What are the solutions to the quadratic equation 3(x – 4)2 = 75?
x= -9 and x = 1
x= -5 and x = 5
x = -4 and x = 4
x= -1 and x = 9

Imagine a right triangle where a and b are the legs and c is the hypothenuse.

Pitagora: a²+b²=c²

Divide by c

(a/c)²+(b/c)²=1

But a/c=sin(B) and b/c=cos(B)

Thus sin² + cos² = 1

-6x + 5 - (x² – 2x – 6) = -6x+5-x²+2x+6 = -x²-4x+11

Answer:

[tex]y=\frac{3}{31} x[/tex]

Step-by-step explanation:

Written in: y = mx + b

Answer:

y = 3/31x

Step-by-step explanation:

Step 1:  Add 30y to both sides

3x - 30y + 30y = y + 30y

3x = 31y

Step 1:  Divide both sides by 31

3x / 31 = 31y / 31

y = 3/31x

Answer:  y = 3/31x

Answer:

[tex]4\sqrt{11}[/tex]

Step-by-step explanation:

you use the Pythagorean theorem, so the longest side is the hypotenuse and so you do 24^2 minus 20^2 to find the shortest side. you would get 176 and you square root this to get about 13.27

Answer:

[tex]x\geq 0[/tex]  Domain

y = 40+1.5x  relationship

[tex]y \geq 40[/tex]  range

Step-by-step explanation:

The domain is the amount of carpet installed.  We can install zero carpeting or any positive amount of carpeting.

[tex]x\geq 0[/tex]

Now writing the equation for the cost

They charge 40 flat rate plus 1.50 per square foot

y = 40+1.5x

Let x = 0

y = 40+0

Even if they do not install anything, they still charge 40 dollars flat rate.  That is the minimum amount we have to pay.  As x increases, the cost will increase.

That is the range, or the values of y

[tex]y \geq 40[/tex]

We want to get the equation for the total cost and its domain and range.

The equation is:

c(x) = $40 + $1.50*x

domain: x > 0ft^2

range: y > $40.

First, let's get the equation.

We know that the carpet installer charges a flat rate of $40 plus $1.50 per square feet.

So if he/she works for x square feets, the cost is:

c(x) = $40 + $1.50*x

This is the cost equation.

Now we want to find the domain and range of this. The domain is given by the possible values of x that we can input in the function. Here we know that x must represent the number of square feet that are worked on, so it only must be a number larger than zero.

x > 0ft^2.

While the range is the set of the possible outputs.

The smallest possible output is the one we get when we evaluate the function in the smallest value of the domain, so we get:

y > $40.

These two define the domain and range.

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Answer:

A. 7(3v-7)(v-1)

Step-by-step explanation:

21v2 - 70v +49

Factor out 7

7(3v2 - 10v +7)

write -10v as a difference

7(3v2 - 3v -7v +7)

Factor out 3v

7(3v × (v-1) - 7 × (v-1))

Factor out (v-1)

7(3v-7)(v-1)

Answer:

X=32 and Y=12

The two numbers are 32 and 12

Step-by-step explanation:

Let the number be represented by X and Y

X = 20 + Y-------- equation 1

3X - Y = 84------- equation 2

solving the equation by substitution;

we substitute equation 1 into equation 2, we have;

3(20+Y)-Y = 84

expanding the bracket;

60 + 3Y - Y = 84

60 + 2Y = 84

2Y = 84 - 60

2Y = 24

divide both sides by 2;

2Y/2 = 24/2

Y = 12

from equation 1, we can find X by using the value of Y;

X = 20 + Y

X = 20 + 12

X = 32

PROOF:

using equation 2;

[3*32]-12=84

96-12=84

84=84

The stock purchased for $77 grew by 17.9%, which equals an increase of $13.78. Therefore, the current stock price is $90.78.

To solve this problem, we need to calculate the percent increase of the stock's price. A percent increase of 17.9% means that the stock price has increased by 17.9% of the original price. To calculate the amount of the increase, we multiply the original price ($77) by the percent increase (17.9%), remembering to convert the percentage to a decimal (0.179).

So, $77 times 0.179 equals ~$13.78. This is the amount by which the stock price has increased. To find the new price of the stock, we add this increase to the original price, which gives us $77 (Original price) + $13.78 (Increase) = $90.78, so the stock is worth $90.78 now.

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Option A: [tex]y=-\frac{1}{2} x+5[/tex] is the equation of the line.

Explanation:

It is given that the equation has a slope is [tex]m=-\frac{1}{2}[/tex]

It also contains the point [tex](8,1)[/tex]

We need to find the equation of line in slope - intercept form.

First, we shall determine the value of y - intercept(b).

Let us substitute the slope [tex]m=-\frac{1}{2}[/tex] and the point [tex](8,1)[/tex] in the slope - intercept form [tex]y=mx+b[/tex] , we get,

[tex]1=-\frac{1}{2} (8)+b[/tex]

Simplifying, we have,

[tex]1=-4+b[/tex]

Adding both sides of the equation by 4, we have,

[tex]1+4=b[/tex]

     [tex]5=b[/tex]

Thus, the y - intercept is [tex]b=5[/tex]

Now, substituting the slope [tex]m=-\frac{1}{2}[/tex] and the y - intercept [tex]b=5[/tex] in the slope - intercept form [tex]y=mx+b[/tex] , we get,

[tex]y=-\frac{1}{2} x+5[/tex]

Thus, the equation of the line is [tex]y=-\frac{1}{2} x+5[/tex]

Hence, Option A is the correct answer.

Graph B is the only straight line, thus the linear function of x and the correct option is B.

A linear function is a function whose graph is a straight line. This means that for any two points on the graph, the change in y divided by the change in x is always the same.

Looking at graph B, we can see that the line is perfectly straight. This means that the change in y divided by the change in x is always the same, regardless of where we are on the line.

Therefore, graph B is a linear function of x.

Graphs A, C, and D are not linear functions of x. Graph A is a quadratic function, meaning that its graph is a parabola. Graph C is a piecewise function, meaning that its graph is made up of two different lines. Graph D is an exponential function, meaning that its graph curves upward.

Therefore, the correct option is B.

Answer:

$3.40

Step-by-step explanation:

Final answer:

To determine the cost Geraldo will pay for 4 pounds of apples, we find the cost per pound from his previous purchase and multiply by the desired weight. At $0.85 per pound, Geraldo will pay $3.40 for 4 pounds of apples.

Explanation:

Last week, Geraldo bought 7 pounds of apples for $5.95. To find out how much he will pay for 4 pounds of apples this week at the same price, we first need to calculate the cost per pound of the apples. We do this by dividing the total cost by the total weight in pounds from the previous purchase.

The cost per pound is $5.95 divided by 7 pounds, which equates to approximately $0.85 per pound (rounding to two decimal places).

So, for 4 pounds of apples, Geraldo will pay 4 times $0.85, which results in a total of $3.40.

Therefore, Geraldo will pay $3.40 for 4 pounds of apples.

Answer:

w

Step-by-step explanation:

In y = f(x), for every x value, there can be at most one y value. All the other tables have duplicate x values.

The number of fluid ounces equivalent to 12 1/4 cups is; 98 fl Oz.

It follows from the task content that it is required to determine the number of fluid ounces in 12 1/4 cups.

Since, 1 Cup contains 8 fluid ounces; it therefore follows that 12 1/4 cups will contain;

= 12 1/4 × 8

= 98 fl Oz.

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Answer:

(i) The length of AH is 7.3784 m

(ii) The length of HC is 10.9389 m

Step-by-step explanation:

The sum of the angles ABC, BAC and ACB is 180º, hence, ACB = 180-90-56 = 34º. Note also that AH breaks the rectangle triangle ABC into 2 rectangle triangles AHB and AHC.

i) In AHB, AB is the hypotenuse, and the angle ABH is equal to ABC, hence it is 56º. AH is the opposite side of that angle and we know that

Sin(ABH) = opposite/hypotenuse = AH/8.9

Thus,

AH = 8.9*Sin(ABH) = 8.9*Sin(56º) = 7.3784 m

ii) In AHC, AH is also the opposite of the angle ACH (which meassures 34º), and HC is the adjacent of that angle (the hypotenuse is AC). As a result

Tan(ACH) = Tan(34º) = 0.6745 = opposite/adjacent = AH/HC = 7.3784/HC

Hence,

HC = 7.3785/0.6745 = 10.9389 m

Final answer:

AH = 8.9 m, HC = 0 m

Explanation:

Given that triangle ABC is right-angled at A, we can use trigonometry to find the lengths of AH and HC.

To find the length of AH, we can use the sine of angle BAC:

AH = AB * sin(BAC) = 8.9 * sin(90°) = 8.9

Since AH = 8.9 m, we can find the length of HC by subtracting AH from BC:

HC = BC - AH = 8.9 - 8.9 = 0 m

Answer:

D. y = -x

Step-by-step explanation:

Hope this helps.

Brainliest...??

Answer:

The number is 20

Step-by-step explanation:

Step 1:  Convert words into an expression

5 less than a number is 15

5 less than a number is n - 5

n - 5 = 15

Step 2:  Add 5 to both sides to get the number

n - 5 + 5 = 15 + 5

n = 20

Answer:  The number is 20

Answer:

18

Step-by-step explanation:

Step 1:  Combine

16 + 8 - 3 + 6 - 9

24 - 3 + 6 - 9

21 + 6 - 9

27 - 9

18

Answer:  18

Answer: 1

Step-by-step explanation:

16+8

23 - 3

2 + 6

8 - 9

1

To solve this problem, we simply must plug in the values.

gz/g + z ⇒ [tex]\frac{12(9)}{12}[/tex] or 9.

When we plug in 12 for g and 9 for z, we will find that option C is correct.

Answer:

The answer is 15 units!!

Step-by-step explanation:

[tex]17^{2} -8^{2} = 225\\\sqrt{225} =15[/tex]

The length of ZY to be a tangent is 15.

Option B is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is pir^2.

We have,

XY = Radius

And,

Radius = 8

Applying the Pythagorean theorem,

XZ² = XY² + ZY²

8² = (8 + 9)² + ZY²

64 = 289 + ZY²

ZY² = 289 - 64

ZY² = 225

ZY = 15

Thus,

The length of ZY is 15.

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Answer:

it has 5 sides and she walks a total of 12.5

Step-by-step explanation:

The Garden have 5 congruent side.

The Perimeter of Pentagon is 12.5 m.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We have, a pentagon having congruent sides as 2.5 cm

So, the Garden have 5 congruent side.

Now, the Perimeter of Pentagon

= 2.5 x 5

= 12.5 m

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Answer:

[tex]x (z) +2y/z[/tex]

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Probability of randomly rolling a 3 is 1/4

Step-by-step explanation:

Step 1:

It is given that a tetrahedron has 4 sides with 1,2,3 and 4 and is randomly rolled. We need to compute the probability of randomly rolling a 3.

Step 2:

Probability of an event = (Favorable outcomes) / (Total outcomes).

There are 4 total outcomes when the tetrahedron is rolled, these are the values 1 to 4.

The only favorable outcome is getting a 3

Probability of getting a 3 when the tetrahedron is randomly rolled = 1/4

Step 3:

Answer:

Probability of randomly rolling a 3 is 1/4

Answer:

3/4

Step-by-step explanation:

Answer:

10 peaches and 5 bananas

Step-by-step explanation:

To solve the problem increase the cost by adding more peaches and less by adding more bananas

7 peaches = 3.50

8 bananas = 3.20 + 3.50 = 6.70

We need 30 more cents so add three more peaches

10 peaches = 5

5 x 0.4 = 2

2 + 5 = 7

Final answer:

To determine the number of bananas and peaches Samantha bought, we can set up a system of equations and solve for the variables. By using substitution, we find that Samantha bought 5 bananas and 10 peaches.

Explanation:

To determine the number of bananas and peaches that Samantha bought, we can set up a system of equations. Let x represent the number of bananas and y represent the number of peaches. From the given information, we know the cost of each banana is $0.40 and the cost of each peach is $0.50. We can write two equations to represent the total cost of the bananas and peaches:

$0.40x + $0.50y = $7 (equation 1)

x + y = 15 (equation 2)

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

From equation 2, we know that x = 15 - y. We can substitute this value of x into equation 1:

$0.40(15 - y) + $0.50y = $7

Simplifying the equation, we get:

$6 - $0.40y + $0.50y = $7

Combining like terms, we have:

$0.10y = $1

Dividing both sides by $0.10, we get:

y = 10

So, Samantha bought 10 peaches. Substituting this value of y back into equation 2, we can solve for x:

x + 10 = 15

Subtracting 10 from both sides, we get:

x = 5

Therefore, Samantha bought 5 bananas and 10 peaches.

Answer:

t = 2 years and 6 months

Step-by-step explanation:

in order to solve this :

t = I/Pr

now input the values given

[tex]t = \frac{81}{1200 * \frac{2.7}{100} }[/tex]

t = 2.5

this means 2.5 years , we can make this value exact :

2.5-2 = 0.5

0.5 * 12 months = 6 months

hence t = 2 years 6 months

Answer:

$660

Step-by-step explanation:

1: Change 5% to a decimal. (0.05)

2: Multiply 600 X 0.05 X 2(years)

3: Add 60 and 600

4: $660

Answer:

$661.5

Step-by-step explanation:

The formula for this question is FV = PV (1 + r)^n so you set it up as 600(1+.05)^2 and you get $661.50 because you  are paying for interest over two years which is n, FV is the future value which is 661.50, PV is previous value which is 600, and r is he interest rate which is .05.

Answer: I would say imaginary numbers...

Step-by-step explanation:

It follows the format of imaginary numbers: bi, where i = [tex]\sqrt{-1}[/tex] and b = -91.

Final answer:

The number -91i is an imaginary number, which is a subset of complex numbers with a real part of 0 and an imaginary part of -91.

Explanation:

The number -91i is a complex number.

Complex numbers consist of two parts: a real part and an imaginary part. In this case, the real part is 0 and the imaginary part is -91.

The 'i' represents the imaginary unit, which is defined as √(-1).

Therefore, -91i is an imaginary number because it exists only with the imaginary unit 'i', and does not have a real part.

[tex]r^{}} = \sqrt{\frac{V}{\pi h }[/tex] is the equation correctly shows the radius.

Option B

Step-by-step explanation:

The cylinder’ volume (density) indicates how much amount of materials it can able to carry or how much amount of material it can immerse in it. The formula for volume of cylinder is given as:

                      [tex]V = \pi r^{2}h[/tex]

where

V = volume of cylinder

r = radius of cylinder

h = height of cylinder

In order to find radius following simplifications are done:

⇒[tex]V = \pi r^{2}h[/tex]

Keep the factor 'r' in one side and keep other in one side as below,

⇒ [tex]\frac{V}{\pi h } = r^{2}[/tex]

Taking square root on both sides,

⇒[tex]\sqrt{r^{2}} = \sqrt{\frac{V}{\pi h }[/tex]

⇒[tex]r^{}} = \sqrt{\frac{V}{\pi h }[/tex]

Therefore, option b is correct as [tex]r^{}} = \sqrt{\frac{V}{\pi h }[/tex].

Answer:

This formula corresponds to find the area of a rectangle/square.  You multiply one side by the other to get the area.

Example:  The sides of a rectangle are 6 in and 14 in.  Find the area.

A = l * w

A = 6 * 14

A = 84

Quotient is 21

Step-by-step explanation:

Step 1:

Divide 85 by 4. Using long division method, find the quotient.   

  21

4|85

  8

-------

     5

  -  4

--------

      1