Write an equation in slope-intercept form for the perpendicular bisector of the segment with the given endpoints. Justify your answer. (Lesson 5-1)
D(-2,-4) and E(2,1)

The solution for equations can be determined by .

-2x + y = 0

5x + 3y = -11

Equating both the equations

-6x+5x = -11

x= 11

substitute x in any one of the equation to find y value.

-2(11) + y = 0

y = 22

A declaration that two mathematical expressions are equal. a phrase that uses chemical symbols to illustrate a chemical reaction.

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

Equation is a mathematical term for a scenario where numerous aspects need to be taken into account. It is commonly expressed as a mathematical expression with equal values on either side and is defined as the state of equality.

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Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

1) The present value of an annuity with annual payments of $300 for 15 years at a 6% interest rate is approximately $3,284.09. 2) The future value of an annuity with annual payments of $2,000 for 9 years at a 3.5% interest rate is approximately $22,077.59.

3) The future value of an annuity with annual payments of $4,000 for 7 years at a 3.75% interest rate is approximately $33,221.83. 4) The present value of an annuity with annual payments of $4,500 for 3 years at a 5.5% interest rate is approximately $12,912.36.

The present value of an annuity formula (PVA) is used to calculate the current value of a series of future cash flows. It involves discounting each cash flow back to its present value using the interest rate. The formula for PVA is provided as: PVA = PMT * ((1 - (1 + r)^(-t)) / r).

The future value of an annuity formula (FVA) is used to determine the value of a series of future cash flows at a specified point in the future. It involves compounding each cash flow forward using the interest rate. The formula for FVA is given as: FVA = PMT * (((1 + r)^t) - 1) / r.

By substituting the given values into the appropriate formula and solving, we can determine the present value and future value of the annuities in each scenario. The calculated values provide the answers for the respective questions.

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Answer:

120poles

Step-by-step explanation:

Given

Length of each poles of the paddock = 30

Since a square has 4 sides, the perimeter of the square shaped paddock is what we are to look for.

Perimeter of a square = 4L

L is the length of each side of the paddock

Perimeter = 4(30)

Perimeter of the square = 120

Hence he used 120poles for the paddock

Surface area of A = 50 square inches, S.A of B = 120 square inches, S.A of C = 60 square inches, S.A of D = 50 square inches, S.A of E = 60 square inches, S.A of F = 120 inches.

S.A of the box = 460 square inches.

A cuboid is a three dimensional solid shape made of 6 rectangles.

Analysis:

surface area of A = surface area of D which is the smallest from the diagram = 5 x 10 = 50 square inches

surface area of C = surface area of E = the second largest = 5 x 12 = 60 square inches

surface area of B = surface area of F = 10 x 12 = 120 square inches

surface area of shape = 2( 50 + 60 = 120) = 2(230) = 460 square inches.

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if we just randomly guess on each of the 4 questions, Then the probability that you get exactly 1 question correct is 1/4.

Probability formula: P(E) = favourable outcomes/Total outcomes

The number of questions is 10

The options for each question are 4.

Possible answers are 1.

Then,

favourable events = 1 × 10= 10

Total events = 4× 10= 40

Now, find the probability by putting the values as follows:

P(E) = favourable outcomes/Total outcomes

P(E) = 10/40

P(E) = 1/4

Therefore, the probability of doing all questions correct is 1/4

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Answer: someone please answer :(((

Step-by-step explanation:

Answer: Hence we have 6 × 3 = 18 words of this type. Therefore, using the equation (i), (ii) and (iii). Total words with 4 letter are : 1680 + 756 + 18 = 2454 ∴ 2454 different permutations can be formed from the letter of the word EXAMINATION taken four at a time.

Answer:

17/5

Step-by-step explanation:

3 + 2/5 = (3*5+2)/5

Answer:

The correct options are;

A circular game piece is moved three squares forward

The flag on a mailbox is turned up

Step-by-step explanation:

An isometric transformation also known as isometry, is the rigid motion transformation or movement that preserves the shape, angles, and distances between of a pre-image (object) and the final image.

Rotation, reflection, translation (parallel motion), glide deflection (transformation involving translation and reflection) such as snow footprints are forms of isometric transformation.

Answer:

Correct answers are

B A circular game piece is moved three squares forward.

C The flag on a mailbox is turned up.

D The letters of words on an emergency vehicle are written from right to left so they appear correctly in a car’s rear-view mirror.

Step-by-step explanation:

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

from the question, we have the following parameters that can be used in our computation:

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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The rectangular prism with the minimum surface area is the fourth rectangular prism with dimensions 4 × 3 × 3 and a minimum surface area of 108 square units. Therefore, the minimum surface area is 108 square units.

A rectangular prism is being designed to have a volume of 36 cubic units. We want to find the minimum surface area in square units for the prism if the edge lengths are positive integers.The volume of a rectangular prism is given by the formula;V = l × w × hWhere V is the volume, l is the length, w is the width, and h is the height. In this case, the volume of the rectangular prism is 36 cubic units.

V = 36We can find the minimum surface area of a rectangular prism given its volume by using the formula;SA = 2lw + 2lh + 2whWhere SA is the surface area, l is the length, w is the width, and h is the height. We want to minimize SA.So, let's minimize SA using the given information.V = lwh = 36This means that the length, width, and height are not all equal.

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Answer:

+40

Step-by-step explanation:

The equation that passes through the given points is the 3 option which is y = -3/2 x + 5

A x + B y = C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x + 3y = 5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx +b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax + b = 0, where a and b are two integers, and x is a variable, is an example of a linear equation with one variable. This equation has only one solution. 2x + 3 = 8, for instance.

According to the given points

x = -1

So

y = (-3/2)(-1) + 5

y = 6.5

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Let f(x) = 3x + 4 and g(x) = 5x² + 3x. After simplifying, (fog)(x) = (gof)(x) = 15x² + 9x + 4

The composition of functions f(x) and g(x) is given by (fog)(x) = f(g(x)) and (gof)(x) = g(f(x)). Given that f(x) = 3x + 4 and g(x) = 5x² + 3x, we can find (fog)(x) by substituting g(x) into f(x): (fog)(x) = f(g(x)) = f(5x² + 3x) = 3(5x² + 3x) + 4 = 15x² + 9x + 4.

Similarly, we can find (gof)(x) by substituting f(x) into g(x): (gof)(x) = g(f(x)) = g(3x + 4) = 5(3x + 4)² + 3(3x + 4) = 45x² + 78x + 47. Therefore, after simplifying, (fog)(x) = (gof)(x) = 15x² + 9x + 4

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Answer:

d

Step-by-step explanation:

I THINK

Answer:

7% of 33= 2.1

2% of 640= 12.8

15% of 470=70.5

7/9 of 51= 119/3

.52 of 62= 32.24

Answer:

1) 2.31

2) 12.8

3) 72

4) 44.625

5) 32.24

Step-by-step explanation:

7% of a number is simply 0.07*the number.

7/8 is just .875*the number

Hope it helps <3

Answer:

101.32 gets rounded to 101.

Why this is your answer:

101 is your answer because...

1. As we can see in the question, it says, "What whole number". That means, we have to see in the decimals in the number "101.32".

2. We can see that In the number "101.32", there is 32 as the decimal number, first we should look at the "tenths" number. Which is 3.

3. As you know, anything 4 and below, stays as it's own number, and 5 and higher, goes to the next whole number. Here, we have 3 as the "Tenths". And according to that rule... You think, what should we do?

4. As we saw that rule, we know that 3 is smaller than 4. That easily means that , The number will get rounded to the whole number it was.

Thanks!

The difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure is ΔU ≈ 0.2511J/K * T

To calculate the difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure, we need to consider the ideal gas law and the difference in pressure.

The ideal gas law states:

PV = nRT

Where:

P = pressure

V = volume

n = number of moles of gas

R = ideal gas constant

T = temperature

Since we are comparing the same volume of air, we can assume V1 = V2, and the equation becomes:

P1 = n1RT

P2 = n2RT

The internal energy (U) of an ideal gas depends only on its temperature. Therefore, the internal energy of the air in the bicycle tire and the equivalent volume of air at atmospheric pressure will be the same if they have the same temperature.

To calculate the difference in internal energy, we need to consider the difference in pressure. The change in internal energy (ΔU) can be expressed as:

ΔU = n1RT - n2RT

To calculate the moles of each gas (nitrogen and oxygen) in the given composition, we need to consider their percentages.

Composition: 78% nitrogen (N2) and 21% oxygen (O2)

Volume: 1.2 liters

Pressure: 5.4×10^5 Pa

We can assume that the temperature is constant.

Let's calculate the moles of each gas:

For nitrogen (N2):

n1 = 78% * V / Vm

= 0.78 * 1.2 L / 22.4 L/mol

≈ 0.0415 mol (rounded to four decimal places)

For oxygen (O2):

n2 = 21% * V / Vm

= 0.21 * 1.2 L / 22.4 L/mol

≈ 0.0113 mol (rounded to four decimal places)

Now, we can calculate the difference in internal energy:

ΔU = n1RT - n2RT

= (0.0415 mol) * R * T - (0.0113 mol) * R * T

= (0.0415 - 0.0113) mol * R * T

= 0.0302 mol * R * T

Since the temperature (T) is the same for both scenarios, we can simplify the equation to:

ΔU = 0.0302 mol * R * T

The value of the ideal gas constant (R) is approximately 8.314 J/(mol·K).

Therefore, the difference in internal energy between the air in the bicycle tire and an equivalent volume of air at atmospheric pressure is:

ΔU ≈ 0.0302 mol * 8.314 J/(mol·K) * T ≈ 0.2511J/K * T

Please note that we need the temperature (T) in order to calculate the exact value of the difference in internal energy.

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Answer:

2 is 60%

3 is 45%

4 is 20%

5 is 55%

Step-by-step explanation:

Want an explanation, or no? Your choice :)

The rate of change of z with respect to t is given by [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2).

To use the chain rule to find dz/dt, we first need to find the partial derivatives of z with respect to x and y.

∂z/∂x = 1/(1 + (y/x)^2) * (y/x^2) = y/(x^2 + y^2)
∂z/∂y = -1/(1 + (y/x)^2) * (1/x) = -x/(x^2 + y^2)

Now we can apply the chain rule:

dz/dt = ∂z/∂x * dx/dt + ∂z/∂y * dy/dt

Substituting in the given values:

dx/dt = e^t
dy/dt = e^(-t)

x = e^t
y = 9 - e^(-t)

∂z/∂x = y/(x^2 + y^2) = (9 - e^(-t)) / (e^(2t) + (9 - e^(-t))^2)
∂z/∂y = -x/(x^2 + y^2) = -e^t / (e^(2t) + (9 - e^(-t))^2)

Substituting these into the chain rule formula:

dz/dt = [(9 - e^(-t)) / (e^(2t) + (9 - e^(-t))^2)] * e^t + [-e^t / (e^(2t) + (9 - e^(-t))^2)] * e^(-t)

Simplifying:

dz/dt = [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2)

Therefore, the rate of change of z with respect to t is given by [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2).

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Answer:

70 dollars

Step-by-step explanation:

he has only 70%left of his initial savings so that make 70%*100=7*10=70usd

Yes, there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be a = 5,184p.

It should be noted that the information is to simply know if there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be:

= Number of pixels / Screen size

= 31.104 / 6

= 5.184

Therefore, the equation representing the relationship will be a = 5,184p.

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Answer:

TRANSALATE!!!!

Step-by-step explanation:

Answer:

Para qué sirve un modelo matemático? Los modelos matemáticos son utilizados para analizar la relación entre dos o más variables. Pueden ser utilizados para entender fenómenos naturales, sociales, físicos, etc.

Step-by-step explanation:

The missing values in the ratio table are:

The equivalent ratios in the order they appear in the table are:

Ratios that are the same when compared are referred to as equivalent ratios. To determine whether two or more ratios are equivalent, they can be put side by side.

An equivalent ratio is, for instance, 1 : 2 and 2:4.

Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.

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Answer:

A: 2:30

B: 13:15.

C: 4:05 A.M

D: 3:25 P.M

Step-by-step explanation:

Answer:

a) 0230 hours

b) 1315 hours

c) 4:05 am

d) 3:25 pm

Step-by-step explanation:

To change a 12 hour clock to a 24 hour clock, note that when it hits p.m., anything over 12 p.m. will have the number added to it.

a) 2:30 am

2:30 am is earlier than 12 pm, therefore, 0230 is your answer. Remember, you must place the 0 in the front to not confuse a user that the 2 is in the tens place value.* *Essentially, use military time:

b) 1:15 pm

1:15 pm is later than 12 pm, therefore, add 12 to the 1 in the hours. Use military time:

0115 + 1200 = 1315

1315 hours is your answer.

To change a 24 hour clock to a 12 hour clock, note the time frame in which the time is given. if over 1200, then subtract by 12, and add the p.m.

0405 = 4:05 am.

1525 = 12 pm + 3:25 = 3:25 pm.

~

Answer:

Slope = - 1/3

Step-by-step explanation:

Y2-Y1 / X2 - X1

49 students should be sampled to be within 0.5 drinks of the population mean with 95% probability. This result is obtained using the Z–distribution.

Z- distribution is one of the cases of normal distribution . On the basis of the given we are using Z-Score formula ,

Z = (x- μ) / σ/√n

Where , Z→ z- value corresponding to confidence level

x – μ → margin of error

σ → standard deviations

n → sample size

We have given , σ = 1.79 and confidence level 95% = 0.95 then

z-value for 0.95 is 1.96 ( from z-table )

Margin of error is difference between population mean and sample mean and here it’s 0.5..

We shall find out the value n i.e., sample size or the number of students

Put all the values in z-score formula we get,

1.96 = 0.5 / 1.79/√n

=> √n = (1.96×1.79)/ 0.5

=> √n= 7.01 => n= 49

So, the sample size is 49 .

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