If f(x) = 2x + 1 and
g(x) = -(x - 1)² + 3 what is the smallest solution for f(x)=g(x)?

Answers

Answer 1

Answer:

The smallest solution is x=-1

Step-by-step explanation:

Quadratic Equation

We have:

[tex]f(x)=2x+1[/tex]

[tex]g(x)=-(x-1)^2+3[/tex]

We'll find the solutions of f(x)=g(x), or:

[tex]2x+1=-(x-1)^2+3[/tex]

Operating:

[tex]2x+1=-(x^2-2x+1)+3[/tex]

[tex]2x+1=-x^2+2x-1+3[/tex]

Rearranging all terms on the left side:

[tex]2x+1+x^2-2x+1-3=0[/tex]

Simplifying:

[tex]x^2-1=0[/tex]

Since the term with the x is missing, we can solve for x:

[tex]x^2=1\qquad\Rightarrow x=\sqrt{1}=\pm 1[/tex]

There are two solutions:

x=1, x=-1

The smallest solution is x=-1


Related Questions

Nicole wants to buy a charm bracelet. Summerfield Fine Jewelry charges $26 per charm, plus $19 for the bracelet. Flynn Jewelers, in contrast, charges $27 per charm and $11 for the bracelet. If Nicole wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. How many charms would that be? What would the total cost of the bracelet be?

Answers

Answer:

There are 8 number of charms

Total cost = $227

Step-by-step explanation:

Let

Number of charms = c

Summerfield Fine Jewelry charges $26 per charm, plus $19 for the bracelet.

26c + 19

Flynn Jewelers charges $27 per charm and $11 for the bracelet

27c + 11

How many charms would that be ?

Equate the cost at both jewelry shop

26c + 19 = 27c + 11

Collect like terms

26c - 27c = 11 - 19

-c = - 8

c = 8

There are 8 number of charms

What would the total cost of the bracelet be?

Using any of the jewelry shop cost

Flynn Jewelers cost

= 27c + 11

= 27(8) + 11

= 216 + 11

= 227

Total cost = $227

The Martinez family is traveling to a play in Richmond. A round trip train ticket costs $8.00. Children under the age of 7 travel for half price. ($4.00) Tickets for the play are $14.00 for an adult and $6.00 for a child. Mr. And Mrs. Martinez will go with their children, Ricky, Ramona, and Thomas. Ricky and Ramona are 12 years old. Thomas is 6 years old. How much did the Martinez family spend for the train ride and play tickets?

Answers

Answer: The Martinex family spent $ 82 for train ride and play tickets.

Step-by-step explanation:

Round trip train cost = $ 8.00

For children it cost $ 4.00.

For adult, ticket for play costs= $ 14.00

For children , ticket for play costs= $ 6.00

Mr. And Mrs. Martinez will go with their children, Ricky, Ramona, and Thomas.

2 adults and 3 children ( only one of them is under 7.)

For train we consider only 1 as child rest as adult.

Train cost =  4 x($ 8.00)+ 1 x ($ 4.00)

= $ 32+4 = $36

For play , total cost = 2 x ( $ 14.00) + 3 x ($6)

= $(28+18)

= $ 46

Total spending ( combined) =  $36+$ 46

= $82

So, the Martinex family spent $ 82 for train ride and play tickets.

PLEASE HELP ME ANSWER DIRECTIONS ARE IN THE PIC PLEASE HELP ASAP!

Answers

y=2x+2 or y=2x+5 hope this helped!

Find x
8(x-27)+49=87+28x

Answers

Answer:

x = -12.7

Step-by-step explanation:

[tex]8(x-27)+49=87+28x\\\\8x-167=87+28x\\\\8x-167+167=87+28x+167\\\\8x=28x+254\\\\8x-28x=28x-28x+254\\\\-20x=254\\\\\frac{-20x=254}{-20}\\\\ \boxed{x=-12.7}[/tex]

Hope this helps.

Answer:

x=-127/10 or x= -12.7

Step-by-step explanation:

8(x−27)+49=87+28x

Step 1: Simplify both sides of the equation.

8(x−27)+49=87+28x

(8)(x)+(8)(−27)+49=87+28x(Distribute)

8x+−216+49=87+28x

(8x)+(−216+49)=28x+87(Combine Like Terms)

8x+−167=28x+87

8x−167=28x+87

Step 2: Subtract 28x from both sides.

8x−167−28x=28x+87−28x

−20x−167=87

Step 3: Add 167 to both sides.

−20x−167+167=87+167

−20x=254

Step 4: Divide both sides by -20.

−20x/−20

=

254/−20

x=

−127/10

Please help
8 square root 5 minus square root 45

Answers

Answer:

[tex]5 \sqrt{5 \: } is \: \: the \: \: answer \: \: of \: \: this \: \: question[/tex]

If y varies drectly with x
and y= 4.5 when x= 2.5,
what is y when x= 12?

Answers

You have to figure out what the difference is first , so we can se le that the difference between y and x will always be 2, we got this number by subtracting 4.5-2.5=2.
So we are given x which is 12 so in order to solve this you just substitute x with 2 in the next equation 12+x=y/ 12+2=14

NEED HELP ASAP!
Which represents the symbolic notation of the compound statement below?
“Memorial Day is in July or parallel lines intersect.”

Answers

Answer:

Option (A)

Step-by-step explanation:

Statement 'p':

"Memorial Day is in July"

Statement 'q':

"Parallel lines intersect"

Since both the statement are joined by the 'OR',

Statements p and q will be joined by disjunction represented by the sign (∧).

Therefore, two statements will be represented as,

p ∧ q

Option (A) will be the correct option.

In the figure below, lines m and n are parallel:

In the diagram shown, 27 measures 97 degrees. The measure of 28 is
degrees?

Answers

Answer:

the measure of angle 8 is 83 degrees

Step-by-step explanation:

.
3. Ada 7 to 3 times of a number will
give you 66 if that number is a
9​

Answers

Answer:

Step-by-step explanation:

Let the no. be x

3 times the no. will be 3x

adding 7 to 3 times the no. will be 3x + 7

the result is 66 so it will be 3x + 7 = 66

Hope this helps

plz mark as brainliest!!!!!

write the nature of roots of quadratic equation 4x square +4 root3x + 3=0​

Answers

Answer:

yes right now because dont unable to ask you.

Pythagorean Therom.What is the length of segment AB?

Answers

Answer:

A square + B square = C square

Step-by-step explanation:

If Mark takes 7 hours to paint a house and Hanna takes 5 hours to paint the same house, how much time will it take both of them to paint the house? Please explain!

Answers

Answer:

2 hours and 42 minutes

Step-by-step explanation:

we can see that both people are painting the same house, however 1 person goes faster than the other one

lets start by putting our numbers into fractions then finding a like value. 35 in this case. 1/7 equals 5/35 and 1/5 equals 7/35 now we add these together and get 13/35. our next step is to flip this to 35/13 and take put any whole numbers. in this case 2 whole numbers can be made

leaving

9/13

(0.69)

converting this to minutes is 42 minutes.

Beginning at the origin, how far do you travel along the x-axis when plotting the point below?
(6, 40)

Answers

Answer:

6 units to the right

Step-by-step explanation:

Hope this helps!

Is -6 greater than, less than, of equal too -4

Answers

Answer:

-6 in less than -4.

Answer:

-6 less than -4

Step-by-step explanation:

-6 is less because on the number line it will look like it's before -4

Hope this helps!!!

ethan planted a tree that was 1.85 meters tall. several year later the tree is 5.30 meters tall

Answers

ANSWER- 3.45 because if you get 5.30 and subtract 1.85 you’d get 3.45
5-0= 5 would be how you get the 5 at the end of the answer- 3.45

Does anyone know this?? Tysm

Answers

Answer:

D

Step-by-step explanation:

hope this helps

4÷6\7 blank 4

I have to figure out if it is < > =​

Answers

Answer:

<

Step-by-step explanation:

because 4/6/7 is less than 0

Answer:

2/21 < 4

Step-by-step explanation:

Lets break this up

4/6=2/3

2/3 / 7 = 2/3 * 1/7

2/21

check all that apply ... 50 points for brainliest answer !!

Answers

(x^(3-6))^2 = (x^-3)^2

x^3*2+x^-6*2 = x^6+x^-12

when the numbers are just next to each other (ex. x²x³) you just ADD the exponents and you get (in this case x^6)when the numbers and exponents are in and out of parentheses          (ex. (x³)²) you MULTIPLY the exponents (in this case you get x^6)when you have both, you solve what is IN the parentheses (ex. (x²x³)²) first, making the equation (ex. (x^6)²) and then you multiply the exponent by 2 (ex. (x^12) and get the answer. NOTE - ^ means to the power

The second from the top, and the second to last expressions should be the answer

Hope this helps!

The x values of a function is the output true or false

Answers

Answer: False

Explanation:

X is input, y is output

write the equation of the line that is parallel to y=-6x+-8 that passes through (-8,8)

Answers

Answer:

y=-6x-40

Step-by-step explanation:

the sum of three consecutive odd integers is 57. what are the three integers

Answers

Answer:

17,19,21

Step-by-step explanation:

let the first odd number be "x"

formular : (x)+(x+2)+(x+4).

3x+6=57

3x=57-6

3x=51

x=51/3

x=17

apply the formular.

17,(17+2),(17+4)

17,19,21.

22. Part-Time Job
You work at a grocery store part-time. You estimate that you spend three-fifths of your time stocking shelves. You work 20 hours each week. How many hours of your work week do you spend stocking shelves?

Answers

Answer: 12

Step-by-step explanation:

You spend 20 hours working at a grocery store each week. You spend 3/5 of that time stocking shelves. You need to find out what 3/5 of 20 is.

Step 1: Turn 20 into a fraction

20 = 20/1

Step 2: Multiply

3/5 x 20/1 = 60/5

Step 3: Simplify

60/5 = 12

A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus. 65% of the 800 students at North High School ride the bus. How many students ride the bus? 100 multiplied by is equal to 800. 65 multiplied by is equal to . out of students ride the bus.

Answers

Answer:

answer one is 8

answer two is 8

answer three is 520

answer four is 520

answer five is 800

Step-by-step explanation:

There are  520 students out of 800 ride the bus,

65% of 800 is 520,

100 multiplied by 8 is 800.

What are ratios and proportions?

The majority of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

Given,

1: There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.

let x student out of 800 rides the bus

so both conditions 65/100 and x/800 are in proportions,

65/100 = x/800

x = 800*65/100

x = 520

2:  65% of the 800 students at North High School ride the bus.

65% of 800 = 65/100 x 800

65% of 800 = 520

3: 100 multiplied by is equal to 800.

let x multiplied by 100 is 800

x*100 = 800

x = 800/100

x = 8

Hence 520 students out of 800 ride the bus,

65% of 800 is 520,

100 multiplied by 8 is 800.

Learn more about ratios and proportions;

https://brainly.com/question/29774220

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How is 9.746 x 1013 written in standard form?

Answers

Answer:

9872.698 is 9.746 x 1013 in standard form

what is the midpoint between point A and B ​

Answers

Answer: (-1,4) is the answer

PLEasEE help me...
i need
an equation with the solution of x=5.
a equation with the solution of 3/2 (1.5)
an equation with the solution of -2
thank you

Answers

Answer:

3x + 3 = x + 13

y=1.5x−6.5,

Step-by-step explanation:

substitute the number in for the first two

Name the longest and shortest side in the triangle.

Answers

Answer:

the answer is C Because the lm is the long side and mn is the short side

n is a positive integer. (i) Explain why n(n - 1) must be an even number.

Answers

Answer:

Since the equation is n(n-1) where n is even, (n-1) will result to an odd number and when multiplied the answer with n( an even number), this will result to an EVEN NUMBER. Therefore, in any number that n can substitute, whether even or odd, the answer will always result to an even number

Step-by-step explanation:

Lynn is making a square picure frame as a gift for her mothers birthday. Lynn would like for the frame to have to an area of 48 inches squared. She also wants the side lengths to be integers.

Part A: Is it possible for Lynn to create a square picture frame with an area of 48 inches sqaured? Yes or No? Support your answer using mathimatical reasoning

Part B: If lynn choses a different sqaure shaped frame, what is an alternative area of that frame that would have integer side lengths? Support your answer using mathimatical reasoning

Answers

Answer:

1)The answer is no

2)48 7 6 = 8. 54 7 6 = 9. 60 + 6

Step-by-step explanation:

1) because if you add it a lot of times you will get a bad answer. But if you do the math like this 48 7 6 = 8. 54 7 6 = 9. 60 + 6.  

2) well 48 7 6 = 8. 54 7 6 = 9. 60 + 6= 75.6 right. So the picture frame is 5 inches

don't forget to make me brainliest

Answer:

1)The answer is no

2)48 7 6 = 8. 54 7 6 = 9. 60 + 6

Step-by-step explanation:

1) because if you add it a lot of times you will get a bad answer. But if you do the math like this 48 7 6 = 8. 54 7 6 = 9. 60 + 6.  

2) well 48 7 6 = 8. 54 7 6 = 9. 60 + 6= 75.6 right. So the picture frame is 5 inches

Step-by-step explanation:

Lines AB and CD are parallel. Find the measures of the three angles in triangle ABF.
What is the angle measurement for A, B, and F. (Make sure they are degrees)
Can you help me with this math question?

Answers

A = 42°

B= 23°

F = 115°

Step-by-step explanation:

The required measures of the three angles in triangle ABF are A = 23°, B = 42°, and F = 115°.

What are Alternate Interior Angles?

Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines

Given that Lines AB and CD are parallel.

To determine the measures of the three angles in triangle ABF.

For finding ∠F,

∠CDF = 180° - 157° = 23°

∠F = 180° - ∠C - ∠CDF

∠F = 180° - 42° - 23°

∠F = 115°

However, if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

So ∠A = ∠CDF = 23°

And ∠B = ∠C = 42°

Thus, the required measures of the three angles in triangle ABF are A = 23°, B = 42°, and F = 115°.

Learn more about Alternate Interior Angles here:

brainly.com/question/2125016

#SPJ2

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