Identifying linear pairs and vertical angles

Answer:

y = (5/9)x + 2

Step-by-step explanation:

Slope intercept form is

y = mx + b then plug in the values

y = (5/9)x + 2

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Explanation:

Cut the x coefficient (10) in half to get 10/2 = 5. Then square this to get 5^2 = 25.

We'll add 1 to both sides so that the "24" turns into "25", thereby completing the square

x^2 + 10x + 24 = 0

x^2 + 10x + 24+1 = 0+1

x^2 + 10x + 25 = 1

Notice on the left hand side we have something of the form A^2+2AB+B^2 where A = x and B = 5. We can factor this into (A+B)^2, which is the whole reason why we completed the square. You can use the FOIL rule to see how (A+B)^2 expands out into A^2+2AB+B^2. Factoring reverses this process.

This means x^2+10x+25 factors to (x+5)^2 and we now have these steps

(x+5)^2 = 1

x+5 = sqrt(1) or x+5 = -sqrt(1)

x+5 = 1 or x+5 = -1

x = 1-5 or x = -1-5

x = -4 or x = -6 are the two solutions

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Let's check x = -4 to see if it works or not

x^2 + 10x + 24 = 0

(-4)^2 + 10(-4) + 24 = 0

16 - 40 + 24 = 0

-24 + 24 = 0

0 = 0

We get a true equation. That confirms x = -4 is a solution.

If we tried x = -6, then,

x^2 + 10x + 24 = 0

(-6)^2 + 10(-6) + 24 = 0

36 - 60 + 24 = 0

-24 + 24 = 0

0 = 0

That x value is confirmed as well.

If two parallel lines are intersected by a transversal, then internal opposite angles are equal.

So, x° = 61°

=> x = 60

Because they are internal opposite angles.

Answer:

fourth time ...

same problem...

the red line crosses a corner of a box at (4,20) and (2,10)

20/4 = 5

and

10/2 = 5

the slope , constant, gradient for this relationship is "5"

Step-by-step explanation:

Answer:

[tex]x = -6.5c[/tex]

[tex]c = -\frac{x}{6.5}[/tex]

Step-by-step explanation:

In both cases, you are simply isolating the variable you are trying to solve for:

[tex]\frac{-x}{c} = 6.5[/tex]

Solve for x. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply c to both sides, and then divide -1 from both sides:

[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c} * c = 6.5 * c\\-x = 6.5c\\\frac{-x}{-1} = \frac{6.5c}{-1}\\x = -6.5c[/tex]

Solve for c. Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Multiply -1/x to both sides of the equation:

[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c}(c)) = 6.5(c) \\-x = 6.5c\\\frac{-x}{6.5} = \frac{6.5c}{6.5}\\c = -\frac{x}{6.5}[/tex]

Answer:

x = -6.5c

-x/6.5 = c

Step-by-step explanation:

-x/c=6.5

Multiply each side by -c

-x/c * -c=6.5*-c

x = -6.5c

-x/c=6.5

Multiply each side by c

-x/c *c=6.5*c

-x = 6.5c

Divide each side by 6.5

-x/6.5 = 6.5c/6.5

-x/6.5 = c

Answer:

Amy has 12 5¢ coins

Step-by-step explanation:

Let x represent 20¢ coins and y represent 5¢ coins.

Amy has four more 20¢ coins than 5¢ coins. Hence:

[tex]x=y+4[/tex]

And the total value of all her coins is $3.80. Thus:

[tex]0.2x+0.05y=3.8[/tex]

This yields a system of equations:

[tex]\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}[/tex]

We can solve by substitution. Substitute the first equation into the first:

[tex]\displaystyle 0.2(y+4)+0.05y=3.8[/tex]

Distribute:

[tex]\displaystyle 0.2y+0.8+0.05y=3.8[/tex]

Combine like terms:

[tex]\displaystyle 0.25y = 3[/tex]

And divide both sides by 0.25. Hence:

[tex]y=12[/tex]

Thus, Amy has 12 5¢ coins.

Using the first equation:

[tex]x=y+4[/tex]

Substitute:

[tex]x=(12)+4=16[/tex]

Thus, Amy has 16 20¢ coins.

In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.

Answer:

Answer 60

Step-by-step explanation:

The distance from an exterior point to the incircle is equal to the tangent length in both cases.

So the 19 is made up of 9 and 10.

The length of the other portion of the tangent from the end of 19 to the tangent point on the right is also 10.

By a similar argument the lower length of the line to the tangent point is 11.

So you have

9 + 9 + 10 + 10 + 11 + 11

18 + 20 + 22 = 60.

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:

14.32

Step-by-step explanation:

Since this is a right triangle, we can us the Pythagorean theorem

a^2 + b^2 = c^2

3^2 + 14^2 = JL ^2

9+196 = JL ^2

205 = JL ^2

Taking the square root of each side

sqrt(205) = JL

14.31782106 = JL

To 2 decimal places

14.32

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

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

Step-by-step explanation:

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

If a ★ b = 0.5ab, then

0.1 ★ b = 0.5 (0.1) b = 0.05b = 10

==>   b = 10/0.05 = 200

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:

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

A two-way table is such that has two categorical variables and as such, the data are presented in rows and columns.

The correct row and column headings for the given dataset are:

Column: above 60°F, below 60°F, Row: sunny, not sunny

Given that:

[tex]Above\ 60^oF=14[/tex]

[tex]Below\ 60^oF=17[/tex]

[tex]Sunny = 19[/tex]

The two-way table would have the following representations;

The following representations are also possible

Base on the above representations, we can conclude that options (b) is true

Read more about two-way tables at:

https://brainly.com/question/20608299

Answer:

r=-11

Step-by-step explanation:

7r+2=5(r-4)

7r+2=5r-20

2r=-22

r=-11

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:

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:

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

Step-by-step explanation:

The triangle is equilateral (OPTION D) because any triangle that has 3 equal side lengths is an equilateral triangle.

Step-by-step explanation:

Malachy's money = 2x

Paul's money = x

=> 2x - x = 24 => x= 24

Total money = 3x = 72

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

Hi

So:   720 -600 = 120

120 for two years makes   120/2 = 60 in a year .  

60 from 600 is   600/60 = 10  

Interest is  10 %  

If interest in 2% more, then it's 12%.  

I'm sure you can count 12% simple interest for two years, so I let you try.  

good luck.

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:

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

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)

1.

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

Answer:

We want to rewrite:

q^2 = a*(p^2 - b^2)/p

as a linear equation, in the form:

y = m*x + c

So we start with:

q^2 = a*(p^2 - b^2)/p

we can expand the left side to get:

q^2 = (a/p)*p^2 - (a/p)*b^2

q^2 = a*p - (a/p)*b^2

Now we can ust define:

a*p = c

Then we can replace that to get:

q^2 = -(a/p)*b^2 + c

now we can replace:

q^2 = y

b^2 = x

Replacing these, we get:

y = -(a/p)*x + c

finally, we can replace:

-(a/p) = m

then we got the equation:

y = m*x + c

where:

y = q^2

x = b^2

c = a*p

m = -(a/p)