Question 7

Solve the following system of equations by using the elimination method.
-4x – 2y = -12
4x + 8y = -24

(5, 3)

(-6, -6)

(3, 1)

(6, -6)

4, 12, 16, 48, 52, 156, 160, ______, _______, _______

x3  +4  x3  +4  x3    +4

That pattern is: multiply by 3, add 4, multiply by 3, add 4, ...

160 x 3 = 480

480 + 4 = 484

484 x 3 = 1452

Answer: 480, 484, 1452

The next 3 numbers are 480, 484, 1452

The given sequence is:

4,12,16,48,52,156,160,_,_,_

The rule of the sequence is:

The last three terms are the 7th, 8th, and 9th terms

The 7th term is:

[tex]T_7=3T_6\\\\T_7=3(160)\\\\T_7=480[/tex]

The 8th term is:

[tex]T_8=T_7+4\\\\T_8=480+4\\\\T_8=484[/tex]

The 9th term is:

[tex]T_9=3T_8\\\\T_9=3(484)\\\\T_9=1452[/tex]

Therefore, the next 3 numbers are 480, 484, 1452

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Answer to the question:

Step-by-step explanation:

Solution

The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.

The given equation is = -1/3 x - 6.

Comparing the given equation with the general form, we get

slope (m) = -1/3 and y-intercept = -6.

The answer is -1/3; -6

Thank you. :)

Answer:

[tex]\frac{4}{5}[/tex] of Steph's annual income is from her full-time job.

Step-by-step explanation:

Suppose, Steph's annual income is  [tex]x[/tex]

Given that, 80% of Steph's annual income is from her full-time job.

So, the amount of income from her full time job will be:  [tex](x\times 80\%)= (x\times\frac{80}{100})= 0.8x[/tex]

Now, for finding the income from her full time job as a fraction of Steph's annual income, we just need to divide "income from full time job" by "total annual income".

So, the fraction will be:  [tex]\frac{0.8x}{x}= 0.8 =\frac{8}{10}= \frac{4}{5}[/tex]

That means,  [tex]\frac{4}{5}[/tex] of Steph's annual income is from her full-time job.

Answer:

4.5 is the answer.

Step-by-step explanation:

80% is fraction form is 80/100 to simplify that it becomes 4/5. Therefore, the answer is 4/5

To factor a number out of an expression means to divide each term of the expression by that number.

So, if you want to factor [tex] a [/tex] from the expression [tex] x+y+z [/tex], you'll write it as

[tex] a\left(\dfrac{x}{a}+\dfrac{y}{a}+\dfrac{z}{a}\right) [/tex]

So, in your case, when you divide both terms by -5 you get

[tex] -10a \div (-5) = 2a,\quad -25\div (-5) = 5 [/tex]

So, the expression becomes

[tex] -10a-25 = -5(2a+5) [/tex]

He product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to find x, the value of the greater number. What is the value of the greater number?

Solution

Here the second number is "x"

The first number is "x - 5"

The equation is x (x - 5) = 750

[tex]x^{2}[/tex]- 5x = 750

Subtract 750 from both sides, we get

[tex]x^{2} -5x -750 =0\\[/tex]

Solving the above quadratic  equation using quadratic formula, we get

[tex]x = \frac{-b+/- \sqrt{b^{2}-4ac } }{2a}[/tex]

Here we have to plug in  a =1, b = -5 and c = -750 in the above formula, we get

[tex]x = \frac{5 +/-\sqrt{3025} }{2}[/tex]

When we simplify the above expression is...

x = 30 and x = -25

x = -25 cannot be the solution since it is negative value.

x = 30 is the solution.

Here "x" represents the second number which is 30, that is the greater number.

Therefore, the answer is 30.

Answer:

 30

Step-by-step explanation:

You can try the answer choices to see what works.

 15·10 ≠ 750

 25·20 ≠ 750

 30·25 = 750 . . . . the larger number is 30

 50·45 ≠ 750

Answer:

2x-3y=20

12x+8y=-192

Solution

In the determinant of the matrix to find the variable "x" [Ax], we replace the coefficients of "x" (2 and 12) by the independent terms (20 and -192 respectively).

In the determinant of the matrix to find the variable "y" [Ay], we replace the coefficients of "y" (-3 and 8) by the independent terms (20 and -192 respectively).

parrotfish:clownfish

4:3

20:x

4 times 5 = 20

multiply 3 by 5 to keep the same ratio. =>   3 times 5 equals 15. therefore there are 15 clownfish.

hope I helped! (:

It seems that you are trying to find the length of hair of Florencia on Tuesday.

Given that length of the hair of Florencia on Monday = h centimeters

On Tuesday, she got hair cut.

So new length of the hair of Florencia on Tuesday = 75% of Monday value

= 75% of (h)

= 0.75* (h)

= 0.75h

Hence final answer is the length of the hair of Florencia on Tuesday is ( 0.75h ) centimeters.

Answer:

3/4h and 0.75h

The graph of this relation is four points on the coordinate plane (see attached diagram).

A function is a special relation, where each input x has a single output y.

This relation is not a function, because for one x (x=-1), here are two different possible y (y=3 or y=2). If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2). This means that option D is true.

Since the x axis represents the number of pen bought and the y axis the number of notebook, the total cost will be 2x+3y, because each pen costs 2$ and each notebook 3$.

You want this quantity to be no more than 30, so you must ask

[tex] 2x+3y \leq 30 [/tex]

which means that the shaded area must be under the graph of the line

[tex] 2x+3y = 30 [/tex]

You can rewrite the equation as

[tex] y = -\dfrac{2x}{3} + 10 [/tex]

So, the y intercept is the point [tex] (0,10) [/tex]

So the answer must be either C or D.

To find the x intercept, set y=0:

[tex] 0 = -\dfrac{2x}{3} + 10 \iff \dfrac{2x}{3} = 10 \iff 2x = 30 \iff x = 15 [/tex]

So, the correct answer is D.

5(x + 3) - 9x + 4

use distributive property

= (5)(x) + (5)(3) -9x + 4 = 5x + 15 - 9x + 4 = (5x - 9x) + (15 + 4)

= -4x + 19

To simplify the expression 5(x + 3) - 9x + 4, distribute 5 to the terms inside the parentheses, combine like terms, and then add the constant terms.

To simplify the expression 5(x + 3) - 9x + 4, we first distribute the 5 to both terms inside the parentheses: 5x + 15. Next, we combine like terms by subtracting 9x from 5x to get -4x. Finally, we add the constant term 15 with the constant term 4 to get 19. Therefore, the simplified expression is -4x + 19.

To simplify the expression 5(x + 3) - 9x + 4, distribute 5 to the terms inside the parentheses, combine like terms, and then add the constant terms.

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To complete the square for the equation x^2 - 9x = 8, the number 81/4 must be added to both sides, resulting in x^2 - 9x + 81/4 = 113/4.

To complete the square for the equation x^2 - 9x = 8, we need to find a number that when added to x^2 - 9x makes it a perfect square trinomial. The formula to complete the square is to take the coefficient of the x term (which is -9), divide it by 2, and square it. The process looks like this:

(-9/2)^2 = 81/4

Therefore, the number to add to both sides of the equation is 81/4. The equation then becomes:

x^2 - 9x + 81/4 = 8 + 81/4

Which simplifies to:

x^2 - 9x + 81/4 = 32/4 + 81/4

x^2 - 9x + 81/4 = 113/4

By adding 81/4 to both sides, we have successfully completed the square.

Answer:

This equation is a line

Step-by-step explanation:

We can tell it's a line because both the x and y values are raised to the first power. In order for it to be any of the others, one or both of the variables would have to have a non-one exponent.

Answer:

It is a line.

Step-by-step explanation:

Since, the general equation of,

A line is ax + by = c

A circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]

An ellipse is [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

A parabola is [tex]y^2=4ax[/tex] or [tex]x^2=4ay[/tex]

A hyperbola is [tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

Where, a, b and c are constants.

Here, the given equation is,

x + y = 5

Which is the type of ax + by = c

Hence, x + y = 5 is a line.

You can subtract that height of volcano which lies below sea level from the total height to obtain height of volcano above sea level.

Thus, height of specified volcano is 4214 meters.

The height of volcano above sea level

You can subtract that height of volcano which lies below sea level from the total height to obtain height of volcano above sea level.

Thus:

Height of volcano above sea level = total height of volcano - depth of volcano below sea level

[tex]\text{Height of volcano above sea level} = 10207 - 5993 = 4,214 \: \rm meters[/tex]

Thus, height of specified volcano is 4214 meters.

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y < - 8  or y > 4

inequalities of the form | x | > a always have solutions of the form

x < - a or x > a

we have to solve

y + 2 < - 6 or y + 2 > 6

y + 2 < - 6 ( subtract 2 from both sides )

y < - 8

or

y + 2 > 6 ( subtract 2 from both sides )

y > 4

these can be combined using interval notation

y ∈ (- ∞, - 8 ) ∪ (4, ∞ )

As a check

substitute chosen values of x from each interval

y = - 10 :  | - 10 + 2 | = | - 8 | = 8 > 6 this is true

y = 12 : | 12 + 2 | = | 14 | = 14 > 6 which is also true

1)

v - 6 ≥ 4

  +6   +6

v      ≥ 10

Graph: 10 -----------------→  the dot at 10 is filled in because of the "equal to" symbol

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2)

-5x < 15

[tex]\frac{-5x}{-5} > \frac{15}{-5}[/tex]  divided by a negative so the symbol flipped

x > -3

Graph: -3 o------------------→ the dot at -3 is NOT filled in because it's NOT "equal to"

********************************************************************************************************

3)

3k > 5k + 12

-5k  -5k      

-2k >          12

[tex]\frac{-2k}{-2} < \frac{12}{-2}[/tex]   divided by a negative so the symbol flipped

k < -6

Graph: ←------------o -6   the dot at -6 is NOT filled in because it's NOT "equal to"

********************************************************************************************************

5)

2t ≤ 4      or    7t ≥ 49

[tex]\frac{2t}{2} \leq\frac{4}{2}[/tex]      or    [tex]\frac{7t}{7} \geq \frac{49}{7}[/tex]

 t ≤ 2      or      t ≥ 7

Graph: ←------- 2        7 ---------→   the dots at 2 and 7 are filled in

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6)

| n + 2 | = 4

n + 2 = 4      or     n + 2 = -4

    -2   -2                 -2   -2

n      = 2        or     n       = -6

Answer: n = {2, -6}

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7)

| 2x - 7 | > 1

2x - 7 > 1       or     2x - 7 < -1

     +7  +7                 +7   +7

2x      > 8       or     2x     <  6

    [tex]\frac{2x}{2} > \frac{8}{2}[/tex]             or       [tex]\frac{2x}{2} < \frac{6}{2}[/tex]

    x > 4          or         x < 3

Graph: ←----------o 3      4 o------------→

********************************************************************************************************

8)

A = {1, 2, 3, 4, 5, 6, 7, 8, 9}    B = {2, 4, 6, 8}

A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9}    union combines both sets

A ∩ B =  {2, 4, 6, 8}   intersection includes only those that are in BOTH sets

********************************************************************************************************

9)

P = {1, 5, 7, 9, 13}   R = { 1, 2, 3, 4, 5, 6, 7}    Q = {1, 3, 5}

P ∩ R ∩ Q = {1, 5}

P ∩ R = {7}  disregard 1 & 5 since they are already in P∩Q∩R

R ∩ Q = {3}  disregard 1 & 5 since they are already in P∩Q∩R

P ∩ Q = { }  disregard 1 & 5 since they are already in P∩Q∩R

P no intersection = {9, 13)

R no intersection = {2, 4, 6}

Q no intersection = {  }

If you can't figure out how to draw it based on the information I provided, please see the attached diagram. Note: Usially, you would only identify P, Q, R.  I identified the intersections so you would understand why those specific numbers are placed in the designated sections.

Based on the graph of the relationship given between time and the amount of popcorn popped, the relationship doesn't yield a straight line, hence, the relationship isn't proportional.

A proportional relationship is one in which there is a constant change in one variable as the value of the other variable is varied.

A proportional relationship will always yield a straight line with either a positive or negative slope.

Since, the trend line isn't straight, then the relationship isn't proportional.

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The actual question is not about the popcorn machine but about testing the hypothesis on mean differences of relaxed and jumping times for eight girls. To assess this, statistical methods like the paired t-test are used to examine the existence of a direct relationship between the two sets of times.

The relationship between time and the amount of popcorn popped could be considered directly proportional if the rate of popping remains constant over time. However, this question appears to be based on a misunderstanding, as it incorrectly states that Rachel had a popcorn machine. Instead, the actual task given is to test the hypothesis that the mean difference between jumping and relaxed times for eight girls at a party would be zero.

To test this hypothesis, a statistical test like a paired t-test could be used to determine if there is a significant difference between the two mean times. Proportionality in the question should be related to rates or ratios. For instance, when data shows a positive correlation as one variable increases, so does the other. This is seen when graphing data that results in a straight line, which signifies a direct relationship.

Therefore, to determine the relationship between two quantities, the concept of direct and indirect proportionalities is important, and having a direct relationship would mean that the variables increase together linearly.

THE ANSWER IS:

the measure of the arc FH is 48 degrees

and btw I flipping love killing stalking :)

Answer:

[tex]48^{\circ}[/tex]

Step-by-step explanation:

Consider we need to find [tex]m\widehat{FH}[/tex],

Since, if two chords of a circle intersect outside the circle then the measure of intercepted angle is half of the difference of the measures of intercepted arcs.

Thus,

[tex]m\angle ADJ = \frac{m\widehat{AJ}-m\widehat{BE}}{2}[/tex]

By the diagram,

[tex]37^{\circ}=\frac{m\widehat{AJ}-38^{\circ}}{2}[/tex]

[tex]74^{\circ}=m\widehat{AJ}-38^{\circ}[/tex]

[tex]\implies m\widehat{AJ}=74^{\circ}+38^{\circ}=112^{\circ}[/tex]

Now,

[tex]m\angle AGJ = \frac{m\widehat{AJ}-m\widehat{FH}}{2}[/tex]

[tex]32^{\circ}=\frac{112^{\circ}-m\widehat{FH}}{2}[/tex]

[tex]64^{\circ}=112^{\circ}-m\widehat{FH}[/tex]

[tex]\implies m\widehat{FH}= 112^{\circ}-64^{\circ}=48^{\circ}[/tex]

Hence, SECOND OPTION would be correct.

8 / 2 = 4

75 x 4 = 300

The unit rate is for every 2 ounces there is 75 calories or for every 1 ounce there is 37.5 calories

The inequality x>35 represents the problem

more than is: >

A bank balance in excess of $35. Julia wishes to create a bank balance disparity. She uses the inequality sign x>35 to match the statement "greater than".

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The inequality symbol should she use to match the phrase “more than” is >.

A bank account with a balance of greater than $35. Julia wants to create a bank balance disparity. She uses the inequality sign x>35 to match the statement "greater than".

Hence, x >35 is the correct answer.

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Answer:

When you join points D(2,3),O(0,0)and E(5,1) which are not collinear it will form a triangle.

Now , Adjacent of ∠ DOE are [ ∠ ODE and ∠OED] .

As we know that  Sum of three interior angles of a triangle is 180°.

∠ DOE + ∠OED+∠EDO = 180°

∠DOE=180°- (∠OED+∠EDO)

Supplementary ,of ∠DOE is  (∠OED+∠EDO).

Answer: angle DOF, with F (-5,-1) and angle EOF, with F(-2,-3)

to help you can write it as 3-1 which is 2

ANSWER 2