Which of the following inequalities matches the graph?
-8 -0
O x>4
O x<4
O y> 4
O y<4
1

The solution set of the system of linear equations represented by the augmented matrix is (x1, x2, x3, x4) = (2, 4, 2, -1)

To determine the values, first express the system of linear equation as represented by the augmented matrix.

The system of linear equations represented by the augmented matrix is:

1x1 + 2x2 + 0x3 + x4 = 3

0x1 + 1x2 + 2x3 + x4 = 3

0x1 + 0x2 + 1x3 + 2x4 = 1

0x1 + 0x2 + 0x3 + 1x4 = 4

By applying row operations to the matrix we can find the solution set

R2 - R1

0 -1 2 0 0

0 0 1 2 1

0 0 0 1 4

R3 - 2R1

0 -1 2 0 0

0 0 1 2 1

0 0 0 -3 2

R4 - 4R1

0 -1 2 0 0

0 0 1 2 1

0 0 0 -7 8

R3 - R2

0 -1 2 0 0

0 0 0 -1 3

0 0 0 -7 8

R4 - 7R2

0 -1 2 0 0

0 0 0 -1 3

0 0 0 0 -1

R4/ -1

0 -1 2 0 0

0 0 0 -1 3

0 0 0 1 -1

x4 = -1

x3 = 3x4 + 1 = 2

x2 = 2x3 = 4

x1 = 3 - 2x2 - x4 = 2

Therefore, the solution set is (x1, x2, x3, x4) = (2, 4, 2, -1)

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Answer:

Part A -   Option B   $382.50

Part B -   11 years

Step-by-step explanation:

The formula for simple interest is

[tex]A=P(1+rt)[/tex]

[tex]A[/tex] is the final amount

[tex]P[/tex] is the initial amount

[tex]r[/tex] is the interest rate as a decimal

[tex]t[/tex] is the time

We are given

[tex]P=3000\\r=0.0425[/tex]

Part A

To evaluate the amount of interest we need to use this equation

[tex]I=Prt[/tex]

[tex]I=3000*0.0425*3[/tex]

[tex]I=382.5[/tex]

Part B

We can start with this equation, but we need to solve for [tex]t[/tex].

[tex]A=P(1+rt)[/tex]

Lets solve for [tex]t[/tex].

Divide both sides of the equation by [tex]P[/tex].

[tex]\frac{A}{P} =1+rt[/tex]

Subtract 1 from both sides of the equation.

[tex]\frac{A}{P}-1 =rt[/tex]

Divide both sides of the equation by [tex]r[/tex].

[tex]\frac{\frac{A}{P}}{r}-\frac{1}{r}=t[/tex]

Simplify the first term by multiplying the numerator by the reciprocal of the denominator.

[tex]\frac{A}{Pr} -\frac{1}{r}=t[/tex]

[tex]t=\frac{A}{Pr} -\frac{1}{r}[/tex]

Now we have an equation for time.

Substituting our values into the equation gives us

[tex]t=\frac{4402.50}{3000*0.0425} -\frac{1}{0.0425}[/tex]

[tex]t=11[/tex]

Therefore ,As a result, the answer to the provided problem of force is (-26.46i-52.92k) Nm.

It is capable of both pulling and pushing. Unbalanced forces are what lead to acceleration. A force is represented by the Newton (abbreviation is N). One Newton of force is required to change a weight of one kilogram's mobility by one meters per seconds (m/s) per sec. It goes like this: 1 N = 1 kg m/s2 (kg metre / second squared)

Here,

Given: There is a force F occurring at a size of F = 165 N along the parallelepiped's diagonal in this situation.

In order to calculate the force moment F around point A.

MA=rBXF

={(-600) (-88.2i+132.3j+44.1k)}

=(-52920k - 26460i) Nm

=(-26.46i-52.92k) Nm

Therefore , the solution to the given problem of force comes out to be (-26.46i-52.92k) Nm.

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The required required value of angles are  31, 118, 31.

An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.

We have,

∠Q = 8x-17, ∠R = 19x+4, ∠S = 5x+1

So,

∠Q + ∠R + ∠S = 180

= 8x-17 + 19x+4 + 5x+1

= 32x - 12 = 180

= 32x = 192

x = 6

Angles are;

∠Q = 8x-17 = 8(6)-17 = 31

∠R = 19x+4 = 19(6)+4 = 118

∠S = 5x+1 = 5(6)+1 = 31

Thus, required value of angles are  31, 118, 31.

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Answer:

choice B ( 7/20) is the right answer.

Step-by-step explanation:

If Gavin's mother poured 1 cup of milk in the glass and Gavin drinks 1/5 of the milk, the fraction of the milk that will remain in the glass is (4/5) of 1 cup.

So, B ( 7/20) is the right answer.

The value of expression after subtraction is, 2,226.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

The expression is,

⇒ three hundred fifty - two thousand five hundred seventy-six

Now, We can write the expression as;

⇒ three hundred fifty - two thousand five hundred seventy-six

⇒ 350 - 2,576

After subtraction we get;

⇒ - 2,226

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The equation that can be used to answer this question concerning speed would be = d=(0.6)(30). That is option C.

Constant speed is defined as the quantity that expresses the an object which travels the same distance in the same period of time.

The constant speed of the zebra = 0.6 miles per minute

Therefore, if 0.6 miles = 1 minute

d miles = 30 minutes

d miles = 30 × 0.6/1

d miles = 18 miles

Therefore the expression that can be used to answer this question would be = d=(0.6)(30).

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Answer: y = -1/6x + 1 1/3

Step-by-step explanation:

In a coordinate plane, a transformation is a function that maps pre-image points (inputs) to image points (outputs).

In (x,y) → (-y,x)

In (x,y) → (x + 4, y - 2)

In(x,y) → (x,-y)

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The interest rate on 7,000 for 10 years with a simple interest of 3500 is 5.

Simple interest is the amount paid on a principal amount of money that is borrowed or loaned to someone. It is calculated using the formula: SI = (P × R × T) / 100. Interest Rate (R) is a percent of the principal earned or paid.

From the question;

P = 7,000

T = 10

SI = 3500

we shall evaluate for the rate R as follows:

3500 = (7,000 × R × 10)/ 100

3500 = 70R

divide through by 70

3500/70 = 70R/70

R = 35/7

R = 5

Therefore, the rate for the amount 7,000 that will give a simple interest of 3500 for 10 years is 5

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The tree's shadow at the same time of day was 113.29 foot long.

Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures (typically 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.

The metre, the fundamental linear unit in the metric system, has largely replaced the foot, with its multiples and subdivisions, in most nations and in all scientific applications. In the United States, the definition of a foot as exactly 30.48 cm went into effect in 1959.

We know that

1 feet = 12 inches

So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet

Now, lets find the shadow of tree

5[tex]\frac{2}{3}[/tex]/2 = 321/x

x = 113[tex]\frac{5}{11}[/tex]

x = 113.29

Thus, the tree's shadow at the same time of day was 113.29 foot long

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The system of linear equations y = x - 6.7 and y = - x + 1.7 have solution at point (x, y) = (4.2, - 2.5).

In this problem we need to construct a system of two linear equations whose solution is point (x, y) = (4.2, - 2.5). Linear equations are algebraic equations of the form:

y = m · x + b

Where:

The procedure is shown below. First, obtain the intercept of the first equation:

b = y - m · x

(x = 4.2, y = - 2.5, m = 1)

b = - 2.5 - 4.2

b = - 6.7

Second, write the first linear equation:

y = x - 6.7

Third, find the intercept of the second equation:

b = y - m · x

(x = 4.2, y = - 2.5, m = - 1)

b = - 2.5 - (- 1) · (4.2)

b = - 2.5 + 4.2

b = 1.7

Fourth, write the second linear equation:

y = - x + 1.7

Please see the image attached below for a representation of the system of linear equations.

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If the acceleration of the object becomes 9m/s², the force will be 24N

From the information, the moving object, the force acting on the object varies directly with the object's acceleration. When a force of 36N acts on a certain object, the acceleration of the object is 6m/s². The constant will be:

y = k/x

y = force.

x = acceleration

k = constant of proportionality.

k = 36 × 6

k = 216

If the acceleration of the object becomes 9m/s², the force will be:

= 216 / 9

= 24

The force is 24N.

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Answer:

Step-by-step explanation:

Step 1: Calculate the slant height of the pyramid.

Slant Height = √(6.9^2 + 8^2) = 10.1 cm

Step 2: Calculate the lateral surface area of the pyramid.

Lateral Surface Area = 4 * (1/2 * 6.9 * 10.1) = 176.5 cm^2

Step 3: Calculate the total surface area of the pyramid.

Total Surface Area = Lateral Surface Area + Base Area

Total Surface Area = 176.5 cm^2 + (1/2 * 6.9 * 8) = 227.7 cm^2

It is surprising to some extent when the probability of getting  pre-1982 copper pennies is 6.6 and you get 11 pre-1982 copper pennies.

As with "point" and "time," which we can't exactly define, the concept of "the probability of something" is one of those concepts that is still useful. The ideas in the paragraphs that follow should help you grasp the idea.

Typically, events are the "somethings" for which we consider the probabilities. We might discuss the likelihood that someone in a particular group will develop a specific disease within the next five years, the probability that the number on a die we rolled is 5, the likelihood that it will rain tomorrow, etc.

The pre-1982 copper pennies are 13.2%

That is for every 100 pennies randomly selected there will 13.2  pre-1982 copper pennies,

And for 50 pennies there will be 13.2/2 pre-1982 copper pennies

= 6.6

So the probability of getting a pre-1982 copper pennies from random 50 pennies are 6.6.

Therefore, it is surprising to some extent when the probability of getting  pre-1982 copper pennies is 6.6 and you get 11 pre-1982 copper pennies.

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Answer:  D

Step-by-step explanation:

The balance (future value) on the card after 1 year if interest is calculated:

1. Annually: $124.00

2. Every 6 months: $125.44

3. Every 3 months: $126.25.

The future value represents the present value compounded at an interest rate into the future, using the principle of the time value of money.

The future value can be computed using an online finance calculator.

1. Interest Calculation Annually:

N (# of periods) = 1 year

I/Y (Interest per year) = 24%

PV (Present Value) = $100

PMT (Periodic Payment) = $0

Results:

FV (Account Balance) = $124.00

Total Interest = $24.00

2. Interest Calculation Every 6 months:

N (# of periods) = 2 semi periods (1 year x 2)

I/Y (Interest per year) = 24%

PV (Present Value) = $100

PMT (Periodic Payment) = $0

Results:

FV (Account Balance) = $125.44

Total Interest = $25.44

3. Interest Calculation Every 3 months:

N (# of periods) = 4 quarters (1 year x 4)

I/Y (Interest per year) = 24%

PV (Present Value) = $100

PMT (Periodic Payment) = $0

Results:

FV (Account Balance) = $126.25

Total Interest = $26.25

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Answer:

Horizontal translation 3 units left

Vertical translation 2 units down

Step-by-step explanation:

Inside the parent function is horizontal.

Outside the parent function is vertical.

Answer:

b = a - 7

Step-by-step explanation:

subtract 7 from both sides of the equation

The graph of the equation x^2-x-2=3 is a parabola which opens downward.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions separated by an equals sign (=). Equations are used to express relationships between unknowns, knowns, and constants. Equations are used to solve problems and describe the behavior of systems.

The graph intersects the x-axis at two points, x=1 and x=3.

Therefore, the solutions to the equation are x=1 and x=3.

To find an estimate of the solution, we can draw a straight line from the x-axis to the point of intersection on the parabola.

The line intersects the x-axis at a point slightly higher than x=1, so the estimated solution is x=1.5.

This is an approximate solution and is only an estimate. To find the exact solution, the quadratic formula must be used.

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Answer: $8

Step-by-step explanation:

one adult ticket costs twice as much as one student ticket so

cost of 1 student ticket=x

cost of one adult ticket=2x

total money made=1040

adults+students=1040 so

64(2x)+132(x)=1040

128x+132x=1040

260x=1040

divide both sides by 260

x=4

1 student ticket=$4

1 adult ticket=2x=2(4)=$8

Ike- I went geek sorry..

The correct option regarding the solution to the system of equations is given as follows:

It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The point of intersection in this problem has a x-coordinate of 3, hence the third option is the correct option.

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The other information required while using the intermediate value theorem to show the existence of zero for the polynomial function plotted is

f(x₁) < 0 and f(x₂) > 0

The intermediate value theorem says that if "f" is a continuous function across a closed interval [a, b] with values f(a) and f(b) at its endpoints, then the function takes any value at a point inside the interval that is between the values of f(a) and f(b).

The root of a polynomial is the value of y when x is zero. hence to show that there is a zero between the points x₁ and x₂ there is a need to show there was a change of sign in the output value

Using the graph

At the point of change of sign is the required zero

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Treat the,, >, or sign as a = sign when graphing an inequality.

Draw a circle over the number to begin plotting an inequality on a number line, such as x>3 (e.g., 3). The circle should be filled in if the sign also includes equal to (or). Leave the circle blank if the sign doesn't contain the equal to symbol (> or ).

By treating the,, >, or sign as a = sign, the inequality can be shown graphically. Make a dotted line graph of the equation if the inequality is either or. Make a solid line out of the equation if the inequality is either or.

Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers. The value is not included, as indicated by the open circle. The value is included, as indicated by the closed circle.

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A given information is inversely proportional when one value decreases at the same rate that the other increases. It should be noted that an example is speed and travel time

Only when two variables are directly proportional to one another's reciprocal can two variables be said to be inversely proportional. Alternately, we can state that when two variables or quantities are in inverse proportion, their product has a constant value.

One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease.

Note that your information is incomplete and a overview was given.

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The line y=—x-2 can be seen on the right-hand graph. the expression for m=273. A slope intercept form is one that offers both a gradient and an intercept.

The slope intercept format can be used once you are aware that Y = mx + b. The point-slope form is a way to express an equation for a line by utilizing just a specific point just on line and its slope. You can use the slope intercept equation, y = mx + b, to get the slope, which is defined as the rise over run and represented by the point form (x,y) (0, b). The point-slope form is a way to expression an equation for a line by utilizing just a specific point on the linear and its slope.

Here,

Given:

The line y = 3x - 1 undergoes dilation with such a scale factor of 2.

The lines y = 3x is enlarged and centered by a factor of two (scaling factor).

The chart on the right displays the equation m=273 and the line y=—x-2.

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Parallelograms are all rectangles because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal.

Parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

There are five important properties of parallelograms such as:

Therefore all rectangles are parallelograms because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal. It abides by all the properties of a parallelogram.

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The y-intercept of the expression y=x^2-6x+8 is y(0,8).

What are intercepts?

The term "intercept" refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.

The given expression is -

y = x²-6x+8

To find the y-intercept, substitute the value of x with 0.

y = x²-6x+8

y = (0)²-6(0)+8

y = 8

Therefore, the y-intercept is (0,8).

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