John saved $33. which was 30% of
the money he eamed. How much did
he earn in total?

Answer:

[tex]l =45[/tex] --- length

[tex]w = 55[/tex] --- width

Step-by-step explanation:

Given

[tex]P = 200[/tex] --- perimeter

[tex]A = 2475[/tex] --- area

Required

The dimension of the farm

Let

[tex]l \to length; w \to width[/tex]

So:

[tex]p = 2(l+w)[/tex] --- perimeter

[tex]2(l+w)=200[/tex]

Divide by 2

[tex]l+w=100[/tex]

Make l the subject

[tex]l = 100 - w[/tex]

Also:

[tex]A= l*w[/tex] --- area

[tex]l * w = 2475[/tex]

Substitute: [tex]l = 100 - w[/tex]

[tex](100 - w) * w = 2475[/tex]

Open bracket

[tex]100w - w^2 = 2475[/tex]

Rewrite as:

[tex]w^2 - 100w +2475 = 0[/tex]

[tex]w^2 - 45w - 55w +2475 = 0[/tex]

Factorize

[tex]w(w - 45) - 55(w -45) = 0[/tex]

Factor out w - 45

[tex](w - 55)(w -45) = 0[/tex]

Take any one of the expression and solve for w

[tex]w -55 = 0[/tex]

[tex]w = 55[/tex]

Recall that: [tex]l = 100 - w[/tex]

[tex]l =100 - 55[/tex]

[tex]l =45[/tex]

Answer:

104 miles (nearest whole number)

Step-by-step explanation:

Applying Pythagorean theorem which is: c² = a² + b². Where,

c = distance between the two planes = ?

a = distance of the first plane from the airport = 80 - 1 = 79 miles

b = distance of the second plane from the airport = 68 - 1 = 67 miles

c² = 79² + 67²

c² = 10,730

c = √10,730

c = 103.585713

c = 104 miles (nearest whole number)

Answer:

The median is 21

Step-by-step explanation:

Since you have 12 numbers in order, that's an even number, once you put them in numerical order and start crossing them off on both sides, you'll have 18 and 24 left, add them together and divide them by 2 and you'll have your median 21.

Answer:

1682.46 cubic feet

Step-by-step explanation:

The formula for volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

---------------------------------------------------------------------------------------------------------------

3.14 × 49 × 11 = 1682.46

---------------------------------------------------------------------------------------------------------------

Have a good day :)

Answer:

[tex]area = 4\pi {r}^{2} \\ = 4 \times 3.14 \times {7.5}^{2} \\ = 706.86 \: {cm}^{2} [/tex]

Answer:

7√2

Step-by-step explanation:

From the diagram given;

Hypotenuse = x

Opposite = 7

Angle = 45 degrees

According to SOH CAH TOA identity

Sin theta = opposite/hypotenuse

Sin 45 = 7/x

x = 7/sin45

x = 7/1/√2

x = 7 * √2/1

x = 7√2

Hence the value of x is 7√2

Answer:

The answer woupd be B, 1, 0

The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0) thus option (B) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

As per the given floor plan,

Th coordinate of dairy is the horizontal and vertical distinctions from the reference axes(0,0).

Since it is 1 unit apart in the x and 0 apart in the y direction.

Thus (1,0) is the right coordinate.

Hence "The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0)".

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Answer:

4th option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{5}[/tex] x - 6 ← is in slope- intercept form

with slope m = [tex]\frac{3}{5}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{5} }[/tex] = - [tex]\frac{5}{3}[/tex]

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - [tex]\frac{5}{3}[/tex] and (a, b ) = (- 2, 5 ) , then

y - 5 = - [tex]\frac{5}{3}[/tex] (x - (- 2) ) , that is

y - 5 = - [tex]\frac{5}{3}[/tex] (x + 2)

Answer:

D. 1/9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3ˣ

f(-2) is x = -2 for function f(x)

Step 2: Evaluate

Answer:

[tex]Pr = 0.20[/tex]

Step-by-step explanation:

Given

[tex]n_1 = 10[/tex] ---- 10 sided

[tex]n_2 = 6[/tex] --- 6 sided

Required

[tex]P(x_1,x_2 > 4)[/tex]

First, list out the sample space

[tex]S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]

[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]

[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]

[tex](7, 1) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (8, 1) (8, 2) (8, 3) (8, 4) (8, 5) (8, 6)[/tex]

[tex](9, 1) (9, 2) (9, 3) (9, 4) (9, 5) (9, 6) (10, 1) (10, 2) (10, 3) (10, 4) (10, 5) (10, 6)\}[/tex]

[tex]n(S) = 60[/tex] --- total outcomes

The event that the outcome of both is greater than 4 is:

[tex]x_1,x_2> 4 = \{(5, 5) (5, 6)(6, 5) (6, 6)(7, 5) (7, 6) (8, 5) (8, 6)(9, 5) (9, 6) (10, 5) (10, 6)\}[/tex]

[tex]n(x_1,x_2>4) = 12[/tex]

So, the probability is:

[tex]Pr = \frac{n(x_1,x_2>4)}{n(S)}[/tex]

[tex]Pr = \frac{12}{60}[/tex]

[tex]Pr = 0.20[/tex]

Answer:

See below.

Step-by-step explanation:

a.

We need degrees C as a function of degrees F.

Just like when we have y as a function of x, we have (x, y) ordered pairs, here we will have (F, C) ordered pairs.

We are given two ordered pairs: (32, 0) and (212, 100).

We can find the slope of the line.

m = (100 - 0)/(212 - 32) = 100/180 = 5/9

y = mx + b

C = mF + b

C = (5/9)F + b

Use point (32, 0) for F and C to solve for b.

0 = (5/9)(32) + b

b = -(5/9)(32)

C = (5/9)F - 5/9(32)

C = (5/9)F - 160/9

b.

The slope is 5/9. The slope is the rate of change of degrees F to degrees C. For each change of 9 degrees F, the corresponding change in degrees C is 5.

c.

The y-intercept is -160/9.

It means that a temperature of 0 degrees F equals -160/9 degrees C.

Answer:

C

Step-by-step explanation:

Step-by-step explanation:

The given function is :

[tex]f(x)=x^2-5x+ 5[/tex]

(a) To find f(9), put x = 9 in the above expression.

[tex]f(9)=9^2-5(9)+ 5=41[/tex]

(b) To find f(x+7), put x = x+7 in the above expression.

[tex]f(x+7)=(x+7)^2-5(x+7)+ 5\\\\=x^2+14x+49-5x-35+5\\\\=x^2+9x+19[/tex]

(c) To find f(-x), put x = -x in the above expression.

[tex]f(-x)=(-x)^2-5(-x)+ 5\\\\=x^2+5x+5[/tex]

Hence, this is the required solution.

x2+10x=6

x2+10x-6=0

x=-10+-Square root of [10^2-4×(-6)]/2.1

x=-10+-Square root of 124/2

x=-5+square root of 31 and -5-square root of 31

Answer:

first create an equation for Jeb flower then for Lori

then solve them by simultaneous linear equations

Answer:

One rose = $2.75

One carnations = $1.25

Step-by-step explanation:

Lets make the rose = x

and carnations = y

Jeb >> 6x + 3y = 20.25

Lori >> 8x + 3y = 25.75

Solve simultaneously using elimination method.

8x + 3y = 25.75

- 6x + 3y = 20.25

_______________

2x =5.5

2x/2 = 5.5/2

x = 2.75

plug 2.75(x) into any of the two equations to find y.

6(2.75) + 3y = 20.25

16.5 + 3y = 20.25

3y = 20.25 - 16.5

3y = 3.75

3y/3 = 3.75/3

y = 1.25

Answer:

I hoped this helped!

Step-by-step explanation:

Answer:

See attached image.

Step-by-step explanation:

You can either use a graphing calculator or make a table to find values for yourself.

X | 0 | 3

Y | -2 | -3

and so forth.

Answer:

[tex]g(x) = -|x+3|-1[/tex]

Step-by-step explanation:

1. horizontal reflection - reflection on x-axis: [tex]g(x) = - f(x)[/tex]

        [tex]g(x) = -|x|[/tex]

2. shift left 3: [tex]g(x) = f(x+h)[/tex]

       [tex]g(x) = -|x+3|[/tex]

3. shift down 1: [tex]g(x) = f(x) - k[/tex]

      [tex]g(x) = -|x+3|-1[/tex]

Answer:

If you are asking for what x is equal too, then x = 8.70968...

Hope that this helps!

Answer:

Number of messages Salma sent = 7

Number of messages Brian sent = 16

Number of messages Chang sent = 32

Step-by-step explanation:

Let

Number of messages Salma sent = n

Number of messages Brian sent = n + 9

Number of messages Chang sent = 2(n + 9)

Total messages sent = 55

n + (n + 9) + 2(n + 9) = 55

n + n + 9 + 2n + 18 = 55

4n + 27 = 55

4n = 55 - 27

4n = 28

n = 28/4

n = 7

Number of messages Salma sent = n = 7 messages

Number of messages Brian sent = n + 9 = n + 9 = 16 messages

Number of messages Chang sent = 2(n + 9)

= 2(7 + 9)

= 2(16)

= 32 messages

Answer:

Step-by-step explanation:

The zero of a function is also known as the x-intercept of a function. The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0     and     -1/2x + k = 0 and then solve each for x:

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k:

5 = 2k so

k = 5/2

The value of the K in the given equation is 5/2.

The zero of a function is also known as the x-intercept of a function.

The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0     and  

-1/2x + k = 0 and then solve each for x:

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k

5 = 2k so

k = 5/2

Therefore the value of the K in the given equation is 5/2.

To learn more about the expression visit:

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Answer:

Is there any image for the question ???

Answer:

Step-by-step explanation:

There’s a total of 10+16+20+18 = 64 candies.

There’s 10 red candies.

10 / 64 = 0.15625

Rounded: 0.2

Answer:

W=42°

X=29°

Step-by-step explanation:

180-138=42

90-42-19=29

Answer:

53/100

Step-by-step explanation:

First, we convert the fraction to a decimal number by dividing the numerator by the denominator:

8 / 15 = 0.533

There are two parts to the decimal number above:

Integer Part: 0

Fractional Part: 533

Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*

In this case, Rule I applies, so 8/15 (or 0.533) rounded to the nearest hundredth in decimal format is:

0.53

Next, we will make 8/15 rounded to the nearest hundredth in fraction format. Since you can divide our decimal format answer above by 1 and keep the same value, you can make it like this:

0.53 = 0.53/1

Then, we multiply the numerator and denominator by 100 to get rid of the decimal point:

(0.53 x 100) / (1 x 100) = 53/100

That's it. 8/15 rounded to the nearest hundredth is displayed below (simplified if necessary):

53/100

Answer:

53.33% is the correct answer

Answer:

2−12+27

Step-by-step explanation:

(−3)(−9)

x(x-9) -3(x-9)

x2 (square lol) - 9x -3 (x-9)

x2-9x-3x+27

x2-12x+27

solution:

2−12+27 answer.

Answer:

Step-by-step explanation:

(x-3)(x-9)

x(x-9)-3(x-9)

x^2-9x-3x+27(add like terms)

x^2-12x+27

Answer:

7. x = 6

8. x = 15/4

9. x = -7

Answer:

Hello there user, looks like your looking for help!

The correct answers should be:

7. x = 6

8. x = 3 3/4

9. x = -7

Step-by-step explanation:

3/2 = x/4

6/4 = x/4

x = 6

x/3 = 1 1/4

4x/12 = 15/12

x = 15/4

x = 3 3/4

(x + 1)/3 = (x-1)/4

(4x + 4)/12 = (3x-3)/12

x/12 =  -7/12

x = -7

Answer:

The median are equal

Step-by-step explanation:

Given

I will answer this question with the attached plot (see attachment 2)

Required

The equal statistical measures

See attachment 1 on how to read a box plot

Using attachment 1 as a guide, we have the following observation

Movie 2                                                   Movie 1

[tex]Minimum=7.5[/tex]                                      [tex]Minimum=10[/tex]

[tex]Q_1 = 22.5[/tex]                                                 [tex]Q_1 = 15[/tex]

                                  [tex]Median = 30[/tex]

[tex]Q_3 = 35[/tex]                                                   [tex]Q_3 = 40[/tex]

[tex]Maximum = 47.5[/tex]                                    [tex]Maximum = 52.5[/tex]

By comparison, they have equal median (30)

Answer:

1x

Step-by-step explanation:

the slope goes up one a positive slope of 1