The roots of a quadratic equation are -7 and 1. Write an equation that could represent this function. Give your answer in standard form and factored form.

Answer:

1. The lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level.

Step-by-step explanation:

The sea level is considered to be zero levels.

Now, the level +x feet means it is at x feet higher than sea level and the level -x feet means it is at x feet lower than the sea level.

Now, the lowest point of the country lies at −9 feet. The highest point of the country lies at +108 feet.

That means, the lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level. (Answer)

Answer:

Step-by-step explanation:

[tex]\dfrac{5}{6}<\dfrac{w}{8}\Rightarrow\dfrac{w}{8}>\dfrac{5}{6}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{w}{8\!\!\!\!\diagup}>8\!\!\!\!\diagup^4\cdot\dfrac{5}{6\!\!\!\!\diagup_3}\\\\w>\dfrac{20}{3}\\\\w>6\dfrac{2}{3}\\\\7>6\dfrac{2}{3}[/tex]

Answer:   D ) 7

Step-by-step explanation:

7 is greater than 5

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Answer: f(3)=11.5

Step-by-step explanation:

In order to solve this equation, all you have to substitute the value inside of the parenthesis with the value of x in the equation after the equals sign. SO...

f(3)=3x+2.5

f(3)=3(3)+2.5

f(3)=9+2.5

f(3)=11.5

Hope this helps!

Answer:

It will be $7602.3

Step-by-step explanation:

The equation [tex] y = 10000(0.97)^{x}[/tex] gives the purchasing power of $10000 after x years.

Therefore, the sum of money $10000 will value [tex] 10000(0.97)^{x}[/tex] after x number of years.

Now, after 9 years i.e. x = 9 years, the sum value of $10000 will become [tex] y = 10000(0.97)^{9} = 10000 \times 0.76023 = 7602.3[/tex] dollars. ( Answer )

Answer   5

Step-by-step explanation:

Answer:

24 Teaspoons

Explanation:

1 tablespoon is equivalent to 3 teaspoons

8 · 3 = 24

Therefore 24 teaspoons is equivalent to 8 tablespoons.

Answer:

ℝ

Step-by-step explanation:

[tex]\displaystyle 10 - 2x = [5 - x] - [x - 5][/tex]

All linear functions have a range and domain of all real numbers.

I am joyous to assist you anytime.

Answer:

f(x): {y| y > 0 }

g(x): {y| y > 6 }

Step-by-step explanation:

Hope this helps!

Because both of these are exponential functions with positive bases, we conclude that the range for both is:

{y| y > 0}.

Here we have two exponential functions:

f(x) = (4/5)^x

g(x) = (4/5)^(x + 6).

You can see that both of these are exponential functions with positive bases, then neither of these can have negative outcomes, while, as x increases, the outcome will also increase.

Then we can see both functions are exponential growths, so the range for both of these are the set of all real positive values, written in both cases as:

{y| y > 0}

If you want to learn more about exponential functions, you can read:

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To promote economic growth, countries would most likely act so that inflation "remains at a low level".

Answer: Option c

Explanation:

The Central Bank and the government basically command Inflation or either of them. The monetary policy is helpful from its changing interest rates parameters . Although there are a different types of tools which can control inflation are as follows

Monetary policy: The demand in the economy is reduced by higher interest rates, and result into lower economic growth with lower inflation.

Commanding supply of money: Monetarists debt huge by setting a close bond between the inflation and money supply.

Supply-side Policies: The scheme to hike the efficiency of the economy and competitiveness by declining pressure on long-term costs.

Fiscal policy: The reduction of spending, demand and inflationary pressures resulted from a higher rate of income tax.

Wage controls: Inflationary pressures can be reduced by controlling wages  , but after 1970 such act is rarely performed.

Answer:

The shipping and handling charge that Bryce paid is $109.65

Step-by-step explanation:

Given as :

The online price of the treadmill = $510

The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price

Let The shipping and handling charge that Bryce paid = $x

Now, According to question

∵ The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price

So, x = [tex]\dfrac{43}{2}[/tex] % of $510

Or, x = [tex]\dfrac{43\times 510}{100\times 2}[/tex]

Or, x = $109.65

The shipping and handling charge that Bryce paid = x = $109.65

Hence,The shipping and handling charge that Bryce paid is $109.65 Answer

Answer:

Graph is below

Step-by-step explanation:

y>3x+10 is represented by the red line, which is dotted because it's values are not included in the solution. Everything above it is shaded red because it is greater than. y<-3/4x-1 is represented by the blue line, which is dotted because it's values are not included in the solution. Everything beneath is shaded blue, because it is less than. The intersection of the two shaded areas is purple. (8,10) is not part of the solution because it does not have an x value beneath -3.

(this was a hard question, but i'm certain that at least the graph is correct.)

Answer:

The points for the given two linear equation as

[tex]x_1 , y_1[/tex] = - 2 , - 6

[tex]x_2 , y_2[/tex] = - 2 , 6

The graph so plotted as shown

Step-by-step explanation:

Given as :

The two linear equation are

y = 3 x                 ........A and

y = - x - 8             .........B

Solving equation A and B

Now, Put The value of y from eq A into eq B

So, 3 x = - x - 8

Or, 3 x + x = - 8

Or, 4 x = - 8

∴ x = [tex]\dfrac{-8}{4}[/tex]

I.e x = - 2

Now , Put the value of x into eq A

∵ y = 3 x

∴ y = 3 × (-2)

I.e y = - 6

Again, Put the value of x into eq B

∵ y = - x - 8

∴ y = - 2 - (-8)

I.e y = 6

So, for x = - 2 , y = - 6

And for x = - 2 , y = 6

Hence , The points for the given two linear equation as

[tex]x_1 , y_1[/tex] = - 2 , - 6

[tex]x_2 , y_2[/tex] = - 2 , 6

The graph so plotted as shown . Answer

Answer:

TU ⊥ MN and MN ║ PQ

Step-by-step explanation:

TU ⊥ MN

As the angle that is created where TU and MN intersect is a 90° angle, these two lines must be perpendicular to each other.

MN ║ PQ

As both MN and PQ intersect the line TU, we can use this to prove that they are parallel.

Both MN and PQ create a 90° angle where they intersect with TU. This means that MN is ⊥to TU and PQ is ⊥ to TU.

As both MN and PQ are perpendicular to TU, they must be parallel.

[tex]E(t) = 40(0.65)^t[/tex]

Step-by-step explanation:

Given,

Current quantity of emission, P = 40 millions,

Reduction in emission per year, r = 35% = 0.35,

Thus, the quantity of emission after t years,

[tex]E(t)=P(1-r)^t[/tex]

[tex]E(t) = 40(1-0.35)^t[/tex]

[tex]\implies E(t) = 40(0.65)^t[/tex]

Which is the required function.

To represent Freedonia's carbon-dioxide emissions E(t), t years from now with a yearly reduction of 35%, use the function E(t) = 40 * (0.65)^t, where 40 million tons is the current emission and 0.65 is the remaining percentage of emissions after reduction.

The student is asking to write a function that models the carbon-dioxide emissions of Freedonia in million tons, E(t), t years from today, given that the emissions are being reduced by 35% each year. The current emission level is 40 million tons of carbon-dioxide.

To create this function, we need to take into account the exponential decay of the emissions due to the percentage reduction. The general form for exponential decay is given by the equation E(t) = E_0 × (1 - r)^t, where E_0 is the initial amount, r is the rate of reduction (as a decimal), and t is the time in years. For Freedonia, E_0 is 40 million tons, and r is 0.35. Therefore, the equation becomes E(t) = 40 × (1 - 0.35)^t.

Chris baked 95 cookies.

Step-by-step explanation:

Given,

Cookies baked by Haley = 50

Cookies baked by Chuck = 65

Cookies baked by Dana = 90

Average of them = 75

Let,

Cookies baked by Chris = x

Average = [tex]\frac{Sum\ of\ quantites}{No.\ of\ people}[/tex]

[tex]75=\frac{50+65+90+x}{4}[/tex]

Multiplying both sides by 4

[tex]4*75=\frac{50+65+90+x}{4}*4\\300=205+x\\300-205=x\\95=x\\x=95[/tex]

Chris baked 95 cookies.

Keywords: addition, average

Learn more about addition at:

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Answer:

[tex]12x^2+4x[/tex]

Step-by-step explanation:

The area of a square or rectangle can be found by multiplying the width by the height. Since we now both, we can create an expression.

[tex](3x+1)*(4x)[/tex]

Now we can apply the distributive law/property to expand the expression.

[tex]3x(4x)+1(4x)[/tex]

Finally, we can simplify.

[tex]12x^2+4x[/tex]

Answer:

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Step-by-step explanation:

Given:

5 more than a product of a number and a

equals 2

Use a variable C for the unknown number

To Find:

Translate above sentence into an equation . ?

Solution:

Let ' C ' for the unknown number

and ' a ' for the other number.

Then according to given condition we have

5 more Product of ( C and a ) = 2

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Answer:

The answer is 74%

Step-by-step explanation:

Method One:

1) Un-reduce the fraction to ger 74/100

2) Your answer is 74%

Method 2:

1) Divide 37 by 50

2) You get .74

3) Your answer is 74%

Answer:

It would be 5.1942486

Step-by-step explanation:

Becuase the 0 is after the 6 the 6 stays as it is and there is no need to round up or down

We're starting with 5.19424860514, and we need to round to the 6th decimal. 1st, we need to identify the 6th place. In this case, that is 8. Everything before that is the same no matter what. 5.19424 is our base. We need to look at the 860514. More specifically, the 86. 6 is over 4, so the 8 becomes a 9 using basic rounding rules. Therefore, our final answer is 5.194249

Hope this helps!

Answer:

37i-16

Step-by-step explanation:

(4+7i)(3+4i)

12+21i+16i+28i^2

12+37i+28(-1)

37i+12-28

37i-16

Answer:

The shop can cut the cost of production per sandwich to $3.75.  The revenue function would then be defined as R(x)=9x.

Step-by-step explanation:

We want to make as big profit as possible by making as little sandwiches as possible. This means that we want the profit, which is [tex]revenue- production\: cost[/tex] to be as big as possible.

For the first choice the profit per sandwich is [tex]8.25-4=4.25[/tex] dollars.

For the second choice the profit per sandwich is [tex]9-3.75=5.25[/tex] dollars.

For the third choice the profit per sandwich is [tex]8.5-3.5=5[/tex] dollars.

We see here that for the second choice the profit is greatest, therefore this choice is most suitably correct.

Answer:

3/4 * 6 x 10 = 45/1 = 45

Step-by-step explanation:

Multiple: 3/4 * 6 = 3 · 6/4 · 1 = 18/4 = 9 · 2/2 · 2 = 9/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 4) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/2.

In other words - three quarters multiplied by six is nine halfs.

Multiple: the result of step No. 1 * 10 = 9/2 * 10 = 9 · 10/2 · 1 = 90/2 = 45 · 2/1 · 2 = 45

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(90, 2) = 2. In the following intermediate step, cancel by a common factor of 2 gives 45/1.

In other words - nine halfs multiplied by ten is forty-five.

The liquid started cooling from 194 degrees. This is calculated by determining the rate of cooling, which is 8 degrees per minute, and extrapolating back to find the initial temperature.

The subject of the question is about determining the initial temperature of cooling liquid. To solve this, we have to first identify the rate at which the temperature is decreasing. Given, after 2 minutes it was 178 degrees and after 5 minutes it was 154 degrees. That's a decrease of 24 degrees over 3 minutes, or 8 degrees per minute.

Since the liquid started cooling 2 minutes before it was first observed at 178 degrees, we can estimate that the liquid would have been 16 degrees hotter at the start of the cooling period. So, it would have started cooling at 178 + 16 = 194 degrees.

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Answer:

The relationship between time and distance is Velocity = Distance / Time

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex]

2. [tex]y=-5x+30[/tex]

Preliminary Material:

A line that is perpendicular to another has the opposite reciprocal slope of the other line.

A line parallel to another has the same slope.

With this in mind, we can begin to answer this question.

1.

Setup for question 1:

A line perpendicular with [tex]-5x+5[/tex] that goes through the point (7, 5).

Before going over the point this perpendicular line must go through, let's make an equation with the slope of the perpendicular line.

A linear function can be represented with this formula: [tex]y=mx+b[/tex].

We know the slope of this function must be an opposite reciprocal to -5, and using the information I first gave in the beginning of this problem, we can have the slope of the function.

If we take this slope and insert it into the linear equation, we will have the function...

So we now know the slope of this function, but what about the y intercept, [tex]b[/tex]? This is where the point given to us in the beginning of this problem comes into play. If we plug the point (7, -5) into our x and y coordinates in the above equation, we can solve for [tex]b[/tex].

Algebra:

[tex]-5=\frac{1}{5}(7)+b[/tex]

[tex]-5=\frac{7}{5}+b[/tex]

[tex]-\frac{25}{5}=\frac{7}{5}+b[/tex]

[tex]-\frac{32}{5}=b[/tex]

Answer:

Our final answer is: [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex].

2.

There will be no setup for 2. I'll show the algebra without explanation as well. If there's any confusion you can ask me :).

Algebra:

[tex]y=mx+b[/tex]

[tex]y=-5x+b[/tex]

[tex]-5=-5(7)+b[/tex]

[tex]-5=-35+b[/tex]

[tex]b=30[/tex]

Answer:

Answer:

x = 11

Step-by-step explanation:

Vertical angles mean that their values are equivalent, which means that:

5x + 10 = 7x -12

Solve for x

22 = 2x

x = 11

Hope this helps :)

The value of x is 10

Step-by-step explanation:

We know that the sum of internal angles of a quadrilateral is 360 degrees

So,

Given

Angle 1 = A1 = 3x+10

Angle 2 = A2 = 9x+50

Angle 3 = A3 = 4x

Angle 4 = A4 = 13x+10

So,

[tex]A_1+A_2+A_3+A_4 = 360\\(3x+10)+(9x+50)+(4x)+(13x+10) = 360\\3x+10+9x+50+4x+13x+10 = 360\\3x+9x+4x+13x+10+50+10 = 360\\29x+70 = 360[/tex]

Subtracting 70 from both sides

[tex]29x+70-70 = 360-70\\29x = 290[/tex]

Dividing both sides by 29

[tex]\frac{29x}{29} = \frac{290}{29}\\x = 10[/tex]

Hence,

The value of x is 10

Keywords: Angles, Quadrilateral

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Mei charges $15 per hour as her regular hourly rate before applying a 40% discount to her next door neighbor, resulting in a discounted rate of $9 per hour.

To calculate the regular hourly rate Mei charges before the 40% discount, we set up an equation where the discounted rate is equal to 60% of the original rate, because 100% - 40% = 60%. Mei charges her neighbor $9 per hour after the discount. Let h represent Mei's regular hourly rate before the discount.

So, the equation would be 0.60h = $9. To find h, we divide both sides of the equation by 0.60:

h = $9 / 0.60

h = $15

Thus, Mei's regular hourly rate before the discount is $15 per hour.

Mei's regular hourly rate before the discount is $15.

To find Mei's regular hourly rate before the discount, let's denote it as h .

Given that Mei offers her neighbor a 40% discount, her neighbor pays only 60% of the regular rate. This can be represented as:

[tex]\[ 0.60h = 9[/tex]

To find ( h ), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.60:

[tex]\[ \frac{0.60h}{0.60} = \frac{9}{0.60} \][/tex]

This simplifies to:

[tex]\[ h = \frac{9}{0.60} \][/tex]

Now, we can calculate:

[tex]\[ h = \frac{9}{0.60} = 15 \][/tex]

So, Mei's regular hourly rate before the discount is $15.

Answer:-523/52

Step-by-step explanation:

The simplified form of the expression is [tex]\(-3245.2\).[/tex]

To simplify the given expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). The expression given is:

[tex]\[ -3152 - 10(4.32 + 5 = 5) \[/tex]

First, we address the equality within the parentheses. The expression \[tex](4.32 + 5\) equals \(9.32\),[/tex] but the equality [tex]\(4.32 + 5 = 5\)[/tex] is not true. However, in the context of this expression, the equality sign does not affect the numerical computation; it seems to be a typographical error or a misplacement. We will treat the expression within the parentheses as [tex]\(4.32 + 5\)[/tex]and ignore the equality for the calculation.

Now, let's simplify the expression step by step:

1. Calculate the expression inside the parentheses:

[tex]\[ 4.32 + 5 = 9.32 \][/tex]

2. Multiply the result by -10 (note that the multiplication comes before addition/subtraction in the order of operations):

[tex]\[ -10 \times 9.32 = -93.2 \][/tex]

3. Finally, subtract the result from -3152:

[tex]\[ -3152 - 93.2 = -3245.2 \][/tex]

So, the simplified form of the expression is [tex]\(-3245.2\).[/tex]