Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.

Answer:

40,12

Step-by-step explanation:

u count how many x's u have.4(for the first square)

add up the regular numbers

so u should have4x+50

repeat for the second one

so u should have 4x+25=6x+20

solve

u get 2x=30 simplify

u get 15

now plug it in and there is ur answer

The value of length and width for Cat's driveway are  25 ft and 7.5 ft respectively.

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

Given that,

The length and width of Cat's driveway are 25 ft and x ft respectively.

And, the length and width of Fred's driveways are 2x ft  and x + 10 ft respectively.

The perimeter of a rectangle is given as,

2(l + b)

Substitute the values to obtain the perimeters as,

Perimeter of Cat's driveway = 2( x + 25) ft

And, perimeter of Fred's driveway = 2(2x + x + 10) ft.

As per the question,

2( x + 25) = 2(2x + x + 10)

=> ( x + 25) = (2x + x + 10)

=> x = 15/2

       = 7.5

Hence, the length and width of Cat's driveway are 25 ft and 7.5 ft respectively.

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City hall to post office = 6 1/2 miles

City hall to library site = 1 1/4 miles

library site to post office = unknown. let it be x.    5 1/4 miles

1 1/4 miles + x = 6 1/2 miles

x = 6 1/2 miles - 1 1/4 miles

Find x.

1) convert the mixed fractions into fractions. 6 1/2 = 13/2 ; 1 1/4 = 5/4

x = 13/2 - 5/4

2) get the common denominator. 4 is twice as much as 2. multiply 13/2 by 2/2

13/2 * 2/2 = 26/4

3) Subtract the top numbers and put over the same denominator

x = 26/4 - 5/4 = (26-5) / 4 = 21 / 4

4) simplify the fraction

x = 21/4 = 5 1/4 miles from library site to post office.

The value of fraction 0.7 is greater than the value of 3/4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the terms are 0.7 and 3/4. The values in the chemical points are,

First = 3/4 = 0.42

Second = 0.7

Here 0.7 is greater than the value 3/4 = 0.42

Hence, the greater value between the two values 3/4 and 0.7 is 0.7.

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The temperature by midnight will be 32°.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Temperature is the randomness of the molecules known as temperature.

At noon the temperature was 12°.

It rose 8° during the afternoon, then dropped 28°by midnight.

Then the temperature by midnight will be given as,

⇒ 12° - 8° + 28°

⇒ 32°

Thus, the temperature by midnight will be 32°.

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The probability that Calista randomly chooses two five-dollar bills from her wallet is 1/36.

To calculate the probability of Calista choosing two five-dollar bills from her wallet, we start by determining the total number of ways she can choose two bills from her wallet, regardless of their denomination. Calista has a total of 9 bills (4 ones, 2 fives, and 3 tens), so the total number of ways to choose two bills is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.

The total number of ways to choose 2 bills from 9 is C(9, 2) = 9! / (2!(9-2)!) = 36. Next, we need to find the number of ways to choose 2 five-dollar bills from the 2 she has, which is simply C(2, 2) = 2! / (2!(2-2)!) = 1. The probability that both bills are five-dollar bills is then the number of ways to choose 2 fives divided by the total number of ways to choose any 2 bills, or P(both fives) = 1 / 36.

The linear equation y=1/2x -2 can be graphed by first plotting the y-intercept, then using the slope to plot additional points.

Such equations can be graphed using a few different methods. One common approach is plotting data pairs on a coordinate grid.

For the given equation y = 1/2x - 2, it is convenient to begin by identifying b, which is the y-intercept. In our case, b equals -2. This is the point where the line crosses the y-axis. Next we need to understand what the slope (1/2 in our equation) means: for every step we move to the right along the x-axis (in the positive direction), we move half a step up along the y-axis.

To graph the equation, you start at the y-intercept (0,-2) and use the slope to identify subsequent points. For instance, if x = 2, then y = 1/2*2 - 2 = -1.  Repeat this process with different x-values to plot enough points, and then connect them to draw the line written by the equation.

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Tony has a total of 150 pieces of gum in three packages, calculated by multiplying the number of packages (3) by the number of packs per package (5) and the number of pieces per pack (10).

To calculate the number of pieces of gum Tony has in all three packages, we need to multiply the number of packages by the number of packs in each package, and then by the number of pieces in each pack. First, we have 3 packages and each package contains 5 packs of gum. So, the total number of packs in the three packages is:

Next, each pack has 10 pieces of gum, so the total number of pieces of gum in all the packs is:

Therefore, Tony has a total of 150 pieces of gum in the three packages.

The Information about Geometric sequence is:

[tex]a_{1}=23 , a_{n}=9\times a_{n-1}[/tex]

→nth term of sequence = 9× (n-1) th term

Also , Common Ratio of a Geometric Sequence =[tex]\frac{\text{Second term }}{\text{First term}}[/tex]

[tex]\frac{a_{n}}{a_{n-1}}= \text{Common ratio}}=9\\a_{n}= a_{1}\times r ^{n-1}\\\\a_{n}=23\times 9^{n-1}[/tex]

Option 4 : [tex]a_{n}= 23 \times 9^{n-1}[/tex] is true.

The length of the room  is  10 m and width is 6m.

We have given that the area is 60 square meters

and perimeter of the square is 32 meters

[tex]Area =L \times W[/tex]

we have given that the area is 60

Therefore,[tex]L \times W = 60.......(1)[/tex]

[tex]Perimeter=2(L + W)[/tex]

From given we get,

[tex]2(L + W) = 32[/tex]

[tex]L + W = 16[/tex]

[tex]L = 16 - W.......(2)[/tex]

Substitute the value of  L = 16 - W into (1) we get,

[tex]L \times W = 60[/tex]

[tex](16 - W) \times W = 60[/tex]

[tex]16W -W^2 = 60[/tex]

[tex]W^2 - 16W + 60 = 0[/tex]

[tex](W - 6)(W - 10) = 0[/tex]

[tex]W - 10 = 0\implies W = 10\\W - 6 = 0\implies W = 6[/tex]

Therefore the length is  10 m and width is 6m.

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