y = x² + 7x - 5 Can be written in the form y = ( x + a )² + b. Find the value of a and the value of b.

Answers

Answer 1

Answer:

[tex]a=\dfrac{7}{2} \\\\b=\dfrac{49}{4} \\[/tex]

Step-by-step explanation:

[tex]y=x^2+7x-5\\\\=x^2+2*\dfrac{7}{2}*x +\dfrac{49}{4} -\dfrac{49}{4} -\dfrac{20}{4} \\\\=(x+\dfrac{7}{2} )^2+\dfrac{69}{4} \\\\a=\dfrac{7}{2} \\\\b=\dfrac{49}{4} \\[/tex]


Related Questions

Find the AREA of the shape​

Answers

Step-by-step explanation:

LxB

8x7

equals :56

Area equals to 56cm

(15-12)2-2+5=

20+23×3-1=

[4(3+2)-4]+42

Answers

Answer:

Here is your answer . Hope this is helpful to you.

Carlo got a pet snake as a birthday present. On his birthday, the baby snake was just 26 cm long. He has been measuring its length weekly and has noticed that it has been growing approximately 2 cm each week.

Write an equation to represent the length of the snake in weeks since Carlo's birthday use L for length and w for weeks.​

Answers

The equation to represent the length of the snake in weeks:

[tex]L=2w+26[/tex]

Given:

A snake of lenght of 26 cemtimeters grows approximately 2 centimeter long each week.

To find:

The equation to represent the length of the snake in weeks

Solution:

Let the length of the snake in' w' weeks be 'L'.

The initial length of the snake on Carlo's birthday = 26 cm

At starting very first week the length of the snake was 26 cm. And after a week the lenght of the snake becomes 28 cm and then aftertwo weeks the length becomes 30 cm and so on.

Increase in length of the snake each week = 2 cm

And increase in length of the snake in 'w' weeks = (2×w) cm

And the length of the snake in terms weeks (w) will be given by equation:

[tex]L=2\times w+ 26\\L=2w+26[/tex]

The equation to represent the length of the snake in weeks:

[tex]L=2w+26[/tex]

Learn more about equation representation here:

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2. 3.6 x 5.5? Explain your answer. (Make sure you include how you knew where to
place the decimal point.)

Answers

Answer:

19.80 or 19.8

Step-by-step explanation:

When multiplying decimal numbers we forget the decimal points and multiply normally; like, 3.6 x 5.5 = 1980, then we count how many decimal numbers(numbers after the decimal point) there are in the factors(In 3.6 we have the decimal number 6. And in 5.5 we have the decimal number 5 ). So here we have 2 decimal numbers resulting in our answer being, 19.80 or 19.8 since the 0 is unnecessary.

Jace recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 11
Bass 14
Drums 11
Keyboard 14
Eighth Grade Students
Instrument # of Students
Guitar 13
Bass 13
Drums 8
Keyboard 3

Based on these results, express the probability that a seventh grader chosen at random will play an instrument other than bass as a percent to the nearest whole number.

Answers

The probability that a seventh grader chosen at random will play an instrument other than bass is 72%.

Sarah is going to pay for an item using gift cards. The clerk tells her tht she will need 2 gift cards and as additional $3 to pay for the item.

Write an algebraic equation to find the cost for any amount of gift cards

Answers

Answer:

Step-by-step explanation:

t=2g+3.

please help me to do this question ​

Answers

Answer:

firdt method is

Length x breath

is equal to ½

Let A={5,8}, B={p,q}, C={r,v} How many elements are in A×B?

Answers

There are 4 elements in the set A* B

How to determine the number of elements in A * B?

The sets are given as:

A={5,8}

B={p,q}

C={r,v}

The expression A * B implies that:

A * B = n(A) * n(B)

Where n( ) implies that the number of elements in......

So, we have

A * B = 2 * 2

This is so because sets A and B have 2 elements each

Evaluate the product

A * B = 4

Hence, there are 4 elements in the set A* B

Read more about sets at

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#SPJ1

Please give this in steps

Answers

Answer:

(x - y)²

Step-by-step explanation:

Given

(x + y)² - 4xy

= x² + 2xy + y² - 4xy

= x² - 2xy + y²

= (x - y)²

Answer:

[tex] {(x + y)}^{2} - 4xy = {x}^{2} + 2xy + {y}^{2} - 4xy \\ = {x}^{2} - 2xy + {y}^{2} \\ = {(x - y)}^{2} \\ thank \: you[/tex]

NJ Transit raises its train fees. Snooki wants to visit her parents which used to cost $28 but they increased the fares by 15%. What will the ticket cost now?

Answers

Answer: 32.20$ Train Fee

Step-by-step explanation:

15% of 28 is 4.20... 4.20 will be added to the current Train Fee

   28.00$

 +   4.20$

    32.20$

Final result: The Train Fee will be 32.20$

Build a function whose domain is all real numbers other than -4, and whose range is all real numbers other than 5.

Answers

Answer:

An example is the rational function [tex]y=\frac{5x}{x+4}[/tex].

Step-by-step explanation:

The graph of the rational function [tex]y=\frac{5x}{x+4}[/tex] has a vertical asymptote at x = -4 where the denominator is equal to zero.  The function is undefined there, so the domain is all real numbers except -4.

The graph has a horizontal asymptote  y = 5  so the domain is all real numbers except 5.

See the attached image for the graph of the function (purple) and it's vertical asymptote (black).

Q16. If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet. What is the
width?
16 feet
O 35 feet
O 37 feet
0 40 feet
42 feet

Answers

Answer:

OPTION A :16 FEET

PERIMETER =26 1/3=76/3yard=76/3×3=76 feet

LENGTH=22feet

Width=76/2-22

WIDTH=38-22=16 FEET

Can anyone help? Most brainiest for the correct answer!!

Answers

Answer:  25

Explanation:

The "large cars" pie slice takes up 7% of a full circle. This means that the degree measure of this slice takes up 7% of a full 360 revolution.

7% of 360 = 0.07*360 = 25.2 degrees

This then rounds to 25 degrees

25

If you like, I can put on the solution.

write the equation of the line in fully simplified slope-intercept form.​

Answers

Answer:

slope intercept form: y=mx+c

Step-by-step explanation:

By using two points form:

y-0/3-0=x-1/2 /0-3

y/3=x-1/2 /3

y=x-1/2

Note:if you need to know any question please let me know.

Type your answers into the boxes.
The ratio of men to women in a gym is 7 : 5
What fraction of the gym members are women?

Answers

Answer:

[tex] \frac{5}{12} [/tex]

Step-by-step explanation:

[tex] \frac{5}{7 + 5} [/tex]

I'm not sure about the answer. Sorry if it's wrong.

a person runs at a constant speed of 9.2 miles per hour for 6 minutes and 30 seconds. How far did they travel in yards.

Answers

Given:

Speed[tex]= \bold{9.2 \ \frac{miles}{hour}}[/tex]  

[tex]\therefore \\\\[/tex]

1-hour= 60 minutes

1-minutes=60 second

So

1-hour= 3600 second

Converting the given time into seconds:

Time= 6 minutes and 30 second

       [tex]=\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\[/tex]

When 3600 seconds covers=9.2 miles

Then equation:

[tex]=\bold{\frac{9.2}{3600}}\\\\[/tex]

390 seconds covers:

[tex]=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\[/tex]  

Let

[tex]\bold{1 \ miles= 1760\ yard}\\\\[/tex]

Convert the traveling value into yards:

[tex]=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\[/tex]

Therefore, total traveling yards are"1754.072".  

Learn more:

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Speed of the person has been given as 9.2 miles per hour.

Therefore, speed of the person in miles per minute = [tex]\frac{9.2}{60}[/tex]

Duration for which the person is running = 6 minutes and 30 seconds

                                                                    = 6 minutes and [tex]\frac{30}{60}[/tex] minutes

                                                                    = 6.5 minutes

Since, Distance = Speed × Time

By substituting the values in the expression we can get the distance traveled.

Distance = [tex]\frac{9.2}{60}\times 6.5[/tex]

               = 0.9967 miles

Since, 1 mile = 1760 yards

Therefore, 0.99667 miles = 1760 × 0.99667

                                           = 1754.13 yards

Total distance traveled by the person is 1754.13 yards.

Learn more,

https://brainly.com/question/13458499

h(1) = 9
h(2) = 3
h(n)=h (n−2) ⋅ h(n−1)
​h(3)

Answers

Answer:

27

Step-by-step explanation:

h(n)=h (n−2) ⋅ h(n−1)

h(3)=h (3−2) ⋅ h(3−1)

h(3)=h (1) ⋅ h(2)

h(3)=9 ⋅ 3

h(3)=27

Answer:

27

Step-by-step explanation:

khan

in a class of 80 students in Debre Berhan university,45 good in mathematics,15 are good in both Mathematics and English,13 are good in both Mathematics and Psychology, 16 are good in both in English and psychology,20 are good in Psychology and 9 are good in both of the three courses A,how many students are good in mathematics only? B,how many students are not good in any of three courses?

Answers

The relationship between the number of students that are good at a given subject is an illustration of sets.

26 students are good at Mathematics only.28 students are not good at all.

We use the following representations:

[tex]M \to[/tex] Mathematics

[tex]E \to[/tex] English

[tex]P \to[/tex] Psychology

From the question, we have the following parameters

[tex]M = 45[/tex] -- Mathematics

[tex]M\ n\ E =15[/tex] -- Mathematics and English

[tex]M\ n\ P =13[/tex] -- Mathematics and Psychology

[tex]E\ n\ P =16[/tex] -- English and Psychology

[tex]P=20[/tex] -- Psychology

[tex]All = 9[/tex] -- All 3 subjects

[tex]Total = 80[/tex] -- All students

The number of students that are good at mathematics only is as follows:

First, we calculate those that are good at mathematics and English only

[tex](M\ n\ E)' = M\ n\ E - All[/tex]

[tex](M\ n\ E)' = 15 - 9 = 6[/tex]

Then those that are good at mathematics and psychology only

[tex](M\ n\ P)' = M\ n\ P - All[/tex]

[tex](M\ n\ P)' = 13 - 9 = 4[/tex]

So, the students that are good at mathematics only are:

[tex]M' = M - (M\ n\ E)' -(M\ n\ P)' - All[/tex]

[tex]M' = 45 - 6 -4 -9[/tex]

[tex]M' = 26[/tex]

Hence, 26 students are good at Mathematics only.

To calculate the number of students that are not good in any of the subjects, we make use of the complement rule

[tex]A + A' = Total[/tex]

Where:

[tex]A \to[/tex] Students that are not good in any

[tex]A' \to[/tex] Students that are good in at least one

So, we have:

[tex]A' =M' + (M\ n\ E)' + (M\ n\ P)' + (E\ n\ P)' + All[/tex]

Where:

[tex](E\ n\ P) = (E\ n\ P)' - All[/tex]

[tex](E\ n\ P) = 16-9 = 7[/tex]

The equation becomes:

[tex]A' =26 + 6 + 4+7+9[/tex]

[tex]A' =52[/tex]

Recall that:

[tex]A + A' = Total[/tex]

[tex]A = Total - A'[/tex]

[tex]A = 80 - 52[/tex]

[tex]A = 28[/tex]

Hence, 28 students are not good at all.

Read more about sets at:

https://brainly.com/question/24388608

In a mathematics class , half of the students scored 84 on an achievement test. With the exception of a few students who scored 50 , the remaining students scored 76. Which of the following statements is true about the distribution of scores ?


A. The mean is greater than the mode.
B. The mean and the median are the same.
C. The mean is less than the median.
D. The mean is greater than the median.

Answers

Answer: B. The mean is less than the median

Step-by-step explanation:

there are some that scored 51 which means - mean<median

What is the solution to
:-7?
A. 81
B. 63
C. 63
D. -81

Please help me I’m dum

Answers

Answer:

-63

Step-by-step explanation:

63/9 = 7, so in order to make the answer -7, 63 must be negative.

A=1/2bh solve for b then h

Answers

Answer:

There is no right or wrong answer

Step-by-step explanation:

You did not give enough information, this formula usually comes with a triangle that you want to solve, therefore no one can answer this correctly since there is nothing to solve.

The question is asking your to restate b in terms of A and h.

A = 1/2 bh

divide by 1/2
2A = bh

divide by h
2A/h = b

8th grade math
5. What is the probability of rolling a 3 on a 6-sided number cube and then NOT rolling 2 or 4 on a 6-sided number cube?

Answers

Answer:

5 in 12 chance or 42% probability of happening

Probably of rolling 3 is 1/6
Probably not rolling 2 or 4 is 4/6
Independent event so:
P(a)*P(b)= 1/6*4/6 = 4/36 =0.111

PLZ HELP ASAP I NEED PLZZZ!!!!!!
Fill in the blank with the correct response. The slope of the graph of y = -2/3x is __.

Answers

Answer:

Solution given:

Equation of line is:

y=-⅔x

comparing above equation with

y=mx+c

we get

m=-⅔

So

slope is -⅔

Answer:

slope is -2/3

Step-by-step explanation:

I. It's linear equation

    y = mx + b

when y is output, x is input, m is slope and b is addition.

The statment above is y = -2/3x + 0

So -2/3 is slope or m.value

Hope that help :D

The cube of an integer is called a __________ ?

Answers

Answer:

a perfect cube

Step-by-step explanation:

Answer:

It is called a perfect cube .

Step-by-step explanation:

Apply the distributive property to factor out the greatest common factor.
40f + 30

Answers

It is 30 because everyone is

What is the perimeter (in feet and inches) of a rectangle that has a length of 12'7" and a height of 11'3"?

Answers

Answer:

p=2l+2w

=2*12'7"+2*11'3"

what is 3 ÷ 2/5??? pls help

Answers

Answer:

7.5

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

3/2/5=3/2×5. a/b/c=a/b×c

1.5×5=7.5

X¹² - 1 แยกตัวประกอบของพหูนาม

Answers

Answer:

[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]

Step-by-step explanation:

Factor of [tex]x^{12}-1[/tex] is

[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]

find the domain of f(x) = 3x + 5

Answers

Answer:

All real numbers

Step-by-step explanation:

All real numbers: f(x) is defined for all values of x. There are no discontinuities or places where f(x) is undefined. f(x) is just a straight line going to infinity.

Answer:

(-infinity, infinity), or all real numbers

Step-by-step explanation:

If you were to look at it graphically, it would be a linear function with a slope of 3 and shifted up 5 units. (i attached a screenshot of what the graph would look like at the bottom :)

since there are no domain restrictions, you're not really going to have any issues or gaps which is when you might need to do something like

(-infinity,4] u(5,inifinity) --> since this isn't the case though, you're totally free to just write all real numbers, because all real numbers in the x-plane (as that is what domain looks at) are included.

When all else fails, (at least for homework), desmos is great for graphing and looking at everything visually

Hope that helps! lmk if you have any questions :)

If X= 9 and Y = 3, what is XY

Answers

Answer:

The most basic question I have ever seen lol

XY = 9*3 = 27

It is 27

XY means X*Y
3*9=27
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