A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer than the side along the building. the third side is 7 feet longer than the side along the building. find the length of all three sides of the reflecting pool

Answer:

B. Linear function and a relation

Step-by-step explanation:

The graph is a straight line and by definition a linear function.

Each point on the line can be expressed as an ordered pair i.e  the coordinates (x,y), implying that there is a relation between x and y.

Answer:

B. Linear function and a relation

Step-by-step explanation:

The following terms are defined like so,

Linear: linear functions show up as straigh lines when plotted on a graph

Non-Linear: non-linear functions show up as curvy or wavvy lines when plotted on a graph

Relation: relation graphs have specific outputs for every input, meaning for every x location on the graph there is only one y point.

Based on the definitions above we can determine that the graph in the diagram is both Linear and a Relation, since it is both a straight diagonal line as well as only having one specific y coordinate for every x coordinate. So the answer would be B. Linear function and a relation.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

she will be taking 3600 mgs. in 90 days

Step-by-step explanation:

if she is taking a 20 mgs. twice a day that will make it 40 mgs. a day.  If she takes it for 90 days

you will multiply 90 by 40

so

90

x40

= 3600 mgs. in 90 days

Answer:

3600 mg

Step-by-step explanation:

She takes 1 capsule  2 times a day

2* 20 mg = 40 mg

She takes 40 mg a day

She takes them for 90 days

40 mg a day for 90 days

40*90

3600 mg

Answer:

The constant of variation is 1.6.

Step-by-step explanation:

y = kx  and x = 5 when y = 8 and k = the constant of variation.

8 = k*5

k = 8.5 = 1.6.

Answer:

8/5

Step-by-step explanation:

Plug in the point given into

y=kx.

The number you get for y will be your constant of variation, also know as constant of proportionality.

(x,y)=(5,8) implies 8=k(5)

So in solving that equation we just need to divide both sides by 5 giving us:

8/5=k.

Answer:

-8

Step-by-step explanation:

Start by multiplying both sides by 4.

[tex]\frac{1}{4} x+2=-\frac{5}{8} x-5\\x+8=-\frac{5}{2} x-20[/tex]

Next, multiply both sides by 2.

[tex]x+8=-\frac{5}{2} x-20\\2x+16=-5x-40[/tex]

Now, combine like terms.

[tex]2x+16=-5x-40\\7x+16=-40\\7x=-56\\x=-8[/tex]

Answer:

-8 on edg

Step-by-step explanation:

Answer:

So the x-intercept is (9,0) and the y-intercept is (0,-3).

So I'm going to graph both points and connect them with a straight-edge.

Step-by-step explanation:

I would graph this using it's x- and y-intercepts.

To find the x-intercept, set y=0.

-3x+9(0)=-27

-3x+0=-27

-3x=-27

Divide both sides by -3:

x=9

To find the y-intercept, set x=0:

-3(0)+9y=-27

 0  +9y=-27

       9y=-27

Divide both sides by 9:  

        y=-3

So the x-intercept is (9,0) and the y-intercept is (0,-3).

So I'm going to graph both points and connect them with a straight-edge.

Answer:

169 feet

Step-by-step explanation:

(see attached)

Answer:

all values of b

Step-by-step explanation:

6b < 36 or 2b + 12 > 6.

First solve the one on the left

6b < 36

Divide by 6

6b/6 < 36/6

b  <6

Then solve the one on the right

2b + 12 > 6

Subtract 12 from each side

2b+12-12 >6-12

2b >-6

Divide by 2

2b/2 >-6/2

b >-3

b<6 or b >-3

Rewriting

b>-3  or b<6

b > -3 is an open circle at -3 with a line going to the right

b < 6 is an open circle at 6 with a line going to the left

The or means we add the lines together

We have a line going from negative infinity to infinity

all values of b

Answer:

All real numbers  b ∈ [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

First we solve the following inequality

[tex]6b < 36[/tex]

Divide by 6 both sides of the inequality

[tex]b<\frac{36}{6}\\\\b<6[/tex]

The set of solutions is:

[tex](-\infty, 6)[/tex]

Now we solve the following inequality

[tex]2b + 12 > 6[/tex]

Subtract 12 on both sides of the inequality

[tex]2b + 12-12 > 6-12[/tex]

[tex]2b> -6[/tex]

Divide by 2 on both sides of the inequality

[tex]\frac{2}{2}b> -\frac{6}{2}[/tex]

[tex]b> -3[/tex]

The set of solutions is:

[tex](-3, \infty)[/tex]

Finally, the set of solutions for composite inequality is:

[tex](-\infty, 6)[/tex]  ∪ [tex](-3, \infty)[/tex]

This is: All real numbers [tex](-\infty, \infty)[/tex]

Answer:

There are are 30 possible ways for the 6 students to be ranked 1st and 2nd

Step-by-step explanation:

There are 6 students, and any of them could receive first place. Therefore, there are 6 possibilities for first place.

A student cannot receive first and second place, so the student who won first place cannot also win second place. Therefore, there are only 5 students who could win second place.

We can multiply these two possibilities to find the number of possible rankings of 1st and 2nd

6*5=30

There are are 30 possible ways for the 6 students to be ranked 1st and 2nd....

Answer:

X  plus 5 equals 8, then whats is X. The answer would be X = 3

Step-by-step explanation: Hope it helps

Answer:

Step-by-step explanation:

[tex]x+5=8\qquad\text{subtract 5 from both sides}\\\\x+5-5=8-5\\\\x=3\\\\Check:\\\\3+5=8\qquad CORRECT :)[/tex]

Answer:

C

Step-by-step explanation:

Parallel and opposite sides of a parallelogram are equal. Hence, we can say:

x + 30 = 2x - 10

and

2y-10 = y +10

Solving first one, we get:

x + 30 = 2x - 10

30+10 = x

x = 40

Also

2y - 10 = y + 10

y = 10 + 10

y = 20

Now, z = x - y, so

z = 40 - 20 = 20

Answer C is right.

I can confirm that the answer is right.

Parallelograms have equal opposite sides. Do the math:

x - y = z

40 - 20 = 20

z = 20

Answer:

GroGain is the more effective hair regrowth system because it yielded a greater hair

Step-by-step explanation:

Answer

FolliclePlus's claim is true

GroGrain's claim is true

GroGrain is the more effective hair regrowth system because it yielded a greater hair growth increase precentage

Step-by-step explanation:

PLATO

Answer:

x ≥ - [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Given

- 12x ≤ 44

Divide both sides by - 12, remembering to reverse the inequality sign as a consequence of dividing by a negative quantity, hence

x ≥ [tex]\frac{44}{-12}[/tex] ← note sign reversed

Dividing the numerator/denominator by 4, gives

x ≥ - [tex]\frac{11}{3}[/tex]

Answer:

Graph #1

Step-by-step explanation:

Compare your

y - 1 = (2/3)(x - 3) to

y - k = m(x - h).  We see that k = 1 and h = 3.

Thus, (1, 3) is a point on the graph.  This matches Graph #1.  

Note: Graph #1 and Graph #3 appear to be the same.  Why?

The graph of the equation is:

                          Graph 1

The equation is given by:

    [tex]y-1=\dfrac{2}{3}\times (x-3)[/tex]

Now, we will see the point through which the graph passes through.

when x=3 we have:

[tex]y-1=\dfrac{2}{3}\times (3-3)\\\\i.e.\\\\y-1=\dfrac{2}{3}\times 0\\\\i.e.\\\\y-1=0\\\\i.e.\\\\y=1[/tex]

i.e. the graph passes through (3,1)

and also when x= -3 we have:

[tex]y-1=\dfrac{2}{3}\times (-3-3)\\\\i.e.\\\\y-1=\dfrac{2}{3}\times -6\\\\i.e.\\\\y-1=2\times -2\\\\i.e.\\\\y-1=-4\\\\i.e.\\\\y=-4+1\\\\i.e.\\\\y=-3[/tex]

i.e. the graph passes through (-3,-3)

The graph which satisfies these two points is: Graph 1

Make n be a number. You must add 8 and the number together then multiply the answer by 3. This means that the verbal expression is:

3 multiplied by the sum of a number and 8.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x = -0.683 (3dp)

x = -7.317 (3dp)

Step-by-step explanation:

Step 1: Apply the quadratic formula

(-b±([tex]\sqrt{b^{2}-4ac}[/tex])) / 2a

a = 1 (x²)

b = 8 (8x)

c = 5 (5)

(-8±([tex]\sqrt{8^{2}-4 x 1 x 5}[/tex])) / 2 x 1

Step 2: Simplify

(-8±([tex]\sqrt{44}[/tex])) / 2

Step 3: Solve

You need to replace the ± with first a + and then a -.

(-8+([tex]\sqrt{44}[/tex])) / 2 = -0.683 (3dp) = x

(-8-([tex]\sqrt{44}[/tex])) / 2 = -7.317 (3dp) = x

Hope this helps!

Well, by definition, it's 9-sided polygon, so the answer should be obvious ;)

Answer:

D

Step-by-step explanation:

A regular nonagon is a nine-sided shape with equal sides and equal angles of 140 degrees each. Each interior angle measure of a regular nonagon is 140 degrees.

Answer:

-1.5

Step-by-step explanation:

So your set of points I believe is:

(1,4)

(2,2.5)

(3,1)

(4,-0.5)

You are asked to find the average rate of change. This just means find the slope.

So you can make sure the slope is the same per pair of points.

So I like to find the slope by lining two points up vertically and subtracting vertically then put 2nd difference over 1st difference.

(2 , 2.5)

-( 1 ,  4)

----------------

 1,  -1.5

So the slope is -1.5/1 or just -1.5.

Check another pair:

 (3  , 1  )

- (2  ,2.5)

------------

 1 ,  -1.5

So the slope is -1.5/1 or just -1.5.

Check one more:

 (4 , -.5)

-(3  , 1)

-----------

1, -1.5

So the slope is -1.5 or just -1.5

So the average rate of change is -1.5.

Answer:

y=x

Step-by-step explanation:

We want a line parallel to y =x+42

The slope of y =x+42 is 1

Parallel lines have the same slope

We have the slope m=1 and a point (2,2)

We can use point slope form to write a line

y-y1 = m(x-x1)

y-2 = 1(x-2) point slope form

Changing to slope intercept form

y-2 = x-2

Add 2 to each side

y-2+2 = x-2+2

y=x

The line parallel to y = x + 42 travels through (2,2) can be represented by the equation y = x. This conclusion is based on the principles of line equations in a two-dimensional space, with slopes determining the parallelism of lines.

The subject of the question pertains to the formula of a line in a two-dimensional space. Specifically, you're asked to find a line that passes through the point (2,2) and is parallel to the line described by the equation y = x + 42.

In a standard equation of a line, y = mx + b, 'm' represents the slope of the line and 'b' indicates the y-intercept. Two lines are parallel if they have the same slope. Bearing this in mind, as the line y = x + 42 has a slope of 1 (since 1 is the coefficient of 'x'), the required line would also possess a slope of 1.

Substituting the point coordinates (2,2) into the equation y = mx + b (replacing 'm' with 1), gives us 2 = 2 + b. Solving for 'b', we find that it equals zero. Hence, the equation of a line parallel to y = x + 42 passing through the point (2,2) is y = x.

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Answer:

The answer is y=5x+50

Hope this helps!!!

Answer:

q = -2

Step-by-step explanation:

-2x²-8x = 10 (divide both sides by -2)

x² + 4x = -5 (Apply completing the square method)

x² + 4x + (4/2)²= -5 + (4/2)²

x² + 4x + 2²= -5 + 2²    (reduce left hand side using a²+2ab+b² =  (a+b)² )

(x+2)² = -5 +4

(x+2)² = -1

(x+2)² + 1 = 0   (multiply both sides by -2)

(-2)(x+2)² + 1 (-2) = 0

-2[x - (-2)]² + (-2) = 0  ---> compare this with -2(x-p)² + q = 0

We can see that p = 2 and q = -2

The value of 'q' in the rearranged form of the given quadratic equation -2(x-p)²+q = 0 is -6. This is obtained by completing the square and comparing the equations.

Given the quadratic equation -2x² -8x = 10, it's rearranged to the form -2(x-p)²+q = 0. The objective is to find the value of 'q'.

To achieve this, you first need to rewrite the given equation -2x² -8x - 10 = 0 in the form -2(x-h)²+k = 0. This is called completing the square. The 'h' value here is equal to -b/2a, where 'b' is the coefficient of 'x' and 'a' is the coefficient of x². In this equation, a is -2 and b is -8 so h=(-(-8)/(2×(-2))=8/4=2.

Substituting h into the equation, you have -2(x-2)²+k=0. Now expand and simplify to get -2x²+8x-4+k=0. Comparing this with the original equation -2x² -8x -10 = 0, you can see that 'k' is equal to -10+4=-6, which is the 'q' value in the form -2(x-p)²+q = 0. So, the value of 'q' is -6.

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[tex]\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ F=\cfrac{k(m_1\cdot m_2)}{r^2}\leftarrow \textit{F varies directly with a product and inversely with }r^2[/tex]

Answer:

[tex]\large\boxed{A)\ 5x^2(2y+5)}[/tex]

Step-by-step explanation:

[tex]10x^2y+25x^2=(5x^2)(2y)+(5x^2)(5)\qquad\text{distributive}\\\\=5x^2(2y+5)[/tex]

The value of equivalent expression is,

⇒ 5x² (2y + 5)

We know that;

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, Given that;

The expression is,

⇒ 10x²y + 25x²

Now, We can simplify the expression as;

⇒ 10x²y + 25x²

⇒ 2×5x²y + 5×5x²

⇒ 5x² (2y + 5)

Thus, The value of equivalent expression is,

⇒ 5x² (2y + 5)

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Answer:

The prime factors of 621 are 3*3*3*23 ....

Step-by-step explanation:

Prime factorization is the process of finding that which prime numbers can be multiplied together to make the original number.

Find the prime factors of 621.

Start with the smallest prime number which is 2. If the number is divisible by 2 then solve further. If not then move to the next prime number.

621 is nor divisible by 2

We move towards the next prime number which is 3.

621 divided by 3 = 207

207 divided by 3 = 69

69  divided by 3 = 23

Now 23 is only divisible by 23 which is also a prime number.

Thus the prime factors of 621 are 3*3*3*23 ....

any other details you could give me ?

It is proved that f and g are inverses by showing that f(g(x)) = x and     g(f(x)) = x.

An inverse function is a function that returns the original value for which a function has given the output.

According to the problem,

Now,   f(g(x)) =  [tex](\sqrt[3]{x-4})^{3} + 4[/tex] = x

           g(f(x)) = [tex]\sqrt[3]{x^{3}+4 -4}[/tex] = x

Thus it is proved that f and g are inverse functions.

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Answer:

A, B, and D

Step-by-step explanation:

A

= 2x+3 < 10

= 2(3)+3 < 10

= 9<10

true

B

= 2x - 3 < 4

= 2(3) -3 < 4

= 3 < 4

true

C

= 5 + 3x > 15

= 5 + 3(3) > 15

= 14 > 15

not true

D

= 12-3x > 2

= 12 - 3(3) > 2

= 3 > 2

true

Answer:

True

Step-by-step explanation:    

The segment ¯AB¯  is congruent to the segment ¯BC¯ .

The point is in between the circle.

Therefore, they are congruent.

True. The segment AB is congruent to the segment BC.

If the length of both the line segments are same, then we can say that both the line segments are congruent to each other.

Here, in the given diagram AC is a chord of the circle centering at O.

B is a point on the chord AC.

The radius of the circle which is perpendicular to AC & passes through B,forms right angle at point B.

Since, AC is a chord of the circle & a radius is perpendicular to AC, the the intersecting point of AC & the radius is midpoint of AC.

So, B is the midpoint of AC.

∴ Line segment AB = Line segment BC

Hence, Segment AB is congruent to segment BC.

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The drawing should be 10 units in width and 5 units in height.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer: x=34

Step-by-step explanation: Divide each side by -1 to get rid of the negatives and isolate x. You will get x = 34 as your answer.