The balance sheet for Tempest, Inc., is shown here in market value terms. There are 19,000 shares of stock outstanding.

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

The given system of equations:

x  +  2y  =  8              (Equation - 1)

-3x - 2y  =  12            (Equation - 2)

This can be written in matrix form as shown:

[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]

Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]

We can use cross multiplication,

= (-2)(1) - (-3)(2)

= -2 + 6

= 4 ≠ 0

So the system has a unique solution,

Then,

[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]

[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]

So, they can solve the X and Y values,

X = D1 / D

X = -40/4

X = -10

Y = D2 / D

Y = 36/4

Y = 9

Therefore,

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

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The coordinates of the point between points a to b are (5, -5/8)

We have the following endpoints on the segment

A = (-2, 2)

B = (6, -1)

The line ratio is given as the following fraction

Ratio, m : n = 7/8

Express the fraction as a ratio

So, we have

m : n = 7 : 8 - 7

Evaluate the difference

So, we have

m : n = 7 : 1

The coordinate of the point is then calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

Substitute the known values in the above equation

Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)

Evaluate the products in the above equation

So, we have

Point = 1/8 * (42 -2, -7 + 2)

Evaluate the sum and the difference

So, we have

Point = 1/8 * (40, -5)

Evaluate the products

So, we have

Point = (5, -5/8)

Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)

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Answer:

4.416 or rounded just 4

Step-by-step explanation:

23×12=276

276-223=53

53÷12=4.416

Probability that first three price winners are omar, kira and elsa is     [tex]\frac{1}{84}[/tex]

Probability that omar is first prize winner and kira is second prize winner and elsa is third price winner is  [tex]\frac{1}{504}[/tex]

When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.

(i)First 3 prizes must be given to 3 persons regardless of order

Hence they can also be arranged in 3! ways.

est 6 can be arranged in 6! ways.

positions                   ___ ___ ___ ___ ___ ___ ___ ___ ___

number of ways         3     2       1     6     5    4       3     2     1

total number of ways to arrange 9 people = 9!

[tex]P(A)= \frac{(3)(2)(1)(6)(5)(4)(3)(2)}{(9).(8).(7).(6).(5).(4).(3).(2))}[/tex][tex]P(A)=\frac{6}{9.8.7}[/tex][tex]P(A)= \frac{1}{84}[/tex]

(ii)Event A

In event A three positions are fixed .

Omar -1 Kira -2 Elsa -3

Therefore there is only 1 way to fill the 1st,2nd and 3rd position

Permutations can only be made among the other positions.

Positions -           ___  ___ ___ ___ ___ ___ ___ ___  ___

Number of ways-  1        1      1       6     5     4      3      2    1

Total number of ways of arranging  9 people =9×8×7×6×5×4×3×2×1

Number of ways to satisfy event A =1×1×1×6×5×4×3×2×1

P(A)=   [tex]\frac{(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}[/tex]

P(A)= [tex]\frac{1}{504}[/tex]

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If Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04  .

In the question ,

it is given that Jaya's account balance at beginning of month was $94.42 ,

first transaction +$31.87 ,

means Jaya deposited $31.87

So Account balance = $94.42+$31.87 = $126.29

Second transaction -$34.19 ,

means Jaya withdraw $34.19

So Account balance = $126.29-$34.19 = $92.10

third transaction -$58.47 ,

means Jaya withdraw $58.47

So Account balance = $92.10-$58.47 = $33.63

fourth transaction +$48.57,

means Jaya deposited $48.57

So Account balance = $33.63+$48.57 = $82.20

fifth transaction -$13.16 ,

means Jaya withdraw $13.16

So Account balance = $82.20-$13.16 = $69.04

Therefore , if Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04  .

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Answer:

  x = 8

Step-by-step explanation:

You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².

The area of a triangle is given by the formula ...

  A = 1/2bh

Then the area of this triangle is ...

  22.5 = 1/2(x -3)(x +1)

  45 = x² -2x -3

  48 = x(x -2) . . . . . . . add 3 and factor out x

We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.

__

Additional comment

x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.

The value derived when 5 is divided by 312 is 62.40.

Division is the process of putting a number into distinct equal groups using another number.  The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other mathematical operations include addition, subtraction and multiplication.

312  ÷ 5 = 62.40

The long division is:

      62.4

5[tex]\sqrt{312}[/tex]

 - 30  

       12

     - 10

          20

        - 20

          00

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So, 13 games were played each month, if each month had the same number of games.

Compared to multiplication, division is the opposite. If three groups of four add up to 12, then division of 12 into three groups of equal size yields four in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. It is referred to as a method of division to divide anything. According to the degree of difficulty, there are three different sorts of division procedures. These include the bus stop approach, the chunking method, and the long division method. The chunking method is also known as division by repeated subtraction.

Given Data

A total of 117 football games in the season, and 33 were played at night.

The season was nine months long.

Each month same numbers of game were played.

So,

117 ÷ 9

13

So, 13 games were played each month, if each month had the same number of games.

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A parking lot's length is 4 yards longer than its width. The dimensions of the parking lot are width=9 and length =12.

Given that,

A parking lot's length is 4 yards longer than its width.

We have to determine the parking lot's measurements if the area is 117 square yards.

Let us take the width as x and we get the length as x+4.

We can write as,

x(x+4)=117

x²+4x=117

x²+4x-117=0

x²+13x-9x-117=0

x(x+13)-9(x+13)=0

(x+13)(x-9)=0

x+13=0    and     x-9=0

x=-13       and      x=9

Therefore, The dimensions of the parking lot are width=9 and length=12.

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a. It should be noted that the equation illustrates that the value of 6a + 9b is 24.

b. The value of 2x + 5y is 25.

a. From the information, 2a + 3b = 8. The value of 6a + 9b will be:

6a + 9b = 3(2a + 3b)

This implies that the value will be multiplied by 3. Therefore, 8 × 3 = 24

(ii) What is the value of 2x + 5y?

4x + 10y = 50

It should be noted that this can be divided through by 2. This will be;

(4x + 10y = 50) / 2

2x + 5y = 25

The value is 25.

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Answer:

  a)  x³, 1/x, x, sin(x)

Step-by-step explanation:

You want to know which list of functions has the same graph when reflected across both the y- and x-axes.

Reflection across the y-axis transforms the function to ...

  f(x) ⇒ f(-x)

Reflection across the x-axis transforms the function to ...

  f(x) ⇒ -f(x)

Hence, reflection across both axes transforms the function to ...

  f(x) ⇒ -f(-x)

A function that has the characteristic that f(x) = -f(-x) is an odd function. Its graph is symmetrical about the origin. We can check to see if the functions of interest match this definition of an odd function:

  x³ = -(-x)³ . . . . true

  1/x = -(1/-x) . . . . true

  x = -(-x) . . . . true

  sin(x) = -sin(-x) . . . . true

  cos(x) = -cos(-x) . . . . false

  e^x = -e^-x . . . . false

  |x| = -|-x| . . . . false

The basic functions that are odd are ...

  x³, 1/x, x, sin(x)

Answer:A) 3

Step-by-step explanation:

Answer: 87, 295,000,000 or eighty-seven two hundred ninety-five Billion

Im pretty sure

Answer:

83

Step-by-step explanation:

3x³+2y-6

x= 3 and y = 4, we will plug in what x equals to for the x value, then we will plug in what y equals to for the y value

3(3³) + 2(4) - 6

now let's use order of operations (PEMDAS: parenthesis exponent multiplication division addition subtraction)

parenthesis first

3³ = 3·3·3= 27

3(27) + 2(4) - 6

there are no exponents so we will use multiplication

3·27 = 81

2·4=8

81 + 8 - 6

83

a) g(3) = -182

b) g(0) = 7

c) g(-1) = 70

a) g(3): To get this, we will substitute 3 for x in the function g(x)

b) g(0): To get this, we will substitute 0 for x in function g(x)

c) g(-1): To get this, we will substitute -1 for x in function g(x)

the fuction f(x) is equal to:

now, to evaluate f(15) we have to replace x=15 so the equation is going to be equal to:

Answer:

3x-2y=10

2y=3x-10

Y=(3/2)x-5

Slope m=3/2

Answer:

See attachment.

Step-by-step explanation:

Slope-intercept form:

[tex]\boxed{y=mx+b}[/tex]

where:

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

Given inequality:

[tex]3x-2y < 10[/tex]

Rearrange the given inequality to make y the subject:

[tex]\implies 3x-2y+2y < 10+2y[/tex]

[tex]\implies 3x < 10+2y[/tex]

[tex]\implies 3x-10 < 10+2y-10[/tex]

[tex]\implies 3x-10 < 2y[/tex]

[tex]\implies 2y > 3x-10[/tex]

[tex]\implies \dfrac{2y}{2} > \dfrac{3}{2}x-\dfrac{10}{2}[/tex]

[tex]\implies y > \dfrac{3}{2}x-5[/tex]

Compare this with the slope-intercept form.  

Therefore:

When graphing inequalities:

To graph the given inequality using its slope and y-intercept:

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Answer: y-intercept is 12

Step-by-step explanation:

y = mx +b

m = slope

b = y-intercept

y | = | x | + | b

f(x) | = | 4x | + | 12

b = y-intercept

Answer:

x=-1/4 or -.25

Step-by-step explanation:

I took the test and double checked it

Answer:

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

Step-by-step explanation:

ASA: Angle, Side, Angle

AAS: Angle, Angle, Side

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

I am going to use the drawer to show the differences:

Given the time, the distance that the.womn drives will be 240 miles.

From the information illustrated, the woman drives out at 40 miles per hour, return over the same road at 30 miles per hour, and spends 8 hours away from home.

It should be noted that the average speed will be illustrated as:

= (2 × r1 × r2) / +r1 + r2)

= (2 × 40 × 30) / (40 + 30)

= 240/7

Since she drive for 7 hours, the distance will be:

= 240/7 × 7

= 240 miles.

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The correct option C { -3, 1, 2, 6} is the domain of the relation given.

For the given relation in the question;

The values which are input in the function is called domain.

In put values are -  { -3, 1, 2, 6}

Thus, domain of the given relation is  { -3, 1, 2, 6}.

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The domain for the rational function is the set of all real numbers except for 8, this is written as:

{x | x ∈ R, x≠8}

For any function f(x), the domain is the set of the possible inputs.

In this case, we have the rational function:

f(x) = (x - 3)/(x - 8)

Now, we start by assuming that the domain is the set of all real numbers, and then we remove all the problematic values.

Now, we can't divide by zero, so the value of x that makes the denominator zero needs to be removed, that is such:

x - 8 = 0

x = 8

So the domain is the set of all real numbers except for 8, this is written as:

{x | x ∈ R, x≠8}

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Step-by-step explanation:

Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.

How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?

..

please post full questions

We know that

• The probability of a head is 1/2.

• The probability of a tail is 1/2.

Notice that the number of times they flip a coin is 7. Since both probabilities are the same, we just have to multiply 1/2 seven times by itself.

Now, we multiply the probability with 7 since there are 7 possibilities.

Then, we multiply by 100 to express it as a percentage.

Answer: CD<AD

Step-by-step explanation:

Just got it right on the test.

Answer: CD<AD

Step-by-step explanation:

Took the test!

Nothing tricky here:

[tex]\displaystyle \int_{-\infty}^0 \sqrt{1+2^2} \, e^{2\theta} \, d\theta = \sqrt5 \int_{-\infty}^0 e^{2\theta} \, d \theta \\\\ ~~~~~~~~ = \frac{\sqrt5}2 \left(e^0 - \lim_{\theta\to-\infty} e^{2\theta}\right) \\\\ ~~~~~~~~ = \frac{\sqrt5}2[/tex]

Recall that

[tex]\phi = \dfrac{1+\sqrt5}2[/tex]

and this is exactly 1/2 more than the value of the integral.

You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.

a) At t = 0

temperature of turkey is 67 degree  Fahrenheit

b) At t = 3.75

temperature of turkey is 165 degree  Fahrenheit

c) t = 3

temperature of turkey is 4 degree  Fahrenheit

d) at t = 3.75

temperature of turkey is 169 degree  Fahrenheit

Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done.

Given that : You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.

a) At t = 0

temperature of turkey is 67 degree  Fahrenheit

b) At t = 3.75

temperature of turkey is 165 degree  Fahrenheit

c) t = 3

temperature of turkey is 4 degree  Fahrenheit

d) at t = 3.75

temperature of turkey is 169 degree  Fahrenheit

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