Write a Linear Equation in the form y = mx + b for the following situation: Syd and her friends are washing cars over the summer. Without a membership, each car costs $10 to wash. With a membership, you would pay a $10 flat fee and receive washes for only $4 per car! Which linear equation below reflects the cost per car with a membership? *

Answer:

t is the independent variable of time

Step-by-step explanation:

t is the independent variable of time

9514 1404 393

Answer:

  (b)  y = -5x

Step-by-step explanation:

When "y varies directly as x" the equation for that is ...

  y = kx . . . . . . . for some constant k

The value of k can be found by solving for it:

  k = y/x . . . . . . divide by x

So, the given point (x, y) = (2, -10) tells you the value of k is ...

  k = -10/2 = -5

and the direct variation equation is ...

  y = -5x

_____

Additional comments

There are a couple of other useful facts about direct variation. When you compare the equation to the slope-intercept form equation for a line, ...

  y = mx + b

you see that b=0 and the slope, or rate of change, (m) is the same as k.

The y-intercept of 0 means that the graph of any direct-variation equation must go through the origin. (If it does not, then the variation is not direct.)

Answer:

12 red marbles in the bag

The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Advantages include:

Disadvantages:

Additional expenses include

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Answer:

136in^2

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]

ii. 29 - 5 = 2x

iii. 24 = 2x

iv. x = 24/2

v. x = 12

Given:

The terms of a sequence are:

[tex]-6,-\dfrac{11}{2},-5[/tex]

To find:

The number of terms whose sum is -25.

Solution:

We have, the given sequence:

[tex]-6,-\dfrac{11}{2},-5[/tex]

Here, the first term is -6.

[tex]-\dfrac{11}{2}-(-6)=-5.5+6[/tex]

[tex]-\dfrac{11}{2}-(-6)=0.5[/tex]

Similarly,

[tex]-5-(-\dfrac{11}{2})=-5+5.5[/tex]

[tex]-5-(-\dfrac{11}{2})=0.5[/tex]

The difference between consecutive terms are same. So, the given sequence is an arithmetic sequence with common difference 0.5.

The sum of n terms of an arithmetic sequence is:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Where, a is the first term, d is the common difference.

Putting [tex]S_n=-25,a=-6,d=0.5[/tex], we get

[tex]-25=\dfrac{n}{2}[2(-6)+(n-1)0.5][/tex]

[tex]-50=n[-12+0.5n-0.5][/tex]

[tex]-50=-12.5n+0.5n^2[/tex]

[tex]0=0.5n^2-12.5n+50[/tex]

Splitting the middle term, we get

[tex]0.5n^2-2.5n-10n+50=0[/tex]

[tex]0.5n(n-5)-10(n-5)=0[/tex]

[tex](0.5n-10)(n-5)=0[/tex]

Using zero product property, we get

[tex](0.5n-10)=0[/tex] and [tex](n-5)=0[/tex]

[tex]n=\dfrac{10}{0.5}[/tex] and [tex]n=5[/tex]

[tex]n=20[/tex] and [tex]n=5[/tex]

Therefore, the sum of either 5 or 20 terms is -25.

According to the information the amount of insurance would be $66,160, the amount of coverage for personal property would be $41,350, the amount of coverage for loss of use would be $16,540 and the amount of coverage for garage would be $8,270.

To calculate the amount of each insurance we have to take into account the main value ($82,700) and the percentage of each insurance. Then, we have to calculate every percentage value as shown.

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Comparing the parabola's equation to the formula [tex]y = ax^2 + bx + c[/tex] in standard form is the first step. In step 2 Apply the formula h = -b/2a to find the vertex's x-coordinate. In step 3 Substitute x = h in the expression [tex]y = ax^2 + bx + c[/tex]  to obtain the vertex's y-coordinate (k).

The equation of the parabola's axis of symmetry is the vertex's x-coordinate. The axis of symmetry for a quadratic function in standard form, [tex]y = ax^2 + bx + c[/tex] is a vertical line, [tex]x=b^2a[/tex].

The intersection of two lines or rays that create an angle is known as the vertex of the angle.

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Answer:

A = 0.5 × [ sqrt(17^2 - 15^2) ] × 15 + 0.5 × [ sqrt(25^2 - 15^2) ] × 15 = 210 in^2

The solution to the inequality is (-∞, 4.05) .An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Both equations and inequalities are mathematical phrases created by connecting two expressions.

The equal sign (=) in an equation denotes that the two expressions are regarded as equal.

In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

Given the inequality:

-3(4 – x) 6 < 9 – 2x

Solving the inequality:

(-12 + 3x)6 < 9 - 2x

-72 + 18x < 9 - 2x

20x < 81

x < 4.05

Therefore the solution to the inequality is (-∞, 4.05)

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Answer:

38.13m²

Step-by-step explanation:

We find the area of ;

Rectangule and semicircle

Area of rectangle :

Length * width

Length = 8m ; width = 3m

Area = 8 * 3 = 24m²

Area of semicircle = 1/2 πr²

Radius, r = 3m

A = 1/2 * 3.14 * 3²

A = 1/2 * 3.14 * 9

A = 14.13 m²

Area of patio :

(24 + 14.13)m²

= 38.13m²

Answer:

S= 76, T= 76, U= 104, R= 104

Y=104, V= 104, X= 76, W= 76

Step-by-step explanation:

Opposite Angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent (equal in measure).

U and V are alternating angles

so U and  are 104

i d k the last one am so sorry

Answer:

12 bananas

9 apples

18 pears

Step-by-step explanation:

You are tripling the recipe.

10 x 3 = 3

4 x 3 = 12

3 x 3 = 9

6 x 3 = 18

Answer:

24

Step-by-step explanation:

You just do 6 / 1/4 = 24

Answer:

P(A) * P(B)

.25*.55

.1375

Step-by-step explanation:

P(A) * P(B)

.25*.55

Answer:

The answer is 7/9

Step-by-step explanation:

Had this on my quiz one time

Answer:

7-9

Step-by-step explanation:

The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)

An equation is an expression that shows the relationship between two or more variables and numbers.

Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:

x = [(-7) + (-3)] / 2 = -5

y = [(-2) + (-5)] / 2 = -3.5

Therefore the coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)

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Answer:

20 inches

[tex]c = \sqrt{12 ^{2} + 16 ^{2} } \\ c = \sqrt{400} \\ c = 20[/tex]

Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.

By observing the given options we conclude that the third option is linear and proportional as,

6 ÷ 2 = 3 and 12 ÷ 2 = 6.

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As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.

The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two collinear and an equal marker in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar).  An identity holds true regardless of the value given to the variables.

given

Equation as given:

y = 6 (x - 1/2)(x+3)

To identify the equation's graph's y-intercept

Put x = 0 in place of it in the equation.

y = 6 (0 - 1/2)(0+3)

Apply the math operation, then find y.

y = -9

As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.

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Answer:

Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).

The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.

Answer:

[tex]m = 10\sqrt 3[/tex]

[tex]n = 10[/tex]

Step-by-step explanation:

Required

Find m and n

Considering the given angle, we have:

[tex]\sin(60) = \frac{Opposite}{Hypotenuse}[/tex]

This gives:

[tex]\sin(60) = \frac{m}{20}[/tex]

Make m ths subject

[tex]m = 20 * \sin(60)[/tex]

[tex]\sin(60) =\frac{\sqrt 3}{2}[/tex]

So, we have:

[tex]m = 20 *\frac{\sqrt 3}{2}[/tex]

[tex]m = 10\sqrt 3[/tex]

Considering the given angle again, we have:

[tex]\cos(60) = \frac{Adjacent}{Hypotenuse}[/tex]

This gives:

[tex]\cos(60) = \frac{n}{20}[/tex]

Make n the subject

[tex]n = 20 * \cos(60)[/tex]

[tex]\sin(60) =\frac{1}{2}[/tex]

So, we have:

[tex]n = 20 *\frac{1}{2}[/tex]

[tex]n = 10[/tex]

Answer:

.45

Step-by-step explanation:

it wants u to divide 5.40 by 12

HOPE THIS HELPS CHU (≧w≦)

Answer:

Step-by-step explanation:

(99)3 =

(99) x 3 =

(90 + 9) x 3 =

(90) x 3 + (9) x 3 =

90 x 3 + 9 x 3 =

270 + 27 =

297

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Evaluate (99)^3 using suitable identities.

(99)^3 = (100 - 1)^3

since, (a - b)^2 = a^3 - b^3 - 3ab (a-b)

Where,

Now,

(99)^3

=> (100)^3 - (1)^3 - 3(100)(1)(100 - 1)

=> 1000000 - 1 - 3(100)(100 - 1)

=> 1000000 - 1 - 300 (99)

=> 1000000 - 1 - 29700

=> 970299 Ans.