Exponent
T-Table
Coincident (Consistent
Dependent)
Systems of Equations
Inconsistent
Consistent Independent
1.
2.
3.
4.
5.
6.
A set of two or more equations
with the same variables.
A system of linear equations with
EXACTLY ONE solution.
A system of linear equations with
INFINITELY MANY solutions.
A system of equations with NO
solution.
A number representing how many
times the Base number should be
multiplied by itself.
A chart of the different values for
an equation or graph.

The area of the triangle is 85 square units

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:

A =  (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

Where:

B: (x₁, y₁) = (-8, 3)

O: (x₂, y₂) = (5, 4)

X: (x₃, y₃) = (-7, -10)

A =  (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

A =  (1/2) [-8 (4 – (-10)) + 5(-10 – 3) + (-7)(3 – 4)]

A = (1/2) [-112 - 65 + 7]

A = 85 square units

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To calculate the area of her rectangular quilt, Mrs. Kuhn needs to multiply the length and width of the quilt in inches. Since each quilt square is 4 inches long, the calculation for the area of the quilt is:

Area of quilt = Length of quilt x Width of quilt x (4 inches) ^2

Therefore, the correct calculation for Mrs. Kuhn to determine the area of her quilt is the product of 4 inches times the sum of the length and width of the quilt.

The statement "The roots of the blues were in New York City" is NOT true.

among the late 19th and early 20th centuries, the blues first appeared among African American communities in the southern United States, particularly Mississippi.

African American musical traditions such field hollers, work songs, and spirituals were among those that influenced the development of the blues. African Americans utilised it to express their joys and achievements as well as their struggles and tribulations.

Even though the blues eventually spread to other parts of the United States and the world, its roots are firmly planted in the rural South.

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630 Liters of hardener will be added to 14 container of resins.

Given,

To add 45 of hardener to each container of resin.

Now,

Total number of containers = 14

Each container will have 45 hardener.

Let the amount of hardener to be added be x,

Then according to unitary method,

1 container = 45 hardener

14 container = x hardener

x = 630 liters.

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The range is 5 years.The median is 18 years.

To determine the range and median from the given dot plot of ages, we need to analyze the distribution of the data points.

The range represents the difference between the maximum and minimum values in a dataset. Looking at the dot plot, the minimum age appears to be 16, while the maximum age is 21. Therefore, the range can be calculated as:

Range = Maximum age - Minimum age = 21 - 16 = 5 years.

Thus, the range of the ages of employees at the summer camp is 5 years.

The median represents the middle value in a dataset when it is arranged in ascending or descending order. To determine the median, we need to organize the ages in order from least to greatest:

16, 17, 18, 19, 20, 21

Since there are six data points, the median would be the value in the middle. In this case, the median would be the third value, which is 18.

Therefore, the median of the ages of employees at the summer camp is 18 years.

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Answer:  C  y-1=7 (x+4)

Step-by-step explanation:

Point slope formula

y - y₁ =  m ( x - x₁ )        Where m= slope and (x₁ , y₁) is your point

Given:

point: (-4, 1); slope: 7

plug in to formula

y -  1 = 7 (x+4)

Check the picture below.

so notice, the area of the pyramid is really just the area of the four triangles with an altitude of 3 and a base of "s", and a square that s² in area, and we happen to know that's 40 inches.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{s})(\underset{h}{3}) \right]}~~ + ~~\stackrel{ square }{(s)(s)}}~~ = ~~40\implies 6b+s^2=40\implies s^2+6b-40=0 \\\\\\ (s+10)(s-4)=0\implies s= \begin{cases} -10\\ ~~ ~~ 4 ~in~~ \textit{\LARGE \checkmark} \end{cases}[/tex]

now, let's notice, we can't use the negative value, because the sides are never negative.

The actual distance from the starting point to the ending point is 39.96 miles.

For someone working with the map or scaled drawing, we can define the scale factor as the ratio between a distance on the drawing or map and the corresponding actual distance in the real world.

From the question,

1.5 inches on the map = 5 miles in actual distance

1 inch on the map =  x miles

Perform cross multiplication

1 inch on the map =  (5 x 1) / 1.5  = 3.33 miles/inch (scale factor)

The scale factor can then be expressed as ratio:

5/1.5 = 1:0.3

0r

5/1.5 = 10:3

So, the actual distance between the starting point and the ending point can be found by multiplying the length on the map by the scale factor:

Actual distance = Map distance x Scale factor

Actual distance = 12 inches x 3.33 miles/inch = 39.96 miles

Therefore, the actual distance from the starting point to the ending point is approximately 39.96 miles.

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Answer:

10.) 152 square feet

11.) 85 degrees

Step-by-step explanation: *Feel free to ask for an explanation*

Answer:

16/40 = 40%

Step-by-step explanation:

I divided 16/40 and got 0.4,

To turn a decimal into a percentage, either multiply by 100 or move the decimal to the right 2 times.

Answer:

1 is a

2 is c

3 is b

Step-by-step explanation:

The number of feet above the submarine is the shark is 23 feet.

Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.

Here, location of shark = 42-19

= 23 feet

Therefore, the number of feet above the submarine is the shark is 23 feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.

The area of triangle A is 98 sq cm. Option B is correct.

Since triangle A is a scaled version of triangle B, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

If the dimensions of triangle A are twice the dimensions of triangle B, then the ratio of their side lengths is 2:1.

The ratio of their areas, therefore, is (2:1)² = 4:1.

Given that the area of triangle B is 24.5 sq cm, we can find the area of triangle A by multiplying 24.5 by the ratio of their areas:

Area of triangle A = 24.5 × 4 = 98 sq cm

Therefore, the area of triangle A is 98 sq cm.

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Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

The value of function (f о g) (5) would be,

⇒ (f о g) (x) = 26

We have to given that;

Functions f and g are,

⇒ f(x) = x + 1

⇒ g(x) = 5x

Now, We can formulate;

⇒ (f о g) (x)

⇒ f (g (x))

⇒ f (5x)

⇒ 5x + 1

At x = 5;

⇒ 5 × 5 + 1

⇒ 25 + 1

⇒ 26

Thus, The value of function (f о g) (5) would be,

⇒ (f о g) (x) = 26

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Answer:

The expression πr2h is a monomial because it is a single term that is the product of three variables: π, r2, and h. The term "mono" means "one," and "monomial" refers to a single term in algebraic expressions.

The degree of a monomial is the sum of the exponents of its variables. In this case, the degree of the monomial is 3, because the variables π, r, and h have exponents of 1, 2, and 1 respectively. Therefore, the degree of the monomial is 1 + 2 + 1 = 3.

The length of XY in the congruent triangle is 8 units.

'

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

Therefore, the triangle XYZ is congruent to the triangle MNL.

Hence,

ΔXYZ ≅ ΔMNL

Therefore,

XY = MN

XZ = ML

YZ = NL

Hence,

XY = MN = 8 units

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The shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%. Option C

To determine the selling price of the pen in order to earn a 15% profit, we can use the concept of a profit margin.

Let's start by finding the cost price of the pen. Since the shopkeeper wants to make a 10% profit when selling the pen for Rs. 13.20, we can set up the equation:

Cost price + 10% profit = Selling price

Let's assume the cost price of the pen is C. Then, we can write theequation as:

C + 0.1C = 13.20

Simplifying the equation, we have:

1.1C = 13.20

Dividing both sides by 1.1, we find:

C = 12

So, the cost price of the pen is Rs. 12.

Now, to determine the selling price that will yield a 15% profit, we can use the formula:

Selling price = Cost price + Profit

Profit is calculated as a percentage of the cost price. In this case, the profit percentage is 15%. Substituting the values, we have:

Selling price = 12 + 15% of 12

Selling price = 12 + (0.15 * 12)

Selling price = 12 + 1.8

Selling price = 13.8

Therefore, the shopkeeper should have sold the pen for Rs. 13.80 in order to earn a profit of 15%.

The correct answer is option c. Rs. 13.80. Option C

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The area of the given kite is,

⇒ A = 26 units²

Now, In this case we have that the area of the kite is given by the area of two triangles,

And, the triangles share the same base with length,

2 + 2 = 4.

And, One of the triangles has height of 6 and the other has height of 7.

So, the total area of kite is,

A = 1/2 × 4 × 6 + 1/2 × 4 × 7

A = 12 + 14

A = 26 units²

Therefore, The area of the given kite is,

⇒ A = 26 units²

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The number of solutions the system of equations have is (a) more than one solutions

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

3y-3x = -9

4y-4x=-12

Simplify the equations

So, we have

y - x = -3

y - x = -3

Subtract the equations

0 = 0

The above equation is true for all values of x and y

This means that the number of solutions in the equation is many i.e. more than one solutions

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The relation shown in the graph is not a function because it violates the vertical line test.

We have,

The relation shown in the graph is not a function because it violates the vertical line test.

The vertical line test states that for a relationship to be a function, every vertical line drawn on the graph should intersect the graph at most once.

However, in this case, the U-shaped graph intersects the vertical line at multiple points, such as (-2, -2) and (2, 2).

Therefore, the relation does not meet the criteria of a function.

Thus,

The relation shown in the graph is not a function because it violates the vertical line test.

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The rotation's angle is -45 degrees.

Quadrilateral A'B'C'D' is the representation of quadrilateral ABCD rotated around (0,0).

Consider D and D's coordinates.

D(2,3) and D'(-2,-3)

Now, Join D and D' then

<DOD = 45

Here, the actual rotation is  -45 degree rotation can be visualized as a reflection across the y-axis followed by a 45 degree rotation in the clockwise direction.

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A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

Given that;

Function is,

⇒ f (x) = x³ - 3x² - 7x + 6

Now, We can check (x + 2) is a factor of function or not as;

If x + 2 is a factor of function, then x = - 2 is satisfy the function.

So, Put x = - 2;

⇒ f (x) = x³ - 3x² - 7x + 6

⇒ f (- 2) = (- 2)³ - 3 (- 2)² - 7 (- 2) + 6

⇒ f (- 2) = - 8 - 12 + 14 + 6

⇒ f (- 2) = 0

Thus, (x + 2) is a factor of the function,

Hence, We can find all the zeroes as;

(x + 2) ) x³ - 3x² - 7x + 6 (x² - 5x + 3

          x³ + 2x²

         ------------

              - 5x² - 7x

              - 5x² - 10x

              ----------------

                       3x + 6

                       3x + 6

                      ------------

                              0

Thus, We get;

⇒ x³ - 3x² - 7x + 6

⇒ (x + 2) (x² - 5x + 3)

Since, x² - 5x + 3 = 0

x = - (- 5) ± √(- 5)² - 4×1×3 / (2×1)

x = (5 ± √25 - 12) / 2

x = (5 ± √13)/2

Thus,

A) Yes, (x+2) is a factor of the function, because the remainder is zero.

B) All the factor are,

⇒ (x + 2) (x² - 5x + 3)

C) All the zeroes are,

x = - 2

x = (5 ± √13)/2

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Doing a change of units, we can see that 2.11 yd³ is equivalent to 1.7513 m³

We know that the relation between one yard and one meter is:

1yd = 0.91m

Then the relation between one cubic yard and one cubic meter is:

(1yd)³ = (0.91m)³

1 yd³ = 0.83 m³

Now we can perform a change of units between the volume in yards and the volume in meters, we will get:

2.11 yd³ = 2.11*(0.83 m³) = 1.7513 m³

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A statement that describes how the graph of his different from the graph of g include the following: D. The graph of h is the graph of g vertically shifted up 1 unit.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, we have:

(x, y)                               →                  (x, y + 1)

g(x) = x²

h(x) = g(x) + 1   → h(x) = x² + 1

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The equation of the functions represented on the graph are (b)

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

The graph

On the graph, we have the following intervals:

When the intervals are represented as inequalities, we have the following:

Interval 1: x ≤ 1

Interval 2: x > 1

This means that the intervals of the graphs are x ≤ 1 and x > 1

From the list of options, we have the graph to be option (b

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The mean of the test is 45.

Let's use the formula for z-score:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the raw score, μ is the mean, and σ is the standard deviation.

For the first score of 30, we know that it falls three standard deviations below the mean:

-3 = (30 - μ) / σ

Simplifying this equation, we get:

-3σ = 30 - μ

μ = 30 + 3σ

For the second score of 60, we know that it falls three standard deviations above the mean:

3 = (60 - μ) / σ

Simplifying this equation, we get:

3σ = 60 - μ

μ = 60 - 3σ

Now we can set these two equations equal to each other, since they both equal μ:

30 + 3σ = 60 - 3σ

6σ = 30

σ = 5

Now we can plug this value of σ back into one of the equations for μ:

μ = 30 + 3σ

μ = 30 + 3(5)

μ = 45

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The probability that exactly 3 of those games were won by the colonies is 25%.

We are given that;

Number of colonies= 4

Number of games= 3

Now,

To find the probability of exactly 3 wins out of 4 games, we can use the binomial probability formula1:

P(X = 3) = nCx * p^x * q^(n-x)

where n is the number of trials (4 games), x is the number of successes (3 wins), p is the probability of success (0.5), q is the probability of failure (1 - p = 0.5), and nCx is the combination of n things taken x at a time.

P(X = 3) = 4C3 * 0.5^3 * 0.5^(4-3) P(X = 3) = (4! / (3! * (4-3)!)) * 0.125 * 0.5 P(X = 3) = (24 / (6 * 1)) * 0.0625 P(X = 3) = 4 * 0.0625 P(X = 3) = 0.25

Therefore, by the probability the answer will be 25%.

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The scale factor is 1/3

The formula for calculating scale factor is expressed as;

SF = IL/PL

Such that the parameters are expressed as;

From the information given, we have that;

IL = 3cm

PL =9cm

Substitute the values, we have;

Scale factor = 3/9

Divide the values, we have;

Scale factor = 1/3

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The cost of the fondue pot after the 45% discount and 6% sales tax is calculated using the following equations:

In this example, the original price of the fondue pot is $92 and the discount is 45%, which would make the discount amount $41.40. The sales tax is 6%, which would be $2.48

Therefore, the final price of the fondue pot would be $43.88