Is (−1, −1) a solution to the following system of inequalities? Show work to verify algebraically. Then, provide an explanation below.

Answer:

D. y = (x + 8) (x + 1)

Explanation:

[tex]\sf y = x^2 + 9x + 8[/tex]

[tex]\rightarrow \sf y = x^2 + 9x + 8[/tex]

middle term split

[tex]\rightarrow \sf y = x^2 + 8x +x + 8[/tex]

factor the common terms

[tex]\rightarrow \sf y = x(x + 8) + 1(x + 8)[/tex]

collect into groups

[tex]\rightarrow \sf y = (x + 1)(x + 8)[/tex]

Option D

Answer:

(4, 4)

Step-by-step explanation:

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]

Match the values in this hyperbola to those of the standard form. The variable h represents the x-offset from the origin, k represents the y-offset from origin, a.

a = 1

b = 3

k = 4

h = 4

Thus,

[tex](x-4)^2 - \frac{(y-4)^2}{9} = 1[/tex]

The center of a hyperbola follows the form of (h, k). Substitute in the values of h and k.

= (4, 4)

Answer:

0.93

Step-by-step explanation:

Answer: six ways

Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.

Answer:

===========================

Given equation and steps to solve it:

All steps given above including the missing one. As we can see, we divided both sides by 4, so the justification for this step is Division Property of Equality.

Hence, the correct choice is C.

Answer:

Four times x over four equals four over four; Division Property of Equality

Step-by-step explanation:

See on antepenultimate step

Now for getting x we have to divide each side by 4

We get.

1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)

2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)

3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)

4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)

5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)

Answer:

5.32⋅10−6

Step-by-step explanation:

Answer:

5320000

Step-by-step explanation:

standard notation form : 5320000

The number of people who can go to the amusement park is 8.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given: the group of friends had $280.

For parking=  $19.50

Remaining will be,

=$(280-19.50)

= $ 260.5

Cost of ticket per person = $33.75

Thus, number of tickets they can buy

=260.5 / 33.75

=7.718 = 8 peoples

Hence, number of people who can go to the amusement park is 8.

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Answer:

check image below

Step-by-step explanation:

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Answer:  [tex]\textsf{y = -2/5x}[/tex]

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Given:  [tex]\textsf{Passes through (5, -2) and slope of -2/5}[/tex]

Find:  [tex]\textsf{The equation that follows the details provided}[/tex]

Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.

Plug in the values

Distribute and simplify

Subtract 2 from both sides

Therefore, the final equation that follows the information that was provided is y = -2/5x.

Using it's concept, it is found that there is a 0.6 = 60% probability that the flower is NOT A ROSE.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 6 + 5 + 4 = 15 flowers, out of which 5 + 4 = 9 are not roses, hence the probability is given by:

p = 9/15 = 0.6 = 60%.

0.6 = 60% probability that the flower is NOT A ROSE.

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Answer:

88

Step-by-step explanation:

Answer:

[tex]x=\dfrac{11}{4}[/tex]

Step-by-step explanation:

Given:

[tex]9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

Rewrite 9 as 3² and 27 as 3³:

[tex]\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}[/tex]

Multiply both sides by [tex]3^{(x-1)}[/tex] :

[tex]\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\implies 3^{(x-2)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x-2=\dfrac{3}{4}[/tex]

[tex]\implies 4(x-2)=3[/tex]

[tex]\implies 4x-8=3[/tex]

[tex]\implies 4x=11[/tex]

[tex]\implies x=\dfrac{11}{4}[/tex]

The range:
[tex]{x|70\leq x\leq 82[/tex]

Answer:

Step-by-step explanation:

Two possible patters of sitting:

⇒ [tex]I) M W M W M W[/tex]

⇒ [tex]II) W M W M W M[/tex]

⇒ Three ways can be used to seat each set of three people, for a total of six.

⇒ There are two groups

2 × 3 = 6 (ways in six groups.)

*The two options can be distributed in two groups.

⇒ Total methods are equal to 6 * 6 * 2 = 72 ways.

Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

Not a factor because there is a remainder.

Step-by-step explanation:

Let's use synthetic division to solve this..

-1  ║ 2 | 4 | -2 | -8

   ║    | -2| -2 |  4

   ║ 2 | 2|  -4 |  -4

[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

PS: if anyone knows a better way to do a synthetic division chart please let me know.

The estimate of the amount carly needs to deposit into the savings account per month over the next 3 years to be able to pay for her first year of college is $250

12,000 = 2900 + 36x

12,000 - 2900 = 36x

9,100 = 36x

x = 9100 / 36

x = 252.777777777777

Approximately,

$250

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Answer:

The answer is B. $250

Step-by-step explanation:

Answer:

2 1/4

Step-by-step explanation:

Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4

The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, option A is the correct answer.

Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.

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The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.

An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, option A is the correct answer.

Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.

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Answer:

B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Answer:

B

Step-by-step explanation:

pythagorus theorem

a² + b² = c²

c² - b² = a²

26² - 24² = a²

676 - 576 = a²

a² = 100

a = 10

Answer:

x = 8

Step-by-step explanation:

An undefined slope indicates that the line is vertical and parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (8, 4 ) with x- coordinate 8 , then

x = 8 ← equation of line

4

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The domain of the given graph is the set of all real numbers from 0 to 8.

The graph showing the water depth on the y-axis in inches against the time in minutes on the x-axis has been attached.

Now, domain is the set of all possible input values and from the graph we see that the set of all possible input values are between 0 and 8.

Thus, we can conclude that the domain of the given graph is the set of all real numbers from 0 to 8.

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Answer:

c ×=4, only

Step-by-step explanation:

4*-8×+16=0

16-32=-16

-16=-16

Answer:

D. x=4 only

Step-by-step explanation:

You can solve using the quadratic equation which is [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]

where in this case a=1, b=-8, and c=16. But there is any easier way to solve the equation. You can solve by completing the square which consists of moving the constant to the right side and then adding [tex](\frac{b}{2})^2[/tex]. To both sides that way you can rewrite the left side as a perfect square binomial. This is because [tex](x+b)^2[/tex] will expand to [tex]x^2 + 2xb + b^2[/tex]. So when you add [tex](\frac{b}{2})^2[/tex] to both equations. You're able to rewrite the left side as [tex](x+(\frac{b}{2}))^2[/tex]. Because once you expand it out, it becomes [tex]x^2 + 2(\frac{b}{2})x + (\frac{b}{2})^2[/tex]. Which simplifies to [tex]x^2 + bx + (\frac{b}{2})^2[/tex] which is the original equation. In this case there is no need to move the constant, which in this case is 16, to the other side. Since if you calculate the value of (-8/2)^2 it's equal to 16! So this can already be written as a perfect square binomial.

So the equation becomes

[tex]0 = (x+\frac{b}{2})^2[/tex]

Plug values in

[tex]0 = (x+(-\frac{8}{2}))^2[/tex]

Simplify

[tex]0 = (x-4)^2[/tex]

Take the square root of both sides

[tex]0 = x-4[/tex]

Add 4 to both sides

[tex]4 = x[/tex]

Answer:

College dropout is the greatest album of all-time

Given the egg has hatched, the egg was kept warmer than room temperature.

                      Cool      Room temperature        Warm             Total

Hatched           5              16                                21                  42

Unhatched        18           10                                 4                   32

Total                 23            26                                25                    74

To fill the blank we need to analyse the temperature carefully if see the table then cool hatched eggs are 5 , unhatched cool eggs are 18, eggs on room temperature and hatched are 16, eggs on room temperature and unhatched are 10, warm hatched eggs are 21 and warm unhatched eggs

So we can notice that hatched eggs are more in room temperature.

Hence hatched eggs are more in room temperature.

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Answer:

Given the egg has hatched the egg was kept warmer than room temperature.

Hope this helped!

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

a) Yes it does, because the graph of their relationship is a Straight line

b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent

C)number of followers depend on the number of locks passing. It is dependent.

D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) =  18/3 = 6

It represents the increase in number of followers per week,

E) y-intercept is value of y when x=0

y-intercept = 82. It means his initial number of followers

F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.

Y=6x+82

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