PrOblem 1: Find the slope of the line containing the points: (3,-5) and (-1, -2)
Problem 2: Find the x and y intercepts of the line: 2x – 3y = 12
Problem 3: Graph the line x-4y=8

Answer:

y = - [tex]\frac{10}{3}[/tex] x - 23

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (- 9, 7 ) and (x₂, y₂ ) = (- 6, - 3 )

m = [tex]\frac{-3-7}{-6-(-9)}[/tex] = [tex]\frac{-10}{-6+9}[/tex] = [tex]\frac{-10}{3}[/tex] = - [tex]\frac{10}{3}[/tex] , then

y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 6, - 3 ) , then

- 3 = 20 + c ⇒ c = - 3 - 20 = - 23

y = - [tex]\frac{10}{3}[/tex] x - 23 ← equation of line

Answer:

y= -10x/3 + 1

Step-by-step explanation:

gradient of a line= (Y2-Y1)/(X2-X1)

= (-3-7)/[-6-(-9)]

=-10/3

equation of a line

(Y-Y1)/(X-X1)= gradient

(Y-7)/(X+9)= -10/3

3(Y-7)= -1d0(X+9)

3y-21= -10x -19

3y= -10x + 3

dividing both sides by 3

y= -10x/3 + 1

Answer:

The gradient is negative.

Step-by-step explanation:

The gradient represents the rise/run ratio. Always read the line's path left to right, and if it goes up, then it is positive, down means negative gradient, and if it doesnt move then it 0. It is undefined if the line is vertical.

x^2 + 5x = -2

x^2 + 5x + 2 = 0

We need to use the quadratic formula.

In the formula, a = 1, b = 5 and c = 2.

See picture for quadratic formula. Plug in the value for a, b, and c into the formula and do the math.

Answer:

217 Seconds.

Step-by-step explanation:

The answer is 217 seconds because 60x3+37=217.

Given that:

[{1(1/5)−(2/5)⋅(−3/4)3}]÷(−9)

= [{(5+1)/5 - (2/5).(-3/4)3}]÷(-9)

= [{(6/5) - (2/5).(-3/4)3}]÷(-9)

= [{(6/5) - (2/5).(-3/4)3}]÷(-9)

= [{(6/5) - (2/5).(-3*3)/4}]÷(-9)

= [{(6/5) - (2/5) . (-9/4)}]÷(-9)

= [{(6/5) - (2/5) × (-9/4)}]÷(-9)

= [{{6/5) - {{2*(-9)}/{5*4}]}]÷(-9)

= [{(6/5) - {-9/(5*2)}}]÷(-9)

= [{(6/5) - (-9/10)}]÷(-9)

Take the LCM of 5 & 10 is 10.

= [{(6*2 + 9*1)/10}]÷(-9)

= [{(12+9)/10}]÷(-9)

= [{-(21/10)}]÷(-9)

= -(21/10) ÷ (-9)/1

= -(21/10) × (1/9)

= {(-21*1)/(10*9)]

= {-21/90)

= {(-21÷3)/(90÷3)}

= -9/30

= {(-9÷3)/(30÷3)}

= (-3/10) = -3/10 Ans.

I think its C sorry if its wrong

Answer:

a + 12 = -6 , a = -18

Step-by-step explanation:

Hi there!

the first half of the statement says “the *sum* of a number a and 12, so we can write that as a+12. The second half of the statement says that the sum of both of those values is -6, meaning that a + 12 = -6. Knowing this, we can now solve. In order to isolate a, subtract 12 from both sides of the equation. You will be left with a = -18.

Hope this helps!

Answer:

  9, 9√2

Step-by-step explanation:

The ratios of side lengths in a 45°-45°-90° triangle are ...

  1 : 1 : √2

The other leg is the same as the first, and the hypotenuse is √2 times that.

The other sides are 9 and 9√2.

Answer:

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

Step-by-step explanation:

You'll need to get this equation in slope-intercept form by solving for y. I do a little extra here to get it in the correct form, but I think it's pretty clear. Let me know if I need to clarify.

[tex]\\\\\frac{8x}{5}-2y=-8\\\\-2y=-\frac{8x}{5}-8\\\\2y=\frac{8x}{5}+8\\\\y=\frac{4}{5}x+4[/tex]

Once it's in slope-intercept form, both the slope and the y-intercept are readily available so you can easily graph it. I graphed both of them in the attached image so you can see that they are the same line.

Answer:

I'm not sure you mean 2-(b/3) = -5/2 or (2-b)/3 = -5/2

Step-by-step explanation:

if

2-(b/3) = -5/2

12-2b = -15

12+15 = 2b

27 = 2b

27/2 = b

else

(2-b)/3 = -5/2

2(2-b) = -5×3

4-2b = -15

4+15 = 2b

19 = 2b

19/2 = b

Answer:

-270,810

Step-by-step explanation:

c.r.  r=-30/-10=3

[tex]a_{n} =a_{1}r^{n-1} \\a_{4}=-10(3)^{4-1}\\=-10(3)^3=-10 \times 27=-270\\a_{5}=-10 \times(3)^{5-1}\\=10 \times3^4\\=-810[/tex]

she drove for 4  hours

Answer:

the person above me is wrong its not an option for me ;-;

Step-by-step explanation:

A. If S is greater than 0.5, T is positive.

The others are false

Answer:

8 x 5..

Step-by-step explanation:

45$

Answer:

SO if you were to find how much Ivan make

So 8 dollars each time he walks his neighbors dog.

ANd already 5 times.

So we can do 8*5=40

$40 earned

Answer:

The number of unique triangles that can be constructed from the given values is; Only one triangle

Step-by-step explanation:

We are given the 2 angles of a triangle as;  

∠1 = 50°  

∠2 = 80°  

Now, we know that sum of angles in a triangle is 180°. This means that if the third angle is denoted as ∠3, then we have;  

∠1 + ∠2 + ∠3 = 180°  

Thus;  

∠3 = 180 - (∠1 + ∠2)  

∠3 = 180 - (50 + 80)  

∠3 = 180 - 130  

∠3 = 50°  

Thus; ∠1 = ∠3 = 50°  

A triangle with two equal angles is called an isosceles triangle. Which means that it will also have 2 of its' sides to be equal.  

Thus, in conclusion, only one unique triangle can be drawn.

Answer:

perimeter: 14+5+6+6+8+10=59

area: 14x5x6x10=4200

perimeter means adding all the sides including the ones that arent labeled, and the area is multiplying all the numbers included.

Answer:

x=19/12

Step-by-step explanation:

(4x-3)/2 = 5/3

4x-3 = 10/3

3 = 9/3

4x = 10/3 + 9/3 = 19/3

x = 19/12

Hey there!

4x - 3/2 = 5/3

ADD 3/2 to BOTH SIDES

4x - 3/2 + 3/2 = 5/3 + 3/2

CANCEL out: -3/2 + 3/2 because it gives you 1

KEEP: 5/3 + 3/2 because it helps solve for the x-value.

NEW EQUATION: 4x = 5/3 + 3/2

SIMPLIFY IT!

4x = 19/6

DIVIDE 4 to BOTH SIDES

4x ÷ 4 = 19/6 ÷ 4

CANCEL out: 4 ÷ 4 because it gives you 1

KEEP: 19/6 ÷ 4 because it helps solve for the x-value

NEW EQUATION: x = 19/6 ÷ 4

SIMPLIFY IT!

x = 19/24

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

d

Step-by-step explanation:

Answer:

Position function is [tex]s(t)=-12t^2[/tex]

Step-by-step explanation:

Given [tex]a(t)=-24[/tex], since velocity is the antiderivative of acceleration, then [tex]v(t)=-24t[/tex].

Also, since position is the antiderivative of velocity, then [tex]s(t)=-12t^2[/tex].

Answer:

124°

Step-by-step explanation:

180°( n - 2 )

180° ( 5 - 2 ) = 540°

( 2x - 3 )° + ( 3x - 2 )° + 2( 3x - 4 )° + ( 2x + 7 )° = 540°

( 2x + 3x + 6x + 2x ) + ( - 3 - 2 - 8 + 7 ) = 540

13x - 6 = 540

13x = 546

x = 42

3(42) - 2 = 124°

Answer:

x.

Step-by-step explanation:

f(g(x)) = x.

Answer:

x = 3

Step-by-step explanation:

a triangle has 180 degrees in all

a square for an angle is 90 degrees

we can add them all together and get 180

90 + 45 + 8x + 21 = 180

combine like terms

156 + 8x = 180

subtract 156 to each side

8x = 24

then find x

x = 3

Answer:

x=3

Step-by-step explanation:

So the sum of angles of triangle is always 180 degrees.

We already have 45 and 90 but 8x+21 is unknown.

We can solve this by making an equation which is

45 + 90 + (8x+21) = 180.

If we solve this it will be

8x+21+135=180

8x+156 (-156) =180 (-156)

8x (/8) = 24 (/8)

x=3

Answer:

Step-by-step explanation:

Same: 30×40 = 1200 . . . . . 2 zeros in the factors; 2 in the product

Different: 20×50 = 1000 . . . 2 zeros in the factors; 3 in the product

__

Same: 0.3×0.4 = 0.12 . . . . no zeros in the factors; no zeros in the product

Different: 0.2×0.4 = 0.08 . . . no zeros in the factors; 1 zero in the product after the decimal point

_____

For a product, the number of zeros will be different if the combined factors of the numbers increase the number of factors of 10 beyond the sum of the factors of 10 of the numbers being multiplied.

Example: neither 2 nor 5 has a factor of 10, but their product does.

__

For a product that is a decimal fraction, the number of leading zeros will increase if the product of the mantissas of the numbers is less than 10. The number of trailing zeros will increase under the conditions discussed above. (0.25×0.4 = 0.100)

_____

Additional comment

Here, the term "mantissa" is used to refer to the portion of the number written in scientific notation that multiplies the power of 10.

Answer:d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

pls give me brainlest

[tex]14+3c^2-15+c\\\\=14+3(4^2)-15+4\\\\=3(16)-1+4\\\\=48+3\\\\=51[/tex]