AABC is rotated 270° counterclockwise about the origin. Which triangle below represents a 270° counterclockwise rotation about the origin?

A) Red image 1

B) Green image 3

C) none of these

D) Purple image 2

The side length of the square is 1/2 - 1/4(x - 7)^2

To find the side length of the square, we need to first express the perimeter in terms of the side length.

Let s be the side length of the square.

Since a square has four equal sides, the perimeter of the square is given by:

y = 4s

Now, we can express s in terms of y:

s = y/4

Substituting this into the given expression for y:

y = 2 - (x - 7)^2

We get:

s = [2 - (x - 7)^2]/4

Simplifying this equation:

s = 1/2 - 1/4(x - 7)^2

Hence, the side length expression is 1/2 - 1/4(x - 7)^2

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Complete question

The perimeter (y) of a square is y =2 - (x - 7)^2. What’s the side length of the square?

The sum of 10 3/4 and 12 1/4 is 23.

To add the mixed numbers 10 3/4 and 12 1/4, follow these steps:

Step 1: Add the whole number of parts.

Add the whole numbers 10 and 12 to get:

10 + 12 = 22

Step 2: Add the fractional parts separately.

Add the fractions 3/4 and 1/4 separately. To do this, find a common denominator, which in this case is 4. Then convert each fraction to have the same denominator and add the numerators.

For 10 3/4, the fraction 3/4 has the same denominator, so we keep it as is.

For 12 1/4, the fraction 1/4 also has the same denominator, so we keep it as is.

Then we add the numerators of the fractions:

3/4 + 1/4 = 4/4 = 1

Step 3: Add the results from Step 1 and Step 2.

Add the result from Step 1 (the sum of the whole numbers) to the result from Step 2 (the sum of the fractions):

22 + 1 = 23

Therefore, the sum of 10 3/4 and 12 1/4 is 23.

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According the question given above the area of ABK is  100 square cm.

a) ACD = 50 square cm

b)AMCN = 225 square cm

c)ABK = 100 square cm

a) Tο calculate ACD, we need tο use the fοrmula fοr the area οf a trapezοid, which is:

Area = (base1 + base2) × height ÷ 2

Since CD is twice the length οf AB, we can let AB = x and CD = 2x. Let's alsο call the height οf the trapezοid h.

Then we have:

450 = (AB + CD) × h ÷ 2

450 = (x + 2x) × h ÷ 2

450 = 3xh ÷ 2

300 = 3xh

100 = xh

Nοw, we can use the fact that MA = MB tο find the area οf triangle ACD:

ACD = AB × h ÷ 2

ACD = xh ÷ 2

ACD = 100 ÷ 2

ACD = 50 square cm

b) Tο calculate AMCN, we need tο first find the length οf MN. Since MA = MB and NC = ND, we can use the fact that οppοsite sides οf a trapezοid are parallel tο find that AMCN is a parallelοgram. Therefοre, MN is equal tο AB.

Using the fοrmula fοr the area οf a parallelοgram, which is base × height, we have:

AMCN = AB × CD

AMCN = x × 2x

[tex]AMCN = 2x^2[/tex]

AMCN = 900 ÷ 2

AMCN = 225 square cm

c) Tο find the area οf triangle ABK, we need tο find the length οf BK. Since AB = x and CD = 2x, we knοw that AK and KC are alsο equal tο x. Therefοre, BK is equal tο DA, which is 2x.

Using the fοrmula fοr the area οf a triangle, which is base × height ÷ 2, we have:

ABK = AB × BK ÷ 2

ABK = x × 2x ÷ 2

[tex]ABK = x^2[/tex]

ABK = 100 square cm

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Answer

Choice C: (1 1/4 + 2 3/8) / 3/4

Step-by-step explanation:

His salad consists of 1 1/4 cups of purple cabbage and 2 3/8 cups of lettuce. First, you would add those two together to get how much the salad is. THEN divide by how much he eats each day which is 3/4.

There are 5 ways we can represent the number of dots shown.

What is the combination?

A combination is a choice of items from a group of different items where the order of the choices is irrelevant. either the process of combining or the condition of combining. a combination of several things a synthesis of concepts. something created through fusion: A chord is made up of several notes.

Here, we have

Given: Dots shown and we have to find the ways can you represent the number of dots shown.

We apply here combination and we get

⁵C₁ = 5!/4!

= 5

Hence, there are 5 ways we can represent the number of

dots shown.

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Answer:

Let's assume Karl rents the bike for x hours. Then the cost of renting the bike can be expressed as:

Cost = 7x + 9.5

We know that the maximum cost Karl can afford is $55. So we can set up an equation:

7x + 9.5 ≤ 55

Subtracting 9.5 from both sides:

7x ≤ 45.5

Dividing both sides by 7:

x ≤ 6.5

Since Karl can only rent the bike for whole hours, the maximum number of hours he can rent the bike is 6 hours (which costs $49 plus the $9.5 flat fee, for a total of $58.5). If he rented it for 7 hours, it would cost $60.5, which is over his budget.

The option (B) is the correct answer.

Given equation is \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \]where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground.Now, we are asked to find the time when the pedal reaches a height of 34.48 inches for the second time.In order to find that, we can solve the equation as follows:\[34.48-30=14.5\cos\left[\frac{2\pi}{5}t\right]\]\[\cos\left[\frac{2\pi}{5}t\right]=\frac{4.48}{14.5}\]\[\cos^{-1}\left(\frac{4.48}{14.5}\right)=\frac{2\pi}{5}t\]\[t=\frac{5\cos^{-1}\left(\frac{4.48}{14.5}\right)}{2\pi}\]This gives us,\[t \approx 1.6 \text{ or } 3.7\]The pedal reaches the given height for the second time when \( t = 3.7\) seconds. Therefore, option (B) is the correct answer.

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Answer:

plot the point at -3

Step-by-step explanation:

-3 is 6 points away from t and 4 away from s. thus 3/5

The value of the range of function is found as f(5) = -21.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The given function:

f(x) = {3x-5;x<5

        {-x^2 +4;x>= 5

f(5) = -x^2 +4

Put x = 5

f(5) = -(5)^2 +4

f(5) = -25 +4

f(5) = -21

Thus, the value of the range of the function is found as f(5) = -21.

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Yes, Pairing arrangements are possible.

[tex]$\frac{n!}{2^n (n/2)!}$[/tex]

If there are n cysteines, then there are n sulfur atoms that can form disulfide bonds. To form a pairing arrangement, we need to choose 2 sulfur atoms from the n sulfur atoms and connect them with a disulfide bond. We repeat this process until all sulfur atoms are paired up.

The number of ways to choose 2 sulfur atoms from n sulfur atoms is given by the binomial coefficient

[tex]$\binom{n}{2}$[/tex]

Once two sulfur atoms are paired up, we can remove them from the pool of sulfur atoms and continue pairing the remaining sulfur atoms in the same way.

Therefore, the total number of pairing arrangements is given by:

[tex]$\binom{n}{2} \cdot \binom{n-2}{2} \cdot \binom{n-4}{2} \cdots \binom{4}{2} \cdot \binom{2}{2}$[/tex]

which can be simplified as:

[tex]$\frac{n!}{2^n (n/2)!}$[/tex]

Since we are choosing pairs, we divide by 2 for each pair and the order of the pairs doesn't matter. Also, we divide by (n/2)! to account for the fact that the pairs can be arranged in any order.

Note- that n must be even for this formula to hold.

Therefore, the general formula for the number of different pairing arrangements when there are n cysteines (and n is even) is:

[tex]$\frac{n!}{2^n (n/2)!}$[/tex]

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The algebra Property used to get  Equation B from Equation A is:

Rewrite one side (or both) using the distributive property​

The 2 equations given are:

A. 5 = -2(x - 1)

B. 5 = -2x + 2

Some of the popular properties of algebra are:

Commutative Property: This states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. For example: a + b = b + a , a b = b a

Associative Property: This is defined as when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped. For example: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c

Distributive Property: This is defined as multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together. For example, a(b + c) = ab + bc

Equation A is given as 5 = -2(x - 1)

To get equation B, we rewrite one side (or both) using distributive property

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Complete question is:

A. 5=-2(x-1)

B. 5=-2x+2

How can we get equation B from equation A?

A. rewrite one side (or both) by combining like terms

B. rewrite one side (or both) using distributive property

C. multiply or divide both sides by the same non zero constant.

D. multiply or divide both sides by the same variable expression.

Answer:

103

Step-by-step explanation:

157-54= 103

Answer: 103

Step-by-step explanation:

subtract 54 from 157

Answer:  Nate have 278 cookies now.

Step-by-step explanation:

the original amount of cookies for Nate is 300, and he dropped 145, which means we need to subtract 145 from 300.  And his mom brought him 123 more, which means we need to add 123.

300 - 145 + 123 = 278

The surface area of the mentioned rectangular prism is calculated to be 168 yd².

The surface area of ​​a three-dimensional object is the total area of ​​all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.

Area of rectangle 1

= 6 × 2

= 12 yd²

Area of rectangle 2

= 9 × 2

= 18 yd²

Area of rectangle 3

= 9 × 6

= 54 yd²

Since the prism is made of 2 faces of each type of rectangle and the area of prism is the sum of area of each face:

Area of prism = (12 × 2) + (18 × 2) + (54 × 2)

Area of prism = 24 + 36 + 108

Area of prism = 168 yd²

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The flat fee that the stοre charge $14 and the cοst fοr 7 hοurs is $56. we sοlve this questiοn using linear equatiοn.

An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant.

let f be the tοtal rental cοst οf a vacuum cleaner fοr x hοurs

And, f(x) = 6x + 14 (Given)

Sο The flat fee that the stοre charge $14.

Reasοnable dοmain is 1  ≤  x  ≤  12

The cοst fοr 7 hοurs is,

f(7) = 6(7) + 14 = 56.

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Answer:

w = 102

m = 78

n = 58

Step-by-step explanation:

Three angles of a triangle add up to 180°

∴ w = 180 - (36 + 42)

= 180 - 78

= 102

w and m are supplementary angles:
m + w = 180

m + 102 = 180

m  = 180 - 102 = 78

Three angles of a triangle add up to 180°

m + 44 + n = 180

78 + 44+ n = 180

122 + n = 180

n = 180 - 122

n = 58

A sample size of 11 would give a standard deviation of 10 pounds for the Florida Manatees

An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.

The standard deviation of a sample is:

[tex]\sigma_n=\frac{\sigma}{\sqrt{n} } \\\\Where\ n\ is\ sample\ size,\sigma\ is\ standard\ deviation\ and\ \sigma_n\ is\ standard\ deviation\ of\ sample[/tex]

Given that:

[tex]\sigma_n=10,\sigma=33,hence:\\\\10=\frac{33}{\sqrt{n} } \\\\n=10.89[/tex]

A sample size of 11 would give a standard deviation of 10 pounds

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According to the property of inequality, the inequality that models this situation is 8m + 12n ≥ 80.

What is inequality?

An inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not, or which one is greater or smaller.

Let's use "m" to represent the number of 8-ounce jars of olives and "n" to represent the number of 12-ounce jars of olives.

The total amount of olives can be found by multiplying the number of 8-ounce jars by 8 and the number of 12-ounce jars by 12, and then adding them together:

total amount of olives = 8m + 12n

The problem tells us that the total amount of olives is at least 80 ounces. We can represent this information as an inequality:

8m + 12n ≥ 80

Therefore, the inequality that models this situation is 8m + 12n ≥ 80.

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The least amount of money Sally still needs to save before she can buy the iPhone is $125 and the inequality that represents this situation is m ≥ $125

Let "m" be the amount of money Sally still needs to save to buy the iPhone.

The total cost of the iPhone is $200, and Sally has already saved $75. Therefore, the amount of money she still needs to save is:

m = $200 - $75

m = $125

So Sally still needs to save at least $125 before she can buy the iPhone.

Therefore, the inequality that represents this situation is

m ≥ $125

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Answer:

Multiplying the first equation by 3 and the second equation by 9, we get:

-27y + 12x - 33 = 0

-27y + 90x + 279 = 0

Now, we can subtract the first equation from the second to eliminate y:

-27y + 90x + 279 - (-27y + 12x - 33) = 0

78x + 312 = 0

78x = -312

x = -4

Substituting x = -4 into the first equation, we get:

-9y + 4(-4) - 11 = 0

-9y - 27 = 0

y = -3

Therefore, the solution to the system of equations is (x, y) = (-4, -3).

The expression which could be used to determine the area of the triangle is: One-half (2) (three-fourths) (StartFraction 7 Over 8 EndFraction).

Expression in math is a combination of numbers, operations, variables, and/or other mathematical symbols that represent a quantity or an action. It is a statement that can be evaluated to a single value, or a set of values. Expressions in math can be used to solve equations, calculate values, and form models of real-world scenarios.

This expression multiplies together the base, two and three-fourths, and the height, StartFraction 7 Over 8 EndFraction, and then divides the result by two to give the area of the triangle.

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Answer:

Step-by-step explanation:

You can do 6x+the number of the amount of squares. Then find find the units of the square unit.

After calculating, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.

Considering that Bert's maximum speed is 270 meters per minute, then his speed when he is paddling at one-third of his top speed is:

270 m/min * (1/3) = 90 m/min

If he is paddling at this speed for 8 minutes, then the distance that he covers is:

distance = speed * time = 90 m/min * 8 min = 720 meters

Therefore, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.

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satisfied=88%

The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%.What is probability?Probability is the branch of mathematics that studies the probability of an occurrence, as well as the likelihood of its occurrence. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.Probability formula is P(E) = n(E) / n(S), where P(E) refers to the probability of occurrence of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of possible outcomes.What is proportion?The proportion is a percentage, a fraction, or a ratio that compares the number in the group to the total number. When looking at a sample from the population, the sample proportion is calculated as the number in the sample with the attribute of interest divided by the total number of people in the sample. It gives us the proportion of people who have the attribute of interest in the sample.Answer:Therefore, the probability will be 88% ±5% and the proportion satisfied is 88%.

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Answer:

Obtuse

Step-by-step explanation:

In general speaking of your options

Straight angles equal exactly 180

Acute angles equal anything less than 90

Obtuse equals anything above 91

Right angles equal exactly 90

Answer:

If x > 5, then y = 2x.

Step-by-step explanation:

If x > 5, then both expressions inside the absolute values are positive, so we can simplify the expression:

y = |x - 5| + |x + 5|

Since x > 5, we know that x - 5 > 0 and x + 5 > 0. Therefore, we can write:

y = (x - 5) + (x + 5)

Simplifying this expression, we get:

y = 2x

So, if x > 5, then y = 2x.

Hope this helped! Sorry if it's wrong. If you need more help, ask me! :]

Homer would have taken approximately 8.11 hours to do the job by himself.

Let h be the time it would take Homer to do the job by himself, and let m be the time it would take Mike to do the job by himself. We know from the problem that:

m = h - 1 (Mike can do the job one hour quicker than Homer)

We also know that they worked together for 4 hours, so they completed 4/h + 4/m of the job. We can set up an equation based on this:

4/h + 4/m = 1 (they completed the entire job)

Substituting m = h - 1, we get:

4/h + 4/(h-1) = 1

Multiplying both sides by h(h-1), we get:

4(h-1) + 4h = h(h-1)

Simplifying:

8h - 4 =

[tex]h^2 - h[/tex]

Rearranging:

[tex]h^2 - 9h + 4 = 0[/tex]

Using the quadratic formula, we get:

[tex]h = (9 ± \sqrt{(9^2 - 414)) / 2} [/tex]

Since we are looking for a positive value of h, we take the positive square root:

h ≈ 8.11

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The proper formula states that a sphere with a radius of [tex]15[/tex] has a volume of 4/3π([tex]15^{3}[/tex]).

The equation for a sphere's size is V = 3/3 r3, wherein r represents the radius and V is its volume. 1⁄2 of an object's circumference makes up its radius. Therefore, you may determine the radius first, then by the volumes, to get the contact area of a globe given its diameter.

Both a circle as well as a sphere are round, if you compare them. The difference among the two forms is that while a sphere has three dimensions, a circle only has two, which is why we can measure a sphere's volume and surface area.

The formula for the volume of a sphere is V = 4/3π[tex]r^{3}[/tex], where r is the radius of the sphere.

Substituting [tex]r=15[/tex], we get

V = 4/3π([tex]15^{3}[/tex])

Therefore, the expression 4/3π([tex]15^{3}[/tex]) gives the volume of a sphere with radius [tex]15[/tex].

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Answer:

[tex] \frac{45}{136} [/tex]

Step-by-step explanation:

The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.

After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.

To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:

[tex] \frac{10}{17} \times \frac{9}{16} = \frac{90}{272} [/tex]

So the probability of selecting two girls in a row is

[tex] \frac{90}{272} [/tex]

which can be simplified to

[tex] \frac{45}{136} [/tex]

Answer: 3690

Step-by-step explanation: i think

The total amount in the account after 5 years is $3690.

Simple interest is the borrowing amount added only to the principal amount.

The Formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100,

Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.

In this case, the principal is $3600, the rate is 0.5% (or 0.005 as a decimal), and the time is 5 years.

Plugging these values into the formula, we get:

Interest = $3600 x 0.005 x 5 = $90

So after 5 years, the interest earned on the account is $90. To find the total amount in the account, we need to add the interest to the principal:

Total amount = Principal + Interest = $3600 + $90 = $3690

Therefore, the total amount in the account after 5 years is $3690.

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