1.1f Homework: Creating and Solving Linear Equations to Model Real World Problems Part I
he document will
1) Use the story below about Sanjeet and his friends' end-of-season basketball statistics to answer the
questions that follow.
Story
Points Scored
Terrence's points:
Sanjeet and his teanit members were looking
Sanjeet's points:
Cole's points:
at the total points scored by each player
during the season. Sanjeet scored twice ay
many pointy ay Terrence. Cole scored 12
more points than Sanjeet. Together the boys
scored 992 points during the season. How
many points did each boy score?
Equation:

Answer:

5/3

Step-by-step explanation:

1.6 repeating is equal to 5/3

The repeating decimal 1.6 can be written as the simplified fraction 5/3.

To rewrite the decimal 1.6 repeating (1.6) as a simplified fraction, we can use algebraic manipulation. Let's denote 1.6 as x:

x = 1.6

Now, to eliminate the repeating decimal, we can multiply both sides of the equation by 10 (since there is one digit repeating after the decimal point):

10x = 16.6

Next, subtract the original equation from the multiplied equation to eliminate the repeating decimal:

10x - x = 16.6 - 1.6

This simplifies to:

9x = 15

Finally, divide both sides by 9 to solve for x:

x = 15 / 9

Now, we simplify the fraction:

x = 5/3

Therefore, the repeating decimal 1.6 can be written as the simplified fraction 5/3.

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x = a number

6(x+5)=16

Answer:

If you're using x for "a number" then: 6(x+5)=16

Answer:

k=-9

Step-by-step explanation:

[tex]2k-3(2k-3)=45\\\\2k-3(2k)-3(-3)=45\\\\2k-6k+9=45\\\\(2k-6k)+9=45\\\\(2-6)k+9=45\\\\-4k+9=45\\\\-4k+9-9=45-9\\\\-4k+0=36\\\\-4k=36\\\\\frac{-1}{4}(-4k) =\frac{-1}{4}(36) \\\\k=\frac{-36}{4} \\\\k=\frac{4*9}{4} \\\\k=\frac{9}{1} \\\\k=-9[/tex]

Answer:

-3d = 43-10

-3d = 33

d = 33/-3

d = -11

Answer:

d = 11

Step-by-step explanation:

Simplifying

3d + 10 = 43

Reorder the terms:

10 + 3d = 43

Solving

10 + 3d = 43

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-10' to each side of the equation.

10 + -10 + 3d = 43 + -10

Combine like terms: 10 + -10 = 0

0 + 3d = 43 + -10

3d = 43 + -10

Combine like terms: 43 + -10 = 33

3d = 33

Divide each side by '3'.

d = 11

Simplifying

d = 11

Hope this helps!

===========================================

Explanation:

Use a calculator to find the decimal form of each of the following below (values are approximate; rounded to 2 decimal places)

We see that the order of the decimal values is: 5.83, 6, 6.28, 6.48

So the order of the terms, from smallest to largest, is [tex]\sqrt{34}, 6, 2\pi, \sqrt{42}[/tex]

Answer:

17. 13

18. 3x + 12

19. 1/4

Step-by-step explanation:

17.

[tex]3a + b = 3(5) - 2 \\ = 13[/tex]

18.

[tex]3(x + 4) = 3x + 12[/tex]

19.

[tex]p \: = \frac{3}{3 + 4 + 5 } \\ = \frac{3}{12} \\ = \frac{1}{4} [/tex]

Answer:

Step-by-step explanation:

17. 3(5) + 2 = 15 + 2 = 17

18. 3(x + 4) = 3x + 12

19. 3/(3+4+5)= 3/12= 1/4

Answer: Increase

Step-by-step explanation: 18 is greater than 12

Answer:

Yes

Step-by-step explanation:

I had this same question on a quiz and it is correct!

The square root of a number is equal to another number that when squared is equal to the original number.

Now we want to see if Is it true that square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol, and we will see that yes, this is true.

To see that this is true:

For example, if the A and B are two numbers larger than 0, such that:

A > B

Then:

√A > √B

For example let's use A = 9 and B = 4.

9 > 4

And obviously the roots are:

√9 > √4

3 > 2

So yes, we can compare and order square roots by comparing the numbers inside of it.

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Answer: vertical translation

Step-by-step explanation:

A function is even if:

f(x) = f(-x)

and a function is odd if:

f(-x) = -f(x).

Now, we want to find a translation that only affects the symmetry of an odd function (but not that one of the even function).

The correct answer will be a vertical translation, now let's prove it.

when we have a function f(x) and we want to transform it into g(x), such that g(x) is a vertical translation of (for example) A units up, we can write the relation as:

g(x) = f(x) + A.

Now, let's see if this preserves the symmetry of the original function.

1) if f(x) is even, then:

g(x) = f(x) + A

g(-x) = f(-x) + A

But we know that f(-x) = f(x)

then:

g(-x) = f(-x) + A = f(x) + A = g(x)

this means that g(x) is even, the symmetry of an even function is not affected by this transformation.

Now suppose that f(x) is odd.

Then:

g(x) = f(x) + A

g(-x) = f(-x) + A

and f(-x) = -f(x)

then:

g(-x) = f(-x) + A = -f(x) + A

and this is clearly different than g(x) = f(x) + A.

Then the odd symmetry is broken.

Answer:

d = [tex]\sqrt{34}[/tex]

Step-by-step explanation:

[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(9-6)^2+(6-1)^2}\\d= \sqrt{(3)^2+(5)^2}\\d= \sqrt{9+25}\\d= \sqrt{34}[/tex]

Answer:

80 miles per an hour

Step-by-step explanation:

400 divided by 5 equals= 80 so 80miles = 1 hour

Answer:

80 miles per hour.

Step-by-step explanation:

Start with the speed formula.

[tex]speed=\frac{distance}{time}[/tex]

In this scenario, the distance is [tex]400[/tex] miles, and the time is [tex]5[/tex] hours.

Substitute:

[tex]speed=\frac{400}{5}[/tex]

Divide.

[tex]400[/tex] ÷ [tex]5[/tex]

Solve:

[tex]400[/tex] ÷ [tex]5=80[/tex]

Answer:

x = -2 y= -2

Step-by-step explanation:

5x+12y= -34

2x+ 4y = -12

2x= -4y -12

x= -2y -6

plug back in

5(-2y -6) +12y = -34

-10y -30 +12y = -34

2y = -4

y= -2

2x+4y=-12

4y= -2x -12

y= -.5x -3

plug back in

5x+ 12(-.5x-3)=-34

5x -6x -36 = -34

-x = 2

x= -2

Answer:

Step-by-step explanation:

5x + 12y = -34

-6x - 12y = 36

-x = 2

x = -2

5(-2) + 12y = -34

-10 + 12y = -34

12y = -24

y = -2

(-2, -2)

Answer:

Step-by-step explanation:

[tex]30x+18=35−4x[/tex]

First of all using the addition property add 4x to both sides

That's

[tex]30x + 4x + 18 = 35 + 4x - 4x \\ 34x + 18 = 35[/tex]

Next using the subtraction property subtract 18 from both sides to make 34x stand alone

We have

[tex]34x + 18 - 18 = 35 - 18 \\ 34x = 17[/tex]

Divide both sides by 34

That's

[tex] \frac{34x}{34} = \frac{17}{34} [/tex]

We have the final answer as

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

Hope this helps you

Answer:

x = 18

Step-by-step explanation:

4x+4(x-6)=3(2x+4)

distribute

4x+4x-24=6x+12

combine like terms

8x-24=6x+12

carry across equal sign

2x-24=12

carry across equal sign

2x=36

divide

x=18

Answer:

X = 18

Step-by-step explanation:

4x + 4(x -6) = 3(2x + 4)

4x + 4x -24 = 6x + 12

8x -24 = 6x + 12

    +24         +24

8x = 6x + 36

-6x   -6x

2x = 36

Divide 2x and 36 by 2

X = 18

Answer:

The Answer to 17 1/3 x 8 is 138.67

There is not enough context to answer the second question.

Answer:

13, 39

Step-by-step explanation:

H +J =52

H=3J

3J +J=52

4J=52

J=52 :4 =13 (Jane is 13

H =3 ×13 =39 (Harvey is 36

Since the measure of angle DOC = 44 degrees and it's the central angle of arc DC, the measure of arc DC = 44 degrees

Answer:

f(-5) = 50

Step-by-step explanation:

Simply plug in -5 for x into the function:

f(-5) = (-5)² - 5(-5)

f(-5) = 25 + 25

f(-5) = 50

Answer:

27.5 is the answer good luck

Step-by-step explanation:

good luck my G

Answer:

$6.00-($2.00+$4.50)

in other terms, 6 - (2 + 4.5)

Step-by-step explanation:

So first, we know that they spent 6 in total. To figure out how much they spent, we need to figure out how much they had all together.

To get how much all together, we have to add. 2 + 4.5

Now that we now how to get the total amount, out them in parentheses and add the 6 infront.

Since we need to find the remaining amount, were subtracting 6 from the total, hence the parentheses.

All this leads to the expression: 6 - (2 + 4.5)

Hope this helps :)

Answer:

1foot(ft.)1yard(yd.)1mile(mi.)===12inches(in.)3feet(ft.)5,280feet(ft.)

Step-by-step explanation:

Answer:

The answerer to this question is a 34

Step-by-step explanation:

Answer:

A. 34

Step-by-step explanation:

Answer:

The y-intercept is -6.

Step-by-step explanation:

Answer:

$0.15

Step-by-step explanation:

3÷20=$0.15

I hope this helps

The cost per message is $0.15

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, a graph,

The graph is showing a straight line,

Considering a coordinate (3, 20),

That means, they cost $20 for 3 messages.

Therefore, for 1 message = 3/20 = 0.15

Hence, the cost per message is $0.15

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Answer:

Fred has saved $115 while Wilma had saved $230

Step-by-step explanation:

Let the amount saved by Fred be F while the amount saved by Wilma be W

Together, they have saved $345

Mathematically;

F + W = 345 •••••••(i)

We are also told that Wilma has have twice as much money as Fred;

Hence; W = 2F ••••••••(ii)

To get the amount of money they both have, we need to solve the equations simultaneously

Substitute ii into i

F + 2F = 345

3F = 345

F = 345/3

F = 115

But W = 2F

W = 2 * 115

W = 230

Answer:

y = -7x + 11

Explanation:

Just get y by itself. Subtract 7x from both sides. Substitute in each x value individually to get the next answers, which will be 25, 11, and -10.

Answer:

w= 7.59

Step-by-step explanation:

Answer:

Proper Subsets = 1023

Step-by-step explanation:

Given[tex]W= \{Hampton\ Hotels, Anytime\ Fitness, Subway, Jack\ in\ the\ Box, Supercuts, \\Jimmy\ Johns, Servpro, Denny's, Pizza\ Hut, 7-Eleven\}[/tex]

Required

Determine the proper subsets

Proper Subset (P) is calculated using;

[tex]P = 2^n - 1[/tex]

Where

[tex]n = number\ of\ elements[/tex]

In this case;

[tex]n = 10[/tex]

So:

[tex]P = 2^n - 1[/tex]

[tex]P = 2^{10} - 1[/tex]

[tex]P = 1024 - 1[/tex]

[tex]P = 1023[/tex]

Hence;

Proper Subsets = 1023

Answer:

1024

Step-by-step explanation: