in the diagram (triangle) ABC = (triangle) PQR. Reflect (triangle) ABC across the line y = x. Describe how to map image to (triangle) PQR.

Point = (8,-4)

When coordinate points (x,y) are rotated by 90° the image became (y,-x)

So, for this case:

Image: (-4,-8)

the area of the windshield, cleaned by the windshield wiper is mathematically given as 0.096inche^2

This is further explained below.

The term "acute area of the windshield glazing" refers to the section of the windshield that measures eight and one-half inches by eleven inches and is located immediately in front of the driver's line of sight, as seen in the image.

Then, let's call the part of the windshield labeled "ABC" A.

[tex]A=\frac{1}{2} r^2 \theta[/tex]

Now, substituting the given values we get,

[tex]\begin{aligned}&A=\frac{1}{2} r^2 \theta \\&A=\frac{1}{2} \times(7)^2 \times \frac{\pi}{180} \\\end{aligned}$$[/tex]

A=0.4276

Then let the area of the windshield, ADE, be denoted by the letter A',

[tex]A^{\prime}=\frac{1}{2} r^2 \theta[/tex]

Now, after replacing those values with the ones we were provided,

[tex]\begin{aligned}&A^{\prime}=\frac{1}{2} r^2 \theta \\&A^{\prime}=\frac{1}{2} \times(1)^2 \times 60 \times \frac{\pi}{180} \\&A^{\prime}=0.5236\end{aligned}[/tex]

In conclusion, In order to calculate the area of the windshield, you need to take the difference between A and A'.

0.5236-0.4276=0.096

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ANSWER

B. 25

EXPLANATION

We want to identify the number of students that live between 1 and 1.9 miles from school.

To do this, we have check the frequency corresponding to the bar for 1 - 1.9 miles on the frequency axis.

From the histogram, we see that the number of students that live between 1 and 1.9 miles from the school is 25.

The correct answer is option B.

Given

a) The car has its original (initial) value when no time has passed since it was bought; in other words t=0. Then,

The initial value is 19900.

b) After 11 years, t=11; then,

Rounded to the nearest tenth, the second answer is 2924

The y-intercept is found replacing x = 0 into the equation as follows:

5*0 + y = 5

y = 5

Then, the line intercepts the y-axis at (0, 5)

The x-intercept is found replacing y = 0 into the equation as follows:

5x + 0 = 5

5x = 5

x = 5/5

x = 1

Then, the line intercepts the x-axis at (1, 0)

The line is graphed connecting these two points

Answer: x=107​=0.7

Step-by-step explanation:

1001​=70x​Multiply both sides by 70.1001​×70=xMultiply 1001​ and 70 to get 10070​.10070​=xReduce the fraction 10070​ to lowest terms by extracting and canceling out 10.107​=xSwap sides so that all variable terms are on the left hand side.x=107​

The graph of the function is

The domain of the function is determined as the x -value of the function that satisfy the given function.

Answer:

I really don't understand much about math sometimes I need help

The centre of mass of 40g, (1,3); 30g, (2,-1); 70g, (0,0) and 50g (0,-2) is located at (10/19,-1/19).

The formula to find the coordinates (X,Y) of centre of mass of a discrete particles system is,

X = (m₁x₁+m₂x₂+m₃x₃+m₄x₄)/(m₁+m₂+m₃+m₄)

Y = (m₁y₁+m₂y₂+m₃y₃+m₄y₄)/(m₁+m₂+m₃+m₄)

As we know,

m = 40

m = 30

m = 70

m = 50

Putting all the values in the formula,

for X coordinate,

X = [(40×1)+(30×2)+(70×0)+(50×0)]/(40+30+70+50)

X =(40+60+0+0)/(190)

X = 100/190

X = 10/19

For Y coordinate,

Y = [(40×3)+(30×-1)+(70×0)+(50×-2)]/(40+30+70+50)

Y= (120-30+0-100)/(190)

Y = -10/190

Y = -1/19

So, the centre of mass of the discrete particle system is at (10/19,-1/19)

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The value of the given expression x^6 -5x^4 - 5 + x simplified as;  x^4(x^2 - 5) - (5 + x)

The statement is given as ;

Factor: [tex]x^6 -5x^4 - 5 + x[/tex]

From the given expression, we have

[tex]x^6 -5x^4 - 5 + x[/tex]

Group the expression in two part;

So, we have;

[tex]x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)[/tex]

Now Factorize each group of the expression;

[tex]x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)[/tex]

The given expression cannot be further simplified.

Hence, the value of [tex]x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)[/tex]

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To write this in standard form, we need to look at the power of 10. In this case, it's a 7. Then, we need to shift the decimal point 7 places to the right:

We can see that behind the 1 (where was the decimal point before) now there are 7 numbers, then what we do is correct.

We have the equation:

And we want to find the value n, correspondign to the number of years necessary in order to the substance to decay in half.

Let's say that we have 1 Kg of the substance, this is Wo, the initial weight. Since we want to find the the decay of half the substance we use W = 1/2

And write:

Now we can use a property of logarithms:

Thus applying natural log on both sides:

By the property:

We can divide on both sides by ln(1/2):

The number of years for the radioactive substance to decay to half its initial weigh are 100 years.

The step to get rid of the ln(1/2) is:

Answer:

5/10

15/30

Step-by-step explanation:

The triangles are similar, so the lengths of corresponding sides are in the same ratio.

One pair of corresponding sides is 5 and 10.

10 is twice 5.

5/10

The other pair of corresponding sides is 15 and ?.

? must be twice 15, so ? is 30.

15/30

From the fact that the sum of the angle measures of a triangle must be equal to 180º and that two angles have measures of 40º and 70º, we can deduce that the third angle must have a measure of 70º.

Therefore, this was a deductive argument.

We are asked to determine the equation of a line that is parallel to:

Two lines are parallel if their slopes are in the following relationship:

Therefore, if m1 is the slope of the given line and m2 is the slope of the parallel line we may determine the value of the slope of the parallel line by replacing it in the relationship. Let's remember that when a line is written in the form:

Where "m" is the slope. Therefore, m1 is -2/3. Replacing in the relationship we get:

Now, we go back to the general form of a line equation and replace the value of the new slope:

The value "b" is the y-intercept and can be found using the point through which the line passes:

Now we solve the operations:

Subtracting 21/2 from both sides:

Solving the operations:

Now we replace in the line equation:

And thus we get the equation of the parallel line.

Answer:

Step-by-step explanation:

Answer:

(0,-4) and (-1,-6) or B

Step-by-step explanation:

Notice that equation 1 and equation 2 are both equal to y.

Substitute equation 2 into equation 1:

[tex]2x-4=x^2+3x-4[/tex]

Simplify:

[tex]x^2+x=0[/tex]

Factor:

[tex]x(x+1)=0[/tex]

Notice that the zeros for x are x = 0 and x = -1.

Now plug both values into either equation 1 or 2 to find y:

[tex]y=0^2+3(0)-4 = -4[/tex]

[tex]y=(-1)^2+3(-1)-4=-6[/tex]

Therefore, our values are (0,-4) and (-1,-6) or option B

To find the number of term, we will use the formula;

when n= 1

for the second term

n = 2

= 3 + 5

=8

For n= 3

=3 + 2(5)

=3 + 10

=13

For n=4

=3+3(5)

= 3 + 15

= 18

For n= 5

= 3 + 4(5)

= 3 + 20

= 23

Therefore, the terms; 3, 8, 13, 18 and 23

Answer:

4 and 1/2.

Step-by-step explanation:

There are 9 oranges, so there are not enough for both to get a whole amount.

They will split the last one into half, so they has 4 and 1/2 oranges each.

Answer: 4 and 1/2

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We have the following equation

Now we solve for "x", we must use the logarithmic properties

The required equation for the line is  y =  x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).

The required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The equation of the line which is given as

2x + 3y = 18

3y = -2x + 18

y = -2x/3 + 6

Here the slope of the line, m = -1/3

Let the required line would be as

⇒ y₀ - y₁ = m₀ (x₀ - x₁ )

The required line passes through the point (1, 5)

Here x₁ = 1 and y₁ = 5 and m₀ = 1/3 (Since required line perpendicular)

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 5 = 1 (x - 1)

⇒ y = x - 1 + 5

⇒ y =  x + 4

Therefore, the required equation for the line is  y =  x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).

The equation of the line which is given as

y = 2x + 6

Here the slope of the line, m = 2

The given coordinates of the line;

points on the line (0, 7)

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

Here x₁ = 0 and y₁ = 7 and m = 2

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 7 = 2 (x - 0)

⇒ y - 7 = 2x

⇒ y = 2x + 7

Therefore, the required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).

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By using commutative property the result after solving expression (1/4 + 1/3 + 3/4) will be 7/4.

The commutative property of addition for three numbers is given by -

a + (b + c) = (a + b) + c

Given is the following expression -

1/4 + 1/3 + 3/4

We have the following expression -

1/4 + 1/3 + 3/4

Now, lets solve the expression by adding first two terms first and than add the third term to result of the addition of first two terms. Mathematically -

(1/4 + 1/3) + 3/4

Let (1/4 + 3/4) = K

Than the expression becomes -

K + 3/4

Now, first solve K, we will get -

K = 1/4 + 3/4

K = 4/4 = 1

Now, adding the resultant [K] to third term -

1 + 3/4

1/1 + 3/4

(4 + 3)/4

7/4

So, using commutative property, we have solved the expression (1/4 + 1/3 + 3/4) and the final value will be 7/4.

Therefore, by using commutative property the result after solving expression (1/4 + 1/3 + 3/4) will be 7/4.

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The statement which best describes Mike's error is that: D) While the graph does pass through the origin, it is not a straight line.

A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.

In this context, we can reasonably infer and logically deduce that even though Mike's graph passes through the origin, his error is that it is not a straight line.

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a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair. FALSE

b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary. TRUE

c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair . FALSE

The given statement is : If two angles are supplementary then the angles are a linear pair .

(a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair.

This statement is FALSE because supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, no, supplementary angles are not always linear pairs. However, linear pairs are always supplementary.

(b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary.

This statement is TRUE because in a linear pair, if the two angles have a common vertex and a common arm, then the non-common side makes a straight line and the sum of the measure of angles is 180°. Linear pairs are always supplementary.

(c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair .

This statement is FALSE because if they are adjacent and share a vertex and one side. See the first picture below. They might not form a linear pair, like in a parallelogram.

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We know that

• The earnings are $7,592.

• The time is 16 years.

• The annual interest rate is 9.04%.

This problem is about simple interest, its formula is

Where A = 7,592, r = 9.04, t = 16, and P is the principal.

Let's replace each value.

Notice that 9.04% is equivalent to 0.0904.

Now, we solve it for P.

Given:

Sum of two numbers-6

Difference of two numbers-12

Required:

To calculate the number

Explanation:

Consider first number-9

Consider second number--3

Sum =9+(-3)=9-3=6

Difference=9-(-3)=12

Required answer:

Option B

Solution

We want to solve

The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.

For the question,

The answer is x = 0 and x = 1/3

Question:

Find the length of AC.

Solution:

Applying the Pythagorean Theorem, we get:

this is equivalent to:

then, we can conclude that the length of AC side is:

Andrew will have $9,450 in his savings account that earns 5% interest per year.

According to the question,

We have the following information:

Principal amount in Andrew's savings account = $9,000

Interest rate = 5% per year

Time = 1 year

We know that we use the following formula to find the simple interest on any amount:

Simple interest = (principal*rate*time)/100

Simple interest = (9000*1*5)/100

Simple interest = $450

Now, the total amount in his savings account will be the sum of the amount earned from the interest and the principal amount submitted by him.

Total amount = interest+principal

Total amount = 450+9000

Total amount = $9,450

Hence, he will have $9,450 in his savings account.

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Given: A system of linear equations in three variables x, y, and z as follows-

Required: To solve the system using elimination.

Explanation: Let the given system as-

We can solve the system by reducing the system to a system of 2 variables. Suppose we would like to remove the variable z.

Multiplying equation (1) by 2, adding to equation (2) as follows-

Now, add equations (1) and (3) as follows-

Now, equations (4) and (5) represent a system of linear equations in two variables. Subtracting the equations as follows-

Substituting x=3 in equation (4)-

Substituting x=3 and y=-1 in equation (1) as follows-

Final Answer: The solution to the system is-