Name
Chapter
5
1.On a calendar, each day is represented by a rectangle. To keep track of the date, you cross off the
previous day by connecting one pair of opposite corners of the rectangle, as shown.
10
E 177
11
F18
12
b. List the five triangle congruence theorems.
G10
a. Classify AABE by its sides and by measuring its angles. Explain your reasoning.
D
Date
c.For each of the triangle congruence theorems you listed in part (b), prove that AFBC = ACGF
using that theorem. (You will need to write five different proofs.)

The equation is given as n = c + 2

The plant grows c inches in the first week.

The plant grows n inches in the second week.

mаthеmаticаlly, the equаtion requires that wea rea to to show thе relаtionship between thе growth in thе first wееk (c) and thе growth in thе seсond wееk (n).

thе growth in thе seсond wееk (n) is said to be  2 inсhes more than thе growth in thе first wееk (c) from the given question.

The equation would be

n = c + 2

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You can treat x and 2x+1 just as though they are real numbers.

So f(2x+1) = 3(2x+1) - 5 = 6x + 3 - 5 = 6x - 2

In the above, I made use of something called the distributive law which says that if a,b and c are real numbers, then a(b+c) = ab + ac.

Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

Time-series plots are used for several reasons:

B. Time-series plots are used to identify any outliers in the data.

C. Time-series plots are used to identify trends in the data over time.

D. Time-series plots are used to present the relative frequency of the data in each interval or category.

First, we need to know that quantitative variable is required when drawing a time-series plot.

We need to also know that data points are graphically represented as time-series plots, with the variable of interest drawn on the y-axis and time commonly depicted on the x-axis. They demonstrate the variable's evolution over time.

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Alice's state income tax based on the state's variable income tax rates will be $380.90.

Variable income tax rates imply different tax rates for each tax bracket.

Variable income tax rates involve many marginal tax rates that are not fixed.

Unlike a fixed rate, variable tax rates are graduated and increase as income exceeds some marginal amounts.

With variable income tax rates, different income amounts are taxed at different tax rates to ensure that the tax is progressive.

For proportional tax systems, the tax rate is fixed and applies a fixed percentage on the taxable income in determining the income tax liability.

Alice's earnings = $30,050

$20,000 x 1% = $200

$10,050 x 1.8% = $180.9

Total tax liability = $380.90 ($200 + $180.90)

Thus, Alice will pay a state income tax of $380.90.

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The value of the integral is 2pi.

To interpret the given integral in terms of areas, we need to recognize that the integrand, \(\sqrt(4-x^2),\) represents the upper half of a circle with radius 2 centered at the origin.

First, we can sketch the graph of\(y = \sqrt(4-x^2)\)over the interval [-2, 2]:

      |         /\            |

   2 |       /    \          |

      |      /        \       |

     |     /            \     |

     |_/_____  __\_|

         -2         2

The integral can be evaluated as follows:

\(int_(-2)^2 \sqrt(4-x^2) dx\) = area of upper half of circle with radius 2 and center at (0, 0)

                         = (1/2) * pi *\(r^2\), where r = 2

                         = (1/2) * pi * 4

                         = 2pi

Therefore, the value of the integral is 2pi.

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The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

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Answer:

$88

Step-by-step explanation:

first, you find 20% of 57 which = 11.4

then subract it with 57 which looks like 57-11.4 = 45.6

= 45.6

first, you find 20% of 53 which = 10.6

then subract it with 53 which looks like 53-10.6 = 42.7

= 42.4

then you add them both  which = 45.6+ 42.4= 88

Answer:

1. Country = 160, Pop= 135

2. Country = 170, Pop = 155

3. Country = 180, Pop = 175

4. Country = 190, Pop = 195

5. Country = 200, Pop = 215

6. Country = 210, Pop = 235

7. Country = 220, Pop = 255

8. Country = 230, Pop = 275

9. Country = 240, Pop = 295

10. Country = 259, Pop = 315

Step-by-step explanation:

Replace the x in the equations with the week number then solve the equation

Answer: 32

Step-by-step explanation:

f(6) = 6^2-4 = 36-4 = 32

The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.

To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.

Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:

X=2, Y=1, Z=1

X=2, Y=1, Z=2

X=2, Y=2, Z=1

Step 2: Calculate the joint probability for each combination:

For X=2, Y=1, Z=1:

f(2, 1, 1) = (2+1) * 1 = 3

For X=2, Y=1, Z=2:

f(2, 1, 2) = (2+1) * 2 = 6

For X=2, Y=2, Z=1:

f(2, 2, 1) = (2+2) * 1 = 4

Step 3: Sum up the joint probabilities:

P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13

They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.

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Step-by-step explanation:

step 1. (13x + 8) + (2x + 7) = 180 (definition of same side interior angles)

step 2. 15x + 15 = 180 (like terms)

step 3. 15x = 165 (subtract 15 from each side)

step 4. x = 11. (divide both sides by 15)

Answer:

The functions given in the question are

Step 1:

To figure out (fog)(x), we will substitute the value of x=x²-7x+6 in f(x)

Hence,

The function for (fog)(x) will be

Step 2:

To figure out (gof)(x), we will substitute the value of x=7x-7in g(x)

Hence,

The value for (gof)(x) will be

The value of k in the given arithmetic sequence is equal to 2

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference

Given the first term as 3k + 1, we have that;

a₁ = a + (1 - 1) d = 3k + 1

a₁ = a = 3k + 1

for the second term k, substituting 3k + 1 for a;

a₂ = 3k + 1 +(2 - 1)d = k

3k - k = -1 - d

2k = -1 - d...(1)

for the third term -3; substituting 3k + 1 for a;

a₃ = 3k + 1 +(3 - 1)d = -3

3k + 1 + 2d = -3

3k = -4 - 2d ...(2)

using elimination method to remove d, we multiply equation (1) by 2 to get;

4k = -2 - 2d...(3)

we subtract equation (2) from (3);

4k - 3k = -2 - 2d - (-4 - 2d)

k = -2 -2d + 4 + 2d {2d is eliminated}

k = 4 - 2

k = 2

Therefore, the value of k for the arithmetic sequence is equal to 2.

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The required answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

Subtraction is mathematical terminology that helps and elaborates the decrease in the original value by some value.

Here,
To perform the subtraction, you line up the decimal points and subtract the digits in each place value starting from the right. In this case, you subtract 8 from 6, which requires borrowing 1 from the digit to the left, giving you 16 - 8 = 8 in the one's place. You then subtract 2 from 5, giving you 3 in the tenth place. Continuing this process, you get the result of 82,727.12.

Thus, the answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

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Answer:

l = \(\frac{P - 2w}{2}\)

Step-by-step explanation:

2l + 2w = P

     2l =  P - 2w

      l = \(\frac{P - 2w}{2}\)

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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Answer:

A = B (base) x H (height)

A = 55 x 55

A = 3025

Answer:

wachu wachu wa

Step-by-step explanation:

Answer: 64.2 ft^2

Step-by-step explanation: to find the answer we know that the parallelogram area is A= bh we see that they are trying to trick us by separating the base we have to add the base together and we then get 10.7 that is the base we then see that the height is 6 and we multiply them together and get the answer.

Answer:

-3.6*10-1

Step-by-step explanation:

(38-9)-(74-8)=29-66=-37

Answer:

40°, 60° and 80°

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 + 4 = 9 parts

Divide 180° ( sum of angles in a triangle) by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio , then

2 parts = 2 × 20° = 40°

3 parts = 3 × 20° = 60°

4 parts = 4 × 20° = 80°

The angles in the triangle are 40°, 60°, 80°

The volume of the gas under a pressure of would be 0.06 cubic meters, or 60 liters, rounded to the nearest hundredth.

Volume is a measure of the amount of three-dimensional space an object occupies. It is measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in many areas of science, including physics, chemistry and geology. It can also be used to describe the capacity of a container, such as a bottle, or the amount of liquid it can hold. Knowing the volume of a substance or object is important in many everyday situations, from measuring food portions to calculating the amount of paint needed to cover a wall.

The volume of a gas is directly proportional to its pressure and temperature. The ideal gas law states that the product of the pressure and the volume of a gas is equal to the product of the mass of the gas, the temperature, and the universal gas constant.

Therefore, using the ideal gas law, the volume of the gas under a pressure of can be calculated using the following equation:
V = (P × M × R × T) / P

where P = pressure, M = mass of the gas, R = universal gas constant, and T = temperature.

Assuming a temperature of , the volume of the gas under a pressure would be 0.06 cubic meters, or 60 liters, rounded to the nearest hundredth.

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The polynomial that is prime is given by Option C: \(10x^2 - 4x +3x +6\)

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

Checking all the listed polynomials for them being prime or not:

Rewriting it as:

\(x^3+3x^2+2x+6 = x^2(x+3) + 2(x+3) = (x^2 + 2)(x+3)\)

shows that this polynomial has factors. Thus, it isn't prime polynomial

Rewriting it as:

\(x^3 + 3x^2 -2x -6 = x^2(x+3) -2(x+3) = (x^2-2)(x+3)\)

shows that this polynomial has factors. Thus, it isn't prime polynomial

We can rewrite it as:

\(10x^2 -4x + 3x -6 = 10x^2 -x -6 = f(x) \: \rm (say)\)

This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.

Case 4: \(10x^2 -10x + 6x - 6\)

It can be factored as:

\(10x(x-1) + 6(x-1) = (x-1)(10x-6)\)

This is not a prime polynomial.

Thus, the polynomial that is prime is given by Option C: \(10x^2 - 4x +3x +6\)

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Answer:

The polynomial that is prime is given by Option C:

What are prime polynomials?

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

Checking all the listed polynomials for them being prime or not:

Case 1:

Rewriting it as:

shows that this polynomial has factors. Thus, it isn't prime polynomial

Case 2:

Rewriting it as:

shows that this polynomial has factors. Thus, it isn't prime polynomial

Case 3:

We can rewrite it as:

This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.

Case 4:

It can be factored as:

This is not a prime polynomial.

Thus, the polynomial that is prime is given by Option C:

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Step-by-step explanation:

Answer:

3V/piR^2

Step-by-step explanation:

to solve for h (height) you have to move all of the other variables to the other side

v = 1/3PiR^2h

divide 1/3 to v (its also the same if you multiply 3 into volume because there is only "1" as the numerator

3v = PiR^2h

you also divide PiR^2 (PiR^2 counts as the whole variable)

3v/PiR^2 = h

Answer:

22.9

Step-by-step explanation:

( just look up "diameter of a sphere caculator")

Based on the tree diagram and the independence of the events, we can conclude that the events represented in the diagram are independent events.

To determine if the events are dependent or independent, we need to examine the branches of the tree diagram and check if the outcomes of one event affect the outcomes of the other event.

In the given tree diagram, the selection of colors for the cubes is represented by different branches. Each branch represents an independent event because the outcomes of selecting one color do not affect the outcomes of selecting another color.

The probabilities associated with each branch can be multiplied to calculate the probability of a specific sequence of events indicating that they are independent.

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