What is the initial value of the function represented by this table? (5 points)

Answer:

x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given

x² - x - [tex]\frac{3}{4}[/tex] = 0

Multiply through by 4 to clear the fraction

4x² - 4x - 3 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × - 3 = - 12 and sum = - 4

The factors are + 2 and - 6

Use these factors to split the x- term

4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term

(2x + 1)(2x - 3) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

The solutions are x = 3 and x = -7.

To solve the quadratic equation, we first need to bring it to the standard form of ax2 + bx + c = 0. In the example given, we have the equation x2 + 4x - 21 = 0, where a = 1, b = 4, and c = -21. To find the solutions for x, we will use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).

Substituting the values of a, b, and c into the quadratic formula, we get:

x = (-(4) ± √((4)2 - 4(1)(-21))) / (2(1))

x = (-4 ± √(16 + 84)) / 2

x = (-4 ± √100) / 2

x = (-4 ± 10) / 2

Which gives us two solutions:

x = (6 / 2) = 3

x = (-14 / 2) = -7

Therefore, the solutions to the quadratic equation x2 + 4x - 21 = 0 are x = 3 and x = -7.

Answer: When you multiply by 0.1 it is the same as dividing by 10. So it gives you a product that is less than 37.4.

Answer: Last option.

Step-by-step explanation:

By definition, a relation is a function if and only if each input value has an unique output value.

For this exercise it is important to remember that the input values are the values of "x" and the ouput values are the values of "y"

Knowing this and given the tables attached which  represent the functions [tex]f(x)[/tex], and [tex]g(x)[/tex],, you can identify that:

1. In the table that represents the function [tex]f(x)[/tex], the input value 1 produces the output value 3.

2. In the table that represents the function [tex]g(x)[/tex], the input value 1 produces the output value 3.

Therefore, based on this, you can determine that the input value that produces the same output value for the two functions is:

[tex]x=1[/tex]

The ratio 60:5 can be described as follows :

The ratio expression is a way of expressing the division of numerator by a denominator.

Here,

The total number of students is the numerator = 60

The denominator is the number of students per group = 5

Hence, the quotient is the value of the divison obtained which is (60/2) = 12

Therefore, there are 12 groups of 5 students.

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The common difference is basically the number at which the pattern increases.

A's common difference: 2

B's common difference: 9

C's common difference: 5

answer: A, C, B

Answer:

Part a) The equation for the volume of the film canister is

[tex]32\pi=\pi r^{2}(8)[/tex]

Part b) The radius of the film canister is [tex]2\ cm[/tex]

Step-by-step explanation:

The complete question is

A film canister in the shape of a cylinder has a height of  8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius of the circular base

h is the height of the cylinder

we have

[tex]V=32\pi\ cm^3[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

[tex]32\pi=\pi r^{2}(8)[/tex]

[tex]32\pi=8\pi r^{2}[/tex]

Simplify

Divide by 8π both sides

[tex]4=r^{2}[/tex]

square root both sides

[tex]r=2\ cm[/tex]

Answer:

(4, -23)

Step-by-step explanation:

To see if a point is on the equation, substitute its "x" and "y" coordinates into the equation. The points are written as (x, y). If the left side equals the right side, the point is on the line. (LS = RS)

Try (4, 12)

y = -5x - 3

12 = -5(4) - 3

12 = -20 - 3

12 = -23

LS ≠ RS

The point is not on the line.

Try (4, -12)

y = -5x - 3

-12 = -5(4) - 3

-12 = -20 - 3

-12 = -23

LS ≠ RS

The point is not on the line.

Try (4, 23)

y = -5x - 3

23 = -5(4) - 3

23 = -20 - 3

23 = -23

LS ≠ RS

The point is not on the line.

Try (4, -23)

y = -5x - 3

-23 = -5(4) - 3

-23 = -20 - 3

-23 = -23

LS = RS

The point (4, -23) is on the line.

The missing choices are:

A. C = 9h + 4

B. C = 4h + 9

C. C = 4(h - 1) + 9

D. C = 13h

C = 4(h - 1) + 9 represents this situation ⇒ answer C

Step-by-step explanation:

The given is:

We need to find which of the following represents this situation

∵ The cost of renting a bicycle is $9 for the first hour

∵ Another $4 for each  additional hour

∵ h represents the number of hours

- Add the cost of the first hour to the cost of the remaining hours

∵ The remaining hours = h - 1

∴ The cost of the remaining hours = 4(h - 1)

∵ C is the cost of renting the bicycle for h hour

- Add 9 to 4(h - 1) to find C

∴ C = 4(h -1) + 9

C = 4(h - 1) + 9 represents this situation

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Answer:

The relationship between the number of scoops and the number of dogs is not proportional

Step-by-step explanation:

Let

x ----> the number of scoops

y ----> the number of dogs

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

First situation

You prepare 8 scoops of dog food for 4 dogs

x=8, y=4

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{4}{8}=0.5[/tex]

Second situation

You prepare 12.5 scoops of dog food for 5 dogs

x=12.5, y=5

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the values of x and y

[tex]k=\frac{5}{12.5}=0.4[/tex]

Compare the values of k

[tex]0.5\neq 0.4[/tex]

The values of k are not equal

therefore

The relationship between the number of scoops and the number of dogs is not proportional

Answer:

y=-4x+1/2

Step-by-step explanation:

2y+8x=1

2y=1-8x

2y=-8x+1

y=-8/2x+1/2

y=-4x+1/2

Answer:

2

Step-by-step explanation:

You have to find unit rate (I feel like this is wrong, sorry in advance!)

Answer:

she passes 2 per 1 kilometer

Step-by-step explanation:

24 / 2 = 12

12 x 2 = 24

24 / 12 = 2

Answer:

Step-by-step explanation:

10, 20, 30, 40

Answer:25

Answer:

1,215

Step-by-step explanation:

39/13=3

45*(3)^x

45*(3)^3

45*(27)

1,215

Final answer:

To find the number of foxes after 39 years, use the population growth function y = 45 *[tex]3^x[/tex]. Since 39 years corresponds to 3 periods of 13 years each, the equation becomes y = 45 * [tex]3^3,[/tex] resulting in 1215 foxes.

Explanation:

The student has asked how many foxes will there be after 39 years, given the population growth function y equals 45 times 3 to the x power, where x represents the number of 13-year periods. To solve this, we calculate the value of x by dividing the total time of population observation (39 years) by the duration of one population tripling period (13 years). This gives us:

x = 39 years / 13 years/period = 3 periods

We then substitute x into the equation and get:

y = 45 *[tex]3^3,[/tex] = 45 * 27 = 1215 foxes

Therefore, there will be 1215 foxes in the wildlife preserve after 39 years.

Working together three workers would take 1 hour 36 minutes to finish the job

Solution:

Given that first worker can finish the job in 8 hours

So in one hour, first worker can do [tex]\frac{1}{8}[/tex] th of the work

The second worker can finish the job in 4 hours

So in one hour, second worker can do [tex]\frac{1}{4}[/tex] th of the work

The third worker can also finish the job in 4 hours

So in one hour, third worker can do [tex]\frac{1}{4}[/tex] th of the work

The three workers working together in 1 hour can do:

[tex]\frac{1}{8} + \frac{1}{4} + \frac{1}{4} = \frac{1 + 2 + 2}{8} = \frac{5}{8}[/tex]

The three worker can thus do [tex]\frac{5}{8}[/tex] th of the work in one hour

Hence the three of them together can finish the work in [tex]\frac{8}{5}[/tex] hours

[tex]\frac{8}{5} = 1\frac{3}{5}[/tex] hours

Thus working together three workers would take 1 hour 36 minutes to finish the job

Answer: -23 feet to sea level

Step-by-step explanation:

start with 0 (sea level)

he dives twenty, -20

he dives ten more, -20 - 10 = -30

he swims up twelve feet; -18

he goes down 5 more; -23 feet

Answer:

20 + 10 = 30

30 - 12 = 18

18 + 5 = 23

His elevation is 23ft below the sea level

Answer:

  36 objects

Step-by-step explanation:

You want the value of x when t=9, so you're solving ...

  9 = 0.007x^2 +0.003x

  9 = 0.007(x^2 + 3/7x)

From here, we observe that an approximation is probably sufficient.

 9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2

  x ≈ 3/√.007 ≈ 35.9 ≈ 36

We can check:

  .007(36)(36 3/7) = 9.18

  .007(35)(35 3/7) = 8.68

To keep the computer busy for 9 seconds, it needs to sort 36 objects.

The Answer is:

The histogram on Answer C.

The histogram will reflect the frequency of shirt sizes as shown in the dot plot, with bars representing the number of shirts for each size range; no bar for size 8, bars of height 1, 3, 5, 4, 2, 1, and 1 for sizes 10 through 24 respectively.

The question relates to the representation of data using a histogram based on the information given for a dot plot. A histogram is a type of graph that depicts the distribution of data through contiguous boxes, where the x-axis often represents the data categories (like a number line indicating shirt sizes) and the y-axis shows frequencies or relative frequencies.

To represent the same data as the described dot plot in a histogram, we need to create intervals or bins that will encompass the range of shirt sizes, and each interval will have a frequency corresponding to the number of dots in that size range from the dot plot. We could have intervals such as 8-10, 10-12, 12-14, and so on, with the height of each bar representing the frequency of shirts in each size range.

Histogram bars will correspond to dot plot points as follows: no bar for size 8, a single bar reaching up to 1 for size 10, a bar up to 3 for both sizes 12 and 14, a bar up to 5 for size 16, a bar up to 4 for size 18, bars up to 2 and 1 for sizes 20 and 22 respectively, and a final bar reaching up to 1 for size 24.

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Answer:

10 X 0.35

OR

10 X 35%

Final answer:

To find 35% of 10, convert the percentage to a decimal (0.35) and multiply by 10, which equals 3.5.

Explanation:

The expression that shows a way to find 35% of 10 is 0.35 *10. To calculate this, you convert the percentage to a decimal by dividing by 100 and then multiplying it by the number you want to find the percentage of. So, to find 35% of 10, you calculate 0.35 *10 which equals 3.5.

To find 35% of 10, you can use the following expression:

(35/100) x 10

This can be simplified to 0.35 x 10 = 3.5. Therefore, 35% of 10 is 3.5.

Answer:

I do not think I can answer this without any pictures.

Step-by-step explanation:

Sorry, but could you attach a link or maybe sketch it out?

Answer:

the answer is 9

Step-by-step explanation:

the answer is 9

Answer:

x< -2.5 or x>1

Step-by-step explanation:

Please see attached picture for full solution.

To find the values of x for which f(x) is positive, we can set f(x) greater than zero and solve for x using factoring or the quadratic formula.

To determine the values of x for which f(x) is positive in the quadratic function f(x) = 2x^2 + 3x - 5, we need to find the values that make the function output positive values.

Therefore, the values of x that make f(x) positive are x < -1 and x > 2.5.

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Answer:

[tex]2x-3y=19[/tex]

Step-by-step explanation:

we have the ordered pairs

(8, –1) and (2, –5)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values in the formula

[tex]m=\frac{-5+1}{2-8}[/tex]

[tex]m=\frac{-4}{-6}[/tex]

simplify

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

The equation of the line in point slope form is

[tex]y-y1=m(x-x1)[/tex]

we have

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

[tex]point\ (8,-1)[/tex]

substitute

[tex]y+1=\frac{2}{3}(x-8)[/tex]

Convert to standard form

The equation of the line in standard form is equal

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

we have

[tex]y+1=\frac{2}{3}(x-8)[/tex]

Multiply by 3 both sides to remove the fraction

[tex]3y+3=2(x-8)[/tex]

apply distributive property right side

[tex]3y+3=2x-16[/tex]

Group the variables in one side and the constants in the other side

[tex]2x-3y=3+16[/tex]

[tex]2x-3y=19[/tex] ---> equation in standard form

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

..

Answer:

30, 40, 50

Step-by-step explanation:

30 x 30 + 40 x 40 = 900 + 1600 = 2500

500 x 500 = 2500

sum of two legs² equals hypotenuse²

Answer:

Step-by-step explanation:

30,50,40

Answer:

3/5

Step-by-step explanation:

4/5 * 3/4 = 12 / 20 = 3 / 5

Answer:

6x-24

Step-by-step explanation:

6(x-4)=6x-24

Answer:

hi there!

The correct answer is: 6x - 24

Step-by-step explanation:

you distribute 6 into the parenthesis

you first multiply 6 by x  and you get 6x

then you multiply 6 by -4 and you get -24

then you combine both to get 6x-24

Answer:

0.0007

Step-by-step explanation:

Answer:

10, 6 and 11.66

Step-by-step explanation:

10, 6 and the hypothenous is equal to : √(10^2 + 6^2)

= √(100+36)

= √136

= 11.66

Answer:

10,6 and 11.66

Step-by-step explanation:

A right angled triangle has three sides which are the adjacent, the opposite and the hypotenuse.

Looking at the triangle in question, the longest side is the hypotenuse while the other two sides are opposite and adjacent respectively.

Before we can get the hypotenuse, we need to know the value of the other sides first.

Based on the diagram the height of the triangle is (20-10) = 10

The base of the triangle = (7-1) = 6

This are gotten be subtracting the initial point from the final point on which the triangle is standing in space.

Hypotenuse is gotten using the Pythagoras theorem expressed as;

Hypotenuse² = Adjacent² + opposite²

Hypotenuse² = 10²+6²

Hypotenuse² = 100+36

Hypotenuse² = 136

Hypotenuse = √136

Hypotenuse = 11.66

The three sides of the triangles are therefore 10, 6 and 11.66

To simplify the ratio 4:2:2, divide each part by the greatest common factor, which is 2, resulting in a simplest form of 2:1:1.

To express the ratio 4:2:2 in its simplest form, you need to divide each term of the ratio by the greatest common factor of all the terms. In this case, the greatest common factor of 4, 2, and 2 is 2. Therefore, when you divide each part of the ratio by 2, the simplest form of the ratio is 2:1:1.

Here's a step-by-step breakdown:

Identify the greatest common factor (GCF) of the numbers in the ratio. GCF of 4, 2, and 2 is 2.

Divide each term of the ratio by the GCF. So, 4 divided by 2 is 2, and 2 divided by 2 is 1.

Write down the simplified ratio: 2:1:1.

This method is similar to the way coefficients in a balanced chemical equation can be simplified, or how ratios can be used in genetics to represent phenotypic distribution in a dihybrid cross. In health sciences, ratios such as 1:1000 are expressed in simplest form. Similarly, in engineering, gear ratios like 2:1 are given in the simplest way to indicate how many turns of an input gear will result in one turn of an output gear.