Diana has z gerbils. Jackie has 4 times as many gerbils as Diana.
a) If w stands for the number of gerbils Jackie has, express w in terms of z.

The required equation is y = -9x - 65.

What is a slope intercept form?

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

Here, we have

Given: the equation of a line parallel to y =-9x + 8, that passes through the point P(-8, 7).

The slope of y = -9x+8.... (1)

can be found as

compare with the standard equation

y = mx+c.... (2)

where m is the slope so

Comparing (1) and (2)

slope = m = -9

So the slope of the parallel line will also be -9

So in order to find the equation we need a point and a slope to put in the point-slope formula

y-y₁ = m(x-x₁)

Point (x,y) = (-8,7) slope m = -9

y-7 = -9(x+8)

y = -9x - 72 + 7

y = -9x - 65

Hence, the required equation is y = -9x - 65.

To learn more about the slope-intercept form from the given link

https://brainly.com/question/25024332

#SPJ1

The length of the line segment QM which is half the diagonal MP is equal to 21 in the parallelogram LMNP.

A parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.

For the parallelogram LMNP; the lines MP and LN are its diagonals, and the both bisect each other, that is they cut each other to form two equal parts.

So QM and PQ are equal halves of the line MP

Therefore, since PQ = 21 then QM = 21 because they form a diagonal of the parallelogram LMNP bisected by the diagonal LN.

Know more about parallelogram here: https://brainly.com/question/20526916

#SPJ1

Answer:

4,080,000,000,000

Step-by-step explanation:

1,200 * 3.4*10⁹

=4080*10⁹

=4,080,000,000,000

Answer:

the answer is 8 just divide

Answer:

8 is the answer just divide

The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

Learn more about demography in brainly.com/question/28243436

#SPJ1

Lisa's remaining of her monthly income is $490. Her net worth is $142.980. Her saving ratio is 17%, liquidity ratio is 23% and Debt-to-asset ratio is 63%.

Based on the given data, we can construct Lisa's personal cash flow statement and personal balance sheet as:

Personal Cash Flow Statement

Cash Inflow:

Cash Outflow:

Debts:

Living expenses:

Total cash = $490

Personal Balance Sheet

Assets:

Total Assets = $383,140

Liabiities:

Total Liabilties = $240,160

Net worth = $142,980

Saving ratio can be calculated by assuming that the amount of Lisa's cash on bank is her saving. Then:

saving ratio = saving : net income

Saving ratio = cash in bank : net income

Saving ratio = $600 : $3,600

Saving ratio = 17%

Liquidity ratio is calculated by comparing Lisa's current assets with her net worth. Hence:
Liquidity ratio = Current assets : Net worth

Liquidity ratio = (Cash in bank + Car + Clothing owned + Furniture) : Net worth

Liquidity ratio = ($600 + $18,000 + $540 + $14,000) : $142,980

Liquidity ratio = 23%

Debt-to-asset ratio = Total Liabilities  : Total Assets

Debt-to-asset ratio = $383,140 : $240,160

Debt-to-asset ratio = 63%

Learn more about Net Worth here: brainly.com/question/13731427

#SPJ1

Answer:

The rate of interest required to make Rs. 2500 amount to Rs. 3200 in 7 years is 8.5%. This can be determined by using the information from pa01000192.schoolwires.net, which states that the formula for finding the rate of interest is: Rate of Interest = (Future Value - Present Value) / (Present Value * Time). Applying this formula to the given values gives a rate of interest of 8.5%.

Step-by-step explanation:

The given function is continuous at  x = 3,  RHL = LHL = F(2)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  (x²-9)/(x² - x -6)(x² + 6x +9)

To check whether it is continuous at x = 2

First taking LHL,

[tex]\lim_{h \to \ 0}[/tex]  ((2-h)²-9)/((2-h)² - (2-h) -6)((2-h)² + 6(2-h) +9)

⇒  -5/(-4x25)

⇒   1/20

Now, taking RHL

[tex]\lim_{h \to \ 0}[/tex]  ((2+h)²-9)/((2+h)² - (2+h) -6)((2+h)² + 6(2+h) +9)

⇒  -5/(-4x25)

⇒   1/20

The value at x = 3

F(3)  =   ((2)²-9)/((2)² - (2) -6)((2)² + 6(2) +9)

       =  -5/(-4x25)

       =   1/20

Hence Proved,   RHL = LHL = F(2)

To know more about limits and continuity check:

brainly.com/question/30328478

#SPJ1

The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

We break up a number according to its place value and expand it to show the value of each digit.

Given that to write expanded form of 706.039

Expanded Factors Form:

706.039 = 7 × 100  + 0 × 10 + 6 × 1  + 0 × 0.1 + 3 × 0.01 + 9 × 0.001

Expanded Notation Form:

706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Learn more about expanded form, click;

https://brainly.com/question/17837892

#SPJ1

Answer:

Student most likely forgot to form 2nd equation.

Step-by-step explanation:

The answers appear to be cut off, but I can clearly see that the other solution isn't considered. When solving an absolute value equation, you form two equations. In this case, we have x-3=4 and x-3=-4 as our equations because |-4|=|4|=4 so this is accounted for. Hence, the two solutions should be x=7 AND x=-1.

Answer:

d. x = 7

Step-by-step explanation:

To find the value of x, you can cross multiply the fractions to get 32 * x = 8 * 28, then simplify:

32x = 224

x = 7.

Answer:

C. 5

D. 5√3*

*Check the last one - choice D - make sure it is 5√3 not 53–√ before marking it correct.

Otherwise only choice C is the correct answer

Step-by-step explanation:

The sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.

If the side opposite the 90° angle(the hypotenuse)  = a

If the side opposite the 30° angle: PQ = a

Then the side opposite the 90° angle = 2a

The side opposite the 60° angle = √3a

Since here we are given the hypotenuse = 10

Side opposite the 30° angle = 2a/2 = 10/2 = 5

Side opposite the 60° angle = √3a = √3 · 5 = 5√3

I believe in your choice for D it should be 5√3 but not sure about that so check if it is before marking it correct

Answer:

Options C) and D) are correct

Step-by-step explanation:

Given:  The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To choose: the correct option

Solution:

ΔKBO is a right-angled triangle.

[tex]sinO=\frac{side opposite to angle}{sideadjacent to angle}[/tex]

[tex]= \frac{BK}{KO} \\= \frac{BK}{10}[/tex]

⇒ sin 60°= [tex]\frac{BK}{10}[/tex]

[tex]\frac{\sqrt{3} }{2} = \frac{BK}{10}[/tex]

BK = [tex]\frac{\sqrt{3} }{2} (10) = 5\sqrt{3}[/tex]

CosO = [tex]\frac{side adjacent to angle}{side opposite to angle}[/tex]

          [tex]= \frac{BK}{KO} \\= \frac{BO}{10}[/tex]

          ⇒ cos 60° = [tex]\frac{BO}{10}[/tex]

            [tex]\frac{1}{2}= \frac{BO}{10} \\BO = \frac{10}{2} = 5[/tex]

Answer:

5.08

Step-by-step explanation:

2.17+2.91 = 5.08

The equation is $230,000 x 0.97^5.

The worth of the house in five years is  $197,508.83.

Depreciation is the decline in the carrying value of an asset. Depreciation occurs as a result of wear and tear.

The equation that would be used to determine the worth of the house in 5 years is

Worth of the house = cost of the house x (1 - depreciation/100)^number of years

= $230,000 x (1 - 3/100)^5

$230,000 x (1 - 0.03)^5

$230,000 x 0.97^5  = $197,508.83

To learn more about depreciation, please check: https://brainly.com/question/25552427

#SPJ1

The correct sample space for the gumballs in her bag is;

A: Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape

The sample space of an experiment is defined as the set of all the possible outcomes. For example, when we toss a coin, the sample space is; {head, tail}.

Now, the parameters for the bag filled with gumballs are;

1 watermelon.

2 lemon-lime.

3 grape gumballs.

Therefore the sample space is the different types of gumballs there and it is; {Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape}

Read more about sample space at; https://brainly.com/question/10673071

#SPJ1

Answer:

5/18

Step-by-step explanation:

We assume they share equally.

5/6 ÷ 3 = 5/6 × 1/3 = 5/18

Answer:

D all of the above is the answer

Answer:

D) All of the above

Runoff can end up in ponds, streams, and rivers.

Step-by-step explanation:

Hope it helps! =D

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

To learn more about surface area of pyramid click :

https://brainly.com/question/15050758

#SPJ1

The number of subsets for R { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 } is given by the equation A = 255 subsets

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the relation set be represented as R

Now , the set R = { x|||xis an odd, negative integer and x>−16 }

The number of elements in the set R is given by

R = { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 }

So , the number of elements n = 8 elements

The number of subsets of any arbitrary set  is equal to 2ⁿ

This means that the number of proper subsets (which is the number of subset minus the set itself, for finite subsets) is equal to 2ⁿ-1

So , the number of subsets for R = 2⁸ - 1 = 255 subsets

Hence , the solution set is  { -15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 }

To learn more about sets click :

https://brainly.com/question/28278437

#SPJ1

Answer: 0.5km per hour

Step-by-step explanation:

Answer:

630

Step-by-step explanation:

36x250 = 9000 ÷ 7 =630

The solution is, she got commission of 2%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission.

so, she got commission = 1200/60000 * 100

                                        =2%

Hence, The solution is, she got commission of 2%.

#SPJ1

Note that in question 28 above:

X = 56° (Alternative Angles)

Y = 124° (Angles in a straight line)

Z = 81° (Sum of angles in an irregular parallelogram).

in Question 29,
x = 126° (Co-interior angles and Bisector theorem).

Question 28: Note that the sum of angles in an irregular parallelogram always equal 360°. Since X and 56° are alternate angles and are therefore congruent, and Y and 56° are on the same line and therefore sum up to 180°, resulting in Y being equal to 124°, then we have three interior angles of an irregular parallelogram:

∠X = 56°

∠Y = 124°; and

∠99° (As given), which is co-interior with ∠Z

Thus whether by the Co-interior principle where two co-interior angels sum up to 180° or by sum of angles in an irregular parallelogram, we will still obtain a result where:

∠Z = 81°. That is

360° = 56 + 124 + 99 + ∠Z

∠Z = 360 - (56 + 124 + 99)
∠Z = 81°

OR

Using the Co-Interior angles theorem, we can state that:

∠Z = 180 - 99
∠Z = 81°

Question 29:
Recall that an angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.

Thus, we can state that 27° is half of the angle whose Co-interior is x.

Thus ∠x = 180 - (27*2)

∠x = 180 -54
∠x = 126°


Learn more about the Angle Bisector Theorem:
https://brainly.com/question/9761841
#SPJ1

The correct form of the expression is x² -9

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y = (x − 3)(x + 3) =

This can be done by opening the brackets

x²+3x-3x-9

⇒x²-9

Therefore, the correct form of the equation is x²-9

The x-intercept  = 1 and the y intercept is -9

Learn more about x and y intercepts on https://brainly.com/question/14180189

#SPJ1

The number of artists that are interns is solved to get 77

From the problem, showing circle graph, it can be deduced that the interns occupy 5 percent of the total number

The total number is 1540

5% of 1540 is solved by

= 5/100 * 1540

= 0.05 * 1540

= 77

The number of interns is 77

Learn more about circle graph at:

https://brainly.com/question/7576009

#SPJ1

Let's call the number of words Trei spelled correctly "x". Then, the number of words she spelled incorrectly is 100 - 60 = 40 words.

Therefore, the ratio of correctly spelled words to incorrectly spelled words is x to 40.

To find the number of words she spelled correctly for each word she spelled wrong, we can simplify the ratio by dividing both values by the greatest common factor:

x / 40 = x / (2 * 20) = x / 2 * 20 / 2 = x / 20.

So for every word Trei spelled incorrectly, she spelled 20 / 1 = 20 words correctly.

Answer:

Supplementary angles are angles that add up to 180 degrees, or on a straight line. If one angle is 163.6 degrees less than its supplementary, then all you have to do is subtract that number from 180. The angles are

180 - 163.6 = 16.4

180 - 16.4 = 163.6

One angle is 16.4 degrees, the other is 163.6. They both add up to make 180.

The measure of HG is 12

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.

The opposite sides of a parallelogram are equal. This means that 3y = y+8

3y = y+8

3y-y = 8

2y = 8

divide both sides by 2

y = 8/2

y = 4

if y = 4 and HG is y+8

therefore

the measure of HG = 4+8

= 12

learn more about parallelogram from

https://brainly.com/question/970600

#SPJ1

Answer:

After 100 days, the amount of the substance will decrease to half its original value, so Yo/2 = 5 mg. The half-life of a substance is the time it takes for half of it to decay or disappear. So, every 100 days, the amount of the substance will be halved until there is none left.

Question is not clear.

Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3  transformed .

Mathematics includes the study of numbers, various variable, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship between the number of inputs and the corresponding outputs for each. Simply explained, a function range is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a realm. The letter f is frequently used to denote functions (x).

Here,

Given :

=>  f(x) = log x

=> g(x) = log (x) - 3

So , it is transformed as logx = f(x)

it is transformed as :

=> g(x) = f(x) - 3

Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3  transformed .

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1