What is the equation of the line in slope intercept form

The correct input to the blank of the question is given below.

What are Triangle Congruence Theorems?

If the corresponding interior angles are equal in measure and the sides of two triangles are equal in size, then the triangles are congruent.

The missing part that completes the proof is given by:

1. Given.

2. Definition of linear pair.

3. m∠ABD + m∠CBD = 180°

4. 90° + m∠CBD = 180°

6. DB ≅ DB

7. HL Congruence Theorem

Hence, these are the missing part to complete the proof.

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The equation of the ellipse in vertex form is (x - 1)² / 25 + (y + 2)² / 4 = 1.

In this question we find a representation of an ellipse with a center at point (h, k) = (1, - 2). The vertex form of the equation of the ellipse is introduced below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Please notice that the major semiaxis is parallel to the x-axis and the minor semiaxis is parallel to the y-axis.

First, write the coordinates of the center of the ellipse:

(h, k) = (1, - 2)

Second, find the lengths of the semiaxes:

Major semiaxis

a = 0.5 · [6 - (- 4)]

a = 5

Minor semiaxis

b = 0.5 · [0 - (- 4)]

b = 2

Third, write the equation of the ellipse:

(x - 1)² / 25 + (y + 2)² / 4 = 1

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An outcome of a statistical analysis is a test statistic. The null hypothesis, which claims that there is no association between the variables or difference between the sample groups, is explained by the observed data's distance from it.

Calculate the test statistic for this problem ?

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If P value < α ; Reject H0 ; otherwise, fail to reject H0

A.) Left tail , Z = - 1.32 ; α = 0.10

We can use the P value calculator from Z score :

P value = 0.934

P value > α ; Hence, we fail to reject the null, H0

B.) Right-tailed test, z = 2.46, α = 0.01

P value from Z score calculator ;

P value = 0.0069

P value < α ; Hence, we reject the null, H0

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The profit is P 12 after selling the bananas for P 2.50 each after applying the simple arithmetic.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

For the first part:

1 Peso=4 pieces of 25 centavo coins  

1 Peso=10 pieces of 10 centavo coins

Total length = 2.5 meters

1 floweret uses 5 decimeters

1 decimeter = 1/10 meters

2.5 meter in decimeter

250 decimeter

Total floweret = 250/5 = 50

Total money = 10x50 = P 500

The total cost of bananas = 18

The bananas sold = 2.50(12) = 30

Profit = 30 - 18 = P 12

Thus, the profit is P 12 after selling the bananas for P 2.50 each after applying the simple arithmetic.

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$6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.

What is annual interest rate?

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.

Invested amount = $7000

Let x be the invested amount at 6% and y be the invested amount at 8%.

According to the question,:

x+y=7000......(1)

annual interest is $430.

Therefore Interest on x + interest on y = $430

Interest=(invested amount*rate*time)/100

Here Time is 1 year.

(6*x)/100+(8*y)/100=430

This shows, 6x+8y=43000.......(2)

From equation (1), we have:

x=7000-y.........(3)

Substitute the value of x in equation (2),

6(7000-y)+8y=43000

On simplifying, y=500

Put y = 500 in equation (3)

we get x=6500

Therefore $6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.

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A linear regression equation that represents the data set is y = 39.7x + 1127.8. Also, the number of new cases for 2011 is equal to 1525 cases.

In this scenario, the Year since 2002 (x) would be plotted on the x-axis of the scatter plot while the New cases (y) would be plotted on the x-axis of the scatter plot.

From the Excel sheet, you should right click on a data point on the graph (scatter plot), select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatter plot (see attachment) which models and shows the relationship given in the table, an equation for the linear regression is given by:

y = 39.7x + 1127.8

For 2011, the value of x is given by:

x = 2011 - 2002 = 9 + 1 = 10 years.

Now, we can determine the new cases for 2011:

y = 39.7(10) + 1127.8

y = 397 + 1127.8

y = 1524.8 ≈ 1525 cases.

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Answer:

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

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

y - 3 = [tex]\frac{1}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ( add 3 to both sides )

y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form

Answer:

2

Step-by-step explanation:
because 1. is true and 3. is true

If A varies jointly as b and inversely as d then value of A when b = 9 and d = 2 is 135/2.

What is proportionality?

If A  is inversely proportional to B, this is expressed as:

A α 1/B

A = k 1/B

where k is the constant of proportionality.

According to the given question:

A varies jointly with b and inversely with d

[tex]A \alpha \frac{b}{d}[/tex]

A = k b/d where k is proportionality constant

If A = 30, b = 6 and d = 3, finding the value of k

30 = k 6/3

k = 15

Now to find A when b = 9 and d = 2, using value of k

A = 15 x 9/2

A = 135/2

Hence the value of A is 135/2.

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The mapping that represents a function is Y.

And the table with the values from the mapping.

                 X                                  Y

             (-1, 4)                              (1, 4)

             (-2, 5)                             (2, 4)

             (-2, 6)                             (3, 5)

In this question we have been given two mappings i.e., we have been given two relations.

We need to select the mapping that represents a function.

We know that a relation is a function when for every input-value there should be associated with exactly one output-value.

From given table the mappings are:

                 X                                  Y

             (-1, 4)                              (1, 4)

             (-2, 5)                             (2, 4)

             (-2, 6)                              (3, 5)

We can observe that in mapping X, for input -2 there are two outputs.

This means, the mapping X is not a function.

Therefore,  the mapping that represents a function is Y.

And the table with the values from the mapping.

                 X                                  Y

             (-1, 4)                              (1, 4)

             (-2, 5)                             (2, 4)

             (-2, 6)                              (3, 5)

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Using the formula of volume of cone, the height of the cone is 3/8.

In the given question,

We have to find the missing dimension of the cone.

Volume of cone is 1/18 pi, radius is 2/3 ft.

As we know that volume of cone is one third of the product of pi, square of radius and height.

The formula of cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

where V=Volume of cone

r=radius of cone

h=height of the cone

We know V=1/18 π, r=2/3 ft.

We don't know the value of h. So we find the value of h.

putting the value in formula

[tex]\frac{1}{18}\pi=\frac{1}{3}\pi\times\frac{4}{9}\times h[/tex]

Simplifying

[tex]\frac{1}{18}\pi=\frac{4}{27}\pi\times h[/tex]

[tex]\frac{\pi}{18}=\frac{4\pi}{27}\times h[/tex]

Multiply by 4/27π on both side

[tex]\frac{\pi}{18}\times\frac{27}{4\pi}=\frac{4\pi}{27}\times\frac{27}{4\pi}\times h[/tex]

Simplifying

[tex]\frac{1}{2}\times\frac{3}{4}=h[/tex]

Simplifying

h = 3/8

Hence, the height of the cone is 3/8.

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The equivalent function of the exponential function is (e) f(x) = 11ˣ

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

f(x) = (1/11)^-x

This function can be properly expressed as

f(x) = (1/11)⁻ˣ

Solving further, we need to apply the exponent law of indices

This is represented as

a⁻ˣ = 1/aˣ

When the above rule is applied, we have

f(x) = 1/(1/11)ˣ

Evaluate the quotient

f(x) = (11/1)ˣ

This gives

f(x) = 11ˣ

Hence, the equivalent is (e) f(x) = 11ˣ

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When the capital letter Y is rotated 180°,  Our point A(x,y) rotates 180 degrees counterclockwise around the origin to become A' (-x,-y). transforming both x and y negative is all we do as a result.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given,

The capital letter Y is rotated 180°.

The coordinates shift from (x, y) to (x, z) when you reflect a figure across the x-axis (x, -y). The coordinates would change from (x, -y) to (x, y) if you then reflected it over the y-axis (-x, -y). As a result, reflecting over the x- and y-axes will be similar to turning 180 degrees counterclockwise. Our point A(x,y) rotates 180 degrees counterclockwise around the origin to become A' (-x,-y). transforming both x and y negative is all we do as a result.

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Answer:  x= -3/7

Step-by-step explanation: If trying to find when the fish will hit the floor you know that the floor is y=0 on a graph, so you can sub in 0 for y and solve for x and that will give you the seconds the fish will swim until hitting the bottom.

The correct options to the statements will be:

All the atoms in a composite are the same - False.

One example of a composite is glass reinforced plastic - True.

The properties of a composite are a combination of the properties of the materials used to make it - True

The materials used to make composites are always arranged in layers - False.

Composite materials are created by fusing two or more materials with very different properties. The different materials work together to give the composite its unique properties, but within the composite, the different materials can be easily distinguished - they do not dissolve or blend into each other.

A composite material is made up of two materials that have distinct physical and chemical properties. When they are combined, they form a material that is specialized to perform a specific function, such as becoming stronger, lighter, or electrically resistant. They can also help to increase strength and stiffness.

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The values of t for which the ball's height is 20 feet are t = 1.64 seconds and t = 0.61 seconds

From the question, we are to determine all values of t for which the ball's height is 20 feet

From the given information,

The ball's height h (in feet) after seconds is given by the following:

h = 4 + 36t - 16t²

To determine all values of t for which the ball's height is 20 feet, we will substitute h = 20 in the equation

h = 4 + 36t - 16t²

Substitute h = 20

20 = 4 + 36t - 16t²

Rearrange

16t² - 36t + 20 - 4 = 0

16t² - 36t + 16 = 0

Divide through by 4

4t² - 9t + 4 = 0

Solve the equation quadratically

Using the quadratic formula,

t = [-b ± √(b² - 4ac)]/2a

a = 4, b = -9, and c = 4

t = [-(-9) ± √((-9)² - 4(4)(4))]/2(4)

t = [9 ± √(81 - 64)]/8

t = [9 ± √(17)]/8

t = [9 ± 4.12]/8

t = [9 + 4.12]/8 and t = [9 - 4.12]/8

t = 13.12/8 and t = 4.88/8

t = 1.64 seconds  and t = 0.61 seconds

Hence, the values of t are t = 1.64 seconds  and t = 0.61 seconds

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The value of one fourth squared times one fourth raised to the zero power end quantity all raised to the second power is 1/256.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, the exponent illustrated will be:

= (1/4^2 × 1/4^0)²

= (1/16 × 1)²

= (1/16)²

= 1/16 × 1/16

= 1/256

The value is 1 / 256.

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The point of intersection is (3,3)

What is meant by intersection?

The intersection points show where both equations have their answers. To put it another way, the intersection point is the answer to both equations. There are multiple intersecting points if there are multiple solutions that satisfy both equations.

If we plot a function, y = f(x), and its inverse, y = f1(x), we can see that the inverse function is the exact opposite of the original function with regard to y = x.

Consequently, only when y = x can both intersect as show in the fig.

Therefore A place where the lines y and x cross must be there.

Find the spot that the line y = x meets at this time.

Of course, the line y = x is satisfied at only one point, which is (3,3).

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Answer:

x = 126

Step-by-step explanation:

The angle indicated with 126° and the angle represented with (5y - 4) are alternate angles and their measures are equal so we can write the following equation to find the value of y:

5y - 4 = 126 add 4 to both sides

5y = 130 divide both sides by 5

y = 26

x and the angle indicated with 126 are also alternate angles so

x = 126

The angle represented with (5y - 4) are the angle represented with (6z + 6) are supplementary angles and their sum is equal to 180, we can write the following equation based on this information:

6z + 6 + 126 = 180 add like terms

6z + 132 = 180 subtract 132 from both sides

6z = 48 divide bot sides by 6

z = 8

The solution to the equation are as follows.

y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂                [tex]e^{\sqrt{-3 -sin²(x)x} }[/tex]

What is differential equation?

In arithmetic, a equation is associate equation that relates one or a lot of unknown functions and their derivatives.

Main body:

Find the first derivative.

dy/dx=r[tex]e^{rx}[/tex]

Find the second derivative.

d²y/dx² =r² [tex]e^{rx}[/tex]

Substitute into the differential equation.

r²[tex]e^{rx}[/tex]+4[tex]e^{rx}[/tex]=cos ²x

Factor [tex]e^{rx}[/tex]out of r²[tex]e^{rx}[/tex].

[tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]=cos²x

Factor [tex]e^{rx}[/tex] out of 4[tex]e^{rx}[/tex].

[tex]e^{rx}[/tex]r²+[tex]e^{rx}[/tex]⋅4=cos²x

Factor out of [tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]

[tex]e^{rx}[/tex](r²+4)=cos²x

Since exponentials can never be zero, divide both sides by

[tex]e^{rx}[/tex]r²+4=cos²x

Use the double-angle identity to transform

cos²x to 1−sin²(x).

r² +4=1−sin²(x)

Subtract 4 from both sides of the equation.

r²=1−sin²(x)−4

Simplify the right side.

r² = -3 -sin²x

r = √-3 -sin²x

By the principle of superposition, the general solution is a linear combination of the two solutions for a second order homogeneous linear differential equation.

y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂

Hence the differential solution is as follows.

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Answer:

2¾miles/hour or 2.75 miles/hour

Step-by-step explanation:

average speed = total distance ÷ total time

total time= 2 hours

therefore his average speed= 5½ mile ÷ 2 hours

= 2¾ miles/hour

The angle a formed at the exterior of the hexagon by a line that goes through a vertex to the center of the hexagon and a second line that touches the adjacent vertex is a = 30°

The properties of a regular hexagon includes;

There are 6 equilateral triangles in a regular hexagon

The triangle ΔOAC formed by the segment that extends into the hexagon is an equilateral triangle.

Therefore;

Triangle ΔABC is an isosceles triangle with segment AC ≅ Segment AB

Therefore;

Angle ∠C is congruent to angle ∠B (base angles of an isosceles triangle

∠C ≅ ∠B

m∠C = m∠B (definition of congruency)

m∠B = a

Therefore;

m∠C = m∠B = a

m∠C = a (substitution property)

From external angle to a triangle, postulate, we get;

m∠OAC = m∠B + m∠C

Therefore;

m∠OAC = a + a

60° = 2·a

a = 60°/2 = 30°

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The actual distance is = 162.5mi

Acc to our question-

Hence,The actual distance is = 162.5mi

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Answer:

The first step is to label the points being (1,2.3),(6,6.8) in which the first ordered pairs is the number of weeks, and the second one is the dollars in millions.

Hence, the slope is: m=(6.8-2.3)/(6-1) = 4.5/5 = 9/10 = 0.9

The slope represents the dollar rate in the millions per week. In this case, the movie grossed $0.9 million per week from week one to the sixth week.

Answer:

Step-by-step explanation:

If is a permutation group of degree, then the permutation representation of is the linear representation of which maps to the corresponding permutation matrix (here is an arbitrary field). That is, acts on by permuting the standard basis vectors.

The end behavior of the following polynomial function is option A.

The leading term of the polynomial is 20x^20, degree of f(x) = 20, and the leading coefficient is 20.

Given function:

f(x)=−2x^3+20x^20+20x^18+60x^7+9

= 20x^20+20x^18+60x^7+2x^3+9

Here the degree is 20.

Leading term = 20x^20.

Leading coefficient = 20.

The degree is even and the leading coefficient is positive so end behavior is upward parabola which is option A .

Therefore the leading term of the polynomial is 20x^20, degree of f(x) = 20, and the leading coefficient is 20.

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You will have $1,09,545.455 in the account in 20 years. An you will put total $72,000 in the account. And you will earn $37,545.455 of total interest.

Here,

We deposit $300 each month earning 4% interest compounded monthly.

we will find the future value of this amount after 20 years.

for finding future value, The general formula is

FV=PV∙(((1+i)ⁿ-1))/i

Where,

FV= future value

PV=present value

i=interest

n=time period

now, our PV=300$ and we have 4% interest compounded monthly

i.e.

i=4/100∙1/12

i=0.0033

And, the period of time is

n=20×12

n=240

Now, we will calculate the future value

FV=300 (((1+0.0033)²⁴⁰-1))/0.0033

FV=300 (((1.0033)²⁴⁰-1))/0.0033

FV=300 (((2.205)-1))/0.0033

FV=300(365.15)

FV=1,09,545.455$

Now, The total money you put into account is

total amount=300×20×12

total amount=72,000$

Total interest,

total interest=109545.455-72000

total interest=37,545.455$

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The equation that best represents the population of the town after x years is C. y = 158,000(1.07)ˣ.

An exponential equation is an equation with exponents.

Exponential equations have the exponents (or) parts of the exponent as variables.

Exponential equations are raised to the power of the indicated exponents or variables.

The population of a town = 158,000

Annual rate of increase = 7%

After x years, the population, y = 158,000 x 1.07ˣ

= 158,000(1.07)ˣ

Thus, in x years, the town's population will become the solution to equation C. 158,000(1.07)ˣ where x is the number of years after the approximation.

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Answer: 3.40687

Step-by-step explanation: 3.40687

Answer:

no it can't be proved similar