Rotate 90° counterclockwise about the origin.
M (3.2), N'(5,5), P'(4,5), Q'(2, 2)
M"1-2.3). N'(-5,5), P'(-5.4), (-2,2)
M(-2,-3). N'(-5.-5), P'(-5.-4). Q'-2,-2)
M*2.3). N'(5,5), P75,4), Q (2.2)

(p ² q ⁵) ⁻⁴ (p ⁻⁴ q ⁵) ⁻²

= (p ⁻⁸ q ⁻¹⁰) (p ⁻⁸ q ⁻¹⁰)

= p ⁻¹⁶ q ⁻²⁰

Answer:

4 and -3

Step-by-step explanation:

So our function is f(x) = x² - x -12

We need to find factors such that 0 = x² - x -12

So, it looks something like this 0 = (x - a)(x - b)

We know that the first term is x², which can only be obtained if we multiply x by another x.

Now, we need to find the other terms a and b. We know that a × b = -12

The correct answer would be that a = 4 and b = -3

0 = (x - 4)(x + 3)

We know this because, if we multiply this out, we get x² + 3x -4x -12, which can be simplified to x² -x -12.

Our zeroes are the values of x that this equation 0 = (x - 4)(x + 3) is true. What values of x will make this zero?

4 and -3

Ans.......

YTC ...................................

Step-by-step explanation:

Answer:

Cubes have 6 equal faces, and the surface area is the sum of all of these faces. Thus, one face would be 1/6 of the cube's surface area, or about 17%.

Step-by-step explanation:

Answer:

25.67

Step-by-step explanation:

One third written as a fraction is 1/3. You can also write it as a decimal by simply dividing 1 by 3 which is 0.33.

If you multiply 0.33 with 77 you will see that you will end up with the same answer as above.

You may also find it useful to know that if you multiply 0.33 with 100 you get 33.33. Which means that our answer of 25.67 is 33.33 percent of 77.

The measure of arcPR and arcRPT are 83 and 208 degrees respectively

The measure of arc ST will be gotten using the expression below:

arcPS = arcPT + arcST

Given the following

arcST = arcPS - arcPT

arcST = 180  - 125

arcST = 55 degrees

Similarly, arcPR = 180 - arcRS

arcPR = 180 - 97

arcPR = 83 degrees

arcRPT = arcPR + arcPT

arcRPT = 83 + 125

arcRPT = 208 degrees

Hence the measure of arcPR and arcRPT are 83 and 208 degrees respectively

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Answer:

arc PR=83 and arc RPT= 208

Step-by-step explanation:

1. 2.50/10 = $.25 per ounce

2. We have one dollar

.25 *4 = 1 dollar, so we can multiply by 4 * 1 ounce

4 ounces will cost 1 dollar

3. c = $.25* p

We can also write this as

c = 1.00 (p/4) where p is the number of ounces

c = p/4

4. Using the last equation

c = p/4

where p is the number of ounces and c is the number of dollars the popcorn costs

Answer:

0.25.2

Step-by-step explanation:

1.51/2

So,halves

0.25.2

Answer:

he spent $18.57 and he can spend $7.43 more

The solution is, he can still spend no more than $6.43.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

Wyatt wants to spend no more than $25 at the grocery store.

He bought a pizza for $7.55 and a cake for $11.02 (including tax).

now, we have to find the inequality that he can use to find how much money he can still spend.

let, we would spend = x

now, we have,

He bought a pizza for $7.55 and a cake for $11.02

so, he had = $ x - ( 7.55 + 11.02)

we have,

x ≥ 25

so, he can still spend ≥ 25 -  ( 7.55 + 11.02)

or, he can still spend ≥ 6.43

i.e.  he can still spend no more than $6.43

Hence, The solution is, he can still spend no more than $6.43.

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Answer:

60

Step-by-step explanation:

Let's name "a number" "q."

The expression we can set up is 6+9q

Plug 6 in for q.

6+9(6)

6+54

60

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

Im pretty sure its x< 3

Step-by-step explanation:

Answer:

the answer is A 3>x hope this helps

Hence, the temperatures in these other cities are

Orlando is \(25\) degree

Salt Lake is \(-10\) degree

Minneapolis is \(-17\) degree

Fairbanks is \(-29\) degree

What is the degree?

A degree, usually denoted by °, is a measurement of a plane angle in which one full rotation is \(360\) degrees.

Here given that,

One winter day, the temperature in Houston is \(8\) Celsius.

In Orlando, it is \(17\) warmer than it is in Houston.

In Salt Lake City, it is \(18\) colder than it is in Houston.

In Minneapolis, it is \(25\) colder than it is in Houston.

In Fairbanks, it is \(12\) colder than it is in Minneapolis.

So, it would be

Orlando = \(25\) degree

because \(17+8=25\) degree

Salt Lake city \(= -10\) degree

because \(8-18=-10\) degree

Minneapolis \(= -17\) degree

because \(8-25=-17\) degree

Fairbanks \(= -29\) degree

because \(-17-12=-29\) degree

Hence, the temperatures in these other cities are

Orlando is \(25\) degree

Salt Lake is \(-10\) degree

Minneapolis is \(-17\) degree

Fairbanks is \(-29\) degree

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We can use the points given to solve for the slope.

Slope formula: y2-y1/x2-x1

7-7/-1-5

0/-6

Since the numerator is 0, the slope is 0.

Best of Luck!

(i) The expanded form of (1 / 2 - 2 · x)⁵ in ascending form is 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵.

(ii) The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.

In this problem we must apply the concept of Pascal's triangle to expand the power of a binomial of the form (x + y)ⁿ and further algebra properties.

(i) First, we proceed to expand the power binomial (1 / 2 - 2 · x)⁵ in ascending order:

(1 / 2 - 2 · x)⁵ = (1 / 2)⁵ + 5 · (1 / 2)⁴ · (- 2 · x) + 10 · (1 / 2)³ · (- 2 · x)² + 10 · (1 / 2)² · (- 2 · x)³ + 5 · (1 / 2) · (- 2 · x)⁴ + (- 2 · x)⁵

( 1 / 2 - 2 · x)⁵ = 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵

(ii) Second, we proceed to expand the following product of polynomials by algebra properties:

(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = (1 + a · x + 3 · x²) · [1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵]

(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = 1 / 32 + (a / 32 - 5 / 8) · x + (- 5 · a / 8 + 163 / 32) · x² + (- 175 / 8 + 5 · a) · x³ + (65 - 20 · a) · x⁴ + (- 92 + 40 · a) · x⁵ + (120 - 32 · a) · x⁶ - 96 · x⁷

In accordance with the statement, we find that:

- 5 · a / 8 + 163 / 32 = 13 / 2

- 5 · a / 8 = 45 / 32

a = - 9 / 4

Thus, the coefficient of x³ is:

C = - 175 / 8 + 5 · (- 9 / 4)

C = - 265 / 8

The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.

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The most convincing explanation I can give for why a = c is supplementary property a+ b

= 180° and b+c = 180° and substraction operation and also one more reason is a = c is also true because they are vertically opposite angles.

A supplementary angle is an angle that sums to 180 degrees. For example, the 130° and 50° angles are complementary because the sum of 130° and 50° is 180°.

We know that, supplementary angles are angles whose sum is 180°. From the above figure, using the property that linear pairs are supplementary , we have b+c = 180° , c+d = 180° , d+a = 180° ,

a+b = 180°

Therefore, consider a+b = 180° and b+c = 180°

Using subtraction property of equality, we have

180°- b = a .........(1)

180°-b = c ..........(2)

Substitute 180°- b = a in equation (2) , we get

=> a = c

Hence, we get the required results.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

Answer:

First table

Step-by-step explanation:

In a table of a proportional relationship, there is always some number that you can multiply by the number in the first column to get the number in the second column for any row. This number is called the constant of proportionality. In the fruit juice example, the constant of proportionality is 0.4.

Answer:

Let the no. be X and Y

X - Y = (-1)

X + Y = 1

X = (-1)+ Y

X = 1 - y

- 1.+ y = 1 - y

Y + Y = 1 + 1

2y = 2

Y = 1

X = 0

Answer:

x = 0 (first number), y = 1 (second number)

Step-by-step explanation:

x will represent the first number, and y will represent the second.

x - y = -1

x + y = 1

Now, it's time to get y by itself in one equation so that we can substitute.

x - y = -1 (subtract x from both sides)

-y = -1 - x (multiply both sides by -1)

y = x + 1

Plug in x + 1 for y in the second equation.

x + x + 1 = 1 (combine the x with the x)

2x + 1 = 1 (subtract 1 from both sides)

2x = 0 (divide both sides by 2)

x = 0

Since x = 0, we can plug 0 in for x into any equation to solve for y.

0 + y = 1

y = 1

Brainliest, please :)

Answer:

Step-by-step explanation:

The image doesn't load for me

Answer:

6/24

Step-by-step explanation:

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

SOLUTION:

Using Poisson distribution

n = 74,090,000

p = 0.000037

Therefore, the mean of the appropriate Poisson distribution

Final answer: Nearest whole number

2470

Answer:

1/10

Step-by-step explanation:

The center of mass for the system (x, y) is \(\left(\frac{a m+b M}{m+M}, 0\right)\).

What is center of mass?

The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.

The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Centre of mass is

\(x=\frac{m a+M b}{m+M}\)

and y=0

\((x, y)=\left(\frac{a m+b M}{m+M}, 0\right)\)

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Answer:

slightly confused on the wording if he got back 3/4 from 16.5 then he earned back 12.375 points

if -16.5 is the 1/4 he didnt get back then he had 66 points

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

\(a^{m}*a^{n}=a^{m+n}\\\\\\\dfrac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\dfrac{7^{8}*7^{3}*7^{4}}{7^{9}*7^{5}}=\dfrac{7^{8+3+4}}{7^{9+5}}\\\\=\dfrac{7^{15}}{7^{14}}\\\\\\=7^{15-14}=7^{1}\\\\= 7\)

Answer:

7^1

Step-by-step explanation:

since all the bases are same, we're going to use the law (a^m × a^n = a^m+n)

8+3+4= 15, hence, it's 7^15

we'll apply the same law for the denominator, 9+5= 14, so we'll get 7^15 ÷ 7^14

next we're gonna use the law (a^m ÷ a^n = a^m-n where m>n)

15-14 = 1

so our final answer is 7^1

Answer:

The coordinates of B is (-8,-5).

Step-by-step explanation:

The midpoint of line AB is M. The coordinate of M is (-6,-4).

The coordinates of A is (-4,-3)

We need to find the mid point of B.

If M(x,y) is the midpoint of the coordinates (x₁,y₁) and (x₂,y₂). The mid point theorem is used as follows :

\(M(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\)

Let the mid point of B is (x₂,y₂). Put (x,y) = (-6,-4), (x₁,y₁) = (-4,-3).

\((-6,-4)=(\dfrac{-4+x_2}{2},\dfrac{-3+y_2}{2})\\\\\dfrac{-4+x_2}{2}=-6\ \text{and}\ \dfrac{-3+y_2}{2}=-4\\\\-4+x_2=-12\ \text{and}\ -3+y_2=-8\\\\x_2=-12+4\ \text{and}\ y_2=-8+3\\\\x_2=-8\ \text{and}\ y_2=-5\)

So, the coordinates of B is (-8,-5).

The coordinates of B are (-8, -5).

Given that,

The midpoint of AB is M(-6, -4). If the coordinates of A is (4,-2),

We have to determine,

The coordinates of B.

According to the question,

The midpoint of line AB is M. The coordinate of M is (-6,-4).

And the coordinates of A is (-4,-3)

If M(x, y) is the midpoint of the coordinates (x₁, y₁) and (x₂, y₂). The midpoint theorem is used as follows :

\(M(x, y) = ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})\)

Let the midpoint of B be (x₂, y₂).

M (x, y) = (-6,-4), and (x₁, y₁) = (-4,-3).

\(M(-6, -4) = ( \dfrac{-4+x_2}{2}, \dfrac{-3+y_2}{2})\\\\\)

Solving the equation for the co-ordinate B.

\(\dfrac{-4+x_2}{2} = -6\\\\-4 + x_2 = -6 \times 2\\\\-4 + x_2 = -12\\\\x_2 = -12+4\\\\x_2 = -8\)

And,

\(\dfrac{-3+y_2}{2} = -4\\\\-3 + y_2 = -4 \times 2\\\\-3 + y_2 = -8\\\\y_2 = -8 + 3\\\\y_2 = -5\)

Hence, The required coordinates of B are (-8, -5).

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