The model represents a division equation.
Determine whether each statement is true or fa
Select True or False for each statement.
Please double check my work!
50 points!!!

The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.

In this question we must solve for t such that (4, 6, 3, t) is a linear combination of vectors (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2), which means that non-zero coefficients have to be found by algebraic handling:

(4, 6, 3, t) = α₁ · (1, 3, - 4, 1) + α₂ · (2, 8, - 5, - 1) + α₃ · (- 1, - 5, 0, 2)

Which is equivalent to this system of linear equations:

α₁ + 2 · α₂ - α₃ = 4

3 · α₁ + 8 · α₂ - 5 · α₃ = 6

- 4 · α₁ - 5 · α₂ = 3

α₁ - α₂ + 2 · α₃ - t = 0

Whose solution is (α₁, α₂, α₃, t) = (38, - 31,  - 28, 13). The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.

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The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

The expression is given as:

(6x - 2)(6 x + 2).

The above expression is a difference of two squares.

And this is represented as

(a - b)(a + b)= a^2 - b^2

So, we have

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

Evaluate

(6x - 2)(6 x + 2) = 36x^2 - 4

Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4

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The ratio between 40,000 and 200 is 200 : 1

The numbers are given as:

40,000 and 200

Express as ratio

Ratio = 40000 : 200

Divide each number by 200

Ratio = 200 : 1

Hence, the ratio between 40,000 and 200 is 200 : 1

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Answer:

in total she spent 10900

Step-by-step explanation:

We know she made a down payment of 2500 dollars and she agreed to pay the balance in 24 monthly installments of 350 dollars. Thus we can do simple multiplying of 24 x 350 which gives us 8400. We also need to add in her down payment which is 2500 so in total we got 10900

The conversion is given as 1, 760 feet per second

We need to convert 20miles per hour to feet per second

First, we should convert miles to feet

1 mile = 5280 feet

Then,

20 miles = x

Cross multiply

20 × 5280 = x

x = 105, 600

Per hour = I hour = 60 seconds

To find the conversion, we divided the conversion to feet by that of the time

= 105, 600/60

= 1, 760 feet per second

Thus, the conversion is given as 1, 760 feet per second

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The fraction of students that play basketball is  [tex]\mathbf{= \dfrac{1}{10}}[/tex].

The fraction of students that play basketball from the given information can be determined by assuming that the whole number of students in the middle school is whole i.e. (1)

Let us first determine the number of students that participate in sports, we have:

[tex]\mathbf{=1- \dfrac{3}{5}}[/tex]

[tex]\mathbf{= \dfrac{2}{5}}[/tex]

If 1/4 of these students play basketball, then we have:

[tex]\mathbf{= \dfrac{1}{4}\times (\dfrac{2}{5})}[/tex]

[tex]\mathbf{= \dfrac{1}{10}}[/tex] students play basketball.

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The correct statement is Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A.

Given that in a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.

From the given figure , it says that Triangle B is a reflection of triangle An across the x-pivot. Triangle C isn't a reflection of triangle A" in light of the fact that Triangle A is in the main quadrant and its appearance with x-axis makes the triangle-B in the fourth quadrant and the triangle C which is in second quadrant can not be a reflection and annot be a rotation of triangle-A. Triangle C is drawn by taking firstly the reflection of triangle A and then rotate on the same place and increased x+3 units in above direction.

Hence, the statement correctly describes the diagram is "Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A".

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Answer:

A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..

Step-by-step explanation:

goodluck

The expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)

The slope of a line is the gradient  or the average rate of change of the line or a line equation

Note that linear equations are equations that have constant average rates of change, slope or gradient

The two points are given as

(2,-4);(-3,1)

The slope of a line is calculated using

m = (y2 - y1)/(x2 - x1)

Substitute the coordinates of the points in the above equation

m = (1 + 4)/(-3 - 2)

Evaluate the numerator

m = 5/(-3 - 2)

Evaluate the denominator

m = 5/-5

Rewrite the quotient as

m = -5/5

Evaluate the quotient

m = -1

Hence, the expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)

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The resulting equation will represent a line whose slope is 1/2 times the slope of the line

The equation of the line is given as:

y = 3x/a + 5

The constant a is a positive constant.

So, when the value of a in the equation is doubled, we have:

y = 3x/2a + 5

A linear equation is represented as

y = mx + b

Where m represents the slope.

So, we have:

m1 = 3/a

m2 = 3/2a

Substitute m1 = 3/a in m2 = 3/2a

m2 = 1/2 * m1

Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line

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The linear equations are given as follows:

A linear function is modeled by:

y = mx + b

In which:

For diagonal AC, the line contains points (-3,3) and (3,-3), hence the line is:

y = -x.

In standard form:

[tex]x + y = 0, -3 \leq x \leq 3[/tex].

For diagonal BD, the line contains points (3,3) and (-3,-3), hence the line is:

y = x.

In standard form:

[tex]x - y = 0, -3 \leq x \leq 3[/tex].

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The solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2

The given equation is:

[tex]3p^2-9p=6[/tex]

This can be re-written as:

[tex]3p^2-9p-6=0[/tex]

Solve for p by factorization

[tex]3p^2-3p-6p+6=0\\\\3p(p-1)-6(p-1)=0\\\\(3p-6)(p-1)=0[/tex]

Equate each of the factors to zero

3p - 6 = 0

3p = 6

p = 6/3

p = 2

p - 1 = 0

p = 1

Therefore, the solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2

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Answer:

7 packs of hots dogs if they had 56 for the party 8 divided by 56 is 7

The equation is 8p=56. Hence p=7 and they bought 7 packs of hot dogs. Hope it helps : )

Considering the definition of an equation and the way to solve it, 43 female contestants have signed up to compete.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "m" the number of male contestants, and knowing that:

the equation in this case is:

m + (m+36) = 50

Solving:

m + m = 50 - 36

2m= 14

m= 14 ÷ 2

m= 7

Since there are 36 more female contestants than male contestants, then m +36= 7 + 36= 43

Finally, 43 female contestants have signed up to compete.

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Answer:

A. the adult human

B. the adult human

Step-by-step explanation:

A. There are 60 minutes in an hour, and the human's heart beats 72 bpm (beats per minute). If you multiply 60 by 72, you get 4,320 bpm. If you multiply 60 by 35, you only get 2,100 bpm.

B. If you use the same logic that 72 is greater than 35, than you can assume that the human hear makes 1,000,000 beats in less time. However, if you want to do the math, then simply divide 1,000,000 by 72. Then, divide 1,000,000 by 35. Whichever has the smaller number is the one that can make more heart beats in a faster time.

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-3, 1), (3, 7) and (0, -2)

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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Part A

[tex]f(x)=(x-1)(2x-3)[/tex]

Part B

[tex](x-1)(2x-3)=0\\\\x=1, \frac{3}{2}[/tex]

So, the x-intercepts are [tex](1,0)[/tex] and [tex]\left(\frac{3}{2}, 0 \right)[/tex]

Part C

As [tex]x \to \infty[/tex], [tex]f(x) \to \infty[/tex] because the leading coefficient is positive.

As [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex] because the degree is even and the leading coefficient is positive.

Part D

Plot the x-intercepts on the graph, and then find the value of [tex]f(x)[/tex] at [tex]x=\frac{5}{4}[/tex] (the midpoint of the two roots) to plot the vertex. Then, draw a curve through these three points that approaches infinity as [tex]x \to \pm \infty[/tex]

The answer is 14.

First, we need to find X using the first statement.

Now, we have to substitute this in the required expression.

The z score corresponding to the sample is -6.25

The formula for calculating the z-score is expressed as

z = x- μ/σ

Given the following parameters

x = 22 (sample size)

Mean  μ = 72

standard deviation σ = 8

Substitute

z = 22-72/8

z = -50/8

z = -6.25

Hence the z score corresponding to the sample is -6.25

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Answer:

2x-3/7x

Step-by-step explanation:

Answer: 77 degrees

mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.

The selling price of an equipment costing $150.00 with 35% markup is $202.50

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given that the mark up is 35%, hence:

Markup = [(selling price - cost price)/cost price] * 100%

Substituting:

$202.50

Selling price = $202.50

The selling price of an equipment costing $150.00 with 35% markup is $202.50

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Answer:

1) y > x² + 4x - 5, y > x + 5

2) Rational

Step-by-step explanation:

For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:

For a line, if the shade is above it then the value of y will be greater or equal to:

Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"

Therefore, the inequality for parabola is y > x² + 4x - 5

For a line, it does not have solid graph so the inequality is ">"

Therefore, the inequality for line is y > x + 5

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The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm  for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.

That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.

Answer:

9.8 is the final anwser

Step-by-step explanation so easy

Answer:

55

Step-by-step explanation:

61.621 rounded to the nearest whole number is 62. We know this by looking at the whole number "61" and rounding its last digit by the digit to the right of it, depending if its <5 or >5. In this case, the right ones digit is "6", being greater than 5 means we can round 61.621 to 62.

The same applies to 7.173, given that "1" is less than 5, we don't round down (because we are rounding up), instead we replace remaining digits with 0, leaving us with 7.

To find the difference means to subtract;

62-7 = 55.

Answer:

x = 60 degrees

Step-by-step explanation:

1. We know that a triangle has a total angle of 180. If we look at the image closely, triangle GEH can be found, and since we know two angles, which are 40 and 80, we can find the other angle. 180 - (40+80) = 60. Angle GEH is 60 degrees.

2. If angle GEH is 60 degrees, angle EFD will also be 60 degrees, since they have the same angle side. To prove this, we can use alternate interior angles. This means that if a line crosses two parallel lines, the inner angles made have the same size.

3. Since angle EFD is x, we can find that x is equal to 60 degrees.

Answer:Rules for rotating points about the origin

1. The point (a,b) rotated 90° counterclockwise about the origin

becomes (-b,a).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)

B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)

C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)

D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)

Step-by-step explanation:

The y-intercept of this function represents C. the minimum amount of electricity consumed

The function is given as:

y = 0.503x + 3.31

The y-intercept of a function represents the minimum or the initial value of the function

This means that the y-intercept of this function represents C. the minimum amount of electricity consumed

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You are expected to lose $ 10 on an average per game

Probability of sum of 7 = 6 / 36

Probability of sum of 7 = 1 / 6

Amount won per game = (1 / 6) × 90

Amount won per game = $ 15

Probability of sum 6 or 8 = 10 / 36

Probability of sum 6 or 8 = 5 / 18

Amount lose per game = (5 / 18) × 90

Amount lose per game = $ 25

Expected earnings = Amount won per game - Amount lose per game

Expected earnings = 15 - 25

Expected earnings = -$ 10

Thus, you are expected to lose $ 10 on an average per game

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