A line is drawn through (–7, 11) and (8, –9). The equation y – 11=-4/3 (x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.

Answer:

(xy + x)and (xy + x)

(2x - 3) and (-3 + 2x)

(4y² + 25) and (25 + 4y²)

Step-by-step explanation:

* Lets explain the meaning of the perfect square trinomial

- If a binomial multiply by itself, then the answer will be a perfect

 square trinomial

- Example: if the binomial (ax + b) multiply by itself, then

 (ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)

 (ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²

∵ (ax + b)(ax + b) = (ax + b)²

∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

* From the example above the perfect square trinomial has 3 terms

# 1st term is the square the first term in the binomial

# 2nd term is twice the product of the two terms of the binomial

# 3rd term is the square of the second term of the binomial

* Lets solve the problem

- The product of (-x + 9)and (-x - 9)

∵ -x + 9 ≠ -x - 9

∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial

- The product of (xy + x)and (xy + x)

∵ xy + x = xy + x

∴ (xy + x)(xy + x) = (xy + x)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (xy + x) and (xy + x) is a perfect square trinomial

- The product of (2x - 3) and (-3 + 2x)

∵ (-3 + 2x) can be written as (2x - 3)

∴ 2x - 3 = -3 + 2x

∴ (2x - 3)(-3 + 2x) = (2x - 3)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial

- The product of (16 - x²) and (x² - 16)

∵ 16 - x² can be written as -x² + 16

- If we take -1 common factor from -x² + 16

∴ -x² + 16 = -(x² - 16)

∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256

∵ x^4 - 32x² + 256 is perfect square trinomial

∵ -x^4 + 32x² - 256 is not a perfect square trinomial

∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial

- The product of (4y² + 25) and (25 + 4y²)

∵ 25 + 4y² can be written as 4y² + 25

∴ 4y² + 25 = 25 + 4y²

∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial

Answer:

Floor 7

Step-by-step explanation:

He entered the elevator on floor x.

Then he rode up 10 floors. Now he is on floor x + 10.

Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.

Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.

Floor x - 6 is the same as Floor 1, so we get the equation:

x - 6 = 1

Add 6 to both sides:

x = 7

Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.

Answer:

He began on floor 7

Step-by-step explanation:

This is a question where you have to use the question from the end and work your way backwards if that makes sense.

He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.

Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.

And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7

Now to make sure it is correct, start from 7 and follow the original order of the question.

7 + 10 = 17

17 - 2 = 15

15 - 14 = 1

Answer:

a) 16 in²

b) 20 cm²

Step-by-step explanation:

In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)

a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².

__

b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².

Answer:

(w - 2.5)(w + 2.5)

(-4v - 9)(-4v + 9)

Step-by-step explanation:

* Lets explain what is the a difference of two squares

- If we multiply two binomial and the answer just two terms with

 negative sign between them and the two terms are square numbers

 we called this answer a difference of two squares

- Examples

# (a + b)(a - b)

- Lets multiply them

∵ (a × a) + (a × -b) + (b × a) + (b × -b)

∴ a² - ab + ba - b²

- Add the like term

∵ ab = ba

∴ -ab + ba = 0

∴ (a + b)(a - b) = a² - b² ⇒ difference of two squares

- From above the difference of two squares appears when we

 multiply sum and difference of the same two terms

# (a + b) ⇒ is the sum of a and b

# (a - b) ⇒ is the difference of a and b

* Now lets solve the problem

- In (5z + 3)(-5z - 3)

∵ (5z + 3) ⇒ is the sum of 5z and 3

∵ (-5z - 3) ⇒ is the difference of -5z and 3

∵ 5z ≠ - 5z

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (w - 2.5)(w + 2.5)

∵ (w - 2.5) is the difference between w and 2.5

∴ (w + 2.5) is the sum of w and 2.5

∴ They are the sum and difference of the same two terms

∴ The product result in a difference of squares

- In (8g + 1)(8g + 1)

∵ The two brackets are the sum of 8g and 1

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (-4v - 9)(-4v + 9)

∵ (-4v - 9) is the difference between -4v and 9

∵ (-4v + 9) is the sum of -4v and 9

∴ They are the sum and difference of the same two terms

∴ The product result in a difference of squares

- In (6y + 7)(7y - 6)

∵ (6y + 7) is the sum of 6y and 7

∵ (7y - 6) is the difference between 7y and 6

∵ 6y ≠ 7y and 7 ≠ 6

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (p - 5)(p - 5)

∵ The two brackets are the difference of p and 5

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

Answer:

option 2 and 4

Step-by-step explanation:

Answer with explanation:

Temperature in the living room =68°F

The equation which satisfies ,the  room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies

 t=2 Cos (0.21 m) +68----------(1)

⇒To determine the period of the function

Z= A cos (sx+q)+r

As period of cos x is 2 π.

So,the given function has period

        [tex]=\frac{2\pi}{s}[/tex]            

So, the period of function 1, is given by

        [tex]=\frac{2\pi}{0.21}[/tex]  

⇒The meaning of period of the function is that after every period of   [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.

⇒Cosine function has maximum value of 1 , and Minimum value of -1.

-1 ≤ Cos x ≤ 1

So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature

And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature

Final answer:

The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.

Explanation:

Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.

The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.

The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.

Answer:

We have 8 liters of 54% alcohol.

We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.

54 * 8 + 66 x =   65 (8 + x)

432 + 66x = 520 + 65x

x = 88 liters

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]

The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:49

Step-by-step explanation: 9+4=13 4x2=8 8+1=9

9 is the units digit

4 is the tens digit

Answer:

120

Step-by-step explanation:

If those 2 polygons are similar, then their corresponding angles are the same.  The thing that makes them similar as opposed to congruent is that their side lengths exist in proportion to one another instead of being the same.

Answer:

[tex]w = 120\°[/tex]

Step-by-step explanation:

In this case we know that

ABCD and FECG are similar polygons.

 This means that their sides are proportional and their corresponding angles are equal.

So if the lines FG and AD are parallel and of proportional length then by definition the angle w is equal to 120 °

Thus

[tex]w = 120\°[/tex]

Answer:

π/3

Step-by-step explanation:

We have to find the principal value of [tex]\text{arc sin}(\frac{\sqrt{3}}{2} )[/tex]

arc sin means sin inverse. The sin inverse is a one to one function with its range between [tex]-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}[/tex]

The principal value of the arc sin will lie within the above given range.

value of sin (60) or sin([tex]\frac{\pi}{3}[/tex]) is [tex]\frac{\sqrt{3}}{2}[/tex].

[tex]\frac{\pi}{3}[/tex] lies between [tex]-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}[/tex]

So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3

The principal value of the function Arc sin(√3/2) is,

⇒ π / 3

We have to given that,

⇒ Arc sin (√ 3/ 2)

Since, Value of arc sin lies between - π/2 and π/2.

Hence, The principal value of the function Arc sin(√3/2) is,

⇒ Arc sin(√3/2)

⇒ Arc sin(sin π/3)

⇒ π / 3

Therefore, The principal value of the function Arc sin(√3/2) is,

⇒ π / 3

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ6

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.

quotient: [tex]4x + 15[/tex]

Divisor: x-3

Dividend: [tex]4x ^ 2 + 3x + 2[/tex]

Remainder: 47

It must be fulfilled that:

Dividend = Quotient * Divisor + Remainder

Answer:

See attached image

Answer:

  A. f(0.6)=0

  C. f(5.1)=5

  D. This is the graph of the greatest integer function.

Step-by-step explanation:

The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.

The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.

Answer:

C, D, E

Step-by-step explanation:

Answer:

  up

Step-by-step explanation:

A graphing calculator, spreadsheet, or web site can help you with this one, or you can simply plot some points on a graph.

___

Only the highest-degree terms matter for answering this question. Leaving the others out, the form is ...

  y = x^2

This tells you that y gets more positive for larger and larger values of x, regardless of their sign. Thus the graph of it is U-shaped, opening upward.

Answer:

  A. $12,993.71

Step-by-step explanation:

Each year, the car's value is multiplied by 1-0.15 = 0.85. After 10 years, the car's value will be ...

  $66,000×0.85^10 ≈ $12,993.71

Answer:

$219.75

Step-by-step explanation:

Just plug in the values

x = final cost

31.95(5) + 0.10(600) = x

159.75 + 60 = x

219.75 = x

Answer:

Step-by-step explanation:

Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...

  Sunitha: 7·5 = 35

  Raseeda: 8·5 = 40

_____

If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:

These can be translated to standard form, which may make some methods of solution easier:

These have solution (r, s) = (40, 35).

Answer:

  B.  12n + 2(25) ≤ 100

Step-by-step explanation:

The inequality you are asked for is intended to express ...

  shirt cost + pant cost (is less than or equal to) Sandy's budget

The cost of n shirts at $12 each will be 12n. The cost of 2 pants at $25 each is 2(25). Then the inequality is ...

  12n + 2(25) ≤ 100 . . . . . matches choice B

Answer:

C

Step-by-step explanation:

at least two have to be in the same place (i think), and that’s the only one that does that

Answer:

  55/56 ≈ 0.982143

Step-by-step explanation:

  nPk = n!/(n-k)!

Your expression is ...

  1 - (6·5·4·3)/(8·7·6·5·4·3) = 1 - 1/(8·7) = 1 - 1/56 = 55/56 ≈ 0.982143

Answer:

Step-by-step explanation:

Answer:

The answer would be c.

Step-by-step explanation:

What I'm understanding from this question is,

In the first attachment, Which has the questions selected on Shows there are two shapes.

Those two shapes have to go in to the identify the tessellation Created using the given regular polygons.

As you can see in answer C. Both shapes are represented in that tessellation.

For example, In the attachment below ] I will be showing you an example of what the question might look like for This certain tessellation.

You obviously know that square is tiltedMake a diamond shaped. That is why the diamond and hexagon is correct!

hope this helps! if it helps in any way plz mark as branliest !

Answer:

B) C,D,B,A

Step-by-step explanation:

Answer:

  B. (6√2 + 12) inches

Step-by-step explanation:

The length of the kite edge at upper left is ...

  x/sin(45°) = x/(1/√2) = x√2

The length of the kite edge at upper right is ...

  x/sin(30°) = x/(1/2) = 2x

The perimeter of the kite is double the sum of the lengths of these edges:

  P = 2(x√2 +2x) = 2x(√2 +2)

For x=3 in, this is ...

  P = 2·(3 in)(√2 +2)

  P = (6√2 +12) in

_____

The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.

  x/hypotenuse = sin(angle)

  hypotenuse = x/sin(angle) . . . . . solve for hypotenuse

Answer:

B

Step-by-step explanation:

I was told to put down A B C or D

And B was right

The right choice here is

"The graph of f is the graph of the equation y = f(x)."

Horizontal and vertical axes of the Cartesian plane are conventionally labeled and referred to as "x" and "y", respectively. When we talk about the graph of f(x) in that context, we usually mean the graph of y = f(x). However, this convention may not be followed in all cases. There may be no "y" label on the graph at all, or the horizontal axis may be labeled something other than "x".

Question 10

cos 45 = x/10

cos 45(10) = x

(1/sqrt{2})*10 = x

10/sqrt{2} = x

Rationalize the denominator.

[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x

10•sqrt{2} ÷ 2 = x

5• sqrt{2} = x

The perimeter of the new garden after extension is 44 feet.

To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.

To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:

P = 2(l + w)

where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:

P = 2(5 + 17) = 2(22) = 44 feet

Therefore, the perimeter of the new garden is 44 feet.

Answer:

  y = 700 +22x

Step-by-step explanation:

The CD account balance is 722 after the first year and increases by $22 each year. The function rule is a linear function with a y-intercept of 700 and a slope of $22 per year.

  y = 700 +22x . . . . . . ending balance after x years

Answer:

Step-by-step explanation:

h(10) would be the height of the balloon at 10 seconds

Hey there! Thanks for asking your question here on Brainly.

First, we can factor a 5 out of each term in the trinomial. This leaves us with: 5(12x^2 - 31x + 20)

Second, we need to multiply 12 * 20 and find a factor pair of the product, 240, which equals -31. This factor pair would be -15 and -16. This now leaves us with: 5((12x^2 - 16)(-15x + 20))

Third, we need to simplify each binomial in parenthesis. By doing so, what is left inside of each parenthesis should be the same if this step is done correctly. This leaves us with: 5(4x(3x - 4)-5(3x - 4))

Fourth and finally, we construct our new factored trinomial! The outside number stays, as well as one of the inner parenthesis binomials. Use the terms you factored out of the parenthesis in step three to construct another

binomial. This leaves us with: 5(4x - 5)(3x - 4) and the correct answer is C.

Hope this helps! If there's anything else I can help you with, please let me know! :)

Check the picture below.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{27.6}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{30^2-27.6^2}=h\implies \sqrt{138.24}=h\implies 11.76\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}bh\implies \cfrac{1}{2}(27.6)(11.76)}\implies 162.288\implies \stackrel{\textit{rounded up}}{162.3}[/tex]

To find the area of the right triangle with a given hypotenuse and adjacent leg, use the Pythagorean theorem to calculate the other leg. Then, use the base and height (the two legs) in the area formula for a right triangle. The area of the triangle is approximately 148.7 cm².

To find the area of a right triangle, you need two perpendicular sides, known as the legs of the triangle. Since we are given the hypotenuse (30 cm) and one adjacent leg (27.6 cm) which is one of the legs, we need to find the other leg. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

In mathematical terms, this is expressed as a² + b² = c². Therefore, the length of the other leg (b) can be found using the equation b² = c² - a², where c is the hypotenuse and a is the given adjacent leg.

Substituting the given values, we have b² = 30² - 27.6². Calculating this gives b ≈ 10.8 cm.

Now, the area of the triangle can be calculated using the formula for the area of a right triangle, which is (1/2) × base × height. In this case, the base and height are the two legs of the triangle. Substituting the lengths of the legs we have, Area ≈ (1/2) × 27.6 cm × 10.8 cm. The result is approximately 148.7 cm², which is the area of the triangle rounded to the nearest tenth.