Given the function:

g(x)=8-2.5x

Find the following values.

a) g(6)

b) g(0)

c) g(-6)

Answer:

y= -3x + 5

Step-by-step explanation:

m= (y2-y1)/(x2-x1)

m= [8-(-4)]/(-1-3)

m=12/-4

= -3

y= mx + b

-4=(-3)(3) + b

-4=9+b

b=5

therefore, y= -3x+5

Answer:

I would say yes they are

Step-by-step explanation:

because you multiply the small one's numbers by 2 and get the big triangle

Answer:

they are similar! :)

Step-by-step explanation:

the best way to figure this out is just by looking to see if they have anything in common. in this case, the larger figure is just two times more on each side than the smaller figure.

Answer:2

Step-by-step explanation:25 students per a teacher and 33 students per a tutor.if the academy has 77student they need 2 tutors

Answer:

178

Step-by-step explanation:

235-113=122

122+56=178

Answer:

178 books

Step-by-step explanation:

235 minus 113 books that werr checked out and plus 56 books that came back in total it's 178, if nobody stole anything :)

Answer:

y = -35x -3

Step-by-step explanation:

We can use the formula y = mx + c to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y-intercept

From these, they have already given the slope of the line.

m ⇒ -35

And now we have to find the c ( y-intercept ) of the line using the given coordinate,

( 0 , -3 ) ⇒ ( x , y )

So, to find the y-intercept you have to replace x, y & m with 0, -3 & -35 respectively, and solve for c.

Let us solve it now.

y = m x + c

-3 = -35 × 0 + c

-3 = 0 + c

-3 = c

And now we can write the equation of the line like this.

y = m x + c

y = -35x -3

Answer:

Equation of line is given as y =mx + c, where m is the slope and c is the y-intercept.

Since slope is -35, equation of line is y = -35x + c.

Substitute (0,-3) into equation to find c.

-3 = -35(0) + c

c = -3

Hence, equation is y = -35x - 3.

Answer: I think the width is 7.

Step by step explanation:

So let's say the length is 12. This means I need to subtract 5 from it, since the width is 5 inches less than the length. Now that we know this, that means the width is 7, which is the area.

I hope this helps.

Arithmetic, Common Difference = -9

The Correct option is (b).

What is Common Difference?

The common difference of an arithmetic sequence is the difference between any of its terms and its previous term. An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same amount. The number added (or subtracted) at each stage of an arithmetic sequence is called the "common difference", because if we subtract (that is if you find the difference of) successive terms, you'll always get this common value. Most often, "d" is used to denote the common difference.

Given,

x =    1     2      3      4

f(x)=  81   72   63    54

Now, According to the question:
2nd term - 1st term = 72 - 81 = -9

3rd term - 2nd term = 63 - 72 = -9

4th term - 3rd term  = 54 - 63 = -9

Hence, Arithmetic, Common Difference = -9

The Correct option is (b).

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Answer:

define the unknown quantity as =variable. Then use the given info to write down an equation in terms of the unknown quantity. At the end, solve the equation for the unknown.

Answer: 9633.4 cubic meters

I only assumed the shape and length, height, width, etc. so this is my best guess. Please provide with a three dimensional shape of the object being calculated and specify which measurements are the length, height, width, depth, or circumfrence. I will answer it right away :)

Answer:

12600 yd^3

Step-by-step explanation:

The equation to finding the volume of 3 dimensional shapes only including cubes, and rectangles.

L * W * H = V

Which means Length multiplied by width, multiplied by height.

So in this instance:

35 * 24 = 840 * 15 = 12600.

Hope this answers your questions.

If so please make brainliest.

Also if it does feel free to ask me any other questions needed.

Answer:

Step-by-step explanation:

5/2

Answer: f(x)= 2x-3

Step-by-step explanation: The formula for slope is y=mx+b, where m is equal to the slope of the line and b is equal to the y-intercept. We can find the slope by looking at the line OR solving algebraically using the following calculations:

(y2-y1)/(x2-x1)

Pick 2 points on the line and plug in.

(x1,y1)-->(2,1) and (x2,y2)-->(3,3)

(3-1)/(3-2)=2/1=2

So, the slope of the line is 2. m=2.

To find the y-intercept, we can solve algebraically or look at the graph.

y=2x+b

Plug in a point from the graph to find b, the y-intercept.

3=2(3)+b

3=6+b

-3=b

So, the y-intercept is b.

Now, we plug our values into the slope intercept equation, y=mx+b

y=2x-3

Again, you look look at the graph and see where x=0 is to find the y intercept. To find the slope you can use rise/run and count to see that to get from one point on the graph to the next, you count up 2 (rise 2) and to the right 1 (run 1) which gives you 2/1. 2/1 is equal to 2, giving you the slope of 2.

Hope this helped :))

Answer:

see below

Step-by-step explanation:

the point-slope equation is

y-1 = 3/2 (x+4)

Answer:

[tex]y=\frac{3}{2}x+7[/tex]

Step-by-step explanation:

To write the equation of a line, two information are needed.

The slope can be calculated using the gradient formula as long as two pairs of coordinates are given. This question provides the slope, hence we can substitute its value into the equation right away.

In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept. The slope gives us the steepness of the line, while the y-intercept is the y value in which the line cuts through the y-axis (vertical axis).

y= mx +c

Given that slope= [tex]\frac{3}{2}[/tex], m= [tex]\frac{3}{2}[/tex].

Substitute the value of m:

[tex]y=\frac{3}{2}x+c[/tex]

Next, find the value of c by substituting a pair of coordinates.

When x= -4, y= 1,

[tex]1=\frac{3}{2} (-4)+c[/tex]

1= -6 +c

Add 6 to both sides:

c= 1 +6

c= 7

Substituting the value of c:

[tex]\bf{y=\frac{3}{2}x +7 }[/tex]

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Answer: 54%

Step-by-step explanation:

24 pieces make up the solution to this puzzle.

I assume the query is how many pieces does she receive.

I'll respond to it. Leave a note if it is incorrect.

6 pieces will be produced from 1 foot, each measuring 1/6 of a foot (12/6 = 2 inches).

4 feet will provide 24 pieces (4 * 6).

24 pieces make up the solution to this puzzle.

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The probabilities from the venn diagram are:

Let A be the event that the Mechanic is AC repairman and T be the event that he does tune ups.

The probability that he does tune ups is:

Hence the required probability is given by:

Hence the probability is 2/3.

The angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L which is determined by the triangle inequality theorem.

When two lines intersect at a location, vertical angles are generated. They are always equal to each other.

The length of each side of the given triangle LMN is shown below.

LM = 18 cm

MN = 29 cm

LN = 20 cm

According to the triangle inequality theorem, in a triangle, the largest angle is the one opposite to the longest side of the triangle.

Therefore, in triangle LMN, we have the greatest angle as angle ∠ L

And the smallest angle is ∠ N

Arrange the angles in ascending order,

angle ∠ N < angle ∠ M < angle ∠ L

Thus, the angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L.

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From the histogram of the distribution, it is found that Zoe is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

An histogram is a graph that shows the number of times each element of x was observed in the distribution. When the input is an interval of values, as is the case in this problem, it shows the number of observations that is in each interval.

Hence, from the histogram in this distribution, it is found that:

75 is a greater amount than 50, hence Zoe's statement is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

The complete problem is given by the image at the end of the answer.

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Answer:

slope = - 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

Answer:

-1, equation is y=-x+2

Step-by-step explanation:

Check the picture below.

so from the picture we can pretty much tell two solutions or zeros and another point where it passes up above, so

[tex]\begin{cases} x=-1\implies &x+1=0\\\\ x=7\implies &x-7=0 \end{cases}\hspace{8em} \begin{array}{llll} a(x+1)(x-7)=0\\\\ a(x+1)(x-7)=y \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=5\\ y=3 \end{cases}\implies a(5+1)(5-7)=3 \\\\\\ a(6)(-2)=3\implies -12a=3\implies a=\cfrac{3}{-12}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-\cfrac{1}{4}(x+1)(x-7)=y\implies -\cfrac{1}{4}\stackrel{F~O~I~L}{(x^2-6x-7)}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{3x}{2}+\cfrac{7}{4}=y \end{array}}~\hfill[/tex]

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Firstly, we needt to identify the coordinates of the vertices of the quadilateral

Afterwards, we then perform the translation

The translation simply means we add 2 to the x-value and add 4 to the y-value

So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)

Let us identify the vertices;

K'

K (-4,-2)

L (-1,-2)

M (-1,-5)

N (-4,-5)

After translation, we have;

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Answer: (D)

the answer would be D

Step-by-step explanation:

The median will be used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean.

The standard deviation indicates; how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency, then the standard deviation should be used as the spread.

If the data is symmetrical, then the mean is the measure of central tendency; and the standard deviation is the best spread to use.

If the data is asymmetrical, the median is the best measure of central tendency; and the inter-quarterly range is the best spread to use.

The median will be used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.

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Answer: This is a linear pair of angles because they are two adjacent angles that have a common side and whose other sides point in opposite directions.

Answer:

  20 m

Step-by-step explanation:

You want to know the uniform width of a lawn around a 120 m by 80 m building such that the area of the lawn is equal to the area of the building.

Let x represent the width of the lawn. Then the dimensions of the area that includes the lawn and building will be (120 +2x) meters by (80 +2x) meters. We want that area to be equal to twice the area of the building:

  (120 +2x)(80 +2x) = 2(120·80)

Dividing by 4 gives a slightly simpler equation.

  (60 +x)(40 +x) = 60(80)

  2400 +100x +x^2 = 4800 . . . . eliminate parentheses

  x^2 +100x -2400 = 0 . . . . . . subtract 4800 and put in standard form

  (x +120)(x -20) = 0 . . . . . . . factor

Values of x that make the factors zero are ...

  x = -120, x = 20

Only the positive solution makes any sense in this context.

The width of the lawn must be 20 m.

__

Additional comment

The total area of the plot is ...

  total area = (building area) + (lawn area)

When the lawn area is equal to the building area, then we have ...

  total area = (building area) + (building area)

  total area = 2·(building area)

This is the relation we used in the solution above.

The algebraic expression to find the cost of the gym membership for 6 months is given by 25+6×14.

An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c. Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of algebraic expressions.

Given, the cost of joining membership = $25

The cost of each month = $14

Cost of 6 months = 6 multiplied by 14

Cost of gym membership for 6 months = 25+6×14

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Answer:

1. PQ

2. PQ + qr= pr

3. the arrow going both ways with p q

4. point p

5. the arrowing going one way with p q

Step-by-step explanation:

I took the test