Write the equation of the line passing through the points (10,3) and (-2,-3).
The equation of the line is

The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = x² - 16x + 24

Convert the equation into vertex form, then we have

y = x² - 16x + 24

y = x² - 2·8·x + 8² - 8² + 24

y = (x - 8)² - 64 + 24

y = (x - 8)² - 40

The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.

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The row of Pascal's triangle that is used to expand the binomial expression  (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.

A binomial expression is an expression that contains only two terms.

Pascal's triangle is an algorithm for finding the coefficients of a binomial expansion.

Since we require the expansion of the binomial expression (2x³ +3y³)⁷ using Pascal's triangle, we note that, the power of the binomial expression is always equal to the second and second to the last coefficient of the terms in the Pascal's triangle.

So, we see that the Row eight: 1 7 21 35 35 21 7 1, satisfies this condition.

So, the row of Pascal's triangle that is used to expand the binomial expression  (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.

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Answer:

The expression is 2 * 3 - 2 + 4 = 8.

Step-by-step explanation:

In this expression, the variables a, b, and c are given specific values. Substituting these values into the expression, we have 2 * 3 - 2 + 4, which simplifies to 8.To evaluate an expression, we substitute the given values for the variables and carry out the operations according to the order of operations (i.e. parentheses, exponents, multiplication and division, addition and subtraction). In this case, the expression is already fully simplified, so we don't need to do any further calculations.

By using the property of congruency, it can be calculated that

Length of line segment AC is 26 units

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides are equal and the corrosponding angles are equal.

There are six axioms of congruency. They are

AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom

In [tex]\Delta[/tex] ABC and [tex]\Delta[/tex] XYZ,

[tex]\angle[/tex]B = [tex]\angle[/tex]Y [Given]

[tex]\angle[/tex]C = [tex]\angle[/tex]Z [Given]

BC = YZ [Given]

[tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] XYZ [ASA axiom]

AC = XZ [Corrosponding parts of congruent triangles are congruent]

AC = 26 units

Length of line segment AC is 26 units

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The solutions of the quadratic equation are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

For a general quadratic:

a*x^2 + b*x + c = 0

The solutions are given by the quadratic formula

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic equation:

2x^2 + x + 3 = 0

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]

So we will have two complex solutions, these are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

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The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Now,

Since, The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Solve the expression by using distributive property as;

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

⇒ [ 7/5 ] × [ - 3/12 ±  5/12 ]

It gives two solution as;

⇒ 7/5 × [ - 3/12 + 5/12 }

⇒ 7/5 × 2/12

⇒ 7/5 × 1/6

⇒ 7 / 30

And,  7/5 × [ - 3/12 - 5/12 }

⇒ 7/5 × - 8/12

⇒ 7/5 × - 2/3

⇒ - 14 / 15

Thus, The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

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The area of the front cover a face perpendicular to the thickness is 72in²

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom, and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

Here, we have

Given:

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.

The volume of the dictionary will be 216in².

Volume = W×L×H

Surface = volume/ height

= 216/3

= 72in²

Hence, the area of the front cover of a face perpendicular to the thickness is 72in².

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Answer: B

Step-by-step explanation:

For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].

For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].

Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.

The indications of the numbers in the linear equations that produces the number of apples in Annie's basket, n = 22·t + 12, are as follows;

The domain of the function n = 22·t + 12 is R⁺ which is the set of positive real numbers, including zero, [0, ∞)

A linear equation is a equation of the line of a straight line graph. The domain of a function is the set of the input values of the function.

The equation that describes the number of apples in Annie's basket, n = 22·t + 12

The number of minutes Annie spends picking apples = t

The number of apples in Annie's basket = n

The number 22 which is the coefficient of the variable t in the linear equation, which is the slope or the rate of change of the number of apples in Annie's, which indicates the number of apples Annie picks per minute.

The number 12 is the y-intercept of the equation y = 22·t + 12

The y-intercept is the value of the function where t = 0, which is the initial value of the function.

Therefore;

The domain of the function n = 22·t + 12, are the possible values of the independent or input variable, t, which is the set of positive integers including 0

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Answer:

I use desmos; what do you need help with?

Answer:zegari6636 is king of brainlist

Step-by-step explanation:

My algebra teacher use Desmos and also thanks for the points have a good day do you need help

Answer:

5 buses

Step-by-step explanation:

Mrs. Smith will need to reserve buses for 7 classes of Fourth graders, with 20 students in each class, for a total of

7 * 20 = <<7*20=140>>140 students.

Since 30 students fit on a bus, Mrs. Smith will need to reserve

140 / 30 = <<140/30=4.67>>4.67 buses.

Since Mrs. Smith can't reserve a partial bus, she will need to reserve 5 buses for the trip.

Answer: 5 busses, you have to multiple the number of students by the amount of classes (7 x 20) to get a product of 140 students. If only 30 can fit on to each bus you have to divide 140 by 30 and you get 4.6666667 so you need to round up to get an answer of 5 busses

Step-by-step explanation:

An expression or equation that shows how many pictures Alexa drew is 8-p.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Given, Evan drew 8 pictures.

Alexa drew p fewer pictures than Evan.

then, Alexa = 8-p

Hence, an expression or equation that shows how many pictures Alexa drew is 8-p.

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Answer:

$2.92

Step-by-step explanation:

Divde $11.67 by the 4 gallons that Dennis bought.

11.67/4=2.9175

round to the nearst cent (or hundreths place)

since 7 is greater than 5, it rounds up

$2.92

Answer:

d = 5m

Step-by-step explanation:

Look at point (1, 5).

When the number of months is 1, the amount in dollars is 5.

The amount in dollars is always 5 times the number of months.

d = 5m

The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;

a. Interest for the first quarter = $8.125

b. First quarter ending balance = $6,508.125

c. Interest for the second quarter = $8.13515625

d. Second quarter ending balance = $6,516.26015625

e. Interest for the third quarter = $8.1432520325

f. Third quarter closing balance = $6,524.40548145

g. Interest for the fourth quarter = $8.15550685975

h. The amount of interest earned in a year is about $32.56

What is an interest earned on an amount?

An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.

The amount Fred deposited, P = $6,500

The interest paid by the account, r = 0.5% compounded quarterly

a. The first quarter interest can be found by the formula;

C.I. = P[tex](1+ r/4)^{4 . 1/4}[/tex] - P

Therefore

C.I. = 6500 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6500 = 8.125

b. The first quarter ending balance is therefore;

A = P + C.I.

A = $6,500 + $8.125 = $6,508.125

c. The second quarter's interest can be found from the formula;

C.I. = 6508.125 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6508.125 = 8.13515625

The second quarter's interest is $8.13515625

d. The second quarter ending balance is therefore;

A = $6,508.125 + $8.13515625 = $6,516.26015625

The second quarter ending balance is $6,516.26015625

e. The third quarters interest is therefore;

C.I. = 6516.26015625 x  (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6516.26015625 = 8.1432520325

The third quarter's interest is about $8.1433

f. The third quarter's ending balance is therefore;

A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145

The third quarter's ending balance is $6,524.40548145

g. The fourth quarter's interest can be found as follows;

C.I. = 6524.40548145 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6524.40548145 = 8.15550685975

The fourth quarter's interest is; $8.15550685975

h. The balance at the end of one year is therefore;

Balance = C.I. fourth quarter + Principal for the fourth quarter

Therefore;

Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831

i. The interest the account earns in a year is therefore;

$6,532.56098831 - $6,500 = $32.5609883

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Answer: $27,000

Step-by-step explanation:

The values obtained after solving the given equation is x  = 6 and y = 10.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equations are,

-5x + 3y = 0   (i)

7x - 4y = 2    (ii)

Multiply equation (i) by -7 and equation (ii) by 5.

35x - 21y = 0       (iii)

35x - 20y = 10       (iv)  

Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.

-y = -10

y = 10

Substitute y = 10 in equation (i)

-5x + 3(10) = 0

-5x = -30

x = 30/6

x = 5

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The average number of customers waiting in the queue is 20

In this question, we have been given that the customers arrive at the rate of two per minute.

On average a customer waits 10 minutes in a queue.

We need to find the number of customers waiting in the queue on average.

Assume that the average number of customers waiting in the queue is N.

We have the average Rate of Arrival = 2 customers per minute

So, by the formula for average waiting time under the Single-Server Queue Model,

10 = N/2

N = 10 * 2

N = 20

The average number of customers waiting according to the single-server queue model given the above conditions is 20

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The value of x = 7 and y = 54.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:  y = 6x+12 and y = x+47

We have to solve this equation and find the value of x and y.

y = 6x+12....(1)

y = x+47.....(2)

We put the value of y in equation (1) and we get

x + 47 = 6x + 12

6x -x = 47 -12

5x = 35

x = 7

Now, we put the value of x in equation(2) and we get

y = 7 + 47

y = 54

Hence, the value of x = 7 and y = 54.

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Answer: The answer to this solution is 5.

If the margin error of the volume of the soap is 354.85 ml to 354.95 ml, then the volume of the soap that he measured is 354.9 ml

The margin of error = 354.85 ml to 354.95 ml

The margin error is defined as the difference between the actual and projected results in a random survey sample.  If the actual measurement is x, there is a chance of error in the measurement because of numerous reasons.

The margin of error in the measurement is 354.85 ml to 354.95 ml

In the given options the correct value is 354.9 ml, because it is the middle value of the given margin or error 354.85 ml to 354.95 ml

Therefore, the volume of soap that he measured is 354.9 ml

I have solved the question in general, as the given question is incomplete

The complete question is:

For the volume of soap in a bottle, Ryan determined the margin of error as 354.85 mL to 354.95 ml. What was the volume of soap that he measured? a) 354.8 mL b) 354.85 mL c) 354.9 mL d) 354.95 mL

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The value of the angle y will be equal to 47.46. The correct option is A.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given that the angle x is equal to 132.54°. The value of the angle y will be calculated as,

x + y = 180

132.54 + y = 180

y = 180 - 132.54

y = 47.46

Therefore, the value of the angle y will be equal to 47.46. The correct option is A.

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The value of f(x)+g(x) is 5x³+7x²+3x+10

Given that,

                 f(x)=3x³+4x²-2x+8

                 g(x)=2x³+3x²+5x+2

f(x)+g(x)=3x³+4x²-2x+8+2x³+3x²+5x+2

            =3x³+2x³+4x²+3x²+5x-2x+8+2

            =5x³+7x²+3x+10

Step-by-step explanation:

This question is a type of quadratic equation. To solve this type of question first, we have to put the values of f(x) and g(x). Then we have to put similar terms(which have similar coefficients with similar power)together. Then we add the similar term of f(x) with the similar term of g(x) like 3x³+2x³=5x³, 4x²+3x²=7x², 5x-2x=3x and 8+2=10

Therefore the value of f(x)+g(x) is 5x³+7x²+3x+10

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Answer:

l

v

Step-by-step explanation:

80, 5, 30, 7, and 3,

Using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.

The order of operations refers to the rules that govern how to solve an expression with several operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

Roanne earns $5 for 1/2 hour.

Roanne will earn in 1/2 * 2 = 1 hour:

5 * 2 = $10

Therefore, using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.

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Answer:

F

Step-by-step explanation:

15/10 = x+12/12

180=10x+120

x=6

x+12=18=AE

Answer:

No

Step-by-step explanation:

If you look at the first numbers, 1 and 3, we can see that 1 is being multiplied by 3 to get 3.

But if you look at the second numbers, 2 and 4, then you can see that 2 is not being multiplied by 3 to get 4.

Therefore, it is not proportional.

We have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

                  tan∅ = sin∅/cos∅

                  cot∅ = cos∅/sin∅

Given:

tanθ.cosθ + cotθ.sinθ = sinθ + cosθ

Now LHS =  tanθ.cosθ + cotθ.sinθ

                = (sinθ/cosθ)cosθ + (cosθ/sinθ)sinθ

                = sinθ + cosθ

LHS = RHS

Hence, we have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.

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