Suppose you transform a square corn field by increasing one side by 2 units and decreasing the other side by 3 units. If the area of the resulting corn field equals 24, what was the length of the original corn field?

Answer: D.

Step-by-step explanation: Same side interior angles are supplementary, meaning they add up to 180. Thus, we can write an equation:

<1 + <2 = 180 --> (substituting expression values)

8x + 40 + 12x + 20 = 180 --> (simplifying)

20x = 120 --> (simplifying further)

x = 60

So, D.

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: He started with 44

Step-by-step explanation: 44/2=22

22+8= 30

Based on the information given the new balance is $289.72.

First step is to calculate the finance charge

\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)

\(\text{Finance charge}=205.16\times0.012\)

\(\text{Finance charge}=2.46\)

Second step is to calculate the New balance

\(\text{New balance}=205.16+2.46+82.10\)

\(\text{New balance}=\bold{\$289.72}\)

In conclusion, the new balance is $289.72.

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Using the Central Limit Theorem, the correct option regarding the shape of the sample mean is given by:

d) The distribution of the sample mean is approximately normal by the central limit theorem.

It states that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

For this problem, we have a skewed underlying distribution, however the sample size is greater than 30, hence the sampling distribution of sample means is normal and option d is correct.

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The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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Answer:

x+2y=2 x-2y=-2. It has infinitely many solutions. It has no solution. It has one solution

So on solving the provided question we can say that here, in triangle ABC and XYZ;  by SSS property they are similar.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

AB = XY

AC = XZ

BC = ZY

by SSS property, they are similar.

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Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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Answer: 20

Step-by-step explanation: 5 times 4 is 20 times 2 is 40, but when you divide by 1/2 you drop down to 20.

Answer:

your answer for that problem is 45.6

9514 1404 393

Answer:

Step-by-step explanation:

ΔBCD is isosceles, so ∠CDB = ∠CBD = x. The sum of angles in the triangle is 180°, so you have ...

  x + x + 50° = 180°

  2x = 130° . . . . . . . . . subtract 50°, collect terms

  x = 65° . . . . . . . divide by 2

__

Triangle ABC is also isosceles, so ∠BAC = ∠BCA = y. Angle ABC is the supplement of angle x. The sum of angles in ΔABC is 180°:

  y + y + (180° -x) = 180°

  2y - 65° = 0 . . . . . . . . . . subtract 180°, substitute the value of x

  y -32.5° = 0 . . . . . . . divide by 2

  y = 32.5° . . . . . . . . . . add 32.5°

Answer:

Step-by-step explanation:

average of x-coordinates of A and B = (4-8)/2 = -2

average of y-coordinates of A and B = (-4+2)/2 = -1

midpoint of AB:  M(-2,-1)

The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

The function in the context of this problem is defined as follows:

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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Answer:A.The triangles are similar but not congruent

Step-by-step explanation:

In a congruent traingle:

the both triangles are same in shape and size

There are five theorems to see if the triangles are congruent

and neither particularly applies here

sss: the sides are not equal

as none of the sides are equal, then despite the angles, congruence is not possible

However it is evident that one of the triangles is proportionally bigger than the other but similar. Hence A is correct.

Step-by-step explanation:

Combining similar terms:

Answer:

1/4 cake

Step-by-step explanation:

Edwin needs to sell 44,625 jars of jam to break even.

To determine how many jars of jam Edwin needs to sell to break even, we'll calculate the breakeven point using the following formula:

Breakeven Point = Fixed Expenses / (Selling Price per Unit - Variable Cost per Unit)

Given information:

Selling Price per Unit (SP) = $1.90

Variable Cost per Unit (VC) = $1.10

Fixed Expenses = $35,700.00 per year

Plugging in the values into the formula:

Breakeven Point = $35,700 / ($1.90 - $1.10)

Breakeven Point = $35,700 / $0.80

Breakeven Point = 44,625 jars

Therefore, Edwin needs to sell 44,625 jars of jam to break even.

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Answer:

4/5

Step-by-step explanation:

4/5 = 80%

1/4 = 25%

3/10 = 30%

Answer:

The table is a quadratic function

Step-by-step explanation:

Given

The attached table

Required

Tell if it is a quadratic function

The difference in the x values are uniform (i.e. difference of 1), so the following method can be applied.

(1) Subtract adjacent y values.

\(d_1=2 - 16 = -14\)

\(d_2=-2 - 2 = -4\)

\(d_3 = 4--2 = 6\)

\(d_4 = 20 - 4 = 16\)

(2) Subtract adjacent differences in (1) above

\(d_5 = d_2 - d_1 = -4 --14 = 10\)

\(d_6 = d_3 - d_2 = 6 --4 = 10\)

\(d_7 = d_4 - d_3 = 16 -6 = 10\)

Notice the calculated differences in (2) are the same.

Hence, the table is a quadratic function

Answer:

d

Step-by-step explanation:

-4/3 - 2/5

HOPE THAT HELPS DUDE

The insect measurement that was the most frequent is given as follows:

1 and 1/4 inches.

A dot plot is a simple graphical display that uses dots to represent data values. It is also sometimes called a dot chart or a scatterplot. In a dot plot, each data point is represented by a dot along a number line or axis, where the position of the dot corresponds to the value of the data point.

Hence, a dot plot shows the number of times that each observation appeared in the data-set.

The observation with the most dots is the observation 2/8 of the way between 1 and 2, hence the most frequent observation is given by the following mixed number:

1 and 2/8 = 1 and 1/4 inches.

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Answer:

36

Step-by-step explanation:

AB=AC+BE

AB=10+26

AB=36

Answer:

B, C, and D........................

The matrix is 3 × 3 square matrix . Its values are:

\(a_{11} = 50 \\ a_{12} = 44 \\a_{13} = -43 \\a_{21} = 31 \\a_{22} = 16 \\a_{23} = 7 \\a_{31} = 37 \\a_{32} = 119 \\a_{33} = 94\)

Given,

Matrix A and Matrix B

Now,

According to matrix multiplication rule first row of one matrix will be multiplied with first column of second matrix if the columns in first matrix is equal to the rows of second matrix.

So,

Apply multiplication rule,

\(a_{11} = 30 + 14 + 6 = 50 \\ a_{12} = 55 + 7 - 18 = 44 \\a_{13} = -20 -35 + 12 = -43 \\a_{21} = 24 - 2 + 9 = 31 \\a_{22} = 44 -1 -27 = 16 \\a_{23} = -16 + 5 + 18 = 7 \\a_{31} = 36 + 16 - 15 = 37 \\a_{32} = 66 + 8 + 45 = 119 \\a_{33} = -24 -40 -30 = -94\)

Thus the values of the matrix can be calculated.

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Answer:

Perimeter=100  area=688.19

Step-by-step explanation:

There's a big formula for area of pentagon and I pretty tired, so unless you want me to show my work I wont