Which graph represents a function?
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The roots of the quadratic equation x² - x - 56 = 0 is x = -7 or x = 8

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

x² - x - 56 = 0   be equation (1)

On simplifying the equation , we get

x² - 8x + 7x - 56 = 0

Taking the common terms in the equation , we get

x ( x - 8 ) + 7 ( x - 8 ) = 0

Now , on factorizing the equation , we get

( x + 7 ) ( x - 8 ) = 0

We have two factors which can solve the equation ,

when ( x + 7 ) = 0

Subtracting 7 on both sides of the equation , we get

x = -7

And , when ( x - 8 ) = 0

Adding 8 on both sides of the equation , we get

x = 8

Therefore , the roots of the equation are x = -7 and x = 8

Hence , the quadratic equation is solved

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Answer:

x = 8

x = -7

Step-by-step explanation:

To find the solutions of the quadratic equation x^2 - x - 56 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = -1, and c = -56. Plug these values into the formula and calculate the discriminant (the value inside the square root):

Discriminant (D) = b^2 - 4ac = (-1)^2 - 4(1)(-56) = 1 + 224 = 225

Now, calculate the two possible solutions:

x1 = (-(-1) + √225) / (2(1)) = (1 + 15) / 2 = 16 / 2 = 8

x2 = (-(-1) - √225) / (2(1)) = (1 - 15) / 2 = -14 / 2 = -7

So, the correct solutions to the equation x^2 - x - 56 = 0 are:

x = 8 (x = 0 is not a solution)

x = -7

Answer:

can you just give me the brainliest.

the answer is in the attached document

Step-by-step explanation:

1. 60% of 330 would fill 6 of the boxes.

2. 45% of 600 would fill 4 and half of the boxes.

3. 42% of 450 is 189.

4.  79% of 800 is 632.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

1. The strip has 10 boxes and totals to 330.

Now, 60% of 330 would fill 6 out of those 10 boxes.

2. The strip has 10 boxes and totals to 600.

So, 45% of it would fill 4 and a half of the boxes.

3. 42% of 450 can be numerically expressed as,

(42/100)×450.

= 189.

Similarly, 4. 79% of 800 is,

(79/100)×800.

= 632.

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Answer:

The 4th one

Step-by-step explanation:

Right on edge!

The time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
Ubehebe crater in Death Valley has a diameter of a little more than 1/2 a mile.
Circumference of the rim,
= πD

= 3.14 × 1/2
= 1.57 mile

Time = Distance/speed
Time = 1.57 / 2
Time = 0.785 hours

Thus, the time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.

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Answer:

3

Step-by-step explanation:

x² -7x + 12 =0

by factoring:

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

x = 4

x = 3

3<4

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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Answer:

Discrete

Step-by-step explanation:

Discrete means it has ends, and continuous means it continues on forever.

The missing measure of the given right-angled triangle is: x = 2.5

Given a right-angled triangle, with one of its angle as 14° ,assume

angle y= 14°. Also given length of one of it's side is 18. Let's assume the side as z = 18.

As it is given it's a  right-angled triangle,

∴ By using trigonometric formula,

 tan y = opposite /adjacent

∴ tan 14° = z/x

 tan 14°  = 18/x

 7.24 = 18/x                   ......( as tan 14°= 7.24)

∴ x = 2.48

∴ x ≈ 2.5

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The average like for each minute of the video that he uploads will be 2,000 likes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The total number of likes is calculated as,

Like / View = 1 / 5

Like / 9,000,000 = 1 / 5

Like = 1,800,000

The total number of minutes is calculated as,

Time length = (9,000,000 / 150,000) x 15

Time length = 60 x 15

Time length = 900 minutes

The average like for each minute of the video that he uploads will be given as,

⇒ 1,800,000 / 900

⇒ 2,000

The average like for each minute of the video that he uploads will be 2,000 likes.

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The complete question is given below.

Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo's videos is 1: 5. Dagogo wants to reach a total of 9,000,000 views on his channel.

Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of the video he uploads?

The unknown angle of the triangle is as follows:

∠BCE =  65 degrees

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, the angle ∠BCE can be found as follows:

∠BAC = 70 degrees

∠ABC = 60 degrees

∠ACB = 180 - 70 - 60

∠ACB = 180 - 130

∠ACB = 50 degrees

Hence, using exterior angle theorem,

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

∠BCD = 60 + 70 = 130 degrees

Hence,

∠BCE = 130 / 2 = 65 degrees

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Answer: 7t+7

Step-by-step explanation: i know

Well, both 4t and 3t have the same variable so add them together to get 7t, then add 4 and 3 to get 7, so your fill in the blank should be 7t+7

Answer:

m∠C = 67°, a = 7.37, b = 15.13

Step-by-step explanation:

There are 180° in a triangle. We know two angles in the triangle, so we can calculate the third angle.

Since this is not a right triangle, we will use the Law of Sines.

SinA/a = SinB/b = SinC/c

see image.

A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]

B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]

c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]

are the value of given algebraic expression.

The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".

here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]

Given .

[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]

upon solving two complex number we solve coefficient of iota together and real number together.

A) to find [tex]$(x+y)$[/tex]

[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]

B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]

c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]

[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]

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The length of ribbon is 48 yards.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Kala got a prepaid debit card with $15.

Price of Ribbon = 24 cents per yard.

After purchase money left $3.48.

So, Price of Ribbon purchased = 15 - 3.48 = $11.52 = 1152 cents

length of ribbon = 1152/ 24

                           = 48 yards

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A single fraction will be;

⇒ 1/(y + 12)

And, Domain of this expression is,

⇒ Domain = (-∞, ∞) - { 12 }

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The expression is,

⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)

Now,

Since, The expression is,

⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)

Simplify the expression as;

⇒ 4 (y - 2) - 3 (y + 2) / (y-2) (y+2) + 12 / (y² - 4)

⇒ 4y - 8 - 3y - 6 / (y² - 4) + 12 / (y² - 4)

⇒ (y - 14) / (y² - 4) + 12 / (y² - 4)

⇒ (y - 14 + 12) / (y² - 4)

⇒ (y - 12) / (y- 12) (y + 12)

⇒ 1/(y + 12)

Hence, A single fraction will be;

⇒ 1/(y + 12)

And, Domain of this expression is,

⇒ Domain = (-∞, ∞) - { 12 }

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The prices of the drum that will reach over $6500 are between $3 and $8

And the inequality expression is (50 + 4x) (120 - 5x) > 6500

From the question, we have the following parameters that can be used in our computation:

Number of models = 50

Initial price = $120

Also from the question, we have:

So, we have

Models = 50 + 4x

Price = 120 - 5x

This means that the revenue function is

R(x) = (50 + 4x) *  (120 - 5x)

When the price reaches over $6500, we have

(50 + 4x) *  (120 - 5x) > 6500

Using a graphing calculator, we have

2.911 <x < 8.5

Approximate

3 ≤ x ≤ 8

Hence, the model reaches $6500 between 3 and 8

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The measure of the missing angle is 17 degrees.

Trigonometry is a method that can by used to solve questions involving the application of functions. Some examples of trigonometric functions are: Sine, Cosine, Tangent, Secant, Cotangent etc.

Now considering the given question, we are to find the measure of the missing angle. We have;

cos θ = 0.9563

where θ is the missing angle the value of which is to be determined.

Thus, divide both sides of the expression by cos to have;

cos θ/ cos = 0.9563. cos

θ = cos^-1 0.9563

θ = 17.0 degrees

Therefore, the value of the missing angle is 17 degrees.

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The effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream is that there will be more production and demand in the market.

This is referred to as a place where buyers and sellers can meet to facilitate the exchange or transaction of goods and services.

A decrease in the price of milk and input to ice cream means that production costs would fall, which will cause the suppliers to produce more thereby shifting the supply curve to the right with the demand for the goods being increased which is therefore the effect on the market.

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Answer:

3 stacks of paper can be purchased.

Step-by-step explanation:

Start by setting up the inequality:

15 = 3.79x

Now that you have set up the inequality, go to solve the inequality.

You should get the answer 3.958 (rounded). Since Mr. Valentino can not by a half stack of paper, drop the decimal so we are left with 3.

I would describe the graph as a straight line increasing, with money on y and stacks of paper on the x axis

Answer: One way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:

the 1/2 teaspoon measuring spoon 3 times to measure 3/2 = 1 1/2 teaspoons

and use the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons

3 1/2 + 2/3 = 3 1/6

Another way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:

the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons

and use the 1/2 teaspoon measuring spoon 6 times to measure 6 * 1/2 = 3 teaspoons

3 + 2/3 = 3 1/6

So, there are two ways to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2-teaspoon measuring spoon, one is by using 3 times 1/2 teaspoon measuring spoon and 6 times 1/3 teaspoon measuring spoon and the second one is by using 6 times 1/3 teaspoon measuring spoon and 3 times 1/2 teaspoon measuring spoon.

Step-by-step explanation:

The expression that represents how much money Kate will collect

is y = 5x + 2x.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, During a fundraiser, Kate wants to sell the same number of $5 candy bars as $2 candy bars.

Let, The number of candies she sold be 'x' and the total cost of the candies be 'y'.

Therefore, The phrase that describes the amount of money Kate will bring in is y = 5x + 2x.

y = 7x.

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The number in the replacement set that will make the equation true is (c) 112

From the question, we have the following parameters that can be used in our computation:

x ÷ 2 = 56

Rewrite the expression properly

so, we have the following representation

x/2 = 56

Also, we have the replacement set to be

{28, 56, 112}

In the given equation, we have the variable to be

The variable is x

Multiply 2 to both sides of the expression

So, we have the following representation

2  * x/2 = 56 * 2

Evaluate the products on both sides of the equation

x = 112

Hence, the solution is x = 112

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Answer:

$576.19

Step-by-step explanation:

The equation −12x+y=10 in slope-intercept form is y = 12x + 10

The general equation showing the slope-intercept form of a graph is represented as;

y = mx+ c

Given that;

From the information given, we have the equation as;

−12x+y=10

Now, let's make 'y' the subject of formula by

-12x + y = 10

Take '12x' to the other side of the equality sign

y = 10 + 12x

Make into slope-intercept form, we have

y = 12x + 10

Hence, the formula is y = 12x + 10

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The slope-intercept form of the equation of line −12x + y = 10 is y = 12x + 10.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the line;

−12x + y = 10

To rewrite in slope intercept form ( y = mx + b ), bring terms containing y to the left and x or constant terms to the write side of the equation.

−12x + y = 10

Add 12x to both sides

−12x  + 12x + y = 10 + 12x

y = 10 + 12x

Reorder in slope intercept form

y = 12x + 10

Therefore, the slope intercept form is y = 12x + 10.

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Gross pay is $360, Health insurance is $50.40, Pension deduction is $21.60, Total deductions is $173.85 and net pay is $186.15.

Gross pay or gross earnings is the amount of money an employer earn before all the tax and other deductions and benefits.

Employee works for 40 hours at a rate of $9.00 per hour.

Gross pay = 40 × 9 = $360

Health insurance = 14% of gross earnings

                             = 14% × 360

                             = 0.14 × 360

                             = $50.40

Pension deduction = 6% of gross earnings

                                = 0.06 × 360

                                = $21.60

Total deductions = $55.00 + $21.80 + $25.05 + $50.40 + $21.60

                            = $173.85

Net pay = Gross earnings - Total deductions

             = $360 - $173.85

             = $186.15

Hence the amount of gross pay is $360, and net pay is $186.15.

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The constant of proportionality is 10 for the proportional relationship shown in the graph.

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

The proportional relationship is shown in the given graph.

As per the given graph, we take two points (1, 10) and (2, 20)

So, the constant of proportionality will be as:

⇒ (20 - 10)/(2-1)

⇒ 10/1

⇒ 10

Hence, the correct answer would be option (A).

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