What is the slope of the line that passes through the points (2, 3)(2,3) and (0, 11)(0,11)? write your answer in simplest form.

Answer:

slope = 4

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, - 13) and (x₂, y₂ ) = (2, 3) ← 2 ordered pairs from the table

m = [tex]\frac{3-(-13)}{2-(-2)}[/tex] = [tex]\frac{3+13}{2+2}[/tex] = [tex]\frac{16}{4}[/tex] = 4

Answer:

[tex]1.9x+3.7[/tex]

Step-by-step explanation:

[tex]3.6x-1.7x+5.9-2.2=1.9x+3.7[/tex]

In this situation, the angles that must be congruent to ∠2 are ∠3, ∠6, and ∠7. Thus, the answer is (a) ∠3, ∠6, and ∠7.

When a transversal intersects two parallel lines, corresponding angles are congruent. In other words, angles that are in the same position relative to the parallel lines and the transversal are congruent. Therefore, in this case, ∠2 and ∠5 are corresponding angles and are congruent, as are ∠3 and ∠6, and ∠4 and ∠7.

Thus, the answer is (a) ∠3, ∠6, and ∠7.

Congruent is a term used to describe two shapes or figures that have the same shape and size. It means that the lengths of the sides and the angles of the shapes are exactly the same. Congruence is an important concept in geometry and is used to prove theorems and solve problems.

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Tyler’s brother made $25 as commission.

Commission, also known as sales commission, is a payment given to employees based on the sales they make. Commission is often calculated as a percentage of the value of a sale.

Given that, Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $1000 worth of shoes.

Since, his commission is 2.5% of the sale.

And, he sold $1000 worth of shoes.

Therefore, commission = 2.5% of 1000

= 2.5 / 100 x 1000

= 25

Hence, the commission is made is $25

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Answer: 3.25 (Add on 0.25 each week)

Step-by-step explanation:

3 + 1/4 = 13/4 = 3 1/4 = 3.25

An extraneous solution is A root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain. It comes from correct solution steps and is not a valid solution of the equation.

We are aware that when we solve an equation, the values that result from the answer are always accurate. When we address the problem, there are various solutions that we may be able to get. The non-extraneous solutions are those that, if plugged back in, would produce the original equation, whereas the extraneous solutions are those that do not.

Therefore, the only way we can tell if something is unnecessary or not is if we re-enter the data we have and check to see if the equation still produces the same answer.

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Check the picture below.

so for the equation y = 40 + 20x, what's an appropriate domain? or namely, what could be some valid values for "x"?

well, Jessica is going to put in 20 bucks only for 12 weeks, so whatever "x" is going to be, is must be from 0 to 12, or in interval notation [0 , 12].

Answer:

72%

Step-by-step explanation:

18/25 are pink.

18*4 = 72.

72 percent.

7^(3/5) * 7^(1/5) is equivalent to (7^3)^(1/5) * (7^1)^(1/5), which is equivalent to 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7.

When you see an expression like 7^(3/5) * 7^(1/5), it is helpful to think about the properties of exponents. One property is that when you have the same base raised to different exponents, you can multiply the exponents. So, for example, 7^3 * 7^1 = 7^(3+1) = 7^4.

Another property is that when you have a base raised to a power, and then that result is raised to another power, you can multiply the exponents. So, for example, (7^3)^2 = 7^(3*2) = 7^6.

Using these properties, we can simplify the original expression as follows:
7^(3/5) * 7^(1/5) = (7^3)^(1/5) * (7^1)^(1/5) = 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7

So, 7^(3/5) * 7^(1/5) is equivalent to 343^(1/5) * 7

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the automobile's average speed in  40 miles per hour.

What is speed?

The speed of an object, also known as v in common parlance and kinematics, is the size of the change in position per unit of time or the size of the change in position over time; as such, it is a scalar quantity. The average speed of an object in a given period of time is equal to the distance traveled by the object divided by the length of the intervalthe instantaneous speed is the upper limit of the average speed as the length of Velocity and speed are different concepts.

formula d=rt, d represents the distance in miles , r represents average speed in miles per hour and t represents time in hours .

given

distance=60m

and time=1.5hr

average speed= 60/1.5 = 40 miles per hour.

Hence, the automobile's average speed in  40 miles per hour.

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Answer:kaka

Step-by-step explanation:

your mom

Answer:

x = 66

Step-by-step explanation:

[tex]\frac{60}{70} =\frac{x}{11+x}[/tex]

[tex]60(11+x)=70(x)[/tex]

[tex]660+60x=70x[/tex]

[tex]10x=660[/tex]

[tex]x=\frac{660}{10}[/tex]

[tex]x=66[/tex]

Hope this helps

Answer:

No Solution

Step-by-step explanation:

The lines are parallel to one another, meaning in no solution!

Answer:

18 men

Step-by-step explanation:

3:7  ==> there are 3 men for every 7 women.

42 / 7 = 6  ==> divide the total number of women by the supposed ratio.

6 * 3 = 18 men

2v+3b=214 and 3v+4b=302 are a linear system to model the situation

Two or more expressions with an Equal sign is called as Equation.

Given that R took two high schools to the Atlanta Hawks Game.

Let v represent the van and b represents the buses.

B took 2 vans and 3 buses with 214 students

2v+3b=214

W took 3 vans and 4 buses with 302 students

3v+4b=302

So the two linear equations are 2v+3b=214 and 3v+4b=302

Hence, 2v+3b=214 and 3v+4b=302 are a linear system to model the situation

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The principal investment required to get a total amount of $3,700.00 from compound interest at a rate of 3.5% per year compounded 365 times per year over 15 years is $2,287.26.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

Rate = 3.5%

Final Amount = $3,700

Time = 15 Years

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 per year,

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 3,700.00 / (1 + 0.035/365)(365)^(15)

P = 3,700.00 / (1 + 0.00010137)^(4745)

P = $2,287.26

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Answer:

Step-by-step explanation:

include the inequality.

Hypotenuse² = Perpendicular² + Base²

10² = 1²+x²

x²= 100 -1

x=√99

x≈9.94

Answer:

Step-by-step explanation:

1 + 2 + 4 = 7

7x = 1400

x = 1400/2 = 200

1(200) + 2(200) + 4(200) = 1400

Sand:  200 kg

Gravel:  400 kg

Cement:  800 kg

You would need 200 kg of sand, 400 kg of gravel, and 800 kg of cement to make 1400 kg of dry concrete using the ratio 1:2:4,

Let's assign variables to represent the quantities:

Let x be the quantity of sand.

Let y be the quantity of gravel.

Let z be the quantity of cement.

According to the given ratio, the quantities will be as follows:

Sand: x

Gravel: 2x (twice the amount of sand)

Cement: 4x (four times the amount of sand)

The total weight of the dry concrete is the sum of the weights of the individual components:

x + 2x + 4x = 1400 kg

Combining like terms:

7x = 1400 kg

Dividing both sides of the equation by 7:

x = 200 kg

Now that we know the quantity of sand, we can find the quantities of gravel and cement:

Gravel: 2x = 2 × 200 kg = 400 kg

Cement: 4x = 4 × 200 kg = 800 kg

Therefore, you would need 200 kg of sand, 400 kg of gravel, and 800 kg of cement.

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After solving this expression into simplest form, we get : [tex]\frac{-4x^{}+ 9 }{2x(x-2)}[/tex]

So, Option (B) is the correct answer.

How to simplify expression into simplest form ?

To simplify a given fractional expression, first convert any mixed number in the expression to improper fraction before carrying out the operation that is involved in the expression

The steps to solve this expression into simplest form are shown below:

[tex]=\frac{1}{2x^{2}-4x } -\frac{2}{x}[/tex]

[tex]=\frac{1}{2x(x-2)}-\frac{2}{x}[/tex]

[tex]=\frac{1-2[2(x-2)]}{2x(x-2)}[/tex]

[tex]=\frac{1-4x+8}{2x(x-2)}[/tex]

[tex]=\frac{-4x + 9}{2x(x-2)}[/tex]

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If a man works for 8 hours a day, he can finish a job in 12 days. to complete the work in 10 days the man must work for 15 hours

For the rate problem, the proportion of the work completed per hour is taken and used to compare for other conditions

Working 8 hours a day, he can finish a job in 12 days. the rate of work is

rate of work = 12 days / 8 hours

= 3/2

for 10 days the man will work

= 3/2 * 10

= 15

hence the man needs to work for 15 hours

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The number of times that the actual flag is wider than Reagan's model would be = 3 times.

Rectangle: What is it?

A rectangle is a particular kind of quadrilateral with opposite sides that are parallel and equal to one another and four right angles, according to the definition.

The rectangular flag measures 39 inches in length in actuality.

Reagan's model measured 13 inches in length.

The formula: = Length of actual flag / Length of model = 39/13 = 3 will tell you how many times broader the model is than the real flag.

The real flag is three times wider than Ronald Reagan's model, for a total of four times.

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The solution of the algebraic expression (8h-1)-(h+ 3) is -25.

Given:

The given expression in the question is:

(8h-1)-(h+ 3); Value of h = -3​

Putting the value of h in the expression

8(-3)-1 - ((-3)+3)

= -24-1 -0

= -25

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For WXYZ to be a parallelogram, the slope of ZY must be -1/4

parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

For two lines to be parallel, their slope must be equal. This means that the slope of ZY must be equal to the slope of WX

The slope of ZY is calculated as:

(y2-y1)/x2-x1

= 0-2/3-(-5)

= -2/8

= -1/4

Therefore the slope of WX = -1/4

His means for WXYZ to be a parallelogram, the slope of ZY = slope of WX = -1/4

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Answer: (5,1)

Step-by-step explanation:

Substitution is where you "plug in" an equation equal to a variable to another equation that contains that variable.

Here you would subtract x from the second equation, leaving you with

-5y = -x.

You can multiply both sides by -1 to get 5y = x

Then, because 5y is equal to x, you plug in 5y where it says x on the first equation.

Now you have 4(5y) + 3y = 23. That simplifies to 20y + 3y = 23, and then 23y = 23

Divide and you get "y = 1"

Now you that you know what y is equal to, you plug in the value for y to either equation and solve for x to find the (x,y) coordinates.

4x + 3(1) = 23

4x + 3 = 23

4x = 20

x = 5

Final answer is (5,1)

Answer:

Point Form:

(5,1)

Equation Form:

x= 5,y= 1

Step-by-step explanation:

:)

Answer: x-4 i think

Step-by-step explanation:

Answer: f^(-1)(x) = 4x (inverse function desired)

Explanation: For if one let f(f^(-1)(x)) = x, (f^(-1)(x))/4 = x, and hence f^(-1)(x) = 4x.

In the given algebraic expression if [tex]x^2+y^2[/tex] = 225 and dy/dt = 4, then dx/dt when y = 9 is ±3.

An algebraic expression is a mathematical expression that can contain numbers, variables, and operators. Examples of algebraic expressions are: [tex]2x + 3, (x^2 - y^2) / (x-y)[/tex], and [tex]4y + 2x^2[/tex]. These expressions can be evaluated by replacing variables with specific values ​​and simplifying the expressions in order of operations.

Given, [tex]x^2+y^2[/tex]  = 225

dy/dt = 4

We have to find dx/dt.

When y = 9,

⇒ [tex]x^2+9(2)[/tex]  = 225

⇒ [tex]x^2+81[/tex] = 225

⇒ [tex]x^2[/tex] = 225 - 81

⇒ [tex]x^2[/tex] = 144

Taking square root,

⇒ x = ±12

Differentiating with respect to t,

2x ([tex]\frac{dx}{dt}[/tex]) + 2y ([tex]\frac{dy}{dt}[/tex]) = 0

x ([tex]\frac{dx}{dt}[/tex]) + y ([tex]\frac{dy}{dt}[/tex])=0

Put dy/dt = 4 in the above expression,

(±12) ([tex]\frac{dx}{dt}[/tex]) + (9)(4)=0

(±12)([tex]\frac{dx}{dt}[/tex]) + 36 = 0

(±12) ([tex]\frac{dx}{dt}[/tex]) = −36

[tex]\frac{dx}{dt}[/tex] = ( -36/ ± 12)

dx/dt = ±3

Therefore, dx/dt = ±3

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So, the equation |x-10|=17 can be transformed into the following two linear equations:

x = 27

x = -7

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, separated by the 'equal' sign.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is its distance from zero on the real number line.

To transform the equation |x-10| = 17 into two linear equations, we need to consider the two possible cases for the absolute value: x-10 = 17 and x-10 = -17.

When x-10 = 17, x = 27

When x-10 = -17, x = -7

So, the equation |x-10|=17 can be transformed into the following two linear equations:

x = 27

x = -7

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Answer:

10

Step-by-step explanation:

Because the triangles are similar, we can say:

[tex]\frac{35}{14} = \frac{40}{16}=\frac{25}{x}[/tex] ⇒ [tex]x= \frac{16*25}{40}[/tex] ⇒ [tex]x = 10[/tex]

Answer:

[tex]56a+40b[/tex]

Step-by-step explanation:

[tex]43a+13a-12b+52b=56a+40b[/tex]

Answer:

56a+40b

Step-by-step explanation:

43a-12b+13a+52b

--> (43a+13a)+(52b-12b)

--> (56a)+(40b)

--> 56a+40b

Hope that helps