Which expression is equivalent to the one that is modeled?

[tex]\large\displaystyle\text{$\begin{gathered}\sf 1) \ \left\{\begin{matrix} 5x-3y-z=1&\\ x+4y-6z=-1& \\ 2x+3y+4z=9& \end{matrix}\right. \end{gathered}$}[/tex]

The coefficient matrix associated with the system is constructed and the columns and rows are reduced.

                [tex]\left ( \begin{array}{ccc|c} 5 & -3 &-1 &1\\ 1 & 4 & -6 &-1\\ 2 & 3 & 4 & 9 \end{array} \right ) \begin{array}{c} \xrightarrow[\textup{F}_3- 2\textup{F}_2]{\textup{F}_1 - 5\textup{F}_2} \end{array} \left ( \begin{array}{ccc|c} 0 & -23& 29 &6\\ 1 & 4& -6 &-1\\ 0 & -5 &16 & 11 \end{array} \right )\\ \ \\ \ \\ \begin{array}{c} \xrightarrow[]{23\textup{F}_3 - 5\textup{F}_1} \end{array} \left ( \begin{array}{ccc|c} 0 & -23& 29 &6\\ 1 & 4& -6 &-1\\ 0 & 0 & 223 & 223 \end{array} \right )[/tex]

So, z=1. Translating the last matrix to the associated system of equations, we have that x=1, y=1, since:

                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} y&=\dfrac{6-29}{-23}=\dfrac{-23}{-23}=1\\ x = -1+6-4=1 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{2) \ \left\{\begin{matrix} x+y=7& \\ x\times y=12& \end{matrix}\right. } \end{gathered}$}[/tex]

Clear an unknown in the first equation and substitute the resulting expression in the second. Next, the quadratic equation is solved.

             [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ y=7-x \quad \Longrightarrow \quad 12=x(7-x)=7x-x^2 } \end{gathered}$}[/tex]

                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ 0=x^2-7x+12=(x-4)(x-3); } \end{gathered}$}[/tex]

                [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x_1=4\qquad x_2=3 \Longrightarrow y_1=3 \qquad y_2=4 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{3) \ \left\{\begin{matrix} x^2+y^2=169& \\ x+y=17& \end{matrix}\right. } \end{gathered}$}[/tex]

Clear an unknown in the first equation and substitute the resulting expression in the second. Next, the quadratic equation is solved.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ y=17-x \quad \Longrightarrow \quad 169=x^2 +(17-x)^2=x^2+x^2 -34x+289 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ 0=2x^2-34x+120=2(x^2-17+60)=2(x-12)(x-5); } \end{gathered}$}[/tex]

               [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{ x_1=4\qquad x_2=3 \Longrightarrow y_1=3 \qquad y_2=4 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{4 \ \left\{\begin{matrix} y^2-2y+1=x & \\ \sqrt{x}+y=5 & \end{matrix}\right. } \end{gathered}$}[/tex]

Substitute the expression that represents x into the second equation. Then both sides of the equation are squared and solved.

   [tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ \sqrt{y^2-2y+1}+y=5\quad \Longrightarrow\quad \left ( \sqrt{y^2-2y+1} \right )^2=(5-y)^2 } \end{gathered}$}[/tex]

                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ y^2-2y+1=y^2-10y+25\quad \Longrightarrow\quad 8y=24; } \end{gathered}$}[/tex]

                                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{ y=6 \qquad x=4 } \end{gathered}$}[/tex]

Answer:

V = 19329.14 cubic inches

Step-by-step explanation:

Volume of cylinder

[tex]V = \text{area of circle} \times \text{height}\\V = \pi r^2 \times h[/tex]

r ... radius of circle
h ... height of cylinder

Given information:

r = 18 in

h = 19 in

Now let's substitute the values in formula.

[tex]V = \pi r^2 \times h \\V = \pi (18)^2 \times 19\\V = 6156\pi\\V = 6156 \times 3.14\\V = 19329.84 \text{ in}^2[/tex]

the answer is B, D and F. I hope this was helpful

Answer:

Option (D): f(x) = 2x^2 – 3

Step-by-step explanation:

Math.

The function that represents the data in the table is y=2x²-3

A relation is a function if it has only One y-value for each x-value.

Let us check the function of the given data by plugging any ordered pair in the given functions

Let us take a point (1, -1) to check each function

(a) y=x/2-3

-1= 1/2-3

-1=-5/2

So y=x/2-3 is not the function

(b) y=2ˣ-3

-1=2-3

-1=-1

Now let us check for other point

5=4-3

5=1

This function is not satisfied for all points

(c) y=2x-3

-1=-1

For point (2, 5)

5=-1

This function is not satisfied for all points

(d) y=2x²-3

-1=2-3

-1=-1

Now 5=8-3

5=5

Hence, the function that represents the data in the table is y=2x²-3

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Answer:

  8

Step-by-step explanation:

After saving 1/3 of 6 dozen for the bake sale, the girls had 2/3 of 6 dozen left to split between them. Each of the 6 girls would receive 2/3 of 1 dozen, or 12×2/3 = 8 cupcakes.

Answer:

It's A

Step-by-step explanation:

y/x

it's starting point is 5 and it goes up 1 and over 2

1 is on the y-axis and 2 is on the x-axis and it is y over x so the answer is 1/2x+5

NOTE:I MAY NOT BE ACCURATE BUT IM PROBABLY IT COULD BE WRONG BUT IF U REALLY ARE STUCK ON A QUESTION THEN CHOOSE A

Answer:

y = 96

Step-by-step explanation:

given that y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

to find k use the condition when y = 24 , x = 2 , then

24 = k × 2² = 4k ( divide both sides by 4 )

6 = k

y = 6x² ← equation of proportion

when x = 4 , then

y = 6 × 4² = 6 × 16 = 96

Answer:

7

Step-by-step explanation:

The median is 7, if you place all the numbers in order then start crossing off the smallest and then largest number, you would be left with the number in the middle which is 7.

Answer:

7

Step-by-step explanation:

3, 3, 5, 7, 8, 9, 11

7 is in the middle.

Answer:

1. How many pupils does Mrs.Anub have in all

I am sorry but I could only solve question 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. How many pupils does she have in the class?

b. 40 pupils failed in the test.

c.  x = all pupil in the class

    percentage

d.   75/100 x = 40

e.   75/100 x = 40

           x        = 40*100/75

                     =  53.33

        pupils   =   53 people

f. There are 53 pupils in the class.

Answer:

it is the answer on the top

Answer:

Given the equations, I plotted 2 lines.

Line 1               Line 2

 x  |  y                x  |  y  

 0  | 101             0  |  -5

  1  |  101             1  |  -6

Answer:  3

Step-by-step explanation:

3/1 or 3

hope it helps...!!!

Answer:

Step-by-step explanation:

4 cups = 1 pint

$3.28/4 = .82 per pint

Step-by-step explanation:

hope it helps if there's any questions feel free to ask me but I'm sure that's how that question is hanled

answer : 9.5 because you subtract and then divide by 2

The categories that the expenses best fit into are:

fixed expenses :

variable expenses:

Fixed expenses are the expenses that are constant. They do not vary with the quantity bought. Variable expenses are the expenses that vary. More quantities can be bought and this increases the expenses.

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Answer:

$38696.84

Step-by-step explanation:

7% interest

so *1.07 per year

10,000*1.07^x=y

10,000*1.07^20=$38696.84

The equation that represent the  value of Alizeh’s investment after 20 years is y = 1000(b)^20

The increase in the amount of his money can be represented using the exponential function as shown:

y = ab^x

Given the following

a = 1000

x = 20 years

Substitute

y = 1000(b)^20

Hence the equation that represent the  value of Alizeh’s investment after 20 years is y = 1000(b)^20

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Answer:

Volume of Cone=1/3πd²/4×h

= 1/3π×7²/4×9

= 36.75cm³

Answer: n=-3 and n=3/2

Step-by-step explanation:

To solve the expression, we want to find the values of n. Since there are no common factors in 2, 3, -9, we directly multiply the "a" and "c" values.

2×(-9)=-18

This means, we want to find two numbers that multiply to -18 and adds to 3. This can also be known as the cross method.

We will find that 6 and -3 multiply to -18, and adds to 3.

In our box method, we want to find the common factors.

|2n²|6n|

|-3n|-9|

Note: Just pretend the lines line up and form a square box, with a term in each box.

After finding that is in common between the boxes, we get (n+3)(2n-3)=0

To solve, we set each factor equal to 0.

n+3=0

n=-3

2n-3=0

2n=3

n=3/2

Answer:

The sophomore in her school is 75

Step-by-step explanation:

Solution

The plot shows the distribution of 30 sophomores

We can see that there are 3 main vertical

line in red pen in the picture above.( distribution)

The first line means Minimum

The third line means the maximum

The second line means the medium

So the Medium is 75. And 30 sophomores in her

School took the survey.

So the medium belongs to them

Answer:

15/56

Step-by-step explanation:

5 people have a license

3 people don't

? = Probability that first person has a license and second does not

We can divide the problem into two sections, the first being the probability of the first person having a license, and the second section is the probability that the second person doesn't have a license.

P1 = Probability of the first person having a license, there are 5 out of 8 person having a license, thus P1 = 5/8.

P2 = Probability of the second person having a license. There are 3 people not having a license, out of 8-1 = 7 persons available, since one is taken already from the first choice, therefore P2 = 3/7.

P1 and P2 are dependent events, thus P(1,2) = P1 * P2.

P(1,2) = P1 * P1 = 5/8 * 3/7 = 15/56

596/1000 and 59.6%

Step-by-step explanation:

because when we make 596/1000 is 0.596

5/6 girls have either blue or brown eyes. Since 2/9=4/18

And 11/18 + 4/18 = 15/18

You can simplify 15/18 to 5/6

Answer:

Mean = 92

Median = 95.5

There is no mode.

What is mean, median, and mode?

Mean, median, and mode are terms in math when it comes to looking at charts and sets/groups of numbers.

1. The mean is the average of a data set.

2. The median is the middle of a data set.

3. The mode is the most common number in a data set.

Mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Before we start, let's put the set of numbers in order from least to greatest,

95, 97, 100, 86, 78, 96

78, 86, 95, 96, 97, 100

Now that we have done that let's find the mean,

78 + 86 + 95 + 96 + 97 + 100 = 552

There are 6 numbers in this set so we need to divide 552 by 6,

552 ÷ 6 = 92

92 is the mean/average of this data set,

Now let's find the median,

If we take a look at the data set we can see that there are two numbers in the middle because there are 6 in total,

78, 86, 95, 96, 97, 100

Because there are two values that are in the middle we need to add them up and divide the sum of them by 2,

95 + 96 = 191

191 ÷ 2 = 95.5

95.5 is the median of this data set,

Now let's find the mode,

If we take a look at the date set we can see that none of the numbers are repeated,

So this means there is no mode to this data set,

Therefore the mean is 92, the median is 95.5, and there is no mode.

Answer:

5

Step-by-step explanation:

It's in the middle of all the numbers

If you do need a more in-depth explanation just comment under here and I'd be happy to show you how I did it :)

Answer: y = 1/2x + 1/2

Given,

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals.

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf∠DBC= 55° and ∠BAC = 45°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf∠CAD = ∠DBC= 55° (Angles \: in \: the \: same \: segment)[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

Thus,

[tex] \sf∠DAB=∠CAD + ∠BAC[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= 55° + 45° [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \sf= 100°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

We know that the opposite angles of a cyclic quadrilateral are supplimentary.

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf ∠DAB +∠BCD = 180°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \sf∠BCD = 180°-100° =80°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \:[/tex]

[tex] \pink{\boxed{\sf{∠BCD = 80°}}}[/tex]

Answer:

∠BCD = 80°

Step-by-step explanation:

ABCD is a cyclic Quadrilateral.

∠DBC = 55°

∠BAC = 45°

∠BDC

=> ∠BAC = ∠BDC

=> 45° = ∠BAC { Angles of same segment BC}

In Triangle BCD

=> ∠BDC + ∠DBS + ∠BCD = 180°

=> 45° + 55° + ∠BCD = 180°

=> 100° + ∠BDC = 180°

=> ∠BDC = 180-100

=> 80° ans.