Evaluate 3 + 2(x + 5)² for x = -2.
OA. 18
OB. 45
OC. 21
OD. 11

Answer:

x ≤-4 or x> 2

Step-by-step explanation:

x+1 ≤-3 or-4x<-8

First solve the inequality on the left

x+1 ≤-3

Subtract 1 from each side

x+1-1 ≤-3-1

x ≤-4

Then solve the inequality on the right

-4x<-8

Divide each side by -4, remembering to flip the inequality

-4x/4 > -8/-4

x > 2

Put them back together

x ≤-4 or x> 2

Closed circle at -4 and line going to the left and open circle at 2 and line going to the right

The sun's diameter as described in the task content is; ; 1.09 × 10⁵ times the earth's diameter.

This follows from the given premise that; the diameter of the sun is approximately 1.4x10⁹ Km and the diameter of Earth is approximately 1.28x10⁴ Km

According to the task content; The diameter of the sun is approximately 1.4x10^9 Km and the diameter of Earth is approximately 1.28x10^4 Km.

The number of times by which the sun's diameter is greater than the earth's diameter can be evaluated as follows;

= 1.4 × 10⁹/1.28 × 10⁴

= 1.09 × 10⁵

Ultimately, The sun's diameter as described in the task content is; 1.09 × 10⁵ times the earth's diameter.

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The value of x that cannot be evaluated in the function F(x) is 3

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

f(x) = (x + 13)/(x - 3)

Set the denominator of the function to 0

So, we have

x - 3 = 0

Evaluate the equation

x =3

This means that x =3 is not in the domain of the function

Hence, the value of x that cannot be evaluated in the function F(x) is 3

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Answer:

500

Step-by-step explanation:

20*25

I don't know if this is right this is just how my teacher taught my class

[tex]\cfrac{1}{2}(4x-2)\leqslant 9+7x\implies 2x-1\leqslant 9+7x\implies -1\leqslant 9+5x \\\\\\ -10\leqslant 5x\implies \cfrac{-10}{5}\leqslant x\implies {\LARGE \begin{array}{llll} -2\leqslant x \end{array}}[/tex]

le's notice that, we divided by a positive number, thus the inequality sign didn't flip.

The solutions of the system of equations are:

x = -2, y = 4, z = -2

Here we have the system of equations:

4x - y - 2z = -8

-2x + 4z = -4

x + 2y = 6

To eliminate one variable, we can add the second equation and two times the third equation, we will get:

(-2x + 4z) + 2*(x + 2y) = -4 + 2*6

Now we can simplify that so we get:

4z + 4y = -4 + 12

4*(z + y) = 8

z + y = 8/4  =2

z + y = 2

With that we can write z in terms of y.

z = 2 - y

And with the third equation we can write x in terms of y.

x = 6 - 2y

Replacing that in the first equation we get:

4*(6 - 2y) - y - 2*(2 - y) = -8

Now we can solve this for y.

24 - 8y - y +2y - 4 = -8

20 - 11y = -8

-7y = -28

y = 28/7  = 4

Now that we know the value of y we can find the values of x and z.

x = 6 - 2y = 6 - 2*4 = -2

z = 2 - y = 2 - 4 = -2

The solutions of the system of equations are:

x = -2, y = 4, z = -2

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Answer:

Hello,

Step-by-step explanation:

[tex]x^4+4x^3-64x-256\\=x^3(x+4)-64(x+4)\\=(x+4)(x^3-64)\\-----------\\s(x)=x^4+4x^3-64x-256\\=(x+4)(x^3-4^4)\\=(x+4)(x-4)(x^2+4x+16)\\[/tex]

Answer: 17/18=34/36

11/12=33/36

Step-by-step explanation:

17/18 and 11/12

First find the LCM, least common multiple, of the denominators 18 and 12.

In order to do that, list the factors of 18 and 12 and find the least common factors of them excluding 1.

18: 1, 2, 3, 6, 9, 18

12: 1, 2, 3, 4, 6, 12

Notice any common small factors? Yes they are 2 and 3. Now, multiply them with 18 and 12.

18*2=36

12*3=36

Hence, LCM is 36.

17/18=(17*2)/(18*2)=34/36

11/12=(11*3)/(12*3)=33/36

Answer:

y=5/2x+3 or [tex]y=\frac{5}{2}x+3[/tex]

Step-by-step explanation:

Step 1:

Compute the slope (-4, -7), (2,8):

m=5/2

Step 2:

Compute the y intercept:

b=3

Step 3:

Add the results together:

y=5/2x+3 or [tex]y=\frac{5}{2}x+3[/tex]

Hence, the final answer is y=5/2x+3 or [tex]y=\frac{5}{2}x+3[/tex]

Greetings from Brasil...

One way to solve this question is through determinant

| X     Y     1 |

| X₁    Y₁    1 |  = 0

| X₂    Y₂   1 |

We have:

(X₁; Y₁) = (-4; -7)

(X₂; Y₂) = (2; 8)

then

| X   Y   1 |

| -4  -7   1 |  = 0

| 2   8    1 |

________________________________

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An Edge of a polyhedron is the intersection of the Vertex of the polyhedron.

A polyhedron  can be described as the 3-dimensional solid that is been formed through the combination of more than one polygons and they usually have different faces which is been used in knowing them as well as their classification.

It should be noted that this polyhedrons  can be categorized based on the  number of faces that can be found on them, however in this case we can conclude that the Vertex serves as the point of intersection that the edges of  polyhedron has.

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Answer:

edge, vertex

Step-by-step explanation:

Answer:

ysfsfdf

Step-by-step explanation:

frfrfrfrb

The Red Savina Habanero is 6. 13 times hotter than the Thai Pepper. Option A

A ratio can be defined as the comparison of two or more numbers on the basis of their sizes in relation to each other;

Given that;

To determine the ratio, we have to divide Red Savina Habanero hotness rating by Thai Pepper hotness rating

This is represented as;

= 4.6 x 10^5 /  7.5 x 10^4

= 6. 13 times

The Red Savina Habanero is 6. 13 times hotter

Thus, the Red Savina Habanero is 6. 13 times hotter than the Thai Pepper. Option A

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By taking the quotient between the ratings, we can see that  Red Savina Habanero is 6.13 times hotter than the Thai Pepper.

We know that the Thai Pepper has a hotness rating of 7.5*10⁴, while the Red Savina Habanero has a hotness rating of 4.6*10⁵.

We want to see how many times hotter is the Red Savina Habanero than the Thai Pepper, to find that we need to take the quotient between the rating for the Habanero and the rating for the Pepper.

It gives:

Q = (4.6*10⁵)/(7.5*10⁴)

This can be rewritten as:

Q = (4.6/7.5)*(10⁵/10⁴)

   =0.613*(10 ⁵⁻⁴) = 0.613*10

Now, we want to write this in scientific notation, so we need to have a single digit different than zero in the left side of the decimal point.

Then we can rewrite:

0.613*10 = 6.13*10⁰ = 6.13

We conclude that the Red Savina Habanero is 6.13 times hotter than the Thai Pepper.

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The coordinates of H are (-9,-1) when H is on FG and divides it such that  FH:GH is 1:2.

It is given that  F(–8,3) and G(–2,–9) and ratio of  FH:GH is 1:2.

The diagram of this question is given below.

Let  coordinates of H be ( x , y) .

By using sections formula , we get

(x , y) = ( 1(-2) + 2(-8) / 1+2 , 1(-9) +2(3) / 1+2 )

(x , y) =  ( -2 -16 / 1 +2 , -9 +6 / 1 +2 )

(x , y) = ( -18 / 3 , -3/3)

(x , y) = ( -9 , -1)

On comparing , we get x = -9 and y = -1.

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passive income

dividends, real estate, interest income

active income

salary, business income,  

let me give you a mouthful of something

the domain of f(x) is the range of its inverse, or namely the domain of f(x) is the same set as the range of f⁻¹(x), so for any (a , b) pair on the domain of f(x), there's a (b , a) on the range of f⁻¹(x).

now, that's a bit of of a mumble, but in short it means, if f(x) has a point of (3 , 5), then the graph of f⁻¹(x) has a point which is the same pair but flipped sideways, namely (5 , 3).

that's pretty much true for any function that has an inverse.

Answer:

I think the answer is B

Step-by-step explanation:

Hope this helps

Sorry if I'm wrong

Answer:

-1

Step-by-step explanation:

When the area A of a rectangle is represented by the formula A= lw, the formula for the length will be l = A / w.

It should be noted that the area A of a rectangle is represented by the formula A= lw

where I is the length

W is the width

It should be noted that based on the information, we want to find the formula to solve for the length.

A = lw

Divide through by w

A/w = lw/w

l = A / w

Therefore, when the area A of a rectangle is represented by the formula A= lw, the formula for the length will be l = A / w.

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Answer:

28/35

Step-by-step explanation:

4/5 *7/7=28/35

Answer:

pre-test

Step-by-step explanation:

(1) identifity my own strengths

interest and challenges.

Using linear functions, it is found that Ginny must attend at least 13 events to make the premier member package cost less.

The complete question is given as follows:

"Ginny wants to join a local dance club that has dance events every week. There are two membership options available: Ginny may become a premier member by paying a fee of $150 per year and attend an unlimited number of dances. Ginny may become a regular member by paying a fee of $50 and then pay $8 per dance she attends. How many dances must Ginny attend such that becoming a premier member will cost less than becoming a regular member? "

A linear function is modeled in slope-intercept form by:

y = mx + b

In which:

For this problem, we have that:

Hence the functions for each option are given as follows:

Being a premier member will cost less when:

P(x) < R(x).

Hence:

150 < 50 + 8x

8x > 100

x > 100/8

x > 12.5 -> at least 13 events.

Ginny must attend at least 13 events to make the premier member package cost less.

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The mean is  12.28

The mode is 9.6.

The median is 10.25.

Mean, median, and mode are measures of central tendency. Mean is the average of a set of numbers. Median is the number that is at the center of a dataset when the dataset is arranged in ascending or descending order. Mode is the number that occurs most frequently in a dataset.

Mean = sum of numbers / total number

(11.3 + 9.9 + 9.6 + 11.5 +9.6 + 11.2 + 10.6) / 6

= 73.7 / 6

= 12.28

The number that occurs most frequently is 9.6. It occurs twice in the dataset. 9.6 is the mode.

The median = (total number + 1) / 2

(6 + 1) / 2

= 7/2 = 3.5 digit

9.6, 9.6, 9.9, 10.6, 11.2, 11.3

(9.9 + 10.6) / 2

= 20.5 / 2 = 10.25

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Answer:

Rational & Integer

Step-by-step explanation:

Rational numbers are real numbers. Unlike Irrational numbers, they have a clear value.

Integers are just counting numbers but including 0 and negative numbers.

Hope this helps :)

Answer:

2,390

18,851

4,004

761,681

624,180

The probability that both the balls are black is  [tex]\frac{1}{9} \\[/tex] .

Probability is the section of mathematics which deals with the likelihood of an event happening.

The value of probability is a fraction which always lies between 0 and 1. it is defined as the ratio of the favorable outcomes of an event to the total outcome of an event.

Given the bag has 10 white balls and 5 black balls. Therefore the total number of balls in the bag is 15 .

Hence the sample space is 15 .

The balls are drawn with replacement. Therefore for the first ball pick:

Number of favorable outcomes = 5

Total number of outcomes = 15

Probability = favorable outcome ÷ total outcome

Therefore  [tex]P_1=\frac{5}{15}=\frac{1}{3}[/tex]

Now the ball is placed back and the second ball is picked.

Number of favorable outcomes = 5

Total number of outcomes = 15

Probability = favorable outcome ÷ total outcome

Therefore  [tex]P_2=\frac{5}{15}=\frac{1}{3}[/tex]

Now the total probability that both the balls are black is :

P = P₁×P₂

[tex]P=\frac{1}{3}\times \frac{1}{3}\\\\P=\frac{1}{9}[/tex]

Hence the probability of picking two black balls is  [tex]\frac{1}{9} \\[/tex]  .

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The evaluations of the quadratic equation at the values of 0, 7 and - 5 are 5, 1356 and - 460, respectively.

In this question we have the definition of a quadratic equation, which has to be evaluated at three distinct values of x. Evaluating a function consists in substituting the independent variable by a value and simplify the expression. Now we proceed to evaluate the function:

f(0) = 4 · 0³ - 7 · 0 + 5

f(0) = 5

f(7) = 4 · 7³ - 7 · 3 + 5

f(7) = 1372 - 21 + 5

f(7) = 1356

f(- 5) = 4 · (- 5)³ - 7 · (- 5) + 5

f(- 5) = - 460

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[tex] \large \bf \implies{ {x}^{2} + 3x - 10}[/tex]

[tex](x + 5)(x - 2)[/tex]

Step 1) : Using the identity

[tex] \bf \longrightarrow{(x+a)(x+b) = x² + (a+b)x + ab}[/tex]

Step 2) : Simplify it with using the identity told earlier in step 1) .

[tex] \bf \longrightarrow(x + 5)(x - 2) \\ \\ \bf \longrightarrow{x}^{2} + (5 + ( - 2))x + (5)( - 2) \\ \\\bf \longrightarrow {x}^{2} + (5 - 2)x + ( - 10) \\ \\\bf \longrightarrow {x}^{2} +3x - 10[/tex]

Step 3) : We have got the answer in step 2) .

[tex] \large\bf \longrightarrow { {x}^{2} + 3x - 10}[/tex]

Answer:

3/20

Step-by-step explanation:

when multiplying fractions, you don't have to worry about changing denominators, since they will multiply together, so just multiply the numerators and denominators

2*3/5*8=6/40

Then, simplify

6/2/40/2=3/20

Answer:

2 quartes is equal to 50 cent, 5 dimes is equal to 50 cent, and 3 pennies is equal to 3 cents.

50 + 50 + 3 = 103

$1.03

Step-by-step explanation:

Hope it helps! =D

Answer:

1 dollar and 3 cents.

2 cents=0.5 dollars

5 dimes=0.5 dollars

3 pennies=0.03 dollars

$1.03

The graph of Camila's data representing temperature on the y-axis and time on the x-axis is as attached

The question is a word problem that involves constructing a table of values and then graph the table values data as below;

Time      Temperature

6:00        56

7:00        59

8:00        62

9:00        65

10:00       66

11:00        67

12:00       68

13:00       69

14:00        70

15:00        70

16:00        70

17:00        70

18:00        70

19:00        67

20:00       64

21:00        61

00:00        60

The graph of Camila's data representing temperature on the y-axis and time on the x-axis is as attached

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