1Determine the vertex of the quadratic function f(x) = (x - 3)^2 +7.

Please give detailed steps!! thank you

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

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.

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Answer:

a perfect cube

Step-by-step explanation:

Answer:

It is called a perfect cube .

Step-by-step explanation:

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

Answer:

5 in 12 chance or 42% probability of happening

Answer:

+or-6

Step-by-step explanation:

This is a trick question. The answer would be the first choice since you're multiplying -6 by +or-6, meaning that it could still end up as a negative or a positive.

Answer:

Step-by-step explanation:

Answer:

[tex] \frac{12 - 23 \sqrt{2} }{46} [/tex]

Step-by-step explanation:

you find the LCM

Answer:

The most basic question I have ever seen lol

XY = 9*3 = 27

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

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.

Answer:

the point (9,-12) is also on the line

Step-by-step explanation:

by using the 2 points the equation is y=-4/3x

use x of 9

y = -12

it will also represent a direct variation function

so two of the 4 will be correct

Answer:

The point (9,-12) is also on the line

Step-by-step explanation:

Please give brainliest

Answer:

Step-by-step explanation:

t=2g+3.

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$

5 students offers all the two subjects.

Student that offers Physic only = 15 students

Student that offers chemistry only  = 13 students

Students that offers only one subject = 28 students

Total student in the class = 35

20 offer physics.

18 offer chemistry

2 offer neither physics nor chemistry.

Therefore,

x = student that offer both subject

35 = 20 + 18 - x + 2

35 - 2 - 20 - 18 = -x

-5 = -x

x = 5

Therefore, 5 students offers all the two subjects.

Student that offers Physic only = 20 - 5 = 15

Student that offers chemistry only = 18 - 5 = 13

Students that offers only one subject = 13 + 15 = 28

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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]

Answer:

-63

Step-by-step explanation:

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

Answer:

c) ten thousand dollars

Step-by-step explanation:

There are 4 elements in the set 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

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The answer is: 250 adult tickets were sold.

To be safe, prove that your answer is correct.

If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.

Explanation:

74 more than 250, or 250+74 is 324.

250+324=574.

Now, you know the answer is correct. It satisfies all of the given conditions.

Also, note that the difference between the number of student tickets and adult tickets is 74.

So, there are 250 adult tickets and 324 student tickets.

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.

After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives

[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]

Then taking differentials, you get

[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]

Replacing everything in the original integral then gives

[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]

Split up the integrand into partial fractions:

[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]

so that

[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]

Answer:

[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]

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]

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Answer: B. The mean is less than the median

Step-by-step explanation:

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

Step-by-step explanation:

LxB

8x7

equals :56

Area equals to 56cm

Answer:

Solution given:

Equation of line is:

y=-⅔x

comparing above equation with

y=mx+c

we get

m=-⅔

So

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

Answer:

$5

Step-by-step explanation:

Number of hours worked = 32

Total pay = $160

So, hourly rate

= Total pay/number of hours worked

= $160/32

= $5

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".  

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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.

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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]