16.-Write an algebraic model for the statement. the difference of a number and -8 is 7

Solution:

Given the data below:

A) Mean monthly flow:

The mean monthly flow is evaluated as

Thus, the mean monthly flow is 338.5 KAF

B) Median monthly flow:

The median is evaluated as

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis. On the graph, each individual in the data is represented by a point.

The relationship between two economic phenomena, such as employment and output, inflation and retail sales, and taxes and economic growth, can be visually illustrated using scatter plots.

Spread Plots. Points on a scatter (XY) plot depict how two sets of data relate to one another. Each dot in this illustration represents a person's weight in relation to their height. (The information is displayed as "Cartesian (x, y) Coordinates")

Display a connection between the data and a trend. Display all data points, including outliers, minimum, and maximum values. can draw attention to relationships. the sample size and exact data values are retained.

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For z varies jointly with x and y. When x=5 and y=4, z=12.

a. Equation that models the relationship is z=(3/5)xy.

b. When x=15 and y=2 then z=18.

As given,

a. Equation that models relationship z varies jointly with x and y is:

z is directly proportional to product of x and y

⇒z∝ xy

⇒z=k xy

where k is symbol of proportionality.

When x=5 and y=4, z=12

12=k(5× 4)

⇒k=12/(5× 4)

⇒k=3 /5

Hence, z=(3/5)xy

b. When x=15 and y=2

z=(3/5)×15×2

 =18

Therefore, for z varies jointly with x and y, when x=5 and y=4, z=12.

a. Equation that models relationship is z=(3/5)xy.

b. When x=15 and y=2 then z=18.

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Charlie has $3.15 in his bank which contains only nickels and dimes. There are 9 more nickels than dimes. Then Number of dimes =18

and Number of nickels =27

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

Given that : Charlie has $3.15 in his bank which contains only nickels and dimes. There are 9 more nickels than dimes

Let d be the number of dimes

d + 9 = Number of nickels

A dime = 0.1

nickle is = 0.05

0.1d + 0.05d + 0.45 = 3.15

0.15d = 2.7

d = 18

Number of dimes =18

Number of nickels = 18 + 9

=27

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Your friend claims that the graph of f(x) = x - 2 can be produced by two distinct translations of the graph of the parent linear function. The graph moves down by 2 units.

Given that,

Your friend claims that the graph of f(x) = x - 2 can be produced by two distinct translations of the graph of the parent linear function.

We have to find how much units the graph moves.

This linear equation's parent function is y=x.

The way your friend described this function wasn't exactly accurate.

If the function's transformation takes the form y=f(x)+c, the graph will move vertically up or down along the y-axis depending on the value of c.

The graph moves up if c>0.

The graph drops down if c>0.

When y=x-2 and y=f(x)+c are compared, we see that c = -2, which is smaller than 0, in the equation y=x-2.

Therefore, the graph moves down by 2 units.

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Given the expression:

The first step to solve it using the square root property, is moving the coefficient on the right side of the equation to the left side, changing it's sign:

Now, remember the rule for conjugates:

in this case we have the following:

therefore, we can factor the expression like this:

Finally, we have that the only values that make true the expression are:

Solution

Where

Now,

Therefore, V = 150

Using the law of syllogism, the conclusion is given as follows:

c. if a quadrilateral is a square, then it is a rectangle.

The Law of Syllogism is a logic axiom which states that if the conditional statements p -> q and q -> r are true, the conditional statement p -> r is also true, basically applying the transitive property.

In the context of this problem, the statements are given as follows:

Hence the conclusion is:

p -> r

Read as:

If p then r.

Replacing the statements, we have that:

If a quadrilateral is a square, then it is a rectangle.

Which means that option c is correct.

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In graphical representation it will get displaced by 0.5 units in x-axis.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

various Transformations are :

The answer choices would ask us to consider some combination of the following transformations:

reflection across the y-axis: (x, y) ⇒ (-x, y)

reflection across the x-axis: (x, y) ⇒ (x, -y)

reflection across the line y=x: (x, y) ⇒ (y, x)

clockwise rotation 90°: (x, y) ⇒ (y, -x)

positive rotation 270°: (x, y) ⇒ (y, -x) . . . same as 90° CW

translation by (h, k): (x, y) ⇒ (x+h, y+k) . . . h units right, k units up

Here, The shoe rental price increases 0.50 that is the new total cost is represented by T(n)=C(n)+0.5, which is 0.5 greater then old price equation that is C(n)=4.5n+2.5  :

Now, In graphical representation it will get displaced by 0.5 units in x-axis.

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Answer:

the answer is B 40 because∆ABC is a triangle

The coordinates of KLMN after reflection along the y-axis is K'(3,2);  L'(-1,4); M'(1,0); and N'(5,-2).

So, the coordinates of KLMN when reflected across the y-axis:

When reflected along the y-axis, the image of (x, y) is (-x,y).

Therefore, the coordinates of KLMN after reflection along the y-axis is K'(3,2);  L'(-1,4); M'(1,0); and N'(5,-2).

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The correct question is given below:
Given a rhombus KLMN with vertices K(-3,2), L(1,4), M(-1,0), and N(-5,-2). What would the coordinates of its image be when reflected across the y-axis?

The graph C shows the proportional relationship between x and y.

A proportional relationship is defined as "y varies proportionally with x" or "y is directly proportional to x."

For the given question;

The graph of the proportional relationship are given.

For the graph C, the relation tween x and y is said to be proportional because when the value of x increases the value of y decreases and also this line passes from the origin.

Thus, the graph C shows the proportional relationship between x and y.

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Answer:

y= - 11

Step-by-step explanation:

A line with a slope of 0 is a horizontal line, parallel to the x- axis with equation

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

the line passes through (- 13, - 11 ) with y- coordinate - 11, then

y = - 11 ← equation of line

Answer:

y = -11

Step-by-step explanation:

A line with slope as 0, is a horizontal line ( In other words parallel to x-axis).

There is no rise, only run.

Equation of the line is y = c.

   y = -11

Answer: 87

Step-by-step explanation:
You would do 26/30 which gives 86.6666666 but we round up to 87

Answer:

0.86666...

Step-by-step explanation:

26/30=0.86666...

rounded  to the nearest tenth is

0.9

Answer:

a = 3 ; b = 1 ;  c = -5

Step-by-step explanation:

     a +b - 2c = 14 -----------------------------(I)

         4b + c = -1  -----------------------------(II)

                 c  = -5 ------------------(III)

Substitute c = -5 in equation (II) and find the value of 'b',

        4b + (-5) = -1

             4b     = -1 + 5

                4b  = 4

                  b = 4 ÷ 4

                 [tex]\sf \boxed{b = 1}[/tex]

Substitute c = -5 and b = 1 in equation (I)

        a + 1 - 2*(-5) = 14

          a + 1 + 10    = 14

                     a +11 = 14

                           a = 14 - 11

                           [tex]\sf \boxed{a = 3 }[/tex]

 a + b - 2c = 14

LHS = a + b - 2c

       = 3 + 1 - 2*(-5)

       = 3 + 1 + 10

       = 14 = RHS

Hence verified.

Answer:

(3, 1, - 5 )

Step-by-step explanation:

a + b - 2c = 14 → (1)

4b + c = - 1 → (2)

c = - 5 → (3)

substitute c = - 5 into (2)

4b - 5 = - 1 ( add 5 to both sides )

4b = 4 ( divide both sides by 4 )

b = 1

substitute b = 1 and c = - 5 into (1)

a + 1 - 2(- 5) = 14

a + 1 + 10 = 14

a + 11 = 14 ( subtract 11 from both sides )

a = 3

solution is (3, 1, - 5 )

as a check substitute values into (1) and (2)

a + b + c = 3 + 1 - 2(- 5) = 4 + 10 = 14 ← correct

4b + c = 4(1) - 5 = 4 - 5 = - 1 ← correct

4 tickets----------------------------->$40

8 tickts------------------------------->$x

Using cross multiplication:

8 tickets cost $80

If the measure of an angle is 136.8 degrees more than the measure of a supplementary angle, then the measure of each angles are 21.6 degrees and 158.4 degrees

The supplementary angles are the angles whose measure add up to 180 degrees.

If x and y are supplementary angles

x + y = 180 degrees

Here the measure of an angle is 136.8 degrees more than the measure of supplementary angle.

So one angle will be x and other angle will be x+136.8

Then the equation will be

x + x+136.8 = 180

2x+136.8 = 180

2x = 43.2

x = 43.2/2

x = 21.6 degrees

Other angle is

21.6+136.8 = 158.4 degrees

Hence, if the measure of an angle is 136.8 degrees more than the measure of a supplementary angle, then the measure of each angles are 21.6 degrees and 158.4 degrees

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In February, Robbins and Myers, Inc. executed a 2-for-1 split, then the

(a) . The shares did she hold after the split is 940 shares.

(b) . The post-split price per share is $34.74

(c) . Janine didn't gain or lose any money during the event.

Based on the given conditions,

In February, Robbins and Myers, Inc. executed a 2-for-1 split.

That means,

2 - for - 1 stock split.

= 2 / 1

= 2

(a) . How many shares did she hold after the split?

Then,

Janine had 470 shares before the split.

Each share was worth $69.48.

= 470 shares * 2

= 940 shares

Hence,

The shares did she hold after the split is 940 shares.

(b) . What was the post-split price per share?

Each share was worth $69.48.

Then,

= $69.48/2

= $34.74

Hence,

The post-split price per share is $34.74

(c) . Show that the split was a monetary non-event for Janine

We can write,

After the split, Janine had 940 share worth $34.74.

Since they doubled the amount of share, but decrease the amount of each share.

So,

Janine didn't gain or lose any money during the event.

Therefore,

Robbins and Myers, Inc. executed a 2-for-1 split,

(a) . The shares did she hold after the split is 940 shares.

(b) . The post-split price per share is $34.74

(c) . Janine didn't gain or lose any money during the event.

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Answer:

Grade A: 0.2

Grade B: 0.3

Grade C: 0.2

Grade D: 0.15

Grade F: 0.15

Step-by-step explanation:

You take the number of the grade and divide that by the total.  The total is 20.  A 4/20 = 0.2

Grade B 6/20 = 0.3 and so on

Answer:

For part b. its grade D so it says how much right so I think u need to times it or divide it or so sorry if this doesn't help u

Rigid transformations, are transformations of the plane that preserves length. Reflections, translations, rotations, and combinations of these three transformations are rigid transformations. In a rigid transformation the pre-image and image are always congruent

Therefore, the answer is:

translations

rotations

reflections

The percentage of graduates from University A having income under $20,000 is 22%.

Percentage may be defined as the fraction which we get after dividing an entity from total number multiplied by 100. We have the total number of students in university A as 160. Now, we divide 35 that is the number of students who have an income under $20,000 in university A by 160 that is the total number of students in university A. We get the percentage as

P = (35/160) × 100

P = 0.218 × 100

P = 21.9 %

rounding off to nearest we get percentage as 22 %.

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The value of the given function, [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } }[/tex], found using L'Hospital's rule is; [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } = 16}[/tex]

L'Hospital's rule states that if the limits [tex]\displaystyle{ \lim \limits_ {x \rightarrow c}f(x)} [/tex] = [tex]\displaystyle{ \lim \limits_{x \rightarrow c}g(x)} [/tex]= 0 or [tex]\pm \infty[/tex], g'(x) ≠ 0 for all x in I and x ≠ c, also, [tex]\displaystyle{ \lim \limits _ {x \rightarrow c}\frac{f ' (x)}{ g ' (x)} } \: exists, \: then;[/tex]

[tex]\displaystyle{ \lim \limits _ {x \rightarrow c}\frac{f (x)}{ g (x)} =\lim \limits _ {x \rightarrow c}\frac{f ' (x)}{ g ' (x)} } [/tex]

The given function is [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } }[/tex]

According to L'Hospital's rule, we have;

Where;

f(x) = sec⁴x - 4

[tex] \displaystyle g(x) = x - \frac{\pi}{4} [/tex]

[tex] \displaystyle f'(x) = \frac{4\cdot sin(x)}{cos^5(x)} [/tex]

g'(x) = 1

Therefore;

[tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} }= \frac{ \frac{4\cdot sin(x)}{cos^5(x)}}{1}=\frac{4\cdot sin(\frac{\pi}{4})}{cos^5(\frac{\pi}{4})} = 16}[/tex]

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Answer:

Below in bold.

Step-by-step explanation:

Using the Cosine Rule:

a^2 = b^2 + c^2 - 2bc cos A

10^2= 11^2 + 13^2 -2.11.13 cos A

cos A = (11^2 + 13^2 - 10^2) / (2*11*13)

          = 0.66434

m < A = 48.368 degrees

          = 48.37 degrees to 2 D. P's.

By the Sine Rule:

a / sin A = b / sin B

10 / sin 48.368 = 11 / sin B

sin B = 11 * sin 48.368 / 10

         = 0.82217

m < B = 55.303

          = 55.30 degrees to 2 D,P's

So, m < C = 180 - 48.37 - 55.30

                = 76.33 degrees

Answer:

C. The cost per pizza for 3 pizzas divided by 8 people

Step-by-step explanation:

This is the only answer where you are multiplying by 3 and dividing by 8

Answer: 5:12

Step-by-step explanation:

[tex]\displaystyle\\30:72=\\\\\frac{30}{72}=\\\\ \frac{6(5)}{6(12)}=\\\\ \frac{5}{12}=\\\\ 5:12[/tex]