Decide which story can be represented by the system of equations y = x + 6 and
x + y = 100. Explain your reasoning.
a. Diego's teacher writes a test worth 100 points. There are 6 more multiple
choice questions than short answer questions.
b. Lin and her younger cousin measure their heights. They notice that Lin is 6
inches taller, and their heights add up to exactly 100 inches.

The expressions for the given questions are substituted and solved using the provided values of x and y. The solutions for the four questions respectively are 109, 15, 19, and 92.

To evaluate the expressions for questions 5-8, you will need to substitute the values of x and y into each given expression.

Through these steps, you can understand how to substitute and solve such expressions.

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To find the slope, use the slope(m) formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]        and plug in the two points

(0, 5) = (x₁, y₁)

(-9, -4) = (x₂, y₂)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-4-5}{-9-0}[/tex]

[tex]m=\frac{-9}{-9}[/tex]    [two negatives cancel each other out and become positive]

m = 1      The slope is 1

Final answer:

The probability of picking a 1 and then a 12 from a deck of cards numbered 1-12 with replacement is 1/144, since each event is independent and each card has an equal chance of being selected.

Explanation:

The student asked about the probability of selecting a 1 and then a 12 from a deck of cards numbered 1-12, with replacement in between the picks. To find this, we need to consider the events independently, since the card is replaced after the first draw, meaning the probability of the second draw is unaffected by the first.

The formula to calculate the probability of independent events is P(A and B) = P(A) × P(B), where P(A) is the probability of the first event and P(B) is the probability of the second event occurring. Since each card has an equal chance of being picked from the deck, and there are 12 cards in total, the probability of picking any specific card, like a 1 or a 12, is 1/12.

Therefore, the probability of picking a 1 first and then a 12 is P(1 and then 12) = P(1) × P(12), which is equal to (1/12) × (1/12) = 1/144. So, the final probability is 1/144, or about 0.00694.

Answer:

C:   $836.08

Step-by-step explanation:

Edg 2020

The Cindy's new rent be if she includes the renters insurance is $836.08

We are given that;

An annual premium = $565.00

Now,

To find Cindy's new rent, we need to add the monthly payment for the renters insurance to her current rent.

To find the monthly payment for the insurance, we need to divide the annual premium by 12, since there are 12 months in a year. We get:

565 / 12 = 47.08

So, the monthly payment for the insurance is $47.08.

Adding this to Cindy's current rent, we get:

789 + 47.08 = 836.08

Therefore, by unitary method the answer will be $836.08.

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Question:

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to  [tex]\frac{1}{2}[/tex].

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4

5n = 3d and 2n - 4 = d - 2

3n = 5d and 2n - 4 = d - 2

Answer:

5n = 3d and 2n – 4 = d – 2

Solution:

Let n be the numerator of the fraction and d be the denominator of the fraction.

Given the numerator and denominator of a fraction are in the ratio of 3 to 5.

This can be written as n : d = 3 : 5.

⇒ [tex]\frac{n}{d}= \frac{3}{5}[/tex] – – – – (1)

Do cross multiplication, we get

⇒ 5n = 3d

When the numerator and denominator are decreased by 2, the fraction is equal to [tex]\frac{1}{2}[/tex].

⇒ [tex]\frac{n-2}{d-2}= \frac{1}{2}[/tex]

Do cross multiplication, we get

⇒ 2(n –2)=1(d – 2)

⇒ 2n – 4 = d – 2

Hence, 5n = 3d and 2n – 4 = d – 2 can be used to solve the problem.

Answer:

5n = 3d and 2n – 4 = d – 2 is the answer

Step-by-step explanation:

Answer:

17.1

Step-by-step explanation:

The required round of number 17.0891 to the nearest tenth is 17.1.

Given that,
To round the number 17.0891 to the nearest tenth.

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

Given number,
17.0891
Since the number on the tenth place after the decimal is 0 and the value next is 0.08 which is near to 0.1 so the number on the tenth place will increase by a unit and the whole number become,
= 17.1

Thus, the required round of number 17.0891 to the nearest tenth is 17.1.

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y is some number and it is equal to -4x+2

y being that same number is also equal to x-3

therefore, we can equate -4x+2 and x-3 to get x-3 = -4x+2

This is the same as starting with y = -4x+2 and replacing the y with x-3

----------------

Let's solve for x

x-3 = -4x+2

x-3+4x = -4x+2+4x .... add 4x to both sides

5x-3 = 2

5x-3+3 = 2+3 .... add 3 to both sides

5x = 5

5x/5 = 5/5 .... divide both sides by 5

x = 1

With this x value, you can now find the y value. Pick any equation that has x and y in it. If we picked the first equation, then

y = -4x+2

y = -4*1+2 ... plug in x = 1

y = -4+2

y = -2

Or we can pick the second equation

y = x-3

y = 1-3 .... plug in x = 1

y = -2

-------------------------------------------------------------------------

Graphing the two lines will have them intersect at this location.

Answer:

x = 127

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6, thus

sum = 180° × 4 = 720°

Sum the interior angles and equate to 720 for x

120 + 100 + 128 + 133 + 112 + x = 720, that is

593 + x = 720 ( subtract 593 from both sides )

x = 127

Answer:

1.032%

Step-by-step explanation:

Answer:

Ali would run 2.8 miles in 24 minutes.

Answer:

I didn't know if you meant that the circumference of tje hemisphere was 44 or if the circumference of the cirkel in which the hemisphere exists is 44 but you rearrange the numbers.

Step-by-step explanation:

The formula for calculating a circumference is 2×pi×r, with r as tje radius of the cirkel. So in this instance we get 2×pi×r=44. r=44/(2×pi)=7.00 centimeters. The total surface area of a cirkel=pi×r^2=pi×7.00^2=154.06 meters squared. 154.06/2=77.03 meters squared (hemisphere is half of a cirkel)

To find the total surface area of the hemisphere, first find the radius of the hemisphere using the formula for circumference. Then, use the formula for the total surface area of a hemisphere to calculate it.

To find the total surface area of the hemisphere, we need to first find the radius of the hemisphere. Since the circumference of the great circle is given as 44 cm, we can use the formula for circumference to find the radius: C = 2πr. Thus, 44 = 2πr. Solving for r, we have r = 44/(2π) = 7 cm.

The total surface area of a hemisphere is given by the formula A = 3πr^2. Plugging in the value of the radius, we get A = 3π(7^2) = 3π(49) = 147π cm^2.

So, the total surface area of the hemisphere is 147π cm^2.

Answer:

225 employees work as instructors.

Step-by-step explanation:

You want to find what 75% OF 300 is, therefore multiplication will be required in this problem. First you want to convert 75% to a decimal which you could do by just bringing the decimal point to the left twice. which will give you the decimal 0.75.

Now multiply. 0.75*300=225. There are 225 employees that work as instructors.

Final answer:

To find out how many employees work as instructors at Bright Mind Learning, multiply 75% by the total number of employees. 225 of the 300 employees at Bright Mind Learning work as instructors.

Explanation:

To find out how many employees work as instructors at Bright Mind Learning, we need to calculate 75% of the total number of employees. First, convert 75% to a decimal by dividing it by 100: 75/100 = 0.75. Then, multiply this decimal by the total number of employees (300): 0.75 * 300 = 225.

So, 225 of the 300 employees at Bright Mind Learning work as instructors.

Answer:

Step-by-step explanation:

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

− sin  ( π 2 )

The exact value of   sin ( π 2 )   is  1 .

-1.1

Multiply  

− 1  by  1 .

−1

SIN (3 PIE/2)

Answer:

ok

Step-by-step explanation:

asap

Answer:

11 cm

Step-by-step explanation:

Answer:

is there a picture

Step-by-step explanation:

Answer:

The first operation performed when evaluating the given expression [tex]5+(\frac{9x-3}{2})[/tex]  for x=5 is given below :

Step 1: Put x=5 in the above given expression we get

[tex]5+(\frac{9(5)-3}{2})[/tex]

Step-by-step explanation:

Given equation is [tex]5+(\frac{9x-3}{2})[/tex] for x=5

To find the first operation performed when evaluating the given expression [tex]5+(\frac{9x-3}{2})[/tex]  for x=5

[tex]5+(\frac{9x-3}{2})[/tex]

Step 1: Put x=5 in the above expression we get

[tex]5+(\frac{9(5)-3}{2})[/tex]

[tex]=5+(\frac{45-3}{2})[/tex]

[tex]=5+(\frac{42}{2})[/tex]

[tex]=5+21[/tex]

[tex]=26[/tex]

Therefore [tex]5+(\frac{9x-3}{2})[/tex] for x=5 is 26

Therefore [tex]5+(\frac{9x-3}{2})=26[/tex] for x=5

Answer:

The other 2 angles combined measure 70

Step-by-step explanation:

all of a triangle's angles together measure 180.

If one angle is 110 the other 2 would be 70.

Answer:

1,140 words

Step-by-step explanation:

57/3 = 19 words per minute

there are 60 minutes in an hour

19x60 = 1140

If Carol is able to type 57 words in 3 minutes, then in one hours time she will be able to type 1140 words.

Let the number of words typed in 1 hours be represented as y

So that;

57 words are typed in 3 min

We know that 60 minutes makes 1 hour

57 words typed in 0.05 hour

y words typed in 1 hours

We cross multiply

57 words × 1 hour = y × 0.05 hour

y = 57hours / 0.05 hours

y = 1140 words

If Carol is able to type 57 words in 3 minutes, then in one hours time she will be able to type 1140 words.

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Answer:

$41.25

Step-by-step explanation:

part=%(whole)

x=55%(75)

x=0.55(75)

x=41.25

Answer:

Angle 2=   110 degrees

Angle 3 =  70 degrees

Angle 4 = 70 degrees

Step-by-step explanation:

Finding angle 2

In the figure attached below,the angles 1 and 2  Corresponding angles

When two lines are crossed by another line that is  called the Transversal, then, the angles in matching corners are called corresponding angles.

Corresponding angles are equal so

angle 2 = 110 degrees

Finding angle 3

Similarly 2 and 3 are consecutive angles and Consecutive angles are supplementary . That is the sum of the consecutive angles is 180 degree

then

angle 2  +angle 3 = 180

110  + angle 3 = 180

angle 3 = 180 -110

angle 3 = 70 degrees

Finding angle 4

Now angle 3 and angle 4 are alternate interior angle and they are equal

angle 3 = angle 4

so angle 4 is 70 degree

Answer:

110

70

70

Step-by-step explanation:

cause i got it right

Answer:

i believe the answer is C

The distributed form of -2(x-3)^2 is -2x^2 + 12x - 18.

Step-by-step explanation:

The given question is -2(x-3)^2

step 1 :The formula for (a-b)^2 = a^2 - 2ab + b^2

step 2 :Here, the term (x-3)^2 = x^2 - (2*3x) + 3^2

                                                  = x^2 - 6x + 9

step 3 :The expanded form = -2 (x^2 - 6x + 9)

step 4 : where -2 can be distributed to each term inside the bracket.

Therefore, -2(x^2 - 6x + 9) = -2x^2 + 12x - 18

the fraction form of 13.2857142857 is[tex]\( \frac{1195714285713}{90000000000} \).[/tex]

To convert the decimal 13.2857142857 into a fraction, we can follow these steps:

Step 1: Let x = 13.2857142857

Step 2: Multiply x by 10 to move the decimal one place to the right:

x = 13.2857142857

10x = 132.857142857

Step 3: Subtract the original x from 10x to eliminate the decimal:

10x - x = 132.857142857 - 13.2857142857

9x = 119.5714285713

Step 4: Simplify the equation:

9x = 119.5714285713

Step 5: Divide both sides by 9:

[tex]\[x = \frac{119.5714285713}{9}\][/tex]

Step 6: Simplify the fraction:

[tex]\[x = \frac{1195714285713}{90000000000}\][/tex]

Now, the fraction form of 13.2857142857 is[tex]\( \frac{1195714285713}{90000000000} \).[/tex]

Answer:

54

Step-by-step explanation:

34 + 4 ⋅ 5  (by PEDMAS, do multiply first)

=  34 + 20

= 54

Answer:

54 :)

Step-by-step explanation:

Answer

It would be 2 liters

Answer:

1.99 liters is the correct answer

Step-by-step explanation:

Answer:

87067=90000

Step-by-step explanation:

because 7 is bigger than 8 so its90000

Answer:

90,000

Step-by-step explanation:

Answer:

OPTION C

OPTION E

Step-by-step explanation:

Distributive property of Addition:

                            a(b + c) = ab + bc

In other words, 'a' is distributed over 'b' and 'c'.

Also, note that a mixed fraction, of the form [tex]$ \textbf{c} \frac{\textbf{x}}{\textbf{y}} = \textbf{c} + \frac{\textbf{x}}{\textbf{y}} $[/tex]

If a mixed fraction is of the type [tex]$ \textbf{-p}\frac{\textbf{q}}{\textbf{r}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-(p + } \frac{\textbf{q}}{\textbf{r}}) \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{-p} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{q}}{\textbf{r}} $[/tex]

OPTION A:

[tex]\textbf{3} \bigg ( \textbf{-4} \frac{\textbf{1}}{\textbf{2}} \bigg )[/tex]

This can be written as: [tex]$ 3 \bigg ( - 4 - \frac{1}{2} \bigg ) $[/tex]

Now, we distribute 3 over -4 and [tex]$ -\frac{1}{2} $[/tex].

[tex]$ = 3(-4) + 3\bigg (-\frac{1}{2} \bigg ) $[/tex]

Therefore, OPTION A is incorrect.

OPTION B: [tex]$ \textbf{2} \frac{\textbf{1}}{\textbf{4}} \bigg ( \textbf{1} \frac{\textbf{3}}{\textbf{4}} \bigg ) $[/tex]

Now, this is written as: [tex]$ 2 + \frac{1}{2} \bigg ( 1 + \frac{3}{4} \bigg ) $[/tex]

We have distribute 2 and [tex]$ \frac{1}{2} $[/tex] separately over 1 and [tex]$ \frac{3}{4} $[/tex].

So, we should have [tex]$ 2 (1) + 2 \bigg ( \frac{3}{4} \bigg ) + \frac{1}{2} (1) + \frac{1}{2}. \frac{3}{4} $[/tex]

So, OPTION B is incorrect.

OPTION C: [tex]$ \textbf{-4} \bigg( - 5 \frac{\textbf{1}}{\textbf{3}} \bigg ) $[/tex]

[tex]$ = - 4 \bigg ( -5 - \frac{1}{3} \bigg) $[/tex]

[tex]$ = -4(-5) + (-4) \bigg (- \frac{1}{3} \bigg ) $[/tex]

Hence, OPTION C is correct.

Similar method will help us know that OPTION D has used the Distributive property incorrectly and OPTION E has.

So, the answers are:

OPTION A

OPTION C

OPTION E

The y intercept of a graph containing the two points (3,1) and (7,-2) is [tex]\frac{13}{4}[/tex]

Solution:

Given points are (3, 1) and (7, -2)

The equation of line in slope intercept form is given as:

y = mx + c ------- eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Let us first find the slope of line

The slope of line is given as:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here the points are (3, 1) and (7, -2)

[tex](x_1, y_1) = (3, 1)\\\\(x_2, y_2) = (7, -2)[/tex]

Substituting in formula, we get

[tex]m = \frac{-2-1}{7-3}\\\\m = \frac{-3}{4}[/tex]

To find the y intercept:

[tex]\text{Substitute } m = \frac{-3}{4} \text{ and } (x, y) = (3, 1) \text{ in eqn 1 }[/tex]

[tex]1 = \frac{-3}{4} \times 3 + c\\\\1 = \frac{-9}{4} + c\\\\ \text{Simplify the above equation } \\\\1 = \frac{-9+4c}{4}\\\\4 = -9 + 4c\\\\13 = 4c\\\\\text{Divide both sides by 4 }\\\\c = \frac{13}{4}[/tex]

Thus  y -intercept is [tex]\frac{13}{4}[/tex]

Answer:

∠AOC

Step-by-step explanation:

The statement "A to O to C" is talking about each of the points that form an angle. Each point is given a letter as its name.

The symbol ∠ means angle.

You need two lines to form an angle, and you need two points to form a line. By reusing one of the points, you need three points to form an angle. The point that is being reused is always the point in the middle, in this case, that point is called 'O'.