Find the sum of the arithmetic series given a1=45, an=85, and n=. 5

Answer: [tex](x,y)=\{(-1,1), (0,4) \}[/tex]

Step-by-step explanation:

[tex]3x^2 +6x+4=-3x^2 +4\\\\6x^2 +6x=0\\\\x^2 +x=0\\\\x(x+1)=0\\\\x=-1, 0\\\\x=-1 \longrightarrow y=1\\\\x=0 \longrightarrow y=4\\\\\therefore (x,y)=\{(-1,1), (0,4) \}[/tex]

The solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given quadratic equations are given as below:-

y = 3x² + 6x + 4

y = -3x² + 4

Equate the equations and solve for the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

x² + x = 0

x ( x + 1 ) = 0

x = 0 and x = -1

At x=0 and x=-1 the values of y are calculated as below:-

y = -3x² + 4

y = 0+ 4 = 4

y = -3 + 4 = 1

Therefore, the solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

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The number of ways when the choice is not relevant is 10

The number of objects are:

Object, n = 5

The object to choose are:

r = 3

Relevant choice

When the choice is relevant, we have:

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^{5}P_3[/tex]

Evaluate

Ways = 60

Hence, the number of ways when the choice is relevant is 60

Not relevant choice

When the choice is not relevant, we have:

[tex]Ways = ^nC_r[/tex]

This gives

[tex]Ways = ^{5}C_3[/tex]

Evaluate

Ways = 10

Hence, the number of ways when the choice is not relevant is 10

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Answer:

116

Step-by-step explanation:

zinc : copper

4      :     11

11 = 319

zinc = 4 / 11 * 319

Zinc = 116

Answer:

2

Step-by-step explanation:

You have the correct answer selected: 2.

The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.

2 times 2 is 4. That's why (8^2)^2 = 8^4

Answer:

p = 2

Step-by-step explanation:

[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]

  [tex]8^{2p}[/tex] =    [tex]8^{4}[/tex]

   [tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]

    p = 2

Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1

Answer: The given equation is

f(x) = x^{4} - 1

x- and y-intercept of the graph of the function f(x) = x^4 - 1 is

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

A graph of the above point is attached

Step-by-step explanation:

Given equation, f(x) = x^{4} - 1

let's assume the above equation with respect to y to find intercept i.e

y = x^{4} - 1 .........................(i)

Now, for the x-intercept put y = 0 in eq.(i)

So, we get,

0 = x^4 - 1

x^4 = 1

x = -1, +1

from above we get the x-intercept (1,0), (−1,0)

Now, for the y-intercept put x = 0 in eq.(i)

So, we get

y = 0^4 - 1

y = -1

from above we get the y-intercept (0, -1)

Therefore, from all above

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

Graph of the given equation f(x) = x^4 - 1 with intercept is

Answer:   About the building of his bed

Answer: Option (1)

Step-by-step explanation:

[tex]3x^3 - 6x^2 + 30x-20=-20\\\\3x^3 - 6x^2 + 30x=0\\\\3x(x^2 - 2x+10)=0\\\\[/tex]

So, either [tex]x=0[/tex] or [tex]x^2 -2x +10=0[/tex]

For the second case, we know x=0.

For the second case, we can use the quadratic formula.

[tex]x=\frac{2 \pm \sqrt{(-2)^2 - 4(1)(10)}}{2}\\\\x=1 \pm 3i[/tex]

Answer:

C. (2;9)

Step-by-step explanation:

for more details see the attachment.

Step-by-step explanation:

++++5

+++++++_2

1=false

true

false

false

Given :

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}[/tex]

[tex] \: [/tex]

Let's solve by using midpoint formula :

[tex] \: [/tex]

[tex] \bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}[/tex]

[tex] \: [/tex]

[tex] \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}[/tex]

[tex] \: [/tex]

[tex] \: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}[/tex]

[tex] \: [/tex]

[tex]\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}[/tex]

[tex] \: \: [/tex]

[tex] \underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓[/tex]

Hope Helps! :)

See below for the complete table and graph of y = x + 4

The function is given as:

y = x +4

Where x = -2, 0, 2, 6 and 8

So, we have

y = -2 +4 = 2

y = 0 +4 = 4

y = 2 +4 = 6

y = 6 +4 = 10

y = 8 +4 = 12

The above computation implies that the complete table is

Input x        x + 4        Output, y        (x, y)

-2               -2  + 4          2                  (-2,2)

0                 0  + 4          4                  (0,4)

2                 2  + 4          6                  (2,6)

6                 6  + 4          10                 (6,10)

8                 8  + 4          12                  (8,12)

See attachment for the graph of y = -x + 4

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The number of years it will take for the world’s population to increase to 8,252,000,000 people is 16

This implies that we calculate the value of x

The equation is given as:

8252=(6080)(1.02)^x

Divide both sides by 6080

1.36 = (1.02)^x

Take the logarithm of both sides

log(1.36) = x * log(1.02)

Divide both sides log(1.02)

x = log(1.36)/log(1.02)

Evaluate the quotient

x = 16

Hence, the number of years is 16

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Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).

The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.

In step 5 where the multiplication property of equality is applied, we would have:

sin(A) = CD/b

Multiply both sides by b

sin(A) × b = CD/b × b

b(sin A) = CD

CD = b(sin A)

This same property is applied to sin B = CD/a to get CD = a(sin B).

Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).

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The length of AC is 12 units . Option D

The formula for area of a kite is given thus;

Area = [tex]\frac{p * q}{2}[/tex]

Where p and q are the lengths

Area of kite = 48 square units

BD, q = 8 units

AC , p = unknown

Substitute the values

[tex]48 = \frac{AC * 8}{2}[/tex]

Cross multiply

[tex]AC * 8 = 48 * 2[/tex]

[tex]8AC = 96[/tex]

[tex]AC = \frac{96}{8}[/tex]

[tex]AC = 12[/tex] units

Thus, the length of AC is 12 units . Option D

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Answer:option 4

Step-by-step explanation:

Answer: 97350

Step-by-step explanation:

The numbers (3251)(30) are separated by using parentheses by multiplying the numbers we get 97350.

When we notice two or more numbers together that exist divided by parentheses, then the parentheses exist pointing us to multiply.  In math, multiplying indicates adding equivalent groups. When we multiply, the number of things in the group rises. The two elements and the product exist as regions of a multiplication problem.

Given: (3251)(30)

Here, the numbers are separated by using parentheses, then the parentheses exist pointing us to multiply.

Therefore, by multiplying the numbers we get

(3,251)(30) = 97350

Therefore, the correct answer is 97350.

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Answer:

E

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

Consider the triangle on the left

3rd angle = 180° - 60° - 90° = 180° - 150° = 30°

the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so

∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°

Answer:

-2

Step-by-step explanation:

When x = 1, 3x² + 2x - 7 = -2.

1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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The value of y at x =15 is 9.

Two variables are said to be in Direct Variation when increasing one variable the other also increases.

The direct variation is represented by

y ∝ x

y = kx

where k is the proportionality constant

the value of y =12 , x = 20

12 = k * 20

12/20 = k

k = 0.6

The equation becomes

y = 0.6 x

The value of y at x = 15 is

y = 0.6 * 15

y =9

Therefore, the value of y at x =15 is 9.

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An appropriate numerical summary is descriptive statistics.

It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.

In this case, descriptive statistics can be used. This is used to describe the data set.

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The value of x comes out to be 6 from the algebraic equation.

Solving the Given Algebraic Equation for x:

Given algebraic equation is,

3x + 12 = 8x - 18

⇒ 12 = 8x - 3x -18

8x - 3x - 18 = 12

5x - 18 = 12

5x = 12 + 18

5x = 30

x = 30 / 5

x = 6

What is an algebraic equation?

A mathematical statement in which two expressions are put equal to one another is known as an algebraic equation. One or more variables, coefficients, and constants make up an algebraic equation in most cases. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

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The probability of selecting two prime numbers is 1/6.

Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.

The probability of selecting two prime numbers  = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]

Prime numbers between 1 and 9 = 2, 3, 5, 7

4/9 x 3/8 = 1/6

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Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)

Answer:

CIRCLE

Step-by-step explanation:

Answer:

it's answer came 20000o

Answer:

11  units

Step-by-step explanation:

We first need to solve for x

3x -28 +3x -30 + x = 33  Combine the x's

7x - 28 -30 = 33  Combine -28 and -30

7x - 58 = 33  Add 58 to both sides

7x = 91  Divide both sides by 7

x = 13  Now plug 13 into the expression for DE

3x - 28

3(13) - 28

39 -28

11