Write an equation in slope-intercept form of the line that passes through the given points.

The rate at which the sloth travels as required in the task content is; -22ft/min.

It follows from the task content that the rate at which the sloth travels is to be determined.

Since the correct representation of the data is such that the distance and corresponding time pairs are as follows;

(98, 1) , (76, 2) , (54, 3), (32, 4).

Hence, the rate of distance change per time is the speed of the sloth and hence, the rate of distance change is;

Rate = ∆Distance/∆time.

Rate, R = (98 - 76)/(1 - 2)

Rate, R = 22/-1

R = -22 ft/min.

Ultimately, the rate at which the sloth travels is therefore; -22 ft/min.

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Answer:

141 degrees

Step-by-step explanation:

The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38

The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.

The equation of a line that passes through a point can be describe as follows:

y = mx + b

where

Therefore, the line passes through (4, 3) and the slope is 1 / 2.

Hence, let's find the y-intercept using (4, 3)

y = 1 / 2 x + b

3 = 1 / 2 (4) + b

3 = 2 + b

b = 3 - 2

b = 1

Therefore, the equation of the line is y = 1 / 2 x + 1.

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The amount of work needed to stretch the spring 18 in. from its natural position is 3.75  ft-lb.

According to the Hooke's Law, the work done on the spring is:

W = 1/2. k . x²

Where:

k = spring constant

x = displacement.

Notice that the work done is directly proportional to x².

Hence,

W₁ : W₂  = x₁² : x₂²

Parameters given:

W₁ = 15 ft-lb

x₁ = 3 ft

x₂ = 18 in. = 1.5 ft

Plug the above parameters into the ratio equation:

15 : W₂  = 3² : (1.5)²

W₂ = (1.5)² . 15 /  3² = 15/4 = 3.75  ft-lb

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Using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

So, candidate A has a projection of winning 53% votes.

A sample of 2436 voters is pulled, then:

Can candidate A be guaranteed 95% votes which are:

Difference: 2,314 - 1,291 = 1,023

Therefore, using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

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Let:

L = length of the road

D = Days of construction

We can write a linear equation in the slope-intercept form:

Where:

m = Slope = rate = 1 mile per day

b = y-intercept = Initial value = 10 miles

Therefore:

The graph is:

Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

The solution of an inequality is the set of numbers that make the inequality true.

In this case, you know that:

Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is

10 + 0.70x <34.50

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Answer:

B

Step-by-step explanation:

The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.

A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.

In conclusion, the standard change illustrates the change.

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Based on the slope of the line and the y-intercept, when graphed, the points that will appear on the graph will be:

The equation of a line takes the form:

y = mx + b

m = slope

b = y - intercept

This line would therefore take the equation form:

y = - 3x + 2

When graphed, the graph would be as attached.

As shown by the graph, the points that will appear include:

(0 , 2) (1 , - 1)

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Answer:

126 units!

Step-by-step explanation:

I hope this helped!! c:

If the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The speed of the swamp vehicle = 3.2 miles per hour

From the figure we can see the two triangles ΔXVM and ΔXYZ

Here we have to use the ratio of the two similar triangles

The ratio will be

VW/WX = YZ/ZX

Substitute the values in the equations

10/6 = YZ/3

We have to find the distance from point Z to point Y

YZ = (10/6)×3

= 5 Miles

We know

Speed = Distance / Time

Time = Distance / speed

= 5/3.2

= 1.56 hours

Hence, if the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The complete question is

You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?

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Answer:

What is the meaning of geometric sequence?

Step-by-step explanation:

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. a n= a 1 r n – 1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.

Answer:

Below.

Step-by-step explanation:

It is a sequence of numbers with a common ratio. That is, each term after the first is obtained by multiplying the previous one by the common ratio.

Examples:

2, 6, 18, 54 ...    is a geometrics sequence with common ratio 3.

1, 1/2, 1/4, 1/8 ... has a common ratio of 1/2.

-1, 1, -1, 1, -1 ...   has a common ratio of -1.

The nth term of a geometric sequence is given by

a r^(n-1) where a = first term and r = common ratio.

Answer:

[tex]-48x^2 - 144x[/tex]

Step-by-step explanation:

[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =12x(-4x-12) \\ \\ =-48x^2-144x[/tex]

Horizontal line with the given function: y = 4

Explanation:

Since the midline of a sine function is the horizontal centerline about which the functions oscilliart above and below, the corresponding line here is y = 4 with x = 0.

NB:

The midline is parrallel to y = 0 ~ the x-axis.

144 yards of string will need to use balloons for the party.

Given,

The length of balloon string Orlando wanted = 6 feet

Number of balloons = 72

We have to find the total length of strings wanted for 72 balloons in yards.

1 yard = 3 feet

Now,

Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet

Now convert 432 feet into yard

That is,

432 / 3 = 144 yards

So,

144 yards of string will need to use balloons for the party.

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Answer:

area of triangle is length *breathe

4.5 * 5.5 = 24.75

Answer:

x=23

Step-by-step explanation:

The amount of degrees in a triangle is 180 degrees.

line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180

5x=115

x=23

we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is

where we used the slope formula:

Then, our searched line has the form:

where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:

then, the searched line in slope-intercept form is

Therfore, the given area can be modeled as

because when a line is dashed it doesn't belong to the given area.

Given

Find

derivatives using increment method.

Explanation

Given

replace x and y by

so ,

now divide by

so ,

now taking limit

Final Answer

Therefore , the derivative of the function using increment method is 12x + 10

The translation observed by shape A after reflection is

Translation refers to a linear movement used in describe repositioning of image during transformation

Transformation is the generally the repositioning of an image. Transformations are usually described in a cartesian plane for ease of comprehension.

The shape A after reflection had a new position. The new position was moved downwards, in the y direction by 2 units representing -2

The shape was further moved to the left 5 units in the x direction  representing -5

Hence we say that c = -5 and d =  -2

This describes the position of the image now labeled shape B

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Answer:

-111/2

Step-by-step explanation:

Please look at the attachment below! :D

The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d

The constant of proportionality is 0.15.

Th amount the organisation will receive if dinner sales is $3600 is $540

The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.

A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.

The form of the linear equation would be:

total amount received by the organisation = percentage x amount the restaurant receives.

a = 0.15d

0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.

a = 0.15 x 3600

a = $540

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The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:

S:L = 1:3

Also, when red coloring is added to both containers, we have:

S:L = 1r:3r

In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.

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Complete Question:

For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?

answer choices

The small bowl's mixture is a darker shade of red.

The large bucket's mixture is a darker shade of red.

Neither. The mixtures are the same shade of red.

Answer:

2.5

Step-by-step explanation:

Plug is -3 for y and solve for x

2x -3 = 2  Add 3 to both sides

2x = 5  Divide both sides by 2

x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5