what is the process of getting 10b+7<8b+7<9b+10 down to -3<b<0 because I have my solution graphed already but I genuinely couldn't track my friend helping me on my homework assignment so can somebody please explain?
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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 distance between the Bumper Boats and the Parachute Plunge is given by:

15 units.

Suppose that we have two points with coordinates given yb [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following rule:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse representing the distance between them.

In the context of this problem, the coordinates of the Bumper Boats and of the Parachute Plunge are given as follows:

Hence the distance between these two points is given as follows:

[tex]D = \sqrt{(6 - (-6))^2+(11 - 2)^2}[/tex]

D = sqrt(12² + 9²)

D = 15 units.

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Answer: its 225

Step-by-step explanation: you should try it and find out. / I did  

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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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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Plot two points of each equation

Equation 1 Equation 2

3x - 2y = 10 9x + 4y = - 50

x y x y

0 -5 0 12.5

10/3 0 -50/9 0

Graph

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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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

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

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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Answer:

3= 95

a= 85

b=85

4=85

Step-by-step explanation:

Angles on a line add up to 180°

Corresponding angles are equal.

Answer:fact

Step-by-step explanation:Opiians have a persianal veiw sush as "the cows should sleep in the shed" while facts are absolute "the cows sleep in the shed"

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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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

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: At most 5 laps.

Step-by-step explanation:

N= # of laps

7mins times the number of laps= 7N

35 mins= at most

[tex]7n\leq 35\\\\\frac{7n}{7} \leq \frac{35}{7} \\\ \ \ \ n\ \leq \ 5[/tex]

Correct option is A, The temperature started at 78°F and decreased by 6°F. Then the temperature decreased by 5°F.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign, One such equation is 3x - 2 = 5 + x.

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Answer: k=-2

Step-by-step explanation:

[tex]\displaystyle\\3 x^2+x+k=\\\\3x^2+3x-2x+k=\\\\3x(x+1)-2(x-\frac{k}{2}) \\\\Hence,\\\\x-\frac{k}{2} =x+1\\\\-\frac{k}{2} =1\\[/tex]

Multiply both parts of the equation by -2:

[tex]\displaystyle\\-\frac{k}{2}(-2) =1(-2)\\\\k=-2[/tex]

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 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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The shortest possible length that Zara's fence could be is 12 feet long.

The fence panels Zara uses are 6 feet long each and the fence panels that Chester uses is each 4 feet long.

The multiple of the number 6: 6, 12, 18, 24

The multiple of the number 4: 4, 8, 12, 16, 20, 24

The numbers 6 and 4 have the same multiple 12, 24. The least common multiple of them is 12.

So Zara's fence has the shortest length is 12 feet, because Zara and Chester have the same length fence as Zara uses fence panels that are each 6 feet long. Chester uses are 4 feet long.

The shortest length of Zara's fence is 12 feet.

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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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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]

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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Answer:

the answer is B 40 because∆ABC is a triangle