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ial Expressions: Mastery Test
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Using the order of operations, what are the steps for solving this expression?
40+8+32+(15-7) × 2
Arrange the steps in the order in which they are performed.
3²
5+9
40+8
14+ 16
8x2
KNOW
15-7

Let A be the point (-2, 9, 10) and n be the normal vector of the plane. The direction vector of the line is <1, 3, -3>, and since the plane is perpendicular to the line, n is orthogonal to the direction vector.

So, n is a vector that satisfies:

n . <1, 3, -3> = 0

The equation of the plane can be written in the form:

n . (x - A) = 0

Where x = (x, y, z) is any point in the plane.

We can find n by taking the cross product of two non-parallel vectors in the plane, such as <1, 0, 0> and <0, 1, 0>. Then,

n = (1, 0, 0) x (0, 1, 0) = (0, 0, 1)

Substituting the values of A and n into the equation of the plane, we get:

0 . (x - (-2, 9, 10)) = 0

0 . (x + 2, y - 9, z - 10) = 0

z - 10 = 0

z = 10

So the equation of the plane is:

z = 10

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Answer:

1. y= (x-3)^2+5 vertex form

2. y= 2(x+2)^2+4 vertex form

3. y= 3x^2+18x+20 general form

4. y= x^2+4x+8 general form

The problem involving exponents (1/5 x 5)⁵ is calculated to get 1

Information made available in the question is an equation of the form

= (1/5 x 5)⁵

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved using parenthesis first

= (1/5 x 5)⁵

= (1)⁵

Then exponents

= (1)⁵

= 1 * 1 * 1 * 1 * 1

= 1

The solution is 1

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Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.

The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.

Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.

In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.

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Answer:
Smallest to Largest =
5.899, 15.2, 50.57, and 150

Step-by-step explanation:

I hope this helps you out :D

Perimeter of Regular Polygon = 92cm (Number of sides) x (Side length of a polygon) units

The total length of a polygon's boundary is calculated as the polygon's perimeter. Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane. A polygon's perimeter is always measured in linear distances such as metres, centimetres, inches, feet, etc.

Based on the length of its sides, we can classify a polygon as either regular or irregular. The formula for several well-known polygons' perimeter is as follows:

A triangle's perimeter is equal to its three side lengths, a, b, and c.

A rectangle's perimeter equals 2 (length + width).

We first determine whether the given polygon is a regular polygon or an irregular polygon before computing the perimeter of the polygon. The polygon's perimeter is then determined using the proper Formula

Therefore, the formula to find the perimeter of a regular polygon is: Perimeter of regular polygon = (number of sides) × (length of one side)

From the given diagram;

Perimeter of the polygon = AB + BC+ CD + DA

Perimeter of the polygon = 10.5 + 11.5 + 12.5 + 11.5 + 11.5 + 12.5 + 11.5 + 10.5

Perimeter of the polygon = 22 + 24 + 24 + 22

Perimeter of the polygon = 46 + 46

Perimeter of the polygon = 92cm

Hence the Perimeter of the polygon is 92cm

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By algebra properties, the value of variable c for linear equation 3 · (x - 1) = 2 · x + c such that x = 3 is equal to 0.

In this problem we need to find the value of a variable c such that the following system of linear equations exists:

3 · (x - 1) = 2 · x + c

x = 3

First, substitute x in the first equation:

3 · (3 - 1) = 2 · 3 + c

Second, simplify and clear the resulting expression:

3 · 2 = 6 + c

6 = 6 + c

c + 6 = 6

c = 0

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Answer:

Step-by-step explain

You have to solve for 5a

Answer:

a) The two variables are the number of years and the height of the tree in feet

b) It is a positive linear relationship.

c) Put a point at (0,3) and one at (3,7), and connect the dots.

The required number in which when subtracted from both 17 and 12 , the product will be 1.04  is  x = 11.8 or 17.2.

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Let the number is x, then

(17 - x)(12 - x) = 1.04

204 - 17x - 12x + x² = 1.04

x² - 29x + 204 = 1.04

x² - 29x + 202.96 = 0

On solving for x, we get

x = 11.8 or 17.2

Thus, the number can be x = 11.8 or 17.2.

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The needed value is either x = 11.8 or 17.2, which when deducted from both 17 and 12 will result in a product of 1.04.

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The logarithmic function that describes the graph is given as follows:

[tex]f(x) = \log_2{(x + 1)}[/tex]

The parent logarithmic function is defined as follows:

f(x) = log(x).

Which, no matter the base, has the vertical asymptote given as follows:

x = 0.

The vertical asymptote of the graphed function is given as follows:

x = -1.

Hence:

[tex]f(x) = \log_a{(x + 1)}[/tex]

When x = 3, f(x) = 2, hence the base a is obtained as follows:

[tex]2 = \log_a{(4)}[/tex]

Meaning that:

a² = 4.

a = 2.

And the function is then defined as follows:

[tex]f(x) = \log_2{(x + 1)}[/tex]

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The percent markup for the scooter that costs a retailer $75 but sells for $125 at the local store is 66.67%.

The markup is the additional price added to the cost of an item for retail sales.

Markups are usually expressed in percentages.

To express the markup in percent determine the difference between the retail price and the cost price.  Then divide the difference by the cost price and multiply by 100.

The cost price of the scooter = $75

The selling price of the scooter = $125

The markup in dollars = $50 ($125 - $75)

The markup percent = 66.67% ($50/$75 x 100)

Thus, the scooter was marked-up at 66.67%.

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The line a and line c are perpendicular to each other.

Lines are known if they are parallel or perpendicular by there slopes.

Therefore, parallel lines have the same slopes and perpendicular have slopes that are negative reciprocals of one another.

The slope of a line is the change in the dependent variable to the change in the independent variable.

Therefore, let's find the slopes of each line.

line a:

slope = -3 - 1 / 6- 0  = - 4 / 6 = - 2 / 3

line b:

slope = -2 - 0 / 3 + 3 = - 2 / 6 = - 1 / 3

line c:

slope = 7 + 2 / 2 + 4 = 9 / 6 = 3 / 2

Therefore, line a and c are perpendicular

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The 14th term of the arithmetic sequence is 109 whose common difference is d = 8 and whose first term is a(1)=5.

The value of 14th term of an AP is 109.

In the given question

The common difference = 8

The value of first term=5

And we have to find the value of 14th term of Arithmetic progression

We utilize the method for locating the nth term to locate a specific term in an arithmetic series. An arithmetic sequence's nth term is determined by an = a + (n - 1)d in step 1.

Putting the given value in formula:

an = a + (n - 1)d

a 14th=5+(14-1)8

a 14th=5+13*8

a 14th=5+104

a 14th=109

So the value of 14th term of an AP is 109.

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The answers to all parts are shown below.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

7. CP of sound system = 499

loss= 45%

So, the selling price = 499 - 45% of 499

                                  = R 274.45

8. original price is =1084

The new price = 1084 + 8% of 1084

                                  = R 1,170.72

9. Percentage decreased

= ( 747 - 599) / 747 x 100

= 19.81%

10. Mandisa left with

= 1000 - (228.95 + 573.38)

= R 197.67

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Answer:

[tex] \sf \: x = 5[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 15 - x = 10

Then the value of x will be,

→ 15 - x = 10

→ -x = 10 - 15

→ -x = -5

→ [ x = 5 ]

Hence, the value of x is 5.

Answer: To check if a given value is a root of the equation 8x-4 = 2, we can substitute the value into the equation and see if it makes the equation true.

When we substitute 3 for x in the equation 8x-4=2, we get 8(3)-4=2, which simplifies to 24-4=2, which is not true. So, 3 is not a root of the equation.

To check if a given value is a root of the equation 4y + 5 = y-7, we can substitute the value into the equation and see if it makes the equation true.

When we substitute -4 for y in the equation 4y + 5 = y-7, we get 4(-4) + 5 = -4-7, which simplifies to -16+5=-11=-4-7, which is true. So, -4 is a root of the equation.

Step-by-step explanation:

The number of years that will take for the schools to have the same number of students is given as follows:

11 years.

The number of students in each school is modeled by linear functions in slope-intercept format, as follows:

y = mx + b.

In which:

The functions for this problem are given as follows:

They will have the same number of students when:

Sp(t) = Se(t).

Hence:

1074 + 19t = 1206 + 7t

12t = 132

t = 132/12

t = 11 years.

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The zeros of the function are -10 and +10

lesser x = -10

greater x = +10

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. . The zeros of quadratic equation will always have two values.

f(x) = 8x²- 800

f(x) = y

y = 8x²-800

when the graph crosses x axis the value of y = 0

therefore 0 = 8x²-800

divide both sides by 8

0 = x² - 00

x² = 100

x= √100

x= ±10

therefore lesser x = -10

greater 10 = +10

therefore the zeros of the quadratic equation f(x) = 8x²- 800 = +10 and -10

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Answer:

9y^8

Step-by-step explanation:

15/5 = 3

y^6 / y^2 = y^4

so you are looking at basically (3y^4)² = 3y^4 * 3y^4 = 9y^8

The function that can be used to get the height of the helicopter above the ground is: H=280m−1,500

A function is a statement, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable).

How to solve for the function

The value 280 is the constant rate that the helicopter is said to be descending.

The altitude from which it is coming down is given as 1500 feet

The function would be written as H=280m−1,500

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That regression model is described as overfitting. The model has identified specific data points in the data that are not universal.

A regression model, which provides a function, describes the relationship between one or more independent variables and a response, dependent, or target variable. To explain the relationship between height and weight, for instance, a linear regression model might be utilized.

Regression analysis is the foundation for many forecasts and evaluations of the effects on target variables. Regression models are widely employed in research to support claims about fuel economy, the causes of pollution, or the effects of screen time on learning.

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The length of the rectangular prism is 4/5x.

What is a rectangular prism?

Six faces make up the three-dimensional shape of a rectangular prism (two at the top and bottom and four are lateral faces). The prism has rectangular shapes on each of its faces. There are therefore three sets of identical faces in this picture. A cuboid is another name for a rectangular prism because of its shape.

We know that Volume of a rectangular prism is a product of length, height and width.

We are given volume as (7/x)-(3/5x).

The width(w) is 2/x and the height(h) is 4/x

Using the formula, we get

⇒ V = lwh

⇒ (7/x)-(3/5x) = l * (2/x) * (4/x)

⇒ l = [(7/x)-(3/5x)] / [(2/x) * (4/x)]

⇒ l = (32/5x) /(8/x^2)

⇒ l = 4/5x

Hence, the length of the rectangular prism is 4/5x.

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Symmetry is a way of measuring the shape of a data set. It is defined as the similarity between the upper and lower halves of a distribution.

A symmetric distribution is one where the data is equally distributed around a central point. To calculate this, you need to subtract the mean (the average of the values) from each data point and then divide by the standard deviation (the measure of how much the data is spread out). The formula for symmetry is: (x-mean)/standard deviation. An example of a symmetric distribution would be the scores of a group of students on an easy test. If the mean score was 70 and the standard deviation was 10, then any score between 60 and 80 would be considered symmetric.

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The number √5 + √16 is an irrational number

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

\sqrt{5}+\sqrt{16}

Express properly

So, we have the following representation

√5 + √16

Take the square root of 16

This gives

√5 + 4

Rewrite as

4 + √5

The above expression is an irrational number

This is so because of the radical symbol on 5

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The relation between the number of hours spent using electronic devices is 2 times the number of hours spent playing sports. ​

The term called relation is defined as the relationship between sets of values of ordered pairs and the set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.

Here we have know that the number of hours spent using electronic devices is 30 and the number of hours spent playing sports 15.

As per the definition of relation, in order to find the relation we need to do the division operation on then we get,

=> 30/15

=> 2

Which means that the first one is 2 times of the second one.

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If the reaction was done with excess sodium bicarbonate, the amount of calcium chloride would determine the amount of precipitate produced.

The theoretical mass of precipitate produced in a reaction between calcium chloride and sodium bicarbonate can be calculated by using the balanced chemical equation for the reaction. The balanced equation for this reaction is given as follows:

CaCl₂ + NaHCO₃ → CaCO₃ + NaCl + H₂O

In this reaction, one mole of calcium chloride reacts with one mole of sodium bicarbonate to produce one mole of calcium carbonate precipitate, one mole of sodium chloride solution, and one mole of water.

The mass of the precipitate can be calculated by multiplying the molar mass of calcium carbonate by the number of moles of calcium carbonate produced.

So, to calculate the theoretical mass of precipitate produced, you need to know the amount (in moles) of calcium chloride and sodium bicarbonate used in the reaction. If the reaction was done with excess sodium bicarbonate, the amount of calcium chloride would determine the amount of precipitate produced.

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Answer:

slope = 1/2

Step-by-step explanation:

The slope formula:

The slope of a line that passes through points [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex] is

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

To find the slope, we find two easy-to-read points. Easy-to-read points are usually on grid line intersections.

Points (0, 0) and (2, 1) are on grid line intersections and are easy to read.

We will now input the information from our two points into the slope formula to calculate the slope.

[tex] slope = m = \dfrac{1 - 0}{2 - 0} = \dfrac{1}{2} [/tex]

Answer:

165/34

Step-by-step explanation:

245=80+(25+9)w We subtract 80 from each side and simplify

165=(34)w Divide each side by 34

165/34 = w