs $4.50. What was the cost for a soft drink?

Answers

Answer:

2$

Step-by-step explanation:

2 medium popcorns = 9$

2 Movie tickets = 16$

One coupon = -4$

This is equal to the cost without the soft drink(21$)

23$ - 21$ = 2$

Answer:

$2

Step-by-step explanation:

It was originally $27 but, Jenny used a $4 coupon. Each movie ticket costs $8, each popcorn cost $4.50.

1. Start from the cost of each item.

8+8=16 (cost of the tickets)4.50+4.50=9 (cost of the popcorn) .

2. Add the totals together.

16+9+ 25

Now subtract 25 from the original amount.

27-25=2

It costs 2 dollars for a soft drink.

The ratio of boys to girls in Mr. Jordan's soccer team is the same as the ratio of boys to girls on Ms. Grolin's soccer team. There are 12 boys and 4 girls in Mr. Jordan's team. There are 9 boys on Ms. Grolin's team. How many girls are on Ms. Grolin's team? A. 2 B.3 C.4 D.6

Answers

Answer:

B

Step-by-step explanation:

Ms. Jordan's girls are divided by 3 than the girls. 12 ÷ 3 = 4

Same with Ms. Grolin. 9 ÷ 3 = 3. The answer is B.

!!20 POINTS!!
What are the names of three collinear points?

Answers

Answer: L, J, K

Step-by-step explanation:

L, J, and K are collinear because they all lie on the same line.

Mr. Alfred’s car gets 12 miles per gallon. He drives to West Harlem for a weekend to visit his grandmother. He uses 6 gallons of gas. How many miles did he drive?

Answers

Answer:

72 miles.

Step-by-step explanation:

If he uses 6 gallons of gas, you would do 6 (gallons he used) x 12 (miles per gallon) equaling 72.

In February, Paul's electric bill was three dollars more then one-half his gas bill. If the electric bill was ninety-two dollars, what was the gas bill?

Answers

Answer:

49$

Step-by-step explanation:

Bryan has a prepaid cell phone with a balance of $75. He is charged the same rate per minute. Which function represents the balance on the phone after (n) minutes?

Answers

Answer:

36 minutes

Step-by-step explanation:

i have a different saying this so dont get mad

Julio is payed 1.2 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 40 hours and earned $495.60 enter and solve an equation to find julios hourly rate, r. Complete the explanation how you know that your answer is reasonable

Answers

Answer: $10.33

Step-by-step explanation:

Given: Julio is payed 1.2 times his normal hourly rate for each hour he works over 30 hours in a week.

Last week he worked 40 hours ( > 30 hours by 10 ) and earned $495.60.

Let r = Julio's hourly rate

if he worked over 30 hours in a week, then hourly rate = 1.2r

According to the question

[tex](1.2r)\times 40=495.60\\\\\Rightarrow\ r=\dfrac{495.60}{1.2\times 40}\\\\\Rightarrow\ r=10.325\approx10.33[/tex]

Hence, his hourly rate = $10.33

Solve the compound inequality 2.1 – 3 < 7 and 5 - 3 < 8

Answers

Step-by-step explanation:

2.1--3<7.

--0,9<7

true

5--3< 8

2<8

true

write the mixed number 11 1/6 as a decimal​

Answers

Answer:

11.1667

Step-by-step explanation:

11 1/6

11*6+1

=67/6

=11.1666666666

=11.1667

rote x+18=x-2 what is the answer

Answers

Answer:

no solution

Step-by-step explanation:

Given

x + 18 = x - 2 ( subtract 18 from both sides )

x = x - 20 ( subtract x from both sides )

0 = - 20 ← not possible

This indicates the equation has no solution

Solve for the equation for x 3x+y/=2

Answers

Answer: x= 2/3 - 1/3y


Explanation step by step:

Step 1: Move variable to the right hand side and change its sign.

3x = 2-y

Step 2: divide both sides of the equation by 3.

x= 2/3 - 1/3y

the diving distance between manchester and london is 195 miles faris inteneds to travels from manchester to london by coach the coach will leave manchester at 3.30 pm faris assumes that the coach will travel at an average speed of 50 mph work out farris arrival time in london

Answers

Answer:

Faris' arrival time = 3:30 pm + 3 h 54 mnt = 7:24 pm

Answer:

19.24

Step-by-step explanation:

Please help me out! I don't understand this

Answers

Answer:

D.

Step-by-step explanation:

Answer:

CD=EF. -(1)

EF=GH. -(2)

Adding (1) and (2)

[LHS(1)+LHS(2) = RHS(1)+RHS(2)]

CD+EF = EF+GH

EF on both sides cancel each other.

CD= GH

Option D is the answer.

Hope this will help :-)

W/-4 + 17=9. Solve for w what is w

Answers

Answer:

w=-32

Step-by-step explanation:

Answer: w=32

Step-by-step explanation:

Given

w/-4 + 17=9

Subtract 17 on both sides

w/-4 + 17 - 17=9-17

w/-4=-8

Multiply -4 on both sides

w/-4 × -4=-8×-4

w=32

how much can an 55 affect my overall 100 grade?

Answers

Answer:

Depends on how many assignments you've completed.

Step-by-step explanation:

The accumulated overall grade is all about percentages, everything's a ratio when it comes to grades.

Answer:

it can bring it down alot

Step-by-step explanation:

it also can make your redo the grade


There was 3/4 of a pizza left over from a party. The next day, Bob ate half of what was left. How much of a whole pizza did Bob eat?

Answers

Answer:

2 and 1/2 if he ate the 1/4th also but if he just ate the half of the 3/4 its 1 and 1/2

Step-by-step explanation:

Which fraction has a repeating decimal as its decimal expansion?
3/25
3/16
3/11
3/8

Answers

Answer:

3/11

Step-by-step explanation:

3/11 equals 0.272727273 which is a repeating decimal.

Answer:

3/11 is C

Step-by-step explanation:

What is the volume of a rectangular prism with l = 412 cm, w = 312 cm, and h = 6 cm?

Answers

Answer:

Step-by-step explanation:

V = l · w · h

V = (412)(312)(6)

V = (1872)(412)= 771,264 cm^3

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{771264 \: \: {cm}^{3} }}}}}[/tex]

Step-by-step explanation:

[tex] \star{ \sf{ \: length \: of \: a \: rectangular \: prism(l) = 412 \: cm}}[/tex]

[tex] \star{ \sf{ \: width \: of \: a \: rectangular \: prism \: ( \: w \: ) = 312 \: cm}}[/tex]

[tex] \star{ \sf{ \: height \: of \: a \: rectangular \: prism \: ( \: h \: ) = 6 \: cm}}[/tex]

Finding the volume of a rectangular prism having length ( l ) of 412 cm , width ( w ) of 312 cm and height ( h ) of 6 cm :

[tex] \bold{\boxed{ \sf{volume \: of \: a \: rectangular \: prism = lwh}}}[/tex]

[tex] \hookrightarrow{ \sf{volume \: of \: a \: rectangular \: prism \: = 412 \times 312 \times 6}}[/tex]

[tex] \hookrightarrow{\boxed{ \sf { volume \: of \: a \: rectangular \: prism = 771264 \: {cm}^{3} }}}[/tex]

Volume of a rectangular prism = 771264 cm³

Hope I helped!

Best regards! :D

~TheAnimeGirl

An Arcticle was sold for Rs250 with a profit of 5% find cost price

Answers

Answer:

I think it should be Rs237

Describe the steps of constructing a segment that is TWICE as long as the given segment BD.

Answers

Answer:

See below

Step-by-step explanation:

From the segment BD, I will consider the point B as the begin and D as the end of the vector, therefore [tex]\overrightarrow{BD} = \vec{v}[/tex]

Once you want a segment that is twice as long as the given segment, we may say that the magnitude of the vector is

[tex]||2\vec{v} || = \sqrt{(2x)^2 + (2y)^2} = \boxed{ \sqrt{4x^2 + 4y^2} }[/tex]

Note: I'm assuming [tex]\vec{v} \in E^2[/tex], which means the segment is in the plain.

How many cm in 92.4 inches?

Thank you!

Answers

Answer:

234.696 cm

Step-by-step explanation:

Answer: 234.696

Step-by-step explanation:

1 inch = 2.54 centimeters so

92.4 times 2.54 is 234.696

Find the distance between the points (6, 9) and (0, 1).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units

Answers

Answer:

D= 10

Step-by-step explanation:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(0-6)^2+(1-9)^2}\\d=\sqrt{(-6)^2+(-8)^2}\\d=\sqrt{(36)+(64)}\\d=\sqrt{100}\\d=10[/tex]

The sum of 5x+y and (2xy + xy) is

8x^2y
6x^2y+2xy^2
7xy^2+x^2y
15x^2y
Which is a “monomial? or binomial

Answers

so monomial in most cases means “one”
binomial equals “two”. if that helps. The first option and last option are monomial and the middle two are binomial

3x + 2y + -2x + 8y pls help

Answers

Answer:

x+10y

Step-by-step explanation:

3x+2y+(-2x)+8y

First of all you cannot substitute x with y, so what u do u make the numbers with the same letters they have,and I put -2x because + &amp; - equals to -(minus) :-

3x-2x+2y+8y= x+10y

I don't add 1 to x coze when x alone stands for 1, I added +10y because both the y equations had + they were positive so I add a +.

Hope it helps

This is trigonometry!
I need help with what it means when it says “adjacent for 20 degrees” , “hypotenuse for 20 degrees” etc. ! Thanks

Answers

Answer:

Adjacent for 20° = 17.3mm

Hypotenuse for 70° = 120mm?

Opposite for 70° = 17.3mm

Hypotenuse for 20° = 120mm?

Adjacent for 70° = 10mm

Opposite for 20° = 10mm

Step-by-step explanation:

I think "Adjacent for 20°" is asking the length of the side adjacent to 20° (Although the Hypotenuse is adjacent to 20° don't answer its length because Hypotenuse are ALWAYS opposite to the 90° of a right triangle). The "Opposite for 70°" is asking the length of side opposite to 70°.

Also, I really don't know why the hypotenuse is 120mm because by the Pythagorean Theorem, it should 19.98mm (20mm if rounded to the nearest tenths).

Answer:

  "adjacent" is the short ray that makes up the angle. "opposite" is the side not touching the angle.

Step-by-step explanation:

Since your question text involves identifying adjacent and opposite, that's what we'll explain.

In a right triangle, the hypotenuse is the side opposite the right angle. For the purposes here, it is always referred to as the hypotenuse. It is the longest side in the right triangle.

__

Each acute angle in the right triangle has the hypotenuse on one side. The other side forming the angle is called the adjacent side.

The remaining side of the triangle (not the hypotenuse, and not the adjacent side) is the one opposite the angle. It is called the opposite side.

__

In the first attachment is a triangle with sides and angles labeled. Each angle is labeled with an upper-case letter (A, B, C), and each side opposite that angle is labeled with the corresponding lower-case letter (a, b, c). This is a customary way to label triangle sides and angles. (The right angle is not always C.)

So, for angle A, the hypotenuse is c, and the adjacent side is b. The side opposite is a.

For angle B, the hypotenuse is c (still), and the adjacent side is a. The side opposite is b.

__

The second attachment applies these ideas to your first (upper left) triangle.

__

As for the applicable formulas, the mnemonic SOH CAH TOA is often helpful. It is intended to remind you that ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

Then the applicable formulas clockwise from left are for Cos, Sin, Cos.

"What went wrong" in the 30° triangle is that somebody used a calculator in radians mode, not degrees mode, when they tried to compute the sine. A couple of errors were made, because sin(30 radians) is about -0.988, so the minus sign was dropped, too. (You always need to check that the calculator is in the right mode.)

Keith had two hundred sixteen dollars to spend on six books. After
buying them he had eighteen dollars. How much did each book cost ? _____________

Answers

Answer:

$34.66

Step-by-step explanation:

216-8= 208 divided by 6 = 34.666666

Answer: 33$ each

Step-by-step explanation:

you start by subtracting 18 from 216 to get rid of the leftover money.

you'll have ended up with the number 198

divide 198 by 6 and that will be your answer.

Find the value of x. If someone could help me, please

Answers

Answer:

8      x = 17

9      x = 36

10     x = 10

Step-by-step explanation:

8

(6x + 5) + (4x+5) = 180

6x + 4x = 180 - 5 - 5

10x = 170

x = 170/10

x = 17

9

2x + 1 = 73

2x = 73 - 1

2x = 72

x = 72/2

x = 36

10

(3x+7) + 53 = 90

3x = 90 - 53 - 7

3x = 90 - 60

3x = 30

x = 30/3

x = 10

Answer:

8) i have no clue

9) x=36

10) x=10

Step-by-step explanation:

9) 73-1=72

72/2=36

x=36

10) 3x+7

90-53=37

37-7=30

30/3

x=10

20-(-3) for algebra to find the difference

Answers

Hey there!

ANSWER: [tex]-60[/tex]EXPLANATION:

[tex]20-(-3)[/tex]

[tex]Subtract:\\20-(-3)\\=-60(ANSWER)[/tex]

Hope this helps!

[tex]-TestedHyperr[/tex]

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