Do this for a brain thingy!!!!
1087^{2}-12(3)=

Hello there. To solve this question, we have to remember some properties about solving equations for a variable.

Given the following equation:

We want to solve it for w.

First, notice we can group some factors

Subtract lh on both sides of the equation

Assuming l + h is not equal to zero, divide both sides of the equation by this factor

This is the answer to this question.

Answer:

36

Step-by-step explanation:

We have the summation:

\(\displaystyle{\sum_{i=1}^{9} 2i-6\)

Essentially, we want to find the sum of (2i-6) from i=1 to i=9.

First, using summation properties, we can split this to:

\(=\displaystyle{\sum_{i=1}^{9} 2i+\displaystyle{\sum_{i=1}^{9} -6\)

On the right, it will simply be -6 evaluated 9 times. We can also move the constant out from the left:

\(=\displaystyle{2\sum_{i=1}^{9} i+9(-6)\)

For the summation on the left, this will simply be the sum (1+2+3+...+9). This yields 45. Therefore:

\(=2(45)+9(-6)\)

Evaluate:

\(=90-54=36\)

So, our final answer is 36.

A falcon can travel 29,998 centimeters farther than a worm in 10 seconds.

Hal learns that a falcon travels about 0.3 kilometers in 10 seconds, and a worm travels about 2 centimeters in 10 seconds. To determine how much farther a falcon can travel than a worm in 10 seconds, we need to convert the distance traveled by the falcon from kilometers to centimeters.1 kilometer = 100,000 centimeters. So, 0.3 kilometers = 0.3 x 100,000 = 30,000 centimeters. Therefore, a falcon travels 30,000 centimeters in 10 seconds .A worm travels 2 centimeters in 10 seconds. To find out how much farther the falcon travels than the worm in 10 seconds, we need to subtract the distance the worm travels from the distance the falcon travels.30,000 - 2 = 29,998

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Answer:

3,-2,-7,-12,-17,-22

when going up add, when going down subtract.

Example: -2+5=3

-17-5=-22

Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Note that the series of transformations that demonstrate that the figures are congruent are: "Reflect Figure A on the y-axis, followed by a 90° clockwise rotation about the origin. (Option D)

Transformation in math refers to the process of changing the position, size, or shape of a geometric figure. Common types of transformations include translations, rotations, reflections, and dilations.

Reflection in math is a type of transformation that involves flipping a figure over a line of reflection. The resulting image is a mirror image of the original figure, and the line of reflection acts as the mirror.

Congruence in math refers to the relationship between two geometric figures that have the same size and shape. In other words, if two figures are congruent, they are identical in every way except for their position and orientation in space. Congruence is typically denoted by the symbol ≅.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Figures A & B are shown on the coordinate grid. Which series of transformations demonstrates that the figures are congruent?

A) Reflect Figure A on the y-axis, followed by a reflection on the x-axis.

B) Translate Figure A 6 units right, followed by a reflection on the x-axis.

C) Rotate Figure A about the origin 1800 followed by a reflection on the x-axis.

D) Reflect Figure A on the y-axis, followed by a 90' clockwise rotation about the origin.

See attached image.

Answer:

\( \frac{9}{10} \)

Step-by-step explanation:

flip 8/9and then multiply by 4/5

Answer:

Symmetry over the y-axis

Step-by-step explanation:

This is an even function, meaning that it as symmetry of the y-axis.

Answer:

a and c have the same x value

Step-by-step explanation:

The line is going up, so that means there is a change in the y-values

If the line was horizontal, then there would be a change in the x-values.

Just picture it or draw it out, it would also help

a and c have the same x value

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

The line is going up, so that means there is a change in the y-values

If the line was horizontal, then there would be a change in the x-values.

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Answer:

4 mi²

Step-by-step explanation:

Area of Square: Length x Length

=> Area of Square: 2 x 2

=> Area of Square: 4 mi²

Therefore, the area of the square is 4 mi².

Hoped this helped

Answer:

4 mi²

Step-by-step explanation:

Area of Square: Length x Length

=> Area of Square: 2 x 2

=> Area of Square: 4 mi²

Therefore, the area of the square is 4 mi².

Answer:

9 yd

Step-by-step explanation:

A cube consists of 6 square faces.

Divide the surface area by 6 for the area of one face

486 ÷ 6 = 81 yd²

The area of a square is

A = s² ( s is the side length )

Here A = 81, then

s² = 81 ( take the square root of both sides )

s = \(\sqrt{81}\) = 9

Thus side length is 9 yd

Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Answer:

150%

Step-by-step explanation:

% change = change/original x 100

45-18 = 27

27/18 x 100 = 150

The percent of change if 18 is increased to 45, to the nearest percent, is calculated as: 150%.

To calculate the percent of change when 18 is increased to 45, we can use the formula:

Percent of change = ((New value - Initial value) / Initial value) * 100

Let's plug in the values and calculate the percent of change:

Percent of change = ((45 - 18) / 18) * 100

Percent of change = (27 / 18) * 100

Percent of change = 1.5 * 100

Percent of change = 150

Therefore, the percent of change is 150%, indicating a 150% increase.

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The "hypothesis of no change," "status quo," and "conventional wisdom" are all alternative names for the null hypothesis. Unless there is overwhelming evidence to the contrary, the null hypothesis is assumed to be correct.

H0: u = 1: u ≠ 1,400

When testing hypotheses with the P value, the null hypothesis is rejected if?

The evidence against the null hypothesis is stronger when the p-value is smaller (closer to 0).If the p-esteem is not exactly or equivalent to the predetermined importance level α, the invalid speculation is dismissed;The null hypothesis is not rejected otherwise.

A statement of expectation or prediction that will be tested by research is called a research hypothesis. Read up on the subject that interests you before coming up with your research hypothesis.

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Answer:

The total cost of adding wallpaper to the room is 487.20

Answer:

The total cost of adding wallpaper to the room is $487.20

Step-by-step explanation:

Basically, how I got the answer is:

1. The shorter sides of the rectangle are 12 and the longer sides are 14.

2. The formula for a rectangle is A = l x w. The "l" means length and the "w" means width. 14 is the length and 12 is the width. So you should now have A = 14 x 12. If you multiply 14 by 12, you will get 168.

3. Since 1 square foot of carpet costs $2.90, then you should multiply by 168, which will give you $487.20 and that's pretty much it.

Hope this helps! :)

Answer:

  a.  F'(0, 5), G'(1, 0), H'(-3, 3)

Step-by-step explanation:

Reflection across x = -1 gives you the transformation ...

  (x, y) ⇒ (-2 -x, y)

Reflection across y = 1 gives you the transformation ...

  (x, y) ⇒ (x, 2 -y)

Together, these give you the transformation ...

  (x, y) ⇒ (-2 -x, 2 -y)

Applying this to point F, we have ...

  F(-2, -3) ⇒ F'(-2 -(-2), 2 -(-3)) = F'(0, 5) . . . . . . matches choice A

_____

How we found the transformation

In general, if M is the midpoint between A and B, then you have ...

  M = (A+B)/2

  2M = A+B

  B = 2M - A

So, if we want x=-1 to be the midpoint between x' and x, then we have ...

  x' = 2(-1) -x = -2 -x

Likewise, if we want y=1 to be the midpoint between y' and y, then we have ...

  y' = 2(1) -y = 2 -y

So, the transformation is ...

  (x, y) ⇒ (x', y') = (-2 -x, 2 -y)

Answer:

40

Step-by-step explanation:

Let the width of the rectangle be w. Let the length of the rectangle be l.

It is given that the area of the rectangle is 112 sq ft. So we have; l × w = 112. We are also given that the length is 6 more than the width. So; l = w + 6. Now substituting the value of l from above in the expression for area of the rectangle, we get; (w + 6) × w = 112

Simplifying we get the quadratic equation; w² + 6w - 112 = 0

Solving for w by factorizing the above quadratic equation;w² + 14w - 8w - 112 = 0w(w + 14) - 8(w + 14) = 0(w - 8)(w + 14) = 0

So we get 2 values for w; w = 8 or w = -14

We reject the negative value of w, so the width of the rectangle is; w = 8

Therefore, the width of the rectangle is 8 ft. An alternative method to solve this problem is using the quadratic formula.

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k=6 classes are needed for this data set.

Now, According to the question:

Determining the Number of Classes:

The most common rule in determining the number of classes needed in classifying a data set is the \(2^k\)  rule. This rule simply estimates the number of classes k given n data points by solving the equation \(2^k\geq n\). This method is straightforward but may not work depending on how the data points are scattered.

The variable k representing the number of classes is the value that will make the expression  \(2^k\geq n\).

When n = 50  and noting that \(2^5=32\) and \(2^6 =64\)

Hence, 64 > 50.

Thus, k=6 classes are needed for this data set.

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it's both a function and relation a function because it has independent variable and dependent variable and it's a relation because there is a relationship between the values

Answer:

0.05n + 0.10 d =24.40

Step-by-step explanation:

Nickel is worth 0.05 of a dollar(1)

The system of equations below would be the best to use to find the number of nickels and dimes Anthony had at the end of the first week is:

n + d = 368

0.05n + 0.10d = 24.40

The number of nickels and dimes Anthony saved at the end of the first week can be determined using two equations. This is known as simultaneous equations.

The total number of nickels and dimes in the jar is 368. This can be represented with the equation:

nickels + dimes = 368

n + d = 368. This would be the first equation.

A nickel is equal to 0.05 of a dollar and a dime is equal to 0.1 of a dollar. The total sum of money in the jar is $24.40. This means that the value of dimes and nickels in the jar is $24.40. This can be represented with the equation: 0.05n + 0.10d = 24.40. This is the second equation.

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The Pythagorean Theorem shows that the triangle is acute

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

Using the Pythagorean Theorem, we have

87^2 < 59^2 + 79^2

Evaluate

7569 < 9722

Since 7569 is less than 9722, we can conclude that the triangle is an acute triangle, not a right or obtuse triangle.

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Answer:

3

Step-by-step explanation:

Divide 1kg or 1000g by 350 and round up to the next integer. That's it.

Answer:

3 packages

Step-by-step explanation:

350+350=700

700+350=1100

1000 grams=1 kilograms

Answer:

the answer is 76.8

Step-by-step explanation:

multiple of the number

Zork's algorithm guarantees that it always gets within a factor of 2 of the optimal solution because of the way that it combines the solutions from the left half and the right half. Zork's algorithm is an algorithm that is used to solve optimization problems.

Zork's algorithm always gets within a factor of 2 of the optimal solution. Zork's algorithm works by dividing the problem into two halves and then recursively solving each half. In each step, the algorithm decides whether the optimal solution lies in the left half, the right half, or across the middle.

If the optimal solution is in the left half, the algorithm recursively solves the left half. If the optimal solution is in the right half, the algorithm recursively solves the right half. I

f the optimal solution is across the middle, the algorithm takes the best solution that it found in the left half and the best solution that it found in the right half and combines them. The algorithm stops when it has solved the problem to the desired accuracy.

Suppose that the optimal solution is across the middle and that the solution in the left half is l and the solution in the right half is r. Without loss of generality, suppose that l ≤ r. Then the combined solution is at most r.

But r is at most twice the optimal solution, because r is in the right half and the optimal solution is across the middle. Therefore, the combined solution is at most twice the optimal solution.

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Answer:

5.190 < 5.195

Step-by-step explanation:

5.195 is bigger than 5.190, so 5.195>5.190

Answer:

To compare who saves the most of their salary each month among Amy, John, and Emily, we need to calculate the amount of salary each person saves.

Let's assume that the monthly salary of each person is 'S'. Then we can calculate the amount saved by each person as follows:

Amy:

Amount saved = 20% of S = 0.2S

Amount spent = S - 0.2S = 0.8S

John:

Amount spent = 2/5 of S = (2/5)S

Amount saved = S - (2/5)S = (3/5)S

Emily:

Let's assume that Emily saves '5x' and spends '8x' of her monthly salary.

Then, according to the question, we have:

Amount saved = 5x

Amount spent = 8x

We know that the ratio of the amount saved to the amount spent is 5:8, so we can write:

Amount saved / Amount spent = 5/8

Substituting the values of amount saved and amount spent, we get:

5x / 8x = 5/8

5x = (5/8) x 8x

5x = 5x

Therefore, the ratio of amount saved to amount spent is equal to 5:8. This means that Emily saves 5/13 of her monthly salary and spends 8/13 of her monthly salary.

So, the amount saved by each person is:

Amy: 0.2S

John: (3/5)S

Emily: 5/13 of S

Now, we need to compare these amounts to find out who saves the most.

To compare these amounts, we can write them in terms of a common denominator:

Amy: 0.2S

John: (3/5)S = (0.6)S

Emily: (5/13)S = (0.3846)S (approx.)

Therefore, we see that John saves the most of his salary each month, followed by Amy and then Emily.

Working out:

Let's assume that each person earns $1000 per month.

Amy:

Amount saved = 20% of $1000 = $200

Amount spent = $800

John:

Amount spent = 2/5 of $1000 = $400

Amount saved = $1000 - $400 = $600

Emily:

Let's assume that Emily saves $5x and spends $8x of her monthly salary.

Then, we have:

Amount saved = $5x

Amount spent = $8x

We know that the ratio of the amount saved to the amount spent is 5:8, so we can write:

$5x / $8x = 5/8

Solving for x, we get:

x = 8/13

Substituting the value of x, we get:

Amount saved = $5 x (8/13) x $1000 = $384.62 (approx.)

Amount spent = $8 x (8/13) x $1000 = $615.38 (approx.)

Therefore, we see that John saves the most of his salary each month, followed by Amy and then Emily.

The expected number of colleges to which the student is admitted .2344

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colours. Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.

Let X= college to which student is admitted

We are given with n=7 and p=1/6

P(X=2)=⁷P₂\(\frac{1}{6^{2} }(1-\frac{1}{6}) ^{7-2}\)

=.2344

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Answer:

40 ounces

Step-by-step explanation:

Number of ounces per day to be consumed = 4 oz

The number of days = 10

The smallest bag that has enough enough food for the cats is one which has atleast :

Number of ounces consumed per day * number of days

4 oz * 10 = 40 ounces

Answer:

109

Step-by-step explanation:

Three consecutive integers:

Sum of them:

The smallest integer out of three is 109

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3 consecutive integers = x+(x+1)+(x+2) or 3x+3 (x is the smallest number)

(Consecutive means one after another)

So 3x+3 = 330.

Now subtract 3 from both sides.

(3x-3)=3x

(330-3)=327

The left side is 3x and the right side is 327.

The equation now is 3x=327.

Now divide each side by 3 (so x is isolated)

3x÷3=x

327÷3=109

The left side is x and the right side is 109.

The final equation is x=109.

Since x is the smallest of these integers we don't have to do anything else.

Okay, so let's check the answer now. 109+110+111=330.

So the smallest of the 3 consecutive numbers is 109.

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