In triangle ABC measure of angle A equals 45°. The altitude divides the side AB into two parts of 20 and 21 units. Find BC.

Remember that

The y-intercept is the value of y when the value of x=0

In this problem

we have the equation

y=7x^2+4

For x=0

substitute

y=7(0)^2+4

y=4

ANSWER

EXPLANATION

When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:

where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.

Therefore, we have that:

Therefore, the coordinates of point C are:

Those are the coordinates of C.

Working 32 hours a week will fetch you $818

From the question, the given parameters are:

Number of hours = 160

Earnings in a month = $4090

Start by calculating the unit rate

This is calculated using the following unit rate formula

So, we have

Unit rate = Earnings in a month/Number of hours

Substitute the known values in the above equation

So, we have

Unit rate =  4090/160

Evaluate the quotient

Unit rate =  25.5625

For 32 hours, the total earnings is

Total = Unit rate x Number of houts

So, we have

Total = 25.5625 x 32

Evaluate

Total = 818

Hence, you will earn $818 weekly

Read more about unit rates at

https://brainly.com/question/4895463

#SPJ1

Solution

For this case we can solve the problem with the following operation:

And rounded the answer we got 3.25 ft

16.24*100 = 1624

5*100 = 500

And we can do this:

1624/500 = 812/250 = 406/125

003

_____

125 / 406

-0

____

-40

-0

____

406

-375

_____

31

Hello!

So, we are given the following to solve:

[tex]-m=9[/tex]

To solve this, simply divide both sides by -1.

[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]

Then, simplify the expression and you have your solution.

[tex]m=-9[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

Answer:

m= -9

Step-by-step explanation:

Divide both sides by -1

[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]

Simplify m = - 9

If the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2),  then the coordinates of the M' = (4,1)

The point is M(4,3)

The translation rules is

(x, y) ⇒ (x, y-2)

The translation states that the movement of the graph either horizontally  or vertically. When we translate the graph, the shape and size will not change, only the coordinates of the graph changes.

We know the values of

x = 4

y = 3

Substitute the values in the equation

The coordinates of the M' = (x, y-2)

= (4, 3-2)

= (4,1)

Hence, if the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2),  then the coordinates of the M' = (4,1)

Learn more about translation here

brainly.com/question/12463306

#SPJ1

The equation which can be used to find the area of the place where guests wait for the ride if the area of the canopy is 7600 square feet is:

2a+100=7600.

Given, The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy.

The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.

let the area of the place where guests wait be represented by 'a'.

the canopy covers the area = 2a + 100

total area of the canopy = 7600

equation  used  to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet = ?

⇒ 2a + 100 = 7600

arrange the like terms.

⇒ 2a = 7600 - 100

calculate the difference.

⇒ 2a = 7500

⇒ a = 7500/2

⇒ a = 3750

Hence the area of the place where guests wait is 3750 square feet.

Learn more about Linear equations here:

brainly.com/question/26310043

#SPJ1

The value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115

The expression is

[tex]10z^2[/tex]+7z+4

The expression is defined as the statements that have a minimum of two terms containing numbers or variables , connected by an operator in between. The operator maybe addition, subtraction, division, multiplication etc..

The expression is

[tex]10z^2[/tex]+7z+4

The value of z = 3

Substitute the value of z in the given expression

= [tex]10(3)^2[/tex]+ 7×3 + 4

= 10×9 + 21 + 4

Multiply the terms first

= 90 + 21 + 4

Add them together

= 115

Hence, the value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115

Learn more about expression here

brainly.com/question/1619296

#SPJ1

C=34.15+0.65M

Given

so

to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence

so, replace and simplify

therefore, the answer is

C=34.15+0.65M

I hope this helps you

C=34.15+0.65M

Given

so

to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence

so, replace and simplify

therefore, the answer is

C=34.15+0.65M

I hope this helps you

Given the function:

when x = 1.9

when x = 1.999

When x = 2.001

When x = 2.1

so, the limit of the function k(x) = 11

The answer is option A. 11

Answer:

70

Step-by-step explanation:

f(1)=6, f(n)=f(n-1)+4

n = 1 → a1 = 6 ← given value

n = 2 → a2 = 6+4 = 10

n = 3 → a3 = 6+4+4 = 14

n = 4 → a4 = 6+4+4+4 = 18

n = 17 → a4 = 6+(4 * 16) =

(its 4 times 16 because 16 is 17 - 1 or n - 1)

n = 17 → a4 = 6+(64) = 70

socraticorg

Tony B

Answer:100 cm

Step-by-step explanation: first, you would find the area of the whole rectangle.

L x W = A

10x14=140

Next, find the area of the unshaded part. To do this, you would subtract 6 from 14

14-6=8

After that, times 8 by 10, then divide by 2

10x8=80

80÷2=40

Take 40 and subtract it from the area of the whole rectangle

140-40=100

Let's begin with what we know:

For an ordered pair, we have (independent variable, dependent variable)

For example, when x is the independent variable & y is the dependent variable, we have (x, y)

y = f(x)

We are to write a short statement that expresses a possible relationship between the variables below:

1. (volume of a gas tank, cost to fill the tank)

Volume of gas is the independent variable & Cost to fill the tank is the independent variable. That means that:

As the volume of the gas tank increases. the cost of filling it increases. Once the volume of the gas tank is filled, the cost to fill the tank is at its maximum

2. (time, price of a Ford sedan), where time represents years from 1975 to 2017​

Time is the independent variable & price of a Ford sedan is the independent variable. That means that:

As the time lapses from 1975 to 2017, the price of the Ford sedan depreciates/reduces.

Answer:

Q18: x = 21, y = 15

Q19: x = 16, y = 10

Q20: x = 24, y = 19

Step-by-step explanation:

Q18:

(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)

9x - 9 = 180

9x = 189

x = 21

11y - 32 = 6x + 7 (vertically opposite angles)

11y - 32 = 6(21) + 7

11y - 32 = 133

11y = 165

y = 15

Q19:

8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)

3x = 48

x = 16

(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)

8(16)-14 + (5y + 16) = 180

114 + 5y + 16 = 180

5y + 130 = 180

5y = 50

y = 10

Q20:

47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)

5x + 60 = 180

5x = 120

x = 24

5y - 23 = 3x (corresponding angles)

5y - 23 = 3(24)

5y - 23 = 72

5y = 95

y = 19

The solution to the compound inequality is x > 6 or x < -3

An inequality is a mathematical expression that has <, >, ≤ and ≥.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality as follows:

2x - 4 > 8 or 3x - 1 < - 10

2x - 4 > 8

add 4 to both sides of the inequality

2x - 4 + 4 > 8 + 4

2x > 12

divide both sides by 2

x > 12 / 2

x > 6

3x - 1 < - 10

add 1 to both sides of the inequality

3x - 1 + 1 < - 10 + 1

3x < - 9

divide both sides by 3

x < -9 / 3

x < -3

Therefore, x > 6 or x < -3

learn more on inequality here: https://brainly.com/question/23012774

#SPJ1

The solution to the compound inequality will be; x > 6 or x < -3

Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.

A compound inequality is defined as an inequality that combines two simple inequalities.

Therefore, solve the compound inequality that will be;

2x - 4 > 8 or 3x - 1 < - 10

2x - 4 > 8

Then add 4 to both sides of the inequality so,

2x - 4 + 4 > 8 + 4

2x > 12

Now, divide both sides by 2

x > 12 / 2

x > 6

3x - 1 < - 10

Again, add 1 to both sides;

3x - 1 + 1 < - 10 + 1

3x < - 9

Then divide both sides by 3;

x < -9 / 3

x < -3

Therefore, solution to the compound inequality is; x > 6 or x < -3

learn more on inequality here:

brainly.com/question/23012774

#SPJ1

Answer:

The three numbers are:

4.62,

23.1, and

462.2

Step-by-step explanation:

Let X be the "first number."

B = What number is five times the first number:  5X

C = third number is 100 more than the first number:  100X

The sum of all three is 490:  X + B + C = 490

----

X + B + C = 490

X + 5X + 100X = 490

106X = 490

X = 4.622

Check:

X = 4.622

B = 5X = 23.11

C = 100X = 462.2

Check:

Sum (4.622 + 23.11 + 462.2) = 490

you didn't attach the figure....

Answer:

Z'(10, 14)

Explanation:

Taking into accoun that the vertex point X(2, 3) is mapped to X'(4, 8), we can say that the translation rule is:

(a, b) ----> (a + 2, b + 5)

Because

X(2, 3) ----> (2 + 2, 3 + 5)

----> X'(4, 8)

So, using this rule, we can find the coordinates for Z' as:

Z(8, 9) ----> (8 + 2, 9 + 5)

----> Z'(10, 14)

Therefore, the answer is Z'(10, 14)

Answer:

9x^2-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply (3x - 1) * (3x + 1)

= 9(x)^2 + 3x - 3x -1

= 9(x)^2 - 1

The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤ 

Let the height of the third tree be x.

By the given condition, this will be:

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

The first relation will give x ≥ 32 - 24 = x ≥ 8

The second relation will give:

8 + 16 + x ≤  42

24 + x ≤  42

x ≤  42 - 24

x ≤  18

The inequality is 8 ≤ x ≤ 18.

Learn more about inequalities on:

brainly.com/question/24372553

#SPJ1

If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let height of the third tree be x.

By the given condition

The sum of three palm tree heights range from 32 to 42 feet

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

Solve these inequalities

8 + 16 + x ≥ 32

24+x ≥ 32

x≥ 32-24

x≥ 8

and 8 + 16 + x ≤  42

24+ x ≤  42

x≤  42-24

x ≤ 18

Hence the inequality is 8 ≤ x ≤ 18.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

System of inequalities

We are given the graph where two lines represent the solution of a system of inequalities.

The solution is the double-shaded region of the graph.

We need to find the equation of the blue line and the red line and then convert them to inequalities.

Let's start with the blue line. We need to find two clear points through which it passes. These are (0,6) and (2,0). Now we write the equation of the line when knowing two points (the point-point form):

For the red line, the points are (0,0) and (2,2):

Now we have the equations of the lines, we must convert the equation to inequality by inserting one of these symbols instead of the equal sign:

> ≥ < ≤

For the blue line, the equation of the line is:

y = -3x + 6

Testing the origin (0,0):

0 = 0 + 6

0 = 6

To convert this to a true inequality we must replace the = for < or ≤

Since the blue line is solid, the points on the line belong to the solution, thus the first inequality is:

y ≤ -3x + 6

Now for the red line. The equation is

y = x. Let's test the point (2,1)

1 = 2

We must use the sign ≤ to make the expression true, thus the second inequality is:

y ≤ x

Thus, the system of inequalities is:

y ≤ -3x + 6

y ≤ x

[tex]\frac{2(x-8)}{5}[/tex] = y

To Solve: value of y

Given: 2x-5y=16

Solution: The solution to this problem involves the following steps:

2x-5y-16=0

2x-16=5y

[tex]\frac{2x-16}{5}[/tex] = y

[tex]\frac{2(x-8)}{5}[/tex] = y

Answer: The final answer is : [tex]\frac{2(x-8)}{5}[/tex] = y

Learn more about equations here: https://brainly.com/question/2030026

The rates of changes of the given function for the corresponding intervals are:  [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.

What is function?

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The rate of change of a function can be calculate using the formula:

[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Putting the value from the question:

given [x₁, x₂] = [-5, -1]

f(-5) = 35 , f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-35}{-1 -(-5)}[/tex]

R = -32/4

R = -8

given [x₁, x₂] = [-4, -1]

f(-4) = 24, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-24}{-1 -(-4)}[/tex]

R = -21/3

R = -7

given [x₁, x₂] = [-3, -1]

f(-3) = 15, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-15}{-1 -(-3)}[/tex]

R = -12/2

R = -6

given [x₁, x₂] = [-2, -1]

f(-2) = 8, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-8}{-1 -(-2)}[/tex]

R = -5/1

R = -5

To know more about function, go to link

https://brainly.com/question/10439235

#SPJ13

Answer:

Regular Polygon:

D

Irregular Polygon:

A, B, F

Not a Polygon:

E, C

Step-by-step explanation:

Polygons are shapes with straight lines.

Regular polygons have uniform side lengths and angles.

The number of miles to drive for 30 gallons is 960 miles

From the question, the function definition is given as

d(g) = 32g

Where g represents the number of gallons and d represents the distance

The function value to calculate is given as

d(30)

This means that we calculate the number of miles to drive for 30 gallons

So, we have

d(30) = 32(30)

This gives

d(30) = 32 x 30

Evaluate the product

d(30) = 960

Hence, the function value is d(30) = 960

Read more about functions at

https://brainly.com/question/28532394

#SPJ1

Answer:

Rhombus:  All sides congruent, two pairs of parallel sides

Parallelogram: Two pairs of parallel lines

Rectangle: 4 right angles, Two pairs of parallel sides

Step-by-step explanation:

Answer: L= 9-.75x

Step-by-step explanation: since it starts at 9 inches tall and is melting at .75 inches per hour, it's going to be the initial length, 9, minus the rate, .75, times the time/hours past, so x