Andrew filled a bucket with 7/10 of a gallon of water. A few minutes later, he realized only
2/5 of a gallon of water remained. How much water had leaked out of the bucket?

Answer:

52.5

Step-by-step explanation:

58.1 - 5.6= 52.5

C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span{u,v} is correct.

To show that a vector b is in Span{u,v}, one way is to determine if it can be written as a linear combination of the vectors in the set, i.e., if there exist scalars h and k such that b = hu + kv. If this is the case, the system containing the equations hu + kv = b is consistent, meaning that there exist values of h and k that make the equation true. Therefore, if the system is consistent, it can be concluded that the vector b is in Span{u,v}.

Therefore, option C is the correct answer.

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f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

m (x-x1) = y-y1 or

y = mx + c

Where,

Straight-line gradient, or m, is the line's slope.

The Cartesian coordinate that the line crosses is x1, y1.

the constant c

The calculation of the gradient (m) between any two locations on a line

m = Δy / Δx

f (-1) = Because x = -1, the function used is

y = 2, so f (-1) = 2 C) f (-3) = Because -3 -1,

the function used is y = -x-4, so f (-3) = - (- 3) -4 f (-3) = 3-4 f (-3) = -1 f (3) Since the function employed is

= -2x + 11 and x = 3, f (3) = -2 (3) +11, f (3) = -6 + 11, and f (3) = 5.

Hence, f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.

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Answer:-1
2
5

Step-by-step explanation:

simple answer

The required vertex form of the given equation is y = x² - 4x  + 7.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
y = (x - 2)² + 3

Simplifying the expression,
y = x² -4x + 4 + 3   {since (a - b)² = a² + b² -2ab}

y = x² - 4x  + 7

Thus, the required vertex form of the given equation is y = x² - 4x  + 7.

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Answer:

[tex]\text{f)} \quad y=80(1.1)^x[/tex]

[tex]\text{g)} \quad y=225(0.8)^x[/tex]

[tex]\text{h)} \quad y=5(3)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 72.73=ab^{-1}[/tex]

[tex]\implies 106.48=ab^3[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{106.48}{72.73}=\dfrac{ab^3}{ab^{-1}}[/tex]

[tex]\implies \dfrac{106.48}{72.73}=\dfrac{b^3}{b^{-1}}[/tex]

Solve for b:

[tex]\implies \dfrac{106.48}{72.73}=b^3 \cdot b^{1}[/tex]

[tex]\implies \dfrac{106.48}{72.73}=b^{3+1}[/tex]

[tex]\implies \dfrac{106.48}{72.73}=b^4[/tex]

[tex]\implies b=1.09998968...[/tex]

[tex]\implies b=1.1[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 72.73=a \cdot (1.09998968...)^{-1}[/tex]

[tex]\implies a=80.0022499...[/tex]

[tex]\implies a=80[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=80(1.1)^x[/tex]

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

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 351.56225=ab^{-2}[/tex]

[tex]\implies 115.2=ab^3[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{ab^3}{ab^{-2}}[/tex]

[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{b^3}{b^{-2}}[/tex]

Solve for b:

[tex]\implies\dfrac{115.2}{351.56225}=b^3 \cdot b^{2}[/tex]

[tex]\implies \dfrac{115.2}{351.56225}=b^{3+2}[/tex]

[tex]\implies \dfrac{115.2}{351.56225}=b^5[/tex]

[tex]\implies b=0.800000113...[/tex]

[tex]\implies b=0.8[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 115.2=a(0.800000113...)^3[/tex]

[tex]\implies a=224.999904[/tex]

[tex]\implies a=225[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=225(0.8)^x[/tex]

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

Given points:

Substitute the given (x, y) points into the exponential function formula to create two equations:

[tex]\implies 405=ab^4[/tex]

[tex]\implies 98415=ab^9[/tex]

Divide the second equation by the first equation to eliminate a:

[tex]\implies \dfrac{98415}{405}=\dfrac{ab^9}{ab^4}[/tex]

[tex]\implies 243=\dfrac{b^9}{b^4}[/tex]

Solve for b:

[tex]\implies 243=b^9 \cdot b^{-4}[/tex]

[tex]\implies 243=b^{9-4}[/tex]

[tex]\implies 243=b^{5}[/tex]

[tex]\implies b=3[/tex]

Substitute the found value of b into one of the equations and solve for a:

[tex]\implies 405=a \cdot 3^4[/tex]

[tex]\implies 81a=405[/tex]

[tex]\implies a=5[/tex]

Substitute the found values of a and b into the exponential function formula:

[tex]\implies y=5(3)^x[/tex]

Answer:

x=91

Step-by-step explanation:

Follow the steps in the image.

add 16 to both sides

subtract 3 from both sides

divide by 1x

Plug answer back into equation

-Hope this helped

Answer:

Step-by-step explanation:

∠ADB=360-90=270°

circumference of circle=2πr=2π×3=6π m

length of arc ADB

[tex]=\frac{270}{360} \times 6\pi \\=\frac{3}{4} \times 6\pi \\=\frac{9}{2} \pi \\\approx 14.137~m\\[/tex]

area of circle =πr²=π×3²=9π m²

area of shaded region

[tex]=\frac{270}{360} \times 9\pi \\=\frac{27}{4} \pi ~m^{2} \\\approx 21.206~m^2[/tex]

Answer:

-87

Step-by-step explanation:

y=2

3y(2-7)-3(y-4)-63 
3(2)(2-7)-3(2-4)-63 

6(2-7)-3(2-4)-63

6(-5)-3(-2)-63

-30+6-63=-87

Answer:

u = -5

Step-by-step explanation:

Isolate the variable, u. Note the equal sign, what you do to one side, you do to the other.

First, combine like terms. Like terms are terms that have the same amount of the same variables:

23 = -8u - 7 + 2u

23 = (-8u + 2u) - 7

23 = -6u - 7

Next, isolate the variable, u. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponsnts (& Roots)

Multiplications

Divisions

Additions

Subtraction

~

First, add 7 to both sides of the equation:

23 = -6u - 7

23 (+7) = -6u - 7 (+7)

23 + 7 = -6u

30 = -6u

Next, divide -6 from both sides of the equation:

-6u = 30

(-6u)/-6 = (30)/-6

u = 30/-6

u = -5

u = -5 is your answer.

~

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Answer:

Step-by-step explanation:

[tex]23= -8u-7+2u[/tex]

[tex]-8u-7+2u=23[/tex]

[tex]-8u+2u-7=23[/tex]

[tex]-6u-7=23[/tex]

[tex]-6x-7+7=23+7[/tex]

[tex]-6u=30[/tex]

[tex]\cfrac{-6u}{-6}=\cfrac{30}{-6}[/tex]

[tex]u=-5[/tex]

The domain and the range of this function shown in the graph include the following;

B. Domain: all real numbers.

   Range = f(x) ≥ -11

In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this function (see attachment), we can reasonably and logically deduce the following domain and range:

Domain = -∞ ≤ x ≤ ∞ or all real numbers.

Range = f(x) ≥ -11 or [-11, ∞].

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The final statement is: The system of equations have unique solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: x-2y = 2 & y=-2x+5

Solving these two equations by method of substitution we get

x-2(-2x+5)=2

x+4x-10=2

5x=12

x=2.4

∴ y=2×2.4+5

    =4.8+5

    =9.8

Hence, The system has one solution.

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Answer:

-5x+5

Step-by-step explanation:

That would be the answer

Answer:

50,000+30,000+13852=93,852

if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10°.

We have to find the length of z.

By using sine rule we find the length of z.

sin117/500=sin10/z

0.891/500=0.174/z

Apply cross multiplication

0.891z=0.174×500

0.891z=87

z=87/0.891

z=97.64 inches

Hence, if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.

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Answer:

97

Step-by-step explanation:

The midpoint of the points A (1, 5) and B (-7, -5) is found to be (-3, 0)

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

Given points A (1, 5) and B (-7, -5)

X= (1 - 7)/2 = -3

Y = (5 - 5)/2 = 0

the midpoint is (-3, 0)

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The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

You download a digital soccer game for $2.50. You can add new players for $1.50 each to upgrade your team.

The number of players will be in a whole number. Then the function is given by the greatest integer function.

Let 'y' be the total cost and 'x' be the number of players. Then the equations are given as,

y = 1.50 [x] + 2.5

The total cost for 5 new players will be given as,

y = 1.50 [5] + 2.5

y = 7.5 + 2.5

y = 10

The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.

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On solving the question, we can say that second function has vertical asymptote at x=2

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.

The function that represents the graph is f(x) = 1/x-2 .

The graph of the function

From the given graph , the vertical asymptote is at x=2

Lets find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator =0

f(x) = 1/2x

2x = 0

x = 0

f(x) = 1/x-2

x-2 = 0

x = 2

The second function has vertical asymptote at x=2

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The P(n) represents the maximum no of regions into which n lines divide the plain then P(k) = P(k-1) + k. (b). The formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex]. (c). The 5152 regions can divide the plane for 100 lines.

When no. lines are drawn, we get one plain region.

Let the number of regions when divided by lines be represented by

P(0), P(1), P(2), P(3), P(n)

Therefore P(0) = 1

P(1) = 2

P(1) = P(0) + 1

P(2) = P(1) + 2

P(3) = P(2) + 3

P(4) = P(3) + 4………………….

P(n) = P(n-1) + n

Therefore, if P(n) represents the maximum no. of regions into which n lines divide the plain

Then P(k) = P(k-1) + k

(b).

⇒ P(0) = 1

⇒P(n) = P(n-1) + n

= P(n-2) + (n-1)+n

= P(n-3) + (n-2) +(n-1)+n……..

= P(0) + 1 + 2+ 4=3 + 4 + 5 +……+n

= P(0) + (Sum of the first n natural numbers)

[tex]$$\begin{aligned}& =P(0)+\frac{n(n+1)}{2} \\& =1+{ }^{n+1} c_2\end{aligned}$$[/tex]

Therefore, the formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex].

(c)

Compute the value for n=100

[tex]$$1+{ }^{n+1} c_2=1+{ }^{101} c_2=1+\frac{101 \times 102}{2}=5152$$[/tex]

Therefore, the 5152 regions can divide the plane for 100 lines.

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A single line divides the plane into two regions. Two lines (by crossing) can divide the plane into four regions; three lines can divide it into seven regions, etc. Let P(n) be the maximum number of regions into which n lines divide a plane, where n is a positive integer.

(a) Derive a recurrence relation for P(k) in terms of P(k-1) for all integers [tex]$k \geq 2$[/tex].

(b) Use iteration to find an explicit (closed) formula for P(n).

(c) Into how many regions can 100 lines divide the plane?

Answer:

Input = 5

Step-by-step explanation:

Output = Answer a.k.a. f(x)

Input = x

We start by replacing f(x) with the output, which is 11

11 = 4x-9. I like making it opposite. It's easier in my eyes.

Making it opposite it's 4x-9 = 11

Now we need to get x by itself. The opposite of -9 is +9. So if we add 9 to each side, it deletes the 9 from the left and puts it on the other side, making it;

4x = 11 + 9. 11 + 9 is 20, so....

4x = 20.

Now 4x is the same as 4 times x. The opposite of times is divide. So let's divide by 4 on both sides. That gets rid of the 4 on the left side and puts it on the other side, making it;

x = 20/4. 20/4 is 5, so...

x = 5

Step-by-step explanation:

f(x) = 4x - 9

4x - 9 = 11

4x = 11 + 9

4x = 20

x = 20 ÷ 4

x = 5

The provided model represents the expression 4x-3.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.

Here,

You have 4 x's, then you minus 3,

=4x-3

The expression is represented by the model given is 4x-3.

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there is not enough information here to complete the problem.

Answer:

Question 8: (-4,7)

Question 10: (5,2)

Step-by-step explanation:

What are equations?:

What is Substitution Method?:

y = -2x - 1

3x - 4y = -40

Question 8:

3x - 4(-2x-1) = -40

3x + 8x + 4 = -40

11x + 4 = -40

11x = -44

x = -4

To find y we can substitute x into the equation.

y = -2(-4) -1

y = 8 -1

y = 7

(-4,7)

Question 8 Solution - (-4,7)

Question 10:

2x - y = 8

x = 5

Since this equation already given x we can substitution to find y.

2(5) - y = 8

10 - y = 8

-y = -2

y = 2

(5,2)

Question 10 Solution - (5,2)

Lenvy~

f(h(x)) = -2x^2 + 12x + (-12) in terms of x.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

To find f(h(x)), we first need to substitute h(x) into f(x).

f(h(x)) = f(4(x-3)²)

Now we can substitute 4(x-3)^2 into f(x)

f(h(x)) = 6 - 1/2(4(x-3)^2)

= 6 - 2(x-3)^2

= 6 - 2(x^2 - 6x + 9)

= 6 - 2x^2 + 12x - 18

Hence, f(h(x)) = -2x^2 + 12x + (-12) in terms of x.

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The area of shaded figure rectangle is 7.5m²

The amount of space occupied by a flat surface with a particular shape is referred to as the area. It is calculated using the "number of" square units (square centimeters, square inches, square feet, etc.) The amount of unit squares that can fit inside a rectangle is its area. The flat surfaces of laptop monitors, blackboards, canvas, etc. are a few examples of rectangular shapes.

step1:

The formula for the area of the Rectangle  is:

A= a+ b/2*h= 3+3/2*7=31.5

step2:

The formula for the area of the rectangle is:

A=w l=3*8=24

Now you rest 31.5 -24 and it gives you 7.5

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In a party of 300 people, 54% of the people who would have someone to kiss is 162 people.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.

To determine the percentage of people with partners to kiss at midnight;

300 people present in party

54% will have someone to kiss = 0.54

Number of people that will have someone to kiss = 300 x 0.54 = 162

The 54% of people with someone to kiss are 162 in number.

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Journalize the adjustment entries on August 31 for the $500 in golf income during the three-month period from June 1 to August 31.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principal amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

given

First FMA Assignment

Jornal 1.

2. Accounts Title Date (Mar) Debit ($) Credit ($)

1 Cash 60,000

60,000 Common Stock

3 Land 23,000

Structures 9,000

6k in equipment

Cash 38,000

5) Marketing Costs 1,600

Cash 1,600

Golf Sales 800

19) Cash (100 x 15) 1,500

1,500 in unearned revenue

25,000 dividends

Cash 1,000

30) salaries and 600 in expenses

Cash 600

30) Payable Accounts 26,000

Cash 26,000

31) Cash 500

500 Golf Revenue

Journalize the adjustment entries on August 31 for the $500 in golf income during the three-month period from June 1 to August 31.

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