You pay $3 per square foot for carpeting. Which equation can be solved to find the
amount you will pay to cover a triangular section of the floor with a base of 2 yards and
a height of 5 yards?

Answer:

A = 1/2b^2 + 3b

Step-by-step explanation:

If the height of the triangle is 6 units longer than the base length, we can represent the height with the variable h and the base length with the variable b.

h = b + 6

We can substitute h with b+6 in the formula for the area of the triangle:

A = 1/2bh

A = 1/2b(b+6)

So, the area of the triangle can be represented in terms of b only, as

A = 1/2b^2 + 3b

Answer:

Yes

Step-by-step explanation:

Yes, water evaporates during periods of dryness which can cause water in wells to dissapear

The total cost = $5000 (Option A) and $9400 (Option B)

Cost per mile = $0.33 (option A) and $0.25 (Option  B)

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: Total costs and cost per mile, when the truck is driven (A) 15000 miles per year (B) 37000 miles per year.

Finding:

(A) By unitary method,

When the truck is driven 1 mile, cost of gasoline = $0.20

When the truck is driven 15000 miles, cost of gasoline = $ 0.20(15000) = $3000 in an year

Cost of insurance in an year = $2000

Thus, total cost = $ 3000 + $2000 = $5000

Now, for per mile cost:

Cost of gasoline = $0.20

Cost of insurance = $0.13

Thus, Cost per mile = $0.20 + $0.13 = $0.33

(B) Again, by unitary method,

When the truck is driven 1 mile, cost of gasoline = $0.20

When the truck is driven 37000 miles, cost of gasoline = $ 0.20(37000) = $7400 in an year

Cost of insurance in an year = $2000

Thus, total cost = $ 7400 + $2000 = $9400

Now, for per mile cost:

Cost of gasoline = $0.20

Cost of insurance = $0.5

Thus, Cost per mile = $0.20 + $0.5 = $0.25

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Answer:

a)    4.95 \(\leq\) 5 pound bag \(\leq\) 5.65

b) See attached files.

Step-by-step explanation:

We can set up an inequality with our information.

Information:

5 pound bag = 4.95 to 5.65

4.95 \(\leq\) 5 pound bag \(\leq\) 5.65

Answer:

use The Law of Cosines first to calculate the largest angle. then use The Law of Sines to find another angle. and finally, use the angles of a triangle add to 180° to find the last angle.

Step-by-step explanation:

The scalene triangle is a type of triangle with sides of three different lengths and angles of three different measurements. In every scalene triangle, the shortest side is opposite the smallest angle and the longest side is opposite the largest angle.

ANSWER:

v = 3 is only a solution to equations 1 and 5.

STEP-BY-STEP EXPLAINATION:

Equation 1:

\( \frac{v}{3} + 9 = 10\)

\( \frac{v}{3} = 10 - 9\)

\( \frac{v}{3} = 1\)

\(v = 1(3)\)

\(v = 3\)

Therefore, v = 3 is a solution.

Equation 2:

\(4 = 7v - 24\)

\(4 + 24 = 7v\)

\(28 = 7v\)

\( \frac{28}{7} = v\)

\(4 = v\)

Therefore, v = 3 is not a solution.

Equation 3:

\(16 = 2 + 5v\)

\(16 - 2 = 5v\)

\(14 = 5v\)

\( \frac{14}{5} = v\)

Therefore, v = 3 is not a solution.

Equation 4:

\(5 - 7v = 19\)

\( - 7v = 19 - 5\)

\( - 7v = 14\)

\(v = \frac{14}{ - 7} \)

\(v = - 2\)

Therefore, v = 3 is not a solution.

Equation 5:

\(3 + 2v = 9\)

\(2v = 9 - 3\)

\(2v = 6\)

\(v = \frac{6}{2} \)

\(v = 3\)

Therefore, v = 3 is a solution.

The new pair of polar Coordinates for the given point is (-3, 2π + 2).

(a) Given point (1, π/2) in polar coordinates, we can find another pair of polar coordinates such that r > 0 and 2π < θ < 4π as follows:

Let us add 2π to the given θ to get a new value greater than 2π. So, θ' = π/2 + 2π = 5π/2.

Therefore, the new pair of polar coordinates for the given point is (1, 5π/2).

To find another pair of polar coordinates such that r < 0 and 0 < θ < 2π, we can use the fact that adding or subtracting any multiple of 2π from θ does not change the point represented by the polar coordinates. So, we can subtract 2π from the given θ to get a new value between 0 and 2π. Thus, θ'' = π/2 - 2π = -3π/2.

Therefore, the new pair of polar coordinates for the given point is (-1, -3π/2).

(b) Given point (-2, π/4) in polar coordinates, we can find another pair of polar coordinates such that r > 0 and 2π < θ < 4π as follows:

Let us add 2π to the given θ to get a new value greater than 2π. So, θ' = π/4 + 2π = 9π/4.

Therefore, the new pair of polar coordinates for the given point is (2, 9π/4).

To find another pair of polar coordinates such that r < 0 and -2π < θ < 0, we can subtract π from the given θ to get a new value between -π and 0. Thus, θ'' = π/4 - π = -3π/4.

Therefore, the new pair of polar coordinates for the given point is (-2, -3π/4).

(c) Given point (3,2) in polar coordinates, we can find another pair of polar coordinates such that r > 0 and 2π < θ < 4π as follows:

Let us add 2π to the given θ to get a new value greater than 2π. So, θ' = 2 + 2π = 2π + 2.

Therefore, the new pair of polar coordinates for the given point is (3, 2π + 2).

To find another pair of polar coordinates such that r < 0 and 0 < θ < 2π, we can use the fact that adding or subtracting any multiple of 2π from θ does not change the point represented by the polar coordinates. So, we can add 2π to the given θ to get a new value between 2π and 4π. Thus, θ'' = 2 + 2π = 2π + 2.

Therefore, the new pair of polar coordinates for the given point is (-3, 2π + 2).

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Answer:

Step-by-step explanation:

is there a height? Is the triangle with a 90 degrees angle? Is there any other conditions that are given?

Answer:

No, because 20 x 6 = 120 and 120 is bigger than 102

Step-by-step explanation:

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

The equation of the parabola in vertex form is y = -5x^2 + 3

The equation represents the given parameters

From the question, we can see that the equation is a parabola or a quadratic function

The function is given as

y = x² + 16x + 65

Start by differentiating the function

So, we have the following representation

y = x² + 16x + 65

Differentiate function with respect to x

So, we have the following equation

y' = 2x + 16

Set the differentiated function to 0

So, we have the following equation

2x + 16 = 0

Divide through by 2

So, we have

x + 8 = 0

Solve for x

x = -8

Substitute x = -8 in the equation y = x² + 16x + 65

So, we have

y = (-8)² + 16(-8) + 65

Evaluate

y = 1

So, we have

x= -8 and y = 1

This means that

Vertex = (-8, 1)

Rewrite as

(h, k) = (-8, 1)

A parabola function is represented as

y = (x - h)² + k

Where

Vertex = (h, k)

Substitute (h, k) = (-8, 1) in y = (x - h)² + k

y = (x + 8)² + 1

Hence, the equation is y = (x + 8)² + 1

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If ∠AOC and ∠COD are complementary angles, then the value of x is 7.5

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

m∠AOC = 68° and m∠COD = (2x + 7)°.

If ∠AOC and ∠COD are complementary angles, then the value of x is calculated as

AOC + COD = 90

Substitute the known values in the above equation, so, we have the following representation

2x + 7 + 68 = 90

So, we have

2x = 15

Divide by 2

x = 7.5

Hence, the value of x is 7.5

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The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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The value that is equivalent is -7/4. Option C

A fraction is simply defined as the part of a whole number, a whole variable or a whole element.

The different types of fractions are;

From the information given, we have that;

3(1/4-2) + |-7|

find the lowest common multiple, we get;

3(1 - 8 /4) + 7

expand the bracket, we get;

3(-7/4) + 7

-21/4 + 7

-21 + 28/4

-7/4

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The complete question:

Which value is equivalent to the expression shown? 3(1/4-2) + |-7| is:

a. 7/4

b.7/2

c. -7/4

d. -7/2

Yes, the LSAT scores follow the normal curve.

The LSAT scores for this law school did follow the normal curve. This is because the average LSAT score was 169 and the standard deviation (SD) was 9. This means that the majority of the scores were within one standard deviation of the average, which is a characteristic of a normal curve.

Additionally, the highest score was 178, which is within one standard deviation of the average (169 + 9 = 178), further supporting that the scores follow a normal curve.

It is important to note that the normal curve, also known as the bell curve, is a type of distribution that is symmetrical and has the majority of the data points clustered around the mean (average) value. The standard deviation is a measure of how spread out the data is from the mean. In a normal curve, about 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In conclusion, the LSAT scores for this law school followed the normal curve because the majority of the scores were within one standard deviation of the average and the highest score was within one standard deviation of the average.

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After 6 years, there will be 23,200 people living there.

A town has 17,000 residents and is expanding at a 3% annual rate.

What is the explanation?

Population after t years equals y(t).

y(t)=y0(1+r)^t

y0 = initial population,

r = growth rate, and

t = time.

A town has 17,000 residents and is expanding at a 3% annual rate.

y(t)= 23,200, = 17,000, r=3%= 0.03, t=

23,200 = 17,000(1+0.03)^t

23200/17000 = (1+0.03)^t

taking both sides of the ln function

(23200/17000)/1.03

⇒ t = 6 year.

After 6 years, there will be 23,200 people living there.

We find the difference (subtract) between the original population and the population at Time 1, divide by the initial population, then multiply by 100 to obtain the Population Growth (PG). For that time (10 years), the population growth rate (PGR) was 12%.

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Given:

The sum of the angles in a hexagon is 720°.

\(m\angle A=90^\circ,m\angle B=126.87^\circ,m\angle C=(3x)^\circ,m\angle D=90^\circ, m\angle E=143.13^\circ, m\angle F=143.13^\circ.\)

To find:

(a) Equation to solve the value of x.

(b) The value of x.

(c) The measure of angle C.

Solution:

(a)

We have,

\(m\angle A=90^\circ,m\angle B=126.87^\circ,m\angle C=(3x)^\circ,m\angle D=90^\circ, m\angle E=143.13^\circ, m\angle F=143.13^\circ.\)

The sum of the angles in a hexagon is 720°.

\(m\angle A+m\angle B+m\angle C+m\angle D+m\angle E+m\angle F =270^\circ\)

\(90^\circ+126.87^\circ+(3x)^\circ+90^\circ+143.13^\circ+143.13^\circ =270^\circ\)

\(90+126.87+(3x)+90+143.13+143.13 =720\)

Therefore, the required equation is \(90+126.87+(3x)+90+143.13+143.13 =720\).

(b)

On solving the above equation, we get

\(593.13+3x =720\)

\(3x =720-593.13\)

\(3x =126.87\)

Divide both sides by 3.

\(x =\dfrac{126.87}{3}\)

\(x =42.29\)

Therefore, the value of x is 42.29.

(c)

We need to find the measure of angle C.

\(m\angle C=(3x)^\circ\)

\(m\angle C=(3\times 42.29)^\circ\)

\(m\angle C=126.87^\circ\)

Therefore, the measure of angle C is 126.87 degrees.

Answer: 4

Step-by-step explanation:

Follow the PEMDAS so the first thing you do is 14:7 which is 2. then you do the division and multiplication so the 44:11 is 4, 5*2 is 10, and 2*2 is 4. The next thing you do is addition and subtraction. 26-4-4-10-4 is 4. So, the answer is 4.

Answer:

Find the relative frequency for the event ​"heads​" for each friend:

Friend 1: 0.59 (41/70)

Friend 2: 0.7 (49/70)

Friend 3: 0.37 (26/70)

If the friends combine their results to get 116 heads and 94 ​tails, what is the relative frequency for the event ​"heads​"?

0.55 (116/210)

Suppose each friend flips a coin 700 times. Is there a value you would expect the relative frequency for the event ​"​heads" to be close​ to?

For Friend 1, basing it off the 0.59 frequency from earlier, I would expect the heads to be around 413.

Friend 2, 490

Friend 3, 259

The equation of the line in fully simplified slope-intercept form is y = -x + 3

From the question, we are to write the equation of the line in fully simplified slope-intercept form

The slope-intercept form of the equation of a straight line is given as

y = mx + b

Where m is the slope of the line

and b is the y-intercept

From the graph,

The y-intercept is 3

∴ b = 3

Now, we will determine the slope, m, of the line

Given any two points (x₁, y₁) and (x₂, y₂) on a line, the slope, m, of the line is

m = (y₂ - y₁)/(x₂ - x₁)

Picking the points, (0, 3) and (2, 1)

m = (1 - 3)/(2 - 0)

m = -2/2

m = -1

Putting in the slope, m, and the y-intercept, b into the equation of a line

y = mx + b

We get

y = -1(x) + 3

Simplify

y = -x + 3

Hence, the equation of the line in fully simplified slope-intercept form is y = -x + 3

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There are default tab stops every one inch on the horizontal ruler is true statement.

In word processing software, there are usually default tab stops set every one inch (or 2.54 cm) on the horizontal ruler. These tab stops are the default positions at which the insertion point will stop when the tab key is pressed.

The purpose of these tab stops is to make it easier to align text in columns or tables. By default, there are left-aligned, centered, right-aligned, decimal-aligned, and bar-aligned tab stops. Users can also add custom tab stops at specific positions on the ruler to suit their formatting needs.

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Answer:

one solution which is -14

Step-by-step explanation:

Answer:

hope that help for you.....

answer

step by step explanation

A type of quantitative analysis in which the amount of a species in a material is determined by converting the species to a product that can be isolated completely and weighed is "gravimetric analysis."

Gravimetric analysis is a quantitative chemical analysis method in which the contribution sought is transformed into a material (of different compositions) that can be separated and weighed from the sample.

Some key features regarding the gravimetric analysis are-

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To evaluate the definite integral of f(g(4)) - f(g(2)), we need to consider the composition of functions and the Fundamental Theorem of Calculus.

Let's break down the steps to find the definite integral: Evaluate g(4) and g(2) using the function g. Substitute the values of g(4) and g(2) into the function f. Find the antiderivative of f(g(x)) with respect to x, denoted as F(g(x)). Apply the Fundamental Theorem of Calculus, which states that the definite integral of F'(x) from a to b is equal to F(b) - F(a), where F'(x) is the derivative of F(x).

Evaluate F(g(4)) - F(g(2)) using the antiderivative F(g(x)). Note that the expression F(g(4)) - F(g(2)) represents the change in the antiderivative F(g(x)) over the interval from g(2) to g(4). Therefore, the definite integral for f(g(4)) - f(g(2)) is F(g(4)) - F(g(2)).

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Given that, the speed of the plane was 140 mph faster than the speed of the car. The speed of the plane was found to be 156.471 mph.

Let's assume that the speed of the car is x mph. Given that a person drove 100 miles in the same amount of time that it took a plane to travel 380 miles.

Speed of the plane = 380/t,

where t is the time taken by both to cover their respective distances.

Using the formula

time = distance/speed,

the time taken by the car to travel 100 miles is 100/x hours.

Since the car and the plane took the same time, we can say that:

100/x = 380/(x+140)

Now we will solve this equation to find x (Speed of car)  

100/x = 380/(x+140)

100(x+140) = 380x

4x + 560 = 38

x = 560/34 ≈ 16.471 mph.\

The speed of the plane = 140 + 16.471 = 156.471 mph.

Finally, we can conclude that the speed of the plane is 156.471 mph.

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Answer:

44°

Step-by-step explanation:

We Know

The sum of three angles in a triangle must add up to 180°.

Let's solve

3x + 15 + 4x - 12 + 79 = 180°

7x + 82 = 180°

7x = 98°

x = 14

Now we put 14 in for the x and find the other 2 missing angles.

3x + 15

3(14) + 15

42 + 15

57°

4x - 12

4(14) - 12

56 - 12

44°

So, the measure of the three angles are: 44°, 57°, and 79°. So, the measure of the smallest angle is 44°

Answer:

3

Step-by-step explanation:

Michael must find the smallest number possible that can divide 60 and 45 then take the two quotients after dividing the 2 types of cookies by the smallest number possible.

2 is not possible as 45 is an odd number

3 can divide both 60 and 45

60/3 = 20 oatmeal cookies in each container.

45/3 = 15 chocolate chip cookies in each container.