write the slope-intercept form of the equation of a line passing through the following two points: (-3, 7) & (6, -5)

Answer:

y = x + 1

Step-by-step explanation:

Step 1: Find the slope.

Parallel lines have the same slope. That means that the line we are seeking is going to have the same slope as line x - y = 7.

To find the slope of the line x - y = 7 let's change it to the slope-intercept form.

Slope-Intercept Form

y = mx + b

m ... slope

b ... y-intercept

Let's change the equation of the parallel line to slope-intercept form (isolate y).

x - y = 7

Add y on both sides.

x - y + y = 7 + y

x = 7 + y

Subtract 7 on both sides.

x - 7 = 7 + y - 7

x - 7 = y

y = x - 7

Let's read the slope from the equation.

Instead of y = x - 7 we can write y = 1x -7.

Now it's obvious that m (slope) is 1.

m = 1

So far, our equation of the line is:

y = 1x + b

which is te same as

y = x + b

Step 2: Find y-intercept.

To find out y-intercept (b), we substitiute the point (-7, -6) in the equation. Points are in form (x, y) so -7 is x and -6 is y.

y = x + b

-6 = -7 + b

Solve for b.

1 = b

Step 3: Substitute slope and y-intercept in general formula for slope-intercept form of the line.

Now substitute m and b in slope-intercept form y = mx + b.

m = 1

b = 1

Equation of the line:

y = x + 1

Answer:

14

Step-by-step explanation:

i think 14 because you have to times two answers and add them form each number

Step-by-step explanation:

the domain is the set or interval of all valid x values.

the range is the set or interval of all valid y values.

1.

domain = {-1, 2, 5}

range = {0, 2, 3, 7}

function : no, because x = -1 has 2 different y values assigned (7 and 2). that violates the definition of a function.

2.

domain = {-3, -2, -1, 1, 4}

range = {-5, -1, 0, 2}

function : yes. every x bake has exactly one y value assigned.

3.

domain = {4, 6, 7}

range = {-1, 2, 3, 5}

function : no, because x = 4 has 2 different y values assigned (2 and 5).

4.

domain = [-3, 3) "3" is not included, hence the empty dot

range = [-4, 5]

function : yes

5.

domain = (-infinity, +infinity) "infinity" is not a possible value, so the limits are not included.

range = [-1, 2]

function : yes

6.

domain = [-2, +infinity)

range = (-infinity, +infinity)

function : no. except for x = -2 all x values have 2 different y values assigned.

Answer:

2000.

Step-by-step explanation:

The hundreds digit is 9 so we round up the 1 so the answer is 2000.

Line segment AB is the same length as line segment CD.

A line segment is defined as the part of a line that is divided in parts using two or more end points for easy observation.

From the given diagram, the line segment AB is the same as the line segment CD because the line segment CD was shifted a bit from the point of origin of line segment AB.

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This  is an equilateral triangle, therefore, all the angles  are 60 degrees.

3 times  60 is  180.

180 is the answer

An equation is formed of two equal expressions. The equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation 7*e^0.1t=47 in terms of logarithm in terms of base-e can be solved as,

[tex]7e^{0.1t}=47\\\\e^{0.1t}=\dfrac{47}{7}\\\\0.1 t = {\rm ln}(\dfrac{47}{7})\\\\t = \dfrac{ {\rm ln}(\frac{47}{7})}{0.1}[/tex]

Hence, the equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.

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Answer:B

Step-by-step explanation:

The amoeba splits 24 times, meaning that the number of amoebas will be

2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24

Answer:

The Median

Step-by-step explanation:

i did the quiz

Answer:

A. the median only

Step-by-step explanation:

Answer: <1 = 26°

Step-by-step explanation:

given that:

• <ABD = 66°

• <2 = 14° + <1 (since ''more than' means we add)

• Find <1

Since it is obvious that <ABD is a sum of <1 and <2:

⇒ <ABD = <1 + <2

now we know that <2 is 14° more than <1 and that <ABD = 66°

⇒ 66° = <1 + (14° + <1)

⇒ 66° = <1 + 14° + <1

⇒ <1 = (66° - 14°) ÷ 2

⇒ <1 = 26° ...Answer...

hope that helps...

Answer:

22.50

Step-by-step explanation:

25 percent 30

= (25/100)30

= (25*30)/100

= 750/100 = 7.50

$30 - $7.50 = $22.50

Answer:

The slope would also be 2/7.

Step-by-step explanation:

The two lines are parallel, meaning that they follow the same slope. If line / has a slope of 2/7, then line M must have the same slope as well. I hope this helps! :)

Answer:

4/8

Step-by-step explanation:

15 1/8 - 1/2(4/8) = 14 5/8

Answer:

angle A=30°

Step-by-step explanation:

[tex]9x + 6 + 4x + 6 + 90 = 180 \\ 13x + 102 = 180 \\ 13x = 180 - 102 \\ 13x = 78 \\ \frac{13x}{ 13} = \frac{ 78}{13} \\ x = 6 \\ 4x + 6 = a \\ 4(6) + 6 = a \\ 24 + 6 = a \\ 30 = a[/tex]

Answer:

(x-9)(x-5)

Step-by-step explanation:

x²-5x-9x+45

x(x-5)-9(x-5)

(x-9)(x-5)

Answer:

(x-9)(x-5)

Step-by-step explanation:

To factor this expression, you need to find two values that have a sum of -14 and also have a product of 45. The values -5 and -9 meet these requirements and become the constants in the two factors of the expression,

x2 − 14x + 45 = (x − 9)(x − 5).

Answer:

yes

Step-by-step explanation:

2/3=6/9

2/3=2/3

it is because 6 and 9 is divided by 3

Answer:

59% chance

Step-by-step explanation:

Statistics from the past ten years predict that the chance of rain on any single day in April in Asha’s hometown is 41%. If Asha’s birthday is April 10, what is the chance of it not raining on Asha’s birthday?

Asha's birthday in in April. The chance of rain on any single day in April is 41%. So, there is a 41% chance of rain.

But, that's not what the problem is asking for. The problem is asking for the chance of not raining. To solve for this, we use simple algebra.

100%(all of the time) - 41%(how much it happens) = 59%

The 59% is the chance of it not raining on Asha's birthday.

Hope this helps! Happy birthday, Asha!

Answer:

Step-by-step explanation:

Answer:

x ≤ 1/2

Step-by-step explanation:

Domain:  input values (x-values)

We cannot take a square root of a negative number, therefore

3 - 6x ≥ 0

Solving the inequality:

⇒ 3 - 6x ≥ 0

⇒ 3 ≥ 6x

⇒ 1/2 ≥ x

⇒ x ≤ 1/2

Therefore, the domain is x ≤ 1/2

The length of the chord AC in the circle is 24 units.

Chords are line segment joining any two sides of a circumference of a circle.

The radius of a circle is half of diameter of the circle.

Therefore, a radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.

Hence, the radius that runs through M is perpendicular to the chord AC. Therefore, the chord AC is divided into two halves namely AM and MC.

Hence,

AC = AM + MC

AC = 12 + 12

AC = 24 units

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The total amount Sam will pay in all will be $2,400,000

From the question, we are to determine the interest Sam pays in all

Using the simple interest formula,

I = PRT

From the given information,

P = $2,000,000

R = 5% = 0.05

T = 4

Putting the parameters into the formula,

I = $2000000 × 0.05 × 4

I = $400000

The interest Sam will pay is $400,000

The total amount Sam will pay in all will be $2,000,000 + $400,000

= $2,400,000

Hence, the total amount Sam will pay in all will be $2,400,000

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Answer:

Step-by-step explanation:400000

The value of sin⁻¹ (sin 17°) is 17° or 17 degree after applying the trigonometric identity sin⁻¹ (sinx) = x

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

= sin⁻¹ (sin 17°)

The above expression represents an angle.

Let's suppose the angle is x and sin of x is sinx

sinx is a ratio of side opposite to the angle to hypotenuse.

If we take sin inverse of sinx we get an angle of x.

sin⁻¹ (sinx) = x

sin⁻¹ (sin 17°) = 17 degree

Thus, the value of sin⁻¹ (sin 17°) is 17° or 17 degree after applying the trigonometric identity sin⁻¹ (sinx) = x

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Applying the difference, it is found that the other trinomial could be given by: 8x² + 9x - 9.

We are working with second degree trinomials, hence:

Hence:

ax² + bx + c - (3x² - 2x + 7) = 5x² + 11x - 16.

(a - 3)x² + (b + 2)x + c - 7 = 5x² + 11x - 16.

Then:

Then, the trinomial is:

8x² + 9x - 9.

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Answer:

5x + [tex]\frac{1}{8}[/tex]y = 3/8

Step-by-step explanation:

Add [tex]\frac{5x}{8}[/tex] to both sides

[tex]\frac{5x}{8}[/tex] + y = 3

Divide both sides by 8

5x +  [tex]\frac{1}{8}[/tex]y = 3/8

Step-by-step explanation:

standard form is given by Ax + By = C

hence,

the answer is:

5x + 8y = 24

Answer:

a 75% chance the weather will stay dry

Step-by-step explanation:

3/4

Answer:

[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]

Step-by-step explanation:

Accorded to trigonometric formula, we know that:

[tex]\displaystyle \large{\cos \theta = \dfrac{x}{r}}\\\\\displaystyle \large{\csc \theta = \dfrac{1}{\sin \theta} = \dfrac{1}{\frac{y}{r}} = \dfrac{r}{y}}\\\\\displaystyle \large{\tan \theta = \dfrac{\sin \theta}{\cos \theta} = \dfrac{y}{x}}[/tex]

We know what x and y are but not yet knowing what r is. We can find r (radius) using the formula:

[tex]\displaystyle \large{r=\sqrt{x^2+y^2}}[/tex]

Input x = -3 and y = 5 in.

[tex]\displaystyle \large{r=\sqrt{(-3)^2+(5)^2}}\\\\\displaystyle \large{r=\sqrt{9+25}}\\\\\displaystyle \large{r=\sqrt{34}}[/tex]

Hence, radius is √34 and we know all we need now. Substitute x = -3, y = 5 and r = √34 in respective areas.

[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]

These are the answers to your question. Please let me know if you have any questions regarding my answer or explanation!