MATHEMATICS HIGH SCHOOL

Select all of the following points that lie on the graph of f(x) = 7 - 3x.(-2, 1)
(-1, 10)
(0, 7)
(1, 5)
(2, 1)

Answers

Answer 1

Answer:

We know that

if the point belongs to the graph, then it must satisfy the given function.

We proceed to verify each of the points

we have

$f(x) = 7 - 3x$

case a) $(-2, 1)$

$x=-2\ny=1$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(-2)$

$f(x) = 13$

$13\neq 1$ --------> the point not lie on the graph

case b) $(-1, 10)$

$x=-1\ny=10$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(-1)$

$f(x) = 10$

$10=10$ --------> the point lie on the graph

case c) $(0, 7)$

$x=0\ny=7$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(0)$

$f(x) = 7$

$7=7$ --------> the point lie on the graph

case d) $(1, 5)$

$x=1\ny=5$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(1)$

$f(x) = 4$

$4\neq 5$ --------> the point not lie on the graph

case e) $(2, 1)$

$x=2\ny=1$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(2)$

$f(x) = 1$

$1=1$ --------> the point lie on the graph

therefore

the answer is

Points that lie on the graph are

$(-1, 10)$

$(0, 7)$

$(2, 1)$

see the attached figure to better understand the problem

Answer 2

Answer:

Answer:

So the person above me got it right (I think) but im small brain and dont wanna read all that so for all the ppl like me the answer is

(-1, 10)

(0, 7)

(2, 1).

Your welcome fellow lazy ppls :3

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Two triangles are similar. The sides of the first triangle are 8,10 and 12. The smallest side of the second triangle is 24. Find the perimeter of the second triangle.

Answers

The perimeter of the second triangle is 90 units.

What are similar figures?

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

$L = k * M$

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

For this case, the two considered triangles are similar. Thus:

A side of first triangle = k times corresponding side of its similartriangle

where k is the scale factor, constant for one pair of similar triangles.

We're given that:

Sides of first triangle are of 8,10 and 12 unit length.

Smallest side of second triangle is of 24 units.

Now, smallest side of first triangle will correspond to the smallest side of its similar triangle.

For first triangle, the smallest side is of 8 units (8 is smaller than 10 and 12, the other two sides).

Let the sides of second triangle be of S = 24 units, M units, and L units.

where M is middle sized side and L is largest side of second triangle.

Let the scale factor be 'k'.

Then, we get:

Smallest side of first triangle = k × smallest side of its similar triangle

$8 = k * 24\n\nk = (8)/(24) = (1)/(3)$

Similarly, middle sized side of first triangle = (1/3) × middle sized side of second triangle

$10 = k * M = (1)/(3) * M\n\nM = 3 * 10 = 30$ units.

Thus, the length of middle sized side of second triangle is 30 units.

Largest side of first triangle = (1/3) × Largest side of second triangle

$12 = k * L = (1)/(3) * L\n\nL = 3 * 12 = 36$ units.

Thus, the length of middle sized side of second triangle is 30 units.

Perimeter of the second triangle = sum of length of its sides

= S + L + M = 24 + 30 + 36 = 90 units.

Thus, the perimeter of the second triangle is 90 units.

Learn more about scale factor here:

brainly.com/question/8765466

so 8*3=24, so multiply all of the sides by 3,
the other 2 are 30 and 36

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

Answers

Answer:

$y = 1200(0.97)^x$

Step-by-step explanation:

Ginny determines that the population is decreasing at an average rate of 3% per year.

So, this is an exponential decay case

Formula : $y = a(1-r)^n$

where a is the amount after n years

a is the initial amount

r is the rate of depreciate

n is the number of years

Now we are given that When she began her study, the frog population was estimated at 1,200.

So, a=1200

r = 3% = 0.03

n =x

Substitute the values in the formula:

$y = 1200(1-0.03)^x$

$y = 1200(0.97)^x$

Hence function represents the frog population after x years is $y = 1200(0.97)^x$

Hello,

$x_(0)=1200$

$x_(1)=(97)/(100)*1200$

$x_(2)=((97)/(100))^2*1200$

$x_(3)=((97)/(100))^3*1200$
...
$x_(n)=((97)/(100))^(n)*1200$

Write an equation of the line
Passes through the points (4,2) and (6,8)

Answers

Work out gradient so change in y/change in x=8-2/6-4=3
So m=3 where m is the slope. As you go across by 1 you go up by 3
I think you would use y-y1=m(x-x1)
Using (4,2) =y-2=3(x-4)
y-2=3x-12
y=3x-10

A student wants to construct the inscribed circle of a triangle. What is the first step he/she should take?a) Construct a circle using one of the vertices of the triangle
b) Construct the perpendicular bisector of each side of the triangle
c) Construct a line parallel to the vertex of the triangle
d) Construct the angle bisector of each angle in the triangle

Answers

The correct answer is:

d) Construct the angle bisector of each angle in the triangle

Explanation:

The incenter, or center of an inscribed circle, is the point where the angle bisectors of a triangle intersect. This means the first thing we will need to construct is the bisector of each angle of the triangle.

Answer:

construct the perpendicular bisector of each side of the triangle

Step-by-step explanation:

The library is to be given 5 books as a gift. the books will be selected from a list of 21 titles. if each book selected must have a different title, how many possible selections are there?

Answers

This is a combination problem. Order does not matter and the books are all different. You would write this as 21C5 or $\tbinom{21}{5}$ . Combinations are not fractions.

The answer is $(21 * 20 * 19 * 18 * 17)/(1 * 2 * 3 * 4 * 5)$

which = 20349 different ways these books can be chosen.

Answer:

20,349.

Step-by-step explanation:

We have been that a library is to be given 5 books as a gift. the books will be selected from a list of 21 titles.

We will combinations to solve our given problem.

$_(r)^(n)\textrm{C}=(n!)/(r!(n-r)!)$

Different ways to choose 5 books from 21 tiles:

$_(5)^(21)\textrm{C}=(21!)/(5!(21-5)!)$

$_(5)^(21)\textrm{C}=(21!)/(5!(16)!)$

$_(5)^(21)\textrm{C}=(21*20*19*18*17*16!)/(5*4*3*2*1*(16)!)$

$_(5)^(21)\textrm{C}=(21*19*18*17)/(3*2)$

$_(5)^(21)\textrm{C}=(21*19*3*17)/(1)$

$_(5)^(21)\textrm{C}=20,349$

Therefore, there are 20349 possible selections.

For a given recipe, 12 cups of flour are mixed with 24 cups of sugar. How many cups of sugar should be used if 21 cups of flour are used?Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x. PLEASE ANSWER THIS QUICK

Answers

42 cups of sugar should be used if 21 cups of flour are used

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

For a given recipe, 12 cups of flour are mixed with 24 cups of sugar

We need to find cups of sugar should be used if 21 cups of flour are used

Let us consider x as cups of sugar should be used if 21 cups of flour are used

Let us form an equation to find x

12/24=21/x

Apply cross multiplication

12x=21×24

12x=504

Divide both sides by 12

x=504/12

x=42

Hence, 42 cups of sugar should be used if 21 cups of flour are used

To learn more on Ratios click:

brainly.com/question/13419413

#SPJ2

Answer:

33 cups of sugar should be used

Step-by-step explanation:

subtract 12 from 21 then add that answer to 24 and you get 33 so 33 cups of sugar should be used

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Select all of the following points that lie on the graph of f(x) = 7 - 3x.(-2, 1) (-1, 10) (0, 7) (1, 5) (2, 1)

Answers

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What are similar figures?

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What is Ratio?

Select all of the following points that lie on the graph of f(x) = 7 - 3x.(-2, 1)
(-1, 10)
(0, 7)
(1, 5)
(2, 1)