A radar beacon 40 feet above the ground picks up an airplane approaching at an angle of elevation
of 43 degrees and a distance of 6,390 feet. How high above the ground is the plane in whole feet?

Answer:

$12.99

Step-by-step explanation:

you take $79.45 and subtract it by $14.59 that equals $64.95. Then you take 64.95 and divide it by 5 and your total of each DVD is 12.99

The price of each DVD from online retailer is, $12.99

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

There was a shipping charge of $14.50 for the complete order but no sales tax.

And, Mia’s total charge for her order was $79.45.

Now, The cost of 5 DVD = $79.45 - $14.50

                                      = $64.95

Hence, The price of each DVD from online retailer is,

⇒ $64.95 / 5

⇒ $12.99

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q/18 = 5

q = 18×5

q = 90

28 men are needed to paint the room in 3 hours

Given that it takes 12 hours for 7 men to paint a room

We are asked to find number of men required to paint the room in 3 hours

Recognize, "paint the room" is 1 task. One job.

7 men -------- 12 hours ------ 1 job

(7/7) = 1 men ------- 12 x 7 (84)  ------- same 1 job

The one men is rate is 84 hours to do the job

We can express this as 1/84 jobs per hour, the one-person rate

Now lets find how many men needed to paint the room in 3 hours

Let the required number of men for 3 hours be "a"

The rates of each person is simply additive.

[tex]a \times \frac{1}{84} \times 3 = 1[/tex]

corresponds to rate x hours = jobs and "a" is a variable for how many men

[tex]a \times \frac{1}{28} = 28[/tex]

Thus 28 men are needed to paint the room in 3 hours

Jeremy’s net income was $514.8

Step-by-step explanation:

The given is:

We need to find what Jeremy’s net income was

The net income = total income - taxes

∵ Jeremy’s pay is $8.25 per hour

∵ Jeremy worked 78 hours in a month

- Jeremy's income =  the pay for an hour × the worked hours

∴ Jeremy's income = 8.25 × 78

∴ Jeremy's income = $643.5 in a month

∵ There was $128.7 as taxes in his pay statement

∴ The taxes = $128.7

- Substitute the values of his income and the taxes in the

   formula of the net income

∵ The net income = total income - taxes

∴ The net income = 643.5 - 128.7

∴ The net income = $514.8

Jeremy’s net income was $514.8

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Answer:

[tex]\large\boxed{y>\dfrac{c-ax}{b}}\\\text{for}\ a>0,\ b>0,\ c>0[/tex]

Step-by-step explanation:

[tex]ax+by>c\qquad\text{subtract}\ ax\ \text{from both sides}\\\\ax-ax+by>c-ax\\\\by>c-ax\qquad\text{divide both sides by}\ b\ (\text{we can, because}\ b>0)\\\\\dfrac{by}{b}>\dfrac{c-ax}{b}\\\\y>\dfrac{c-ax}{b}[/tex]

To solve the inequality ax - by > c for y, you first subtract ax from both sides which gives -by > -ax + c. Then you divide both sides by -b, remembering to flip the inequality sign, which gives y < (ax - c) / b.

To solve the inequality ax - by > c for y, you need to isolate y on one side of the inequality.

This is the solution for the inequality in terms of y.

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Answer:

x=10

Step-by-step explanation:

3x-5=1/2x+2x

3x-5=1/2x+4/2x

3x-5=5/2x

3x-5/2x=5

6/2x-5/2x=5

1/2x=5

x=5/(1/2)

x=(5/1)(2/1)

x=10/1

x=10

There were 69 children, 83.5 students, and 34.5 adults in attendance at the movie theater.

To solve this problem, we can set up a system of equations.

Let's denote the number of children as 'c', the number of students as 's', and the number of adults as 'a'.

From the given information, we have the following equations:

c + s + a = 187 (equation 1)

5c + 7s + 12a = 1356 (equation 2)

We also know that there are half as many adults as children, so we have the equation:

a = (1/2)c (equation 3)

Substituting equation 3 into equations 1 and 2, we can solve for the variables.

Substituting (1/2)c for a in equation 1:

c + s + (1/2)c = 187

(3/2)c + s = 187 (equation 4)

Substituting (1/2)c for a in equation 2:

5c + 7s + 12((1/2)c) = 1356

5c + 7s + 6c = 1356

11c + 7s = 1356 (equation 5)

Now we can solve equations 4 and 5 simultaneously:

Multiplying equation 4 by 11:

(33/2)c + 11s = 2057/2

11c + 7s = 1356

Subtracting the second equation from the first:

(33/2)c - 11c = 2057/2 - 1356

(-1/2)c = -69/2

c = 69

Substituting c = 69 into equation 4:

(3/2)(69) + s = 187

103.5 + s = 187

s = 83.5

Finally, substituting c = 69 and s = 83.5 into equation 3:

a = (1/2)(69)

a = 34.5

Therefore, there were 69 children, 83.5 students (which is not a whole number, so it could be rounded to 84 students), and 34.5 adults (which could be rounded to 35 adults) in attendance at the movie theater.

Answer:

x=-27

Step-by-step explanation:

x/-9=3

x=3*-9=-27

Answer:

[tex] \frac{3x}{2y + 3} + \frac{ {x}^{2} + 3x}{4xy - 3 - 2y+6x} [/tex]

combine like terms afterwards .. for the polynomial

2≤4 so you have to do that by seeing that 3 iss less that 7

Answer:

They tagged 90 male deer s

Explanation:

Given a park ranger calculated 60% of male deer

Consider the deer they tagged to be x

According to question,

20% of deer were older than 4 years which equals 18

Then, 20% of x = 18

Solving for x,

x = 1800/20

x = 90

So, they tagged 90 male deer

Answer:

Step-by-step explanation:

  Inch   =   Cm

        1   =   2.54

       15   =   ?

We have to find out the question mark. So to do this we have to find out how we got from 1 to 15. We did this by multiplying by 15.

Inch   =   Cm

        1   =   2.54

×15

       15   =   ?

So we must do the same on the other side.

         1   =   2.54

×15                 ×15

       15   =   ?

2.54×15=38.1

   1   =   2.54

×15                 ×15

       15   =   38.1

The answer is therefore 38.1cm

Hope this helped!

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-10, 5) and (5, 5).

Substitute:

[tex]m=\dfrac{5-5}{5-(-10)}=\dfrac{0}{15}=0[/tex]

The slope is equal 0. Therefore given line is a horizontal line.

Answer:

x + y = -5

Step-by-step explanation:

standard form is ax + by = c

equation is y - 2 = -x - 7

Add x to both sides.

x + y - 2 = -7

Now add 2 to both sides.

x + y = -5

Answer:

{(-5, 7), (-4, -9), (–5, – 4), (2, -6)}

Step-by-step explanation:

In a function, no two points can have the same x-coordinates. In other words, all x-coordinates of the points must be different.

{(5, -6), (-1, - 2), (2, –9), (–8, -2)} : All x-coordinates are different: 5, -1, 2, -8. This is a function.

{(-5, 7), (-4, -9), (–5, – 4), (2, -6)} : Two x-coordinates are the same: -5, -5. This is not a function.

{(-4,2), (-2,8), (-1,6), (5,6)} : All x-coordinates are different: -4, -2, -1, 5. This is a function.

{(2,2), (-4,9), (9, -3), (-3, 2)}: All x-coordinates are different: 2, -4, 9, -3. This is a function.

To solve 50 1/2 divided by 1/4, convert the mixed number 50 1/2 to an improper fraction (101/2), then multiply by the reciprocal of 1/4 (which is 4), resulting in 202. The numbers are related through these multiplication and division steps.

Step by Step Solution:

To understand how the numbers are related in the equation 50 1/2 divided by 1/4, follow these steps:

First, convert the mixed number 50 1/2 to an improper fraction. This is done by multiplying the whole number part by the denominator of the fractional part and adding the numerator. Therefore, 50 1/2 becomes:

50 × 2 + 1 = 101/2

Next, when dividing by a fraction, you multiply by its reciprocal. So, dividing by 1/4 is the same as multiplying by 4/1.

Now multiply the improper fraction 101/2 by 4/1:

(101/2) × (4/1) = 101 × 4 / 2 × 1 = 404/2

Simplify the result by dividing the numerator by the denominator:

404 / 2 = 202

Therefore, the numbers are related through these multiplication and division operations, confirming that 50 1/2 divided by 1/4 equals 202.

Answer:

0.75

Step-by-step explanation:

P(A | B) = P(A and B) / P(B)

P(vanilla | sundae) = P(vanilla and sundae) / P(sundae)

P(vanilla | sundae) = 0.15 / 0.2

P(vanilla | sundae) = 0.75

the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75

Given :

P(vanilla) =0.3,  P(sundae)=0.2,  P(vanilla and sundae) =0.15

we need to find the probability that a customer ordered vanilla ice cream given they ordered a sundae.

[tex]P(vanilla | sundae)=\frac{P(vanilla \; and \; sundae)}{P(sundae)}[/tex]

Substitute the values  and find the probability

[tex]P(vanilla | sundae)=\frac{ 0.15}{0.2}=0.75[/tex]

[tex]P(vanilla | sundae)=0.75[/tex]

the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75

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Answer:

B. x < 5

Step-by-step explanation:

Lets go first with 3x – 8 < 23  then with - 4x + 26 > 6 and after that we put them together. (I will use the < > signs but as I see on the pictures these include the =, being less and greater OR equal).

3x – 8 < 23

Lets sum 8 in both sides:

3x < 23 +8

3x < 31

Now, divide both sides by 3:

3x/3 < 31/3

x < 31/3

Here we found one condition. Lets go with the other inequality for the other condition:

- 4x + 26 > 6

Lest sum 4x in both sides to get a potive x:

- 4x + 26 + 4x > 6 +4x

26 > 6 +4x

Now subtract 6 in both sides

26 - 6 > 6 +4x - 6

20 > 4x

Finally, divide both sides by 4:

20/4 > x or 5 > x (simplifying we get the second)

So, our second condition says that x must be less than 5.

So, putting both conditions together:

x < 5

x < 31/3 = 10.33

So, if x must be less than 5 and less than 10.33, is the same that saying that x mus be less than 5. We con obviate the condition that x must be less than 10.33 as it is included in the other. So our answer is:

x < 5

It is the option B in the image (remember I didnt use the less or equal sign because you didn't included it in the statement).

Answer:

C

Step-by-step explanation:

That is her final answer.

A statement that best describes how to translate the graph y = Ixl to obtain the graph of y = |x - 1| - 1 is: C. 1 unit right and 1 unit down.

In Mathematics, the vertex form of the equation for an absolute value function can be modeled by the following:

y = a|x - h| + k.

Where:

By critically observing the equation of the transformed absolute value function, we can logically deduce that the parent absolute value function y = |x| was horizontally shifted to the right by 1 unit and then vertically shifted 1 unit down as follows;

y = a|x - h| + k.

y = |x - 1| - 1

Complete Question:

Which of the following describes how to translate the graph y = Ixl to obtain the graph of y = |x - 1| - 1?

1 unit left and 1 unit down

1 unit left and 1 unit up

1 unit right and 1 unit down

1 unit right and 1 unit up

Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]

Step-by-step explanation:

Solving the expression:

[tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex]

Solving the expression:

We will find factors of the quadratic terms:

[tex]x^2-12x+32\\=x^2-8x-4x+32\\=x(x-8)-4(x-8)\\=(x-4)(x-8)[/tex]

So, factors of [tex]x^2-12x+32[/tex] are [tex](x-4)(x-8)[/tex]

[tex]x^2-10x+16\\=x^2-8x-2x+16\\=x(x-8)-2(x-8)\\=(x-2)(x-8)[/tex]

So, factors of [tex]x^2-10x+16[/tex] are [tex](x-2)(x-8)[/tex]

Placing factors instead of quadratic equation and finding common terms:

[tex]\frac{(x-4)(x-8)}{(x-2)(x-8)}.\frac{6(x-5)}{-5(x-5)}[/tex]

Cancelling the common terms:

[tex]\frac{(x-4)}{(x-2)}.\frac{6}{-5}\\-\frac{6(x-4)}{5(x-2)}[/tex]

So, Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]

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Answer:

I would estimate 61.3

Step-by-step explanation:

I don't think I answered right but I tried

Answer:

Jayce's fee for his [tex]10^{th}[/tex] drive is equal to [tex]K[/tex] dollars.

Step-by-step explanation:

[tex]M(n)[/tex] models Jayce's fee (in dollars) for his [tex]n^{th}[/tex] drive on a certain day.

Substitute [tex]n=10,[/tex] then

[tex]M(10)[/tex] models Jayce's fee (in dollars) for his [tex]10^{th}[/tex] drive on a certain day.

This means Jayce's fee for his [tex]10^{th}[/tex] drive is equal to [tex]K[/tex] dollars.

Answer:

C

Step-by-step explanation:

Jayce's fee for his 10th drive is equal to K  dollars.

Answer: y=19

Step-by-step explanation:

The figure of the triangle is attached and we have the following data:

[tex]A=45\°[/tex]

[tex]s=18[/tex] is the length of arc

[tex]r=14[/tex] is the radius

This problem can be solved by the Law of Sines:

[tex]\frac{sin A}{r}=\frac{sin C}{y}=\frac{sin D}{r+x}[/tex]

In order to find [tex]C[/tex], we will use the formula of the length of arc:

[tex]s=\frac{2 \pi r C}{360\°}[/tex]

Then: [tex]C=\frac{360\° s}{2 \pi r}[/tex]

[tex]C=\frac{360\° (18)}{2 \pi (14)}=73.66\°[/tex]

Returning to the Law of Sines:

[tex]\frac{sin A}{r}=\frac{sin C}{y}[/tex]

Finding [tex]y[/tex]:

[tex]y=\frac{sin C r}{sin A}[/tex]

[tex]y=\frac{sin (73.66\°) 14}{sin (45\°)}[/tex]

Finally:

[tex]y=18.99 \approx 19[/tex]

The length of side y is approximately 19 units.

The problem can be approached using the Law of Sines, which relates the angles and sides of a triangle. Given the data:

Angle A (A) is 45°, the side opposite angle A (s) is 18 units, and the radius of the circumcircle (r) is 14 units.

This problem can be solved by the Law of Sines:

sinA / r = sinC / y= sin D/ r + x

To find the length of side y, we can first calculate the measure of angle C (C) by using the formula for the length of an arc:

s= 2πrC/ 360

Then:

C= 360 s/ 2πr

C= 360 (18) / 2π(14)

C= 73.66

Now, we can use the Law of Sines to find the length of side y. The Law of Sines states:

sinA / r = sinC / c

In this case, we want to find side y, which is opposite angle C:

sinA / r = sinC / y

Solving for y :

y = sinCr/ sinA

y= sin ( 73.66 )14/ sin 45

Finally:

y = 18.99 = 19

So, the length of side y is approximately 19 units.

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Step-by-step explanation:

it can be expressed in the form of p/q where p and q are co primes,

the basic definition of rational number

Answer:

it can be expressed as a fraction

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

2-(8-5x6) = 24

Answer:

i) C; x=y= 80°, ii) B; x= 58°, iii) D; x= 62° and y= 56°, iv) D; none of these are correct.

Step-by-step explanation:

i) Full angle around is 360°

 As given one angle is 100°,which means vertically opposite angles are equal to 100°

Now, remaining angle is equal to [tex]360-200= 160°[/tex]

∵ x and y are vertically opposite angle, which means they are equal.

∴x=y= 80°

ii) As we know straight angle is equal 180°

  As given one of the angle is 32° and other says, it is a right angle which   is equal to 90°.

∴ ∠x= [tex]180-(90+32)= 58°[/tex]

∴∠x= 58°

iii) Full angle = 360°

2∠x = 124° (∵ Vertically opposite angle are equal )

⇒∠x= [tex]\frac{124}{2}[/tex]

∴∠x= 62°

∠x+∠x+∠y= 180° (∵ it is a straight angle)

2∠x+∠y= 180°

⇒[tex]124+ y= 180[/tex]

Subtracting both side by 124

⇒∠y= [tex]180-124= 56°[/tex]

∴∠y= 56°

iv) Full angle= 360°

∴ ∠x+22°+32°+51°= 360°

Subtracting both side by 105

∠x= [tex]360-105= 255°[/tex]

∴∠x= 255°

Which means none of the given option are correct.

Answer:

(4y +8 )÷6 -12

Variable = y

Sum = 4y +8

Quotient = 6

coefficient =4

Answer:

6x^2-2x-5

Step-by-step explanation:

(3x^2+3x-2)+(3x^2-5x-3)

3x^2+3x^2+3x+(-5x)-2+(-3)

6x^2+3x-5x-2-3

6x^2-2x-5