Does the equation y = x(x - 3) represent a linear function

Answer:

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

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that the line passes through are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (1,-3) and (-3,17)

[tex]=\frac{17-(-3)}{-3-1}\\=\frac{17+3}{-3-1}\\=\frac{20}{-4}\\=-5[/tex]

Therefore the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:

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

2) Determine the y-intercept (b)

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

Plug in one of the given points and solve for b

[tex]-3=-5(1)+b\\-3=-5+b[/tex]

Add 5 to both sides of the equation to isolate b

[tex]-3+5=-5+b+5\\2=b[/tex]

Therefore, the y-intercept of the equation is 2. Plug this back into [tex]y=-5x+b[/tex]:

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

I hope this helps!

Answer:

Standard form: 62,080,126

Word form: Sixty-two million, eighty thousand, one hundred twenty-six

Expanded form: 60,000,000 + 2,000,000 + 80,000 + 100 + 20 + 6

Answer: 24/87 or 8/29

Step-by-step explanation:

24+13+15+10+15+10=87, the total amount of M&M's.

24 are brown, so 24/87 chance that he will draw a brown one.

24/87 = 8/29 simplified.

Answer:

1/7^10

Step-by-step explanation:

7^-10

=1/7^10

Answer:

[tex] \frac{3}{x - 1} - \frac{4}{2 } - \frac{2}{x - 1} \\ = \frac{(3 - 2)}{x - 1} - 2 \\ = \frac{1}{x - 1} - 2 \\ = \frac{1 - 2x + 2}{x - 1} \\ = \frac{3 - 2x}{x - 1} [/tex]

Answer:

y=3/5x+1

Step-by-step explanation:

Hi there!

We are given the equation -3x+5y=-8 and we want to find the equation of the line that is parallel to -3x+5y=-8 and contains the point (-15,-8)

parallel lines have the same slopes, but different y intercepts.

So let's first find the slope of -3x+5y=-8

We can do this by converting the equation from standard form (ax+by=c where a, b, and c are free coefficients (numbers)) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

add 3x to both sides

5y=3x-8

divide by 5 on both sides

y=3/5x-8/5

3/5 is in the place of where m is, so that means that 3/5 is the slope of the line

we can write the equation of the new line in slope-intercept form.

Here it is so far:

y=3/5x+b

we need to find b

Because the line will pass through the point (-15,-8), we can use it to solve for b

substitute -15 as x and -8 as y

-8=3/5(-15)+b

multiply

-8=-9+b

add 9 to both sides

1=b

substitute 1 as b into the equation

y=3/5x+1

There's the equation of the line :)

Hope this helps!

Answer:

The equation has 0 solutions (answer C).

Step-by-step explanation:

Starting with x = x - 9, we subtract x from both sides.  This leaves us with:

0 = -9,

which is never true.

The equation has 0 solutions (answer C).

Rewrite the equation in expanded form:

(X+2)^2 -1 = x^2 + 4x + 3

The parabola parameters are : a = 1, b = 4, c = 3

The x vertex is -b/2a = -4/2(1) = -2

Replace x with -2 in the expanded equation to solve for the y vertex:

Y = -1

The vertex is (-2,-1)

x-value of the vertex:-2

Answer:

Solution given:

we have

f(x)=(x+2)²-1

y=x²+4x+3......(I)

parameters of parabola are:

a=1

b=4

c=3

we have

vertex=-b/2a=-4/(2*1)=-2

substitute value of x in equation 1.

y=4-8+3= -1

So

vertex(-2,1)

Answer:

100 students were asked.

Step-by-step explanation:

11+21+ 33+ 23+ 12

11+12=  23

23+ 23= 46

46+ 21= 67

67+ 33= 100

Answer:

18. C

19.A

20. C

Step-by-step explanation:

18.

x< 15 where x is the average that each person contributes.

This gives 3x <45, limiting the gift basket's total cost to < $45. (Actually ≤ 14.99 per person, so max cost is $44.97.

19. simple algebra

a <= -4 + 7

a <= 3

20.

since u divide and the co efficient is negative u flip the sign

-3m<15

m>-5

Answer:

AB

Step-by-step explanation:

Definition of a chord

Answer: [tex]x^2+16x-612=0[/tex]

Step-by-step explanation:

Let x be the length of the poster.

As per given , width = [tex]\dfrac{x}{2}+8[/tex]

Area = Length x width

i.e.

[tex]306=(\dfrac{x}{2}+8)\times x\\\\\Rightarrow 306=(\dfrac{x+16}{2})\times x\\\\\Rightarrow 306\times2=x^2+16x\\\\\Rightarrow\ x^2+16x-612=0\\\\\Rightarrow\ x=18, x=-34[/tex].

Required equation: [tex]x^2+16x-612=0[/tex]

Answer:

53,901

Step-by-step explanation:

Here is the complete question :

In which number does the digit 5 have a value that is ten times greater than the value of the digit 5 in the number 245,093?

43,567

45,248

53,901

562,011

In the number 245,093 :

3 = units

9 = tens

0 = hundred

5 = thousand

4 = ten thousand

2 = hundred thousand

the value of 5 in the number is 5000. the number that would have a value that it 10 times greater than 5 in 245,093 must occupy the value  of ten thousand.

looking through the options, it is only in 53,901 that 5 occupies a value of ten thousand

Answer:

x = -30

Step-by-step explanation:

g(x)= -2/3x+5

Let g(x) = 25

25= -2/3x+5

Subtract 5 from each side

25-5= -2/3x+5-5

20 = -2/3x

Multiply each side by -3/2

-3/2 * 20 = -3/2 * -2/3 x

-30 = x

Answer:

x = -30

Step-by-step explanation:

g(x)= -2/3x+5

25 = -2/3x + 5

20 = -2/3x

x = -30

Answer:

r=2p

Step-by-step explanation:

If r is ruler and p is pen, ruler equals pen times 2, so its r=2p

Answer:

His time would be least likely greater than 27.9 minutes or smaller than 21.5 minutes.

Step-by-step explanation:

With an standard deviation of 3.2 minutes, it is clear that the maximum time taken by Roman to complete his run of 3 miles would be

Average time + standard deviation = 24.7 minutes + 3.2 minutes = 27.9 minutes

The minimum time taken by Roman to complete his run of 3 miles would be

Average time - standard deviation = 24.7 minutes  - 3.2 minutes = 21.5 minutes

Hence, his time would be least likely greater than 27.9 minutes or smaller than 21.5 minutes.

Answer:

I hope the above picture help you mate

have a great day

I did it in white board so that I can explain better.i hope you understand if u have any problem in understanding be sure to reach out

#liliflim

Answer:

see below

Step-by-step explanation:

all formulas of exponent given by:

[tex] \displaystyle {x}^{1} = x \stackrel{ \rm example}{ \iff} 2^{1} = 2[/tex]

[tex] \displaystyle{x}^{0} = 1\stackrel{ \rm example}{ \iff} 2^{0} = 1[/tex]

[tex] \rm \displaystyle {x}^{m} \cdot { x }^{n} = {x}^{m + n} \stackrel{ \rm example}{ \iff} x^{1 } \cdot {x}^{2} = x^{1 + 2 } = {x}^{3} [/tex]

[tex] \displaystyle \sqrt[n]{{x} }= x^{1/n} \stackrel{ \rm example}{ \iff} \sqrt[3]{x} = x^{1/3}[/tex]

[tex] \rm \displaystyle \frac{{x}^{m} }{ { x }^{n}} = {x}^{m - n} \stackrel{ \rm example}{ \iff} \frac{x^{3} }{ {x}^{1} } = x^{3 - 1} = {x}^{2} [/tex]

[tex] \rm \displaystyle ({x}^{m} {)}^{n} = {x}^{m n} \stackrel{ \rm example}{ \iff} (x^{1 } {)}^{2} = x^{ 2 } [/tex]

[tex] \rm \displaystyle ({x}^{m} {y}^{m} {)}^{n} = {x}^{m n} {y}^{mn} \stackrel{ \rm example}{ \iff} (x^{1 } { {y}^{1} )}^{2} = x^{ 2 } {y}^{2} [/tex]

[tex] \rm \displaystyle \left(\frac{{x}^{} }{ { y }^{}} \right) ^{m} = \frac{{x}^{m} }{ { y }^{n} } ^{} \stackrel{ \rm example}{ \iff} = \left(\frac{ {x}^{2} }{ {y}^{2} } \right)^{2} = \frac{ {x}^{4} }{ {y}^{4} }[/tex]

[tex] \displaystyle {x}^{ - n} = \frac{1}{ {x}^{n} } \stackrel{ \rm example}{ \iff} x^{ - 2} = \frac{1}{ {x}^{2} } [/tex]

Answer:

4X+5

Step-by-step explanation:

Dan : X

Harry: X+5

Regan: 2X

X+X+5+2X

Answer:

[tex]Mean = \frac{4x + 5}{3}[/tex]

Step-by-step explanation:

Given:

Dan sold = x

Harry sold 5 more than Dan, that is = x + 5

Regan sold twice as Dan = 2x

[tex]Mean = \frac{ Total \ cars \ sold}{number\ of \ them \ sold \ it }\\\\Mean = \frac{x + ( x+ 5) +2x }{3} = \frac{4x + 5}{3}[/tex]

Answer:

slope

Step-by-step explanation:

The slope is the rise divided by the run

Answer: The slope.

Step-by-step explanation: That's what I think.

Answer:

6'12 inches long might be the answer

Step-by-step explanation:

Answer:

4, x-1

Step-by-step explanation:

The first piece of this function goes from -1 to 1. Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

The second piece of this function goes from 3 to 5. This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1. Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis). When putting this equation together we get x-1 being the second part.

The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

The first piece of this function goes from -1 to 1.

Since that part of the function is a horizontal line at y=4, and has no slope, this first part is just 4.

so, we have,

The second piece of this function goes from 3 to 5.

This piece does have a slope that you can either solve or just from reading the graph will give you a slope of 1.

Since one of the points is (3, 2), we can figure out that the y-intercept is -1. (You can also just extend the line across the y-axis).

When putting this equation together we get x-1 being the second part.

Hence, The solution is:

The graph represents the piecewise function:

f(x)= { 4, if -1 ≤ x ≤ 1;

         (x - 1), if 3 ≤ x ≤ 5 }

To learn more on graph click:

brainly.com/question/17267403

#SPJ7

Answer:

27.7

Step-by-step explanation:

Pythagorean Theorem

[tex]88.3^{2}[/tex] - [tex]10.7^{2}[/tex] = [tex]x^{2}[/tex]  (10.7 comes from half of the 21.4 side)

[tex]x^{2}[/tex] = height

Answer:

2x+6>20

2x>20-6

2x/2>14/2

x>7

So your answer would be B

Answer:

The angles are 78° and 102°.

Step-by-step explanation:

Let the one angle is y and the other number if y + 24.

The sum of the angles of the linear pair is 180°.

So, according to the question

y + y + 24 = 180

2 y = 180 - 24

2 y = 156

y = 78°

So, one angle is 78° and the other is 78° + 24° = 102°.

Answer:

6.28km

Step-by-step explanation:

Hey,

We know that the circumfrence is the perimetert of a full circle. If we want to find the perimeter of a semicircle all we have to do is find the circumfrence and then divide it by 2 since we want to know the perimeter of half the circle.

Circumfrence is equal to 2πr. Where r is the radius and since we know the radius we an solve for the circumfrence.

2(π)(1km)=2kmπ.

The problem tells us to use 3.14 for pi so let's multiply 2 by 3.14.

6.28km is the answer!

Answer:

7.6 inches

Step-by-step explanation:

We solve the above question using the Law of Cosines.

The formula is given as:

h² = i² + j² - 2ij Cos H

h = √i² + j² - 2ij Cos H

From the above question:

i = 6.6 inches

j = 6.4 inches

Length h = ?

Angle H=62º.

Hence:

h= √6.6² + 6.4² - 2 × 6.6 × 64 × Cos 62

h = √43.56 + 40.96 - 84.48 × Cos 62

h = 7.64292 inches

Approximately to the nearest tenth, Length h = 7.6 inches

Answer:

6.7

Step-by-step explanation:

square root and round

Answer:

she needs at least a 93 on her next quiz

Step-by-step explanation:

hope this helps mate

Answer:

19.8 m

Step-by-step explanation:

To find the height of the tree, we can use the trig ratio tangent:

θ = angle, h = height

tan θ [tex]= \frac{opposite}{adjacent}[/tex]

tan 33° = h / 30.5

h = (tan 33°)(30.5)

h = (0.6494)(30.5)

h = 19.8 m