F.E.O.L. Perpendicular to a Given Line
Write the slope-intercept form of the equation of the line described.
1) through: (-2,-3), perp. to y=-x
5
3) through: (2,-2), perp. to y=-
2) through: (5,-2), perp. to y = 5x +4
4) through: (-4,-3), perp. to y=-x+2

Bin had 7.25 gallons of gas to start with using the unitary method.

Unitary method is a problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units. In this case, we will use unitary method to find the number of gallons Bin had to start with.

Firstly, we need to find the rate of gas consumption. The slope of the line, which is the change in the gas level over time, gives us this information. Since the slope is -1.25, this means Bin is losing 1.25 gallons of gas per hour.

Next, we need to find the total time Bin has been driving. From the problem, we know that after 1 hour, she had 7.25 gallons left, and after 4 hours, she had 3.5 gallons left. This means that she drove for 3 hours (4-1).

Using the unitary method, we can calculate the total amount of gas Bin had to start with. We know that she lost 1.25 gallons of gas per hour, and she drove for 3 hours. Therefore, she lost a total of 3.75 gallons of gas during the trip.

To find the initial gas level, we need to subtract the amount of gas she lost from the gas level she had at the end of the trip. This gives us:

Initial gas level = Gas level at end of trip + Gas lost during the trip

Initial gas level = 3.5 gallons + 3.75 gallons

Initial gas level = 7.25 gallons

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Complete question:

As Bin is driving her car, she notices that after 1 hour her gas tank has 7.25 gallons left and after 4 hours of driving, it has 3.5 gallons of gas left in it. The rate at which she is LOSING gas is 1.25 gallons....So, the slope is -1.25. How many gallons did she have to START?

The company profit is decreasing by 1/3 thousand dollars per year.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represents a company's profit in thousands of dollars, and x represents the time in years.

From the graph, using the point (-3, 4) and (3, 2):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Substituting:

[tex]y-4=\frac{2-4}{3-(-3)} (x-(-3))\\\\y=-\frac{1}{3}x+3[/tex]

The company profit is decreasing by 1/3 thousand dollars per year.

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Answer: y = x(x+1)(x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,y=x^3-3x^2-4x

taking x commonly

y=x(x^2-3x-4)

y=x(x^2+x-4x-4)

y=x[x(x+1)-4(x+1)]

y=x(x+1)(x-4)

The number of cups of mix that is needed to be used will be 12.8 cups.

Any value assigned to a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal, is a solution to a formula. To solve a problem, you must find the formula's workable answer.

For every 2 cups of mix in a lemonade recipe, there should be 3 cups of water. Lemonade made with this recipe makes 5 cups.

Let 'W' be the amount of water in gallons and 'M' be the amount of mix in gallons.

Then the equations are given as,

W / M = 3 / 2            ...1

W + M = 2               ...2

From equations 1 and 2, then we have

(3/2)M + M = 2

(5/2)M = 2

M = 4/5

M = 0.80 gallons

We know that in one gallon, there are 16 cups. Then we have

M = 0.80 x 16

M = 12.8 cups

The number of cups of mix that is needed to be used will be 12.8 cups.

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A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.

In order to solve the given quadratic equation, we would use the completing the square method as follows;

n² - 12n - 10 = 0

By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;

n² - 12n - 10 + 10 = 0 + 10

n² - 12n = 10

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

n² - 12n + (12/2)² = 10 + (12/2)²

n² - 12n + 36 = 10 + 36

n² - 12n + 36 = 46

(n - 6)² = 46

By taking the square root of each side, we have:

n - 6 = ±46

n = 6 ±46

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Complete Question:

Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?

Add 10 to each side

Add 36 to each side

Factor n² - 12n - 10 = 0

Take the square root of each side

The area of the composite figure is 24m², which is option C.

What is a composite figure?

A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. To get the area of a composite shape, first determine the individual areas of every component. The total of the individual regions will then represent the area of the composite shape.

From the figure, we can see that from a big rectangle, 4 small identical squares of side 1m are cut from each corner.

We are asked to find the area of the rest of the rectangle which makes the composite figure.

W first find the area of the original rectangle.

Its length  = 5 + 1 + 1 = 7 m

Its breadth = 2 + 1 + 1 = 4 m

So the area of the rectangle = length * breadth = 7*4 = 28 m²

Now the side length of the square = 1 m

Area of one square = 1*1 = 1m²

So are of four identical squares = 4 * 1 = 4 m²

Therefore area of the composite figure = area of big rectangle - area of 4 squares = 28 - 4 = 24m²

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Answer:

24m^2 is ur answer

Step-by-step explanation:

Hope this helps

On solving the provided question we can say that from the graphs,

y = f(x) = |x| and g(x) = |x-h| + k

Mathematicians use diagrams to logically bring facts or values ​​using visual representations or charts. A graph point usually reflects a contact between two or more things. Nodes or vertices and corner form a graph, which is a nonlinear data construction. We often glue knots together called vertices. This graph has vertices V=1, 2, 3, 5 and edges E=1, 2, 1, 3, 2, 4 and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) are graphical representations of expanding growth. Logarithmic graph in the format of a triangle 

from the graphs,

y = f(x) = |x|

y = f(x) + k

y = f(x+h)

g(x) = |x-h| + k

now, it will be

k>0 and h<0

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The translation of the graph is represented by y = -6(x+2)² - 7.

A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.

Given that the graph of y= x² translated left 2 units and up 8 units. The translated equation is:-

Start with y = x².

Shift 2 units left to get y = (x+2)².

Vertically stretch to get y = 6(x+2)².

Reflect across x-axis to get y = -6(x+2)².

Shift 7 units down to get y = -6(x+2)² - 7.

Hence, the translation of the graph is represented by y = -6(x+2)² - 7.

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The question is incomplete so solved for,

Suppose the graph of y= x^2 translated left 2 units, and up 8 units

Answer:

37

Step-by-step explanation:

AAA   1 way

AAB, AAC, AAD      3 ways each     3*3=9  ways

ABB, ACC, ADD      3 ways each     3*3=9 ways

ABC, ABD, ACD       3*2=6 ways each     3*6=18ways

1+9+9+18 = 37 ways

Answer:

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

Recall triangle angle sum property, the sum of three interior angles is 180°.

Add up the three angle measures, then solve the equation for x:

Substitute the value of x and find the value of each angle:

Answer:

27,5%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the original number and the new number and then divide it by the original number and multiply by 100%.

The difference is 40 - 29 = 11.

The percent decrease is (11/40) * 100% = 27.5%

So the percent decrease in staff is 27.5%

The number of seats in each raw by the given graph is 30.

Suppose the considered function whose graph is to be made is

f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f(x)

are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Let the number of rows in the original arrangement be x. Then, the number of seats in each row in original arrangement = x

Total number of seats = x x x = x²

From the given information,

2x(x-10)= x²+ 300

2x²-20x = x²+300

x²-20x-3000

(x-30) (x+10) = 0

x = 30, -10

Since, by the function number of rows or seats cannot be negative. So, x = 30.

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The lower and upper bounds of the given confidence interval of 95% with sample size= 1,555 , sample mean = 2.938 and standard deviation 2.837 is equal to ( 2.797 , 3.079 ).

Upper and lower bounds of the confidence interval is :

= Sample mean ± Margin of error

And Margin of error is :

=  Z-critical × ( σ/√(n ) )

Standard deviation 'σ ' = 2.837

Sample size 'n' = 1,555

Sample mean 'μ' = 2.938

Z-critical for 95% confidence interval

= Zα/2

= 1.96

Margin of error

= 1.96 × (2.837/√1,555)

= 1.96 × (2.837/ 39.43 )

= 0.1410

Confidence interval:

Upper boundary

= 2.938 + 0.1410

= 3.079

Lower boundary

= 2.938 - 0.1410

= 2.797

Therefore, for the given confidence interval of 95% the lower and upper bounds of the interval are ( 2.797 , 3.079 ).

The above question is incomplete , the complete question is:

find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:

Sample size      Sample mean      Standard deviation

1,555                  2.938                    2.837

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Answer:

9 - y

Step-by-step explanation:

less than means Subtraction

The transformations are matched accordingly is given below.

A function transformation takes whatever the underlying function f (x) is and "transforms" (or "equates") it, which is a fancy way of saying you alter the equation and shift the graph over.

Parent function is given as f(x) = 2x - 6

The transformations are shifts f(x) 4 units down

f(x) → f(x) - 4

⇒ g(x)= 2x - 6 - 4 = 2x - 10

Then stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x)

⇒ g(x) = 4(2x - 6) = 8x - 24

Now shifts f(x) 4 units right

f(x) → f(x - 4)

⇒ g(x) = 2(x - 4) - 6 = 2x - 14

To compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x)

⇒ g(x) = 2*4x - 6 = 8x - 6.

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The amount of money in the account after 2 years is $573.04.

What is compound interest?

Compound interest is the interest earned on an initial principal deposit as well as on the accumulated interest from previous periods. In other words, it is interest on interest.

To calculate the amount of money in the account after 2 years, we can use the formula for compound interest:

A = P(1 + r/n)ⁿᵗ

where A is the final amount, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period (in years).

In this case, P = $500, r = 0.07 (7%), n = 1 (compounded annually), and t = 2.

Plugging these values into the formula, we get:

A = 500(1 + 0.07/1[tex])^{(1 \times 2)}[/tex]

A = 500(1.07)²

A = $573.04

Therefore, the amount of money in the account after 2 years is $573.04.

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The two consecutive integers whose squares have a difference of 279 is 140 and 139.

The uninterrupted series of integers is represented by consecutive meaning in mathematics. It implies that the numbers are continuously following one another in a series. First, we must comprehend the idea of predecessors and successors in order to comprehend the consecutive meaning of consecutive numbers in mathematics. The number that is written immediately before the number is referred to as the predecessor. As opposed to successors, which refer to the number that follows the number. Think about the range 4, 5, 6, and 7. In this case, 4 comes before 5, while 6 comes after 5.

Let us suppose a number = x.

The consecutive number is given as (x - 1)

Two consecutive integers whose squares have a difference of 279, is given as:

x² - (x - 1)² = 279

x² - x² + 2x - 1 = 279

2x - 1 = 279

2x = 280

x = 140

x - 1 = 140 - 1 = 139

Hence, the two consecutive integers whose squares have a difference of 279 is 140 and 139.

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The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.

The equivalent is the expression that is in different forms but is equal to the same value.

The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.

The expression is given below.

[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}[/tex]

Simplify the expression, then we have

[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}\\\\\rightarrow x^{-3/4 } \cdot y ^{(4/3)} \cdot (16x^2y^4)^{1/4}\\\\\rightarrow x^{-3/4 } \cdot y ^{4/3} \cdot 2x^{1/2}y\\\\\rightarrow 2 x^{1/2 - 3/4} \cdot y^{4/3 + 1} \\\\\rightarrow 2x^{-1/4} \ \cdot y^{7/3}[/tex]

The given expression is [tex]\rm ax^by^c[/tex]. Compare the expression with given expressions, then we have

a = 2, b = - 1/4, and c = 7/3

Then the product of a, b, and c is given as,

⇒ 2 x (-1/4) x (7/3)

⇒ - 7/6

The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.

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Answer:

C = 3.14

Step-by-step explanation:

Center of the circle is (h, k)

h = 4,  k = 1

Use the equation of a circle and the given point (4, -4) to find r:

r² = (x-h)² + (y-k)² = (4-4)² + (-4-1)² = 0 + (-5)² = 25

r = √25 = 5

Find circumference, C:

C = 2πr = 2π(5) = 31.4

Brainly doesn't provide drawing tools, but you can easily draw this circle.  Just plot the center point (4, 1), then draw a circle with a radius of 5 around it.  You'll see that this circle passes through the point (4, -4).

The square root of 378 is 19.4422

The square root of a number is a value that, when multiplied by itself, gives the original number. The symbol used to denote the square root is √, and it is placed in front of the number for which we are looking for the square root.

First, let's define what factorial means. The factorial of a non-negative integer is the product of all positive integers less than or equal to that number.

Next, we have to compute the square root of 378, which is a much simpler task. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 x 5 = 25. Using a calculator, we can find that the square root of 378 is approximately 19.4422.

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Complete Question:

What is the square root of 378?

There is a 0.06% chance that a randomly selected individual from the population would have the same genotype as the evidence sample at the FGA locus.

As a forensic scientist, one of your important tasks is to determine the likelihood that a particular piece of evidence matches a specific individual.

To determine the random match probability for the evidence sample at the FGA locus, you will need to compare it to the reference sample. The reference sample is typically obtained from a suspect or a known individual who is not a suspect in the crime. The reference sample for the FGA locus has a genotype of 16,17.

The random match probability is the probability that a randomly selected individual from the population would have the same genotype at a specific locus as the evidence sample. To calculate this probability, you will need to use the allele frequency of the FGA locus in the population. This frequency is typically obtained from a large database of individuals.

Let's assume that the allele frequency for the FGA locus is 0.03 for the 16 allele and 0.02 for the 17 allele. To calculate the random match probability, you will need to multiply these two frequencies together since the evidence sample has both alleles present. This gives us a probability of 0.0006 or 0.06%.

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Complete Question:

You are a forensic scientist and you are able to obtain the following 3 CODIS STR genotypes from an evidence sample found at a crime scene:

Locus       Evidence Genotype

D55818    6,10

FGA         16,17

VWA        11,12

Based on the reference sample, what is the random match probability for the evidence sample at the FGA locus?

Using the unit conversions, the height of the tree in yards is 126.33 yd

Let h be the height of the tree.

It is given that the Height of the tree is 379 feet and we need to find the height of the tree in yards.

From the given statement, Hyperion is the tallest tree in the park, with a height of approximately 379 feet,

We need to convert the height of the tree from feet to yards. So, We divide the height of the tree by three for the yard.

So, for one foot: h = (1/3) yd

For, 379 feet: h = 379/3 yd

                         = 126.33 yd

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Answer:

0.75

Step-by-step explanation:

The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

If the presented hypothesis is confirmed, it can be assumed that individuals in the experimental group suffer from headaches more frequently than those in the control group.

The study examines how stress affects headaches. The theory can be stated as follows: People who encounter stress episodes more than twice per day would feel headaches more frequently than people who do not experience stress. This question concerns a cause and effect analysis, which can be done with reliable results when using an experimental investigation. Therefore, it is advised to use an experimental design for dealing with headaches brought on by stress. Stress events are the only unchanging factor in our study, however they do cause changes in the frequency of headaches. The degree of headaches, which fluctuates when the independent variable is changed, can be thought of as the dependent variable. Here, the technique can be applied as follows: Informed consent is obtained from a sample of 400 persons, all of whom fall within the age range of 25 to 40 (to lessen the impact of any auxiliary variables on the results). The volunteers are divided into two groups at random, one of which is the experimental group and the other the control group (double-blind design to avoid any potential biases). Three times a day, participants in the experimental group are exposed to a show that is heavy on the negative feelings that can lead to stress; in contrast, individuals in the control group are not exposed to any of the shows mentioned above. Then, the presence of headaches is assessed in both groups' members.

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Answer:

lol

Step-by-step explanation:

that sucks

The standard form of the equation of the quadratic function is y = -1/8x^2 + 1/4x - 41/8

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

(h, k) = (1, -5)

(x, y) = (5, -7)

A quadratic function is represented as

y = a(x - h)^2 + k

So, we have

y = a(x - 1)^2 - 5

Given that

(x, y) = (5, -7)

We have

-7 = a(5 - 1)^2 - 5

This gives

16a = -2

So, we have

a = -1/8

Recall that

y = a(x - 1)^2 - 5

So, we have

y = -1/8(x - 1)^2 - 5

Expand

y = -1/8(x^2 - 2x + 1) - 5

This gives

y = -1/8x^2 + 1/4x - 41/8

So, the required equation is y = -1/8x^2 + 1/4x - 41/8

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Answer:

(-1, 2)

Step-by-step explanation:

The solution to a system of equation will always intersect on a graph, which means that at a certain point, they will have the same x and y coordinate.

As we can see from the table, for both f(x) and g(x) when x = -1, y = 2, which is the intersection point.