What value of x makes the equation true?
3 - 14x = 17
A-1
B-1
C-28
D-2

The tangential component of the acceleration is At=0 and the normal component of the acceleration is An=2j.

To find the tangential and normal components of the acceleration vector, we first need to find the velocity and acceleration vectors.

The velocity vector is the derivative of the position vector:

r(t) = ti + t^2j + 8tk

v(t) = r'(t) = i + 2tj + 8k

The acceleration vector is the derivative of the velocity vector:

a(t) = v'(t) = 2j

The acceleration vector is constant and is directed entirely in the y-direction, so the tangential component of the acceleration is zero.

The normal component of the acceleration is the magnitude of the acceleration vector, which is:

|a| = √(0^2 + 2^2 + 0^2) = 2

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Answer:

A.P(t) = Po (1 + r)^t

P(t) = 1200( 1 + 0.024)^t

B. 1417 termites

Step-by-step explanation:

Rosanne and Jimmy are looking to purchase a house. They found one that they like, but the inspection report showed that there was a problem. The foundation has termites. The report states that the foundation of a house has 1200 termites. The termites grow at a rate of about 2.4% each day.

A. Formulate an equation in exponential form that represents the termite situation.

The formula for exponential growth or increase =

P(t) = Po (1 + r)^t

Where:

P(t) = Population growth after time t

P(o) = Initial Population = 1200 termites

r = Growth rate = 2.4% = 0.024

t = Time in days

Hence, the equation in exponential form that represents the termite situation is given as:

P(t) = 1200( 1 + 0.024)^t

B. The extermination is scheduled out for one week from the date of the report. Use your equation to determine how many termites will be in the home at the time of the extermination.

The time of extermination = 1 week

1 week = 7 days

Hence,

t = 7 days

P(t) = Po (1 + r)^t

P(7) = 1200( 1 + 0.024)⁷

P(7) = 1200(1.024)⁷

P(7) = 1416.7099449 termites

Approximately

= 1417 termites

Answer:

51

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

Solution

For this case we have the following function:

And we want to find the steps to obtain the above function from this one:

So we can do the following:

Reflection over the x axis

horizontal shift to the left 2 units

Answer:

45

Step-by-step explanation:

Subtract the numbers

(3+(8-2)). x5

[3+6)]. x5

Add the numbers

[3+6]. x5

[9]. x5

If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

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

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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\(i^7 + \dfrac 1{i^4}\\\\=i^2 \cdot i^2 \cdot i^2 \cdot i + \dfrac 1{i^2 \cdot i^2}\\\\=(-1)(-1)(-1)i + \dfrac 1{(-1)(-1)} ~~~;[ i^2 = -1] \\\\\ = (-1)^3 i+ \dfrac 1{(-1)^2} \\\\=-i+1\)

Answer:

One edge of a painting is 6 in. longer than the shorter edge. The picture has a 2-in.-wide frame. There is one rectangle inside the other rectangle. The distance between two edges of two rectangles is 2. The length of the rectangle is x + 6 and width is x. The portion between two rectangles is shaded. Part A Which quadratic function represents the total area of the picture and frame? A. f(x) = x2 + 8x + 12 B. f(x) = x2 + 10x + 24 C. f(x) = x2 + 12x + 32 D. f(x) = x2 + 14x + 40 Part B What is the total area of the %3D %3D framed picture if its shorter edge is 8 inches long? Enter your answer in the box. _in.2 x+ 6

Step-by-step explanation:

A motorist drives 146km at a certain average speed she then increases the speed by 9km/h and takes the same time to travel the next 164km.

find her speeds for both parts of the journey.

:

let s = his original speed

then

(s+9) = the increased speed

:

Write a time equation; time = dist/speed

146%2Fs = 164%2F%28%28s%2B9%29%29

cross multiply

164s = 146(s+9)

164s = 146s + 1314

164s - 146s = 1314

18s = 1314

s = 1314/18

s = 73 km/h is his original speed

:

The tables is completed as follows

5.1.1

1    8

2   16

4    24

6   48

8    64

12    96

5.1.2

The type of proportion is Direct Proportion

5.2.1

1    8

2   4

4    2

6     1

8    0.5

5.1.3

The type of proportion is Inverse Proportion

Direct Proportion: A direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable, and a decrease in one variable results in a proportional decrease in the other variable.

The general formula for a direct proportion is y = kx,

where

k is the constant of proportionality.

Inverse Proportion: An inverse proportion is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable, and a decrease in one variable results in a proportional increase in the other variable.

The general formula for an inverse proportion is y = k/x,

Joint Proportion: A joint proportion is a relationship between three or more variables where one variable is directly proportional to the product of the other variables.

The general formula for a joint proportion is y = kxy,

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Answer:

fraction: 99/1000 Step-by-step explanation:

Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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Answer:

I am 14 why are you asking

Answer:

Step-by-step explanation:

4x is in a multiplication form

4x=36

meaning a number when multiplied with 4 gives the answer 36

hence in order to find the answer

36 divided by 4 which is equivalent to 9

answer is 9

Answer:  \(x = 9\)

Step-by-step explanation:

We must isolate \(x\) on one side of the equation in order to solve the equation \(4x = 36\) for \(x\).

Step 1: Divide both sides of equation by 4:

\(\frac{4x}{4} = \frac{36}{4}\)

Step 2: Simplify

\(x = 9\)

Therefore, the solution to the equation is \(x = 9\).

----------------------------------------------------------------------------------------------------------

Rearranging an algebraic equation so that \(x\) is on one side and all other terms are on the other side of the equal sign is known as isolating \(x\).

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

51.1 ≈ r

Step-by-step explanation:

"A bicycle wheel travels 321 in for each revolution"- means that 321 is the circumference of the wheel that is a circle.

C = 2· π· r

What is the radius of the wheel ​?

321 = 2· π· r, divide both sides of the equation by 2 π

(321/2·π) = r , use calculator, solve and round the answer

51.1 ≈ r

The value of the variable of the rectangular prism 'x' will be 7.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

The equation is given below.

308 = 2(10 · x) + 2(2 · x) + 2(2 · 10) + 6(5 · 5) - 2(5 · 5)

Simplify the equation, then we have

308 = 2(10 · x) + 2(2 · x) + 2(2 · 10) + 6(5 · 5) - 2(5 · 5)

308 = 20x + 4x + 40 + 150 - 50

308 = 24x + 140

24x = 168

x = 7

The value of the variable of the rectangular prism 'x' will be 7.

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Answer:

160 square units

Step-by-step explanation:

First, lets focus on the triangles.

To find the area of a right triangle, we need to multiply the length by the width, and divide by 2.

(5 * 8) / 2 = 20

(And since there is two triangles, the area of the two is 40.)

To find the area of a rectangle, we need to multiply the length by the width.

15 * 8 = 120

Now we add all the areas together.

120 + 20 + 20 = 160

Is the answer is 160 square units.

The number of shots attempted by the player until he misses is considered a binomial equation because the probability of success is always constant.

Therefore, the particular criteria for forming a binomial equation is

Therefore, for the given case, the hockey player uses 21% of his shots and is requested to make his shots until he misses. The total number of shots attempted is observed.

Since each shot has only dual possible outcomes (success or failure), and probability of success is constant then this experiment meets all the  four characteristics of forming a  binomial experiment.

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Using the normal distribution, it is found that there are 68 students with scores between 72 and 82.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given, respectively, by:

\(\mu = 72, \sigma = 10\)

The proportion of students with scores between 72 and 82 is the p-value of Z when X = 82 subtracted by the p-value of Z when X = 72.

X = 82:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{82 - 72}{10}\)

Z = 1

Z = 1 has a p-value of 0.84.

X = 72:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{72 - 72}{10}\)

Z = 0

Z = 0 has a p-value of 0.5.

0.84 - 0.5 = 0.34.

Out of 200 students, the number is given by:

0.34 x 200 = 68 students with scores between 72 and 82.

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The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

According to the statement

we have given that the a identity and we have to use in the given conditions.

So, For this purpose, we know that the

Given that the required identity of Tangent is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)),

we have:

tan(x + y) = sin(x + y)/(cos(x + y))

sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

After solving this identity according to the statement it is clear that all the options are correct.

So, The correct options according given identity of tangent are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Examine the following steps. Which do you think you might use to prove the identity Tangent (x) = StartFraction tangent (x) + tangent (y) Over 1 minus tangent (x) tangent (y) EndFraction question mark

Check all that apply.

-Write tan(x + y) as sin (x + y) over cos(x +y).

-Use the sum identity for sine to rewrite the numerator.

-Use the sum identity for cosine to rewrite the denominator.

-Divide both numerator and denominator by cos(x)cos(y).

-Simplify fractions by dividing out common factors or using the tangent quotient identity.

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Answer:

False

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 1, 7 ) → (1, 7 )

Answer: True

Step-by-step explanation:

Because since it's getting reflected over the Y-axis it's gonna be all negatives.

Answer:

92°

Step-by-step explanation:

We can say that the angle that is of x degrees is an inscribed angle because its vertex is on the circle and its sides are made up of rays. When you have an inscribes angle, it measures exactly half the angle it intercepts. In this case that angle is 184°. So, because of this we can say:

x = 184° / 2

x = 92°

Answer:

0 over 12

Step-by-step explanation:

3/4 is equal to 9/12

so your basically taking 9/12 from 9/12

The function g(x) is a transformation of the parent function f(x) it was transformed to make g(x) - Horizontal or vertical stretch.

Let's start thinking about vertical stretching and compression by simply looking at the graphs rather than starting with a ton of math.

Vertical stretching is the process of making a function taller by stretching it out vertically.

Vertical compression entails squashing the function down vertically, making it shorter.

Stretching and compression genuinely appear like that. It's time to start doing some math to figure out how to modify the function so that the graph can be stretched or compressed.

When the function that generated the original graph is changed in a way that necessitates a smaller x-value in order to get the same y-value, this is known as horizontal compression.

This happens when a constant c with a value larger than 1 is multiplied by the x-value of a function.

Hence, The function g(x) is a transformation of the parent function f(x) it was transformed to make g(x) - Horizontal or vertical stretch.

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Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Corrected Question

e(x)=840-52.5x

Let e(x) be the elevation, in meters, of a cable car from the ground, x minutes after it begins descending from the top of a hill. Since e(14) = ?, the elevation of the cable car will be meters from the ground minutes after it begins descending from the top of the hill.

Answer:

e(14) =105 meters

Elevation of the cable car 14 minutes after it begins descending from the top of the hill= 105 meters from the ground

Step-by-step explanation:

Given the elevation, e(x) in meters, of a cable car from the ground , x minutes after it begins descending from the top of a hill.

e(x)=840-52.5x

e(14)=840-52.5(14)

e(14)=840-735

e(14)=105 meters

Since e(14) =105 meters, the elevation of the cable car will be 105 meters from the ground 14 minutes after it begins descending from the top of the hill.