The graph below shows triangle L’M’N’ , after a 90 counterclockwise rotation about the origin. What were the coordinates of pre-image point L ? A. (-8,5) B. (-5,8) C. (5,-8) D. (8,-5)

This image shows two similar triangles, which can be expressed as:

in which K is the constant of similarity, this can be obtain by making the proportion on 2 sets of corresponding sides.

solve the relationship for x

Now this 21 is the corresponding measurement of the side in the smaller triangle, however the questions ask for the portion thats between the vertex at the top and the vertex at the top for the smaller triangle, to find this measurement we find the difference between the sides.

The missing length is 28.

To calculate the margin of error, we use the formula:

So, we got n, the number of students, sigma, the standard deviation, and gamma, the confidence level. z for 95% is 1.64, so:

So, the margin of error goes from mean - 267 to mean + 267:

the first and third quartile are represented as the sides of the box. The left side is the first quartile and the right side is the third quartile.

In this case, the left side of the box is located at 9, thus, the third quartile is 9

Solution

Step 1:

Write the two equations:

2x + 3y = 12

2x + y = 6

2x = 6 - y

Answer

The first step in solving by substitution would be to solve the second equation for x, since the coefficient is 2.

First

y = 6 - 2x

y = 3

Find the frequency of each class:

11-15:

Data: 11,14,13

Frequency: 3

16-20:

Data: 16,19,20,17

Frequency: 4

21-25:

Data: 24,22

Frequency: 2

26-30:

Data: 29

Frequency: 1

31-35:

Data: 32,31

Frequency: 2

Then, the histogram that represents the given data is:

Given:

Answer:

The solution to the problem is;

Explanation:

Applying GEMDAS;

Grouping comes first (bracket)

We need to first solve the grouped operations.

GEMDAS means; Grouping, Exponent, Multiplication, Division, Addition and Subtraction Order of operations.

Therefore, the solution to the problem is;

What is the common denominator of 13/14 and 9/10

Remember that

14=2*7

10=2*5

so

Calculate LCM, the least common multiple of the denominators of the fractions

LCM=2*5*7=70

the answer is 70

We want to graph the compound inequality below on the number line;

We can show the inequality on the number line below;

The shaded dot on 8 is because of the less than or equal to sign,

hello

the question given is to find an expression that's equivalent to the exponent of 3^3

now we just simply look for another way to write 3^3 to give 27

the answer to the question is 3*3*3

b)

the number of factors of three here is one

In this problem, we have an exponential growth function of the form

where

a=500

r=0.7

substitute

For x=6 days

substitute

therefore

The system of equations that we have are:

3x - 2y = -8 ________(1)

y = 3/2x - 2 ________(2)

Multiply both sides in (2) by 2x:

=> 2xy = 3 - 4x ______(3)

From (1), make y the subject of the formula:

3x + 8 = 2y

=> y = 3x/2 + 4

Put this into (3):

2x(3x/2 + 4) = 3 - 4x

Open the bracket:

Collect like terms:

We

Explanation

Exponential decay function describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula

Step 1

a)

Let

b) now, replace in the formula

therefore, the answer is

Blank: 925

I hope this helps you

The value of Cos A is postive in fourth quadrant , Cos A=5/[tex]\sqrt{61}[/tex]

Here we can solve the problem using  the Pythagoras theorem . Hence we draw triangle with  the details given in the question.

It is given  that A is lying  in IV quadrant . So that Sin A is less than zero and thus Cos A will be positive value.

As the value of sinθ= -6/[tex]\sqrt{61}[/tex]=Altitude/ Hypotenuse . Thus here with the help of Pythagoras theorem  we can solve the problem.

That is ,

[tex]Base^{2} =Hypotenuse ^{2} -Altittude ^{2} \\B^{2} =\sqrt{61}^{2} -36\\B= \sqrt{25}=5[/tex]

We know that Base\Hypotenuse =Cos A. Which is positive and in fourth quadrant .

Thus we get answer as Cos A=5/[tex]\sqrt{61}[/tex]

To know more about Pythagoras theorem here:

https://brainly.in/question/2829237

#SPJ1

Explanation

Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution, in a set of data.

There are two main things that make a distribution skewed left: The mean is to the left of the peak. This is the main definition behind “skewness”, which is technically a measure of the distribution of values around the mean. The tail is longer on the left.

A "skewed right" distribution is one in which the tail is on the right side. A "skewed left" distribution is one in which the tail is on the left side. The above histogram is for a distribution that is skewed right.

From the given question

Part B

Since the answer to part A is option C

We can infer from the definition above that the tail is on the right-hand side

Therefore, It is Right-Skewed.

EXPLANATION

Given the line in the graph, in order to find the slope, we must apply the following relationship:

Now, we need at least two ordered pairs to get the slope.

Let's consider (x1,y1)=(0,-6) and (x2,y2)=(6,-2)

Then, replacing into the equation:

So, the slope is 2/3

this is a 2x2 system of equations.

Let:

-2x = 4y + 6 (1)

and

2(2y+3) = 3x - 5 (2)

Let's rewrite (1) as:

2x + 4y = -6 (1)

and (2) as:

3x - 4y = 11 (2)

Now, from (1)

Let's solve for x:

2x + 4y = -6

Subtract 4y from both sides:

2x + 4y - 4y = -6 - 4y

2x = -6 - 4y

Divide both sides by 2:

2x/2 = (-6 - 4y)/2

x = -3 - 2y (3)

Replacing (3) into (2)

3x - 4y = 11

3(-3 - 2y) - 4y = 11

Using distributive property:

-9 - 6y - 4y = 11

Add like terms:

-10y - 9 = 11

Add 9 to both sides:

-10y - 9 + 9 = 11 + 9

-10y = 20

Divide both sides by -10:

(-10y)/-10 = 20/-10

y = -2

Finally, replace the value of y into (3)

x = -3 - 2y

x = -3 - 2(-2)

x = -3 + 4

x = 1

Therefore the solution is :

x= 1 and y=-2

(x,y) = (1,-2)

The probability of choosing a coin that is worth at leas 10 cents is:

then the probability of obtaining a penny is:

Then the probability to obtain a coin of at least 10 cents and then a penny is:

Which of these expressions CANNOT be simplified by combining like terms?

The answer:

to simplify the terms , the terms must be similar like ab and 3ab the result will be 4ab.

So for our giving options:

1) 5ab3 +7 - 3a²b2 + a'b – 10

2) 5ab3 + 3a2b2 + ab - 10

3) 5ab3 + 3a2b2 + a363 - 10ab

4) 5ab3 + 26(3ab2) + a’b – 10​

so, as shown at the options:

option 1) Can be simplified to 5ab3 - 3a²b2 + a'b – 3

becuse it has only two like terms {7 - 10}

Option 2) CANNOT be simplified

Becuse, it is not contain like terms

Option 3) CANNOT be simplified

Becuse, it is not contain like terms

Option 4) CANNOT be simplified

Becuse, it is not contain like terms

So, the answer is all: All expressions CANNOT be simplified by combining like terms except the first expressions.

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The ratio of their perimeters is the same ratio between corresponding sides.

Looking at the image, the side ST corresponds to the side BC.

Calculating their ratio, we have:

So the ratio of their perimeters is 3 : 2

Solution

Given the equilateral triangle ABC;

The following are the numbers of right triangles:

There are 12 right triangles in the diagram.

Solution

A solution to a system of linear equations is the point of intersection of both lines when graphed.

Parallel lines do not ever cross so there are zero solutions.

However, there could be a chance that there is a solution because often, the equation of two lines that look parallel are actually the same line, in which case the system will produce an infinite number of solutions.

The way to be sure is just to pick an x value randomly and put it in both equations and see if the answers are equal. If it is really two parallel lines, they will not be equal otherwise, they will be equal.

Hence from the graph, we will first get the equation for both lines

Line 1

For line 2

So picking a random value of x= -1

we will have

Since both values of y using a constant random value of x gives us different answers, the lines, therefore, are not images of each other and the system has no solution.

Final answer------ No solution

we have

step 1

Multiply by 2 both sides

step 2

Group terms

Combine like terms

divide by 2 both sides

Verify

substitute the value of x in the original expression

is ok

the value of x satisfy the equation

The relative frequency can be calculated using the formula:

The completed table can be shown below:

This is a sample calculation of the relative frequency:

(b) The class 121-160 list the data values that are in the third class of your frequency distribution table

(c) The data value 99 falls in the 81-120 class

Because the number is multiplied by 10 to the power of 3, it becomes times 1000. Also you move three numbers in front of the decimal starting with the number 2 (the first behind the decimal) and then followed by 2 zeros

We define the following events:

• A = a person aged 25 years or older is male,

• B = a person aged 25 years or older is a smoker,

• A | B = a person aged 25 years or older is male, ,given, that he or she smokes,

• A ∩ B = a person aged 25 years or older is male ,and, he or she smokes.

From the statement of the problem, we know that:

1) there is a 16.6% probability that a randomly selected person aged 25 years or older is a smoker, so we have:

2) there is a 17.9% probability that a randomly selected person aged 25 years or older is male, given that he or she smokes, so we have:

Now, we know that the conditional probability P(A | B) is given by:

From the last equation, we have:

Replacing the values of P(A | B) and P(B), we get:

Answer

• So the probability that a randomly selected person aged 25 years or older is male ,and, smokes is ,0.030, in decimal form to three decimal places.

• So from 100 random persons, approximately 3 will be aged 25 years or older, male and smoker. We conclude that it will be unusual to randomly select a person with those atributes.

we know that

To find out the percentage, divide the number of strikes by the total attemps, and multiply by 100

so

(14/70)(100)=20%

therefore

the answer is