In order for the two figures shown below to be similar, the length of the unknown side must be . If necessary, round your answer to the nearest tenth 12 8 4 2 5 15

See below for the examples of combinations

Combinations are instances where items and objects are chosen or selected from a collection or group of items and objects such that the order in which the items and objects are selected does not matter

There are several applications of combinations in our daily activities.

Some of them include:

An example of combination with repetition is the selection of a food item from a food menu

While an example of combination without repetition is the selection of students to represent the school in a debate competition

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Answer:

638.4

Step-by-step explanation:

You could make 2 triangles (One on each side)

91.2*7=638.4

You could cut this in half, but it would be pointless as you are going to add it back again.

Answer:

\(5 + (9 + b) \\ 5 + 9 + b \\ 14 + b \: answer\)

Step-by-step explanation:

As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

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Answer:

A = - 3 and B = 10

Step-by-step explanation:

(x + 3)² = 10 ( take square root of both sides )

x + 3 = ± \(\sqrt{10}\) ( subtract 3 from both sides )

x = - 3 ± \(\sqrt{10}\) ← in the form A ± \(\sqrt{B}\)

where A = - 3 and B = 10

Answer:

1 solution

Step-by-step explanation:

The two equations have different slopes and different y-intercepts, so they represent two lines that intersect at 1 point.

Answer: 1 solution

The total money Paloma made = $117.25

In this question,

The price of Marigold(M) is $5.75.

The price of Daisy(D) is $6.25.

The price of Roses(R) is $2.50.

The price of Lilies(L) is $3.75

She sold 8 marigold flats and 10 daisy flats. An hour before closing, she sold 5 bunches of roses at half price and 2 bunches of lilies for 1/3 of the price.

Let s be the total money Paloma made

so we get an expression,

S = 8M + 10D + 5(R/2) + 2(L/3)

Now substitute the respective value

S = 8(5.75) + 10(6.25) + 5(2.5/2) + 2(3.75/3)

S = 46 + 62.5 + 6.25 + 2.5

S = $117.25

Therefore,  the total money Paloma made = $117.25

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Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

The value of x that will make both lines A and B to be parallel is:  20

The line transversal theorem states that:

If two parallel lines are cut by a transversal line, then it means that the Alternate Exterior Angles are congruent.

Similarly, If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Now, we see that the two given angles will be corresponding angles using the line transversal theorem and as such they are congruent. thus:

3x + 20 = 80

3x = 80 - 20

3x = 60

x = 60/3

x = 20

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The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer:

A

Step-by-step explanation:

The group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.

According to the given chart, calculate that each crate contains a total of 48000 calories. Therefore, two missing crates result in a total loss of 96000 calories (48000 x 2).

Determining whether the group has enough food to reach the South Pole and return to base camp, calculate the total number of calories required for the entire trip. Supposing a round trip of 10 days to the South Pole and back, the total number of calories required would be:

Total Calories = (6000 calories/person x 5 people x 10 days) x 2 (round trip)

Total Calories = 600,000 calories

To cover for the lost calories, the group would need to sacrifice one member's trip to the South Pole and send them directly back to base camp. This would leave four members to continue to the South Pole, where they would have to ration their food carefully to make sure they have enough for the entire trip.

Below is a plan to ensure enough food:

Day 1-2:

Day 3-5:

Day 6-7:

Day 8-10:

Add up all the total calories consumed:

60,000 + 18,000 + 180,000 + 48,000 + 90,000 = 396,000 calories

This is less than the total calories required, which was 600,000 calories. Therefore, the group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.

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Answer:

"If one angle is equal to 40 degrees and the other two angles are equal, what is the number of degrees in each angle? A right angle is 90°, one angle is 40°, 90° - 40° = 50°. So the remaining two angles have a total measurement of 50°. If these two angles are equal, then each of the remaining angles are 50°/2, or 25°."

Step-by-step explanation:

Excerpt from Textbook :)

Answer:

in ABC,if<B=90,then AB^2+BC^2=AC^2

Step-by-step explanation:

the third option

i did that khan assignment

The appropriate rephrase statement to proof the Pythagorean theorem is

In ΔABC , if ∠B = 90°, then AB² + BC² = AC²

Pythagoras's theorem is used to calculate the sides of a right angle triangle. The formula is represented as follows

where

c = hypotenuse

a and b are either adjacent or opposite sides of the triangle.

A right angle triangle is a triangle that has one angle as 90°. Therefore, from the triangle below, the appropriate rephrase statement to proof Pythagoras theorem is as follows:

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Answer:

225

Step-by-step explanation:

Answer:

255

Step-by-step explanation:

One example of a number that meets this criteria is 255.

Answer: perfect squares are the squares of the whole numbers: 1, 4, 9,25,36,49,64,81,100...... For example, 9 is a squared number because it can be written as 3x3. However, imperfect squares are numbers whose square roots contain fractions or decimals. For example square root of 20 = 4 1/2

The square number, sometimes known as a perfect square, is an integer that is the square of another integer and numbers with fractional or decimal square roots are considered imperfect squares.

We need to compare and contrast perfect squares and imperfect squares.

Perfect squares: When you multiply an integer by itself, you get a perfect square, which is a positive integer. Perfect squares are sums that are the products of integers multiplied by themselves, to put it simply. A perfect square is typically expressed as x², where x is an integer and x²'s value is a perfect square.

Imperfect squares: Numbers with fractional or decimal square roots are considered imperfect squares.

Therefore, the square number, sometimes known as a perfect square, is an integer that is the square of another integer and numbers with fractional or decimal square roots are considered imperfect squares.

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Answer:

it would be C

hope this helps

Step-by-step explanation:

Answer:

9r/1 is the correct answer that satisfies the given conditions or if you wanna express your answer in the form of just 9r would be your answer

Step-by-step explanation:

(27r)1/3

9r/1 (9 times 3 is 27)

The simplified Expression of  (27\(r)^{1/3\) is 3\(r^{1/3\).

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as \(3^4\), where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.

Given:

We have to simplify (27\(r)^{1/3\)

Now, prime factorizing 27 = 3 x 3 x 3

(27\(r)^{1/3\)

= (3 x 3 x 3 x \(r)^{1/3\)

= (3³ \(r)^{1/3\)

= \(r^{1/3\) \((3^3)^{1/3\)

= 3\(r^{1/3\)

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Answer:

2.) x = 99

4.) x = 12

6.) x = 5

8.) n = 20

10.) x = 4

12.) y = 88

Step-by-step explanation:

Answer:

4x-7>13

add 7

4x>20

divide by 4

x>5

Step-by-step explanation:

divide

Step-by-step explanation:

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The solution of the given expression for w is (4xz-2z)/y -2. The correct option is D.

Given the expression is (2x-1)/y=(w+2)/2z.

We have to find the value of w for given expression.

A inverse operation can be defined as the operation that undoes what was done by the previous activity. The set of two opposite operations is called the inverse operation.

The expression is (2x-1)/y=(w+2)/2z

multiply both sides by 2z, we get

(2z(2x-1))/y=(2z(w+2))/2z

(2z(2x-1))/y=w+2

Now, we will apply the distributive property, we get

(2z×2x-2z×1)/y=w+2

(4xz-2z)/y=w+2

Further, we will subtract 2 from both sides, we get

(4xz-2z)/y-2=w+2-2

(4xz-2z)/y-2=w

Hence, the solution of the given expression (2x-1)/y=(w+2)/2z fpr w is (4xz-2z)/y-2.

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The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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Answer:

Step-by-step explanation:

When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.

__

If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":

  g(x) = (-2x +3)x -5

Then we have ...

  g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19

  g(0) = (-2(0) +3)(0) -5 = -5

  g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14