find the measures of the angles of a right triangle where one of the acute angles is *3.5* times the other

Answer:

5 units

Explanation:

Given the points:

We use the distance formula below:

Substitute the given values:

The distance between the two points is 5 units.

Answer

(-12, -8) after R270°.D¼ becomes (-2, 3)

Explanation

The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.

When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.

Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.

The coordinates to start with is (-12, -8)

R270° changes A (x, y) into A' (y, -x)

So,

(-12, -8) = (-8, 12)

Then, the second operation dilates the new coordinates obtained after the first operation by ¼

D¼ changes A (x, y) into A' (¼x, ¼y)

So,

(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)

Hope this Helps!!!

The factors of a polynomial tell us the points where the graph intersects the x-axis.

From the graph provided in the question, the graph cuts the x-axis at the points:

Therefore, the factors will be:

Therefore, the polynomial will be:

OPTION C is the correct option.

The behavior of any polynomial function is determined by the exponent and the signal of the first term of the function.

In the case of f(x), the leading term is negative, and its expoent is odd. Therefore, when x is negative, the leading term will be positive and, when x is positive, the leading term is negative.

Therefore, we have:

Given:

Sheila can wash her car in 15 minutes. Bob takes time twice as long to wash the same car.

Required:

Find the time they take both together.

Explanation:

Sheila can wash her car in 15 minutes.

Work done by sheila in a minute =

Bob takes time twice as long to wash the same car. He washes the car in 30 minutes.

Work done by Bob in a minute

If they work together let them take time x per minute.

Solve by taking L.C. M.

If they work together they will take 10 minutes.

Final Answer:

Sheila and Bob wash the car together in 10 minutes.

Okay, here we have this:

Considering that in a parallelogram the opposite sides are congruent, we obtain the following:

AB=CD

AB=9 units

AC=BD

AC=4 units

The length of the building's shadow = 550.66 ft

The height of the Empie State Building = 1250 feet

The friend's height = 75 inches

The length of the friend's shadow = 33 inches

We are asked to solve the exponential equation given below:

e^5x - 5 * e^-2x = 2e

First let's apply the exponent rules:

5x - 5 - 2x = In(2e)

Solving 5x - 5 - 2x = In(2e)

3x - 5 = In(2e)

Add 5 to both sides:

3x = In(2e) + 5

Divide both sides by 3

x = In(2e) + 5

3

x = 2.23104

x = 2.231 (To the nearest thousand)

Therefore, the correct option is A, which is The solution set is 2.231 (Round to the nearest thousand).

If I sent 4/9 of the leftover pizza home with your friends the pizza do I have left in the box is 16/45.

What is pizza?

Pizza is an Italian food consisting of a typically flat, spherical foundation composed of leavened wheat dough that is topped with cheese, tomatoes, and frequently a number of additional toppings. Following that, the pizza is baked at a high temperature, typically in a wood-fired oven. A small pizza is also known as a pizzetta. A pizza maker is referred to as a pizzaiolo.

To get the quantity of the leftover pizza, we need to subtract the pizza sent by me to home from the total pizza I had in my lunch box.

So,

Pizza I have left = Pizza in lunch box - Pizza I have sent

Pizza I have left = 4/5 - 4/9  

Pizza I have left = (4(9) - 4(5))/45

Therefore, Pizza I have left is 16/45.

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The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is

Simplifying it, we have

So, the playing ratio is 2 to 3 for Jason.

Question 4

The x values for which g(x) = 3

From the graph, we have this value to be:

Question 5

f(x) = 6, What is x?

From the graph, we can determine the value of x corresponding to f(x)= 6:

Question 6:

f(x)= 0, What is x?

From the graph, we can determine the value of x corresponding to f(x) = 0

Question 7

The domain of the function:

The domain is the set of allowable inputs.

Question 8

The range is the set outputs

Derivative and Maximum Value of a Function

The critical points of a function are those where the first derivative is zero or does not exist.

Out of those points, we may find local maxima or minima or none of them.

One example of a function with a derivative that does not exist is:

This function has a local maximum at x=0 where the derivative does not exist.

The graph of this function is shown below:

We will have the following:

We will recall that the surface area of a sphere is given by:

So, the surface area of the given sphere will be:

So, the surface area of the sphere will be 28 yd^2.

*The reason we can use "mental math" is that we are using an approximation of pi, which makes it so it cancels with the 3.14 in the denominator after a point; leaving a simple multiplication at the very end.

According to the Inscribed Angle Theorem, the measure of an angle inscribed in a circle equals half the arc that it intercepts.

Then:

Since the measure of the arc AC is equal to 84º, then:

Therefore, the answer is:

The measure of ABC is 42º.

When two angles are adjacent on a straight line, then the sum of the two angles equals 180 (that is sum of angles on a straight line). Therefore;

The measure of r is 15

Speed formula:

d is the distance

t is the time

As you need to find a time having the distance and speed, solve the equation above for t:

Use the given data to find the time:

Your answer can't be simplified but it's also slightly incorrect. No worries!

You can simplify (64v^4 - 225w^10) by applying the difference of squares --> a^2 - b^2 = (a + b)(a - b)

Here, (64v^4) is a^2, and (225w^10) is b^2.

[tex]\sqrt{64v^4 }[/tex] = a = 8v^2

[tex]\sqrt{225w^{10} }[/tex] = b = 15w^5

Substitute the values:

(8v^2 + 15w^5)(8v^2 - 15w^5)

Therefore, the factorization of [tex]64x^{4} -225w^{10}[/tex] is:

[tex](8v^{2} + 15w^5)(8v^2-15w^5)[/tex]

The factorization is already the simplest. It can't be simplified further.

Answer

The angles given can easily be the measurements of one triangle because they sum up to give 180°.

Explanation

The sum of angles in a triangle is known to be 180°

So, for the given angles to be to belong to one triangle, the sum of all the angles must be equal to 180°

So, we check by adding them

37° + 111° + 32° = 180°

Hope this Helps!!!

The given equation is

To solve this equation we have to isolate x on one side and put the numbers on the other side

To do that we will add 3 to each side to move 3 from the left side to the right side

Simplify it

Now we need to move 2 from the left side to the right side, then

Divide both sides by 2

Then the solution of the equation is

x = 6

The table show piszzas (P) on the left column and the slices of Pepperonin (S) on the right column.

To determine the equation models first check the ratio S/P to determine whether they are proportinal or not.

Now as the ratios are constant it mean the variation is linear and the relationship is proportional.

Thus the model equation can be determine as,

Thus, the above equation gives the required model equation.

We have the following equation of a hyperbola:

Let's divide all the equations by 4, just to simplify it

Just to make it easier, let's put the term if "x" isolated

Now we can complete squares on both sides, just remember that

Now let's complete it!

We already completed one side, now let's complete the side with y^2, see that we will add 4 again, then

And now we can write it using the standard equation!

And now we can graph it like all other hyperbolas, the vertices will be:

And the foci

Then the foci are

Now we can plot the hyperbola!

Given:

To solve,

Step 1:

Express each value to a common decimal place.

We can express each value to two decimal places.

Thus, we have

Step 2:

Sum up the values.

Hence, 16.02 + 8.5 + 14 gives 38.52.

We have the following equation.

Where m is the number of feet in a mile.

Let us subtract 20,000 from both sides of the equation then simplify

The negative sign cancels out and the equation becomes

Finally, we can apply the Division Property of Equality which states that when we divide both sides of the equation with same number then the equation remains valid.

Let us divide both sides of the equation by 1.8939 then simplify

Therefore, there are 5280 feet in a mile (rounded to nearest whole number)

Answer:

f=11

Explanation:

Given the function:

When the input, t=7

The value of the output, f will be gotten by substituting 7 for t.

The output, f is 11.

Since this situation can be represented by a right triangle, we can use the pythagorean theorem. Doing so, we have:

We have the next given information:

China has a population of approximately 1,382,323,332 people.

The United States has a population of about 324,118,787 people.

a) We need to use scientific notation which is given by the next form:

Where a is the coefficient rounded to the nearest tenth.

and a is the terms moved to the decimal point.

For China:

1382323332.0, we moved the decimal point nine spaces to the right.

then

1.382323332

Expressed in scientific notation and rounded to the nearest tenth:

For the United States:

324,118,787 with the decimal point 324,118,787.0

then

324118787.0

Move the decimal point 8 spaces to the right, then:

3.24118787

Expressed in scientific notation and rounded to the nearest tenth:

Part b:

To find how many more people live in China than in the United States, we need to subtract between China and the United States:

Then:

1,382,323,332 - 324,118,787 = 1,058,204,545

Now

1,058,204,545 equal to 1058204545.0

We need to move the decimal point 9 spaces:

1.058204545

Expressed as scientific notation and rounded to the nearest hundredth:

Answer:

29 units

Step-by-step explanation:

BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/sqrt2

If In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Then BC is 29 units

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units.

We need to find BC

In triangle ACD,

tan 45° = CD/AD

CD = tan 45° x AD

= 1 x 20= 20 units

In triangle CDB,

tanФ = CD/BD

Ф = tan⁻¹(CD/BD)

= tan⁻¹(20/21)

= 43.6°

so, sin 43.6° = CD/BC

BC = CD/sin 43.6°

= 20/0.689

= 29 units

Hence the length of BC will be 29 units.

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Recall that the constant of variation of a straight line is the slope of the line.

To compute the slope we will use the following formula for the slope of a line:

Now, notice that points (-1,3) and (1,-3) are on the line, then substituting these points in the above formula we get:

Answer: -3.

The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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Solution

For this case we can use the definition of average given by:

The final score needs to be 90 so we can do this:

And solving for x5 we got:

5*90 = 88+91+95+89+ x5

x5= 450 - 88- 91- 95 -89 = 87

Final answer:

c.87