Using The Midpoint And Distance Formulas, Calculate The Coordinate Of The Midpoint And The Length Of (2024)

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.

[tex](-\infty,-4)\cup(-4,1)\cup(1,\infty)[/tex]

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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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

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

[tex]y=-\frac{2}{3}x+3[/tex]

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

[tex]m_2=-\frac{1}{m_1}[/tex]

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:

[tex]y=mx+b[/tex]

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

[tex]m_2=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}[/tex]

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

[tex]y=\frac{3}{2}x+b[/tex]

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

[tex]3=\frac{3}{2}(7)+b[/tex]

Now we solve the operations:

[tex]3=\frac{21}{2}+b[/tex]

Subtracting 21/2 from both sides:

[tex]3-\frac{21}{2}=b[/tex]

Solving the operations:

[tex]-\frac{15}{2}=b[/tex]

Now we replace in the line equation:

[tex]y=\frac{3}{2}x-\frac{15}{2}[/tex]

And thus we get the equation of the parallel line.

Question:

Find the length of AC.

Solution:

Applying the Pythagorean Theorem, we get:

[tex]AC\text{ = }\sqrt[]{CB^2_{}-AB^2}\text{ = }\sqrt[]{13^2_{}-5^2}[/tex]

this is equivalent to:

[tex]AC\text{ = }\sqrt[]{13^2_{}-5^2}\text{ = }\sqrt[]{144}=12[/tex]

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

[tex]AC\text{ }=12[/tex]

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

[tex]A=P(1+rt)[/tex]

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

Let's replace each value.

[tex]7,592=P(1+0.0904(16))[/tex]

Notice that 9.04% is equivalent to 0.0904.

Now, we solve it for P.

[tex]\begin{gathered} 7,592=P(1+1.4464) \\ 7,592=P(2.4464) \\ P=\frac{7,592}{2.4464} \\ P\approx3,103.34 \end{gathered}[/tex]Therefore, James needs to invest $3,103.34 as his principal in order to achieve the goal.

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.

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 number written in scientific notation is 1.12 × 10⁻² .

Scientific notation can be used to describe values that are either too large or too little to be conveniently presented in decimal form (typically would result in a long string of digits).

In the UK, it is also known as standard form, scientific form, and standard index form.Since it may make a number of mathematical operations simpler, this base ten notation is frequently employed by scientists, mathematicians, and engineers.Scientific notation for non-zero integers is written as m × 10ⁿ, or m times ten and raised to the power of n, where n is an integer and m is a non-zero real number.

The given number is 4.501795324E⁻⁶

So simplifying we get :

4.501795324E⁻⁶ = 1.11588350 × 10⁻²

Therefore the number written in scientific notation is 1.12 × 10⁻² .

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Given

[tex]v(t)=19900(0.84)^t[/tex]

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

[tex]\text{ initial value: }v(0)=19900(0.84)^0=19900*1=19900[/tex]

The initial value is 19900.

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

[tex]\begin{gathered} v(11)=19900(0.84)^{11}=2923.64894... \\ \Rightarrow v(11)\approx2924 \end{gathered}[/tex]

Rounded to the nearest tenth, the second answer is 2924

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:

[tex]1.304\cdot10^7=13,040,000[/tex]

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

The system of equations given has infinitely number of solutions.

System of Equation

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

In the given question, we can solve for the equation given;

[tex]y = 4x + 5\\-8x + 2y = 10\\[/tex]

Solving for both x and y;

The solution of the equation is y = 4x + 5

The system has infinitely many solutions;

In the second system of equations;

y = 0.5x + 3, x = 2y = -16

This equation is not correct.

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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).

What is the slope of the line?

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

[tex]U_{n\text{ = }}a+(n-1)d[/tex]

when n= 1

[tex]U_1=\text{ 3 + (1-1)5}[/tex][tex]=\text{ 3+0}=3[/tex]

for the second term

n = 2

[tex]U_2=\text{ 3 + (2-1)5}[/tex]

= 3 + 5

=8

For n= 3

[tex]U_3=3+\text{ (3-1)5}[/tex]

=3 + 2(5)

=3 + 10

=13

For n=4

[tex]U_4=3+(4-1)5[/tex]

=3+3(5)

= 3 + 15

= 18

For n= 5

[tex]U_5=3+(5-1)5[/tex]

= 3 + 4(5)

= 3 + 20

= 23

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

Answer:7464

Step-by-step explanation:

90 is the score to get

let c represent correct and w represent wrong

if they get 134 points for it being correct, we can look at it like 134c

if they get -14 points for it being incorrect, we can look at it like -14w

now to put this in the right sense we fill in those letters with how many they got right and wrong : 134(58) -14(22)

This would get 7772 -308

after subtracting these two you'd get: 7464

Answer:

Step-by-step explanation:

[tex]undefined[/tex]

Volume of a cone =

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

From the question;

r= 4 h=7

π is a constant and it is equal to 22/7

substitute the values into the formula;

[tex]V=\frac{1}{3}\times\frac{22}{7}\times4^2\times7[/tex][tex]V=\text{ }\frac{2464}{21}[/tex]

[tex]V=117.33inch^3[/tex]

The value of the set (A∪C)'∩B is {9 , 12} .

A subfield of mathematical logic called set theory examines sets, which are essentially collections of objects.

Set theory is a discipline of mathematics that largely addresses problems that are pertinent to mathematics as a whole, despite the fact that any kind of object can be constructed into a set.Set theory is founded on a simple binary relationship between an object o and a set A.It is written as o A if o is a part (or member) of A. Members of a set are enumerated with commas to denote separation when describing them, or a property of those parts is enclosed in braces.Sets can be associated by the membership relation since they are objects.

The given sets are:

U ={1,2,3,4,5,6,7,8,9,10,11,12,13}

A = {3,7,11,13}

B = {3,6,9,12,13}

C = {2,3,5,6,7,8}

Now B' = {1,2,4,5,7,8,10,11}

b) B'∩C = {2,5,7,8,}

c) A∪C = {2,3,5,6,7,8,11,13}

(A∪C)' = {1,4,9,10,12}

(A∪C)'∩B = {9 , 12}

Hence the value of the set (A∪C)'∩B is {9 , 12} .

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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

Answer:

-3

Step-by-step explanation:

the 'y- intercept ' is ACTUALLY the 'y-axis intercept'.......this is where the graph crosses the y - axis ....for this graph this is -3

The Factors of x² - 5x + 6 are (x-3) (x-2)

Step 1: Add the constant term to the first term's coefficient. i.e (6 x 1) = 6

Step 2:Find the two factors of 6 whose total matches the middle term's coefficient., i.e -5.

Thus, the factors are -3 and -2 as,

-3 × (-2) = 6 (Product)

-3 + (-2) = -5 (Sum)

The polynomial may be expressed as follows after dividing the middle term by the two components, -3 and -2:

x² - 3x - 2x + 6 = 0

⇒ x(x-3) -2(x-3) = 0

⇒ (x-3)(x-2) = 0

Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).

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Answer:

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

The equation for the function after the transformation is f'(x) = 2x^2 - 3

How to write the image for the function?

The initial equation is given as

f(x) = x²

The above represents the parent function

The sequence of transformations is given as

Vertically stretched by a factor of 2Shifted a distance of 3 units down

The rules of the above sequence of transformations are

Vertically stretched by a factor of 2: (x, 2y)Shifted a distance of 3 units down: (x, y - 3)

When the rules are applied, we have

Stretch: f(x) = 2x^2Shifted: f'(x) = 2x^2 - 3

Hence, the equation in its final position is f'(x) = 2x^2 - 3

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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.

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.

What is a graph?

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

What is the commutative property of addition?

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

How to factor the expression?

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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a) The required down payment is $47,800.

b) The mortgage loan is $191,200.

c) The amount for the three points at closing is $5,736, which is 3% of the mortgage.

d) The monthly payment (excluding escrowed taxes and insurance) is $-1,677.92.

e) The total interest cost for the mortgage over its 30-year period is $412,850.06.

What is the down payment?

The down payment is an upfront payment required to reduce the mortgage loan and assure the financier that the mortgagee is financially ready to engage in the mortgage transaction.

The price of a dream house = $239,000

Down payment = 20% = $47,800 ($239,000 x 20%)

Mortgage loan = $191,200 ($239,000 - $47,800)

Three points at closing = 3% of $191,200

= $5,736

Periodic Payment:

N (# of periods) 360 months (30 years x 12)

I/Y (Interest per year) = 10%

PV (Present Value) = $191,200

FV (Future Value) = $0

Results:

PMT = $-1,677.92

Sum of all periodic payments = $-604,050.06

Total Interest = $412,850.06

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