How is the graph of y= 1/3x related to its parent function y=1/x

A)It is horizontally stretched by a factor of 3 and reflected over the x-axis.
B)It is horizontally stretched by a factor of 3 and reflected over the y-axis.
C)It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D)It is horizontally compressed by a factor of 3 and reflected over the y-axis.

Answers

Answer 1

B it is horizontally stretched by a factor of of 3 and reflected over the y

Answer 2

Answer:

itś C on edge :)

Step-by-step explanation:


Related Questions

What does the symbol for factorial function (n) mean

Answers

Answer:

see explanation

Step-by-step explanation:

The meaning of n factorial → n !

n ! = n(n - 1)(n - 2)........ × 3 × 2 × 1

For example

7 !

= 7 × 6 × 5 × 4 × 3 × 2 × 1

Another name for a hexahedron

Answers

Answer: a cube

(you could have looked this up on google that's what I did)

They are making me write an answer with at least 20 characters sorry

Answer:

cube

lol true about the 20 characters

A family has two cars. The first car has a fuel efficuency of 15 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1925 miles, for a total gas consumtion of 75 gallons. How many gallons were consumed by each of the two cars that week?​

Answers

Answer:

x= 35 gallons consumed by 1st car

and y= 40  gallons consumed by 2nd car

Step-by-step explanation:

Fuel efficiency of 1st car = 15 miles per gallon

Fuel efficiency of 2nd car = 35 miles per gallon

Let x= gallons consumed by 1st car

and y= gallons consumed by 2nd car

Total gallons consumed by both cars = 75

so, we can write

x + y = 75

Miles covered by both cars = 1925 miles

and we know, Fuel efficiency of 1st car = 15 miles per gallon

Fuel efficiency of 2nd car = 35 miles per gallon

we can write the equation as

15 x + 35 y = 1925

where x and y are gallons consumed by 1st and 2nd car.

We have two equation now,

x + y = 75                   (1)

15 x + 35 y = 1925     (2)

Multiplying eq(1) with 15 and subtracting eq (1) and 2

15 x + 15 y = 1125

15 x + 35 y = 1925

-       -            -

_______________

0 - 20 y = -800

y= -800 / -20

y = 40

Putting value of y in equation 1

x + y = 75

x + 40 = 75

x= 75 - 40

x = 35

x= 35 gallons consumed by 1st car

and y= 40  gallons consumed by 2nd car

Final answer:

The first car consumed 50 gallons of gas and the second car consumed 25 gallons of gas that week.

Explanation:

Let's denote the number of gallons consumed by the first car as x and the number of gallons consumed by the second car as y. Then, we have the following two equations based on the mileage and the total gas consumption:

The total distance covered by the two cars is given by: 15x + 35y = 1925 The total gas consumption by the two cars is: x + y = 75

To solve these two equations, you can first solve the second equation for x, x = 75 - y, and then substitute it into the first equation: 15(75 - y) + 35y = 1925. This gives you y = 25. So, the second car consumed 25 gallons of gas. As the total gas consumption is 75 gallons, the first car must have consumed 75 - 25 = 50 gallons of gas.

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What is the measure of angle F?
100
130
140
150

Answers

Answer:

140

Step-by-step explanation:

The sum of angles is 360.

9x+14x+4x+90 = 360 => 27x+90 = 360 => 27x = 270 => x = 10 => 14x = 140 => the angle is 140

The measure of angle F is 140

What is a right-angled trapezoid?

Two consecutive right angles make up a right trapezoid, also known as a right-angled trapezoid. The trapezoidal rule employs right trapezoids to calculate the areas under a curve. An obtuse trapezoid has one acute and one obtuse angle on each base, whereas an acute trapezoid has two consecutive acute angles on its longer base edge.

Given

Sum of all angles of trapezoid = 360

9x + 14x + 4x+ 90 = 360

27x + 90 = 360

27x  = 270

x = 10

F = 14x = 14* 10 = 140

Therefore, The measure of angle F is 140.

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The Pythagorean theorem is a2+b2=c2. Solve for b.

Answers

Answer:

b = √c²-a²

Step-by-step explanation:

b² = c² - a²

b = √c²-a²

Final answer:

The Pythagorean theorem, denoted as a² + b² = c², can be rearranged as b = √(c² - a²) to solve for one of the sides of a right triangle. Once the lengths for a and c are known, they can be substituted into the formula to find the length of b.

Explanation:

The Pythagorean theorem, a key geometric principle, can be used to solve for one of the sides in a right triangle given the lengths of the other two. Usually, it's denoted as a² + b² = c², where a and b are the lengths of the triangle's legs, and c is the length of the hypotenuse. In the question, you want to solve for b.

First, let's isolate b in the formula. Rewrite the formula as b² = c² - a². To find the length of b, take the square root of both sides, resulting in b = √(c² - a²).

Now, once you have the values for a and c, you can substitute them into the formula to find b. This application of the Pythagorean theorem can be very useful in various situations where you have a right triangle, and you know the lengths of two of its sides but need to find the length of the third side.

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Find the distance between the points (1,0) and (0,2).

Answers

Answer:

3 points, I believe.  

Step-by-step explanation:

ANSWER

[tex] \sqrt{5} [/tex]

EXPLANATION

The given points are (1,0) and (0,2).

We use the distance formula:

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]

We substitute the given points into the formula to get:

[tex]d = \sqrt{(0-1)^2 +(2-0)^2} [/tex]

We simplify to get:

[tex]d = \sqrt{1+4} [/tex]

[tex]d = \sqrt{5} [/tex]

Therefore the distance between the two points is √5 units.

For v= -5i - 2j, find unit vector u in the direction of v, and write your answer as a linear combination of the standard unit vectors i and j.

Answers

Answer: Third option

[tex]u = -\frac{5\sqrt{29}}{29}i -\frac{2\sqrt{29}}{29}j[/tex]

Step-by-step explanation:

A unit vector [tex]u[/tex] is a vector that has magnitude 1.

To find a unit vector in the direction of the vector v we must first calculate the magnitude of v and then divide the vector v by its magnitude

The vector v is:

v = -5i - 2j

The magnitude of the vector is:

[tex]| v | =\sqrt{(-5)^2 +(-2)^2}\\\\|v|= \sqrt{29}[/tex]

Now we divide the vector v by its magnitude

[tex]u = \frac{1}{\sqrt{29}}v[/tex]

[tex]u = -\frac{5}{\sqrt{29}}i -\frac{2}{\sqrt{29}}j[/tex]

Simplifying we have to

[tex]u = -\frac{5\sqrt{29}}{29}i -\frac{2\sqrt{29}}{29}j[/tex]

Final answer:

To find the unit vector u in the direction of v = -5i - 2j, compute the magnitude of v and then divide each component of v by this magnitude. The result is u = (-5/√(29))i + (-2/√(29))j.

Explanation:

The question involves finding a unit vector in the direction of a given vector v = -5i - 2j. A unit vector is a vector with a magnitude of 1 that points in the direction of a given vector. To find the unit vector u in the direction of v, we first calculate the magnitude of v and then divide each component of v by its magnitude.

Calculate the magnitude of v,  which is |v| = √((-5)² + (-2)²).Find the unit vector u by dividing each component of v by |v|. Thus, u = (-5/|v|)i + (-2/|v|)j.

Upon calculating, the magnitude of v is sqrt(29), so the unit vector is u = (-5/√(29))i + (-2/√(29))j.

Find the surface area 12 ft, 8ft, and 2ft

Answers

Answer:

S = 2((12(8) + 8(2) + 12(2))

= 2(96 + 16 + 24)

= 2(136)

= 272 square feet

IF kjsxpress.com sells 500 cookies on Monday , 300 cookies on Tuesday, 400 cookies on Wednesday, 800 cookies on Thursday, and 200 cookies on Friday, how many cookies will this website have sold in total for the whole week?


Also if they sell 9 gooey chocolate chip cookies and 15 peanut butter blossoms how many cookies will they have sold in total?


marking branliest;) plz check out the website

Answers

Answer: 2200 cookies for the week

24 total for the chocolate chip / peanut butter

Step-by-step explanation:

500 + 300 = 800 + 400 = 1200 + 800 = 2000 + 200 + 2200

9 + 15 = 24

Final answer:

To find the total number of cookies sold for the week, add up the number of cookies sold each day. The total is 2200. When considering both types of cookies, the website will have sold 24 cookies in total.

Explanation:

To find the total number of cookies sold for the whole week, we will add up the number of cookies sold on each day. Using the given numbers, the total number of cookies sold is

= 500 + 300 + 400 + 800 + 200 = 2200.

For the second part, we need to find the total number of cookies sold when considering both gooey chocolate chip cookies and peanut butter blossoms. We add up the number of each type of cookie: 9 + 15 = 24.

Therefore, the website will have sold 2200 cookies in total for the week, and when including both gooey chocolate chip cookies and peanut butter blossoms, they will have sold 24 cookies in total.

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Is y= 3(x-1)^2+3 vertex form?

Answers

Answer:

Yes.

Step-by-step explanation:

The vertex is 1,3. The vertex is in quad 1. The graph is shifted 1 to the right and up 3.

6(2 + x) = 12 + 6x illustrates the

distributive property
commutative property
associative property

Answers

Answer:

Distributive Property

Step-by-step explanation:

6(2 + x) = 12 + 6x illustrates the distributive property.

What is distributive property ?

An algebraic property called the distributive property is utilized to multiply a single value by two or more values contained between parenthesis.

The distributive property of binary operations generalizes the distributive law, which declares that equality exists always accurate in elementary algebra.

Given

6(2+x )

[tex]= 6*2 + 6*x[/tex]

= 12+6x

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Solve and show your work for each question.
What is 0. 45 expressed as a fraction in simplest form?
What is 0.45 expressed as a fraction in simplest form?
What is 0.45 expressed as a fraction in simplest form?

SHOW YOUR WORK

Answers

Answer:

9/20

Step-by-step explanation:

You set the fraction up at first as 45/100. Then you know that 5 goes into each so you divide by 5 [tex]\frac{45}{100} /5[/tex]

45/5=9

100/5=20

You get 9/20, and this is in simplest form.

Answer:Y9/20

Step-by-step explanation:

What is the answer to p-4=-9+p

Answers

Answer: No Solution

Step-by-step explanation:

When you subtract p on both sides, you get -4=-9 and that is not a true statement.

Hope this helps!

The net of a composite space figure is shown below.
A. What figures make up the composite space figure?
B. What is the surface area of the composite space figure? Round your answer to the
nearest square centimeter.

Answers

Answer:

A. What figures?: Hexagonal prism topped by a hexagonal cone

B. 246 sq cm

Step-by-step explanation:

A. What figures?

Imagine you're rolling up all 6 vertical pointy pieces around the base hexagon.  Then you'll have like a crown top with all the triangles.  You can fold these triangles to have their tips meet and form a hexagonal cone...

So, you'll have a hexagonal prism, topped with a hexagonal cone.

B. Surface area.

That's just a matter of calculating the areas of all triangles, rectangles and hexagon of the assembly.

Triangles: base: 4 cm, height: 5 cm, quantity: 6

A = (b * h) / 2 = (4 * 5) / 2 = 10 sq cm

AT = 6 * V = 6 * 10 = 60 sq cm

Rectangles: base: 4 cm, height: 6 cm, quantity: 6

A = b * h = 4 * 6 = 24 sq cm

AR = 6 * V = 6 * 24 = 144 sq cm

Hexagon: side: 4 cm, quantity: 1

Since it's a regular hexagon and we know its side length...

AH =  (3√3 * s²)/2 = (3√3 * 16)/2 = 24√3 = 41.57 sq cm

Then we add everything together:

A = AT + AR + AH

A = 60 + 144 + 41.57 = 245.57 sq cm

Rounded answer: 246 sq cm

Answer:

246 cm²

Step-by-step explanation:

The composite space figure consists of:

One hexagon (side length 4 cm)Six rectangles (4 cm x 6 cm)Six triangles (base 4 cm, height 5 cm)

The surface area is the sum of all the areas of each figure.

Area of a hexagon = ½√(27) s²

Area of a rectangle = wl

Area of a triangle = ½ bh

So the total area is:

A = ½ √(27) (4)² + 6(4×6) + 6(½×4×5)

A = 8√(27) + 204

A ≈ 246 cm²

how to divide decimals

Answers

Answer:

It is easy to divide decimals

Step-by-step explanation

To do it

First: Take an example 5/0.2

Second: Make the division more easier by multiplying the denominator and numerator by 10 ( the number of zeros vary according to the number of places in the decimal part, for example if there where three places in the decimal side the use 1000 to multiply, look at the numer of the decimal places and the numer of zeros in the number to multiply). 5*10/0.2*10 = 50/2

Third: Now divide it normaaly in the example we get 25 as the answer.

I hope you liked the answer.

| 10. Write an equation of a line that is parallel to
the line-3x + 4y = 5 and passes through the
point (2.1)

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange - 3x + 4y = 5 into this form

Add 3x to both sides

4y = 3x + 5 ( divide all terms by 4 )

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{4}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes, thus

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (2. 1) into the partial equation

1 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{1}{2}[/tex]

y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of parallel line

Charlie, a science teacher, worked 10 months out of the year. What percent of the year did he work?

Answers

Answer:

10/12x100%= 83.3%

Step-by-step explanation:

Answer:

83.3%

Step-by-step explanation:

Charlie worked 10 of the 12 months so

[tex]\frac{10}{12}[/tex] × 100 = 83.3333

Approximate the value of V110 to the nearest hundredth. HURRRYYYY PLZZZZZ NOWWWW​

Answers

Answer:

10.49

Step-by-step explanation:

(picture shows)

That would be:

10.49

Hope this helped!

~Just a girl in love with Shawn Mendes

What set of numbers does NOT form a right triangle?
A. 14, 48, 50
B. 15, 20, 25
C. 21, 28, 35
D. 27, 35, 46

Answers

D 27,35,46

You can use the Pythagorean theorem a squared plus b squared equals c squared

the set of numbers that does NOT form a right triangle is option D: 27, 35, 46.

To determine whether a set of numbers forms a right triangle, we need to check if the Pythagorean theorem holds true for them. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's calculate the squares of the sides for each option:

A. 14, 48, 50

14² + 48² = 196 + 2304 = 2500

50² = 2500

B. 15, 20, 25

15² + 20² = 225 + 400 = 625

25² = 625

C. 21, 28, 35

21² + 28² = 441 + 784 = 1225

35² = 1225

D. 27, 35, 46

27² + 35² = 729 + 1225 = 1954

46² = 2116

Now, let's compare the squares of the two smaller sides with the square of the largest side for each option:

A. 2500 = 2500 (Forms a right triangle)

B. 625 = 625 (Forms a right triangle)

C. 1225 = 1225 (Forms a right triangle)

D. 1954 ≠ 2116 (Does NOT form a right triangle)

So, the set of numbers that does NOT form a right triangle is option D: 27, 35, 46.

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Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation?

because both triangles appear to be equilateral
because∠MNL and ∠ONP are congruent angles
because one pair of congruent corresponding angles is sufficient to determine similar triangles
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN

Answers

Answer:

C: because one pair of congruent corresponding angles is sufficient to determine similar triangles

Step-by-step explanation:

on edge! hope this helps!!~ (‐^▽^‐)

The information in the diagram is enough to determine that △LMN ~ △PON using a rotation and dilation because one pair of congruent corresponding angles is sufficient to determine similar triangles. Therefore, option c is the correct answer.

The information in the diagram is enough to determine that △LMN ~ △PON using a rotation about point N and a dilation because one pair of congruent corresponding angles is sufficient to determine similar triangles.

In order to determine that two triangles are similar, you need to establish that their corresponding angles are congruent, and their corresponding sides are in proportion.

In the given scenario, you have △LMN and △PON. The key information is that ∠MNL and ∠ONP are congruent angles. This means that one pair of corresponding angles is equal.

According to the Angle-Angle (AA) similarity theorem, if you have two pairs of corresponding angles that are congruent, the triangles are similar. In this case, you have one pair of congruent corresponding angles, ∠MNL ≅ ∠ONP, which is sufficient to determine that △LMN ~ △PON.

The statement "because one pair of congruent corresponding angles is sufficient to determine similar triangles" is the correct explanation for why △LMN is similar to △PON using a rotation about point N and a dilation.

Therefore, option c is the correct answer.

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Find the slope and y intercept
In simplest form
-7x-4y=-8

Answers

Hey there! :)

-7x - 4y = -8

To find the slope, we must turn this equation into slope-intercept form.

Slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

To get here, we must isolate y by adding 7x to both sides of our original equation.

-7x + 7x - 4y = 7x - 8

Simplify!

-4y = 7x - 8

Then, divide both sides by -4.

-4y ÷ -4y = (7x - 8) ÷ -4y

Simplify!

y = -7/4x + 2

Congrats, we got y isolated! Now, review the slope-intercept form equation to figure out what our slope & y-intercept are.

After reviewing our slope intercept form equation, we can come to the conclusion that -7/4 is our slope because it's in the "m" value slot, and 2 is our y-intercept because it's in the "b" spot.

So, our answer is :

Slope = -7/4

Y-intercept = 2

Hope this helped! :)

Solve the equation for X.

Answers

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}10&-30\\-10&-2\end{array}\right]}[/tex]

Step-by-step explanation:

[tex]X-3\left[\begin{array}{ccc}2&-8\\-4&2\end{array}\right] =\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right]\\\\X-\left[\begin{array}{ccc}(3)(2)&(3)(-8)\\(3)(-4)&(3)(2)\end{array}\right]=\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right]\\\\X-\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]=\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right][/tex]

[tex]X-\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]+\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]=\left[\begin{array}{ccc}4&-6\\2&-8\end{array}\right]+\left[\begin{array}{ccc}6&-24\\-12&6\end{array}\right]\\\\X=\left[\begin{array}{ccc}4+6&(-6)+(-24)\\2+(-12)&-8+6\end{array}\right]\\\\X=\left[\begin{array}{ccc}10&-30\\-10&-2\end{array}\right][/tex]

Given the quadratic equation below, determine which it could represent.
X^2-4x=60

A: A wall in Liza's bedroom has an area of 60 square feet. She covers 4 square feet of the wall with a poster.
B: on Tuesday, a packaging company packed 4 fewer boxes of cashews than they did on Monday. They packed a total of 60 boxes.
C: In a meeting room for a business event, there are 4 fewer chairs laid out in each row than the number of rows. The total number of chairs in the room is 60.
D:Mr.Bass is 4 years older than his sister. The total of their ages is 60 years.

Answers

Answer:

C

Step-by-step explanation:

Correct option is C.

Let x be the number of rows in a meeting room. If there are 4 fewer chairs laid out in each row than the number of rows, then in each row there are x-4 chairs.

The total number of chairs is

[tex]x(x-4)[/tex]

The total number of chairs in the room is 60. Hence,

[tex]x(x-4)=60[/tex]

What is the value of y?
3
4
5
6

Answers

Answer:

It’s 3

Step-by-step explanation:

multiply 3 time 2 and add 4

Since the length of the side labeled 10 and the other side labeled 2y +4 are the same. Set them equal to each other and subtract 4 to the other side and then divide 2 to other side to get y=3. Your welcome.

a circle has a center at (1,-2) and a radius of 4. does the point (3.4,1.2) lie on the circle? justify your answer​

Answers

Answer:

YES

Step-by-step explanation:

If point (3.4, 1.2) lies on a circle, the distance between this point and the center (1, -2) is equal to the radius r = 4.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute:

[tex]d=\sqrt{(1-3.4)^2+(-2-1.2)^2}=\sqrt{(-2.4)^2+(-3.2)^2}\\\\=\sqrt{5.76+10.24}=\sqrt{16}=4=r[/tex]

The point (3.4, 1.2) lies on the circle, and distance between the two is 4 units.

To determine whether the point (3.4, 1.2) lies on the circle with a center at (1, -2) and a radius of 4, we can use the distance formula to calculate the distance between the center of the circle and the given point. If this distance is equal to the radius of the circle, then the point lies on the circle; otherwise, it does not.

The distance formula between two points[tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Let's calculate the distance between the center of the circle (1, -2) and the given point (3.4, 1.2):

[tex]\[ d = \sqrt{(3.4 - 1)^2 + (1.2 - (-2))^2} \]\[ d = \sqrt{(3.4 - 1)^2 + (1.2 + 2)^2} \]\[ d = \sqrt{(2.4)^2 + (3.2)^2} \]\[ d = \sqrt{5.76 + 10.24} \]\[ d = \sqrt{16} \]\[ d = 4 \][/tex]

The calculated distance between the center of the circle and the given point is equal to the radius of the circle, which is 4 units.

What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent and the compound interest earned when you invest the same sum for 2 years at 5 percent ?
The simple interest earned when you invest $1,000 for 3 years at 10 % is $
. The interest compounded when you invest the same sum for 2 years at 5 % is $
.






There are 7 trout fish in a pond,
and the population doubles every year.
Find the population after t years.
arrowBoth

A company buys a machine for $3,000.
The value of the machine depreciates
by 7% every year. Find the value of
the machine after t years.
arrowBoth

The initial population of a colony of ants
is 300. The number of ants increases
at a rate of 1.5% every month. Find the
population of ants after t months.
arrowBoth

A research laboratory is testing a new
vaccine on 300 infected cells. The decay
rate is 1.5% per minute. Find the
number of infected cells after t minutes.
arrowBoth

Answers

Answer:

Part 1) The simple interest earned when you invest $1,000 for 3 years at 10 % is $300

Part 2) The interest compounded when you invest the same sum for 2 years at 5 % is $102.50

Part 3) [tex]f(t)=7(2)^t[/tex]

Part 4) [tex]f(t)=3,000(0.93)^t[/tex]

Part 5) [tex]f(t)=300(1.015)^t[/tex]

Part 6) [tex]f(t)=300(0.985)^t[/tex]

Step-by-step explanation:

Part 1) What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=3\ years\\ P=\$1,000\\r=0.10[/tex]

substitute in the formula above

[tex]I=\$1,000(0.10*3)=\$300[/tex]

Part 2) What will be the compound interest earned when you invest $1,000 for 2 years at 5 percent ?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

I is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\ P=\$1,000\\ r=0.05\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$1,000(1+\frac{0.05}{1})^{1*2}[/tex]  

[tex]A=\$1,000(1.05)^{2}=\$1,102.50[/tex]  

The interest is equal to

[tex]I=\$1,102.50-\$1,000=\$102.50[/tex]  

Part 3) There are 7 trout fish in a pond,  and the population doubles every year.

Find the population after t years.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

In this problem we have

There are 7 trout fish in the pound ----> initial value a=7

The population is double every year ------> the base is b=2

substitute

[tex]f(t)= 7(2)^t[/tex]

Part 4) A company buys a machine for $3,000.  The value of the machine depreciates  by 7% every year. Find the value of  the machine after t years.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

we have

Company buys a machine for $3,000 --> initial value is a=3,000

The value depreciate 7% a year

Since it was decreased by 7% every year, it will become: 100%-7%=93%

the base is 93%, b=0.93

substitute

[tex]f(t)=3,000(0.93)^t[/tex]

Part 5) The initial population of a colony of ants  is 300. The number of ants increases  at a rate of 1.5% every month. Find the  population of ants after t months.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

we have

Initial population of ants is 300----> initial value is a=300

The number of ants increases 1.5% per month.

Since it will increases by 1.5% every month, it will become: 100%+1.5%=101.5%

the base is 101.5%, b=1.015

substitute

[tex]f(t)=300(1.015)^t[/tex]

Part 6) A research laboratory is testing a new  vaccine on 300 infected cells. The decay  rate is 1.5% per minute. Find the  number of infected cells after t minutes.

we know that

This question is about exponent function of the form

[tex]f(x)= a(b)^t[/tex]

where

a is the initial value

b is the base of the exponent.

we have

A research laboratory is testing new vaccine on 300 infected cells

 initial value is a=300

The decay/decrease rate is 1.5% per minute

Since it will decrease by 1.5% every min, it will become: 100%-1.5%=98.5%  

the base is 98.5%, b=0.985

substitute

[tex]f(t)=300(0.985)^t[/tex]

To solve the equation 5x−1=4x−8 , Sasha graphs the functions f(x)=5x−1 and g(x)=4x−8 on the same set of coordinate axes.

Which statement describes the solution of the equation ​ 5x−1=4x−8 ?


The solution of the equation is the y-intercept of the linear equations.

The solution of the equation cannot be found graphically. Sasha should solve the equation algebraically.

The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.





Answers

Answer:

The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

Step-by-step explanation:

These two lines do intersect and do not have the same y intercept so it cannot be the first two options

And since the problem is in term of x only, the third option is true

ANSWER

The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

EXPLANATION

The given functions are:

f(x)=5x-1

g(x)=4x-8

To solve the equation 5x−1=4x−8 graphically, we need to graph f(x)=5x-1 and g(x)=4x-8 on the same graph sheet.

The x-coordinates of the point of intersection of the graphs of the two functions is the solution to the equation:

5x−1=4x−8

The third choice is correct.

**************** :-)

Answers

I think the answer is n-20- first choice.

ANSWER

n-20

EXPLANATION

The terms of the sequence are:

-19,-18,-17,-16,-15,...

The first term of the sequence is

a=-19 and the common difference is d=-18--19=1

The rule is given by:

f(n)=a+d(n-1)

f(n)=-19+1(n-1)

f(n)=-19+n-1

f(n)=n-20.

Therefore the rule for the given sequence is n-20.

The first option is correct.

A water reservoir is in the form of a right circular cone. The cone is 21 ft deep and has a radius of 7ft. Water has collected in the cone to a depth of x ft, and has a radius of 3ft. Find the volume of the water

Answers

Check the picture below.

so notice,  in a cone the height and radius are always at a ratio of each other in a right-triangle, since the water level, in red, makes a similar triangle with the cone's volume, let's use proportions to get "x".

[tex]\bf \cfrac{21}{7}=\cfrac{x}{3}\implies 3=\cfrac{x}{3}\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=3\\ h=\stackrel{x}{9} \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies \stackrel{V=27\pi }{V\approx 84.823}[/tex]

Final answer:

The volume of water in a conical water reservoir can be calculated using the formula for the volume of a cone, substituting the values for the radius and height of the water.

Explanation:

In this problem, we are trying to calculate the volume of water in a water reservoir that is shaped as a right circular cone. We are told that this cone has a depth of 21ft and a radius of 7ft, while the water in the cone has a depth of x ft and a radius of 3ft.

In order to solve this problem, we first need to understand that the volume V of a cone is calculated using the formula, V = 1/3πr²h, where r is the radius and h is the height of the cone. This formula can be applied to determine the volume of water in the cone.

Substituting the given values into the formula, the volume of the water would be as follows: V = 1/3 * π * (3ft)² * x ft.

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45. if m angle r=40 degrees in circle O, what is m angle O
46. in the circle m BC=69 degrees, what is m angle BCP

Answers

Answer:remove the radical and try not to simplify

Step-by-step explanation:

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