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Answer

TRUE

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.

The function is

f(x) = 2*cos(π*x) + sin(π*x)

Which can be seen in the picture below

We can notice that f(x) is a sinusoid. It has periodic amplitudes, and the function has a period T = 2

The maximum and minimum values are

Max = 2.236

Min = -2.236

Answer: OPTION C

Step-by-step explanation:

 Given the equation [tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex], you need to solve for  the variable "x".

First, you need to multiply both sides of the equation by [tex]\sqrt{4x}[/tex]:

[tex](\frac{\sqrt{3-2x}}{\sqrt{4x}})(\sqrt{4x} })=2(\sqrt{4x} })\\\\\sqrt{3-2x}=2\sqrt{4x}[/tex]

Now you need to square both sides of the equation:

[tex](\sqrt{3-2x})^2=(2\sqrt{4x})^2\\\\3-2x=4(4x)\\\\3-2x=16x[/tex]

Subtrac 3 and 16x from both sides:

[tex]3-2x-(3)-(16x)=16x-(3)-(16x)\\\\-18x=-3\\[/tex]

Divide both sides by -18:

[tex]\frac{-18x}{-18}=\frac{-3}{-18}\\\\x=\frac{1}{6}[/tex]

Answer:

3x(3x-2)(12x-5) D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

This is a game in which you figure out what the terms of the expression have in common.  Clearly, x is a common factor, as 108x³ = x(108x²), -117x² = x(117x) and 30x = x(30).  Factoring out x, we get:

x(108x² - 117x + 30).

Next, note that 3 is a factor common to 108, 117 and 30, so now we have:

x(108x² - 117x + 30) → 3x(36x² - 27x + 10).  Knowing this enables us to eliminate answers A and B, because neither has that factor 3 in it.

Now take a look at D.  This is the only answer choice that produces a '10,' which stems from multiplying -2 and -5.  So the only possible answer choice is D.

Answer:

Part 1) The width of the pad is [tex]1\ m[/tex]

Part 2) The solutions are

[tex]x=\frac{5(+)\sqrt{97}} {4}[/tex]  and [tex]x=\frac{5(-)\sqrt{97}} {4}[/tex]

Step-by-step explanation:

Part 1)

Let

x----> the width of the pad

we know that

[tex](15+2x)(18+2x)=340[/tex]

Solve for x

[tex]270+30x+36x+4x^{2} =340\\ \\4x^{2}+66x-70=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=1\ m[/tex]

see the attached figure

Part 2) we have

[tex]2x^{2} -5x-9=0[/tex]

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2} -5x-9=0[/tex]  

so

[tex]a=2\\b=-5\\c=-9[/tex]

substitute in the formula

[tex]x=\frac{5(+/-)\sqrt{-5^{2}-4(2)(-9)}} {2(2)}[/tex]

[tex]x=\frac{5(+/-)\sqrt{97}} {4}[/tex]

[tex]x=\frac{5(+)\sqrt{97}} {4}[/tex]

[tex]x=\frac{5(-)\sqrt{97}} {4}[/tex]

Answer:

A) {x | -1 < x < 7}

Step-by-step explanation:

Given in the question two inequalities,

Inequality 1

(x - 2 < 5)

 x < 5 + 2

 x < 7

x is smaller than 7

Inequality 2

(x + 7 > 6)

 x > 6 - 7

 x > -1

x is greater then -1

When (x - 2 < 5) U (x + 7 > 6).

              (x < 7)   U  (x > -1)    

                    -1 <  x  < 7

When combined, x is greater than -1 but smaller than 7

The height of Blue Mountain is determined by setting up two equations based on the tangent of the observed angles of elevation from two different points and solving for the distance to the mountain. The height is then calculated using this distance and rounded to the nearest tenth.

Tony is trying to find the height of Blue Mountain using trigonometry and the angles of elevation observed from two different points. We can solve this problem using right-angled triangles and trigonometric functions (specifically tangent).

Step-by-Step Calculation

First, we use the angle from the first observation point:
tan(23°) = height / distance
Height = distance * tan(23°). We call this height 'h'.

Then, when Tony moves 210 yards closer, the distance from the mountain is 'distance - 210 yards', and we use the angle from this second point:
tan(28°) = height / (distance - 210)
Height = (distance - 210) * tan(28°). We call this height 'h' as well because the height of the mountain doesn't change.

Therefore, we have two equations:
h = distance * tan(23°)
h = (distance - 210) * tan(28°).

By equating the two expressions for 'h', we find the distance 'd':
distance * tan(23°) = (distance - 210) * tan(28°).

We can now solve for 'distance' numerically. After calculating distance, we can use it to find the actual height 'h' using the tangent function with any of the two angles.

Final Result

We round intermediate results to 3 decimal places and the final height to 1 decimal place, giving us the height of Blue Mountain.

Answer:

1 inch : 6.4 feet

Step-by-step explanation:

Since the wall is 51.2 feet tall, and then wall on the blueprint is 8 inches long, we can make a scale. So 8 in: 51.2 ft or 1 inch: 6.4 feet.

Answer is

1 inch:6.4 feet

ANSWER

The length is 10 inches and the width is 24 inches

EXPLANATION

The diagonal of the rectangular painting is d=26 inches.

Let l and w be the length and width of the painting respectively.

From Pythagoras Theorem,

[tex] {l}^{2} + {w}^{2} = {26}^{2} [/tex]

[tex]{l}^{2} + {w}^{2} = 676..(1)[/tex]

Its area is 240 square inches.

This implies that,

[tex]l \times w = 240[/tex]

[tex]l = \frac{240}{w} ...(2)[/tex]

Put equation (2) into (1).

[tex]{( \frac{240}{w} )}^{2} + {w}^{2} = 676[/tex]

This implies that,

[tex] {w}^{4} - 676 {w}^{2} + 57600 = 0[/tex]

[tex]( {w}^{2} - 100)( {w}^{2} - 576) = 0[/tex]

[tex]{w}^{2} - 100 = 0 \: or \: ({w}^{2} - 576= 0[/tex]

[tex]{w}^{2} = 100 \: or \: {w}^{2} = 576[/tex]

Take positive square root to get,

[tex]{w} = 10\: or \: {w} = 24[/tex]

When w=24,

[tex]l = \frac{240}{24} = 10[/tex]

when w=10

[tex]l = \frac{240}{10} = 24[/tex]

Hence the length is 10 inches and the width is 24 inches.

The dimensions of the painting can be found by setting two equations, one for the area of the rectangle, and another based on the Pythagorean theorem, and solving for the length and the width. The key is to remember that these values must be positive, as they represent physical dimensions.

First, let's recall what we know. The area of a rectangle is given by the formula length x width = area. Here, we know that the area of the painting is 240 square inches.

Next, remembering the Pythagorean theorem, which states that for any right-angle triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides. Here, we can write the Pythagorean theorem as length² + width² = diagonal² (26 inches).

Setting up these two equations, we would solve for length and width. Keep in mind that we're seeking positive and realistic solutions, as these represent the physical dimensions of the painting.

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Answer: yes, 1 of each

You can also get a second salad or drink because of the total as shown below:

$2.49 × 2 + $.99 × 2 = $6.96

I think it’s 11.

A=.5bh

A=1/2x5 1/2x4

=11

Answer:

11

Step-by-step explanation:

Answer:

The measure of angle VPJ is [tex]140\°[/tex]

Step-by-step explanation:

Let

x-----> the measure of arc PIV

y-----> the measure of arc PKV

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m<VPJ=\frac{1}{2}(x)[/tex]

[tex]x=3.5y[/tex] -----> equation A

[tex]x+y=360\°[/tex] -----> equation B

substitute equation A in equation B

[tex]3.5y+y=360\°[/tex]

[tex]4.5y=360\°[/tex]

[tex]y=80\°[/tex]

Find the value of x

[tex]x=3.5(80\°)=280\°[/tex]

Find the measure of angle VPJ

[tex]m<VPJ=\frac{1}{2}(280\°)=140\°[/tex]

About 13099.6 square miles of Wisconsin is not land area.

To find the amount of square miles of Wisconsin that is not land area, we need to calculate 20% of the total area. First, we find 1% of the total area by dividing it by 100. 65498 square miles / 100 = 654.98 square miles. Then, we multiply this by 20 to find 20%: 654.98 square miles * 20 = 13099.6 square miles. Therefore, about 13099.6 square miles of Wisconsin is not land area.

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Answer:

Step-by-step explanation:

As we move from (-2, 5) to (1, 3), x increases by 3 and y decreases by 2.

Hence, the slope of this line is m = rise / run = -2/3.

Start with the slope-intercept form y = mx + b.

Substitute 3 for y and 1 for x and -2/3 for m:

3 = (-2/3)(1) + b.

Remove fractions by mult. all three terms by 3:

9 = -2 + b, so b = 11, and y = (-2/3)x + 11

Again, mult. all three terms by 3:

3y = -2x + 33, or, in standard form,

Answer:

c=20

Step-by-step explanation:

200=10c

200/10=c

20=c

Answer:

a = 7

Step-by-step explanation:

45 45 90 right triangle so it's an isosceles triangle (A triangle with two equal sides)

a = 7

Answer:

Step-by-step explanation:

Answer:

amplitude; [tex]\frac{2}{3}[/tex]

Phase shift; [tex]\pi[/tex] units right

Period;[tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]y=-\frac{2}{3}\cos(3t-3\pi)[/tex]

This function is of the form;

[tex]y=A\sin (Bt+C)[/tex]

The period is given by:

[tex]|A|=|-\frac{2}{3}|= \frac{2}{3}[/tex]

The period is given by:

[tex]T=\frac{2\pi}{|B|}= \frac{2\pi}{|3|}=\frac{2\pi}{3}[/tex]

The phase shift is given by;

[tex]\frac{C}{B}=\frac{-\3pi}{3}=- \pi[/tex] or [tex]\pi[/tex] units right.

5 liter bucket with the 3 liter bucket twice, and then use the 3 liter bucket and the 4 liter bucket twice.

To determine the shipping cost of a 2-pound package, convert the weight to ounces (32 ounces), account for the initial charge for the first 3 ounces (1.95), and add the cost for the remaining 29 ounces at 0.17 each, totaling 6.88.

To calculate the cost of shipping a 2-pound package, we use the given postal rates. Since there are 16 ounces in 1 pound, a 2-pound package equals 32 ounces. The post office charges 1.95 for the first 3 ounces. Every additional ounce costs 0.17. So we subtract the first 3 ounces from the total weight and then calculate the cost for the remaining ounces.

The calculation can be done as follows:

This approach to calculating postage makes it easy to understand the incremental cost structure of shipping packages.

Answer:  The correct option is (C). 0.78125.

Step-by-step explanation:  We are given to find the 10th term of the following geometric sequence

400,  200,  100, . . . .

We know that,

the n-th term of a geometric sequence with first term a and common ration r is given by

[tex]a_n=ar^{n-1}.[/tex]

In the given sequence,

first term, a = 400

and

common ration is given by

[tex]r=\dfrac{200}{400}=\dfrac{100}{200}=~.~.~.~=0.5.[/tex]

Therefore, the 10th term of the sequence is

[tex]a_{10}= ar^{10-1}=400\times (0.5)^9=400\times0.001953125=0.78125.[/tex]

Thus, the correct option is (C). 0.78125.

Answer:

the answer is c 60%, may i have brainlyiest

Final answer:

To find the probability that a voter did not vote for a new school tax when 2/5 did, subtract 2/5 from 1 to get 3/5, then convert to a percentage to get 60%.

Explanation:

In the given problem, we know that 2/5 of the voters voted for a new school tax. To find the probability that a randomly selected voter did not vote for the tax, we need to calculate the fraction of those who did not vote for the tax. Since the total probability must be 1 (or 100%), those who did not vote for the tax would account for the remaining fraction of 1 - 2/5, which is 3/5. To express this as a percentage, we convert 3/5 into a decimal and then into a percentage.

First, calculate 3/5 as a decimal: 3/5 = 0.6. Then, to convert it to a percentage, multiply by 100: 0.6 × 100 = 60%.

Therefore, the probability that a randomly selected voter did not vote for the new school tax is 60%, which corresponds to answer choice c. 60%.

Answer:

c. 4.0

Step-by-step explanation:

To find a, we'll use the Law of Sines that says:

[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]

And we'll isolate a to get:

[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]

Then we will plug-in the information we already have (changing 16°55' into 16.92)

[tex]a = \frac{sin(16.92) * 13.7}{sin(90)} = 3.99[/tex]

So, let's round it to 4 to match the answer number C.

Answer:

C

Step-by-step explanation:

Use the definition of the sine function:

[tex]\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}.[/tex]

Substitute [tex]\angle A=16^{\circ}55'[/tex] and [tex]c=13.7[/tex] into the previous formula:

[tex]\sin 16^{\circ}55'=\dfrac{a}{c},\\ \\\sin 16^{\circ}55'=\dfrac{a}{13.7},\\ \\a=13.7\cdot \sin16^{\circ}55',\\ \\a\approx 13.7\cdot 0.284\approx 4[/tex]

Answer:

So the maximum amount of gasoline the tank can contain is 13 gallons and there are already 7 gallons of gasoline in the tank. Therefore, we want to make sure that the amount of gasoline put in the tank doesn't reach any higher than 13 gallon.

The amount of gasoline that Lou bought with x dollars is x/2.50 gallons.

We have the inequality:

x/2.50 + 7 ≤ 13

*If you solve it, x should be smaller or equal to $15.

The math problem can be solved by setting up a compound inequality expressing the range that Lou can spend on gasoline. This factors in the total capacity of his tank, the current amount of gas, and the price per gallon. The result is 0 <= x <= $15.

For this problem, Lou needs to fill the remainder of his gas tank, which is 13 gallons total but already has 7 gallons. That means he needs to fill 13 - 7 = 6 gallons more. Gasoline costs $2.50 per gallon, so the total amount of money he spends, represented by x, can be calculated using the inequality $2.50 * number of gallons <= x.

But because Lou can add anywhere from 0 to 6 gallons, we will have a compound inequality. So, the inequality will be: $2.50 * 0 <= x <= $2.50 * 6.

This simplifies to 0 <= x <= $15, meaning Lou can spend anywhere from $0 to $15 on gasoline, depending on how much more he wants to put in his tank.

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Answer:

Option c.

No damping

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool.

The function is

f(x) = (√11)*cos(3.7x)

Which can be seen in the picture below

We can notice that f(x) is a cosine with maximum amplitude of  (√11). Neither this factor nor the multiplication of x by 3.7 serve as a damping factor since they are constants.

f(x) does not present any dampening

Answer:

C) No damping.

Step-by-step explanation:

This is the correct answer on ed-genuity, hope this helps! :)

Answer:

Answer:

t = 3.8 s

option 3

Step-by-step explanation:

For this case we have the following equation:

 h (t) = at ^ 2 + v * t + h0

 Substituting values we have:

 h (t) = - 16 * t ^ 2 + 60 * t + 3

 We equate the equation to zero:

 -16 * t ^ 2 + 60 * t + 3 = 0

 We look for the roots of the polynomial:

 t1 = -0.04935053979258153

 t2 = 3.7993505397925817

 We are left with the positive root and round:

 t2 = 3.8 s

Answer:

7,55 seg

Step-by-step explanation:

Initial Velocity = 60 ft/s

High = 3ft

Acceleration = -16 ft/s2

According to the next formula

H = Vi(t) - 1/2 gt2

We got a cuadratic formula which roots are

t1 = -0,04 seg and t2 = 7,55 seg

the time not negative so t= 7,55 seg

Answer: The probability of the histogram is 0.6.

Step-by-step explanation:

Look at the images below for the step-by-step explanation. It's a lot easier to write on docs, rather than on this website. Anyway, I hope you've learned something. Bye!!!

Answer:

[tex]18.98\°[/tex]

Step-by-step explanation:

Let

x-----> the angle of depression

we know that

The sine of angle x is equal to divide the altitude (opposite side to angle x) by the distance from the runway (hypotenuse)

[tex]sin(x)=\frac{2.7}{8.3}[/tex]

[tex]x=arcsin(\frac{2.7}{8.3})=18.98\°[/tex]

Answer:

18.02°

Step-by-step explanation:

Formula to find angle of depression is given as

tan y = opposite / adjacent

where y = angle of depression

Where opposite = height or altitude of a person or thing

adjacent = distance

In this question ,

opposite = altitude of the plane = 2.7 miles

adjacent = distance of the plane from the runaway = 8.3 miles

Angle of depression is calculated as

tan y = ( 2.7/8.3)

y = tan⁻¹ ( 2.7÷8.3)

y = 18.02°

Angle of depression that the plane must make to land safely = 18.02°

Answer:

12x^2=6

Divide by 12

x^2=1/2or.5

square root

x=0.707

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue.  We have the work form of a positive upwards-opening parabola as

[tex]y=a(x-h)^2+k[/tex]

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex.  We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1).  Now we will fill in the work form equation and solve for a:

[tex]-1=a(-2-(-3))^2-3[/tex]

which simplifies a bit to

[tex]-1=a(1)^2-3[/tex]

and

-1 = a(1) - 3.  Therefore, a = 2 and our parabola is

[tex]y=2(x+3)^2-3[/tex]

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4.  Do this by subbing in the values of x one at a time to find y.  When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3).  When x = -4, y = -1 so the coordinate of that point is (-4, -1).  The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

[tex]m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2[/tex]

And there you have it!  I'm very surprised that this question sat unanswered for so very long!  I'm sorry I didn't see it earlier!

Certain means the event will happen.

Impossible means the event would never happen.

To be "certain" to occur means the event will definitely happen without any doubt.

For an event to be "impossible" to occur means that there is no chance whatsoever that the event will happen.

When we say an event is "certain" to occur, we mean that the event will definitely happen. In terms of probability, if an event has a probability of (1) (or 100%), it is certain to occur. For example, if you flip a fair coin, the probability of it landing either heads or tails is (1), meaning it's certain to land on one of the two sides.

On the other hand, when we say an event is "impossible" to occur, we mean that the event will definitely not happen. In terms of probability, if an event has a probability of (0) (or (0%), it is impossible to occur. For example, if you roll a six-sided die and ask for a result that is not within the range of 1 to 6, the probability of that happening is (0), so it's impossible for the die to show that result.

These concepts are fundamental to understanding the certainty or impossibility of events in probability theory and are essential for making predictions and decisions based on probabilistic models.