8. The interest on $2,000 for 2 years is $320.
What is the simple interest rate?
$
= $2,000 r.
$
= $
=r
% = r
r

Answer:

Step-by-step explanation:

step 1 of 2:  

We got pairs: (-3, y) and (x, 2), to compute the missing x and y values, we plugin the number into the equation.

(-3, y)

y = -3x - 1

y = -3(-3) - 1

y = 9 - 1

y = 8

So we solve this pair as (-3, 8).

(x, 2)

y = -3x - 1

2 = -3x - 1

3 = -3x

x = -1

So we solve this pair as (-1, 2).

Sorry that I cannot see the following questions.

the answer to that question is 34cm² of the circumference

The quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.

According to the question,

We have the following information:

([tex]x^{2} -25[/tex]) is divided by (x+5)

Now, we can solve this using two ways. First method is to use the long division method and second is to solve the expression using an identity.

We know that the following identity can used to expand the dividend:

[tex]a^{2} -b^{2} = (a+b)(a-b)\\[/tex]

In this case, we have a = x and b = 5.

[tex]x^{2} -(5)^{2} = (x-5) (x+5)[/tex]

Now, we have the following expression:

(x+5)(x-5)/(x+5)

(x-5)

Now, the remainder is 0.

Hence, the quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.

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a) The value  sets of n(A) = 5, n(B) = 8

b)  33 ∈ A is false, -4 ∈ B is true, 25 ∈ A is true, 5 ∉ B is true.

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

A = { 25, 26, 27, 28, 29}

B ( is greater or equal to -6 and equal to 1) = { -6, -5, -4, -3, -2, -1, 0, 1}

n(A) = number of elements in A which is 5 and n(B) = 8

33 ∈ A The symbol ∈ means element of. so 33 is not an element of A.

-4 is an element of B so it is true, -4 ∈ B is true

25 ∈ A is true because 25 is an element of A

5 ∉ B is true because 5 is not an element of B

In conclusion, n(A) = 5, n(B) = 8

-4 is an element of B so it is true, -4 ∈ B is true

25 ∈ A is true because 25 is an element of A

5 ∉ B is true because 5 is not an element of B

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The five number summary from the given box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

These values are the values marked from left to right on the box plot, from the minimum value to the maximum value, passing through the first quartile, the median and the third quartile, and form the five number summary.

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The exponential function will be written as y = 14⁰.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,

[tex]y = ab^x \\[/tex]

14 = ab⁰

a = 14

The equation will be written as,

y = 14b⁰

y = 14⁰

Therefore, the exponential function will be written as y = 14⁰.

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The focus of parabola is (4 , -1) and directrix is 5

The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Focus: The point (a, 0) is the focus of the parabola

Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.

Given equation of parabola is :

y = - 1/12 (x - 4) - 2

Comparing it with standard equation,

h = 4

k = 2

a = -1/12

using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)

=> focus = (4 , 2+(12/4×-1))

=> focus = (4 , 2-3)

=> focus = (4 , -1)

and directrix is : y = 2-(1/4×-1/12)

y = 2 + 12/4

y=2 + 3 => 5

So, the focus is (4,-1) and directrix is 5

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let the number be = x

[tex] = > \frac{3x}{5} = 150[/tex]

[tex] = > 3x = 150 \times 5[/tex]

[tex] = > 3x = 750[/tex]

[tex] = > \frac{3x}{3} = \frac{750}{3} [/tex]

[tex] = > x = 250[/tex]

The number can be found by multiplying 150 by 5 and then dividing the result by 3. Therefore, the number is 250 by solving equations.

To find the number, we can set up the equation: (3/5) * x = 150. To isolate x, we multiply both sides of the equation by 5/3, resulting in x = 250. This means that the number is 250.

Start with the equation: (3/5) * x = 150.

To isolate x, multiply both sides of the equation by the reciprocal of (3/5), which is 5/3. This yields (5/3) * (3/5) * x = (5/3) * 150.

Simplify the left side of the equation: x = (5/3) * 150.

Multiply 5 by 150 and divide the result by 3: x = (750/3).

Simplify the fraction by dividing the numerator (750) by the denominator (3): x = 250.

Therefore, the number is 250.

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Equation for the perpendicular bisector of the line segment is  

2y = 3x +20.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

Given coordinates of the endpoints of a line segment  (-9, 3) and (-3,-1).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between  (-9, 3) and (-3, -1). :

slope = [tex]\frac{-1-3}{-3+9} =\frac{-2}{3}[/tex]

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 3/2

Now, we need to find the midpoint of the given coordinates.

[tex]Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)[/tex]

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - 1 = 3/2 (x + 6)

2y = 3x +20

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The angle measurements are 5.38°, 87.31° and 87.31°.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are the sides of triangle as AB = 18cm, BC = 18cm, AC = 16cm.

The given triangle is a isosceles triangle with two sides equivalent. Angles opposite to these sides will be equal. So, we can write -

2∠x + ∠y = 180°

from the figure, it can be seen that angle B is 5.38 degrees.

2∠x + 5.38 = 180

2∠x = 174.62

∠x = 87.31°

Therefore, the angle measurements are 5.38°, 87.31° and 87.31°.

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Answer:

B (5,9)

Step-by-step explanation:

when working with fractions as slopes we use rise over run (broken down)

3 (numerator)--rise-how unit to go up or down

--

4 (denominator)--run--how many units to the left or right

since our slope is positive we will be going up 3 and 4 to the right.

if the slope is negative we go down and to the left.

hope this explanation helps for future questions

The equation that relates x and y is given as y = 2.5x

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a.

The formula for direct variation is in the form of

y = kx

where we have the value of y = 5, the value of x = 2

we have to put this in the formula above

5 = 2k

to get the value of k we would have to divide through by 2

k = 5 / 2

k = 2.5

Hence we would have y = 2.5x

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Answer: x=25/4 or 6.25, y=79/16 or 4.9375

Step-by-step explanation:

Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.

Answer:

1) 7:4

2) 11: 7

Step-by-step explanation:

Answer:

Angle 1: 27

2: 153

3: 58

4: 138

Step-by-step explanation:

1. 180-(116+37)=27

2. 180-27=153

3. 180-(48+74)=58

4. 122+16=138

180-138=42

180-42=138

Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.

How to get distance/displacement using velocity?

According to given data:

A particle moves with velocity (dx)/(dt) = 3t² in x- direction

and (dy)/(dt) = 12t in y-direction

Integrating both sides of these derivatives with respect to t

x=  ∫3t² dt = (3t³)/3 + A = t³ + A

where A is integration constant

y= ∫12t d t = (12t²)/2 + B = 6t² + B

where B is integration constant

At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.

Therefore, the difference in position of a from t = 0 t = 3 is

27 + A - (0 + A) = 27 units.

Similarly,

At t = 0 , we get y = B and at t = 3 we get

y = 6 * 3² + B = 54 + B

Therefore, the difference in position of y from t = 0 tot t = 3 is

54 + B - (0 + B) = 54 units.

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The statement that best describes the relationship between the two triangles is the option;

Two triangles are similar if they satisfy the following conditions.

The length of the sides of the triangles are;

First triangle, a₁ = 3, b₁ = 5. c₁ = 15

Second triangle. a₂ = 9, b₂ = 6, c₂ = 18

The ratio of the corresponding sides is therefore;

[tex]\dfrac{a_1}{a_2} = \dfrac{3}{9} =\dfrac{1}{3}[/tex]

[tex]\dfrac{b_1}{b_2} = \dfrac{5}{6}[/tex]

[tex]\dfrac{c_1}{c_2} = \dfrac{15}{18} =\dfrac{5}{6}[/tex]

The ratio of the three corresponding sides of the triangles are not the same such that the corresponding sides of the triangles are not constantly  proportional.

Therefore the two triangles are not similar because all the corresponding sides are not proportional.

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If f(x) = x², the graph of g(x) = f(x) is x².

What is a Graph of a function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

How to find the graph of a function:

You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.

We are given the function; f(x) = x²

Also, we want to find the graph of g(x) = f(x)

From the above, it means that we put x in place of x for function f(x) to get the function g(x).

so, g(x) = f(x)

     g(x) = (x)²

Hence the graph of g(x) = f(x) is x².

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Answer:

Step-by-step explanation:

The number of months required to pay off the loan will be 15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.

The number of the months will be calculated as,

N = ( 1178.8 - 547.30) / 42.10

N = 631.5 / 42.10

N = 15

Therefore, the number of months required to pay off the loan will be 15.

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Option D. The sample space when one marble is to be chosen is given as S =  {green, blue, yellow, orange, purple, red}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

The sample space here have been listed based on the colors of the marbles that was presented in the question that we have here.

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Answer:

OPTION D is not correct I took the test and its B

Step-by-step explanation:

also here is a picture

The difference in lengths is 9 cm and the length of the carrot is 9 cm longer than the pea pod.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have to determine the difference in lengths

The length of the carrot = 14 cm

The length of the pea pod = 5 cm

The difference in lengths = maximum length - minimum length

The difference in lengths = 14 cm - 5 cm

Apply the subtraction operation, and we get

The difference in lengths = 9 cm

We conclude that the length of the carrot is 9 cm longer than the pea pod.

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x = 3

Step-by-step explanation:

[tex]{ \blue{ \sf{n(x) = 4x + 4}}}[/tex]

[tex]{ \blue{ \sf{16 = 4x + 4}}}[/tex]

[tex]{ \blue{ \sf{16 - 4 = 4x}}}[/tex]

[tex]{ \blue{ \sf{12 = 4x}}}[/tex]

Divide both the sides with 4

[tex]{ \blue{ \sf{ \frac{12}{4} = \frac{4}{4}x}}}[/tex]

[tex]{ \green{ \boxed{ \red{ \sf{x = 3}}}}}[/tex]

Answer:

394,200

Step-by-step explanation:

You have to multiply the house value by 1.08 or 108%

365,000*1.08=394,200

The simplified expression is 3a + 5ay - 3y -52 .

(a) There are 4 terms in the simplified expression

(b) there are 2 negative terms in the simplified expression .

In the question ,

the algebraic expression is given as 3a+2y+5ay-2y-52-3y

to simplify it , we first group them in like terms

the expression becomes .

= 3a [tex]+[/tex] 2y [tex]+[/tex] 5ay -2y - 52 -3y

= 3a + 5ay + 2y - 2y - 3y - 52

= 3a + 5ay - 3y -52

Part(a)

the number of terms in the simplified expression is 4 ,

Part(b)

as we can see that the terms -3y and  -52 are negative

So , there are 2 negative terms in the expression.

Therefore , (a) There are 4 terms in the simplified expression

(b) there are 2 negative terms in the simplified expression .

The given question is incomplete , the complete question is

Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.

a. How many terms are in the simplified expression?

b. How many of the terms in the simplified expression are negative?

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The proposition ~ (~ q ⇒ p) ⇒ ~ q represents a tautology, as it is true for all combinations of p and q.

Propositions are constructions that contains a truth value, which are two according to classical logic (T - true, F - false). There are simple propositions and compound propositions. Compound propositions are formed by combining simple propositions and operators. There are the following operators:

A tautology is a compound proposition that is always true. We can prove whether a proposition is a tautology by the use of a truth table:

p        q      ~ q       ~ q ⇒ p        ~ (~ q ⇒ p)       ~ (~ q ⇒ p) ⇒ ~ q

T        T        F              T                      F                           T

T        F        T              T                      F                           T

F        T        F              T                      F                           T

F        F        T              F                      T                           T

The proposition ~ (~ q ⇒ p) ⇒ ~ q is a tautology.

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Answer:

x = 3.2

Step-by-step explanation:

[tex] \sf \frac{x}{2} = \frac{8}{5} \\ [/tex]

Use cross multiplication.

[tex] \sf5x = 8 \times 2 \\ \sf 5x = 16[/tex]

Divide both sides by 5.

[tex] \sf \: x = 3.2[/tex]

By using the concept of proportionality, it can be concluded that

y = 5x is the proportional relation

Third option is correct

What is proportionality?

Suppose there are two quantities. Proportionality indicates that if there's a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Proportionality are often direct or inverse

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of an article and quantity of an article are in direct proportion

Inverse proportion

Two quantities are said to be in inverse proportion if on increasing the value of one quantity,  the value of other quantity decreases and vice versa.

For example Number of men and number of days taken by those men to complete a work are in inverse proportion

For the first option

7x - 2 = y

y = 7x - 2

Here a non zero constant (-2) is added after the term with variable x

So this relation is not proportional

For the second option

y = 2x + 4

Here a non zero constant (4) is added after the term with variable x

So this relation is not proportional

For the third option

y = 5x

Here, no non zero constant is added after the term with variable x

So this relation is proportional.

For the fourth option

y + 1 = 3x

y = 3x - 1

Here a non zero constant (-1) is added after the term with variable x

So this relation is not proportional

So the correct option is the third option

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