3. Elena walked 12 miles. Then she walked 0.25 that distance. How far did she walk all together? Select all that apply.
A. 12 + 0.25 ⋅ 12
B. 12(1 + 0.25)
C. 12 ⋅ 1.25
D. 12 ⋅ 0.25
E. 12 + 0.25

The width and length of the rectangle is 27 cm and 36 cm. respectively.

To solve the problem, we can use the Pythagorean theorem since the diagonal, width, and length of the rectangle form a right triangle. The Pythagorean theorem states that:
a² + b² = c²
where a and b are the legs of the right triangle and c is the hypotenuse (diagonal of the rectangle).

Let's denote the width of the rectangle as w, the length as l, and the diagonal as d. According to the problem, we have:
d = w + 18
l = w + 9

Substituting these equations into the Pythagorean theorem, we get:
(w + 9)² + w² = (w + 18)²

Expanding and simplifying the equation, we get:
w² - 18w - 243 = 0

We can solve for w by factoring the expression:
(w - 27)(w + 9) = 0

w = 27 or w = -9

The positive solution for w is 27. We can use this value to find the length of the rectangle:
l = w + 9
l = 27 + 9
l = 36

Therefore, the width of the rectangle is 27 cm, and the length of the rectangle is 36 cm.

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Triangle ABC is an equilateral triangle.

In triangle ABC, the perpendicular bisectors and the angle bisectors meet at D in such a way that CD is twice the length of DE. Triangle ABC is an equilateral triangle. Here's a way to prove it:First, we'll show that AD is an altitude of the triangle.

Because BD is an angle bisector, it splits angle ABC into two equal parts, so m∠ABD = m∠CBD. This means that triangles ABD and CBD are similar because they have an equal angle.

We also know that the perpendicular bisectors of the sides AC and BC pass through D, which means that AD and BD are both perpendicular to AC. As a result, AD and BD must be perpendicular to each other, and AD is an altitude of triangle ABC.Next, we'll prove that AD is also a median of the triangle.

Because ABC is an equilateral triangle, all of its sides are congruent, so AB = BC = AC. Since BD is an angle bisector, it bisects side AC, so AD = DC. Since CD is twice as long as DE, that means that AD is also twice as long as DE. As a result, point D must be the midpoint of AB, so AD is a median of triangle ABC.

We have now shown that AD is both an altitude and a median of triangle ABC, which can only occur in an equilateral triangle.

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Answer:

sqrt(26) units

Step-by-step explanation:

Use the formula d=sqrt((x2-x1)^2 + (y2-y1)^2). d is the distance, and (x1, y1) and (x2, y2) are the points.

d=sqrt((4-(-1))^2 + (2-3)^2)

 =sqrt(5^2 + (-1)^2)

 =sqrt(25+1)

 =sqrt(26)

The joint probability mass function (PMF) for the random variables x and y can be represented in a table with rows and columns corresponding to the possible values of x and y, respectively.

In this case, x represents the number of heads on the first toss, and y represents the total number of heads over all three tosses. There are two possible outcomes for each coin toss: heads (H) or tails (T). Thus, there are 2^3 = 8 possible outcomes for three coin tosses, which can be listed as follows: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. For the first toss, there are two possible outcomes: H or T. Thus, x can take on the values x = 0 or x = 1, with probabilities P(x = 0) = 1/2 and P(x = 1) = 1/2.

For the total number of heads over all three tosses, there are four possible outcomes: 0, 1, 2, or 3 heads. The joint probabilities can be calculated by considering the possible outcomes for each value of x. For example, if x = 0 (i.e., the first toss is a tail), then y can only be 0 or 1, depending on the outcomes of the second and third tosses. The probabilities of these outcomes are P(x = 0, y = 0) = 1/8 and P(x = 0, y = 1) = 3/8. The joint probability mass function for x and y can be summarized in a table as follows:

y=0 y=1 y=2 y=3

x=0 1/8 3/8 3/8 1/8

x=1 1/8 3/8 3/8 1/8

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The contrast coefficients would be as follows:

The farmers are interested in whether there is any difference between the low-low combination (it is the cheapest) and the average of the remaining three levels. The hypotheses they want to test are:

To test this hypothesis, the following contrast would be used:

To compare the high- to low-nitrogen content fertilizers, the following contrast would be used:

To compare the high- to low-phosphorus content fertilizers, the following contrast would be used:

To compare the ll combination to the hh combination, the following contrast would be used:

For each of the contrasts above, the contrast coefficients would be as follows:

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

-2

Step-by-step explanation:

Step by step explanation is in the picture

a) 0.bar(36) expressed as a fraction in simplest form is 4/11. b) 0.3bar(6) expressed as a fraction in simplest form is 0.4. c) 0.36 expressed as a fraction in simplest form is 9/25.

(a)  To express 0.bar(36) as a fraction in simplest form, we can use the concept of repeating decimals. Let x = 0.bar(36). Multiplying x by 100 gives:

100x = 36.bar(36)

Subtracting the original equation from the multiplied equation eliminates the repeating part:

100x - x = 36.bar(36) - 0.bar(36)

99x = 36

x = 36/99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

x = (36/9) / (99/9) = 4/11

Therefore, 0.bar(36) expressed as a fraction in simplest form is 4/11.

(b) o express 0.3bar(6) as a fraction in simplest form, let's call it x. Multiplying x by 10 gives:

10x = 3.6bar(6)

Subtracting the original equation from the multiplied equation eliminates the repeating part:

10x - x = 3.6bar(6) - 0.3bar(6)

9x = 3.6

x = 3.6/9

x = 0.4

Therefore, 0.3bar(6) expressed as a fraction in simplest form is 0.4.

(c) To express 0.36 as a fraction in simplest form, we can write it as 36/100 and simplify it. Both the numerator and denominator have a common factor of 4, so we can divide both by 4:

36/100 = 9/25

Therefore, 0.36 expressed as a fraction in simplest form is 9/25.

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Answer:

X= 55/3 = 18.333

Step-by-step explanation:

Step  1  : Solving a Single Variable Equation : 1.1      

Solve  :    3x-55 = 0

Add  55  to both sides of the equation : 3x = 55

Divide both sides of the equation by 3: x = 55/3 = 18.333

Answer: X= 55/3 = 18.333

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Answer:

\(x = 18.33\)

Step-by-step explanation:

\(3x + 13 = 68 \\ 3x = 68 - 13 \\ 3x = 55 \\ \frac{3x}{3} = \frac{55}{3} \\ x = 18 .33\)

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Answer:

lengths are 25 ft and 12 ft

Step-by-step explanation:

let x and y be the areas of the 2 square peanut beds, with x being greater than y , then

x + y = 769 → (1)

x - y = 481 → (2)

add (1) and (2) term by term to eliminate y

(x + x) + (y - y) = 769 + 481

2x + 0 = 1250

2x = 1250 ( divide both sides by 2 )

x = 625

substitute x = 625 into (1) and solve for y

625 + y = 769 ( subtract 625 from both sides )

y = 144

the areas of the 2 beds are 625 ft² and 144 ft²

the area (A) of a square is calculated as

A = s² ( s is the length of side )

then

s² = 625 ( take square root of both sides )

s = \(\sqrt{625}\) = 25

and

s² = 144 ( take square root of both sides )

s = \(\sqrt{144}\) = 12

length of each bed is 25 ft and 12 ft

For the area of triangle, the constant of variation is 1/2.

The link between the independent (x) and dependent (y) variables is shown by a constant of variation. A continuous relationship between the variables indicates to the user that there is one; it does not alter regardless of how the scenario changes.

It can be employed to ascertain how the dependent variable will alter in response to changes in the independent variable. For instance, if a person drives continuously at the same pace, they may calculate their distance by multiplying the number of hours they spent driving by the speed they were moving at. In this instance, the speed is the constant since it remained constant regardless of how long or how far they travelled during the journey.

A triangle's area is equal to (1/2) * (base) * (height).

It fluctuates in tandem with both the base length and the height.

The (1/2) represents the variational constant.

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Answer:

Step-by-step explanation:

40 x 4 = 160

160 - 142.68 = 17.32

Answer:It will take 4 weeks and you will have 17.32$ left

Step-by-step explanation:Multiply 40x4= $160 and subtract $142.68-$160.00= $17.32

Answer:

A

Step-by-step explanation:

the cost and weight are directly proportional, so decreasing one decreases the other at the same rate.

ratio is cost : weight, which is 15:10. the simplest ratio is 3:2, on the graph find where the cost is 3 and weight is 2. only graph A satisfy the condition

Answer:

1.2 mph

Step-by-step explanation:

3/5 = 0.6

Multiply 0.6 by 2 to find the distance gone in a whole hour

0.6*2 = 1.2

Answer:

I think it is 50:1

Step-by-step explanation:

The value of z is 1.16, because the area between -1.16 and 1.16 under the standard normal curve is 0.754.

Answer: a. 1.16

If the area between -z and z is 0.754, this means that the area to the left of -z is \((1-0.754)/2 = 0.123\), and the area to the right of z is also 0.123.

Since the standard normal distribution is symmetric around the mean of 0, we can use a standard normal distribution table or calculator to find the z-score corresponding to an area of 0.123 to the left of the mean.

Looking up the area 0.123 in a standard normal distribution table, we find that the corresponding z-score is approximately -1.16.

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Answer:

42

Step-by-step explanation:

Answer:42

21 x2 = 42. Therefore 1/2 or 50% of 42 is 21

Step-by-step explanation:

Answer:

-2/3  is greater than  -0.8

Step-by-step explanation:

-2/3 when made into a decimal is about -0.67

This is greater than -0.8 because -0.67 covers less area when put into a visual.

Answer:

Convert -0.8 into a fraction or -2/3 into a decimal;

-2/3 in decimal form = -0.666...

Compare the two decimals;

-0.8 __ -0.666...

-0.8 < -0.666..., so -2/3 is greater.

Answer:

Step-by-step explanation:

To solve for the variable n in the equation 1/3 = n + 3/4, you can follow these steps:

Subtract 3/4 from both sides of the equation to isolate the variable n on one side:

1/3 - 3/4 = n

Find a common denominator for 1/3 and 3/4, which is 12. Multiply the numerator and denominator of 1/3 by 4 to get 4/12, and multiply the numerator and denominator of 3/4 by 3 to get 9/12:

4/12 - 9/12 = n

Simplify the expression on the left side of the equation by subtracting the numerators:

-5/12 = n

Rewrite the solution as a fraction or mixed number in simplest form:

n = -5/12

Therefore, the solution to the equation 1/3 = n + 3/4 is n = -5/12.

Answer:

I think its the first one

Step-by-step explanation:

Answer:

84 students practices everyday.

Step-by-step explanation:

Sample size: Sample size is the number of observations that was included in the statistical sample.

b) Sample size = 144

\(\sf a) Number \ of \ students \ who \ practices \ everyday = \dfrac{7}{12}*144\)

                                                                     = 7 * 12

                                                                     = 84

The step 1 will process with beginning, mapping, and optimising. The step 2 will includes matrices calculation, creating control chart and analysis.

The steps to be followed for step 1 are as follows-

Begin with value identification which is the creation of word document. Map the value stream to remove redundant activites followed by waste elimination. Then work on to improve the efficiency by using templates, headers, using keyboard shortcuts and enabling autosave.

To proceed to step 2 and check if the process could benefit from other tools, consider these three actions: 1. Calculating the metrices that includes variation and process capability. 2. Formulate the control chart for process. 3. Analyse the metrices and control chart via the SPC method.

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Answer:

The second option. y = 3x +3

Step-by-step explanation:

※ x = -4

y = 3(-4) + 3

= -12 + 3

= -9

※ x = 3

y = 3(3) +3

= 9 + 3

= 12

Answer:

10 is the y-intercept

Step-by-step explanation:

Since the linear equation is -2 every time the x gets larger, that means it would be plus 2 every time the x gets smaller. The y-intercept is when x = 0 so to get from 1 to zero we subtract 1, then we add 2 to the y which gets us 10.

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Answer:

Step-by-step explanation:

(3 + 1)/(-2 - 4) = 4/-6 = -2/3

y + 1 = -2/3(x -4)

y + 1 = -2/3x + 8/3

y + 3/3 = -2/3x + 8/3

y = -2/3x + 5/3

2x + 3y - 5 = 0 is the standard form

The required equation of the line that passes through (4, -1) and (-2, 3) is 2x+3y-5 = 0

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, A line is passing through points (4, -1) and (-2, 3)

We know that, the equation of a line passing through two points is given by, (y-y₁) = (y₂-y₁)/(x₂-x₁)(x-x₁)

y+1 = (3+1)/(-2-4)(x-4)

y+1 = -2/3(x-4)

3y+3 = -2x+8

2x+3y-5 = 0

Hence, The required equation of the line that passes through (4, -1) and (-2, 3) is 2x+3y-5 = 0

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Step-by-step explanation:

We need to find the value of x for all problems if Y is between X and Z.

For all cases, XZ = XY+YZ

4. XY = 5x, YZ=x, and XZ=25

Putting all values

25 = 5x + x

25 = 6x

\(x=\dfrac{25}{6}\)

5. XY = 12, YZ=2x, and XZ = 28

28 = 12 + 2x

x = 8

6.  XY = 4x. YZ=3x, and XZ = 42

XZ = XY+YZ

42 = 4x + 3x

42 = 7x

x = 6

7. XY=2x + 1. YZ = 6x, and XZ=81

XZ = XY+YZ

81 = 2x + 1 + 6x

80 = 8x

x = 10

The value of the equation A as c as the subject is c = ( 3p² - 8 ) / ( a - p² )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the equation will be

p = √ ( ac + 8 ) / ( 3 + c )   be equation (1)

On simplifying the equation , we get

Taking square on both sides of the equation , we get

p² = ( ac + 8 ) / ( 3 + c )

Multiply by ( 3 + c ) on both sides of the equation , we get

p² ( 3 + c ) = ac + 8

3p² + p²c = ac + 8

On simplifying the equation , we get

Subtracting p²c on both sides of the equation , we get

ac + 8 - p²c = 3p²

Subtracting 8 on both sides of the equation , we get

ac - p²c = 3p² - 8

Taking c as the common factor , we get

c ( a - p² ) = 3p² - 8

Divide by ( a - p² ) on both sides of the equation , we get

c = ( 3p² - 8 ) / ( a - p² )

Therefore , the value of A is ( 3p² - 8 ) / ( a - p² )

Hence , the equation as c as the subject is c = ( 3p² - 8 ) / ( a - p² )

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Answer:

(2, -3)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Where the 2 lines intersect is the solution to the system of equations.