Find the values of a and b such that

X^2 + 2x - 7 = (x + a)^2 + b

Answers

Answer 1

The values of a and b are 1 and -8 respectively.

What are the values of a and b?

[tex]x^{2} + 2x- 7 = (x+a)^{2}+b[/tex]

Let us consider the Right Hand Side of the given equation.

[tex](x+a)^{2}+b = x^{2} +2ax+a^{2} +b\\[/tex]

So,  

[tex]x^{2} + 2x- 7 = x^{2}+2ax+a^{2}+b\\\\= x^{2}+2x(1)+1^{2}-8\\\\= (x+1)^{2} -8\\\\[/tex]

Here, a = 1 and b = -8

What is an equation?Equation is also known as a statement of equivalence between two expressions with variable and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them. likewise see equation system. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship.

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Related Questions

1 4/5 as a decimal thank you (will be giving brainliest to first answer that is correct) : D

Answers

Answer:

yes its decimal

Step-by-step explanation:

The given fraction into percent and decimal are; 2.8  and 280%

How to convert percent to fraction and decimal?

Percent counts the number compared to 100.

There is a fraction, containing numerator(upper value) and denominator(lower value).

So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get,

For each 1, there are a/100 parts.

Thus, 50% = 50/100 = 0.50 (in decimal)

There is a fraction, containing numerator(upper value) and denominator(lower value).

The mixed fraction contains a sum of whole number and a proper fraction.

WE have been given a fraction as;

14/5

Then Fraction Decimal Percentage

2.8  and 280%

The given fraction into percent and decimal are; 2.8  and 280%

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Please I need help does anyone know a hack for khan academy

Answers

Answer:

Answer:

0.3643

Step-by-step explanation:

Standard Form and Scientific Notation

What is standard form of numbers?

Standard form is the normal way of writing numbers no matter how big or small the number is.

Examples:

15,000,000

0.0000000678

What is scientific notation?

Scientific notation is a different way of expressing numbers. It is a short way of expressing very big numbers or very small numbers. It is also known as exponential form. Scientific notation is written as the product of a number and a power of 10.

Examples:

1.3 × 10⁶

34.5 × 10^⁻9

Going back to the question above, we need to convert the given scientific notation to its standard form.

Converting of Scientific Notation to Standard Form

To convert a number from scientific notation to standard form, move the decimal point.

The exponent tells the direction and the number of times we need to move the decimal point.

The positive exponent indicates a large number so we need to move the decimal point to the right.

The negative exponent indicates a small number so we need to move the decimal point to the left.

Do not write the power of 10 anymore.

Solution:

Now, let us convert 3.643 x 10^-1 in standard form.

The exponent is negative 1 so we will move the decimal point to the left once.

3.643 = 0.3643

Perform the indicated operation.
f (x) = x2 − 4 g(x) = −3x Find f (g(x))

Answers

Answer:

-6x-4

Step-by-step explanation:

2(-3x)-4

-6x-4

r F(x) is your frame function since it is on the outside, when every you get to an x in the F function you plug in the G function then solve as normal.

um dado de 6 faces numeradas de 1 a 6 e lançado de maneira aleatória deseja-se que ele caia com uma face para cima . Qual a probabilidade de se obter a face com um dos valores desejados​

Answers

Answer: The translation: is "a die with 6 faces numbered from 1 to 6 and thrown in a random way is desired to fall face up. What is the probability of obtaining the face with one of the desired values"

In The autumn 40% of the leaves on a tree are yellow and 24% of them are green the remaining 72 leaves are half yellow how many leaves are on the tree

Answers

Percentage of yellow leaves on a tree during Autumn = 40%

Percentage of green leaves on a tree during Autumn = 24%

Percentage of half yellow leaves on the tree during Autumn :

[tex] = \tt100 - 40 + 24[/tex]

[tex] = \tt 100 - 64[/tex]

[tex] = \tt 36 \%[/tex]Thus, the percentage of half yellow leaves on the tree during Autumn = 36%

Number of half yellow leaves on the tree = 36%

Let the total number of leaves on the tree be x.

Which means :

[tex] = \tt36 \% \: of \: x = 72[/tex]

[tex] = \tt \frac{36}{100} \times x = 72[/tex]

[tex] = \tt \frac{36 \times x}{100} = 72[/tex]

[tex] = \tt \frac{36x}{100} = 72[/tex]

[tex] = \tt 36x = 72 \times 100[/tex]

[tex] = \tt36x = 7200[/tex]

[tex] = \tt x = \frac{7200}{36} [/tex]

[tex] \color{plum} = \tt \: x = 200[/tex]

Thus, total number of leaves on the tree = 200

Number of yellow leaves on the tree :

[tex] = \tt40 \% \: \: of \: \: 200[/tex]

[tex] = \tt \frac{40}{100} \times 200[/tex]

[tex] = \tt \frac{40 \times 200}{100} [/tex]

[tex] = \tt \frac{8000}{100} [/tex]

[tex] \color{plum} \tt = 80 \: yellow \: \: leaves[/tex]

Thus, total number of yellow leaves on the tree = 80

Number of green trees on the tree :

[tex] = \tt24 \% \: \: of \: \: 200[/tex]

[tex] = \tt \frac{24}{100} \times 200 [/tex]

[tex] = \tt \frac{24 \times 200}{100} [/tex]

[tex] = \tt \frac{4800}{100} [/tex]

[tex] \color{plum} = \tt 48 \: green \: \: leaves[/tex]

Thus, the total number of green leaves on the tree = 48

Since the sum of all types of leaves form 200[80+48+72=200], we can conclude that we have found out the correct number of each type of leaf.

▪︎Therefore, the total number of leaves on the tree = 200

The number of leaves is on the tree is 200.

Given that,

There is 40% of the leaves that should be yellow.24% of them should be green.And, the remaining should be 72 leaves that represent half yellow.

Now as per the above explanation:

The percentage of half yellow trees should be

= 100 - 40 + 24

= 100 - 64

= 36

Here we assume the number of leaves on the tree be x

So,

36% of x = 72

x = 200

Therefore we can conclude that the number of leaves is on the tree is 200.

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It takes lucas 3 hours to cycle from his home to his friend's village. But if he travels 5 mph slower, it will take him 1.5 hours longer. How far is the friend from lucas' house

Answers

Answer:

Step-by-step explanation:

It takes Lucas 3 hours to cycle from his home to his friend’s village:  

3 hours • (a certain speed) = distance in miles  

If he travels 5mph slower, it will take him 1.5 hours longer:

4.5 hours • (the same speed - 5mph) = the same distance in miles

 4.5 • (x - 5) = 3x

4.5x - 22.5 = 3x

1.5x = 22.5

x = 15mph  

3hours • 15mph = 45 miles

8123 divided by 7 please help!

Answers

The answer to this is 0.14285714


HELP ASAP DUE IN 20 MINUTES

Answers

Answer:

x = 3

< D = 26

< E = 54

Step-by-step explanation:

I did the math

Use distributive property to simplify the following expression then combine like
terms: -5(a-6)+6a. Then identify the coefficient for the simplified expression.
Your answer

Answers

Answer:

Step-by-step explanation:

distribute:

-5a+30+6a

simplify:

a+30

not sure what u mean by coefficient, the coefficient of a is 1.

Answer: a + 30

Step-by-step explanation:

Using the distributive property, we can figure out the expression unsimplified = -5a+30+6a

By combining like terms, -5a+6a = a

Therefore, this expression = a + 30

I am not a professional, simply using prior knowledge!

Note- It would mean the world to me if you could mark me brainliest!

John joined a gym for 6 months. He pays 20$ per month plus a membership fee. If his bill is 150$, what was the membership fee?

Answers

Answer:

Step-by-step explanation:

If he's been at the gym for 6 months, and he is charged $20 each month, then he has paid $120 dollars, not counting his membership fee. His total bill is $150.

150-120= $30

His membership fee was $30.

Hope this helps!

Mark Brainliest plz!

x is the number of months and y is the membership fee

[tex]cost = 20x + y[/tex]

[tex]150 = 20(6) + y[/tex]

[tex]150 = 120 + y[/tex]

[tex]150 - 120 = 120 - 120 + y[/tex]

[tex]30 = y[/tex]

The membership fee was $30.

Prism A is similar to Prism B. The volume of Prism A is 540 cm.
What is the volume of Prism B? (determine scale factor first)

Answers

Answer:

1080

Step-by-step explanation:

540x2/ or 540 + 540

I need the answer as soon as possible

Answers

Reflection .........................

Answer:

Reflection on the Y axis.

Step-by-step explanation:

(I cannot see the rest of the answers but I am assuming reflection is one of them). The shape reflects perfectly on the Y axis.

4. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!


Write a rule for the linear function shown in the graph.


A. y = 2x - 2

B. y = -2x + 2

C. y = 1/2x - 2

D. y = -x + 2

Answers

Answer:

The answer is A (y = 2x - 2)

Step-by-step explanation:

B and D aren't correct because the y-intercept is a positive 2 instead of negative 2 like the graph shown. We're now left with A and C. Go on one point of the graph and count up or down to go on the same y value as the other point. Go left or right and count until you go to the same point. Remember that the slope equation is rise/run. Rise meaning up or down. Run meaning left or right.

Answer:

y = -x+2

Step-by-step explanation:

For first one

For a National Junior Honor Society Induction Celebration, Ahmed is renting tables and chairs. He wants to have only tables for 4 and tables for 6. The total number of people that can be seated in the school cafeteria with these tables is 160. Which equation represents this situation? (hint draw a picture) *

Answers

Answer:

i am not smart

Step-by-step explanation:

2.) Find the value of n in the equation 1/2(n+4) = 6 *

Answers

Answer:

2

Step-by-step explanation:

N = 8
Hope this helps

Directions: Identify the slope and y intercept. Then write an equation in y = mx + b form. 11) 40 2 1 r 0 -4 -3 -2 +1 0 1 2 3 -1 -2 -3 -4 Slope = y-intercept =​

Answers

Answer:

55555555

Step-by-step explanation:

X, Y and Z form the vertices of a triangle with area 59.7cm2. If XZ = 21.5cm and XY = 13.5cm, work out the acute angle ∠YXZ. Round to 1 DP.

Answers

Answer: The acute angle ∠YXZ = 24.3°.

Step-by-step explanation:

If in triangle ABC, C is the angle included between sides a and b then

Area of triangle = [tex]\dfrac12a\cdot b\cdot sin C[/tex]

here, XZ = 21.5cm and XY = 13.5cm are sides that includes acute angle ∠YXZ..

Area of a triangle = 59.7cm²

then, as per given, we have

[tex]59.7=\dfrac12(21.5)(13.5)\ \sin X\\\\\Rightarrow\ 59.7=145.125\ \sin X\\\\\Rightarrow\ \sin X = \dfrac{59.7}{145.125}\\\\\Rightarrow\ \sin X =0.41137\\\\\Rightarrow\ X = \sin ^{-1}(0.41137)\approx24.3^{\circ}[/tex]

Hence, the acute angle ∠YXZ = 24.3°.

9. An inequality is shown
2x - 5 < 33
Select all the values that are solutions to this inequality
a. 28
b. 26
C. 19
d. 18
e. 12

PLEASE HELPP!!

Answers

The answer is c 19
38/2=19
Step-by-step explanation
The answer is d. 18 and e. 12.

Explanation:

2x - 5 < 33

2x < 33 + 5

2x < 38

x < 38/2

x < 19

x must be smaller than 19.

It can’t be 19 because it didn’t say smaller than or equal to.

So the answer is 18 and 12.

whats 667453x765678-543

Answers

Answer:

511054077591

Step-by-step explanation:

Answer:

511,054,077,591

Step-by-step explanation:

Is this an actual question tho?

List the possible rational roots of the equation. 0 = 22x4 - x2 + 121​

Answers

Answer:

22×4=88÷2=44+121=165

Answer:

±1

±1/2

±1/11

±1/22

±11

±11/2

±121

±121/2

can you guys help me out

Answers

Answer:

a. S = 3n + 2

b. There while be 62 squares.

Step-by-step explanation:

We know the first term of this sequence is 5. To figure out the equation, subtract the following term from the previous. Do you see a common difference?

8 - 5 = 3

11 - 8 = 3

14 - 11 = 3

We're seeing a constant difference of 3 (which makes this an arithmetic sequence), but the first term is 5. That mean something is being added to make the first term 5. Subtract 3 from 5 to get 2. This means 2 is being added to every multiple of 3, which leads us to the equation: S = 3n + 2.

To find the 20th term of this sequence, substitute n for 20 and do the operations.

S = 3(20) + 2

Multiply 3 by 20, then add 2.

S = 62

The 20th term will have 62 squares.

Which scenario best matches the inequality x greater than 3 ?

Answers

Answer:

d

Step-by-step explanation:

i got an 100 on the test :)

40 is 8% of what number?​

Answers

Answer:

500

Step-by-step explanation:

40×100÷8=500

Number 40 is 8 percent of 500.

What is the percentage?

The percentage refers to a number that is out of 100. When describing components of a whole in mathematics, percentages are employed similarly to fractions and decimals. When employing percentages, the idea is that there are 100 equal pieces that make up the whole. In addition to the shorthand "pct," which is used less frequently, the symbol "%" is used to indicate that a number is a percentage.

Let the unknown number be "x" whose 8% is 40.

Hence,

8% of x = 40

1% of x = 40/8 = 5

Thus, the value of x = 500

Therefore, 8 percent of 500 if 40.

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If the lines in a system of equations have different slopes and the same y-intercept, how many solutions does the system have?

Answers

Answer:

289819

Step-by-step explanation:

Micah has 294 songs stored in his phone,which is 70% of the songs that Jorge in his phone.How many songs are stored on Jorge'S phone ?​

Answers

Answer:

206

Step-by-step explanation:

70% of 294

70/100 × 294/1

205.8

round it off to 206

What is the rate of change of
the function when x=-1 and
x = 1?
A
A. 2
B. 4
C. -2
D. -4
0.

Answers

Answer:

c!!!!!!!!!!!!!!!!!!!

Tucker got in his car and started driving toward his grandmother's house. After driving for 1 hour and 30 minutes, Tucker took a break for 40 minutes to have a snack. Then Tucker drove 1 hour and 40 minutes and finally arrived at his grandmother's house at 6:05 P.M. What time did Tucker start driving?

Answers

Answer: He started driving at 2:15 P.M.

Step-by-step explanation:

Answer:

3:05 P.M

Step-by-step explanation:

6:05 - 1 hour and 30 min = 5:25

5:25-40 minutes = 4:45

4:45 - 1 hour 40 minutes = 3:05 P.M

Cuánto costará cercar una finca cuadrada de 14 metros de lado a razón de $150 el metro lineal de alambrada

Answers

Answer:

$ 2100

Step-by-step explanation:

De la pregunta anterior:

1 metro de cerca de alambre = $ 150

14 metros = x

Cruz multiplicar

x = 14 × $ 150

x = $ 2100

Por lo tanto, costaría $ 2100 por una cerca de 14 metros

In AOPQ, o = 700 cm, p = 840 cm and q=620 cm. Find the measure of _P to the
nearest degree

Answers

Given:

In triangle OPQ, o = 700 cm, p = 840 cm and q=620 cm.

To find:

The measure of angle P.

Solution:

According to the Law of Cosines:

[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]

Using Law of Cosines in triangle OPQ, we get

[tex]\cos P=\dfrac{o^2+q^2-p^2}{2oq}[/tex]

[tex]\cos P=\dfrac{(700)^2+(620)^2-(840)^2}{2(700)(620)}[/tex]

[tex]\cos P=\dfrac{490000+384400-705600}{868000}[/tex]

[tex]\cos P=\dfrac{168800}{868000}[/tex]

On further simplification, we get

[tex]\cos P=0.19447[/tex]

[tex]P=\cos^{-1}(0.19447)[/tex]

[tex]P=78.786236[/tex]

[tex]P\approx 79[/tex]

Therefore, the measure of angle P is 79 degrees.

Answer:

79

Step-by-step explanation:

Find the area of the circle. Use 3.14 or 22/7 for pi. Round your answer to the nearest hundredth, if necessary.

Answers

Step-by-step explanation:

Given

diameter (d) = 9 ft

radius (r) = 9/2 = 4.5 ft

Area of the circle

= πr²

= 3.14 * ( 4.5) ²

= 3.14 * 20.25

= 63.585

= 63.59 ft

Hope it will help :)

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