What are the equations of the lines with the given slope and y-intercept
1. Slope:2, y-intercept: -3
2. Slope: 4, y-intercept: -2

Answer and Step-by-step explanation:

For question A)

ABC is similar to PQR because of the AA similarity postulate. This postulate states that if any two angles in a triangle are congruent to the other two angles in a triangle, then the triangles are similar.

For question B)

The area would be k times more than the area of ABC.

The area of a triangle is bh/2, or base times height, divided by 2.

And since they both have 4, the one with the k will be k times greater.

Hopefully this helps!!

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Answer:

Step-by-step explanation:

(a) As per the diagram, the triangles are similar.

ΔABC ~ ΔPQR as per AA similarity postulate (two congruent angles)

(b) The area is the product of two dimensions. Area of ΔABC

Since each side of ΔPQR is k times greater than corresponding sides of ΔABC, the base and height will be both k times greater.

So the area of ΔPQR will be:

The area of PQR is k² times greater than the area of ΔABC

Table of trigonometric function values for y = sin(x) using multiples of π/4 for x:

x | y

0 | 0

π/4 | \(\sqrt2/2\)

π/2 | 1

3π/4 | \(\sqrt2/2\)

π | 0

5π/4 | -\(\sqrt2/2\)

3π/2 | -1

7π/4 | -\(\sqrt2/2\)

2π | 0

The table above shows the values of x and the corresponding values of y for the function y = sin(x), where x takes multiples of π/4.

To calculate the values of y, we substitute each value of x into the equation \(y = sin(x)\) and evaluate it. The sine function represents the ratio of the length of the side opposite the angle to the hypotenuse in a right triangle.

For x = 0, sin(0) = 0.

At x = π/4, sin(π/4) = \(\sqrt2/2\).

For x = π/2, sin(π/2) = 1.

As x progresses through 3π/4 and π, the values of y repeat but with opposite signs.

At x = 5π/4, sin(5π/4) = -\(\sqrt2/2\). , and

at x = 3π/2, sin(3π/2) = -1.

Finally, at x = 7π/4 and 2π, the values of y repeat the same as at x = π/4 and 0, respectively.

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The expression that will work to find the z in the figure provided is 7(sin(30°)) using the concept of SOH-CAH-TOA. We use SOH here anyways.

The three primary trigonometric functions are:

It is from the above trigonometric functions that we form the SOH-CAH-TOA. Below shows what each of them stands for:

These three ratios are used to calculate the lengths of the sides of a right triangle when one angle and the length of one side are known. For example, if we know the length of the hypotenuse and one of the acute angles in a right triangle, we can use SOH CAH TOA to find the lengths of the other two sides.

To use SOH CAH TOA, you identify which ratio you need based on the information given in the problem, then plug in the values and solve for the missing side or angle.

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Answer:

4791.7

Step-by-step explanation:

This would make a right triangle. Use the Pythagorean theorem to solve.

X = sqrt(14^2+ 3^2)

X = sqrt( 196 + 9)

X = sqrt(205)

X = 14.3178

Rounded = 14.3 miles

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

-4

Step-by-step explanation:

Ok so you get two sets of proportional pairs: -3 and -1 , and -30 and -10.

The relationship between these is that the first term is 3 times the second. So you divide the first term by 3 to get the second.

So you divide -12 by 3 to get -4.

Hope this helps!

Answer:

-4 (*/ω＼*)

Step-by-step explanation:

Answer:

-45

Step-by-step explanation:

9*(-5)=-45

Answer:

-45

Step-by-step explanation:

x÷9= -5

multiply

answe is -45

========================================================

Reason:

Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".

It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.

Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.

Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)

As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4

Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.

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

Here's another way to look at it:

The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.

This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4

Each is spin is independent of any other.

The response variable in this study is the exam performance of the students.

The response variable is the main outcome measure of interest in a study. In this case, the researcher is interested in testing the effect of light level on the exam performance of students, which is the response variable. The researcher is also concerned about the potential differences in the effect of light levels between men and women, so wants to ensure that both groups are equally represented in each treatment.

By measuring the exam performance of the students under different lighting conditions, the researcher can determine whether light levels have a significant impact on exam performance and whether this effect differs between men and women.

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Answer:

13.75

Step-by-step explanation:

6.25+7.50=13.75

Answer:

$11.05

Step-by-step explanation:

The hot dog is $3.55, and the cheeseburger is $7.50. Thus, adding them together, the whole total is $11.05.

Hope this helps

Answer:

12 pounds of Kenyan French Roast coffee

8 pounds of Sumatran coffee

Step-by-step explanation:

if you use x pounds of Kenyan French Roast coffee and y pounds of Sumatran coffee then you know that

11x + 10y = 10.6 * 20

x+y=20

10x+10y=200

11x+10y=212

x=12

y = 20-x = 20-12 = 8

so you want to use

12 pounds of Kenyan French Roast coffee

8 pounds of Sumatran coffee

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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A right square pyramid formed by the junction of the solid would have a square-shaped cross section.

This is thus because a square pyramid has four triangular sides that meet at a shared vertex on its square base. The cross section of a pyramid formed when a plane meets it parallel to the base and perpendicular to one of the triangular sides is a square. Because the pyramid's base is square, the intersecting plane will cut all four of the triangle faces at the same distance from the peak, giving the pyramid a square shape.

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Answer

The missing value is 4/9

When you multiply a negative number by another negative number, the result is always a positive number.

This rule is based on the properties of multiplication and the concept of negative numbers.

When two negatives are multiplied, the negative signs "cancel out" each other. Mathematically, if you have -a multiplied by -b, where a and b are positive values, the result is given by ab.

For example, if you multiply -2 by -3, the product is 6, which is a positive number. This can be explained by the idea that multiplying two numbers with opposite signs results in a negative product, while multiplying two numbers with the same sign (both negative) produces a positive product.

Therefore, when you multiply a negative by a negative, the outcome is a positive number.

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Answer:

Step-by-step explanation:

Let's call the first number x.

We can write an equation representing the problem using x:

x+x+20=200 (because the second number is 20 more than the first, or x)

Combine like terms: 2x+20=200

Subtract 20 from each side of the equation: 2x=180

Divide by 2: x=90

The first number is 90, the second number is 110.

Hope this helps!

The length and width of the piece of​ metal are 28 and 18 inches respectively.

What is volume?

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Dimension of the rectangle;

Width(w)

Length,L= 10 + w

volume of the box = length  * width * height

Dimension of the box;

length of box, (x + 10) - 4  = x + 6

width of box,(x - 4)

height of box =  2

The volume of the box is 672 in³;

⇒V=lwh

⇒V=2 (x -4)( x + 6)

⇒672 in³ = 2x² + 4x - 48

⇒2x² + 4x - 720 = 0

⇒x^2  + 2x - 360 = 0

⇒(x +20)(x - 18) = 0

⇒x = 18

⇒x=-20 (value of the dimension will not be negative.

The width of an original piece of metal is;

Width,w=18 inches

length,l= 28 inches

Hence. the length and width of the piece of​ metal are 28 and 18 inches respectively.

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The correct option is, there is a main effect for Factor A but there is no interaction.

What is two factor anova?

The mean of a quantitative The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the levels of two categorical variables.

Two-way analysis of variance is an extension of one-way analysis of variance in statistics that looks at the impact of two different categorical independent variables on a single continuous dependent variable.

The parallel lines indicates no interaction effect.

For the above problem option 'a' is correct.

There is a main effect for Factor A but there is no interaction

Hence, the correct option is, there is a main effect for Factor A but there is no interaction.

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Complete question:

A two-factor ANOVA is conducted and the data are plotted. The chart shows two parallel lines separated by a distance of 9 points. The lines represent Factor A and the x axis of the chart represents the levels of Factor B. How should you interpret these results?

Select one:

a. There is a main effect for Factor A but there is no interaction

b. There is a main effect for Factor A and there is also an interaction effect

c. There is a main effect for Factor B and there is an interaction effect

d. There is no interaction effect and no main effects

The measure of the long -run average value of a random variable used to represent the central location of a probability distribution is called an expected value E(x).

As given in the question,

Reason with explanation :

Therefore, the measure of the long run average value of a random variable representing central location of the probability distribution is called the expected value.

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The volume of the large emerald is 294.22 cubic centimeters.

The density of any given substance or an object is defined as the ratio of its mass to its volume. This can be expressed as:

Density = Mass/ Volume

Considering the parameters given in the question, we have;

mass = 812.04 grams, density = 2.76 grams/ cubic centimeters

Thus,

density = mass/ volume

So that;

volume = mass/ density

            = 812.04/ 2.76

            = 294.22

volume = 294.22 cubic centimeters

The volume of the large emerald is 294.22 cubic centimeters.

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The distribution of weight is based on a continuous random variable.

What is Continuous Random Variable?

In statistics, a continuous random variable can take on any value within a certain range, as opposed to a discrete variable, which can only take on a finite number of values.

Qualitative variables are categorical variables that do not have a numerical value, but instead represent characteristics or qualities of a population or sample.

Therefore, the weight of an offensive linesman is an example of a continuous random variable.

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The third side should have a length of 16 inches.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have two sides of lengths 7 and 10 inches.

Let's denote the length of the third side as x.

Therefore, the third side should have a length of 7 + 10 - 1 = 16 inches.

By setting the third side to be 16 inches, we ensure that the triangle is degenerate (a straight line) and the area is maximized.

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There is no success probability for which the first success is most likely to occur on the fourth attempt.

Assuming the success probability of an experiment is p and the number of trials until the first success occurs is denoted by X, X follows a geometric distribution with the probability mass function P(X=k) = (1-p)^(k-1) * p, where k is the number of trials until the first success occurs.

Given that the first success occurs on the 4th attempt, P(X=4) is maximum when p is maximum. To find the value of p, we need to maximize the function P(X=4), which can be represented by (1 - p)^(3) * p.

Differentiating this function with respect to p, we get d[P(X=4)]/dp = -3(1 - p)^(2) * p + (1 - p)^(3).

Equating the above equation to zero, we get -3(1 - p)^(2) * p + (1 - p)^(3) = 0, which further leads to (1 - p)^(2)[(1 - p) + 3p] = 0 and (1 - p)^(2)(1 + 2p) = 0.

Since (1 - p)^(2) > 0, the solution is given by: 1 + 2p = 0, which results in p = -1/2.

However, the probability of success cannot be negative. Therefore, p cannot be equal to -1/2. Hence, there is no success probability for which the first success is most likely to occur on the fourth attempt.

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Given a table represents the class 8 attendance

We need to find the median of the data set, so we will arrange the data in order from the least to the greatest as follows:

20 , 21 , 24 , 25 , 25

The number of data = 5

So, the median will be the data number = (5+1)/2 = 6/2 = 3

so, the median of the dat = 24

The solution to the logarithm equation is log5(2x-7) = 0 is x = 4.

What is logarithm ?

A logarithm is a mathematical function that represents the exponent to which a fixed number, called the base, must be raised to produce a given value. In other words, a logarithm is the inverse operation of exponentiation.

For example, if we have the equation \(10^3 = 1000\), the logarithm of 1000 with base 10 is 3, because \(10^3 = 1000\). Similarly, the logarithm of 8 with base 2 is 3, because \(2^3 = 8.\)

According to the question:

To solve for x in the equation:

log5(2x-7) = 0

We can use the definition of logarithms which states that log_b(x) = y is equivalent to \(b^y = x.\)

Applying this to the given equation, we get:

\(5^0 = 2x - 7\)

\(1 = 2x - 7\)

\(2x = 8\)

\(x = 4\)

Therefore, the solution to the equation is log5(2x-7) = 0 is x = 4.

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Answer:

The average temp was 4

Step-by-step explanation:

Answer: <D, < E, <C

Step-by-step explanation: