Solve the following quadratic-linear system of equations. y=x^2-x-6 and y=2x-2

Answer:

-11, 11

Step-by-step explanation:

You have to find when the function crosses the x-axis. You could find this using algebra by solving for x in the equation but I prefer to simply graph it using something like desmos and see when it crosses the x-axis. Doing that I can see the answers would be -11 and 11

Answer:

x = -11,11

Step-by-step explanation:

G(x)=4x^2-484

To find the zero's, set the function equal to zero

0 = 4x^2 - 484

Add 484 to each side

484 = 4x^2 -484+484

484 = 4x^2

Divide each side by 4

484/4 = 4x^2/4

121 = x^2

Take the square root of each side

sqrt(121) = sqrt(x^2)

±11 =x

x = -11,11

Answer:

  y = –4x + 5

Step-by-step explanation:

We can put the offered choices into standard form and compare.

y = –4x + 5 ⇒ 4x +y = 5 . . . . . intersecting line; one solution

y = 4x – 5 ⇒ 4x -y = 5 . . . . . .  same line, infinite solutions

2y = 8x – 10 ⇒ 4x -y = 5 . . . .  same line, infinite solutions

–2y = –8x – 10 ⇒ 4x -y = -5 . . . . parallel line, no solutions

Answer:

IS A: y = –4x + 5

Hope this helps!

The domain are the x values.

The problem is saying the x value is all numbers between 4 and 8

Replace x in the equation with 4 and 8 and solve to find the range for the y values:

y =4(4) -1 = 16-1 = 15

y = 4(8) - 1 = 32-1 = 31

So Y would be between 15 and 31.

The first answer is the correct one.

Answer:

Final answer is approx 6.644 years.

Step-by-step explanation:

Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.

So we can use growth formula:

[tex]A=P\left(1+r\right)^t[/tex]

Then we get equation for motorcycles and cars as:

[tex]A=5.75\left(1+0.16\right)^t[/tex]

[tex]A=3.5\left(1+0.25\right)^t[/tex]

Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:

[tex]3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t[/tex]

[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]

[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]

[tex]\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}[/tex]

[tex]\left(\frac{1.25}{1.16}\right)^t>1.64285714286[/tex]

[tex]t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)[/tex]

[tex]t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}[/tex]

[tex]t>6.6436473051[/tex]

Hence final answer is approx 6.644 years.

Final answer:

To determine when car sales will surpass motorcycle sales given their growth rates, we use exponential growth formulas for both, set them equal to find the crossover point, and solve for the time required.

Explanation:

To find when the sale of cars will be more than the sale of motorcycles given their respective annual growth rates, we'll use the concept of exponential growth.

The initial sale of motorcycles is 5.75 million with an annual growth rate of 16%, and the initial sale of cars is 3.5 million with an annual growth rate of 25%. We will set up an equation where the sales of cars equals the sales of motorcycles and solve for the number of years it takes for this to occur.

The formula for exponential growth is:

Final Amount = Initial Amount × (1 + Growth Rate) ^ Years

For motorcycles, the formula becomes:

M = 5.75 × (1 + 0.16)^t

For cars, the formula becomes:

C = 3.5 × (1 + 0.25)^t

We want to find when C > M, so we set the formulas equal to each other and solve for t:

5.75 × (1 + 0.16)^t = 3.5 × (1 + 0.25)^t

After finding a common base and applying logarithms, we can solve for t, the number of years until the sale of cars surpasses that of motorcycles.

Answer:

Step-by-step explanation:

first fit:

115 -> 300

500-> 600

358 -> 750

200 -> 350

375 -> not able to allocate  

Best fit:

115 -> 125

500 -> 600

358 -> 750

200 -> 200

375 -> not able to allocate

worst fit:

115 -> 750

500 -> 600

358 -> not able to allocate

200 -> 350

375 -> not able to allocate

Answer: The volume is about 226 feet squared

Step-by-step explanation:

Answer:

$148.21

Step-by-step explanation:

A suitable financial calculator, web site, or spreadsheet can figure this for you. Or you can use the formula given in your reference material (text or web site).

Answer:

Michelle's monthly payment will be $148.21.

Step-by-step explanation:

The EMI formula is =

[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1}[/tex]

Here,

p = $10125

r = [tex]12.5/12/100=0.010417[/tex]

n = [tex]10\times12=120[/tex]

Putting all these values in the formula we get,

[tex]\frac{10125\times0.010417\times(1+0.010417)^{120} }{(1+0.010417)^{120}-1}[/tex]

=>[tex]\frac{10125\times0.010417\times(1.010417)^{120} }{(1.010417)^{120}-1}[/tex]

=$148.21

So, Michelle's monthly payment will be $148.21.

Answer:

There are 13 boys in Mr. Marshals class

Step-by-step explanation:

Hello there! Mr. Marshal has 9 boys.

To find the number of boys Mr. Marshal has, start by finding the ratio. If there are 6 boys and 14 girls, the boys to girls ratio is 6:14. Simplified, the ratio is 3:7. So, if there are 21 girls, you want to find how many boys there are. To find this, find what you need to multiply 7 by to get 21 by and multiply 3 by that number.

21/7 = 3.

So, now we multiply 3 by 3 to get the number of boys.

3 x 3 = 9.

This means there are 9 boys, with a ratio of 9:21. If we simplify this, we get 3:7, making this answer correct.

I hope this helps and have a great day!

Answer:

[tex]\boxed{5x^{11}, x < 0}[/tex]

Step-by-step explanation:

[tex]5\sqrt{x^{22}}[/tex]

Remember that we evaluate the term under the radical first.

Even though x < 0, x²² > 0

So,

[tex] 5\sqrt{x^{22}} = 5x^{11}[/tex]

The simplified expression is

[tex]\boxed{5x^{11}, x < 0}[/tex]

Answer:

The percentage of the people who live in the forests that are indigenous is [tex]20\%[/tex]

Step-by-step explanation:

we know that

To find the percentage of the people who live in the forests that are indigenous, divide the number of people that are indigenous by the total number of people that live in forests

so

[tex]\frac{60}{300} =0.2[/tex]

Convert to percentage

Multiply by 100

[tex]0.2*100=20\%[/tex]

Answer: INTRODUCTION

"Of all the environmental impacts of the study projections, deforestation probably poses the most serious problems for the world, particularly for the developing world."

Global 2000

"It has been predicted that within the next 25-30 years, most of the humid tropical forest as we know it, will be transformed into unproductive land, and the deterioration of the savannah into desert will continue at ever-increasing speed."

As you read this sentence, 50 to 100 acres of primary tropical forests will be eliminated, disrupted, degraded or impoverished. Yearly, an area of tropical forest the size of Great Britain is "converted" from an area equal to the size of Europe.

If present trends continue, by the year 2000, all tropical forests, with the exception of two areas - the western Brazilian Amazon and Central Africa - will have been destroyed. Since 1950, according to the U.N. Food and Agriculture Organization (FAO), half of the world's forests have disappeared. Latin America has lost 37 percent of its tropical forests; Central America, 66 percent; Southeast Asia, 38 percent; Central Africa, 52 percent. Nearly 20 million acres are destroyed annually.

As areas of tropical forests are destroyed or degraded, tribal groups are forced to change their resource base. In some cases they move into areas occupied by other groups, straining the area's resources. In other cases they are forced to relocate outside of forests, permanently altering their way of life by converting to agriculture or to cash employment. Rarely are the rights of these groups to the lands they occupy recognized. Further, their intimate knowledge of the area's resources and how to manage them are nearly always ignored.

Millions of indigenous people live in tropical moist forests which cover some 3.6 million square miles in 70 countries. More than 80 percent of these forests are found in Bolivia, Brazil, Colombia, Gabon, Indonesia, Malaysia, Peru, Venezuela, and Zaire, while 30 additional countries contain sufficient tracts to have significant ecological and biotic values. If these areas are to be managed effectively into the next century, the indigenous peoples that inhabit them should be consulted.

Answer:

48.3 cm²

Step-by-step explanation:

The area (A) of the yellow region = area of square - area of quarter circle, that is

A = 15² - ([tex]\frac{1}{4}[/tex] πr² )

  = 225 -( [tex]\frac{1}{4}[/tex] × π × 15² )

  = 225 - 176.71 ≈ 48.3

Answer:

b.  .897x - 3.790 (that's in slope-intercept form; same thing as putting the y-intercept first)

Step-by-step explanation:

On your calculator, hit the "stat" button.  Hit #4 to "ClrList", then hit 2nd and the number 1 to clear the list in L1.  Then do the same to clear the list in L2.  Hit #4, then hit 2nd and the number 2 to clear the list in L2.

Hit "stat" then 1 (edit) and you'll be at your table to enter the values.  Use the left arrow key if needed to make sure you're entering your first values under column L1, which is our x values.  Enter one at a time, hitting "enter" after each, even the last one.  Then arrow over to the right and enter the y values one at a time under L2.  Hit enter after each, even the last one.  When you're done, hit "stat" again and arrow over to "calc".  If you have a TI 83, choose "4:LinReg" and hit "enter".  If you have a TI 84+, you will have to arrow down to choose "calculate".  When the word "calculate" is highlighted, hit enter and you'll have your equation!

  Equation of the regression line for the data given will be represented by the equation given in option B.  

    By using the utility for the regression line of the given data, equation of the regression line will be,

y = 0.89745x - 3.79005

y = 0.897x - 3.79

Or y = -3.79 + 0.897x

   Therefore, equation of the regression line given in option B will be the answer.

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Answer:

3x^2+2x-1

Step-by-step explanation:

Start by plugging in the 2 equations into their assigned places then simplify.

Answer:14

Step-by-step explanation:( 3X2+1)-(1-X)

=3X2+1 -1+X

=3X2+X

ANY WHERE WE SEE X WE PLACE 2

=3(2)(2)+2

3*4+2

=12+2

14

Answer:

x = 74°

Step-by-step explanation:

The angle whose vertex lies on the circle, that is angle x is one- half the measure of it's intercepted arc, that is

x = 0.5 × 148° = 74°

Use trigonometry to find the ramp distance.

sin(4.76°) = 2/r

Let r = ramp distance in feet

r = 2/sin(4.76°)

r = 24.1015718106

Round off to the nearest foot.

Doing so we get r = 24 feet.

The ramp is 24.0 feet long.

Answer: Choice C

assuming 10 inches is the diameter

Answer:

≈

79

square inches.

Explanation:

The area of a circle is given by formula:

π

r

2

Where,

π

has a constant value of

3.14

and

r

denotes the radius.

The radius of the circle is , half the diameter =

d

2

=

10

2

=

5

inches

The area

=

π

r

2

=

3.14

×

(

5

)

2

=

3.14

×

(

25

)

=

78.5

square inches.

≈

79

square inches

The area of the ten-inch service plate is approximately 78.54 square inches.

To calculate the area of a circle, we use the formula:

Area = π * r²

where:

π (pi) is a mathematical constant approximately equal to 3.14159

r is the radius of the circle

Given:

Diameter = 10 inches

Finding the radius:

Radius = Diameter / 2 = 10 inches / 2 = 5 inches

Calculating the area:

Area = π * (5 inches)² ≈ 3.14159 * 25 square inches ≈ 78.54 square inches

Answer:8 ounces of oysters per minute

Step-by-step explanation:

Answer:

5 ounces of oysters per minute

Step-by-step explanation:

We are given a graph of the total weight, in ounces, of Steve's bag of oysters, y, with respect to the amount of time that he spends looking for them in minutes, x,

Now we are supposed to find the average rate of change over the interval [2, 10]

Formula of Average rate : [tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Now At x = 2 , f(2)= y = 20

At x=10  , f(10)= y = 60

Substitute the values in the formula

Average rate : [tex]\frac{f(10)-f(2)}{10-2}[/tex]

Average rate : [tex]\frac{60-20}{10-2}[/tex]

Average rate : [tex]\frac{40}{8}[/tex]

Average rate : [tex]5[/tex]

Thus he average rate of change over the interval [2, 10]  is 5 ounces of oysters per minute

Answer:

  1,417.64 km³

Step-by-step explanation:

The formula for the volume of a cylinder in terms of its diameter is ...

  V = (π/4)d²·h

Fill in the given numbers and do the arithmetic.

  V = π/4×(19 km)²×(5 km) ≈ 1,417.64 km³

The volume of a cylinder is found using the formula V = πR²h. To find the radius, we divide the diameter by 2, giving us 9.5 km. The volume is therefore approximately 1413.716 km³.

To find the volume of a cylinder, we use the formula: V = πR²h. In this case, we are given the diameter and height of the cylinder. The diameter is double the radius, so to find the radius, we divide the diameter (19km) by 2, which gives us 9.5km. Substitute the radius and height into the formula, we get: V = π * (9.5 km)² * 5 km.

Now, we can calculate it. π is approximately 3.14159, (9.5 km)² equals 90.25 km², and multiply it all together with the height (5 km), we get approximately 1413.716 km³.

This is the volume of the cylinder.

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Answer:

Part 1) The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]

Part 2) The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]

Step-by-step explanation:

Part 1) What is the ratio of the perimeters of the larger figure to the smaller figure?

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Let

z-----> the scale factor

In this problem

The scale factor is equal to

[tex]z=\frac{32}{26}[/tex]

Simplify

[tex]z=\frac{16}{13}[/tex]

Remember

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The ratio of the perimeters of the larger figure to the smaller figure is equal to [tex]\frac{16}{13}[/tex]

Part 2) What is the ratio of the areas of the larger figure to the smaller figure?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

we have

[tex]z=\frac{16}{13}[/tex]

so

[tex]z^{2}=(\frac{16}{13})^{2}=\frac{256}{169}[/tex]

therefore

The ratio of the areas of the larger figure to the smaller figure is [tex]\frac{256}{169}[/tex]

Answer:

  down

Step-by-step explanation:

Subtracting 1 from the y-coordinate moves a point down 1 unit. You know this because you know that the y-coordinate tells you the number of units the point is above the x-axis.

Every point on the graph of f(x) has coordinates (x, f(x)). If you subtract 1 from the y-coordinate, you have (x, f(x) -1) = (x, g(x)). The graph of this is a graph of f(x) that is 1 unit down from its original position.

In the equation g(x)=f(x)-1, g(x) translates the original function, f(x), one unit downward. This is an instance of vertical translation in mathematics.

In the equation g(x)=f(x)-1, the function g(x) is a translation of the function f(x). This process is specifically called a vertical translation. The -1 in the function g(x) = f(x) - 1 implies that the translation is downward. Therefore, g(x) translates the function f(x) 1 unit downward.

To further illustrate, let's consider the function f(x) = x^2 and its translation g(x) = x^2 - 1. If we graph both of these functions, you can observe that the graph of g(x) is exactly the same as the graph of f(x), but it is shifted one unit downward. This is the meaning of vertical translation in mathematics.

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Answer:

A.  5 seconds

Step-by-step explanation:

This quadratic (second degree polynomial) models parabolic motion.  The vertex of the function is the projectile's max height.  When the height of the object is 0 is when it hits the water.  Set the function equal to 0 then and factor.  I used the quadratic formula on my calculator, but if you need to, stick it into the quadratic formula and do it long hand.  The values of x (which is actually time here) are -1 and 5.  The two things in math that will never ever be negative are distance measurements and time, so we can disregard the -1 and say that it takes 5 seconds for the rocket to hit the water.

It would take 5 seconds for the rocket to hit the lake.

An equation is used to show the relationship between two or more variables and numbers.

Let g(x) represent the height of the rocket at time x seconds. Given that:

g(x)= -16x² + 64x + 80

The rocket touches the lake, when the height is 0. Hence:

0 = -16x² + 64x + 80

x = 5 seconds.

It would take 5 seconds for the rocket to hit the lake.

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Answer:

Step-by-step explanation:

The product of two even numbers will have at least two factors of 2, so will be even: even numbers are closed under multiplication.

The product of two odd numbers will be an even number plus 1, so will be odd: odd numbers are closed under multiplication.

The product of two cubes will be the cube of the product of their cube roots: cubes are closed under multiplication.

__

The product of two negative numbers will be positive, so the set of negative numbers is not closed under multiplication.

Answer:

157 cm²

Step-by-step explanation:

volume = (1/3) * π * r² * h

volume = (1/3) * π * 5² * 6

volume = (1/3) * π * 25 * 6

volume = (1/3) * π * 150

volume = (1/3) * 471

volume = 157 cm²

Answer:

157 cubic centimeters

Step-by-step explanation:

Answer:

In the figures attached, the complete question is shown.

What is the difference between a minor arc and a major arc?

the measure of a minor arc is less than 180°

the measure of a major arc is greater than 180°

How many letters do we use to name a MINOR arc? 2

How many letters do we use to name a MAJOR arc? 3

How many degrees are in a semi-circle? 180°

How many letters to name a SEMI CIRCLE? 3

1. Name of arc: AB Type of arc: minor

2. Name of arc: ADB Type of arc: major

3. Name of arc: PSQ  Type of arc: semi-circle

4. AE: minor

5. AEB: semi-circle

6. FDE: semi-circle

7. DFB: major

8. FA: minor

9. BE: minor

10. BDA: semi-circle

11. FBD: major

12. PQ and ST

13. QPT and  PUS

14. PUT and QPU

15. There are 360° degrees in a circle.

16. There are 180° degrees in a semi-circle.

17. The measure of the arc is equal to the measure of the central angle.

18. mPQ: 50°, mPXQ: 310°

19. mPQ: 90° , mPRQ: 270°

20. mPQ: 150° , mPXQ: 210°

21. mQS: 45°, mQRS: 315°

22. mGH: 30°, mGFH: 330°

23. mAB: 75°, mADB: 285°

Answer:

5 meters

Step-by-step explanation:

If the perimeter of the rectangle on the right is 24 m, and the length is 8, the width has to be 4, since 8+4+8+4=24. Since the scale factor is 24÷30=0.8 or 4/5, and the width of the rectangle on the right is 4, 4÷0.8=5, which is the width of the rectangle on the left.

Hope this helps! (P.S. I got it right on Edgenutiy, spelled wrong on purpose).

The width of the original rectangle is 5m.

The perimeter of a shape can be described as the path or boundary that surrounds it .

Perimeter of Rectangle = 2 (L + B)

L = length of rectangle

B = breadth of rectangle

Perimeter of the reduced rectangle = 24m

Let the length of original rectangle be L1

Let the breadth of original rectangle be B1

Let L1 = 8m, B1 = 4m

P = 2( L1 + B1) = 2(8 + 4) = 24m

Scale factor = P(Original Rectangle) / P(reduced rectangle)

Scale factor = 30 / 24 = 1.25

So, width of original rectangle = Scale factor * reduced width

Width of original rectangle = 1.25 * 4 = 5m

Hence, the width of the original rectangle is 5m.

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Jackie's total spending on 2 packages of paper and 4 notebooks is represented by the equation 2(5.80) + 4d = 32, where d stands for the cost per notebook.

The student is looking to create an equation to represent the cost of Jackie's purchases of paper packages and notebooks. The given information is that Jackie bought 2 packages of papers for $5.80 each and 4 notebooks for d dollars each, and in total, she spent $32. To formulate the equation, we can use the following expression:

We know the cost of the paper packages is 2 multiplied by $5.80, and the cost of the notebooks is 4 multiplied by d dollars.

So the equation using D that represents the situation is:

Where d represents the cost of each notebook, and solving for d would give us the price per notebook.

Answer:

The relationship is linear; y – 5 = 5/4*(x – 1)

Step-by-step explanation:

We have been given the following data set;

x: 1, 5, 9, 13

y: 5, 10, 15, 20

The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.

The average rate of change is equivalent to the slope;

(change in y) / (change in x)

Using the first two pair of points we have;

(10-5) / ( 5-1) = 5/4

The point-slope form of equation of the line is thus;

y - 5 = 5/4 (x - 1)

What we have here is called INTERSECTING CHORDS IN A CIRCLE.

The equation is:

10 times x = 7 times 7

10x = 49

x = 49/10

x = 4.9

answer 4.9cm

10times x=7times7(multiple it)

10x=49

x=49/10

x=4.9

Answer:

D. 46

Step-by-step explanation:

Put 12 where n is, then do the arithmetic.

t12 = 4·12 -2 = 48-2 = 46

Answer:

40.82 is the surface area of this solid.

For this case we have that the surface area of the figure is given by the surface area of a cone plus the surface area of a cylinder.

The surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

h: It's the height

A: It's the radio.

Substituting the values:

[tex]SA = 2 \pi * 1 * 3 + 2 \pi * 1 ^ 2\\SA = 6 \pi + 2 \pi * 1\\SA = 8 \pi\\SA = 25.12 \ units ^ 2[/tex]

On the other hand, the surface area of a cone is given by:

[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]

Where:

A: It's the radio

s: inclination

Substituting the values:

S[tex]A = \pi * 1 * 6 + \pi * 1 ^ 2\\SA = 6 \pi + \pi\\SA = 7 \pi[/tex]

[tex]SA = 21.98 \ units ^ 2[/tex]

Thus, the surface area of the figure is:

[tex]47.1 \ units ^ 2[/tex]

ANswer:

[tex]47.1 \ units ^ 2[/tex]