The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find an expression for the area of the tiled floor.

Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]

Step-by-step explanation:

To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that

[tex](4)(10) = 40[/tex]

Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40

Now split 13x into 5x+8x and solve by grouping

[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]

Factor out the GCF in each quantity

[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]

Now group x+2 together

[tex](x+2)(4x+5)[/tex]

Finally, set each factor equal to 0 and solve for x

[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]

Answer:

c .26

Step-by-step explanation:

Male AND drama is 124  out of 479 total

124/479 = .26

The number of minutes of the ride that are spent higher than 22 meters above the ground is; 2.64 minutes

We are given;

bottom of the Ferris Wheel is 4 meters off the ground.

Radius = diameter/2 = 24/2; r = 12 meters.

Thus, the center of the Ferris Wheel is 4 + 12 = 16 meters off the ground.

A horizontal line through the center of the Ferris Wheel is 16 meters off the ground, and therefore the lower half of the Ferris Wheel is always below 22meters.

The distance from the horizontal to 22 meters is 22 - 16 = 6 meters.

The angle between the horizontal and a radius to 22 meters is;

sin(θ) = 6/16

θ = sin⁻¹(6/16)

θ = 22.02°.

This angle height is on both sides of the Ferris Wheel and as such;

180° + (2 * 22.02) = 224.04° is always under 16 meters.

Thus, what is above 16 meters is 360° - 224.04° = 135.96°

Since it takes 7 minutes for 1 revolution, then the amount of time the Ferris Wheel is above 16 meters is;

(135.96/360) * 7 min ≈ 2.64 minutes

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Answer:

d

By the alternate interior angles theorem,

By the reflexive property, AB is congruent to itself.

Thus, the triangles will be congruent by ASA.

Answer:

155°

Step-by-step explanation:

z = 65° + y

y is a right angle

=> y = 90°

=> z = 65° + 90° = 155°

Given the data from the question, the expressions that are equal to 10⁵ are

To determine the expressions that are equal to 10⁵, we shall evaluate the options given from the question.

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(10⁴)¹ = 10⁴

Recall

Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ

Thus,

10³ ⋅ 10² = 10³⁺²

10³ ⋅ 10² = 10⁵

Recall

1 / Aᵐ = A⁻ᵐ

Thus,

1 / 10⁵ = 10⁻⁵

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(10³)² = 10⁶

Recall

Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10¹⁺¹⁺¹⁺¹⁺¹

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵

SUMMARY

(10⁴)¹ = 10⁴

10³ ⋅ 10² = 10⁵

1 / 10⁵ = 10⁻⁵

(10³)² = 10⁶

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵

From the above illustrations, only 10³ ⋅ 10² and 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 are equal to 10⁵

Complete question

See attached photo

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The value of (abscissa of P) -(abscissa of Q) is -1.

The given coordinates are P(4,6) and Q(5,-7).

We need to find (abscissa of P) -(abscissa of Q).

The horizontal coordinate of a point in a planar Cartesian coordinate system that is determined by measuring parallel to the x-axis is what abscissa stands for.

Now, (abscissa of P) -(abscissa of Q)=4-5=-1

Hence, the value of (abscissa of P) -(abscissa of Q) is -1.

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The relationships between angles 1, a, b, and 2 can be defined using the angles between parallel lines.

In the diagram, we can see the fences, making angles 1 and 2 with the parallel lines X and Y respectively.

Using the angles among parallel lines, we can state the relationships between angles 1, a, b, and 2 as follows:

These were the relations among angles 1, a, b, and 2, using the parallel lines X and Y.

Refer to the diagram for a better understanding.

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Use the Pythagorean theorem.

The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

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Answer:

40 dollars

Step-by-step explanation:

Profit is what he earned minus his costs

Profit = 125 -85

Profit = 40

Answer:

Additive

-2 = 2

18 = -18

-30 = 30

2/5 = -2/5

Multiplicative

8/9 = 9/8

12/15 = 15/12

-6 = -1/6

10 = 1/10

Step-by-step explanation:

an additive inverse is a number you must add to another number to get 0

(think of it as the negative version of the number)

{but WHY? In math, you can imagine comparing numbers on a number line. If we are finding the opposite of a number, we want to find the same distance from 0, but on the opposite side of 0. So, 2 would be two to the right of 0, -2 would be two to the left of 0}

-2 + 2 = 0

18 - 18 = 0

-30 + 30 = 0

2/5 - 2/5 = 0

a multiplicative inverse is a number that you multiply by another number to get 1.

We are finding the "reciprocal" of a number; you are essentially flipping it as a fraction

(reciprocal of 2 = 1/2  {remember, 2 is the same thing as 2/1 }   ; reciprocal of 1 / 8 = 8)

note: reciprocal is being used interchangeably with multiplicative inverse here

8/9 · 9/8 = 1

12/15 · 15/12 = 1

-6 · -1/6 = 1                     {-6  = -6/1}

10 · 1/10 = 1                    {10 = 10/1}

hope this helps!! have a lovely day :)

Answer:

Additive: number that you add to get 0

2

-18

30

-2/5

Multiplicative: number that you multiply to get 1

9/8

15/12

-1/6

1/10

hope this is helpful!!  ^u^

Answer: C

Step-by-step explanation: The graph is going to go up because the +9.5 isn't in any parentheses. If it was, that would mean it would move horizontally. I hope this helps!

The correct statement:

It is the graph of y = x translated 9.5 units up.

The correct option is c.

The equation y = x represents a straight line passing through the origin with a slope of 1. When we have the equation y = x + 9.5, it means that for every x-value, the corresponding y-value is obtained by adding 9.5 to the original x-value. This translation in the y-direction shifts the entire graph upward by 9.5 units.

To visualize this, imagine the original line y = x. Each point on this line has an x-coordinate and a corresponding y-coordinate, which are the same due to the equation y = x. When we add 9.5 to each y-coordinate, the line shifts vertically by 9.5 units without any change in slope or horizontal position.

The other options can be eliminated because the statement does not mention changing the slope or the horizontal position of the graph. Instead, it specifically describes a vertical translation, indicating a movement in the y-direction. Therefore, the correct answer is c.

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Answer:

Step-by-step explanation:

AFR = VFN (opposite angle rule)

7x + 33 = 9x + 7

33 - 7 = 9x - 7x

26 = 2x

x = 26 : 2

x = 13°

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

check

7 * 13 + 33 = 9 * 13 + 7   (remember PEMDAS)

91 + 33 = 117 + 7

124 = 124

the answer is good

Answer:

Step-by-step explanation:

-4(5x-3)+12

-20x+12+12

20x+24

my answer is 20x+24.

The simplified form of the given expression -4(5x-3)+12 would be 20x+24.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

-4(5x-3)+12

Open the bracket

-20x+12+12

Solve the like terms;

20x+24

Hence, the simplified form of the given expression -4(5x-3)+12 would be 20x+24.

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Answer:

When 68.321 rounded to the nearest tenth the result is 68

Answer:

A

Step-by-step explanation:

Use the Pythagorean Theorem: a^2 + b^2 = c^2

The cable will be the hypotenuse, so c = 11.3 m

One leg is the distance of the anchor, so a = 4.2 m

(4.2)^2 + b^2 = (11.3)^2

17.64 + b^2 = 127.69

Subtract 17.64 from both sides

b^2 = 110.05

Square root both sides

b = ~10.5 m

x=  10, NL= 8 , NP = 12

A secant is a line that intersects a curve at a minimum of two distinct points.

Using secant theorem,

NL* NM = NP* NO

(3+5)*3 = (2+x)*2

24=  (2+x)*2

12= 2+x

x= 12-2

x= 10

So, NP= 2+x

     NP = 12

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The highest common factor is [tex]\boxed{y}[/tex].

g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.

First, a vertical shift of N units is written as:

g(x) = f(x) + N

A horizontal shift of N units is written as:

g(x) = f(x + N).

In this case, we have:

g(x) = f(x + 8) + 4

So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.

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The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.

A graphing calculator is a portable computer that can plot graphs, solve multiple equations at once, and carry out other variable-related activities.

We have points shown in the coordinate plane.

As the window of a graphing utility is set at:

X(min) : -6

X(max): 6

Y(min) : -6

Y(max) : 6

The points out of 6 will not be visible.

We can draw a square as shown in the attached picture.

The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible.

Thus, the points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.

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-5≥

so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)

Answer:

x> -6

Step-by-step explanation:

Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6

Answer:

21/428 or 0.04 906542056074...

Step-by-step explanation:

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

Given the log function expressed as:

log(x-3) + logx=1

According to the law of logarithm, addition becomes product to have:

log x(x -3) = log₁₀10

x² - 3x = 10

x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0

x = -2 and 5

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

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The angle BAC will be 29 and the angle BOC will be 58.

The angle in a circle's centre is twice that at its perimeter when two angles are subtended by the same arc. So, angle AOB = 2 angle ACB. Angles that the same arc subtends at its circumference are equal. As a result, angles inside a section are equal.

Here the given angle is ∠BDC = 29 so from the given theorem the angle BEC will be equal to the angle BDC.

∠BDC = 29

The centre angle BOC will be twice the angle at the circumference so the angle will be twice.

∠BOC = 59

Therefore the angle BAC will be 29 and the angle BOC will be 58.

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Using the tangent theorem, the length of the radius is: B. 10 units.

According to the tangent theorem, since KL is tangent to the circle, therefore, angle JKL = 90°.

Since the triangle is a right triangle, apply the Pythagorean theorem:

(r+16)² = r² + 24²

r² + 32r + 256 = r² + 576

r² - r² + 32r + 256 = 576

32r + 256 = 576

32r = 576 - 256

32r = 320

r = 320/32

r = 10

The radius is: B. 10 units.

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Answer:

B. 10 Units

Step-by-step explanation:

The coefficient of the variable Q is 36 , Option A is the correct answer.

The complete question is

The coefficient of 2(3)(6)Q is _____. a.36 b.18 c.12

Coefficient is the constant term written in front of  variable in an expression.

The expression given in the question is

2(3)(6)Q

The coefficient is 2 * 3 * 6 = 36

Therefore , the coefficient of the variable Q is 36 , Option A is the correct answer.

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