Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x +2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x- 7.
Calculate the limit as

Answer:

C) (-2 , 4)

x = -2

y = 4

Step-by-step explanation:

    We can use substitution method.

     3x + 2y = 2 -------------(I)

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

Make y as the subject in equation (II)

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

Substitute y = 8 + 2x in equation (I) and we can find the value of 'x',

          3x + 2*(8 + 2x) = 2

     3x + 2*8 + 2*2x    = 2 {Distributive property}

           3x + 16 + 4x    = 2

           3x + 4x + 16    = 2

Combine like terms,

                      7x + 16 = 2

Subtract 16 from both sides,

                           7x   = 2 - 16

                           7x   = -14

Divide both sides by 7,

                             x  = - 14 ÷ 7

                             [tex]\boxed{\bf x = -2}[/tex]

Substitute x = -2 in equation (III)

           y = 2*(-2) + 8

              = -4 + 8

           [tex]\boxed{\bf y = 4}[/tex]

Answer:

486 square feet

Step-by-step explanation:

To calculate the area of the path, first find the dimensions of the garden, including the path. Then find the area of this larger outer rectangle and subtract the area of the inner rectangle (the garden without the path).

The garden measures 28ft by 47ft.

The path is 3ft wide, so it adds a total of 6ft to the length (3ft on each side) and 6ft to the width.

The dimensions of the garden, including the path:

Length: 47ft + 6ft = 53ft

Width: 28ft + 6ft = 34ft

Find the area of the outer rectangle (including the path):

Area_outer = Length * Width = 53ft * 34ft = 1802 sq ft

Find the area of the inner rectangle (the garden without the path):

Area_inner = 28ft * 47ft = 1316 sq ft

Now subtract the area of the inner rectangle from the area of the outer rectangle to find the area of just the path:

Area_path = Area_outer - Area_inner = 1802 sq ft - 1316 sq ft = 486 sq ft

So, the area of the path is 486 square feet.

Answer: 486 square feet;

Step-by-step explanation:

Area of the garden = 28 x 47 = 1316ft.²

-

Length of the garden and path = Length of the garden + 3 ft. on both sides

Length of the garden and path = 28 + 3 + 3 = 34 ft.

-

Width of the garden and path = Width of the garden + 3 ft. on both sides

Width of the garden and path = 47 + 3 + 3 = 53ft.

-

Area of the garden and path = Length x Width

Area of the garden and path = 34 x 53 = 1802 ft²  

-

Area of the path = Area of the garden and path - Area of the garden

Area of the path = 1802 - 1316 =  486ft²

-

Answer: 486ft²

The all four data sets can be represented on a dot plot, as dot plots are both decimal and Integer values.

A dot plot is a graphical representation that displays data points as dots along a number line. It is commonly used to show the distribution of a small set of quantitative data.

The data set should be shown on a dot plot, we need to consider the characteristics of the data.

1. Data Set 1: {0.012, 0.078, 0.093, 0.147, 0.187}

This data set consists of decimal values. A dot plot can effectively represent decimal values, where each dot represents a data point. Therefore, Data Set 1 should be shown on a dot plot.

2. Data Set 2: {1.3, 1.9, 2.5, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0}

Similar to Data Set 1, this data set consists of decimal values. Hence, it can also be effectively represented on a dot plot. Each value would be represented as a dot along the number line.

3. Data Set 3: {712, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730}

This data set consists of integer values. Dot plots are commonly used for discrete data, including integers. Therefore, Data Set 3 can be appropriately represented on a dot plot.

4. Data Set 4: {16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97}

This data set also consists of integer values dot plots can effectively display discrete data. Hence, Data Set 4 can be shown on a dot plot.

all four data sets can be appropriately represented on a dot plot, as dot plots are suitable for displaying both decimal and integer values.

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The amount that Jetta spends on gas in one year is $1,905.

Assume regular unleaded fuel costs $3.81 per gallon. A Volkswagen Jetta uses unleaded fuel. It gets about 30 miles per gallon.

The rate is the ratio of the amount of something to the unit.

Imagine that a driver of the Jetta drives 15,000 miles each year.

The amount that Jetta spends on gas in one year is calculated as,

⇒ 15,000 x $3.81 / 30

⇒ $1,905

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Part 1: methods did not consider the number of repetitions or combinations of the same item that could be used in different outfits. Part 2: Jenny can wear 1,920 different outfits by choosing one blouse, one skirt, one pair of socks, and one pair of shoes at a time from her closet.

Part 1:

Because they only considered a limited number of clothing items and did not take into account the fact that different combinations of these items could create a larger number of outfits, the methods used in the previous two problems would be inefficient in determining the number of different outfits Jenny could wear.

Part 2:

Using the Fundamental Principle of Counting, the number of different outfits Jenny could wear can be determined by multiplying the number of choices for each clothing item together. Therefore, the total number of different outfits can be calculated as:

6 blouses x 4 skirts x 20 pairs of socks x 4 pairs of shoes = 1,920 different outfits

Therefore, Jenny can wear 1,920 different outfits by choosing one blouse, one skirt, one pair of socks, and one pair of shoes at a time from her closet.

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Based on the information, the line segments PR and QR and PQ to form an equilateral triangle.

The three blue line segments are PQ, PR, and QR. In order to construct an equilateral triangle with PQ as one side using a compass and straightedge:

1.  Draw a line segment PQ.

2. Place the compass at point P and draw a circle with radius PQ.

3. Without changing the radius of the compass, place the compass at point Q and draw another circle.

4. The intersection of the two circles is point R.

Draw line segments PR and QR to form an equilateral triangle.

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Answer:

Based on the information, the line segments PR and QR and PQ to form an equilateral triangle.

How to explain the triangle

The three blue line segments are PQ, PR, and QR. In order to construct an equilateral triangle with PQ as one side using a compass and straightedge:

1.  Draw a line segment PQ.

2. Place the compass at point P and draw a circle with radius PQ.

3. Without changing the radius of the compass, place the compass at point Q and draw another circle.

4. The intersection of the two circles is point R.

Draw line segments PR and QR to form an equilateral triangle.

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Hello

4x² - 28x = -33

4x² - 28x + 33 = 0

(4x² - 6x) + (-22x + 33) = 0

2x(2x - 3) - 11(2x - 3) = 0

(2x - 11)(2x - 3) = 0

2x - 11 = 0               2x - 3 = 0

2x = 11                     2x = 3

x = 11/2                    x = 3/2

The amounts of koalas are given as follows:

a. Initially: 47.

b. 13 weeks: 21.

c. 23 weeks: 19.

d. The virus will not kill all the koalas, as when t -> ∞, N(t) -> ∞.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

N(t) = 15 + 96/(t + 3).

For the initial number of koalas, we have that t = 0, hence:

N(0) = 15 + 96/3 = 47.

After 13 weeks, the number is given as follows:

N(13) = 15 + 96/16 = 21.

After 23 weeks, the number is given as follows:

N(23) = 15 + 96/26 = 19.

As t -> ∞, we have that:

N(∞) = 15 + 96/∞ = 15 + 0 = 15.

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Based οn bοth the median and mean values, it appears that Bus 47 typically has the faster travel time cοmpared tο Bus 18.

We know that

Statistics is the discipline of mathematics concerned with data collection, analysis, interpretation, presentation, and organisation. It includes approaches for summarising and describing data, as well as inferring and forecasting based on the data.

Tο determine which bus typically has the faster travel time, we need tο cοmpare the measures οf center (mean and median) οf the twο buses.

The median represents the dataset's midway, where half of the values are above and half are below. The mean represents the dataset's average value, which is computed by adding all of the values and dividing by the total number of values.

When the medians are compared, we can see that Bus 47 has a higher median of 16, while Bus 18 has a lower median of 13. This shows that Bus 47 may have a faster average trip time.

However, we must also consider the methods. When the means are compared, we can see that Bus 47 has a higher mean of 16, whereas Bus 18 has a lower mean of 13. This lends credence to the notion that Bus 47 may have a faster average travel time.

Therefοre, based οn bοth the median and mean values, it appears that Bus 47 typically has the faster travel time cοmpared tο Bus 18.

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The complete question is:

Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 18, with a median of 13

Bus 47, with a median of 16

Bus 18, with a mean of 13

Bus 47, with a mean of 16

Answer:f(27)=-6

Step-by-step explanation:

The cube root of both sides to solve for x variable is

x = (k - y^3 - z^3)^(1/3)

You can solve for y or z in terms of the other variables by rearranging the original equation.

Given the equation: x^3 + y^3 + z^3 = k.

To solve this equation for one of the variables (x, y, or z), you would need additional information or constraints. However, I can provide you with a general method to express one variable in terms of the others. Let's solve for x:
Step 1: Subtract y^3 and z^3 from both sides of the equation.
x^3 = k - y^3 - z^3
Step 2: Take the cube root of both sides to solve for x.
x = (k - y^3 - z^3)^(1/3)
Now, x is expressed in terms of y, z, and k. If you have any specific values for y, z, and k, you can substitute them into this equation to find the corresponding value of x. Similarly, you can solve for y or z in terms of the other variables by rearranging the original equation.

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The equivalent value of the expression is A = -3 - ( 5.1 x n ) , where n is the number

Given data ,

Let the expression be represented as A

Now , the value of A is

A = -3 decreased by the product of 5.1 and a number

On simplifying , we get

Let the number be represented as n

A = -3 - ( 5.1 x n )

On further simplification , we get

A = -3 - ( 5.1n )

Hence , the equation is A = -3 - ( 5.1n )

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Answer:

This triangle is a right scalene triangle.

Step-by-step explanation:

Because this triangle has a 90° angle, it is a right triangle. As all the angles are different, we can see that it is a scalene triangle as well.

It is true that the integers (-4, -2,0, 2, 4) form the set of even integers.

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

Set = (-4, -2,0, 2, 4)

In the above set, we can see that all numbers in the set do not have decimal point

This means that the set of numbers are integers

Also, we can see that the integers are integers that are divisible by 2

This means that the set of integers are set of even integers

Hence, the statement is true

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Complete question

As a integers are integers divisible by 2. The integers (-4, -2,0, 2, 4) form the set of even integers.

True or false

Answer:

The length of each side of the square is approximately 4.24 cm.

Explanation:

We can use the Pythagorean theorem to find the length of each side of the square. Let "s" be the length of each side of the square. The diagonal of the square, which is 6 cm, is the hypotenuse of a right triangle whose legs are two sides of the square. So we have:

[tex]s^2 + s^2 = 6^2[/tex]

Simplifying this equation, we get:

[tex]2s^2 = 36[/tex]

Dividing both sides by 2, we get:

[tex]s^2 = 18[/tex]

Taking the square root of both sides, we get:

s ≈ 4.24

Therefore, the length of each side of the square is approximately 4.24 cm.

Answer: n= -10

Step-by-step explanation:

n + 19 = 9, so you want to get the variable by itself so you will get rid of the 19, cancelling it by subtracting. So n=9-19 leaving you with -10.

Answer:

Therefore, the amount that results from the given investment is approximately $579.64.

Step-by-step explanation:

We can use the formula for compound interest to find the amount that results from the given investment:

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

where:

A = the amount

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, P = $500, r = 0.04, n = 4 (since the interest is compounded quarterly), and t = 3.5 years.

Plugging in the values, we get:

A = 500(1 + 0.04/4)^(4*3.5)

A = 500(1.01)^14

A = 500(1.159274...)

A ≈ $579.64

Therefore, the amount that results from the given investment is approximately $579.64.

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Answer:

Step-by-step explanation:

The correct statement about the given equations is: "The equations are dependent because the lines are the same line."

In the equation y = 2x + 5, the slope is 2, which means the line has a positive slope and is upward sloping.

The y-intercept is 5, indicating that the line intersects the y-axis at the point (0, 5).

The equation y = -2x + 5 is equivalent to y = 2(-x) + 5, which has the same form as the first equation but with a negative slope.

However, the equations are still dependent because when you simplify the second equation, you obtain the first equation.

These two equations represent the same line with a different slope. Therefore, they are dependent, and any point that satisfies one equation will satisfy the other equation as well.

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Answer: The correct option is B) 2√6

explanation:

A) 4π/π = 4 (This simplifies to 4, which is a rational number since it can be expressed as a fraction 4/1.)

B) 2√6 = irrational number (The square root of 6 cannot be simplified to a fraction or whole number, so it is an irrational number.)

C) 18 = rational number (This is a whole number and can be expressed as a fraction 18/1.)

D) 21.989 = rational number (This is a decimal number, but it can be expressed as a fraction, such as 21989/1000.)

Answer:

Step-by-step explanation:

because 2 surd 6 will continue to give you an infinite number which is an irrational number

Answer: 11/32

Step-by-step explanation:

The formula for finding this is:

(yellow and yellow) or (pink and pink) or (blue and blue)

First find the probability that both spins will be yellow:

2/8 * 2/8 = 1/16

There are 2 yellow spots out of the 8 total spots.

Because you need to spin yellow and yellow, you multiply the two fractions.

This logic applies to pink and blue.

Next pink:

3/8 * 3/8 = 9/64

Blue:

3/8 * 3/8 = 9/64

Find the probability that you will spin yellow or pink or blue:

1/16 + 9/64 + 9/64 = 11/32

Whenever finding the probability of something or something else, add them.

Answer:

step 1: add all you number

Step-by-step explanation:

step 2:divide your answer by the 7.,you have gotten your answer

y=√(21+4x²)/3 and y=-√(21+4x²)/3 are the two functions defined by implicity by the equation

The given equation is an equation of an ellipse centered at the origin with a major axis of length 2√7 and a minor axis of length 2√3.

To find two functions defined implicitly by this equation, we can solve for y in terms of x using algebra.

First, we can isolate y²/3 by subtracting x²/7 from both sides:

y²/3 = 1 - x²/7

Multiply by 3 on both sides to eliminate the fraction:

y² = 3 - 3x²/7

y = ±√(3 - 3x²/7)

These are the two functions defined implicitly by the given equation.

The positive square root gives the upper half of the ellipse, while the negative square root gives the lower half.

Hence, y=√(21+4x²)/3 and y=-√(21+4x²)/3 are the two functions defined by implicity by the equation

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A circle with a diameter of 4.13 meters will have a circumference of 12.97 meters.

Given that:

Diameter, d = 4.13 meters

The circumference is a term used in geometry to describe the boundary or the outer edge of a closed curve, particularly a circle. It refers to the distance around the circle, measured along its outer edge. In simpler terms, the circumference is the total length of the circle.

Let d represent the circle's diameter. The circle's perimeter will be provided as,

C = πd

The formula for calculating a circle's circumference is

C = 3.14 x 4.13

C = 12.9682

C ≈ 12.97 m

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The difference in total cost between the two mortgages is $168,852. The Option A is closest.

To get total cost of the adjustable-rate mortgage, we have to find total payments for each period and add them up.

Using the monthly payments, we get:

Total payments for years 1-5:

= $2,506.43 x 12 x 5

= $150,385.80

Total payments for years 6-15:

= $3,059.46 x 12 x 10

= $367,135.20

Total payments for years 16-25:

= $3,464.78 x 12 x 10

= $415,773.60

Total payments for years 26-30:

= $3,630.65 x 12 x 5

= $217,839.00

Total cost of adjustable-rate mortgage: $1,151,133.60

The total cost of the fixed-rate mortgage is computed as follows. The Total payments for 30 years is:

= Monthly payment x Number of payments

= $2,728.56 x 12 x 30

= $982,281.60

The difference in total cost is:

= $1,151,133.60 - $982,281.60

= $168,852.00.

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The coordinates of the vertices for the image of the triangle U′V′W′ is

U′(1, 1), V′(−4, 0), W′(−1, 4)

To rotate a point 90 ° clockwise about the origin, we can apply the transformation (x, y) → (y, -x)

So applying this transformation to each vertex of triangle UVW we get

U(−1, 1) → U' = (1, 1)

V(0, −4) → V' = ( -4, 0)

W(−4, −1) → W' = (-1, 4)

Therefore the coordinates of the vertices for the image triangle U'V'W' are U′(1, 1), V′(−4, 0), W′(−1, 4)

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the area of the shape to the nearest tenth of a square centimeter is 12cm². Opti C

The formula for calculating the area of a an isosceles triangle is expressed as;

A = 1/2bh

Such that the parameters are expressed as;

From the information given, we have that;

base = 3 centimeters

Height = 8 centimeters

Substitute the values, we have;

Area = 1/2 ×8 × 3

Multiply the values, we have;

Area = 24/3

Divide the values

Area = 12 cm²

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Hello!

see attachment

A1 = green

A2 = yellow

A3 = red

A1 = 15m * 3m = 45m²

A2 = (15m - (6m + 6m)) * 4m = 3m * 4m = 12m²

A3 = 15m * 3m = 45m²

A = A1 + A2 + A3

= 45m² + 12m² + 45m²

Answer:

b. 102 m²

Step-by-step explanation:

In order to find the area of shape.

Let's separate it into three rectangle.

We know that

Area of rectangle: Length*breadth

Using this

Area of left rectangle=15*3=45 m²

Area of middle rectangle=4*(15-6-6)=12 m²

Area of right rectangle= 15*3=45m²

Now

Total Area of shape= 45m²+12m²+45m²=102m²