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What is the y-intercept of the line?

0
1
1/2
-2

Given a system of two equations in two variables, solve using the substitution method.

Word problems that require us to write systems of linear equations have two unknown quantities and two different ways to relate them.

This means we need to write two linear equations, and each contains the two unknowns as variables. The Understanding linear relationships lesson details how to translate verbal descriptions into equations.

After we write the equations, we can solve the system using our preferred method(s) for solving systems of linear equations covered in the Solving systems of linear equations lesson.

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Answer:

3/7

Step-by-step explanation:

[tex]g(-2)=\log_{2}(1)-4=-4 \\ \\ g(5)=\log_{2}(8)-4=-1 \\ \\ \frac{g(5)-g(-2)}{5-(-2)}=\frac{-1-(-4)}{5-(-2)}=\frac{3}{7}[/tex]

The vertex form of our quadratic equation is:

y = (x - 5)^2 - 4

A quadratic equation with a vertex (h, k) and a leading coefficient a is:

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

We know that the quadratic function has roots of 3 and 7, then if the leading coefficient is a, we can write:

f(x) = a*(x - 3)*(x - 7)

We also know that it passes through the point (1, 12), then:

12 = a*(1 - 3)*(1 - 7)

12 = a*(-2)*(-6)

12 = a*12

12/12 = a

1 = a

Then the quadratic is:

y = (x - 3)*(x - 7)

Expanding that we get:

y = x^2 - 3x - 7x + 21

y = x^2 - 10x + 21

The x-value of the vertex is halfway between the two roots:

x' = (3 + 7)/2 = 5

So evaluating in x = 5 we get:

y = (5)2 - 10*5 + 21

y = 25 - 50 + 21 = -4

The vertex is (5, -4), then the vertex form is:

y = (x - 5)^2 - 4

The correct option is the last one.

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Answer:

f(x) = (x − 5)2 − 4

Step-by-step explanation:

i got it right on my quiz

The vertex of the graph of f(x) = 2x² + 8x - 3 is (-2, -11). It lies in the third quadrant.

Therefore the answer is (-2, -11).

Simplifying the given graph to the form f(x) = a(x - h)² + k

f(x) = 2x² + 8x - 3

f(x) = 2×(x² + 4x) - 3

f(x) = 2×(x² + 4x + 4) - 3 - 2×4

f(x) = 2×(x + 2)² - 11

So f(x) = 2x² + 8x - 3 is symmetrical about the line x = -2. At x = -2, y = -11.

Therefore, the vertex of the graph is (-2, -11).

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = 2x² + 8x - 3?"

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Answer: 56 – 41 = 15

Step-by-step explanation:

Answer: Part A: 994 feet higher thanks to absolute value.

Part B: -86 feet.

Step-by-step explanation: math

For solving algebra Determine the issue, Describe your knowledge, Plan beforehand, Execute the plan ,and Check to see whether the response makes sense.

One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is, roughly speaking, the study of mathematical symbols and the rules for using these symbols in formulae. With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems. We employ integers that have a fixed or definite value in algebra, such as 2, 7, 0.068, etc. In addition to using numbers, algebra also makes use of variables like x, y, and z.

to do algebra for beginners - Determine the issue, specify your knowledge, Plan, execute, and confirm that the solution makes sense.

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The name of the condition in which factors f and g are correlated and may not be independent is confounded

What is  Fractional factorial?

In statistics, fractional factorial designs are experimental layouts made up of a carefully selected subset of full factorial design's experimental runs.

In a fractional factorial experiment, confounded factors are those that cannot be varied independently of each other because they are correlated. Confounded factors can affect the interpretation of the results of the experiment, as it may not be clear which factor is responsible for a particular effect. To control for confounded factors, it may be necessary to include them both in the experimental design or to use additional statistical techniques to account for their correlated nature.

Confounded factors are also known as aliased factors.

Hence, Name of the condition in which factors f and g are correlated and may not be independent is confounded

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Constant, variable, operator and terms are four types of expression.

A constant term in mathematics is a term in an algebraic expression whose value is fixed or cannot change since it lacks any variables that may be changed. As the component is not yet included in the new term, a constant term that has a constant applied as a multiplicative coefficient likewise indicates a constant term. The term identify themselves as constants because the phrase has been modified. 5 is a constant term, in the quadratic polynomial 2x^2 + 5.

Yes, negative sign have nothing to do with the definition of constant. -4 is still a constant.

There are four types of expression in mathematics:

1. Constant: any numeric value e.g. 6

2. Variable: any alphabetic/unknow value e.g. x,y etc.

3. Operators: +,-, *, / (addition, subtraction, division, multiplication)

4. Term: it can be constant, variable, constant multiplied by variable. It is separated by an operator.

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The value of c in the given convex polygon is 2°

What is the sum of interior angles of a convex polygon?

If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = (n −2) × 180°

According to the given question:

Number of sides in the given polygon n = 5

Therefore, sum of interior angles of the polygon S = (n -2 ) x 180°

S = (5 -2) x 180°

S = 3 x 180°

S = 540°

Now to find the value of c we can simply add all the interior angles given in the figure and equate it to S

Hence,

136° + 119° + 147° + 48° + 45c = 540°

                            450° + 45c = 540°

                                        45c = 90°

                                            c = 2°

So the value of c is 2°

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The two triangles are similar if all three sides of one triangle are in proportion to the three sides of another triangle.

SSS, which stands for "side, side, side," denotes that we have two triangles with the same number of sides on each pair of corresponding sides. Two triangles are comparable if they have three pairs of sides that are in the same ratio. According to the SSS test for triangle similarity, two triangles are considered similar if their third sides are proportionate to one another.

In our daily lives, the idea of comparable triangles is really useful. By measuring the shadows' lengths and then utilizing triangles that are comparable to them, we can determine an object's height, such as the height of a building or a tower. Compare the shortest sides first, followed by the longest sides, when applying the SSS Similarity Theorem. Two triangles are similar if their corresponding side lengths are proportionate to one another.

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Answer:

Step-by-step explain

∛12↔3³≈4x↑

The probability of selecting a number greater than 19 from 1 to 25 is 6/25 or 0.24.

The probabilities of an event occurring are defined by probability.

The ratio of favorable outcomes to all possible outcomes of an event is known as probability.

The formula for the Probability of an event is given by

Probability(Event) = Favorable Outcomes/Total Outcomes

Here we have

The set of numbers is from 1 to 25

Total number of numbers from 1 to 25 = 25

In given set of numbers, the number which is greater than 19 are

=> 20, 21, 22, 23, 24, and 25.

The number of favorable outcomes (getting a number, > 19 ) = 6

From the above information,

Probability of selecting a number greater than 19 = 6/25 = 0.24

Therefore,

The probability of selecting a number greater than 19 from 1 to 25 is 6/25 or 0.24

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The graph of the function is illustrated below and the domain of the function is [-2, 2].

The term domain in math is referred as the set of all inputs of the function

Here we have to find and sketch the domain of the function f(x, y, z) = ln(64 − 4x² − 16y² − z²)

In order to sketch the function, we have to use the graphing calculator, and following the listed steps to sketch the graph.

The first step is to label the graph with appropriate axis like x, y, and z.

Now we have to input the function f(x, y, z) = ln(64 − 4x² − 16y² − z²) on the input field and then click on generate.

Now, we get the graph for the function.

After that we have to adjust the limit for the given graph.

Then we finally get the resulting graph as follows.

As per the definition of domain, and with the help of the given graph, we have identified the value of the domain is [-2, 2].

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Answer:

Step-by-step explanation:

To find the area of the base of the box, we need to determine the length, breadth, and height of the box. We can set up a system of equations to represent the given information:

breadth = 2/3 * length

height = 1/3 * length

volume = length * breadth * height

Substituting the second equation into the third equation, we get:

volume = length * breadth * (1/3 * length)

      = length^2 * (2/3) * (1/3)

      = (2/9) * length^2

      = 48

      = 2^4 * 3

Solving for length, we find that length = 6. Plugging this value back into the first equation, we find that breadth = 4.

Therefore, the area of the base of the box is length * breadth = 6 * 4 = 24 square meters.

Answer:

Step-by-step explanation:

it is actually in the textbook pg 119

The required property that will change with the addition of values in the set will change the mean, median, and mode, While multiplication changes the standard deviation and also the mean by constant.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Each of the statistic properties will change by adding the number to each number in the set, except properties such as standard deviation and variance. While multiplying the set element with a number each and every property of the statistic corresponding to the set will change.

Thus, Options A, B, and D are correct.

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r stands for the Pearson correlation coefficient, which measures the strength and direction of the linear relationship between two variables. p stands for the critical value for the correlation coefficient, which is used to determine the significance of the correlation coefficient.

The Pearson correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. The correlation coefficient is a good way to determine the strength of the relationship between two variables.The critical value for the correlation coefficient (p) is used to determine the significance of the correlation. It is determined by the sample size, the number of variables being correlated, and the level of significance. The lower the P value, the more significant the correlation is. If the P value is below the chosen level of significance, then the correlation is considered statistically significant.In conclusion, r is the Pearson correlation coefficient and p is the critical value for the correlation coefficient. R measures the strength and direction of the linear relationship between two variables, while P indicates the significance of the correlation. Both measures are important when assessing the relationship between two variables.

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A slope of 5 indicates that the corresponding y varies by 5 units for every unit change in x

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.

Given:

The slope of 5.

Think of a slope of 5, which entails climbing 5 steps for each step you take. Much more quickly, you ascend to the top.

The slope is a measurement that indicates how much y shifts when x shifts.

For instance, a slope of 5 indicates that the corresponding y varies by 5 units for every unit change in x.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Therefore, think of a slope of 5, which entails climbing 5 steps for each step you take. Much more quickly, you ascend to the top.

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The result of the each of the following set is

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

The given values are

A = {1, 3, 5, 7, 9}

B = {3, 6, 9}

C = {2, 4, 6, 8}

Then find the each given terms in set roaster notation

Union of the set, intersection of the set  and the difference of the set are the basic operations of set

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

Therefore, all the given terms has been found

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Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. the missing lengths of HF is 4 and missing length PR =84.

What are Similar Triangles?

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Triangle QRS is similar to triangle FGH.

Let us find the length of unknown side.

By comparing the sides.

SR/QR=HF/HG

8/14 = x/7

Apply cross multiplication

14x = 56

Divide both sides by 14

x = 56/14

x = 4

HF = 4

8)

By properties of triangle we have

QP/BP=PR/PC

56/24= x/36

Apply cross multiplication

24x = 2016

Divide both sides by 24

x = 2016/24

x = 84

PR = 84

Hence the missing lengths of HF is 4 and missing length PR =84.

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The survey reports that 80%, percent actively observed mammals = 0.4246

Given that,

The 2011 national survey of fishing, hunting, and wildlife-associated recreation, there were over 71 million wildlife watchers in the us.

The survey reports that 80%, percent actively.

A simple random sample of only 500 wildlife watchers.

Following are the solution to the given question:

By using the approximation of normal for the proportions so, the values:  

P ( p⁻ < p ) = P ( Z < ( p⁻ - p ) / [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

So,

P ( 0.79 < p⁻ < 0.81 ) = P ( p⁻ < 0.81 ) - P ( p⁻ < 0.79 )

= P ( Z < (0.81-0.80) / [tex]\sqrt{\frac{0.80(1-0.80)}{500} }[/tex] ) - P ( Z < (0.79-0.80) / [tex]\sqrt{\frac{0.80(1-0.80)}{500} }[/tex] )

=  P ( Z < 0.56 ) - P ( Z < -0.56 )

= 0.7123 - 0.2877 (using the Z table )

P ( 0.79 < p⁻ < 0.81 ) = 0.4246

Therefore,

The survey reports that 80%, percent actively observed mammals = 0.4246

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There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS (side, side, side)-If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side) -If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle)-If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side)-If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg)

This one applies only to right angle triangles

From the figure,

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

It doesn't matter which leg since the triangles could be rotated.

For example: From fig(2)

is congruent to fig(3)

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

The additional information need to know in order to prove the two triangles congruent using HL is the hypotenuses to be congruent.

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Simplification of the given numbers  (1.1)^ 10000 or 1000 gives

(1.1)^ 10000 is larger number than 1000.

As given in the question,

Given two numbers are:

(1.1)^ 10000  and 1000

Simplify the numbers to get the larger number we have,

Apply Binomial theorem in the expression   (1.1)^ 10000

( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +.....+ ⁿCₙa⁰bⁿ

(1.1)¹⁰⁰⁰⁰

= ( 1 + 0.1)¹⁰⁰⁰⁰

Here a = 1, b = 0.1 and n= 10000

( 1 + 0.1)¹⁰⁰⁰⁰

=¹⁰⁰⁰⁰C₀1¹⁰⁰⁰⁰(0.1)⁰ + ¹⁰⁰⁰⁰C₁1¹⁰⁰⁰⁰⁻¹(0.1)¹ + ¹⁰⁰⁰⁰C₂1¹⁰⁰⁰⁰⁻²(0.1)² +..........+ ¹⁰⁰⁰⁰C₁₀₀₀₀1⁰(0.1)¹⁰⁰⁰⁰

= 1 + 1000+......

= 1001+ ....

> 1000

Therefore, from the given numbers (1.1)^ 10000 or 1000 the larger number is (1.1)^ 10000 compare to 1000.

The above question is incomplete , the complete question is :

Which number is larger (1.1)^ 10000 or 1000?

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The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.

The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.

example;

If f(x)=1/4x+7 and x=3, then

f(3) = (1/4)3 + 7

7.75

The inverse of f is f^-1(x) = (x + 7) / 4.

If f^-1(7.75) = (7.75 + 7) / 4, then

f^-1(7.75) = 14.75 / 4

3.6875

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Answer:

4

Step-by-step explanation:

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.

The square root of 16 is 4, because 4 x 4 = 16. Therefore, the value of the square root of 16 is 4.

Answer:

D

Step-by-step explanation:

It can't be A or B because those graphs are positive, and our graph is negative.

It can't be C because there is a point at (2,-5), but we don't see that point on this graph!

So, the answer is D

Answer:

d

Step-by-step explanation:

f(x) = \sqrt{x+2} - 5

Answer:

Flax: 80 acres

Sunflowers: 160 acres

Step-by-step explanation:

Let's

x = acres of flax

y = acres of sunflowers

We have the equations:

x + y = 240

y = x + 80

Let's do it in standard form

x + y = 240

x - y = -80

2x = 160

x = 80 acres

Now put 80 back in the equation to find sunflowers

80 + y = 240

y = 160 acres

So, 80 acres of flax and 160 acres of sunflowers!

Answer:

3

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Scalar projection}\\\\Scalar projection $=\dfrac{u \cdot v}{|u|}$\\\\where:\\ \phantom{ww}$\bullet$ $u$ is the vector being projected onto.\\\end{minipage}}[/tex]

Given:

Calculate the magnitude of vector u:

[tex]\implies |u|=\sqrt{(0)^2+(-1)^2}=1[/tex]

The scalar projection is the magnitude of the vector projection.

Therefore, the magnitude of the projection of vector v onto vector u is:

[tex]\implies \dfrac{u \cdot v}{|u|}=\dfrac{\langle0, -1\rangle \cdot \langle-5, -3\rangle}{1}=\dfrac{0 +3}{1}=\dfrac{3}{1}=3[/tex]