Find the equation of the line formed made by joining the pints (-2,-4),(-8,10)

Answer:

x = 10

Step-by-step explanation:

smaller triangle / bigger triangle = 20 / 28

hence,

3x / (4x+2) = 20/28

28(3x) = 20(4x+2)

84x = 80x + 40

4x = 40

x = 10

Answer:

1. a. 2

b. -½

c. y - 3 = -½(x - 8) => point-slope form

y = -½x + 7 => slope-intercept form

2. a. -1

b. 1

c. y - 5 = 1(x - 3) => point-slope form

y = x + 2 => slope-intercept form

Step-by-step explanation:

1. (8, 3) and (10, 7):

a. The gradient for the line joining the points:

Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Let,

[tex] (8, 3) = (x_1, y_1) [/tex]

[tex] (10, 7) = (x_2, y_2) [/tex]

Plug in the values

Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]

Gradient = [tex] \frac{4}{2} [/tex]

Gradient = 2

b. The gradient of the line perpendicular to this line = the negative reciprocal of 2

Negative reciprocal of 2 = -½

c. The equation of perpendicular line if it passes through the first point, (8, 3):

Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).

Where,

(a, b) = (8, 3)

Slope (m) = -½

Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).

Thus:

y - 3 = -½(x - 8) => point-slope form

We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:

Thus:

y - 3 = -½(x - 8)

y - 3 = -½x + 4

y - 3 + 3 = -½x + 4 + 3

y = -½x + 7

2. (3, 5) and (4, 4):

a. The gradient for the line joining the points:

Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Let,

[tex] (3, 5) = (x_1, y_1) [/tex]

[tex] (4, 4) = (x_2, y_2) [/tex]

Plug in the values

Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]

Gradient = [tex] \frac{-1}{1} [/tex]

Gradient = -1

b. The gradient of the line perpendicular to this line = the negative reciprocal of -1

Negative reciprocal of -1 = 1

c. The equation of perpendicular line if it passes through the first point, (3, 5):

Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).

Where,

(a, b) = (3, 5)

Slope (m) = 1

Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).

Thus:

y - 5 = 1(x - 3) => point-slope form

We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:

Thus:

y - 5 = 1(x - 3)

y - 5 = x - 3

y - 5 + 5 = x - 3 + 5

y = x + 2

The quotient of 40 and 5

40÷5=8

=> Product of that number with 7 and 8

So number to find is : 7x8=56

The product of 7 and the quotient of 40 divided by 5 is 56.

The quotient is the result which is derived by the division of two numbers.

For example, the quotient of 30 divided by 3 is 10.

The product is the multiplication of two numbers which is written as a*b.

For example, the product of 8 and 9 is 72.

Here given we have to calculate the product of 7 and the quotient of 40 divided by 5.

The quotient of 40 divided by 5 is 40/5= 8

The product of 7 and The quotient of 40 divided by 5= 7*8= 56

Therefore the product of 7 and the quotient of 40 divided by 5 is 56.

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Answer:

r=-11

Step-by-step explanation:

7r+2=5(r-4)

7r+2=5r-20

2r=-22

r=-11

Answer:

The radius is 3.5cm

Step-by-step explanation:

Given

[tex]V = 192.5cm^3[/tex]

[tex]h = 5cm[/tex]

Required

The volume (V)

The volume of the vase is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]192.5 = 22/7 * r^2 * 5[/tex]

Divide by 5

[tex]38.5 = 22/7 * r^2[/tex]

Multiply by 7/22

[tex]12.25= r^2[/tex]

Take positive square roots

[tex]r = 3.5[/tex]

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Algebra i

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle x^2 = y^2 + z^2[/tex]

Step 2: Solve for x

The calculated measure of the angle QSR is 68 degrees

From the question, we have the following parameters that can be used in our computation:

Angle b = 136 degrees

The measure of angle QSR can be calculated using

QSR = 1/2 * Angle b

substitute the known values in the above equation, so, we have the following representation

QSR = 1/2 * 136 degrees

Evaluate

QSR = 68 degrees

Hence, the measure of angle QSR is 68 degrees

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Step-by-step explanation:

what to find then??.........

Answer:

a. 6m

b. m-2

c. 5(m-2)

d. 6m +5m -10= 56

E. 11m=66

divide by 6: m=6

Maple Granola= 6$

Apple Granola= 4$

Answer:

When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution.

Step-by-step explanation:

6|x| + 25 = 15

Subtract 25 from each side

6|x| + 25-25 = 15-25

6|x|  = -10

Divide by 6

6|x| /6 = -10/6

|x|  = -5/3

There is no solution because the absolute value must be greater than or equal to zero.  This equation has it negative.

1.

C. 5x + 4 - 2x is an algebraic expression

Answer:

4x+y=-32

Step-by-step explanation:

given,

slope (m) = -4

point: (-8,0)

as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]

so,

b = 0-(-4)×(-8) = -32

y=mx+b

or, y=-4x-32

or, 4x+y=-32

(this is the standard form of the line)

Using the equation y - y1 = m(x - x1)

y - 0 = -4(x - (-8))

y = -4(x + 8)

y = -4x - 32

Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

Answer:

[tex]\frac{dy}{dx}[/tex] = 2x + 3

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

y = x² + 3x

[tex]\frac{dy}{dx}[/tex] = 2[tex]x^{(2-1)}[/tex] + 3[tex]x^{(1-1)}[/tex]

   =  2x + 3[tex]x^{0}[/tex]

   = 2x + 3

9514 1404 393

Answer:

  (a)  42.3°

Step-by-step explanation:

Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.

  a² = b² +c² -2bc·cos(A)

  cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050

  A = arccos(777/1050) ≈ 42.3°

The measure of angle A is about 42.3°.

_____

Additional comment

The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.

Answer:

 (a)  42.3°

Step-by-step explanation:

Answer:

Multiply the bottom equation by 2

Answer:

To find the leading coefficient, first expand the function:

[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]

The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².

To find the vertex: see image below

Vertex = (-3, -5)

Answer:

8.75 cups

Step-by-step explanation:

We can write a ratio to solve

5 cups         x cups

----------   = -----------

8 people       14 people

Using cross products

5*14 = 8x

70 = 8x

Divide by 8

70/8 = 8x/8

8.75=x

Step-by-step explanation:

8 people => 5 cups

1 person => 5/8 cups

14 people => 5/8 ×14 = 35/4 cups

ig so this is correct I can give u 93.69% guarantee

9514 1404 393

Answer:

  g(x) = 7x -1

Step-by-step explanation:

The y-coordinate of a function tells how many units the function value lies above the x-axis. Translating that value down 4 units is the same as subtracting 4 from the function value.

  g(x) = f(x) -4

  g(x) = 7x +3 -4

  g(x) = 7x -1

it depends upon a persons pace a average pace is 9-10 mins

Answer:

3/4

Step-by-step explanation:

Let's say that r is the radius of the large circle or the diameter of the small circle.

Area of the big circle is [tex]\pi r^{2}[/tex] .

Area of the small circle is [tex]\pi \frac{r}{2} ^{2} = \pi \frac{r^{2}}{4}[/tex].

The ratio of these 2 circles is 1/4 (calculation in the comments).

So the shaded part represent 1 - 1/4 = 3/4.

Answer:

2:50pm

Step-by-step explanation:

You have to find the least common multiple (LCM) between the 3 times. If you don't know what is the LCM, just say it and I'll try to explain for you in the comments.

10, 35, 40 have as LCM the number 560

So it means they'll leave together 560 minutes after 5:30am

One hour is 60 minutes, so we can divide 560 by 60 to find the time in hours:

560/60 = 9 hours and 20 minutes (the rest of the division will be the minutes)

So, they'll leave together at 2:50pm

Answer:

Step-by-step explanation:

To solve this divide the amount of sugar by the number of dollars:

Per 10dollar she brought=19pounds

Per dollar

[tex]\\ \sf\longmapsto \dfrac{19}{10}[/tex]

[tex]\\ \sf\longmapsto 1.9pounds[/tex]

Answer:

[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]

Answer:

the correct answer is b and I know this because I just had it

Answer:

Hello

Step-by-step explanation:

Axis of symmetry is vertical:

x=-7 (since (-7,-3) is the vertex)

Answer:

x = -7

Step-by-step explanation:

y = (x+7)^2 -3

This is in vertex form

y =a(x-h)^2+k  where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h

y = (x- -7)^2 -3

x = -7

Answer:

Below,...

Step-by-step explanation:

They are saying that if you add a odd number + a odd number than you'd get a even number,... odd + even = odd,... odd x even = even,... and so on,...

Hope it helps,... Chow!

19/25 which is likely

count the ones with y and put that over 25

Answer:

Step-by-step explanation:

Step 1

Find the height:

Step 2

Find the area:

Answer:

x = 7

Step-by-step explanation:

27 = 7x + 6 - 4x      (Given)

27 = 3x + 6             (Simplify)

27 - 6 = 3x + 6 - 6  (Subtract 6 on both sides)

21 = 3x                    (Simplify)

21/3 = 3x/3             (Divide 3 on both sides)

7 = x                        (Simplify)