Identifying Slope and y-Intercept of a Line
Identify the slope and y-intercept of each linear function's equation
y = 1 - 3x
slope = 3 y-intercept at -1
y = 3x - 1
slope = -1 y-intercept at 3
X-3 = y
slope = -3; z-intercept at 1
--> + 3 = y
slope = 1:y-intercept at -3
Previous Activity

Answer:

B

Step-by-step explanation:

x² + 8x + 7 = 0

x²+x+7x+7=0

x(x+1)+7(x+1)=0

(x+1)(x+7)=0

Either x=-1or x=-7.

Answer:

See Below.

Step-by-step explanation:

I'm going to take the equation to be

y = x3 + 2x2 + 3x + 6

That is, the first term is a typo

make 2 groups. Put brackets around both groups.

group 1: x^3 + 2x^2   Take out the common factor of x^2

group 1: x^2(x + 2)

group 2: 3x + 6       Take out the common factor of x^2

group 2: 3(x + 2)

Now put the two groups together

Cubic = group 1 + group 2

Cubic = x^2 (x + 2) + 3(x + 2)

Now take out the common factor of x + 2

Cubic = (x + 2) (x^2 + 3)

Answer:

(4,3)

Step-by-step explanation:

asoming 4 is x and 5 is y down 2 turns 5 into 3

Start at the point (4,5). Moving 2 units down decreases the y-coordinate by 2, thus bringing you to the new point (4,3). Draw a graph to visualize this better.

In the context of a grid in Mathematics, the first quadrant is where both x and y coordinates are positive. The given point starts at (4,5). If you move 2 units down, it means you are reducing the y-coordinate by 2 units. So, starting at (4,5) and moving 2 units down would land you at a new point, which will be (4,3).

To visualize this, you may want to draw a graph on an x-y axis and plot the points (4,5) and (4,3) to see how the position change looks.

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Answer:

$10d

Step-by-step explanation:

The unit price is $d per pound. It is a dollar amount divided by the number of pounds. If you multiply the unit price by pounds, then the units work out like this:

$/lb * lb = $

When you multiply the unit price in dollars per lb by lb, you get dollars.

In your case:

$d/lb * 10 lb = $10d

That value of the nuts is $10d.

Answer:

The shaped is being reflected.

Answer: Reflection

Step-by-step explanation:

When we look at the picture, the two rectangles QRST and Q'R'S'T' appears as the mirror images of each other , also the corresponding sides and angles are congruent.

The transformation that create a mirror image of the figure is known as reflection. It is a rigid transformation because it produces congruent shapes.

Therefore, the transformation maps rectangle QRST to rectangle Q'R'S'T' is reflection.

Answer:

$4 per pound

Step-by-step explanation:

To find how much one pound of cashew nuts cost you have to use money over unit.

So money/unit, in this problem the money is 32 and the unit is 8.

So 32/8, now you divide 32 by 8 to get the price for one pound.

32 divided by 8 is 4

So $4 per pound

Answer:

The total cost of one pound is $4.

Step-by-step explanation:

[tex]\Large\textnormal{First, you divide the numbers from left to right to find the answer.}[/tex]

[tex]\displaystyle 32\div8=4[/tex]

[tex]\displaystyle \frac{8}{8}=1[/tex]

[tex]32\div4=8[/tex]

[tex]\displaystyle \frac{32}{8}=4\times1=4[/tex]

[tex]\Large \boxed{4}[/tex], is the correct answer.

I hope this helps you and have a wonderful day!

Answer:

all her patients patients with no cavities

patients younger than 18

every patient with braces

Step-by-step explanation:

when a sample is selected in a manner that some elements, in this case patients, of population have higher or lower probability of sampling then that sample is biased.

From given case, all the following are biased samples

all her patients patients with no cavities

patients younger than 18

every patient with braces

because they are non-random sample of a population in which all other elements were not equally likely to be chosen!

The dentist should avoid biased sampling methods.

The biased samples in this case would be:

1. All her patients: This would only include the dentist's current patients, which may not be representative of the entire population.
2. Patients with no cavities: This would only include a specific subset of patients who do not have cavities, which may not be representative of the entire population.
3. Patients younger than 18: This would only include patients below the age of 18, which may not be representative of the entire population.

It is important to have a random and representative sample in order to make accurate conclusions about the population's flossing habits.

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Answer:

[tex]\frac{4x^{2}-2x+5}{2x-6} =2x + 5 + \frac{35}{2x-6}[/tex]

Step-by-step explanation:

We know that the height of a parallelogram can be found by divind the area by the lenght of the base.

The area is 4x2 – 2x + 5 and the base is 2x – 6. To find the height, we need to divide both polynomials:

[tex]\frac{4x^{2}-2x+5}{2x-6} =2x + 5 + \frac{35}{2x-6}[/tex]

Answer:

[tex]2x+5+\frac{35}{2x-6}[/tex]

Step-by-step explanation:

Given,

The area of the parallelogram, A = [tex]4x^2-2x+5[/tex]

The length of its base, b = [tex]2x-6[/tex]

∵ The height of the parallelogram.

[tex]h=\frac{A}{b}[/tex]

[tex]\implies h=\frac{4x^2-2x+5}{2x-6}[/tex]

[tex]=2x+5+\frac{35}{2x-6}[/tex]   ( by long division shown below )

Hence, the height of the given parallelogram is,

[tex]2x+5+\frac{35}{2x-6}[/tex]

Answer:

= 9x³+ 0x²+0x -52....

Step-by-step explanation:

Descending powers means you start with highest power and then decrease.

In this expression the highest power is 3. We do not have any variable with power 2 and 1. So we will write it as:

9x³ -  52

= 9x³+ 0x²+0x -52....

Answer:

sqrt( 146)

Step-by-step explanation:

To find the distance between two points, we use the formula

d = sqrt( ( y2-y1)^2 + (x2-x1)^2)

Where (x1,y1) and (x2,y2) are the two points.

(–9, 0) and (2, 5).

Substituting into the equation

d = sqrt( (5-0)^2 + (2- -9)^2)

d = sqrt( ( 5^2 + (2+9)^2)

      sqrt( ( 5^2 + (11)^2)

   = sqrt( 25+121)

  = sqrt( 146)

The distance between the two points is sqrt(74)

Final answer:

The distance between the points (–9, 0) and (2, 5) in the Cartesian plane is approximately [tex]\sqrt{146}[/tex] units.

Explanation:

To find the distance between two points in the Cartesian plane, we can use the distance formula.

The distance formula is:

distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}[/tex]

Using the given points (–9, 0) and (2, 5), we can plug in the values:

distance = [tex]\sqrt{((2 - (-9))^2 + (5 - 0)^2)}[/tex]

distance = [tex]\sqrt{((11)^2 + (5)^2)}[/tex]

distance = [tex]\sqrt{(121 + 25)}[/tex]

distance = [tex]\sqrt{146}[/tex]

So, the distance between the points (–9, 0) and (2, 5) is approximately [tex]\sqrt{146}[/tex] units.

Answer:

x^2  +  y^2  = 4

Step-by-step explanation:

The center-radius form (formally called the standard form) of a circle is

(x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.

So if we replace (h,k) with (0,0) since the center is the origin and r with 2 since the radius is 2 we get:

(x-0)^2+(y-0)^2=2^2

Let's simplify:

x^2  +  y^2   = 4

Answer:

C.

Step-by-step explanation:

If Erin has 9 more shells than Jamie, then 27 minus 9 would be equivalent to the amount of shells Jamie has.

This can be represented by:

[tex]27-9=j[/tex]

Which can be rewritten as:

[tex]27=j+9[/tex]

by adding 9 to both sides.

To solve, subtract 9 from 27.

[tex]27-9=18[/tex]

Jamie has collected 18 shells.

Answer:

C. 27=j+9; Jamie collected 18 shells.

Step-by-step explanation:

First, you do is switch sides.

[tex]\displaystyle j+9=27[/tex]

Then, you subtract 9 from both sides.

[tex]\displaystyle j+9-9=27-9[/tex]

Simplify, to find the answer.

[tex]\displaystyle 27-9=18[/tex]

Therefore, Jamie got collected of 18 shells.

[tex]\huge \boxed{18}[/tex], which is our answer.

The correct answer is C.

Answer:

[tex]\large\boxed{y-8=\dfrac{5}{7}(x-4)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope [tex]m=\dfrac{5}{7}[/tex] and the point [tex](4,\ 8)[/tex].

Substitute:

[tex]y-8=\dfrac{5}{7}(x-4)[/tex]

1,547.489

4 - Bold and underline one above is in the ten place.

Answer:

1,547.489

Step-by-step explanation:

Note that there is a decimal point in between 7 & 4, and the numbers to the left are whole numbers, while the numbers to the right is part of the decimal.

From the decimal point, count to the left two place value (to find the tens place):

1,547

1,547

4 is your digit in the ten's place, & is your answer.

~

Answer:

1. The base is a triangle.

Step-by-step explanation: This one seems like it's the only corret one, You might have to wait and see the other answers roll in.

Answer:

2,3&5

Step-by-step explanation:

got it right on edg 2020

Answer:

4x - y = 7.

Step-by-step explanation:

We substitute for x and y and see if they fit.

4x - y = 7

4(2) - 1 = 7

So it is the first line.

Answer: First option.

Step-by-step explanation:

To find which line contains the point (2,1), we can substitute the coordinates into each equation of the line provided in the options:

First option:

[tex]4x-y=7\\4(2)-1=7\\7=7[/tex]

It contains the point (2,1)

Second option:

[tex]2x+5y=4\\2(2)+5(1)=4\\9\neq 4[/tex]

It does not contain the point (2,1)

Third option:

[tex]7x-y=15\\7(2)-1=15\\13\neq15[/tex]

It does not contain the point (2,1)

Fourth option:

[tex]x+5y=21\\2+5(1)=21\\7\neq 21[/tex]

 It does not contain the point (2,1)

Answer:

Last option: Translate each point of the graph of h(x) 3 units left.

Step-by-step explanation:

There are some transformations for a function f(x). The following is one of these transformations:

If [tex]f(x+k)[/tex], then the function is shifted "k" units to the left.

Given the function  [tex]h(x)=log_6(x)[/tex] and the function  [tex]m(x)=log_6(x+3)[/tex], you can notice that the function m(x) is the function h(x) but shifted left 3 units.

Therefore, you could graph the function m(x) by translating each point of the graph of the function h(x) 3 units left.

This matches with the last option.

Answer:

Last option (D) Translate each point of the graph of h(x) 3 units left.

Answer:  24/4=D

Step-by-step explanation:

24LEGS/4LEGS=6DOGS

Answer:

4d=24

Step-by-step explanation:

4(dogs)=24 legs

so the answer is 6 dogs (in case you need it)

Answer:

The one that is not equivalent is 7x^3

Step-by-step explanation:

7x^3= 7 * x*x*x

4x+3x = 7x = 7*x

(4+3)x = (7)x = 7*x

7x= 7*x

Answer:

7x^3

Step-by-step explanation:

All of the following are equivalent except 7x^3.

7x^3 = 7x^3

4x+3x = 7x

(4+3)x = 7x

7x = 7x

Answer:

45 meters

Step-by-step explanation:

If x represents the seconds after the launch, then the time of launch is when x=0 so you just need to solve for h(0)

h(0) = -5(1)(-9)

h(0) = 45

Answer:

45 m

Step-by-step explanation:

At the time of launch, the time x = 0

Substitute x = 0 into h(x)

h(0) = - 5 (0 + 1)(0 - 9) = - 5(1)(- 9) = - 5 × - 9 = 45

Answer:

[tex] 2 ^ { \frac { 5 } { 2 } [/tex]

Step-by-step explanation:

We are given the following expression which we are to find its simplest form:

[tex] \frac { 4 ^ { \frac { 5 } { 4 } } \times 4 ^ { \frac { 1 } { 2 } } } { 4 ^ { \frac { 1 } { 2 } } }[/tex]

Cancelling the like terms to get:

[tex] 4 ^ { \frac { 5 } { 4 } } [/tex]

[tex] 2 ^ { 2 .\frac { 5 } { 4 } } = 2 ^ { \frac { 5 } { 2 } } [/tex]

[tex] 2 ^ { \frac { 5 } { 2 } [/tex]

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\ on\ a\ line\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\======================================[/tex]

[tex]\text{We have the points:}\ (2,\ -2)\ \text{and}\ (1,\ -6).\\\\\text{Substitute:}\\\\m=\dfrac{-6-(-2)}{1-2}=\dfrac{-4}{-1}=4\\\\y-(-2)=4(x-2)\\\\y+2=4(x-2)[/tex]

[tex]h(6)=3\cdot6-4=14[/tex]

Answer:

a. 14 is your answer.

Step-by-step explanation:

h(x) = 3x - 4

h(6) = ?

Plug in 6 for x: x = 6

h(6) = 3(6) - 4

Remember to follow PEMDAS. First, multiply, then subtract:

h(6) = (3 * 6) - 4

h(6) = (18) - 4

Simplify:

h(6) = 18 - 4

h(6) = 14

a. 14 is your answer.

~

For this case we must find an expression equivalent to[tex]6 ^ {- 3}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, we can rewrite the given expression as:

[tex]6 ^ {3} = \frac {1} {6 ^ 3}[/tex]

This is equivalent to:

[tex](\frac {1} {6}) ^ 3[/tex]

Answer:

Option D

Answer:

The correct answer option is D. ( 1 / 6 ) ^ 3.

Step-by-step explanation:

We are given the following expression and we are to determine whether which of the given answer options is equivalent to this:

[tex] 6 ^ { - 3 } [/tex]

Rewriting this as a fraction to get:

[tex] \frac { 1 } { 6 ^ 3 } [/tex]

Therefore, the correct answer option is D. ( 1 / 6 ) ^ 3.

Answer:

x=4

Step-by-step explanation:

AB + BC = AC

AB= 6x, BC= x-5, AC= 23

Substituting what we know

6x + x-5 = 23

Combine like terms

7x -5 = 23

Add 5 to each side

7x-5+5 =23+5

7x = 28

Divide each side by 7

7x/7 = 28/7

x=4

Answer:

[tex]\large\boxed{3.\ V\approx130.88\ m^3}\\\boxed{4.\ V\approx35.21}\\\boxed{6.\ V\approx1.06\ in^3}[/tex]

Step-by-step explanation:

3.

The formula of a volume of a sphere:

[tex]V=\dfrac{4}{3}\pi R^3[/tex]

R - radius

We have R = 3.15 m. Substitute:

[tex]V=\dfrac{4}{3}\pi(3.15)^3\approx\dfrac{4}{3}\pi(31.26)\approx\dfrac{4}{3}(3.14)(31.26)\approx130.88\ m^3[/tex]

4.

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have 2r = 11.6 → r = 5.8 and H = x. Substitute:

[tex]V=\dfrac{1}{3}\pi(5.8)^2(x)=\dfrac{1}{3}\pi(33.64)x\approx\dfrac{1}{3}(3.14)(33.64)x\approx35.21[/tex]

6.

The formula of a volume of a cube:

[tex]V=s^3[/tex]

s - edge

We have s = 1.02 in. Substitute:

[tex]V=(1.02)^3\approx1.06\ in^3[/tex]

For this case we have the following system of equations:

[tex]y = x ^ 2-6x + 12\\y = 2x-4[/tex]

Equating the equations:

[tex]x ^ 2-6x + 12 = 2x-4\\x ^ 2-6x-2x + 12 + 4 = 0\\x ^ 2-8x + 16 = 0[/tex]

We look for two numbers that when multiplied, get 16, and when added together, get -8.

These numbers are -4 and -4.

[tex](x-4) (x-4) = 0\\(x-4) ^ 2 = 0[/tex]

So, the solution is[tex]x = 4[/tex]

We look for the value of y:

[tex]y = 2x-4\\y = 2 (4) -4\\y = 8-4\\y = 4[/tex]

Finally, the solution is:[tex](4,4)[/tex]

ANswer:

[tex](4,4)[/tex]

Answer:

For [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656[/tex]

[tex]46,656 > 500,000[/tex]

Inequality is not met because [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

[tex]7^7=823,543[/tex]

[tex]823,543 > 500,000[/tex]

Then the smallest positive integer that will make [tex]x^x > 500,000[/tex] is 7

Inequality is met.

In the same way the largest negative integer that will make [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse [tex]7^{-(-7)}=823,543[/tex]

Answer:

Smallest positive integer value for [tex]x^x>5000[/tex] is,

x = 7,

Largest negative integer value for [tex] x^{-x} >500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

∵ If x is a positive integer then the possible values of x = 1, 2, 3, 4, 5, 6, 7.....

Case 1 : If x < 7,

[tex]x^x < 500000[/tex]

Case 2 : If x ≥ 7,

[tex]x^x > 500000[/tex]

Hence, smallest positive integer value of x is 7.

Now, if [tex]x^{-x}>500000[/tex]

∵ If x is negative integer then the possible value of x = -1, -2, -3, -4,.....

Case 1 : if x is odd negative integer,

[tex]x^{-x} < 50000[/tex]

eg : -1, -3, -5, -7,...

Case 2 : If x is even negative integer then there are further two cases,

(i)  x is more than or equal to -6,

[tex]x^{-x} < 500000[/tex]

eg x = -6, -4, -2,

(ii) x is less than -8,

[tex]x^{-x} > 50000[/tex]

eg : x = -10, -12, -14,...

Hence, the largest negative integer value that will make [tex]x^{-x}> 500000[/tex] is x = -8.

hey! the value of y is 57