The diagram represents a rectangular garden of length 14 m and width 10 m. The flower bed is a triangle and the vegetable patch is a trapezium. The rest of the garden is lawn. Work out the are of the lawn.

The x-intercepts of the graph of the function are (-2, 0), (5, 0)

The midpoint of the x-intercept is 1.5.

The extremum of the function is a minimum and the value of x at which it occurs is k(1.5) = -61.25.

In Mathematics, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this exercise, we would use an online graphing calculator to plot the quadratic equation in order to determine the x-intercepts as shown in the graph attached below.

Therefore, the x-intercepts of the graph of the given quadratic equation k(x) = 5x² - 15x - 50 including the following:

Since a line of symmetry must lie in the middle of the x-intercepts, the symmetry is given by;

x = (-2 + 5)/2

x = 3/2

x = 1.5

For the extremum, we have;

k(1.5) = 5(1.5)² - 15(1.5) - 50

k(1.5) = 11.25 - 22.5 - 50

k(1.5) = -61.25

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Answer:

Step-by-step explanation:

8. \(4\geq x+\frac{3}{4}\)

\(4(4\geq x+\frac{3}{4} )\)

\(16\geq 4x + 3\)

\(-3\)         \(-3\)

\(13\geq 4x\)

\(\frac{13}{4}\geq \frac{4x}{4}\)

\(\frac{13}{4} \geq x = x\leq \frac{13}{4}\)

\(x\leq \frac{13}{4}=3.25\)

9. \(x-3\leq -8\)

       \(+3\)     \(+3\)

\(x\leq -5}\)

10. \(4\leq x-7\)

  \(+7\)         \(+7\)

\(11\leq x=x\geq 11\)

11. 6.9 < x - 2.3

 + 2.3      + 2.3

 9.2 < x = x > 9.2

Hope this helps!

The probability of selecting a 5 and then an odd number is 1/12.

Probability= required outcome/ total possible outcomes

total number of cards = 4

1st pick:

Probability of picking a 5 :

P(5) = 1/4

Since , selection is done without replacement:

2nd pick:

P(odd number ) = 1/3

P(5, then odd number) = 1/4 × 1/3 = 1/12

Therefore, the probability is 1/12.

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If Maria incorrectly placed the decimal point when she wrote 0.65 inches for the width of her tablet computer, we need to determine the correct placement of the decimal point based on the known size of the tablet.

Assuming that the width of the tablet is greater than 1 inch, we can't have a width of 0.65 inches since that is less than one inch.

If Maria accidentally moved the decimal point one place to the left, then the width should be 6.5 inches. If she accidentally moved the decimal point two places to the left, then the width should be 65 inches.

Without more information about the size of the tablet, we cannot determine the correct decimal number for the width. However, we can be sure that the correct width is either 6.5 inches or 65 inches, depending on where Maria misplaced the decimal point.

Answer: agree

Step-by-step explanation:

According to the given statement While spring training records can provide some insight, they should not be the sole basis for predicting a team's success during the regular season.

There is a correlation between a major league baseball team's record during spring training and its performance during the regular season. Over a six-year period, the correlation coefficient between a team's winning percentage in spring training and its winning percentage in the regular season is .

However, it's important to note that this correlation does not imply causation. While a strong performance in spring training may suggest a team's potential success, it does not guarantee it. Factors such as injuries, roster changes, and overall team strategy can also significantly impact a team's performance during the regular season.

Therefore, while spring training records can provide some insight, they should not be the sole basis for predicting a team's success during the regular season.

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Answer:

Step-by-step explanation:

possibilities with Large Pizza- 4

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

possibilities with massive- 4

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

possibilities with gargantuan- 4

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

assuming you can't mix the varieties there should be 12 possibilities

Answer:

Length = 7cm, Width = 15cm

Step-by-step explanation:

Length = p

Width = 3(p-2)

          = 3p-6

Perimeter = length + width + length + width

                = p + 3p-6 + p + 3p-6

                = 8p-12

8p - 12 = 44

Isolate 8p.

8p = 44+12

    = 56

Find p.

p = 56 ÷ 8

p = 7

Length = 7cm

Width = 3(7)-6

          = 21-6

          = 15cm

Answer:

64,81,100

Step-by-step explanation:

Answer: 64,81 and 100

Step-by-step explanation: 8^2=64, 9^2=81 and 10^2=100

Answer:

12 should be 41

Step-by-step explanation:

12) the pattern is an increase by 5 each time. This would mean the 8th term is 40. However, it starts at 1, so you should add 1 to this answer, making it 41. This pattern is y=5x+1 if x is that number in the pattern and y is the answer.

Answer:

Well let me help you with 12! :)

Step-by-step explanation:

Wellit really isn't adding it is a pattern. So you see 1, 6, 11, 16? See the pattern of how it is only with the numbers 1 and 6 and and it goes like 1, 6, 11, 16, then you keep going.

Your Welcome! :)

Answer:

i got you

Step-by-step explanation:

2 is 142

4 is 142

(they are parallel therefore they are the same :))

Answer:

B. how long the toy rang

Step-by-step explanation:

In order to test the battery, you need to see which will last the longest. Therefore, you should time how long it rang.

A spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

a spherical astroid has a radius of approximately 8.5 x 10^2 m.

we know,

the volume =  4/3 π r^3

so, by calculating, we get.

volume = 2.57 x 10^9 m^3

Hence, a spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

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The linear approximation of f at x = π/4 is  1 + 2(x - π/4), the value tan(π/5) is 1 - 3π/40 ≈ 0.3634.

Linear approximation is a technique used in calculus to approximate the value of a function near a particular point using the tangent line of the function at that point. This approximation is often used to simplify calculations and solve problems in a variety of fields, including physics, engineering, and finance.

The linear approximation of a function f(x) near a point a is given by:

L(x) = f(a) + f'(a)(x-a)

where f'(a) is the derivative of the function f(x) evaluated at a. The linear approximation L(x) is the equation of the tangent line to the function at the point (a, f(a)), and it provides an approximation of the function's behavior near that point.

We have,

f(x) = tan x

f'(x) = sec² x

At x = π/4, we have

f(π/4) = tan(π/4) = 1

f'(π/4) = sec²(π/4) = 2

So the linear approximation of f at x = π/4 is given by

L(x) = f(π/4) + f'(π/4)(x - π/4)

 = 1 + 2(x - π/4)

Now, we can use this to estimate tan(π/5) as follows:

tan(π/5) ~ L(π/5)

      = 1 + 2(π/5 - π/4)

      = 1 + 2π/20 - 2π/16

      = 1 + π/40 - π/8

      = 1 - 3π/40

So the estimated value of tan(pi/5) using the linear approximation of f(x) = tan x at x = π/4 is

tan(π/5) ≈ 1 - 3π/40 ≈ 0.3634 (using π ≈ 3.14159).

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The unit circle is the circle centered at with radius The unit circle is a circle centered at the origin with a radius of 1 unit. It plays a fundamental role in trigonometry, providing a geometric representation of the trigonometric functions

The unit circle is a circle that is centered at the origin (0, 0) of a coordinate plane and has a radius of 1 unit. In other words, it is a circle with a diameter of 2 units.

The unit circle is particularly significant in mathematics, especially in trigonometry. Its properties and relationships with angles are extensively used in various mathematical applications.

One of the main reasons the unit circle is so important is due to its connection with the trigonometric functions sine and cosine. As an angle rotates around the origin,

the coordinates of the point on the unit circle where the terminal side of the angle intersects the circle correspond to the values of sine and cosine of that angle.

For example, if an angle of 30 degrees is measured counterclockwise from the positive x-axis, the coordinates of the corresponding point on the unit circle would be (√3/2, 1/2), which are the values of sine and cosine for that angle.

Additionally, the unit circle provides a convenient way to visualize and understand other trigonometric functions such as tangent, cotangent, secant, and cosecant.

By examining the ratios of the coordinates on the unit circle, we can relate these trigonometric functions to the lengths and angles associated with right triangles.

In summary, the unit circle is a circle centered at the origin with a radius of 1 unit. It plays a fundamental role in trigonometry, providing a geometric representation of the trigonometric functions and aiding in the understanding of angles, ratios, and relationships within the field of mathematics.

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Answer:

There were 45 pies sold in all.

Step-by-step explanation:

10 + 15 = 25

25 + 20 = 45

Answer:

1/4

Step-by-step explanation:

Slope = (change in the y-values)/(change in the x-values)

Slope = (4 - 2)/(1 - (-7) )

Slope =  (4 - 2)/(1 + 7)

Slope = 2/8

Slope = 1/4

Answer:

Step-by-step explanation:

p(x) = 8x^2 is an increasing exponential curbed graph which starts from quadrant 2 , passes through the point (0, 8)  on the y axis and rises steeply to the right.

g(x) = x^2 is a parabola ( shaped like a U) which has a minimum value at (0, 0).

and opens upwards either side of the y-axis. This type of curve is called a parabola.

Jamie's annual interest rate is 5%.

To find Jamie's annual interest rate, we need to consider the relationship between the quarterly interest payments and the loan amount. Let's break it down step by step:

1. We know that Jamie's quarterly interest payments are $150. Since there are four quarters in a year, the total annual interest payments can be calculated by multiplying the quarterly payments by four: $150 * 4 = $600.

2. Now, let's determine the interest rate. We have the annual interest payment, but we need to express it as a percentage of the loan amount. The formula to calculate interest rate is (Interest Payment / Loan Amount)  100.

3. Substituting the values into the formula, we have ($600 / $12,000)

100 = 0.05  100 = 5%.

Therefore, Jamie's annual interest rate is 5%.

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Answer:

scroll down to image :)! u can store 10 imgs. or u can change bg color! but thats for ti-84 ce!

Step-by-step explanation:

Answer:

D.) y-4=3[(x-(-1)]

Step-by-step explanation:

just took the test hope this helps

Answer:

70

Step-by-step explanation:

n =2  ;  3n + 2 = 3*2 + 2 = 6 + 2  = 8

n = 3 ; 3n + 2 = 3*3 + 2 = 9 + 2 = 11

n =4 ; 3n+ 2   = 3*4 + 2 = 12 + 2 = 14

n= 5;   3n +2 = 3*5 + 2  = 15 + 2 = 17

n = 6; 3n + 2 = 3*6 + 2 = 18 + 2 = 20

∑ (3n + 2) = 8 + 11 + 14 + 17 + 20 = 70

Answer:

70

Step-by-step explanation:

TTT

The value of the indicated variable x is 6

A quadrilateral is a polygon having four sides, four angles, and four vertices.

Given is trapezoid, with sides 28, 20 and x with two angles 90° and one angle 60°

We need to find the value of x,

Please to the figure attached,

In Δ ABC,

∠ C = 60°

Therefore,

∠ BAC = 90° - 60°

∠ BAC = 30°

Using the trigonometric ratios,

BC / AC = sin 30°

BC = 1/2 × 28

BC = 14

EC = EB+BC

20 = EB+14

EB = 6

Since, DABE is a rectangle, therefore,

EB = DA = x

∵ EB = 6

∴ x = 6

Hence, the value of the indicated variable x is 6

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The result of the expression (3+4i) / (1+i) is (7/2) - (1/2)i

The expression is  the complex numbers

(3+4i) / (1+i)

The complex number is the combination of real number and the imaginary number. The imaginary number is represented by adding i with the number

Multiply the expression with (1-i) / (1-i)

Then the expression will be

(3+4i) / (1+i) × (1-i) / (1-i)

= (3+4i) × (1-i) / (1+i) × (1-i)

Expand the terms by multiply the terms

= (3-3i+4i+4 ) / 1+1

= (7-i) / 2

Split the terms

= (7/2) - (1/2)i

Hence, the result of the expression (3+4i) / (1+i) is (7/2) - (1/2)i

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The length of one side of the pool if the pool has an area of 121 square feet is 11 feet

The formula for calculating the area of the square pool is expressed as:

\(A_s=L^2\)

L is the length of one side of the pool

If the area of the square pool is 121 square feet, hence;

\(121 = L^2\)

Take the square root of both sides;

\(\sqrt{121}= \sqrt{L^2}\\ \sqrt{121}=L\\11=L\\Swap \ sides\\L = 12ft\)

Hence the length of one side of the pool if the pool has an area of 121 square feet is 11 feet.

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The degree measure for angle B is 28° and angle D is 62°.

We are given that:

∠ C = 90°

∠ B = ( 2 x + 10 )°

∠ D = ( 5 x + 17 )°

Now, using the angle sum property of a triangle, we get that:

∠B + ∠ C + ∠ D  = 180°

Substituting the values:

2 x + 10 + 90 + 5 x + 17 = 180

7 x + 117 = 180

7 x = 63

x = 63 / 7

x = 9

∠ B = ( 2 x + 10 )

∠ B = 2(9) + 10

∠ B = 18 + 10

∠ B = 28°

∠ D = ( 5 x + 17 )

∠ D = 5 (9) + 17

∠ D = 45 + 17

∠ D = 62°

Therefore, the degree measure for angle B is 28° and angle D is 62°.

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Answer:

Step-by-step explanation:

Since there are 985 square feet to cover, and it costs 12.50 per square foot, you multiply 12.50 by 985 to get 12,312.50, the total cost and answer.

Answer:

$1247.97

Step-by-step explanation:

$42 per month of service

new phone monthly service is $415.99

415.99 x 3 = 1247.97