which graph shows the dilation image of rectangle ABCD with the center of dilation at the origin and a scale factor of 1/3

Answer:

first term (a)=-2

common difference (d)=8

Now,

87th term=a+(n-1)d

=-2+(87-1)×8

=-2+86×8

=-2+688

=686

Answer: 1/50, or 0.02

Step-by-step explanation:

I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.

12 ft maybe? i dunno im sorry if this is wrong

Answer:

See below

Step-by-step explanation:

Answer:

the answer is 26.32

Step-by-step explanation:

The relative change from what Susan counts her class needs (old) to what Thomas counts his class needs (new) should be 26.32.

Since it required 24 sets of supplies for the week. Susan counts that her class only needs 19 supplies

So here the relative change be

= (24 - 19) / 19

= 0.263157 * 100

= 26.32

Hence, the relative change is 26.32.

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Answer:

y = 5000x

Step-by-step explanation:

Let x = number of days

Let y = number of widgets

Given, factory produces 5000 widget per day:

⇒ y = 5000x

Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

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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If a value of 98° is added to the data, then the mean change is 1.35, if a value of 48° is added to the data, then the median change from the 6th number to the 7th number but the value still same, if a value of 80.8° is added to the data then the range still same.

In the given question we have to find the change in mean, median and range after the addition of another value.

(1) The list of average high temperatures in degrees for a city is

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

So the mean is find as the sum of value divided by the total number of values.

As we see that the total number of values are 12.

Now the sum of values

∑x=58+61+71+77+91+100+105+102+95+82+66+57

∑x=965

Mean = ∑x/n

Mean = 965/12

Mean = 80.42

If a value of 98° is added to the data, then the sum of values will be

∑x'=58+61+71+77+91+100+105+102+95+82+66+57+98

∑x'=1063

The total number of values = 13

So the

Mean'=∑x'/n'

Mean'=1063/13

Mean'=81.77

Now the change in mean=Mean'−Mean

change in mean=81.77−80.42

change in mean=1.35

(2) The list of average high temperatures in degrees for a city is

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

So the median is find after arranging the values in ascending order.

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Total number=12

Meadian=n/2 th number

Meadian=12/2 th number

Meadian=6 th number

Meadian= 77

If a value of 48° is added to the data.

So the ascending order of the number is

48, 57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Total number=13

Meadian=(n+1)/2 th number

Meadian=13+1/2 th number

Meadian=14/2 th number

Meadian=7 th number

Meadian=77

Now the range changes from the 6th number to the 7th number but the value still same.

(3) The list of average high temperatures in degrees for a city is

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

So the range is find after subtracting the greatest number to the smallest number.

So the range=Greatest Number−Largest Number

range=105−57

range=48

If a value of 80.8° is added to the data then the range still same because the added value is between the largest and smallest number.

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When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

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The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10

Answer:

\(127.3 - 1.578 \approx 125.7\)

Step-by-step explanation:

Given

\(127.3 - 1.578 = 125.722\)

Required

Round to the precision of the 1.578

The number in the subtraction column is 1.578; so, the question implies that we round up 125.722 to the precision of 1.578

The precision of 1.578 is 4 (i.e. it has 4 digits). Hence, 125.722 will be approximated to 4 significant digits.

So, we have:

\(125.722 \approx = 125.7\)

or

\(127.3 - 1.578 \approx 125.7\)

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

D) Exponential growth

Step-by-step explanation:

Either by testing points or simply using common sense, we can clearly see that this graph is not linear.

We can see that the graph is "moving away" from the x-axis as x grows larger, so the graph is not decaying, it's growing.

So, the graph is of D) Exponential growth.

The function showed in the graph is an exponential decay.

The term exponential decay refers to a situation whereby a function is decreasing exponentially. It can easily be observed from the graph of a function.

Looking at the graph of the function, we can easily observe that the function showed in the graph is an exponential decay.

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Answer:

30

Step-by-step explanation:

Answer:

About -4.286

Step-by-step explanation:

First, let's set up the equation.

(24 + 6)/(3 - 2 [4 + 1])

Now, let us do the parenthesis first. (4 + 1). While we are at it, we can also do 24 + 6.

30/(3 - 2[5)]

Now, -2(5)

30/3 - 10

Let us do 3 - 10

30/-7

Lastly, 30/-7, which unfortunately, is a non-terminating decimal, which is about:

-4.286, rounded to the nearest thousandth.

Hope this helps!

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

A

Step-by-step explanation:

it is Arithmetic because if you subtract 12 from 40 you'll get 28 , same for the others. but if you get the common ratio by dividing 40/12 which is 3.333... it's doent work for the sequence

He needs to buy 7 bags of fertilizer to fertilize the garden

The radius of the garden = 10 feet

The area of the garden A = π × \(r^2\)

Where A is the area of the garden

r is the radius of the garden

Substitute the values in the equation

A = π × \(10^2\)

= π × 100

= 314.16 feet square

Each bag of fertilizer covers 50 square feet

Then the number of bags required to fertilize the garden = The area of the garden / 50

Substitute the values in the equation

= 314.16 / 50

= 6.28

≈ 7 bags

Hence, he need to buy 7 bags of fertilizer to fertilize the garden

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Answer: $1.65

Step-by-step explanation: 19.80 / 12 = 1.65

Answer:

20

Step-by-step explanation:

8 is near to 10 so +1

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Answer:

1

Step-by-step explanation:

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Therefore , coordinate problem solution is A) 3140 pulses per minute , B) 2915 beats per minute , C) heartbeat of 2915 beats per minute (D) or 2915.5 beats per minute .

When locating points or other mathematical objects precisely on a region, such as Euclidean space, a coordinate system is a technique that uses one or more numbers or coordinates. Locating a point or item on a the double plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y vectors are used to define a point's location on a 2D plane. a collection of numbers that indicate specific locations.

Here,

The slope method can be used to calculate the patient's heart rhythm after 42 minutes that use the secant line connecting the points with the specified values of t:

Heartbeat change / time change is the trend.

The heart rate can then be estimated using this slope value along with the number for heartbeats at t = 42 minutes.

A)Using coordinates 36, 2510, and 42, 2915 as examples:

Cardiac rate at 42 minutes = 2510 + (42 - 36) * 75 = 3140 Slope = (2915 - 2510) / (42 - 36) = 75

b) Using coordinates (38, 2647) and (42, 2915), respectively:

Cardiac rate at 42 minutes = 2647 + (42 - 38) * 67 = 2915 Slope = (2915 - 2647) / (42 - 38) = 67

c) Applying the values (40, 2784) and (42, 2915):

Heart rate at 42 minutes = 2784 + (42 - 40) * 65.5 = 2915.5 Slope = (2915 - 2784) / (42 - 40) = 65.5

Using coordinates (42, 2915), and (44, 3048), respectively:

Cardiac rate at 42 minutes = 2915 + (42 - 42) * 66.5 = 2915 Slope: (3048 - 2915) / (44 - 42) = 66.5

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The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Answer:

Step-by-step explanation:a

Answer:

C

Step-by-step explanation:

Prime factors: 2, 3, 3