What is the equation of the line in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

The show is 1 hour 4 minutes long.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Ben watched 3/8 of his television show.

There are still 40 minutes left.

let the show be x long.

So, 3/8x + 40 = x

x- 3/8x= 40

5x/8 = 40

x= 320/5

x= 64 minutes

x= 1 hour 4 minutes

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James average pay per hour is $17.40

How to find James average pay per hour

information given in the problem are

Last year, James earned £2,100 per month

This year, he's had a 6% increase in his monthly pay

35 hours per week for 46 weeks in the year

The question is a percentage problem

6% increase a factor of  1.16

2100 * 1.16 = 2436

number of hours in a month

35 hours = 1 week

? hours = 4 weeks

? = 4 * 35

? = 140 hours in 4 weeks = 1 month

James average pay per hour is gotten form the calculation below

if 140 hours pays 2436 then1 hour will pay ?

140 = 2346

1  =  ?

cross multiplying

? * 140 = 2436 * 1

? = 2436 / 140

? = $17.40

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Answer:

B and D

Step-by-step explanation:

A is wrong because x has a negative exponent

C is wrong because x is a denominator

The area of the garden is 7 square feet.

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.

Given,

Width = 3/4

Length = 9 + 1/3

Length = 28/3

Area:

Length × Width

3/4 × 28/3

84/12

7

The area of the garden is 7 square feet.

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x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.

Given the system of equation in the question;

To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10  and solve for x.

y = -2x - 15

3x - 10 = -2x - 15

Add 10 to both sides

3x - 10 + 10 = -2x - 15 + 10

3x = -2x - 15 + 10

Add 2x to both sides

3x + 2x = -2x + 2x - 15 + 10

3x + 2x = - 15 + 10

Add like terms

5x = -5

x = -5/5

x = -1

Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.

y = 3x - 10

y = 3( -1 ) - 10

y = -3 - 10

y = -13

Therefore, the solution to the system of equation is (-1,-13).

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{8}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~3 - 8~~)^2 + (~~8 - 2~~)^2} \implies PQ=\sqrt{( -5 )^2 + ( 6 )^2} \\\\\\ PQ=\sqrt{ 25 + 36 } \implies PQ=\sqrt{ 61 }\implies PQ\approx 7.8[/tex]

Answer:

[tex]x^3-10[/tex]

Step-by-step explanation:

Let the number be x.

"A number cubed" refers to x³.

"Difference" means to subtract, so the answer is [tex]x^3-10[/tex].

Answer:

1. 5x +2

2. 6x/5

Step-by-step explanation:

The dimension of pen that maximize the area is 150 ft by 150 ft.

What is the dimension of a area?

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

Given the perimeter of the rectangular is 600 ft.

Assume that the length of the rectangular be l and the breadth be b.

The perimeter of the rectangular is 2(l+b).

According the question:

2(l+b) = 600

Divide both sides by 2:

(l+b) = 300

l = 300 - b

The area of rectangular is A = lb

Substitute the value of l in the above equation:

A = (300 - b) b

A = 300b - b^2

The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).

Compare Ax^2+BX+C  with 300b - b^2:

A = -1 and B = 300.

Putting A = -1 and B = 300 in b= - B/(2A).

b= - 300/(2×(-1))

b = 150.

Putting b =150 in l = 300 - b

l = 300 - 150

l = 150

The dimension is 150 ft × 150 ft.

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The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.

Find the greatest common factor of 32 and 48

The greatest common factor of 32 and 48 is 16

So, the greatest number of bags Caesar can make is 16 bags

Number of pasta in each bag = 32/16

= 5 boxes of pasta per bag

Number of sauce in each bag = 48/16

= 8 jars of sauce per bag

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.

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The number of green marbles removed from the bag is 3.

We will use the Formula of Probability:

In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.

p(A) = n(A) / n(S)

p(A) is the probability of event A.

n(A) is the number of outcomes with respect to A.

n(S) is the total number of possible outcomes.

Given in the Question:

A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.

So the total number of marbles in the bag = 40

It is given that 25 marble are removed from the bag randomly

thus, the remaining marbles in the bag = 40 - 25 = 15

It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.

So, for finding the number of green marbles in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of green marbles and p(A) = 3/5 and  n(s) = 15 (after removing)

Thus, the number of green marbles in the bag after removing = 3/5 × 15

So, the number of green marbles left in the bag = 9

then, the green marbles removed from the bag = 12 - 9 = 3.

Therefore, only 3 green marbles are removed from the bag.

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In  linear equation ,Shirley takes 1.66 hours to paint the deck alone.

What in mathematics is a linear equation?

Let Shirley's time = x

Let Craig's time  = 5x

(5x + x)/2 = 5

We split up the hours by 2 because we want to find out how much time individually.

6x/2 = 5

6x = 10

 x = 1.66

Shirley takes 1.66 hours to paint the deck alone.

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Answer: is 16.6%

Step-by-step explanation: Use the rule of three (mathematic).

Answer: D.

Step-by-step explanation:

Answer:

24.4 km

Step-by-step explanation:

The Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse of the triangle, and a and b are the legs. Plugging in your values, we get:

20^2 + 14^2 = c^2

Simplify: 400 + 196 = c^2

Simplify again: 596 = c^2

Square root both sides to cancel out the exponent on the right: 24.4131=c

Round: 24.4

B) The missing angle at the intersection point of both triangles is; x = 15°

C) The missing angle is gotten as; x = 61°

B) In the second image given, we can see two angles;

Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;

90 + 5x - 14 + y = 180

where y is the third interior angle

Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;

y = 180 - (9x + 16)

Put 180 - (9x + 16) for y into the first equation to get;

90 + 5x - 14 + 180 - (9x + 16) = 180

180 will cancel out to get;

90 + 5x - 14 - (9x + 16) = 0

4x = 90 - 14 - 16

4x = 60

x = 60/4

x = 15°

C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;

Missing angle = 63°

Sum of angles in a triangle is 180 degrees. Thus;

56 + 63 + 3rd angle = 180

3rd angle = 180 - (56 + 63)

3rd angle = 61°

Thus, x = 61° because they are opposite angles

Also, the two given sides are equal to each other as shown. Thus;

51 = 12y + 3

12y = 51 - 3

12y = 48

y = 48/12

y = 4

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If the receiver is placed at the focus, it is 4 inches from the bottom of the dish. The result is obtained by using the equation of parabola with the vertex is at (0,0).

With the vertex at (0,0), the equation of a parabola can be expressed as

x² = 4ay

Where

Given

How far is the receiver from the bottom of the dish if it is placed at the focus?

Suppose that the vertex is at (0,0).

x = 1/2 × diameter

x = 1/2 × 48

x = 24

Now, we got two points (-24, 36) and (24,36). See the picture in the attachment!

By using the x and y value, the value of a is

x² = 4ay

24² = 4a(36)

576 = 144a

a = 576/144

a = 4 inches

Hence, the receiver is placed at 4 inches from the bottom of the dish.

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Calculation

Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]

Find the function's x-intercept: x= 5

Find the dependent variable by itself: [tex]y= \frac{4x}{9} -\frac{20}{9}[/tex]

Find the function's y-intercept: y = [tex]-\frac{20}{9}[/tex]

The chart for : 4x-9y = 20

see the attachment

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The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction. x = 20 + 9y /4

Given

x, 4x - 9y = 20  

x = 20 + 9 /4 y

Steps

4x - 9y = 20

Add 9 y to both sides

4x - 9y + 9y = 20 + 9y

Simplify

4x = 20 + 9y

Divide both sides by 4

4x/4 = 20/4 + 9y/4

Simplify

x = 20 + 9y /4

Hence, The x- and y-intercepts of the graph 4x - 9y = 20 In the simplest form, state each answer as an integer or an improper fraction.

x = 20 + 9y /4

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Answer:

y = 119

30 =x

Step-by-step explanation:

61 and y are same side interior angles and they add to 180

61+y = 180

y = 180-61

y = 119

y and 6x-61 are vertical angles and they are equal

y = 6x-61

119 = 6x-61

Add 61 to each side

119 + 61 = 6x

180 = 6x

Divide each side by 6

180/6 = x

30 =x

Answer:

y = 119°

x = 30°

Step-by-step explanation:

We know that if two lines are parallel, the co - interior angles are added up to 180°°.

Accordingly,

y + 61 = 180

y = 180 - 61

y = 119°

Also, we know that, vertically opposite angles are equal to each other.

y = 6x - 61

119 = 6x - 61

Now, we have to make x the subject.

For that, first, add 61 for both sides.

119 + 61 = 6x

180 = 6x

Now, divide both sides by 6.

30° = x

The postulate that can be used to prove the two triangles are congruent is the HL this is the last option

HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.

The theorem says that, two angles of a right angle triangle that have equal

then two triangles are congruent

The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal

Therefore, this theorem says that the two triangle are congruent

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The probability that no one enters between 12:00 and 12:05 is 0.082.

The probability that at least 4 people enter the casino during that time is 0.242

Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.

P(X=0) = [tex]e^{-2.5}[/tex] = 0.082

Hence the probability that no one enters between 12:00 and 12:05 is 0.082.

The required probability is simply

P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

= 1 - [tex]e^{-2.5}[/tex] - 2.5[tex]e^{-2.5}[/tex] - (((2.5)² / 2)[tex]e^{-2.5}[/tex] ) - (((2.5³)/3!)[tex]e^{-2.5}[/tex])

= 0.242

Hence, the probability that at least 4 people enter the casino during that time is 0.242

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Answer:

16

Step-by-step explanation:

40/5 then x the answer by 2 and you get 16 with now deposits or withdraws

The length of the line segment BD is 3 centimeters.

Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:

AB / AD = BC / DE = AC / AE

By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:

12 cm / AD = 8 cm / 10 cm

AD = (10 cm / 8 cm) × 12 cm

AD = 15 cm

And the length of the line segment BD is:

BD = AD - AB

BD = 15 cm - 12 cm

BD = 3 cm

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If now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive. The amount of  honey that Bert’s new beehive hold is 200.

Given data:

Number of frame beehive = 6

Pound of honey = 40

Current Frame beehive = 30

First step is to formulate an equation and then use the formulated equation to find  the number of honey

40 × 30 ÷ 6

Hence,

40 × 5

= 200 honey

Therefore the number of honey is 200.

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The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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The 20 and 21 unit leg lengths of the right triangles ΔACD and ΔBCD formed by the altitude CD indicates, by using Pythagorean theorem that the length of BC is 29 units

A right triangle is a triangle that has two perpendicular sides. The altitude of a triangle is perpendicular to the base of the triangle, forming two right triangles in acute triangle.

Angle ∠A = 45°

The length of the segment the altitude CD divides AB into = 20 and 21 units

Please find attached a drawing created using MS Word based on the question parameters.

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

AD = 20

Therefore;

[tex]tan(45^{\circ}) = \dfrac{CD}{20}[/tex]

CD = 20 × tan(45) = 20

Pythagorean theorem applied to right triangle ΔCBD, indicates that;

[tex]\overline{BC}^2[/tex] = [tex]\overline{CD}^2[/tex] + [tex]\overline{DB}^2[/tex]

DB = 21 units, which gives;

[tex]\overline{BC}^2[/tex] = 20² + 21² = 841

BC = √(841) = 29

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The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11

The equation of the function is given as

f(x) = 2x⁵ - x³ + x² + 4

The sequence of transformations is given as follows:

When the above transformations are combined, we have:

g(x) = 3f(-x) - 1

So, we have

3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1

This gives

3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1

Expand

3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11

So, we have

g(x) = -6x⁵ + 3x³ + 3x² + 11

Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11

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