5. ( 2 points) How many basic variables does each augmented matrix have? I. \( \left[\begin{array}{rrrr|r}1 & 0 & 0 & 10 & -9 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & -6\end{array}\right] \) - A. None

A. Is 88

B. Is 24

C. Is none

D. Is 17 because

8 12 17 22 29

X. X. X. X

From the graph of the function we determine, [tex]y = 1.(2^{\frac{1}{3}})^x[/tex].

A function is said to be an exponential function when the exponent is the independent variable.

Let, The given function be f(x) = abˣ.

Now, At x = 0,

1 = ab⁰.

a = 1.

Again at,

x = 3,

2 = a.b³.

b³ = 2.

b = [tex]2^{\frac{1}{3}[/tex].

Therefore, The given function is, [tex]y = 1.(2^{\frac{1}{3}})^x[/tex].

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The expressions that can be used to determine the total area, in square feet, of Rajiv's garage after he removes the wall are

We have to solve for the total area of the garage of Rajiv after he had removed the wall

This is given as

12 * x + 12 * 14.5

= 12(14.5 + x)

Option B

When we expand the expression 12(14.5 + x)

174 + 12x

re written as

12x + 174

Option G

The expression that can be used to determine the total area, in square feet, of Rajiv's garage after he removes the wall is given as 12(14.5 + x), 12x + 174

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The value for the function f(g(-2)) is obtained as f(g(-2)) = 0.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The graph for the function y = f(x) is given.

The graph for the function y = g(x) is given.

We need to evaluate the function f(g(-2)).

From the graph of y = g(x) the value for g(-2) is obtained as -

g(-2) = 1

So, now we have -

f(g(-2)) = f(1)

From the graph of y = f(x) the value for f(1) is obtained as -

f(1) = 0

Therefore, the value is obtained as 0.

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The difference in area between a circle with a radius of 10cm and regular pentagon inscribed in it is  142cm².

The difference in area between a circle with a radius of 10cm and a regular pentagon inscribed in it can be found by first finding the area of the circle and then the area of the pentagon, and then subtracting the two values.

To find the area of the circle, we use the formula

A = πr²,

where r is the radius of the circle. In this case, r = 10cm, so the area of the circle is:

A = π(10cm)²
A = 100π cm²

To find the area of the regular pentagon, we can use the formula

A = (1/4)n*a² * cot(π/n),

where n is the number of sides of the polygon and a is the length of one side. Since the pentagon is inscribed in the circle, we can use the radius of the circle to find the length of one side of the pentagon.

The length of one side of the pentagon is:

a = 2r * sin(π/n)
a = 2(10cm) * sin(π/5)
a = 11.756cm

Now we can plug this value into the formula for the area of the pentagon:

A = (1/4)(5)(11.756cm)² * cot(π/5)
A = 172.047cm²

Finally, we can subtract the area of the pentagon from the area of the circle to find the difference in area:

Difference in area = 100π cm² - 172.047cm²
Difference in area = 314.159cm² - 172.047cm²
Difference in area = 142.112cm²

To the nearest whole, the difference in area between the circle and the pentagon is 142cm².

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The solution sets are written in proper solution set notation, using the set builder notation {x | condition}. The "n ∈ Z" indicates that n is an integer.

Solving each equation on the interval [0, 2π):

a. tan 3x = √3/3
3x = tan^-1(√3/3)
3x = π/6
x = π/18

Solution set: {π/18 + 2nπ/3 | n ∈ Z}

b. 2θ/3 = -1
2θ = -3
θ = -3/2

Solution set: {-3π/2 + 2nπ | n ∈ Z}

c. sin(2x - π/4) = √2/2
2x - π/4 = π/4
2x = π/2
x = π/4

Solution set: {π/4 + nπ | n ∈ Z}

d. 2 cos^2 x + 3 cos x + 1 = 0
(2 cos x + 1)(cos x + 1) = 0
2 cos x + 1 = 0 or cos x + 1 = 0
cos x = -1/2 or cos x = -1
x = 2π/3 or x = π

Solution set: {2π/3 + 2nπ, π + 2nπ | n ∈ Z}

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Answer: x = 9

Step-by-step explanation:

We must use Pythagorean's Theorem, a² + b² = c².

Let a = x

a² + 12² = 15²

a² + 144 = 225

a² = 81

a = 9

x = 9

Hope this helps!

The average rate of change of Q(x) from x=3 to x=3+h for h=0.2 is 21.2.

To find the average rate of change of Q(x) from x=3 to x=3+h, we need to plug in the values of h and a into the difference quotient and simplify.

When h=0.2, the difference quotient becomes:

(Q(3+0.2)−Q(3))/0.2

= (Q(3.2)−Q(3))/0.2

= ((3(3.2)^2+5(3.2)+10)−(3(3)^2+5(3)+10))/0.2

= ((30.24+16+10)−(27+15+10))/0.2

= (56.24-52)/0.2

= 4.24/0.2

= 21.2

Therefore, when h=0.2, the average rate of change of Q(x) is 21.2.

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26. The equation in slope-intercept form is y = 3x + 20.

27. The equation in slope-intercept form is y = (1/4)x - 11.

30. The equation in point-slope form is y - (-3) = -6(x - 2)

31. The equation in slope-intercept form is y = -6x + 9.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

26.

y-8 = 3(x+4)

y - 8 = 3x + 12  (distribute the 3)

y = 3x + 12 + 8 (add 8 to both sides)

y = 3x + 20

The equation in slope-intercept form is y = 3x + 20.

27.

y+5= (1/4)(x-24)

y + 5 = (1/4)x - 6

y = (1/4)x - 6 - 5

y = (1/4)x - 11

The equation in slope-intercept form is y = (1/4)x - 11.

To find the equation of a line with a slope of -6 that goes through (2,-3), we can use the point-slope form.

Point-slope form:

y - y₁ = m(x - x₁) where m is the slope and (x₁,y₁) is the point

Substituting m = -6, x₁ = 2, and y₁ = -3, we get:

y - (-3) = -6(x - 2)

y + 3 = -6x + 12

y = -6x + 9

The equation in slope-intercept form is y = -6x + 9.

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The average rate of change between the years 2002 and 2007 was  2,.939.8 (option B).

In demographics, the average rate of change refers to how much the population of a city, country, etc. changes over a year period usually by increasing or decreasing. Due to this, the rate of change can be calculated by using the following formula change in the population/ number of years.

239,839 (population in 2002) - 254,538 (population in 2007)

2007 - 2002 = 5 years (number of years)

14699 / 5 years = 2,.939.8 (option B)

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Answer: 3

Step-by-step explanation:

Each number is being multiplied by 3 to get the next number

Answer:

The common ratio is 3

Step-by-step explanation:

Since this is a geometric sequence you know you will be either adding or dividing. If you do 3159/3 you get 1053 and if you divide 1053 by 3 you get 351. So therefore the common ratio of this sequence is 3

I'm assuming this problem is going left to right. Right?

Answer: kdsl.dmcs

Step-by-step explanation:

The value of a is 92.17 when b=3 and c=7.

Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.

The variable a is jointly proportional to b and c, which means that a = k*b*c, where k is the constant of proportionality.

We can use the given values of a, b, and c to find the value of k:
79 = k*6*3
79 = 18k
k = 79/18

Now that we know the value of k, we can use it to find the value of a when b=3 and c=7:
a = k*b*c
a = (79/18)*3*7
a = 92.17

Therefore, the value of a when b=3 and c=7 is 92.17.

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Answer:

(a) Since Zul's password consists of 4 digits and the first three digits are 970, there is only one possible digit for the fourth digit. Thus, the probability to unlock the screen in one attempt is 1/10.

(b) If there are three 1s in the password, there is only one possible arrangement for the other digit. There are four places where the other digit can be placed, so there are four possible passwords. Thus, the probability to unlock the screen in one attempt is 4/10^4, which simplifies to 1/2500.

(c) If the last two digits are 00, there is only one possible arrangement for the first two digits. There are ten possible digits for the third digit and one possible digit for the fourth digit. Thus, the probability to unlock the screen in one attempt is 1/(101010*1), which simplifies to 1/1000.

Answer: 5.25

Step-by-step explanation:

     First, a percent divided by 100 is a decimal.

15% / 100 = 0.15

     Next, we are finding 15% of 35. In mathematical terms, "of" usually represents multiplication. We will multiply 0.15 by 35 to find 15% of 35.

0.15 * 35 = 5.25

The interval that contains a local minimum for this function is (0,2).

A local maximum is present on the graph of the function y = f(x) at the location where the graph shifts from increasing towards decreasing.

Thus, over the span, a local minimum happens (0,2)

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The table for the function is given:

Answer:

Step-by-step explanation:

This question doesn't say how much her lunch cost.

Based on these numbers, M Venkaiah Naidu secured around 68% of the valid votes cast, while Gopalkrishna Gandhi received around 32%.

In the vice-presidential election, M Venkaiah Naidu received 516 valid votes, while his opponent Gopalkrishna Gandhi received 244 valid votes. The total number of valid votes cast was 760, which is the sum of the votes received by the two candidates.

It's worth noting that the 68% figure only represents the proportion of valid votes cast, which excludes any abstentions or spoiled ballots. Additionally, this percentage reflects the support M Venkaiah Naidu received among the MPs who voted and may not necessarily reflect the views of the general public or the broader electorate.

Overall, M Venkaiah Naidu's victory in the election was decisive, with a difference of 272 valid votes between him and Gopalkrishna Gandhi, which was greater than the latter's total number of votes.

Complete question:

According to BJP sources, around two dozen MPs from opposing parties disobeyed their leaders and supported M Venkaiah Naidu for vice president of the NDA. Against the estimated 495 votes of pledged support, Mr. Naidu received 516 votes.

With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to the opposition's Gopalkrishna Gandhi, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.

What is the % of the votes did MRS Naido receive to write the answers to the east wholw%

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The length and width of the rectangle are 10 and 3, respectively.

Let's use "l" to represent the length of the rectangle and "w" to represent the width. From the problem statement, we've got portions of information:

The perimeter is 26. The formulation for the perimeter of a rectangle is P = 2l + 2w. So we are able to write:

2l + 2w = 26

The length is four extra than twice the width. In equation shape:

l = 2w + four

Now we can use substitution to resolve for the length and width. we will alternative the expression 2w + 4 for l within the first equation:

2(2w + 4) + 2w = 26

Simplifying:

4w + 8 + 2w = 26

6w + 8 = 26

6w = 18

w = 3

So the width of the rectangle is three. To discover the length, we're going to substitute w = 3 into the equation for l:

l = 2w + 4 = 2(3) + 4 = 10

So the length of the rectangle is 10.

Thus, the length and width of the rectangle are 10 and 3, respectively.

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The amount ( 3 /10 ) of total money given by Jeremy to Owiredu is equal to GHC 150.6.

Total amount of money with Jeremy in GHC is equal to 502.0

Amount of fraction of the money Jeremy gave to Owiredu is equal to

3 / 10.

Amount of money Jeremy gave to Owiredu is equal to

= ( 3 / 10 ) of GHC 502.0

= ( 3 / 10 ) × GHC 502.0

Multiply 3 to the 502.0 in the given expression we get,

= GHC ( 1506 / 10 )

Divide 1506 by 10 in the given expression we get,

= GHC 150 .6

Therefore, amount of money Jeremy gave to Owiredu is equal to GHC 150.6.

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In response to the aforementioned query, we may say that As a result, expressions the response is A. A quotient of two sums is this.

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

It is better to refer to the phrase (8+5)/(y+6) as "a quotient of two sums" since it divides the sum of 8 and 5 by the sum of y and 6.

As a result, the response is A. A quotient of two sums is this.

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The value fo x is 4 and the angle is 45 degrees

From the question, we have the following parameters that can be used in our computation:

The rectangle

The diagonals of a rectangle bisect each other

Using the above as a guide, we have the following:

2 * (3x + 6) = 5x + 16

So, we have

6x + 12 = 5x + 16

Evaluate the like terms

x = 4

Next, the diagonals of rectangle bisect the angles

So, we have

IHE = 45 degrees

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We have the following answers:

Solution:
(a) To simplify [tex]f(-3)[/tex], we need to plug in [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f(x) = x - x^2[/tex]:

[tex]f(-3) = (-3) - (-3)^2\\f(-3) = -3 - 9\\f(-3) = -12[/tex]

(b) To simplify [tex]g(x^2)/2[/tex], we need to plug in [tex]x^2[/tex] for [tex]x[/tex] in the function[tex]g(x) = 4x - 2[/tex], and then divide the result by 2:

[tex]g(x^2)/2 = (4(x^2) - 2)/2\\g(x^2)/2 = (4x^2 - 2)/2\\g(x^2)/2 = 2x^2 - 1[/tex]

(c) To simplify [tex]f(g(x))[/tex], we need to plug in the function [tex]g(x) = 4x - 2[/tex] for [tex]x[/tex] in the function[tex]f(x) = x - x^2[/tex]:

[tex]f(g(x)) = (4x - 2) - (4x - 2)^2\\f(g(x)) = 4x - 2 - (16x^2 - 16x + 4)\\f(g(x)) = -16x^2 + 20x - 6[/tex]

(d) To simplify [tex]g(g(x)) - x[/tex], we need to plug in the function [tex]g(x) = 4x - 2[/tex] for [tex]x[/tex] in the function [tex]g(x) = 4x - 2[/tex], and then subtract x from the result:

[tex]g(g(x)) - x = (4(4x - 2) - 2) - x\\g(g(x)) - x = (16x - 8 - 2) - x\\g(g(x)) - x = 15x - 10[/tex]

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Answer:  1.09 is closer to 1

(A). The largest target is Target B since it has the widest radius. (B). The size of Object A is around 44 inches around. (C). Target C has a surface area of around 254 square inches.

The length of a circle and perhaps other circular geometric object is referred to as its circumference. Anything in a double circular shape that is linear in one dimension is the perimeter.

A). We must contrast the radii of the three objects in order to compare their sizes.

Target A consists of a radius of 7 inches and a width of 14 inches.

The radius of Target B is 10 inches.

Target C has a circumference of 18π inches, so we can use the formula C = 2πr to find its radius:

18π = 2πr

r = 9 inches

Target B is the main market since it has the greatest radius.

B). The circumference of a circle is given by the formula C = 2πr, where r is the radius. For Target A, r = 7 inches, so:

C = 2πr

C = 2π(7)

C ≈ 44 inches (using 3.14 to approximate)

Target A's circumference is therefore around 44 inches.

C). The area of a circle is given by the formula A = πr², where r is the radius. For Target C, we know its circumference is 18π inches, so we can use the formula for circumference to find its radius:

C = 2πr

18π = 2πr

r = 9 inches

Target C's area is as follows because of its 9-inch radius:

A = πr²

A = π(9)²

A ≈ 254 square inches (using 3.14 to approximate)

Target C therefore has a surface area of around 254 square inches.

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If I understand your question correctly, pure water is 0% alcohol, so by adding water, this will dilute your 15% alcohol solution and lower the percentage of alcohol in the solution.

Many word problems are set up like "You have some amount of 15% alcohol solution and you add some pure water.  You end up with some other amount of the diluted mixture.  How much 15% alcohol solution and how much pure water were mixed."  

For those ones, use 0% alcohol for your pure water.

If Ranjit made pies for a fundraiser. The number of pies Ranjit made for the fundraiser is: 26.

Let p = total number of pies that Ranjit made

Let s = Total number of slices of pie that he made.

Since each pie is cut into 8 slices, we have:

s = 8p

After the first day of the fundraiser, Ranjit sold 10 slices, which means he had s - 10 slices left. Since he had 2 whole pies left, we know that he had 16 slices left. Therefore:

s - 10 = 16

Substituting s = 8p, we get:

8p - 10 = 16

Adding 10 to both sides, we get:

8p = 26

Dividing both sides by 8, we get:

p = 3.25

This means that Ranjit made 3.25 pies for the fundraiser.

The total number of slices would have been:

s = 8p = 8(3.25) = 26

On the first day, he sold 10 slices, which means he had 16 slices left. This matches our initial calculation and confirms that our solution is correct.

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The y-intercept of a polynomial function is the point at which the graph of the function intersects the y-axis.

This occurs when the x-coordinate is 0. So, to find the y-intercept of the given polynomial function, we need to substitute 0 for x and simplify:
f(x)=-2x^(5)-3x^(2)+2x-3x^(4)-6x^(3)
f(0)=-2(0)^(5)-3(0)^(2)+2(0)-3(0)^(4)-6(0)^(3)
f(0)=0-0+0-0-0
f(0)=0

Therefore, the y-intercept of the given polynomial function is (0,0).

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