Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s claim is below.

Jeremiah: The y-intercept is at (15, 0).
Lindsay: The x-intercepts are at (–3, 0) and (5, 0).
Stephen: The vertex is at (–4, –1).
Alexis: The midpoint between the x-intercepts is at (4, 0).


Which student’s claim about the function is correct?

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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Answer:

V= 76 π cubic units

Step-by-step explanation:

y= \((x-3)^{2}\) -----> \(x=\sqrt{y} +3\)

Here we will apply the risk method.

Risk method: consider a strip of length x and width dy as

a) Radius= R(y) = x = \(\sqrt{y} + 3\)

[We rotate this disc about y-axis to get a disk]

b) Cross-section area = A(y)= π \((radius)^{2}\)

                                    = A(y)= π (y+9+6 \(\sqrt{y}\))

--------> Volume of the disc = A(y) x dy

c) Required volume= v = \(\int\limits^4_0\) A(y) x d(y)

                         V= \(\int\limits^4_0\)  π (y + 9 + 6\(\sqrt{y}\) ) dy

                         V=  π [ \({\frac{y^{2} }{2} + 9y + 4y^{\frac{3}{2} }\)\(]_{0} ^{4}\)

                          V= 76  π cubic units.

9514 1404 393

Answer:

  240

Step-by-step explanation:

Your calculator can tell you the answer.

__

If you're doing this by hand, it can be convenient to combine the multipliers of 48:

  (2 5/7)·48 +(2 2/7)·48 = (2 5/7 +2 2/7)·48 = ((2+2) +(5/7+2/7))·48

  = (4 +7/7)·48 = 5·48 = 240

Answer:

“The Beginnings of the Maasai.”

These cattle are sacred, bec

Step-by-step explanation:

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.

Step-by-step explanation:

The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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The mean is 0.477514 (rounded to 6 decimal places).

The standard deviation is 0.288919 (rounded to 6 decimal places).

To calculate the mean and standard deviation, we will use the following formulas:

Mean = (sum of all values) / (number of values)

Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]

Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:

Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514

Therefore, the mean is 0.477514 (rounded to 6 decimal places).

Now we will calculate the standard deviation:

Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919

Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).

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Answer: 30

Step-by-step explanation:

(8+7) x 2

= 15 x 2

= 30

Answer

Circumference is 400m

The circumference is the perimeter of a circle is

To find the radius since the circumference is given as 400

Make radius the subject of the formula

Now the radius of the big circle

It is plus 2

The circumference of big circle is

Finally

The final answer

Answer:

0.196

Step-by-step explanation:

Let :

Expresso drink = A

Plain coffee = B

Food = F

P(A) = 0.56

P(B) = 0.44

P(F) = 0.40

P(F|A) = 0.35

P(F|B) = 0.30

Probability that a customer purchases a specialty expresso coffee and a food item :

P(F|A) =. P(F n A) / P(A)

P(F n A) = P(F|A) * P(A)

P(F n A) = 0.35 * 0.56

P(F n A) = 0.196

Answer:

  $50,000

Step-by-step explanation:

The given relations can be used to write and solve an equation for the amount invested in stocks.

Let s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...

  0.18s +0.12(120,000 -s) = 17,400

Simplifying the equation, we have ...

  0.06s +14,400 = 17,400

  0.06s = 3000 . . . . . . . . . . subtract 14,400

  s = 50,000 . . . . . . . . . . . . divide by 0.06

Neal invested $50,000 in stocks.

__

Additional comment

The amount invested in bonds was 70,000. The profit earned was ...

  0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

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You are requested to provide an estimate of the building's total window cleaning expense so that the board can make a decision.

Some window cleaners charge by the hour, though the majority bill by the square foot or the number of windows. For home work, professionals bill between $40 and $75 per hour.

Due of the increased safety dangers in high-rises, they usually charge $85 per hour. Many cleaners may charge by the pane if the house is medium-sized, anything from $2 to $7 for each one or more for larger windows. It's typical to charge an hourly rate in large homes when counting each window by itself would take too long or be impossible.

Window cleaning costs typically run between $40 and $75 per hour. If the house is medium-sized, many cleaners may charge per the pane; for larger windows, they may charge anywhere from $2 to $7 for each one or more.

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You are requested to provide an estimate of the building's total window cleaning expense so that the board can make a decision.

Some window cleaners charge by the hour, though the majority bill by the square foot or the number of windows. For home work, professionals bill between $40 and $75 per hour.

Due of the increased safety dangers in high-rises, they usually charge $85 per hour. Many cleaners may charge by the pane if the house is medium-sized, anything from $2 to $7 for each one or more for larger windows. It's typical to charge an hourly rate in large homes when counting each window by itself would take too long or be impossible.

Window cleaning costs typically run between $40 and $75 per hour. If the house is medium-sized, many cleaners may charge per the pane; for larger windows, they may charge anywhere from $2 to $7 for each one or more.

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Answer:

1575 ft

Step-by-step explanation:

Convert 1/10 to decimal to make the math simpler.

1/10 = 0.1

Divide 3.5 by 0.1.

3.5/0.1 = 35

Multiply 35 by 45.

35 × 45 = 1575

The train will travel 1575 feet in 3.5 seconds.

The distance covered by the train in 3.5 seconds will be 1575 feet.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A train travels 45 feet in 1/10 in a second.

Then the speed will be

Speed = 45 / (1/10)

Speed = 45 x 10

Speed = 450 feet per second

The distance covered by the train in 3.5 seconds will be

Distance = 450 x 3.5

Distance = 1575 feet

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Answer:

C

Step-by-step explanation:

find the plot and interpret the point in the equation

The value of the side length x is equal to 14 using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

sin45 = 7√2/x {opposite/hypotenuse}

√2/2 = 7√2/x {sin45 = √2/2}

x = 7√2 × 2/√2 {cross multiplication}

x = 7 × 2

x = 14

Therefore, the value of the side length x is equal to 14 using the trigonometric ratio of sine.

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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

the rug should be 10 feet by 16 feet

this makes the area 160 foot squared

Step-by-step explanation:

there is a 2 foot border on each side so the total area loses 4 feet from length. this gives 10 feet by 16 feet.

160

top correct lolssssss

Answer: 0.07

Step-by-step explanation:

To find the relative frequency of people in the sample whose place of residence is suburban and whose highest degree is a two-year degree, we need to calculate the ratio of the number of people with those characteristics to the total sample size.

Looking at the contingency table, we can see that the number of people in the suburban category with a two-year degree is 21.

The total sample size is given as 311.

Therefore, the relative frequency can be calculated as:

Relative frequency = (Number of people in suburban category with two-year degree) / (Total sample size)

= 21 / 311

≈ 0.0676

Rounded to two decimal places, the relative frequency is approximately 0.07.

I think it's an= 13.5 - 2.5n

\(a_n=13.5-2.5n\)

\(11,\ 8.5,\ 6,\ 3.5,\ 1...\)

\(So\ d=8.5-11=b-8.5=3.5-6=1-3.5\)

       \(=-2.5\)

\(And\ a_1=\parallel \left\{Anithmetic\ \left.\ sequence\right\}\right.\)

\(so\ a_n=a_1+d(n-1)\)
         \(=11-2.5(n-1)\)
         \(=13.5-2.5n\)

\(The\ answer:a_n=13.5-2.5n\)

I hope this helps you

:)

Answer:

2

Step-by-step explanation:

Answer: x<-21 or x>-9

Step-by-step explanation:

|x+15|> 6

x+15>6

x>6-15

x>-9

x+15<-6

x<-6-15

x<-21

x<-21 or x>-9

Answer:

m = 2, c = 1

Explanation: In the y = mx + b (or y = mx + c) format, the m is the slope of the line and the c/b is the y-intercept, or where the line crosses the y-axis. If we substitute the information from the given equation, y = 2x + 1, into the general formula, we know that the m is 2 and c is 1.

The x-coordinate at which F(x) = G(x) is 0.667. By graphing the functions, the answer has been discovered.

Making a graph of the pertinent function is the first step in graphing a function. The function equation will be satisfied by a curve if it reflects the function at that location.

We are given two functions as f(x) = log (2x) and g(x) = 3x - 2

The graph of the given functions has been plotted and attached below.

In the graph, the red line represents the log function i.e. f(x) and the blue line represents the linear function i.e. g(x).

From the graph, we can observe that the two functions meet at two points which are (0.667, 0) and (0, -2).

Hence, the x value where F(x) = G(x) is 0.667.

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Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

16.67

Step-by-step explanation:

Each side is about 4.167 yards so the perimeter is roughly 16.67 yards

Answer:

20200

Step-by-step explanation:

As you're in a hurry, I can give it later? xx