The picture below shows a pole and its shadow:

What is the height of the pole?

121 centimeters
220 centimeters
225 centimeters
231 centimeters

Answer: 28/17 or 1.647........

Step-by-step explanation: reduce it by canceling the common factors ;)

Answer:

7 7/16

Step-by-step explanation:

(7*17)/(2*8)

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

$356.44

Step-by-step explanation:

Answer:  448 dollars

=============================================

Work Shown:

P = 400 is the balance

r = 0.12 is the decimal form of the interest rate

t = 1 is the number of years

Use those values to get the simple interest to be

i = P*r*t

i = 400*0.12*1

i = 48

The amount of interest charged is $48

Add this onto the balance of 400 dollars and the total amount Aaron owes is P+i = 400+48 = 448 dollars.

Answer: -1 Is the answer.

Answer:

Hope the picture will help you

Answer:

huh

Step-by-step explanation:

Use the data to create a stemplot.

Twenty-four workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes.

20 35 42 52 65 20 60 49 24 37 23 24

22 20 41 25 28 27 50 47 58 30 32 48

The data in a stem-and-leaf plot:

3/0257

2/0002344578

4/12789

5/028

6/05

Another presentation that is similar to a histogram is a stemplot. In statistics, a stemplot is a tool for presenting quantitative data in a graphical format, similar to a histogram, namely to assist in visualizing the shape of the data distribution which is often used in exploratory analysis. Stemplots were introduced by Arthur Bowley in the early 1900's. However, its general use only began in 1980 after John Tukey's published Exploratory Data Analysis in 1977.

Stem-and-leaf plots provide more information about true values than histograms. As in a histogram, the length of each bar corresponds to the number of events that fall into a given interval. On Histograms. we can only see the frequency value of the data but we don't know what the actual number value is. In contrast to the histogram, in SLP besides we can know the frequency value, we can also know what the actual data value is. This is done by dividing the observed values into two components, stem and leaf.

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The function f(x) = 4x² + 12x + 9 has an inverse f⁻¹(x) = -(3 - √x)/2 , (3 + √x) / 2 and the restriction of it's domain is for all values of x

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.

The function f(x) = 4x² + 12x + 9 has an inverse of

f⁻¹(x) = -(3 - √x)/2 , (3 + √x) / 2

2).

The domain of the given function is for all values of x and can be represented in function notation as

domain = (-∞, ∞)

3) The inverse of the domain function is for all values greater than or equal to x or can be represented as [0, ∞)

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Answer:

1) No, as it is not a one-to-one function.

2) The domain should be restricted to either the left or the right of the vertex.

\(\textsf{3)} \quad f^{-1}(x)=\dfrac{-3 + \sqrt{x}}{2}\)

Step-by-step explanation:

To determine if the function y = 4x² + 12x + 9 has an inverse, we need to check if it is a one-to-one function.

A function has an inverse if and only if it is one-to-one, meaning that each input value (x) corresponds to a unique output value (y), and no two different x-values produce the same y-value.

To check if y = 4x² + 12x + 9 is one-to-one, we can use the horizontal line test. If any horizontal line intersects the graph of the function at more than one point, the function is not one-to-one, and hence, it does not have an inverse.

The function y = 4x² + 12x + 9 is a quadratic function, and all quadratic functions have a U-shaped graph, which means any horizontal line intersects the graph at two points. Therefore, the function y = 4x² + 12x + 9 is not one-to-one, and it does not have an inverse.

\(\hrulefill\)

To allow the function y = 4x² + 12x + 9 to have an inverse, we need to restrict its domain to make it one-to-one. Since the function is a parabola that opens upwards and has its vertex at the minimum point, we can restrict the domain to only consider the portion of the parabola to the right (or left) of the vertex. By doing this, we can make the function one-to-one and allow it to have an inverse.

\(\hrulefill\)

The x-coordinate of the vertex of a quadratic function in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-coordinate of the vertex of the given function is:

\(x=-\dfrac{12}{2(4)}=-\dfrac{12}{8}=-1.5\)

To find the y-coordinate of the vertex, substitute x = -1.5 into the given function:

\(y=4(-1.5)^2+12(-1.5)+9\)

\(y=4(2.25)+12(-1.5)+9\)

\(y=9-18+9\\\)

\(y=0\)

Therefore, the vertex of given function is (-1.5, 0).

Let's restrict the domain to the right of the vertex.

Therefore, the restricted domain is [-1.5, ∞).

To find the inverse of the domain-restricted function, swap x and y:

\(x = 4y^2 + 12y + 9\)

Switch sides:

\(4y^2 + 12y + 9=x\)

Subtract x from both sides:

\(4y^2 + 12y + 9-x=0\)

Now we can use the quadratic formula to find y, where a = 4, b = 12 and c = (9 - x):

\(y=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)

\(y=\dfrac{-12 \pm \sqrt{(12)^2-4(4)(9-x)}}{2(4)}\)

\(y=\dfrac{-12 \pm \sqrt{144-144+16x}}{8}\)

\(y=\dfrac{-12 \pm \sqrt{16x}}{8}\)

\(y=\dfrac{-12 \pm 4\sqrt{x}}{8}\)

\(y=\dfrac{-3 \pm \sqrt{x}}{2}\)

Replace y with f⁻¹(x):

\(f^{-1}(x)=\dfrac{-3 \pm \sqrt{x}}{2}\)

The range of the inverse function is the domain of the original function.

As the domain of the original function is restricted to [-1.5, ∞), then the range of the inverse function is also restricted to [-1.5, ∞).

Therefore, the inverse of the domain-restricted function is:

\(f^{-1}(x)=\dfrac{-3 + \sqrt{x}}{2}\)

Answer:

5(x−3)(x2+3x+9)

Step-by-step explanation:

Factor 5x3−135

5x3−135

=5(x−3)(x2+3x+9)

Answer:

5(x−3)(x2+3x+9)

Answer:

5(x - 3)(x² + 3x + 9)

Step-by-step explanation:

5x³ - 135

~Factor out 5

5(x³ + 27)

~Factor x³ + 27

5(x - 3)(x² + 3x + 9)

Best of Luck!

as 20+11>30 it is a triangle

now for angle

let us consider a=20,b=30,c=11 and their opposite angle be A,B,C respectively

then B =cos-inverse((a^2 +c^2-b^2)/2ac))

p.s We are calculating value of B because it is opposite of largest side b so it will be highest angle

or B = cos-inverse((400+121-900)/(2*30*11))

B = 125.04 degree

since B> 90 the triangle is obtuse triangle

Answer:

obtuse

Step-by-step explanation:

Given the 3 sides 20, 30 and 11

For the sides to form a triangle then the sum of any 2 sides must be greater than the third side.

20 + 30 = 50 > 11

20 + 11 = 31 > 30

30 + 11 = 41 > 20

Thus the 3 sides form a triangle

To determine what type of triangle it is

let c be the longest side and a, b the other 2 sides

• If a² + b² = c² then triangle is right

• If a² + b² > c² then triangle is acute

• If a² + b² < c² then triangle is obtuse

Here c = 30, a = 20, b = 11

c² = 30² = 900

a² + b² = 20² + 11² = 400 + 121 = 521

Since a² + b² < c² then triangle is obtuse

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

x = -5 and y = 1

Step-by-step explanation:

a) 2x + 5y +5 = 0

a) 2x + 5y = -5

b) 2y = 3x + 17

b) y = 3/2x + 17/2

a) 2x + 5(3/2x + 17/2) = -5

a) 2x + 15/2x + 85/2) = -5

a) 19/2x = -5 - 85/2

a) 19/2x = -95/2

a) x = (-95/2) / (19/2)

x = -5

b) 2y = 3(-5) + 17

b) y = 2/2

y = 1

Answer:

x=20

4=140

1=40

Step-by-step explanation:

7x=2×+100

5×=100

×=20

4=7(20)=140

1=180-140=40

Answer:

x=20

m<4=140

m<1=40

Step-by-step explanation:

to figure out angle 1 just subtract 140 from 180

Answer:

Step-by-step explanation:

First, we need to find the total interest earned in a year:

For 9 months with a balance of at least $500, the interest rate is 4%. So, the interest earned is:

9/12 * 0.04 * $600 = $21.60

For 3 months with a balance below $500, no interest is earned.

So, the total interest earned in a year is $21.60.

Next, we need to calculate the total monthly service charge for the year:

For 3 months with a balance below $500, a monthly service charge of $15 applies. So, the total service charge for the year is:

3 * $15 = $45

Finally, we need to calculate the net earnings (interest minus service charge) for the year:

Net earnings = Interest earned - Service charge

= $21.60 - $45

= -$23.40

Since the net earnings are negative, this account had a net loss of $23.40 for the year.

Answer:

B (-1, 6)

Step-by-step explanation:

I took the test.

Answer:

Total amount of tickets is 48

Step-by-step explanation:

Step 1:  Determine the amount of tickets they solid in all

We see that the movie theater has a ratio of 4 adult tickets for every children ticket which means that wen a child purchases a ticket there are 2 adult tickets that come along.

32 adult tickets / (2 adult tickets per child)

16 children tickets

Total tickets: 32 adult tickets + 16 children tickets = 48 tickets

Answer:  Total amount of tickets is 48

Answer:you bought 10 candy bars and 24 bags of chips

Step-by-step explanation:

The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

check the attachment given belοw tο understand.

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Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

PQ AND SR on ED

Step-by-step explanation:

Based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.

The vertical angles theorem is a theorem that states that when two lines intersect and form vertically opposite angles, each pair of vertical angles has the same angle measures. A pair of vertically opposite angles are always equal to each other.

For the given situation,

Angles PTQ and STR are vertical angles and congruent.

Line segments T P, T Q, T R, and T S are radii.

So, T P = T Q = T R = T S.

The two sides T P = T Q and T R = T S and \(\angle PTQ = \angle RTS\),

then by SAS similarity theorem two triangles,

Δ PTQ ≅ Δ STR.

When two triangles are congruent, then the corresponding arc are also congruent.

The congruent central angles intercept congruent arcs PQ and SR.

Hence we can conclude that based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.

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The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

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Answer: $252

Step-by-step explanation:

21$ an hour x 12 hours = $252 total :)

Answer:

She earned $252 thsi month.

Step-by-step explanation:

1  hour = $21

12 hours = $?

21*12 = 252

Answer:

the answer is y=-3x+5

since it's parallel, the slope is the same. so m=-3

use point slope formula y-y1=m(x-x1) and plug in the slope and the point

y-2=-3(x-1)

y-2=-3x+3

y=-3x+5

Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

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Answer:

The roots of this function are at -4 and -1.

f(x) = (2x + 8)(-2x - 2)

= (2x + 8)(-2x + (-2))