Directions: Graph each equation by using the y-intercept and slope( make sure too show your work)
FIRST QUESTION: y= -2/3x-1
y-intercept=____
Slope:____

Answer:

Step-by-step explanation:

This equation turns out to be a quartic. I'm not sure what should be done with. I can't believe you were asked to find its roots which are unbelievably complex. Here is a graph with the only 2 points that are easily found. If I am not solving what you need, please leave a note.

The ratio of the number of students who went to the zoo to the number of students who did not go to the zoo is 1: 5. Hence option C is true.

Given that;

The students in Shawn's class got to choose whether to visit the zoo or the aquarium.

Here, 3 students went to the zoo and 15 students went to the aquarium.

Hence, the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo is,

Ratio = 3 : 15

Ratio = 3/15

Ratio = 1/5

Ratio = 1 : 5

Thus, option C is true.

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Explanation:

The gradient is the same as the slope

m = slope

m = rise/run

m = (change in y)/(change in x)

m = (y2-y1)/(x2-x1)

m = (6-1)/(6 - (-4))

m = (6-1)/(6+4)

m = 5/10

m = 1/2

In decimal form, this becomes 0.5

A slope of 1/2 means we move up 1 and to the right 2 units each time to generate points along the diagonal line.

A positive slope goes uphill as we move to the right (due to the positive rise value).

Answer:

One way to find the gradient is using the expression :

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{y_{B} - y_{A}}{x_{B} - x_{A}}[/tex]

So [tex]m = \frac{6 - 1}{6- (-4)} =\frac{5}{10} =\frac{1}{2}[/tex]

Answer:

To find the point of intersection, you have to set both equations equal to each other and solve. After solving, plug it back into one of the equations. (Its pretty simple so don't worry :] )

y1 = 2x + 4

y2 = 3x-9

y1 = y2

2x + 4 = 3x - 9

4 = x - 9

x = 13

--> Plug x back into an equation for y coordinate. I will be using y1.

2(13) + 4

26 + 4 = 30

y = 30

The point of intersection is (13,30)

=========================================================

Explanation:

We don't have a direct variation because the initial cost isn't $0

The equation for this situation is y = 25x+375, where x is the number of yearbooks purchased and y is the total cost.

Notice how this line doesn't go through the origin. All direct variation graphs are straight lines through the origin.

So that's why we have partial variation instead.

The initial cost is simply the set up cost, aka the cost when x = 0. That initial cost is $375. The initial cost is located at the y intercept.

From that initial cost, we then add on multiples of $25 depending on how many yearbooks are purchased.

-----------------

In short, because the initial cost is $375, which is some nonzero value, this means we don't have direct variation. Instead, we have partial variation.

Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

Answer:

Step-by-step explanation:

[tex]a^{m}* a^{n}=a^{m+n}\\\\\\(\frac{-1}{2})^{-19}*(\frac{-1}{2})^{8}=(\frac{-1}{2})^{-2x +1}\\\\(\frac{-1}{2})^{-19+8}=(\frac{-1}{2})^{-2x+1}\\\\\\(\frac{-1}{2})^{-11}=(\frac{-1}{2})^{-2x+1}[/tex]

As bases are equal in boht sides, we can compare the exponents.

-2x + 1 = -11

Subtract 1 form both sides

-2x = -11 - 1

-2x = -12

Divide both sides by -2

x = -12/-2

x = 6

Answer:

44.4

Step-by-step explanation:

Since we have a right triangle, we can use trig functions

sin theta = opp / hyp

sin x = 7/10

Taking the inverse sin of each side

sin^-1 (sin x) = sin^-1(7/10)

x = 44.427

Rounding to the nearest tenth

x = 44.4

Answer:

7

Step-by-step explanation:

10 minus 3 will give you the number

Answer:

7

Step-by-step explanation:

let the number added to 3 be 'x'

we know;

X+3=10

X=10-3

X=7

Answer:

(19-29x) over (x-4)

Step-by-step explanation:

Answer:

answer is 6

Step-by-step explanation:

f(x) = x2 - 4x

f(-3)= -3*2-4*-3

      =-6-(-12)

      =6

Answer:

1. Angles 2, 3 and angles 1,3 are complementary angles(Given)

2. To prove :

Since Angles 2, 3 and angles 1,3 are complementary.

When angles are complementary, then the sum of the measures of angles is 90 degrees.

So,  and  (Definition of Complementary angles)

3.  (Substitution)

4.  (Subtraction property of equality)

Step-by-step explanation:

Answer:

Just use m a t h w a y for the answer

Step-by-step explanation:

Thank me later,or dont thank me at all

Answer:

30.7

Step-by-step explanation:

Assuming the angled are degrees and not radian.

side BC= (11÷sin67)•sin28= 5.6

angle ABC= 180-67-28=85°

A= 11•5.6•sin85÷2≈30.68

Answer:

(2/3)n + 7

Step-by-step explanation:

Represent the number by n.

Then "two thirds of (that) number" is (2/3)n.

Finally, we add 7:

"Two-thirds of a number increased by seven" is (2/3)n + 7

Answer:

25

Step-by-step explanation:

5 cents = 0.05

1.25 / 0.05 = 25

let me know if i'm wrong

Answer:

25

Step-by-step explanation:

$1.25=125cents

125/5 = 25

Answer:

58%

Step-by-step explanation:

10*5=50

7*3=21

21/50 chance to choose inside small rectangle

21/50*2 = 42/100 chance to choose inside small rectangle

100-42=58%

Here, we are to find the length and the , breadth of the rectangle

The length of the rectangle = 7 units and Breadth of the rectangle = 3 units

Let

length = l units

Breadth = b units

Perimeter of the rectangle = 20 units

length is the distance measured along the longest dimension of an object

width is the wideness of an object

perimeter refers to the total measurements of an objects

The breadth of a rectangle is 4 units less than its length

If,

Length = l

Then,

b = l - 4

Perimeter of a rectangle = 2(length + breadth)

20 = 2{l + (l - 4)

20 = 2(l + l - 4)

20 = 2(2l - 4)

20 = 4l - 8

20 + 8 = 4l

28 = 4l

l = 28/4

l = 7

b = l - 4

b = 7 - 4

b = 3 units

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Answer:

3. (1-7/9)÷2 = 2/9÷2 = 1/9

reciprocal of 1/9 is 9

4. x+2/x=3

if you solve it, you get x = 1 and x = 2, so last option, 1 and 2, is the answer

Answered by GAUTHMATH

Answer:

y=1

Step-by-step explanation:

5=2-3y+6

3y=2-5+6

3y= -3+6

3y= 3

3y÷3=3÷3

y=1

Answer:

16

Step-by-step explanation:

Substitute y = 5 into the expression

y² - 3y + 6

= 5² - 3(5) + 6

= 25 - 15 + 6

= 16

Answer:

Step-by-step explanation:

Table I

Given function is,

f(x) = [tex]b^x[/tex]

From the table attached,

For x = 0.827, value of function f(0.827) = 5,

f(0.827) = [tex]b^{0.827}[/tex]

Therefore, [tex]b^{0.827}=5[/tex]

[tex]\text{log}(b^{0.827})=\text{log}(5)[/tex]

0.827[log(b)] = log(5)

log(b) = 0.8452

b = [tex]10^{0.8452}[/tex]

b = 7

Therefore, function 'f' will be,

f(x) = [tex]7^x[/tex]

For f(x) = 9,

9 = [tex]7^x[/tex]

log(9) = log([tex]7^x[/tex])

log(9) = x[log(7)]

x = 1.129

Table II

Given function is g(x) = [tex]\text{log}_b(x)[/tex]

From the given table,

For x = 7, g(x) = 1

1 = [tex]\text{log}_b(7)[/tex]

[tex]b^1=7[/tex]

b = 7

Therefore, the function 'g' will be,

g(x) = [tex]\text{log}_7(x)[/tex]

For g(x) = 1.318

1.318 = [tex]\text{log}_7(x)[/tex]

[tex]x=7^{1.318}[/tex]

[tex]x=12.9968[/tex]

[tex]x=13.997[/tex]

Answer:

Step-by-step explanation:

I think you mean 35 seconds because if it was 36 then the answer would be too long so assuming it is 35 seconds the answer is 1 minute or 60 seconds

Answer:

8×4=32 and 8 groups of 4 equals 32.

Answer:

[tex]9\ days[/tex]

Step-by-step explanation:

[tex]We\ are\ given:\\No.\ of\ days\ A\ takes\ to\ complete\ some\ amount\ of\ work=15\ days\\No.\ of\ days\ B\ takes\ to\ complete\ the\ same\ amount\ of\ work=12\ days\\No.\ of\ days\ C\ takes\ to\ complete\ the\ same\ amount\ of\ work\ as\ A\ and\ B\ =20\ days\\[/tex]

[tex]Now,\\We\ can\ say\ that\ an\ object\ has\ to\ complete\ \frac{1}{n}th\ of\ the\\ work\ daily,\ to\ complete\ the\ work\ in\ n\ number\ of\ days.\ This\ is\ however\\ only\ true\ if\ the\ object\ covers\ equal\ amounts\ of\ work\ each\ day.[/tex]

[tex]Here,\\In\ 1\ day,\\A\ would\ cover\ \frac{1}{15}th\ of\ the\ work.\\B\ would\ cover\ \frac{1}{12}th\ of\ the\ work.\\C\ would\ cover\ \frac{1}{20}th\ of\ the\ work.[/tex]

[tex]Now,\\We\ are\ also\ given\ that:\\They\ work\ together\ for\ 2\ days\ on\ the\ same\ work.\\Hence,\\Total\ work\ done\ in\ 1\ day\ by\ A,B\ and\ C=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}\\Hence, Total\ work\ done\ in\ 2\ days\ by\ A,B\ and\ C=2*\frac{1}{5}=\frac{2}{5}[/tex]

[tex]Hence,\\The\ portion\ of\ the\ total\ work\ left=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\\So,\\Since\ A\ has\ to\ complete\ \frac{3}{5}th\ of\ the\ work,\ lets\ compute\ the\ no.\ of\ days\ it\ takes\ to\ do\ so.\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ the\ entire\ work=15\ days\\Hence,\\No.\ of\ days\ A\ takes\ to\ complete\ \frac{3}{5}th\ of\ the\ entire\ work=15*\frac{3}{5}=9\ days[/tex]

Answer:

9 days

Step-by-step explanation:

A does in 15days, so A in 1day does 1/15part

B does in 12days, so B in 1day does 1/12part

C does in 20days, so C in 1day does 1/20part

So. A+B+C in 1 day-- 1/15+1/12+1/20=(4+5+3)/60= 12/60=1/5 and in 2days 2/5 part..hence remaining work=1/1–2/5=(5–2) =3/5part.

Now A in 1/15 part takes 1day

So, in 3/5 part 15×3/5 = 9 days.

Answer:

good evening good evening good evening good evening

Step-by-step explanation:

w

Answer:

∠b = 54°

they add up to 180

7x + 14 + 5x - 26 = 180

12x = 192

x=16

thus ∠b = 54°

Step-by-step explanation:

( − 2 ) ( 3+ 2 2 − − 2 )

Hope this helps, have a great day!

Answer:

D

Step-by-step explanation:

Note that I will be using a, b, and y instead of their Greek counterparts.

First, we know that sin(c+d) = sin(c)cos(d) + cos(d)sin(a) and sin(c-d) = sin(c)cos(d) - cos(d)sin(a). We can apply these here to get

sin(b+y) = sin(b)cos(y) + cos(b)sin(y)

sin(b-y) = sin(b)cos(y) - cos(b)sin(y)

sin(a+y) = sin(a)cos(y) + cos(a)sin(y)

sin(a-y) = sin(a)cos(y) - cos(a)sin(y)

Plugging these into our equation, we get

(sin(b)cos(y) + cos(b)sin(y) - (sin(b)cos(y) - cos(b)sin(y)))

/

(sin(a)cos(y) + cos(a)sin(y)-(sin(a)cos(y) - cos(a)sin(y)))

=

2cos(b)sin(y) / 2cos(a)sin(y)

= cos(b)sin(y)/cos(a)sin(y)

= cos(b)/cos(a)

Next, we can see that a+b = π, so we can subtract b from both sides to get a = π -b. Plugging that in for a in our equation, we get

cos(b) / cos(π-b)

After that, we know that cos(c-d) = cos(c)cos(d) - sin(c)sin(d). Plugging that in here, we get

cos(π-b) = cos(π)cos(b) - sin(π)sin(b)

= -cos(b) + 0

= -cos(b)

Plugging that back into our equation, we get

cos(b) / -cos(b) = -1

Answer:

(-4, 2) y(2, -8)

{-4 y(2, -8), 2 y(2, -8)}

-4 y(2, -8) + 2 y(2, -8) = -2 y(2, -8)

-y(2, -8)

2 sqrt(5) abs(y(2, -8))

Step-by-step explanation:

D

Answer:

C

Step-by-step explanation:

The center will be the midpoint of the line connecting A and B.

x=(-4+2)/2=-2/2=-1

y=(2-8)/2=-6/2=-3