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3 years ago

Find the equation of the line that passes through the points (-4,-2) and (-3,5) in both point-slope form and

Mathematics

1 answer:

kaheart [24]3 years ago

6 0

<h2>Answer:</h2>

First, we must determine the slope, then we find the y-intercept using slope formula and slope-intercept form.

For slope:

$m = \frac{5 + 2}{-3 + 4} = \frac{7}{1} = 7$

Slope (m) = 7

For y-intercept:

$5 = 7(-3) + b\\\\5 = -21 + b\\\\26 = b$

Y-intercept (b) = 26

Using this information, we can now create the equations for this line.

$y= 7x + 26\\\\y - 5 = 7(x + 3)$

Formulas:

Slope formula: y₂ - y₁/x₂ - x₁

Slope-intercept form: y = mx + b

Point-slope form: y - y₁ = m(x - x₁)

*Note: (x₁, y₁), (x₂, y₂) = 2 points on the line

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A hat is on sale for h dollars. The regular price is 7 times as much. Charlie has enough money to buy two hats at the regular pr

Nostrana [21]

Answer:

Charlie can buy 14 hats at the sale price

Step-by-step explanation:

Let

h ----> the sale price of the hat

x ---> the regular price of the hat

we know that

$x=7h$ ----> equation A

Two hats at the regular price is equal to multiply 2 by x

Multiply by 2 equation A both sides

$2x=(7h)*2$

$2x=14h$

2 hats at the regular price cost the same that 14 hats at the sale price

therefore

Charlie can buy 14 hats at the sale price

8 0

3 years ago

The product of 8 and the sum of a number x and 3

Olin [163]

Answer:

8(x+3)

Step-by-step explanation:

thats the answer

7 0

3 years ago

Read 2 more answers

the empire state building is 1250 feet tall. IF an object is thrown upward from the top of the building at an initial velocity o

ss7ja [257]

Answer:

Time for the object to get h(max) s = 1.1875 sec

h (max) = 1272.57 feet

Down time for the object to hit the ground = 4.25 sec

Step-by-step explanation:

The relation

h(s) = - 16*s² + 38* s + 1250 (1)

Is equivalent to the equation for vertical shot

Δh = V(i)*t - 1/2g*t² (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.

The description of the movement is:

V(s) = V(i) - g*s ⇒ V(s) = 38 - 32*s

At h(max) V(s) = 0 38/32 = s

So the maximum height is at s = t = 1.1875 sec

The time for the object to pass for starting point is the same

t = 1.1875 sec

h(max) is

h(max) = - 16* (1.1875)² + 38 (1.1875) + 1250

h(max) = - 22,56 + 45.13 + 1250

h(max) = 1272.57 feet

Time for the object to hit the ground is

h(s) = - 1250 feet

-1250 = - 16 s² + 38*s + 1250

-16s² + 38s = 0

s ( -16s + 38 ) = 0

First solution for that second degree equation is x = 0 which we dismiss

then

( -16s + 38 ) = 0 ⇒ 16s = 38 s = 38/16

s = 2.375 sec and we have to add time between h (max) and to get to starting point ( 1. 1875 sec)

total time is = 2.375 + 1.875

Total time = 4.25 sec

4 0

3 years ago

50 Points: Name the similar triangles & Prove the similarity with details

Leno4ka [110]

Let's consider the facts at hand:

By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
∠BEC = ∠DFC
Sides BE = DF

Based on the diagram, triangles BCE and triangles DCF are similar

⇒ based on the Angle-Angle theorem

⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC

⇒ the two triangles are similar

Hope that helps!

Definitions of Theorem I used:

Vertical Angle Theorem: opposite angles of two intersecting lines must be equal
Angle-Angle Theorem: if two angles of both triangles are equal, then the given triangles must be similar

8 0

2 years ago

What is 35+20/-4 times 7=?

saw5 [17]

The answer would be 210 because 20/-4 equals -5 and 35+(-5) equals 30. 30×7 equals 210. Hope that helped :D

6 0

3 years ago