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Answer:

acos(bxc)+d

h(x)=acos(bxc)+d

The function has a maximum point at (3,6) and a minimum point at (6.5,-9) so

h(x)=6-acos(3bx)+9

or

h(x)=-acos(3bx)+15

Step-by-step explanation:

Please analyze and reasure that this answer is correct.

An exact expression of h(x) is  7.5cos(51.4x - 154.3)-1.5.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions.

the difference in y values from max to min = 15. 15/2 = a

max cosine = 1, min cosine =-1

7.5 x 1 - 1.5 = 6

7.5x -1 -1.5 = -7.5-1.5= -9

h(x) = 7.5cos(bx+c) -1.5

now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c

at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...

if x=3, then 3b +c=0 and c=-3b

for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180

c= 180-6.5b

c=-3b

180-6.5b =-3b

add 6.5b to both sides to get

180= 3.5b

b = 180/3.5 = 51 1/7

c=-3b = -153 3/7

h(x) = 7.5cos(51.4x - 154.3)-1.5

Therefore, exact expression of h(x) is  7.5cos(51.4x - 154.3)-1.5.

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The function will begin to have real output when the input value is 2

The function is given as:

[tex]f(x) = -\sqrt{x - 2} + 2[/tex]

Set the radical greater than or equal to 0

[tex]x - 2 \ge 0[/tex]

Add 2 to both sides

[tex]x \ge 2[/tex]

This represents the domian

Hence, the function will begin to have real output when the input value is 2

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Complete question

At what input value will the function [tex]f(x) = -\sqrt{x - 2} + 2[/tex] begin to have real outputs?

Answer:

d.)

Plot these inequalities:

Graphed below (shaded yellow region):

where all the inequalities meet or touches each other.

The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

μρ=ρ

The standard deviation of this sampling distribution of sample proportion is:

σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]

The information provided is:

n = 533

p = 0.09

As the sample size is quite large, i.e. n = 533 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.

The mean and standard deviation are:

μρ=ρ=0.09

σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]=[tex]\sqrt\frac{0.09(1-0.09)}{533}=0.01239[/tex]

Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows:

[tex]p(p^-p > 0.03)=P(p^ > 0.12) \\=P(z > \frac{0.12-0.9}{0.012}) \\= P(Z > 2.5) \\= 1-P(Z > 2.5) \\ = 1- 0.993 \\ = 0.00621[/tex]

Thus, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

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No solutions exist to this system of equations

A system of equations is said to be inconsistent if the two equations do not agree, meaning that there is no set of values that can simultaneously satisfy each equation. For example, the most basic inconsistent system of equations could be x = 4 a nd x = 5 at same time which is not possible.

A single equation in three unknowns can be interpreted geometrically in 3-dimensional space. If we look at a system of such linear equations, the solution set is the set of all points lying in all of the corresponding planes.

Systems of equations in three variables that are inconsistent could result from three parallel planes, two parallel planes and one intersecting plane, or three planes that intersect the other two but not at the same location.

Hence, No solutions exist to this system of equations

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Answer:

a

Step-by-step explanation:

The reflection of the quadrilateral DEFG will be given in the figure.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the quadrilateral DEFG will be given in the figure.

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Answer:

SR and RZ

Step-by-step explanation:

A perpendicular bisector is a line segment that passes through the midpoint of a side of a triangle. In other words, If it goes through a side, it should split the segment in half perfectly. Furthermore, it must be perpendicular to the side it passes through (it should form a ninety-degree angle with the side). Given these two rules, one can say that one of the perpendicular bisectors is SR. SR forms a right angle with (and is thus perpendicular to) side AB. Furthermore, AS is congruent to (has the same length as) SB, which means SR cuts AB in half exactly. Another bisector would be RZ (for similar reasoning). Let me know if that doesn't make sense.

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

The set of the whole numbers is {0, 1, 2, 3...}

Then the first possible value is when g = 0.

0^2 + 3 = 3

The second possible value is when g = 1

1^2 + 3 = 4

The third possible value is when g = 2.

2^2 + 3 = 7

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

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Answer:

3,4,7

Step-by-step explanation:

jus took the test

Equations are written by equating the expressions to each other. The value of x is 7

Equations are written by Equating the expressions to each other.

Given the equation below:

10 - x = 3

Subtract 10 from both sides

10 - x - 10 = 3 - 10

-x = -7

Multiply both sides by -1

-(-x) = -(-7)

x = 7

Hence the value of x is 7

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The probability of randomly selecting a student that is either a female or a senior is 3/4.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

                            Males          Females             Total

Freshman                8                   17                      25

Sophomores          15                   10                      25

Juniors                   12                    13                       25

Seniors                   15                   10                        25

Total                       50                   50                      100

Now, the probability of randomly selecting a student that is either a

female or a senior

= 50/100 + 25/100

= 75/100

= 3/4

Hence, the probability of randomly selecting a student that is either a female or a senior is 3/4.

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Answer:

x = -3/2, -2

Step-by-step explanation:

2x^2 + 7x + 6 = 0

(2x + 3)(x + 2) = 0

(2x + 3)

2x = -3

x = -3/2

(x + 2)

x = -2

Answer:

[tex]\large {\textsf{A and C}}\ \implies x_1=-2,\ x_2=-\dfrac{3}{2}}[/tex]

Step-by-step explanation:

In this problem, we can use two methods to solve for the values of x (roots) of the given equation. Those methods are: using the quadratic formula and factoring.

Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0

Given equation: 2x² + 7x + 6 = 0

⇒ a = 2, b = 7, c = 6

Method 1: Using the Quadratic Formula

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Step 1: Substitute the values of a, b, and c into the quadratic formula.

[tex]\implies x=\dfrac{-7\pm\sqrt{7^2-4(2)(6)}}{2(2)}\\\\[/tex]

Step 2: Simplify

[tex]\implies x=\dfrac{-7\pm\sqrt{\bold{7^2}-4(2)(6)}}{\bold{2(2)}}\\\\\implies x=\dfrac{-7\pm\sqrt{49-4\bold{(2)(6)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{49\bold{-4(12)}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{49-48}}}{4}\\\\\implies x=\dfrac{-7\pm\sqrt{\bold{1}}}{4}\\\\\implies x=\dfrac{-7\pm1}{4}[/tex]

Step 3: Separate into two possible cases and solve for the values of x.

[tex]\implies x_1=\dfrac{-7-1}{4}\implies \dfrac{-8}{4}\implies \boxed{-2}\\\\\implies x_2=\dfrac{-7+1}{4}\implies \dfrac{-6}{4}\implies\boxed{-\dfrac{3}{2}}[/tex]

Method 2: Solve by Factoring

In order to be able to solve this equation by factoring, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = 12) and give us the sum of the middle term (b = 7).

Factors that give a product of a • c: 4 • 3 = 12

Factors that give a sum of b: 4 + 3 = 7

Step 1: Rewrite the given equation with those factors.

2x² + 7x + 6 = 0

⇒ 2x² + 4x + 3x + 6 = 0

Step 2: Factor out 2x and 3.

(2x² + 4x) + (3x + 6) = 0

⇒ 2x(x + 2) + 3(x + 2) = 0 [ Factor out the the common factor. ]

⇒ (2x + 3)(x + 2) = 0

Step 3: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0).

a) 2x + 3 = 0 ⇒ 2x = -3 ⇒ x = -³⁄₂

b) x + 2 = 0 ⇒ x = -2

Therefore, the two roots of this equation are x = -³⁄₂ and x = -2.

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Answer: = 14a + 9b

Step-by-step explanation:

distribute:

2(a+3b) + 3(4a+b)

2a + 6b + 12a + 3b

combine like terms:

2a + 6b + 12a + 3b

14a + 6b + 3b

14a + 6b + 3b

= 14a + 9b

Answer:A

Step-by-step explanation:125 miles divided by 5 gallons would equal 25, meaning 25 gallons per mile

The ladder reaches 19.938 foot high from the ground on the wall.

A right angled triangle is a triangle that has one of its angle measure as 90  degree.

It is given that

Ladder Length = 22 foot

The angle between the ladder and the ground is 65 degree.

When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.

The figure is attached with the answer.

sin 65 = Height of the wall / Hypotenuse

0.9063 = Height of the wall / 22

Height of the wall = 19.938 foot

Therefore the ladder reaches 19.938 foot high from the ground on the wall.

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Answer:

19.94

Step-by-step explanation:

The equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is y = 50. Hence, 4th option is the right choice.

The slope-intercept form of a line is written as y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) can be calculated using the formula, slope (m) = (y₂ - y₁)/(x₂ - x₁).

Therefore, slope of the line passing through the points (-25, 50) and (25, 50) can be calculated as m = (50 - 50)/(25 - (-25)) = 0/(-50) = 0.

We can find the equation of the line using the point-slope formula, according to which, a line having a slope m and passing through the point (x₁, y₁) can be written as y - y₁ = m(x - x₁).

Therefore, the equation of the given line can be written as:

y - 50 = 0(x - 25)

or, y - 50 = 0,

or, y = 50.

Therefore, the equation of the line passing through the points (-25, 50) and (25, 50) in slope-intercept form is y = 50. Hence, 4th option is the right choice.

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The force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N

A tangible body's mass is the amount of matter it possesses. It's also a metric of inertial or the resistance to velocity when a net force is exerted.

We have:

The mass of the body m = 0.8 kg

As we know,

F = mg

F is the force acting on the body and g is the acceleration due to gravity.

g = 9.8 m-s⁻²

F = (0.8)(9.8)

F = 7.84 kg-m-s⁻²

or

F = 7.84 N

Thus, the force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N

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The original amount Sara has left is 172/209

The calculation can be done as follows

Let y represent the amount left

9/11 × 836

= 7524/11

= 110

Y  can be calculated as follows

Y + 38 +110= 836

148 + Y= 836

Y= 836 - 148

Y= 688

Therefore the fraction is

688/836

= 172/209

Hence the fraction of the original amount left is 172/209


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The value of x that makes sense in this context is; 32.

The dimensions of the new garden is; 64 by 16.

The expression that represents the problem statement is;

x² = (2x)(x – 16)

Expanding the bracket gives us;

x² = 2x² – 32x

x² - 32x = 0

x(x - 32) = 0

Thus; x = 0 or x = 32

x can't be 0 and as such the value of x is 32.

Thus;

The length of the new garden is; l = 2x = 64.

The width of the new garden is; w = x - 16 = 32 - 16 = 16

The dimensions of the new garden are therefore; 64 by 16

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The value of y, the length of each leg, must be greater than 7.

This is a type of triangle with two equal sides.

Let the first, second and third side = a, b and c respectively

     (b - a) < c < (a + b)

For an isosceles triangle with base of 14 units, the two other sides must be equal.

c <  (a + b)

c = 14

a = b = y

14 < (y + y)

14 < 2y

7 < y

Thus, the value of y, the length of each leg, must be greater than 7.

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Answer: C. greater than 7.

Step-by-step explanation:  Trust Me!

Did it on Edge got the answer correct! :)  

At times, latitudes with values higher than 66.5  degrees can have ~ 24 hours of continuous sunshine.

Locations above the Arctic Circle (north of latitude 66.5 degrees, 90 degrees minus the tilt of the Earth's axis) are exposed to 24-hour sunlight. Below the Arctic Circle (latitude 66.5 degrees south), there is 24-hour darkness.

When at the equator, the sun is directly above – at the poles, the sun is on the horizon. However, regardless of the current location (from the pole to the equator), all parallels are bisected, so we have 12 hours a day and 12 hours a night in all locations.

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Answer:

6(2)x = 384

12x = 384

12x/12 = 384/12

x = 32

Step-by-step explanation:

Answer:

9m²-n²

Step-by-step explanation:

(3m+n)(3m-n)

This is so easy algebraic expression.

Just rewrite as,

Simplifying,

[Alternate method is there]

Using translation concepts, the value of k is given as follows:

B) 1/5.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this graph, we have that g(x) = f(kx), hence since g(-2) = f(-10):

-2 = -10k

k = 2/10

k = 1/5.

Hence option B is correct.

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The radius of the area the sprinkler has watered is 8.06 yards.

Rotation is spinning around a fixed point with a fixed radius in circular motions.

It is given that a sprinkler rotates 360 degree

The area watered is 204 sq. yards

Radius = ?

A sprinkler rotates in circle

Therefore the area of the circle = π r²

204 = π r²

204 * 7 /22 = r²

r² = 64.91

r = 8.06 yards

Therefore the radius of the area the sprinkler has watered is 8.06 yards.

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1081.44 is the value of the quantity after 0.1 hours, to the nearest hundredth.

What Is percent in simple words?

Based on the given conditions, formulate = [tex]6500 * (1 - \frac{45}{100} )^{( 0.1 * 60/2)}[/tex]

Evaluate the equation/expression=  1081.4375

Round the number: 1081.44

Therefore, 1081.44 is the value of the quantity after 0.1 hours, to the nearest hundredth.

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The correct answer is 108° i.e Option A.

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HOPE IT HELPS! :)