Example 2
3. FOOTBALL The flight of a football thrown by a quarterback can be
modeled by an interval of a function. Sketch a nonlinear graph that
shows the height of a football y, in feet, as a function of time x, in
seconds.
Positive: between 0 seconds and 5 seconds
Negative: for time greater than 5 seconds (represents time after
the ball hits the ground)
Increasing: for time less than 2 seconds
Decreasing: for time greater than 2 seconds
Relative Maximum: at 2 seconds, when the height of the football is 9 feet
Height of Football (ft)
End Behavior: As time increases, the height of the football decreases.
Symmetry: The height of the football for time between 0 seconds and 2 seconds
is the same as the height for time between 2 seconds and 4 seconds.

Answer:

\(15 \geqslant - 3x \\ \frac{15}{3} \geqslant - x \\ 5 \geqslant - x \\ - 5 \leqslant x\)

\( \frac{2}{5}x \geqslant - 2 \\ x \geqslant - 2 \times \frac{5}{2} \\ x \geqslant - 5\)

Answer:

{x | x ≥ -5}

Step-by-step explanation:

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

The production figure to maximize the profit is is Z = 15x + 10y  subject to

2x + 3y ≤ 600 ; 2x + y ≤ 480  ; x,y≥ 0 .

In the question ,

it is given that ,

a company named Universal Electric manufactures sell two models of lamps that is Lamp X and Lamp Y  and

Whose profit is  $ 15 and $ 10 respectively.

let the number units the company manufactures of lamp X be = x units

let the number units the company manufactures of lamp Y be = y units

let the total profit be = Z ,

So , the profit to maximize be Z = 15x + 10y

worker A assembles Lamp X in 20/60 hours and Lamp Y in 20/60 hours ; and that he is available for 100 hours per month;

So , the inequality is

(20/60)x + (30/60)y ≤ 100.

20x + 30y ≤ 6000

2x + 3y ≤ 600

Similarly , worker B assembles Lamp X in 20/60 hours and Lamp Y in 10/60 hours ; and that he is available for 80 hours per month;

the inequality will be ,

(20/60)x + (10/60)y ≤ 80.

20x + 10y ≤ 4800

2x + y ≤ 480  .

Therefore , the LPP to maximize the profit is Z = 15x + 10y  subject to

2x + 3y ≤ 600 ; 2x + y ≤ 480  ; x,y≥ 0 .

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Answer:

Step-by-step explanation:

The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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Answer:

D

Step-by-step explanation:

A triangle with sides 2, 4.5, and 6 is similar to a triangle with sides 4, 9, and 12.

\( \frac{4}{2} = \frac{9}{4.5} = \frac{12}{6} = 2\)

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.

Answer:

Carl

Step-by-step explanation:

There are 52 weeks in a year, and Carl reads 3 books a week, so he reads 3*52= 156 books a year. There are 12 months in a year, and Rose reads 6 books a month, so Rose reads 6*12=72 books a year. Carl reads the most books

Answer:

7600

Step-by-step explanation:

Because it is just x 100

The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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Answer:Its B

Step-by-step explanation:

Bc I just got it right

ARM for which interest will stay fixed for 8 years and then be adjusted every year after that = 8/1 ARM

The correct option is (B).

The term adjustable-rate mortgage (ARM) refers to a home loan with a variable interest rate. With an ARM, the initial interest rate is fixed for a period of time. After that, the interest rate applied on the outstanding balance resets periodically, at yearly or even monthly intervals.

Given statement

ARM for which Interest rate stay fixed for 8 years and then be adjusted every year after that.

Above information is typically expressed in two numbers. The first number indicates the length of time that the fixed rate is applied to the loan, while the second refers to the duration or adjustment frequency of the variable rate.

By the above method ARM for Interest rate stay fixed for 8 years and then adjusted every year after that can be expressed as 8/1 ARM.

Hence, for 8/1 ARM, interest rate will stay fixed for 8 years and then

be adjusted every year after that.

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Answer:

question 22 ) 3.325

Step-by-step explanation:

I use the app photo math. Its free and shows you all the steps.

Answer:

3 + 3x = 45 ; x = 14

Step-by-step explanation:

45 = 3x + 3 ⇒ x = 14

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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Answer:

2 hot dogs to 4 hamburgers

Step-by-step explanation:

there are 2 hot dogs and there are 4 hamburgers so its 2 hotdogs to 4 hamburgers

it is false but 4 is not y-4x=0

Answer:

that looks like the directions

Step-by-step explanation:

can you put a screenshot of the problem.

Answer:

Hi!

The slope of the line is marked as rise over run and in slope intercept form it is mx. We can tell from the way the line is slanting that it is a positive slope. It goes up 1, over 6. So therefore, the slope is 1/6.

The y intercept of the line is -4, which we know because that is where the line and the y axis meet. The y intercept is b in slope intercept form.

The slope intercept form is y = 1/6x -4.

For standard form, we subtract 1/6x from both sides to get

-1/6x + y = -4

Hope this helps!

Step-by-step explanation:

Answer:

7.7

Step-by-step explanation:

For the 57° angle, d is the opposite leg, and 5 in. is the adjacent leg. The trig ratio that relates the opposite and adjacent legs is the tangent.

\( \tan 57^\circ = \dfrac{d}{5~in.} \)

\( d = 5~in. \times \tan 57^\circ \)

\( d = 7.7~in. \)

Answer: 7.7

The logarithmic equation is equivalent to this exponential equation is x = log (8/25) (option c).

In this case, we are asked to find the logarithmic equation that is equivalent to the given exponential equation:

2,400 = 7,500(10)⁻ˣ

To solve for x, we need to isolate it on one side of the equation. We can start by dividing both sides by 7,500:

2,400/7,500 = (10)⁻ˣ

The choice of base for the logarithm doesn't matter, as long as we use the same base for both sides. Let's use base 10:

log(2,400/7,500) = log(10⁻ˣ)

Using the properties of logarithms, we can simplify the right-hand side:

log(2,400/7,500) = -x*log(10)

We know that log(10) = 1, so we can simplify further:

log(2,400/7,500) = -x

x = log(8/25) = log(8) - log(25) = 0.9031 - 1.3979 = -0.4948

So the only answer choice that gives us the same equation as the original exponential equation is (C) x = log (8/25).

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Complete Question:

Which logarithmic equation is equivalent to this exponential equation?

2,400 = 7,500(10)^(-x)

A. x= -log (25/8)

B. x = log(-25/8)

C. x = log (8/25)

D. x = -log (8/25)

Answer:

A' (7,7)

B' (10,4)

C' (6,5)

Step-by-step explanation:

Add 9 to every x value and 3 to every y value.

Answer:

A'(7,7)

B'(10,4)

C'(6,5)

Step-by-step explanation:

⭐What is a translation?

⭐What is the translation notation?

The problem tells us to translate ΔABC 9 units to the right, and 3 units up because it is inside the <>, and the numbers are positive.

To translate the vertices of ΔABC, we have to add the respective x and y coordinates of the translation rule to each vertecie of ΔABC.

A(-2,4):

B(1,1):

C(-3,2):

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:A

Step-by-step explanation:

Answer:

Correct answer is 6x(x+2)(2x-3)

Step-by-step explanation:

best answer choice I got and also I got it correct!!!

Answer:

Zero. The sum of anything and it's opposite is zero, that's how an opposite is defined . In this case, the opposite of 2x+1 is -(2x+1)=-2x-1 by the distributive property . Adding like terms, 2x+-2x+1+-1=0+0=0.

Answer:

\(100\%\)

Step-by-step explanation:

\( \frac{64}{65} \times 100\% \\ \frac{64 \times 100}{65} \\ \frac{6400}{65} \\ = 98.461\% \\ \)

When you round it to nearest tenth....

The answer is,

\(100\%\)

Hope this helps you.

Let me know if you have any other questions :-):-)