In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.

The given information is the shape is a rectangle.

About the diagonals of rectangles, there are two known properties:

- The diagonals of a rectangle bisect each other

- Both diagonals have the same length

Then, the answer is option C. They have the same length

Answer:

The value of f is;

Explanation:

Given the triangle in the attached image.

Recall that;

from the given figure;

substituting the values;

Therefore, the value of f is;

If we have:

To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:

Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:

So, the answer we would get is

The equation of this parabola is Y = -1/2 X². So option C is correct.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Given that,

The graph of parabola,

the vertex (0, 0)

Y - 0  = 4a (X - 0)²

Y  =  4aX²

It can be seen in the graph it is downward parabola so value a should be  less than zero

So possible equation could be Y = -1/2 X²

Hence, the equation is Y = -1/2 X²

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The athlete will cover 17 yards in 22 minutes of his running.

The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.

Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.

We will use the unit conversions to solve the given problem.

The speed of the athlete is 9 mph. We can write it as -

9 mph = (9 x 1760) yards per hour = 15840 yards per hour.

15840 yards per hour = (15840/60) yards per minute = 264 yards per min.

Total yards covered in 22 minutes = 22 x 264 = 5808 yards

one lap is equivalent to 349 yards.

1 yard is equivalent to (1/349) laps

5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.

Therefore, the athlete will cover 17 yards in 22 minutes of his running.

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To find a value of θ theta given a value of sin(θ) we must use the arcsin function, it receives a value of an sin as argument and returns the value of the angle θ. Then we must use a calculator and input

The result is already rounded to the nearest degree. Therefore, one value of θ that satisfies sin θ = −0.966 is θ= -75°

Now to find the other value we will look at the symmetry in the trigonometric circle:

Then, the other value of theta will be

Final answer:

Solution

- The question gives us a composite figure made up of a cylinder and a cube.

- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.

- The formulas needed for this calculation are:

- With the information above, we can proceed to solve the question

Volume of the Cylinder:

Volume of Cube:

Volume of Composite Figure:

Final Answer

The volume of the composite shape is 842.04 cm³

Answer:

11 and -11.  Usually you only want the positive form

Step-by-step explanation:

[tex]\sqrt{121}[/tex]  is asking what number times itself is 121?  11

11 x 11 = 121

-11 x -11 = 121

Probability that Deandre missed at least 1 day is;

Write out the values of each probability and sum them

Hence,

The probability that Deandre missed at least 1 day is 0.93

To factor an expression of the form:

we find two numbers B and C that fulfills the following properties:

In this case we have b=-4 and c=-12. We can choose B=-6 and C=2. Then we write the expression as:

and we factor the common factors in the first two and last terms:

Therefore:

Answer: The largest cube has volume of 64 cubic units, and the sides are 4 units long.

Step-by-step explanation:

Elena has 80 unit cubes and she has to build the largest cube using the unit cubes she has

Unit cube has a dimension of 1 unit on each side (Cube has all sides equal)

To make the largest cube, she needs to calculate the maximum volume which is near 80 units of cubes

Therefore,

We have a cube with each side 4 units whose volume is 64 and a cube with each side 5 units whose volume is 125

Elena has only 80 unit cubes to build the maximum-sized cube

Therefore she will be able to build a cube with each side as 4 units with a volume of 64 units with 16 spare cubes

Answer

f(3) = -1, f(2) = -3, f(1) = -5, f(0) = -7, f(-1) = -9

g(3) = 125, g(2) = 25, g(1) = 5, g(0) = 1, g(-1) = 0.2

Step-by-step explanation:

Given the following functions

f(x) =2x - 7

g(x) = 5^x

find f(3), f(2), f(1), f(0), and f(-1)

for the first function

f(x) = 2x - 7

f(3) means substitute x = 3 into the function

f(3) = 2(3) - 7

f(3) = 6 - 7

f(3) =-1

f(2), let x = 2

f(2) = 2(2) - 7

f(2) = 4 - 7

f(2) =-3

f(1) = 2(1) - 7

f(1) = 2 - 7

f(1) =-5

f(0) = 2(0) - 7

f(0) =0 - 7

f(0) = -7

f(-1) = 2(-1) - 7

f(-1) = -2 - 7

f(-1) = -9

g(x) = 5^x

find g(3), g(2), g(1), g(0), and g(-1)

g(3), substitute x = 3

g(3) = 5^3

g(3) = 5 x 5 x 5

g(3) = 125

g(2) = 5^2

g(2) = 5 x 5

g(2) = 25

g(1) = 5^1

g(1) = 5

g(0) = 5^0

any number raised to the power of zero = 1

g(0) = 1

g(-1) = 5^-1

g(-1) = 1/5

g(-1) = 0.2

To simplify this fraction, we will have to find the common factors of both the numerator and denominator, then divide.

Common factors of 30 and 36 are: 2, 3, and 6

Now both numerator and denominator by the highest common factor which is 6:

After simplifying the fraction, we have:

The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.

In general, the following surds are conjugate to each other:

Therefore, the conjugate of the surd:

will be:

The statement is true.

Part A.

Chase has successfully delivered 18 out of the 30 meals to senior citizens.

We have to calculate how many more meals (lets call it x) she has to deliver to have a 75% successful delivery record.

In order to do that, (18+x) meals have te be delivered successfully out of (30+x), and the successful meals (18+x) divided by (30+x) has to be 0.75:

Chase has to deliver 18 more meals successfully in order to have a 75% success delivery record.

Part B.

We apply the same analysis but we replace 0.75 with 0.9 as the delivery record.

Chase has to deliver 90 more meals successfully in order to have a 90% success delivery record.

Part C.

She won't be able to achieve 100% successful delivery record. We can prove it mathematically, but we already know as there are 12 meals that weren't successfully delivered, so we can get close to 100% but it can't never be reached.

Mathematically we have:

This solution is not valid, so there is no valid solution for x.

We need to compare the number of bones in the arms and legs with the number of bones in the face.

The question says that there are 30 bones in the arms and legs.

The question also says that there are 14 bones on the face.

So, the difference between these will be how many more bones there are in the arms and legs than in the face:

we can write equations from the statements

a washer and dryer cost 1001 combined

where w is the price of the washer and d the price of the dryer

the washer costs 51 more the than the dryer

then we can replace the value of w from the second equation to the first equation

and solve for d

the cost of the dryer was $475

By using the Distributive Property, the equivalent expression to 6 x 7 is option (B) (5 x 6) + (2 x 6) and option (E) (2 x 6) + (5 x 6).

Distributive property:

The distributive Property defines that when a factor is multiplied by the addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.

This property can be stated symbolically as:

A ( B+ C) = (A x B) + (A x C)

Where A, B and C are three different values.

Given,

Here we have the expression 7 x 6.

Now, we need to find the equivalent expression by using the distributive expression.

AS per the definition of distributive property,

First we have o identify in which term is got separated,

Here they separated the term 7.

So, there three way for dividing it,

They are,

6 + 1 = 7

2 + 5 = 7

3 + 4 = 7

Based on these, we have two way to write the expression,

one is,

(5 x 6) + (2 x 6)

Another way is,

(2 x 6) + (5 x 6)

So, the correct options are option (B) and (E).

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We have the parallel sides of the rectangle are equal, therefore:

The perimeter is the sum of all sides, then:

Substitute the given data:

And solve for x:

Next, we find the length of side RS:

Answer: RS = 51 units

Given:

Number of boys=10

Number of girls=12

Out of 22 members, 4 members is need to be selected.

To find probability to form a committee consisting of 2 boys and 2 girls:

So, we get

Hence, the correct option is B.

Allison must score 280 on Exam B to do equivalently well as she did on Exam A

Note that:

Since we want Allison to perform similarly in Exam A and Exam B, their z-scores will be the same

Therefore for exam B:

Allison must score 280 on Exam B to do equivalently well as she did on Exam A

Linear Optimization

It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.

We'll use the graphic method to solve the problem.

The problem is as follows:

Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.

The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:

x + y ≤ 130 (1)

She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:

3.75x + 6y ≥ 600

Multiply this inequality by 4:

15x + 24y ≥ 2400

And divide it by 3:

5x + 8y ≥ 800 (2)

We are given a final condition that she can sell a minimum of 80 burritos, thus:

y ≥ 80 (3)

There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:

x ≥ 0 (4)

y ≥ 0 (5)

Let's put this all together:

x + y ≤ 130 (1)

5x + 8y ≥ 800 (2)

y ≥ 80 (3)

x ≥ 0 (4)

y ≥ 0 (5)

The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).

We need to graph all five lines in one common grid. It's shown below.

According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos

we have that

You have 1 in 3 probability of guessing the correct answer for a single question

you have 19 opportunities to guess

so

19*(1/3)=19/3=18/3+1/3=6 1/3

therefore

would be unusual to get 7 or more questions correct by guessing alone

Answer:

0 real solutions

Explanation:

First, we need to transform the equation into the form:

So, the initial equation is equivalent to:

Now, the discriminant can be calculated as:

If the discriminant is greater than 0, the equation has 2 real solutions.

If the discriminant is equal to 0, the equation has 1 real solution

If the discriminant is less than 0, the equation has 0 real solutions

So, in this case, a is 5, b is -8 and c is 15. Then, the discriminant is equal to:

Since the discriminant is less than zero, the equation has 0 real solutions

The question is given to be:

Recall the rule:

Therefore, the expression becomes:

Recall that:

Hence, the expression becomes:

Dividing through by 2, we have:

Therefore, the answer is:

To find a slope of a line we need two points, so we will do it as follows.

Therefore it is (a) the slope is 3.

Answer:

a.3

Step-by-step explanation:

To find the slope, use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 10-4)/(7-5)

   = 6/2

   = 3

Given:

The trinomial equation is given as,

The objective is to choose the correct value for which the factors are to be obtained for factorization.

Explanation:

From the step 1, to perform the factorization the values of a and c has to be multiplied.

Then in step 2, the factors need to be calculated for the product of a and c.

Product of a and c :

The product of a and c will be,

Thus, factors are to be listed for the number 21.

Hence, option (1) is the correct answer.

From the question, we were told that a subway company decides to reward their customers if they go online and answer a few questions about the restaurant.

We are to determine what the process means.

The general view, examination, or description of something or someone in most cases for a reward is known as a survey.

So since subway wants its customers to go online and answer some question about the restaurant and get a reward, then it is a survey.

So, the process that was carried out is a survey.

Therefore, the correct option is D, which is survey.

S={(-24,7/3)}

1) When we're dealing with Complex Numbers we can rewrite this expression:

Considering that their real and their imaginary parts can be taken as equal, so:

2) Rewrite that into the Standard form for complex numbers y= ax +bi combining like terms:

Finally writing those two expressions as a System of equations we have:

3) Hence, the answer is S={(-24,7/3)}