line n passes through the points (-3, -7.5) and (2, -5). tahlia determined that the equation of line n is y = 0.5x. explain the error tahlia made while determining her equation. be sure to include the correct equation in your explanation​

The distance between points A and B is: A. 4√5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-4))² + (-2 - 2)²]

Distance = √[(8)² + (-4)²]

Distance = √(64 + 16)

Distance = √80

Distance = √16 × √5

Distance = 4√5 units.

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Answer:

none of them are right it is 4 to the 10

Step-by-step explanation:

Answer:

in image...

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The angles on the diagram are vertical angles and the value of x is 25.

The two angles are said to be adjacent angles when they have a common vertex and side.

On the other hand, vertical angles are angles that are opposite of each other when two lines cross and they are conguent.

Therefore, the angles on the diagram are vertical angles.

Now, since vertical angles are congruent.

Angle 75 and angle (4x - 25 ) are equal.

Hence;

4x - 25 = 75

Solve for x

4x - 25 = 75

Add 25 to both sides

4x - 25 + 25 = 75 + 25

4x = 75 + 25

4x = 100

Divide both sides by 4

4x/4 = 100/4

x = 100/4

x = 25

Therefore, the value of x is 25.

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The best interpretation of the y-intercept of the linear function is given as follows:

D. The model indicates that 1-bedroom apartments in New York had an average rent of 800 dollars in 2000.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The variables for this problem are given as follows:

Hence option D gives the correct interpretation of the intercept of the line.

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Answer:

Step-by-step explanation:

If Sara is making 3 batches of chocolate chip cookies using 2 1/4 cups of flour per batch, then the total amount of flour she uses for the chocolate chip cookies is:

3 batches x 2 1/4 cups per batch = 6 3/4 cups of flour

Since she will use 12 3/4 cups of flour for all six batches, the amount of flour used for the oatmeal cookies can be found by subtracting the amount of flour used for the chocolate chip cookies from the total amount of flour:

12 3/4 cups - 6 3/4 cups = 6 cups

To determine how many cups of flour are needed for each batch of oatmeal cookies, we can divide the total amount of flour used for the oatmeal cookies by the number of batches:

6 cups ÷ 3 batches = 2 cups per batch

Therefore, the equation that can be used to determine how many cups of flour are needed for each batch of oatmeal cookies is:

Flour needed per batch of oatmeal cookies = Total flour needed for oatmeal cookies ÷ Number of oatmeal cookie batches

Or, in this case:

Flour needed per batch of oatmeal cookies = 6 cups ÷ 3 batches = 2 cups per batch.

Step-by-step explanation:

What we do here is divide 43 by 50

[tex] \frac{43}{50} = 0.86 = 86\%[/tex]

Mech #1 charged 45$/hr and Mech #2 charged 75 $/hr. We can find the solution in the following manner:

Let's make,

mechanic #1's rate = x

mechanic #2's rate = y

Their rate is dollars per hour ($/hr)

Mechanic #1 worked for 20 hours (hr × $/hr = $)

20x = money earned by mechanic #1

And mechanic #2 worked for 15 hours

15y = money earned by mech#2

Together they charged a total of $2175. So the amount of money earned by both mechanics.

20x + 15y = 2175

The sum of the two rates was $120 per hour.

x + y = 120

which means

x = 120- y

Putting (120 - y) in for "x" in the other equation to get everything in terms of one variable.

20(120 - y) + 15y = 2175

Now we can solve for y and get the solution:

20(120 - y) + 15y = 2175

y=45 $/hr

Now use this to solve for x

x + y = 120

x + 45 = 120

x =75

x = 75 $/hr

Mech #1 charged 45$/hr

Mech #2 charged 75 $/hr

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Answer:

A rotation about the origin 180 degrees means that the pre-image essentially rotates half an actual circle

The rule for 180 degrees rotation is (x,y)-->(-x, -y)

So the points of this quadrilateral are now

(1,3) = (-1, -3)

(4,1)=(-4, -1)

(4,4)=(-4, -4)

(1,4)=(-1,-4)

So it moves from 1st to 3rd quadrant

HOPE THIS HELPS

The table of the piecewise function is shown below and the point of maximum growth rate for the function is (8.96, 7.5)

Given that

g(x) = x² - 1 if x ≤ 3

g(x) = x - 5 if x > 3

For values greater than 3, we use the function g(x) = x - 5;

Otherwise, we use g(x) = x² - 1

This means that

x               Workings              g(x)

-2              g(-2) = (-2)² - 1         3

0               g(0) = (0)² - 1           -1

1                g(1) = (1)² - 1              0

3                g(3) = (3)² - 1           8

5                g(5) = 5 - 5             0

Given that

f(x) = 15/(1 + 6e⁻⁰°²ˣ)

The point of maximum growth rate for a logistics function represented as f(x) = c/(1 + ae⁻ᵇ⁺) is

t = ln(a)/b

y(t) = c/2

So, we have

t = ln(6)/0.2 = 8.96

y(t) = 15/2 = 7.5

Hence, the point is (8.96, 7.5)

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Answer:

How?

Step-by-step explanation:

Answer:

the missing ratio is 12

Step-by-step explanation:

essentially all of these ratios should simplify to 3:4

The solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

First, let's graph the line x = -2, which is a vertical line passing through -2 on the x-axis.

Next, let's graph the line x - y = 1, which can be rewritten as y = x - 1. This is a line with a slope of 1 (meaning it goes up 1 unit for every 1 unit it goes to the right) and a y-intercept of -1 (meaning it passes through -1 on the y-axis).

Now, we need to shade in the region that satisfies both inequalities. We know that x has to be greater than or equal to -2, so we shade to the right of the vertical line x = -2. We also know that x - y has to be greater than or equal to 1, so we shade above the line y = x - 1.

The shaded region is the overlapping region that satisfies both inequalities. It is the region above the line y = x - 1 and to the right of the vertical line x = -2.

Therefore, the solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

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The complete question is as follows:

What is the solution to the system of inequalities?

x ≥ -2

x - y ≥ 1

Answer:

Below

Step-by-step explanation:

If the 'y'-axis is # larvae  and the  'x' axis is °C  then the peak  would show the greatest # larvae (450) would be at 5 °C

Answer:

B) This means that the number of larvae is greatest at 5 degrees Celsius.

Step-by-step explanation:

On the given graph:

The curve is a parabola that opens downwards. Therefore, its vertex is the maximum value.

From observation of the graph, the vertex (peak) is (5, 450).

This means that the number of larvae reaches its maximum value of 450 at a temperature of 5 degrees Celsius.

Answer:

(1 , -2)

Step-by-step explanation:

We are told that there is a translation of (x-4 , y-3)

This simply means that the x-axis moves to the left by 4 points and that the y-axis moves down 3 points. (if it was a plus not minus then points would move up and to the right)

1) Move the x-axis

We can see that the x-axis of b is 5. To move it to the left 4 we subtract 5 by 4

2) Move the y-axis

We can see that the y-axis of b is 1. To move it down we subtract 1 by 3

This leaves us with (1 , -2)

Hope this helps, have a lovely day! :)

The true statement of the equation 4+-2=5 is false

From the question, we have the following parameters that can be used in our computation:

4+-2=5

To determine the trie statement, we evaluate the expression 4 + (-2)

Using the above as a guide, we have the following:

The sum of 4 and -2 is:

4 + (-2) = 2

So, we have

2 = 5

The above is not true

Hence, the statement "4 + (-2) = 5" is false.

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The altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.

What is right angled triangle ?

A right-angled triangle is a triangle that has one angle that measures 90 degrees (a right angle). This means that the other two angles must add up to 90 degrees as well. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem, which states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse, is a fundamental concept in mathematics and has many practical applications. Right-angled triangles are used in fields such as engineering, architecture, and physics to calculate distances, heights, and angles.

a) Let's use the Pythagorean theorem to find the altitude of the plane. We have a right triangle with the slant range as the hypotenuse, the ground range as one leg, and the altitude as the other leg. So, we can use:

altitude² + ground range² = slant range²

altitude² + 10.15² = 14.5²

altitude² = 14.5² - 10.15²

altitude² = 84.9025

altitude ≈ 9.21 km or 9210 meters (rounded to the nearest meter)

b) If the plane descends at a rate of 750 meters per minute, the pilot will have:

time = altitude / descent rate

time = 9210 / 750

time ≈ 12.28 minutes (rounded to two decimal places).

Therefore, the altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.

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2 quart of blue paint and 5/4 quart of red paint is needed to make 3 1/4 quart purple paint

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

2/5 quart of blue paint is mixed with 1/4 quart of red paint to make purple paint. Hence:

Ratio of blue paint to red paint = (2/5) : (1/4) = 8 : 5

Therefore for 3 1/4 quart of purple paint:

Amount of blue paint = (8/13) * 3 1/4 = (8/13) * 13/4 = 2 quart

Amount of red paint = (5/13) * 3 1/4 = (5/13) * 13/4 = 5/4 quart

2 quart of blue paint and 5/4 quart of red paint is needed to make the purple paint

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The same solutions equations are  B)2.3p – 10.1 = 6.49p-4 and C)230p-1010=650p-400-p.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is,

=> 2.3p – 10.1 = 6.5p – 4 – 0.01p

To remove decimal we need to multiply by 100 on both side of the equation then,

=> (2.3p – 10.1)*100 = (6.5p – 4 – 0.01p)*100

=> 2.3*100p-10.1*100=6.5*100p-4*100-0.01*100p

=> 230p-1010=650p-400-p

And simplifying then,

=>2.3p – 10.1 = 6.5p – 4 – 0.01p

=>2.3p – 10.1 = 6.49p-4

Hence the correct options are, B)2.3p – 10.1 = 6.49p-4 and C)230p-1010=650p-400-p.

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The equation for the function with the described transformations is y(x) = -2f(x+1) + 8.

Starting with the basic function of f(x), we can apply the described transformations in the following order:

Vertical stretching by a factor of 2: We multiply the output of the function by 2. This results in a new function g(x) = 2f(x).

Reflection across the x-axis: We flip the sign of the output of the function. This results in a new function h(x) = -g(x) = -2f(x).

Translation 1 unit left and 8 units up: We shift the graph of the function 1 unit to the left and 8 units up. This can be achieved by replacing x with (x+1) and adding 8 to the output.

This results in a new function y(x) = h(x+1) + 8 = -2f(x+1) + 8.

Putting it all together, the equation for the function with the described transformations is:

y(x) = -2f(x+1) + 8

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The complete question is below:

Write an equation for f(x) when it is vertically stretched by a factor of 2, reflected across the x-axis, then translated 1 unit left and 8 units up.​

The required number of tubs are 17.55 tubs.

To solve the problem, we need to find the total amount of ice cream used in ounces and then convert it to pounds to find the number of tubs used.

Number of scoops for regular cones = 2 scoops/cone

Number of scoops for large cones = 3 scoops/cone

Total number of scoops of ice cream used for regular cones = 2 scoops/cone x 234 cones = 468 scoops

Total number of scoops of ice cream used for large cones = 3 scoops/cone x 156 cones = 468 scoops

Total number of scoops of ice cream used = 468 scoops + 468 scoops = 936 scoops

Total amount of ice cream used in ounces = 936 scoops x 3 ounces/scoop = 2808 ounces

Total amount of ice cream used in pounds = 2808 ounces / 16 ounces/pound = 175.5 pounds

Number of tubs of ice cream used = 175.5 pounds / 10 pounds/tub = 17.55 tubs

Rounding up to the nearest whole number, we get:

Answer: (C) 17.55 tubs.

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Given - the system of the equations as

[tex]y=-2x+1\\y=-11x-3[/tex]

To find - the solution of the set of equation

Explanation- given the set and we can see that left hand side of the equation is equal.

we get

[tex]-2x+1=-11x-3\\-2x+11x=-3-4\\9x=-7\\x=-7/9=-0.77[/tex]

we get

[tex]y=-2(0.77)+1\\y=-1.54+1\\y=-0.54[/tex]

Hence the value is x =-0.77, y=0.54

Final answer- the value of x = 0.77, y = -0.54

There for the answer is the volume of the pyramid is equal to V = 1/3 (n³ - n²).

What do math lengths mean?

The measurement or size of a thing end to end is referred to as its length. In other words, it is the larger of an object's upper two or three geometric dimensions. The dimensions of a rectangle, for instance, are its length and width.

We know that.

The volume of pyramid is equal to

V =1/3 (area of base) × height

In this problem

Area of base = n² units²

Height = (n - 1) units

Substitute in the formula above

V = 1/3 n² × (n - 1)

V = 1/3 (n³ - n²) units³

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Cason must read for at least 22 weeks to meet his goal. The correct answer is D. x ≥ 22

Let x be the number of weeks Cason needs to read to meet his goal. In each week, he can read 2 books. Therefore, the total number of books he will read in x weeks is:

2x

Since Cason has already read one book, the total number of books he will have read after x weeks is:

2x + 1

We want Cason to read at least 45 books, so we can set up an inequality:

2x + 1 ≥ 45

Subtracting 1 from both sides, we get:

2x ≥ 44

Dividing both sides by 2, we get:

x ≥ 22

Therefore, Cason must read for at least 22 weeks to meet his goal.

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In response to the aforementioned query, we may say that The interest for the previous month, rounded to the nearest cent, is $289.84.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

The Annual Percentage Rate (APR) can first be changed to a monthly interest rate as follows:

r = APR/12 = 0.085/12 = 0.0070833

Then, we may determine how many months the loan will last:

n = 2.5 years * 12 months a year = 30 months.

We can now calculate the total amount owing at the conclusion of the loan term using the compound interest formula:

A= P(1 + r)^n

where P is the loan's principle, r is the interest rate each month, and n is the number of months.

A = $3000(1 + 0.0070833)^30\s= $3,789.64

At the conclusion of the loan period, there will be a balance of $3,789.64.

B = $3000(1 + 0.0070833)^(30-1) - [((1 + 0.0070833)^30 - 1)/(0.0070833)]

= $3,499.80

I = $3,789.64 - $3,499.80\s= $289.84

The interest for the previous month, rounded to the nearest cent, is $289.84.

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The width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth.

We know that the area of the rectangle is given by the function A(x) = x² + 8x, where x is the width of the rectangle. We also know that the area of the rectangle is 33 in². So we can set up the equation:

x² + 8x = 33

To solve for x, we can rearrange the equation and set it equal to zero:

x² + 8x - 33 = 0

We can now use the quadratic formula to solve for x:

[tex]x = (-b\±\sqrt{(b^2 - 4ac)}) / 2a[/tex]

where a = 1, b = 8, and c = -33. Substituting these values, we get:

[tex]x = (-8\±\sqrt{(8^2 - 4(1)(-33))}) / 2(1)[/tex]

[tex]x = (-8\± \sqrt{(256)}) / 2[/tex]

x = (-8 ± 16) / 2

So x = -12/2 or x = 4.

Therefore, the width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

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The area of the circle with a radius of 10 meters is given as follows:

314.16 m².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr².

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle, on a segment that passes through the center. Hence, the diameter’s length is twice the radius length.

Considering the above concept, the measure of the radius for the circle in this problem is given as follows:

r = 10m.

Thus the area of the circle is given as follows:

A = π x 10²

A = 314.16 m².

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5[1-[tex](2/3)^{8}[/tex]/1-2/3] can be used to evaluate the series 8 E k=1 5 (2/3) k-1 through geometric series.

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios. In other words, the following term is obtained by multiplying each phrase in a geometric series by a constant.

Hence, a geometric series has the formula a, ar, ar2, where an is the first term and r are the sequence's common-ratio. Either a positive or negative integer can be used to describe the common ratio.

The given series is:

Now,we want to write an expression that can be used to evaluate this series.

Since this is a geometric series, we use the formula for the sum of the first k terms: Sk = a (1-[tex]r^{k}[/tex]/1-r)

From the given series the first term a= 5 is, and the common ratio is r =2/5 and k=8

We substitute the values to obtain:

S8= 5[1-[tex](2/3)^{8}[/tex]/1-2/3]

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Answer:

2

Step-by-step explanation:

Take out 25% of 8

25/100*8= 2

Required Amount=2

The Area of Garden is 62/3 feet².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm² and m² are used to measure area. A shape's area is a two-dimensional measurement.

Given:

Length = 7 3/4 feet = 31/4 feet

Width = 2 2/3 feet = 8/3 feet

So, Area of Garden

= l w

= 31/4 x 8/3

= 62/3 feet²

and, Now, 5/6th of the Garden

= 62/3 x 5/6

= 31 / 3 x 5 / 2

= 155 / 6 feet²

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Answer:

Inverse Operation

Step-by-step explanation: