Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims. Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. (5 points) Part B: How much time does Melvin spend swimming every day? Show your work. (3 points) Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning. (2 points)

Answer:

y = x + -5

Step-by-step explanation:

Solution

To complete the equation, let's take two different points and plug their x- and y-coordinates into the equation. Then, we can solve for the question mark and see if we get the same number. I'll take (1, -4) and (2, -3):

(1, -4):

(2, -3):

Thus, the equation is y = x + (-5).

Answer:

x = 40°

Step-by-step explanation:

using the cofunction identity

cos(90 - x) = sin x , so

90 - x = 50 , then

x = 40

that is sin40° = cos50°

The probability that each person gets off on a different floor is; 3/32

We are told that there are 4 people on the elevator. We are also told that there are four stops on four different floors. Thus;

Total number of ways to get off on the floors = 4 * 4 * 4 * 4 = 256 ways

Now, the number of ways that each person can get off on a different floor is 4! = 24. Thus, the probability that each person gets off on a different floor is;

P(each person gets off on a different floor) = 24/256 = 3/32

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What percent of students prefer aerobic excersize: 53%

88+69 /350= 0.5257 x 100

52.57 round up 53

53%

Answer:

Certain and likely.

Answer:

1457.7 cubic ft

Step-by-step explanation:

Volume of a cylinder= πr²h

where, r = radius = 8/2 = 4 ft

h = 29

Volume=  π × 4² × 29 = 1457.7 cubic ft

[tex]\rule{300}{1}[/tex]

[tex]\diamond\large\blue\textsf{\textbf{Given question:-}}}[/tex]

      A cylinder has a base of 8 feet and a height of 29 ft. What is its volume

in cubic feet (ft³)?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

We are asked to find the volume of a cylinder, which can be found using the following formula:-

    [tex]\hookrightarrow\boxed{\bold{V=\pi r^2h}}[/tex]

Where:-

Provided Information:-

Solving for Volume:-

        ✳︎ [tex]\sf{V=\pi (4)^2(29)}[/tex]

On simplification,

    ✳︎ [tex]\sf{V=\pi (16)(29)}[/tex]

On further simplification,

   ✳︎ [tex]\sf{V=464\pi }[/tex]

Final step:-

✳︎ [tex]\sf{V\approx1,457.7\:ft^3}[/tex]

So we conclude that the volume of the given cylinder is

[tex]\ast[/tex] [tex]\sf{V\approx{1,457.7\:ft^3}}}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

See below ~

Step-by-step explanation:

Solving for F

Finding F when K = 310.15 K

Check the picture below, the assumption being that the 6ft line is perpendicular to the 18ft line and thus making a right-triangle.

now, if we just get the whole area of the containing parallelogram and then get the area of the triangle and subtract it from that of the parallelogram's, what's leftover is the area we didn't subtract, the shadead area.

[tex]\stackrel{ \textit{\LARGE Areas}}{\stackrel{parallelogram}{(18)(10)}~~ - ~~\stackrel{triangle}{\cfrac{1}{2}(18)(6)}}\implies 180~~ - ~~54\implies 126[/tex]

Exponential functions are known to increase geometrically. An example of exponential function is  p(x) = 500(1.02)^x

Exponential functions are known to increase geometrically. The standard exponential function is given as:

y = ab^x

a is the base

x is the exponent

From the given options, the function written in this form is

p(x) = 500(1.02)^x. Hence an example of exponential function is

p(x) = 500(1.02)^x

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Answer:

78125

Step-by-step explanation:

We conclude that the distance between the home plate and the second base is 107.48 feet.

We know that the distance will be equal to the diagonal of the square. Remember that for  a square of side length S, the diagonal is:

D = S*√2

In this case, the side length is S = 76ft, then the diagonal is:

D = 76ft*√2 = 107.48ft

From this, we conclude that the distance between the home plate and the second base is 107.48 feet.

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Answer:

1/2 < 3/5 < 2/3 < 5/6

Step-by-step explanation:

Using the given inputs:

1/2 5/6 2/3 3/5

The least common denominator (LCD) is: 30.

Rewriting as equivalent fractions with the LCD:

1/2 5/6 2/3 3/5

15/30 25/30 20/30 18/30

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

1/2 3/5 2/3 5/6

15/30 < 18/30 < 20/30 < 25/30

Therefore, the sorted inputs in order from least to greatest is:

1/2 < 3/5 < 2/3 < 5/6

[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Volume of a rectangular prism is ~

[tex] \sf{Volume_{cuboid}= Length × Width × Height} [/tex]

[tex]\qquad \sf  \dashrightarrow \: v = (4x + 2) \times (3x - 5) \times (7x + 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = (12 {x}^{2} - 20x + 6x - 10) \times (7x + 4) [/tex]

[tex]\qquad \sf  \dashrightarrow \: v = (12 {x}^{2} - 14x- 10) \times (7x + 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 84 {x}^{3} + 48 {x}^{2} - 98x {}^{2} - 56x - 70x - 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 84 {x}^{3} - 50 {x}^{2} - 126x - 40[/tex]

So, the correct choice is B

Answer:

It's AAS congruent theorem.

Answer:

[tex]\huge\boxed{\sf AAS\ postulate}[/tex]

Step-by-step explanation:

The two triangles have:

So, 2 angles and 1 side congruency makes it AAS postulate (Angle-Angle-Side).

[tex]\rule[225]{225}{2}[/tex]

Answer:

you can approximate it to 61°

Answer:

19/20

Step-by-step explanation:

380÷ 20= 19

400÷20= 20

Answer:

$2756.01  to the nearest cent.

Step-by-step explanation:

A = P(1 + r)^t     where A is the amount after t years, P = amount invested, r = rate as a decimal fraction.

So here, we have:

A = 1500(1 + 0.052)^12

= 1500 * 1.837337

= $2756.01

Answer:

63

Step-by-step explanation:

score 75 is one standard dev below the mean ====>to the mean  encompasses approx 34% of scores

.34 * 186 = 63

Answer:

y int = -12

vertex = (-4,4)

Axis of Symmetry = x = -4

It has a Maximum

Opens up

Step-by-step explanation:

Answer:

∠ 1 = 36° , ∠ 2 = 144°

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles on a straight line and sum to 180° , that is

x + 12 + 6x = 180

7x + 12 = 180 ( subtract 12 from both sides )

7x = 168 ( divide both sides by 7 )

x = 24

Then

∠ 1 = x + 12 = 24 + 12 = 36°

∠ 2 = 6x = 6 × 24 = 144°

Step-by-step explanation:

6) The sum of the length of any two sides of a triangle is always equal to the third side.

Option C 3,4,7

7) The sum of the length of any two sides of a triangle is always equal to the third side.

Option B 5 units

8) The sum of the length of any two sides of a triangle is always equal to the third side.

Option D 13 units

9) The sum of the length of any two sides of a triangle is always equal to the third side.

Option A 5<x<13

Answer:

Part A: (2x−5)(x+2)

Part B: (5/2,0) and (-2,0)

Part C: The graph of f(x) has both "ends" of the graph pointing upward. You can describe this as heading toward infinity.

Part D: To graph function we can use x-intercepts and "ends" to sketch.In order to graph better use one more point of parabola that you can find as the average of x-intercepts: (-2+5/2)/2 =1/4.This is just x coordinate and you need to plug in 1/4 in the f(x) and find y coordinate -10 1/8. You can use y-intercept (0,-10) as well to graph.

Step-by-step explanation:

2x^2-3x-5=y

(2x-5)(x+1)=y

(2x-5)(x+1)=0

2x-5=0

2x=5

x=2.5

x+1=0

x=-1

you have an even degree (2) and a positive coefficient (2)

therefore as x---> -∞, f(x)----> +∞

also, as x----> +∞, f(x)----> +∞

also notice that this is a parabola that opens upwards so both "ends" approach positive infinity

plot the x-intercepts, find the vertex using h=-b/2a and substituting this value into the equation to find k and make a table of values to graph the parabola unless you only want a rough sketch of the graph-you know the x-intercepts and you found the vertex using h=-b/2a

Step-by-step explanation:

Answer: hes right

Step-by-step explanation: i took the test

well, since we know the point L is on the circle, that means that the segment RL is really the length of the radius of that circle, hmmm let's see what that might be

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ R(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad L(\stackrel{x_2}{0}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ RL=\sqrt{[0 - 2]^2 + [8 - 4]^2}\implies RL=\sqrt{(-2)^2+4^2}\implies \boxed{RL=\sqrt{20}}[/tex]

since RL is its radius, anything larger than that is outside the circle, and anything smaller than that is inside it.  Let's check for the distance RQ.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ R(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{6}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ RQ=\sqrt{[6 - 2]^2 + [7 - 4]^2}\implies RQ=\sqrt{4^2+3^2}\implies RQ=\sqrt{25}[/tex]

needless to say RQ is larger than RL.

Answer :

[tex] \: [/tex]

Step-by-step explanation :

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\[/tex]

Here,

[tex] \: [/tex]

So, substituting the values in the formula we get :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}= (7) {}^{2} + (8 {)}^{2} }}} \\ [/tex]

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}=49 +64}}} \\ [/tex]

[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}=113 }}} \\ [/tex]

[tex]\\ {\longrightarrow \pmb{\sf {\qquad x= \sqrt{113} }}} \\ [/tex]

[tex]\\ {\longrightarrow \pmb{\sf {\qquad x \approx10.63 }}} \\ [/tex]

Therefore,

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

n ≤ − 2

Answer:

Step-by-step explanation:

Solving :

Q1

Q2

Q3