Mae Ling earns a weekly salary of $315 plus a 5.5% commission on sales at a gift shop. How much would she make in a work week if she sold $4,700 worth of merchandise?

Each point listed is of the form (x,y). The x coordinate is always listed first. We dont have any repeat x values, so this is enough to conclude we have a function.

If you wanted to, you could graph each point given on the same coordinate grid. Note how none of the points stack on top of each other. Or put another way, note how it is impossible to draw a single straight line through more than one point graphed. This graph passes the vertical line test.

A function is where plugging in any x value leads to exactly one y value.

If you had two points like (5,2) and (5,7) then the input x = 5 leads to more than one output y = 2 and y = 7 at the same time, making this example not a function.

Answer:

C. (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

Step-by-step explanation:

The function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The parent function is:

g(x) = IxI

And we have:

f(x) = I6x - 2I - 7

Rearranging the function:

f(x) = 6Ix - 1/3I - 7

Then, now let's define some transformations:

If we start with g(x), a translation of N units to the right is:

f(x) = g(x - N)

if we start with g(x), a translation of N units up is:

f(x) = g(x) + N

A translation down would be:

f(x) = g(x) - N

And a vertical dilation of scale factor A is written as:

f(x) = A × g(x)

Then in this case we have:

A translation to the right of 1/3 units.

A dilation of scale factor 6.

A translation down of 7 units.

And the axis of symmetry will be when the absolute value part is equal to zero, or when

6Ix - 1/3I = 0

And that is when x = 1/3.

Therefore, the function is (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units.

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Answer:

y=x/2−1/2

Step-by-step explanation:

The equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have given:

Length of Mother manatee = 12 feet.

Let's suppose the length of a baby manatee is 'x'.

So the equation can be framed as:

3x = 12

x = 4 feet

The length of blue whale is = 9(length of mother manatee)

The length of blue whale is = 9(12) = 108 feet

Thus, the equation for baby manatee is 3x = 12 and length is 4 feet and length of blue whale is 108 feet.

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The probability of drawing a red marble out of the bag without looking is 1/3.

The probability of drawing a red marble out of the bag without looking can be calculated by dividing the number of red marbles by the total number of marbles in the bag. In this case, there are 3 red marbles out of a total of 9 marbles, so the probability is 3/9, which simplifies to 1/3.

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]

In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.

coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.

Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].

Answer:

1) Expression is

[tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]

2) The standard form of the expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

3) The expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

Where [tex](n+1)^3[/tex] is the cube of the middle integer

Step-by-step explanation:

1) Given three consecutive integers are n. n+1, and n+2

Now multiplying the three consecutive integers

[tex](n)(n+1)(n+2)=(n^2+n)(n+2)[/tex]

[tex]=n^3+2n^2+n^2+2n[/tex]

[tex]=n^3+3n^2+2n[/tex]

Therefore [tex](n)(n+1)(n+2)=n^3+3n^2+2n[/tex]

Now adding the middle integer to the result of the multiplication.

ie, adding (n+1) to the result of the multiplication [tex]n^3+3n^2+2n[/tex]

[tex](n+1)+(n^3+3n^2+2n)=n+1+n^3+3n^2+2n[/tex]

[tex]=3n+1+n^3+3n^2[/tex]

Therefore [tex](n+1)+(n^3+3n^2+2n)=n^3+3n^2+3n+1[/tex]

2) Expression is [tex]n^3+3n^2+3n+1[/tex]

Now we simplify the above expression

[tex]n^3+3n^2+3n+1=n^3+3n^2(1)+3(n)(1)^2+1^3[/tex]

[tex]=(n+1)^3[/tex]      (by using [tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]  , Here a = n and b=1)

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

3) The expression is

[tex]n^3+3n^2+3n+1=(n+1)^3[/tex]

Where [tex](n+1)^3[/tex] is the cube of the middle integer.

ie, expression is equivalent to the cube of the middle integer

Answer:

The difference is [tex]\frac{3}{4}[/tex] inches.

Step-by-step explanation:

See the attached number line where the worm lengths in inches are plotted.

From the number line plotted in the attached photo, it is clear that the shortest worm has the length of [tex]\frac{3}{4}[/tex] inches and the longest worm has the length of [tex]1\frac{1}{2}[/tex] inches i.e. [tex]\frac{3}{2}[/tex] inches.

Therefore, the difference in length between the shortest and longest worm is [tex](\frac{3}{2} - \frac{3}{4}) = \frac{3}{4}[/tex] inches. (Answer)

The bearing of A from B according to the diagram is 82.86°

Using trigonometric relations ;

B = bearing of A from B

Now we have;

Tan B = 40 /5

Tan B = 8

Take the inverse value of the tangent ;

[tex]B = Tan^{-1} (8) [/tex]

B = 82.86°

Hence, the bearing of A from B is 82.86°

If the area is 10 square meters than double that is area of a rectangle with height = 5m and base of 4m because height • base should produce 20m^2.

Hope this helps.

Answer: base length = 4 metres

Step-by-step explanation:

A = ½bh

10m² = ½ * b * 5m

10 = 5b/2

Cross multiply

20 = 5b

b = 4m

By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0

Here, we have,

To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:

Step 1: Move the constant term to the right side of the equation:

x² - 20x = -100.

Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.

Step 3: Add the result from step 2 to both sides of the equation:

x² - 20x + 100 = -100 + 100.

Simplifying:

x² - 20x + 100 = 0.

Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:

(x - 10)² = 0.

Therefore, by completing the square, the equation x²- 20x + 100 = 0,

we get, (x-10)²=0

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Final answer:

The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.

Explanation:

The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:

We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.

Answer:

w=12.6

Step-by-step explanation:

2w+2(w+3.8)=58

2w+2w+7.6=58

4w+7.6=58

4w=58-7.6

4w=50.4

w=50.4/4

w=12.6

Answer:

0.60

Step-by-step explanation:

Again, we have a 10x10 space, which means there are 100 squares.

In this case, there are 60 shaded squares. This gives the probability of [tex]\frac{60}{100}[/tex] which simplifies to 0.60

Answer:

0.60

Step-by-step explanation:

Because there are 100 squares and 60 out of it is shaded if you chose a random point amongst these 100 square the probability of choosing a shaded one is 60/100 which is equal to 0.60.

Answer: Robert has 22 video games.

Step-by-step explanation:

Let be "r" the number of video games that Robert has and "s" the the number of video games that Samuel has.

Set up a system of equations:

[tex]\left \{ {{r=5s+7} \atop {r+s=25}} \right.[/tex]

You can use the substitution method to solve the system:

- You need to substitute the first equation into the second equation and solve for "s":

[tex](5s+7)+s=25\\\\6s=25-7\\\\s=\frac{18}{6}\\\\s=3[/tex]

- Finally you must substitute the value of "s" into the first equation and evaluate:

[tex]r=5(3)+7\\\\r=22[/tex]

Answer:3

Step-by-step explanation:

5x+7=25

So lets subtract 7 from 25 to get 5x alone...

5x=18

5x/5=x

18/5=3.3

You cant have 0.3 of a video game so the answer is 3

Answer:

Answer 1.) f(x)=0x-4

Answer 2.) f(x)=2/3x+4

Answer 3.) i don't really get this one so sorry

Answer 4.) f(x)= -1/5x+2

hope this helped it took me a while to figure out this but looks like the guy ahead of me beat me to it

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

all you have to do is split the shape in half to create a square and a triangle then for the triangle the equation would be 2*2=4 then divide by 2 witch is 2 the do the square witch is 2*2=4 then you add 4+2=6 and i'm only in 7th grade.

Let us take 'a' in the place of 'y' so the equation becomes

(y+x) (ax+b)

Step-by-step explanation:

Step 1:

(a + x) (ax + b)

Step 2: Proof

Checking polynomial identity.

(ax+b )(x+a) = FOIL

(ax+b)(x+a)

ax^2+a^2x is the First Term in the FOIL

ax^2 + a^2x + bx + ab

(ax+b)(x+a)+bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term  

= ax^2 + a^2x + bx + ab

Step 3: Proof

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

Identity is Found .

Trying with numbers now

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)

((10)+8)(7) =(2*25)+(4*5)+(40)+(16)

(18)(7) =(50)+(20)+(56)

126 =126

Answer:

A

Step-by-step explanation:

Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]

In this sequence,

[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]

Hence,

[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]

Find 56th term:

[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]

The sum of 56 terms is

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]

Answer:

The actual distance is 127 miles.

Step-by-step explanation:

Given:

On a map, the distance from Los Angeles to San Diego is 6.35 cm.

The scale is 1 cm = 20 miles.

Now, to find the actual distance.

Let the actual distance be [tex]x\ miles.[/tex]

And the distance on map is 6.35 cm.

So, 6.35 cm is equivalent to [tex]x\ miles.[/tex]

And as given on the scale 1 cm is equivalent to 20 miles.

Now, to get the actual distance by using cross multiplication method:

[tex]\frac{6.35}{x} =\frac{1}{20}[/tex]

By using cross multiplication we get:

⇒  [tex]127=x[/tex]

⇒  [tex]x=127\ miles.[/tex]

Therefore, the actual distance is 127 miles.

Answer:

$114

Step-by-step explanation:

Sales price = Original Cost - $35

Sales price - $35 = Original Cost

Substitute in known values

$149 - $35 = Original Cost

$114 = Original Cost

Hope this helps :)

Answer:

Step-by-step explanation:

g(h(x))=g(3x + 7). Since h(x)=3x + 7

g(h(x))= 2(3x + 7) - 5

g(h(x))= 6x + 14 -5

=6x +9

Answer:

x<=5

Step-by-step explanation:

Two things

Equation for line: y=mx+b where m is the slope and b is the y-intercept

We have the slope. We just need to find the y-intercept. Plug in the point and the slope and solve for b.

y=mx+b

1=4(-5)+b

b=21

Answer: y=4x+21

Answer:

The area of cardboard required is 40750 cm².

Step-by-step explanation:

Given:

Length (L) = 25 cm

Width (W) = 5 m = 5 × 100 = 500 cm

Height (H) = 15 cm

Area of the cardboard is same as the total surface area of the closed rectangular box.

Total surface area of the rectangular box is given as:

[tex]SA=2(LW+WH+LH)\\\\SA=2(25\times 500+500\times 15+15\times 25)\\\\SA=2(12500+7500+375)\\\\SA=2\times 20375=40750\ cm^2[/tex]

So, the area of cardboard required is 40750 cm².

Answer:

if f(x)=24

24=-12x+72

24-72=-12x

-48=-12x

x=48/12

x=4

so it's (C)

Answer:

x=4; Option C is your answer.

Step-by-step explanation:

Plug in 24:

[tex]f(x)=24\\[/tex]

[tex]24=-12x+72[/tex]

Solve For X:

[tex]-12x+72-72=24-72\\-12x=-48\\\frac{-12x}{-12} =\frac{-48}{-12}\\ x=4[/tex]

Answer:

82

Step-by-step explanation:

Mean of a set of data is simply the average. It's calculated by adding up all the numbers, then divide by how many numbers there are.

57 + 59 + 64 + 72 + 76 + 77 + 77 + 78 + 85 + 87 + 88 + 88 + 88 + 92 + 94 + 96 + 98 + 100 = 1,476

1476/18 = 82

Therefore 82 is the mean of the set of numbers

Answer:

Median = 86

Step-by-step explanation:

the middle of the data set is 85 and 87. to find the median you would do 85+87/2= 172/2 median = 86

Answer:

initial value=2

Step-by-step explanation:

equation of line,

y-[tex]y_1[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex][tex](x-x_1)[/tex]..............(1)

put co ordinate (0,3) and (2,7) in the equation (1)

y-3=[tex]\frac{7-3}{2-0}[/tex](x-0)

y-3=2x

y=2x+3

rate of change of linear equation=[tex]\frac{\partial (2x+3)}{\partial x}[/tex]

[tex]\frac{\partial y}{\partial x}[/tex]=2

hence, initial value=2 answer

Answer:

Step-by-step explanation:

Answer:

x=-5, x=9

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2} -8x-90[/tex]  

equate to zero

[tex]2x^{2} -8x-90=0[/tex]  

so

[tex]2=-1\\b=-8\\c=-90[/tex]

substitute in the formula

[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{784}} {4}[/tex]

[tex]x=\frac{8\pm28} {4}[/tex]

[tex]x=\frac{8+28} {4}=9[/tex]

[tex]x=\frac{8-28} {4}=-5[/tex]

therefore

The solutions are x=-5, x=9