Write the equation of the line in fully simplified slope-intercept form.

Answer:

± 3

Step-by-step explanation:

let n be the number then the number squared is n² , so

6n² = 54 ( divide both sides by 6 )

n² = 9 ( take the square root of both sides )

n = ± [tex]\sqrt{9}[/tex] = ± 3

That is the number is 3 or - 3

Answer:

Step-by-step explanation:

(D). The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

The location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

The dilation of a line segment is longer or shorter in the ratio given by the scale factor. If the scale factor is greater than 1, the image of line segment will be larger than the original line, and if the scale factor is less than 1 , the image will be smaller than the original line.

The original line segment is given in the figure with points A and B as A(0,2) and B(2,0) .

When the line segment is dilated by a scale factor of 3, we can draw a parallel line which will be larger than the pre-image of the original line segment.

Also, the new coordinates of the points A and B will also increase by a factor of 3.

Therefore, we have A'(0,6) and B'(6,0) as the new coordinates of the line segment.

Thus, the location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

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Answer: D

Step-by-step explanation:

[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]

Answer:

D

Step-by-step explanation:

Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.

Answer:

d

Step-by-step explanation:

h

9514 1404 393

Answer:

Step-by-step explanation:

Reflection over 'a' then over 'b' will result in a translation of 2(b -a). Here, we have a=2, b=0, so the translation is 2(0-2) = -4. The reflection is over horizontal lines, so the transformation is ...

  (x, y) ⇒ (x, y -4)

  A(3, 3) ⇒ A"(3, -1)

  B(2, 5) ⇒ B"(2, 1)

  C(4,3) ⇒ C"(4, -1)

Answer:

-2 from both sides

Step-by-step explanation:

32=5x+2

-2        -2

________

30=5x

__=__

5      5

6=x

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.

We are given the algebraic equation;

32 = 5X + 2

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;

32 - 2 = 5X + 2 - 2

30 = 5X

Divide both sides by 5 using division property of equality to get;

X = 6

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9514 1404 393

Answer:

  61.5°

Step-by-step explanation:

The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.

  Tan = Opposite/Adjacent

  tan(α) = 35/19

  α = arctan(35/19) ≈ 61.5°

The angle made by v and the positive x-axis is 61.5°.

Answer:

x = 1

Step-by-step explanation:

-2x + 8x + 3 - 7 = 2

Combine like terms

-2x + 8x = 6x

3 - 7 = -4

We now have

6x - 4 = 2

Add 4 to both sides

6x - 4 + 4 = 2 + 4

6x = 6

Divide both sides by 6

6x/6 = 6/6

x = 1

5(2x+1)+4=6(3x+2)-7

10x+5+4=18x+12-7

10x-18x=12-7-5-4

-8x=-4 (-1)

8x=4

x=4/8 (/4)

x=1/2

Answer:

x = 1/2

Step-by-step explanation:

5(2x + 1) + 4 = 6 (3x + 2) - 7

~Simplify both sides

10x + 9 = 18x + 5

~Subtract 9 from both sides

10x = 18x - 4

~Subtract 18x to both sides

-8x = -4

~Divide -8 to both sides

x = 1/2

Best of Luck!

9514 1404 393

Answer:

  |x| = 1/2

Step-by-step explanation:

Perhaps the simplest equation is ...

  |x| = 1/2

__

You could get more elaborate:

  |2x| = 1

  3 -|6x| = 0

Answer:

➕

Step-by-step explanation:

i know the answer ok it is easy

Answer:

12.65

Step-by-step explanation:

Pythagoras :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90 degree angle).

a and b are the side legs.

so, here we have

14² = 6² + b²

196 = 36 + b²

160 = b²

b = sqrt(160) = sqrt(16×10) = 4×sqrt(10) = 12.65

Answer:

x = -1/4

Step-by-step explanation:

[tex]81^{x}[/tex] = 1/3

[tex]3^{4}^{x}[/tex] = [tex]3^{-1}[/tex]

4x = -1

x = -1/4

Answer:

x = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Using the rules of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

Given

[tex]81^{x}[/tex] = [tex]\frac{1}{3}[/tex] [ note that 81 = [tex]3^{4}[/tex] ] , then

[tex](3^4)^{x}[/tex] = [tex]3^{-1}[/tex] , that is

[tex]3^{4x}[/tex] = [tex]3^{-1}[/tex]

Since the bases on both sides are equal, both 3, then equate exponents

4x = - 1 ( divide both sides by 4 )

x = - [tex]\frac{1}{4}[/tex]

Answer:

200 is equal to 20 tens I guess lol

Answer:

20 tens

Step-by-step explanation:

200÷10=20 groups of ten

Answer:

-3

Step-by-step explanation:

Slope is y2 - y1 / x1 - x2.

So, let's take two random points; I have chosen (0, 3) and (2, -3).

Excellent. Let's calculate the slope.

Slope = (-3 - 3) / (2 - 0) = -6 / 2 = -3.

Hope this helps!

Answer:

1.8

Step-by-step explanation:

First, find 40% of 15:

15(0.4)

= 6

Next, find 30% of this:

6(0.3)

= 1.8

So, the answer is 1.8

Answer:

30% of 30 has the least value out of all answer choices.

Step-by-step explanation:

Solve for the values of the given percentages of each number:

30% of 50:

Divide 50 by 100 to get 1%

50/100 = 0.5

Multiply 1% (0.5) by 50:

0.5 x 50 = 15

So 30% of 50 = 15

50 % of 30:

50% of a number means half of it since 50% is half of 100% so:

30/2 = 15

So 50% of 30 = 15

30% of 30:

Divide 30 by 100 to get 1%:

30/100 = 0.3

Multiply 1% (0.3) by 30:

0.3 x 30 = 9

So 30% of 30 = 9

50% of 50

50% of a number means half of it since 50% is half of 100% so:

50/2 = 25

So 50% of 50 = 25

Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:

25, 15, 15, 9

9 is the most least, it is the value equal to the answer choice “30% of 30”

HOPE THIS HELPED!

Answer:

Step-by-step explanation:

vxcvxcvxcvxcvxcvcxvxcbcvbcvnxcgjfgjfgjghjghjghjghj

The revenue function is y₁ = –4x² + 400x, the cost function is y₁ = x² – 100x + 8000, and the break-even number of units is 20 or 80.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Jua Kali Products Ltd has been in operation for the last 10 years.

Its annual revenue and cost functions take the form of quadratic functions.

The following data was obtained from the records of the company.

Year          Unit Sold            Revenue             Cost

2017              5                        1900                 7525

2018             10                       3600                7100

2019             15                        5100                6725

We know that the quadratic equation is given as

[tex]\rm y = ax^2 + bx + c[/tex]

Let y₁ be the revenue function, y₂ be the cost function and x be the unis sold.

Then the revenue function will be

1900 = 25a + 5b + c  ...i

3600 = 100a + 10b + c  ...ii

5100 = 225a + 15b + c  ...iii

From equations (i), (ii), and (iii), we have

a = –4, b = 400, and c = 0

Then the revenue function will be

y₁ = –4x² + 400x

Similarly, the cost function will be

7525 = 25a + 5b + c  ...1

7100 = 100a + 10b + c  ...2

6725 = 225a + 15b + c  ...3

From equations 1, 2, and 3, we have

a = 1, b = –100, and c = 8000

Then the cost function will be

y₁ = x² – 100x + 8000

For the break-even units, the cost function and the revenue function will be equal. Then we have

[tex]\begin{aligned} x^2 -100x + 8000 &= -4x^2 + 400x\\\\5x^2 -500x + 8000 &= 0\\\\x^2 - 100x + 1600 &= 0\\\\x^2 - 80 x - 20x + 1600 &= 0\\\\x(x-80) - 20 (x-80) &= 0\\\\(x-80)(x-20) &= 0\\\\x &= 20, 80 \end{aligned}[/tex]

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Answer:

The width is 36 feet

Step-by-step explanation:

If the width of the fence is x then its length is x+3.

The perimeter is 150 feet, so we have the equation:

2(x + x + 3) = 150

4x + 6 = 150

x = 144/4 = 36 feet

Answer:

henc X = 30°

Step-by-step explanation:

here is the proof

when X=30° then

sin2x = sin2×30

=sin 60°

= √3/2

or else,

putting value of X = 30° then

sin2x= 2sinxcosx

= 2×sin30°×cos30°

=2×1/2×√3/2

= 2√3/4

= √3/2

hence proved sin2x= √3/2.

Answer:

232.045

Step-by-step explanation:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

5105 / 22 = 232.045454545

Answer:

300, 16.67%

Step-by-step explanation:

Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%

Answer: See explanation

Step-by-step explanation:

From the information given in the question, we are informed that a newsletter publisher believes that less than 61% of their readers own a laptop.

The null hypothesis will be: H0: p ≥ 0.61

The alternative hypothesis will be: Ha: p < 0.61.

The original number is 38

A 2-digit number can be written as:

N = a*10 + b*1

Where a is the tens digit, and b is the units digit, these two are single-digit numbers.

We know that:

"the tens digit is 5 less than the units digit."

This means that:

a = b - 5

(notice that a must be larger than zero and smaller than 10, from this, we can conclude that b is a number in the range {6, 7, 8, 9})

"If you reverse the number, the result is 7 greater than double the original number"

The reverse number is:

b*10 + a

and this is 7 greater than 2 times the original number, then:

b*10 + a = 7 + 2*(a*10 + b)

Then we found two equations:

a = b - 5

b*10 + a = 7 + 2*(a*10 + b)

Replacing the first equation in the second, we get:

b*10 + (b - 5) = 7 + 2*((b - 5)*10 + b)

Now let's solve that:

b*10 + b - 5 = 7 + 2*(11*b - 50)

11*b - 5 = 7 + 22*b - 100

-5 - 7 + 100 = 22*b - 11*b

88 = 11*b

88/11 = b = 8

Now that we know that b = 8, we can use the equation:

a= b - 5

a = 8 -5 = 3

Then the original number is:

a*10 +  b = 3*10 + 8 = 38

The original number is 38

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Answer:

Step-by-step explanation:

Note that the equation should be

f(t) = t^2 + 6t - 20

A. Completing the square

coefficient of the t term: 6

divide it in half: 3

square it: 3²

add 3² to complete the square and subtract 3² to keep the equation balanced:

f(t) = (t² + 6t + 3²) - 3² - 20

f(t) = (t+3)² - 29. This is the equation in vertex form.

:::::

B. Vertex (-3, -29)

The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.

:::::

The axis of symmetry is the vertical line passing through the vertex: x = -3