help fast plsss bout to turn it in

The triangle proof that shows that angle Q and angle S are congruent to each other is explained below.

The side-angle-side congruence theorem (SAS) states that if the two sides and an included angle in one triangle is congruent to two corresponding sides and an included angle in the other triangle, then both triangles are congruent to each other.

If two triangles are congruent to each other, the CPCTC theorem states that all their corresponding parts are also equal or congruent to each other.

The triangle proof is given as:

Statements                                     Reasons                                                      

1. PR bisects ∠PQS                        1. Given

2. ∠1 ≅ ∠2                                      2. Definition of bisection

3. PQ ≅ PS                                     3. Given

4. RP ≅ PR                                     4. Reflexive property

5. ΔQPR ≅ ΔSPR                           5. SAS theorem

6. ∠Q ≅ ∠S                                    6. CPCTC

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The Least number of baseball cards Isabella could have is 49

To solve the problem, the multiples of seven will be necessary to ascertain the one that will:

multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63....

14 is short of 1 when divided by 5 but it is divisible by 2 without remainder

49 is the least number that fall short of 1 card to make it a multiple of 5 and have a remainder one when divided by 2

Hence the answer is 49

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The graph and factor to the given equation are x= 50 or x=0.

What is equation?

An equation may be a formula in arithmetic that expresses the equality of 2 expressions by connecting them with the sign =.

Main body:

I am assuming the equation as : -0.01[tex]x^{2}[/tex] + 0.5x =0

Now first removing the decimal from the equation ,

-[tex]x^{2}[/tex]/100 + 5x/10 = 0

-[tex]x^{2}[/tex] + 50 x = 0

switching signs , we get

[tex]x^{2}[/tex] - 50x= 0

taking x as common

x(x-50) =0

so either x = 0

or

x- 50 = 0

x =50

Hence the value of x are 0 or 50.

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As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.

Therefore,

45/5 = 9

45/6 = 7.5

45/7 = 6.42

45/8 = 5.62

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Answer:

  6922 TV sets

Step-by-step explanation:

You want the production in the 15th year if production in the first year is 1000 and it increases yearly by a constant amount. The total production in the first 10 years is 29035.

An arithmetic series is one that has a constant difference from one term to the next. If a1 is the first term of the series, and d is the common difference between terms, the n-th term is ...

  an = a1 +d(n -1)

And the sum of n terms is ...

  Sn = (2a1 +d(n-1))(n/2)

To find the 15th term, we can make use of the given values to find the common difference, then use the formula for the n-th term.

  S10 = (2(1000) +d(10 -1))(10/2) . . . . . sum formula with a1=1000

  29035 = 10000 +45d . . . . . . . . . . . simplified

  d = (29035 -10000)/45 = 423 . . . . the increase in production each year

Production in the 15th year is ...

  a15 = 1000 +423(15 -1) = 1000 + 5922 = 6922

The output in the 15th year was 6922 TV sets.

By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.

In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.

Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.

For this exercise, the elements of the given data set would be listed in ascending order as follows:

Set = {-4, -3, -3, -1, 0, 1, 2, 2}

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The equation of the parallel line t is y = -4x  - 9

The equation of line s given as

y = -4x - 5/3

Also, from the question

The point on line t is given as

Point = (-3, 3)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope of y = -4x - 5/3 is -4

The slopes of parallel lines are equal

This means that the slope of the line t is -4

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4

(x₁, y₁) = (-3, 3)

Substitute the known values in the above equation

y = -4(x + 3) + 3

Evaluate

y = -4x - 12 + 3

Evaluate the sum

y = -4x  - 9

Hence, the parallel line has an equation of y = -4x  - 9

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For x = -3 the relation will be a function.

We know that a relation is a function when for each input there is exactly one output.

In this question, we need to find the value of x for which the relation will be a function.

We need to select the value of x such that x ≠ 1, 3, 4, -4

This means x must be -3

Therefore, For x = -3 the relation will be a function.

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A recording of $0 for the family simply means that they have not saved anything or have spent all the savings.

Savings simply means keeping of miney for a period of time in order to cater for future expenses. Saving is defined as income that is not spent or deferred consumption. Saving methods include putting money aside in a deposit account, a pension account, an investment fund, or as cash. Saving also entails lowering expenses, such as recurring costs.

Here, the family wants to save $100 each month and they record their progress toward this goal at the end of each month.

A recording of $0 simply means no savings.

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Answer:

3(3+4) IS NOT EQUAL TO 3^3

Step-by-step explanation:

3(3+4)

Expand brackets to get 21 (3x3 = 9, 3x4 = 12, 9 + 12 = 21)

3^3 = 3 x 3 x 3

3x3 = 9

9 x 3 = 27

21 < 27

The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.

As given in the question,

Given expression is equal to :

f(x) = 4 ( 7x )

Calculate the value of the given function for x = -2 is given by :

Substitute value of x = -2 we get.

f(-2)

= 4 ( 7 ( -2) )

Seven is positive and 2 is negative , multiplication of positive to negative is always negative.

So, 7 ( -2 ) is -14 Substitute in above equation we get,

= 4 ( -14 )

= -56

Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to

f( -2 ) = -56.

The complete question is  :

If f(x) = 4 (7x) , what is the value of f(-2)?

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The principal amount invested at the rate of 6% for 3 years, then the investment results in $717.38.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the given information in the question,

Principle, P = $600

Rate, r = 6%

Time, t = 3 years.

Compound quarterly, r = 6/4

t = 4 × 3 = 12

Use the formula,

[tex]A = P(1+\frac{r}{100} )^t[/tex]

A = 600(1 + 6/4 × 100)¹²

A = 600 × (203/200)¹²

A = $717.38

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Answer:

n=90/80

Step-by-step explanation:

you make n the subject of the formular

An equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x

In this question, Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework.

So,  his total homework time would be,

(30 + 60 + x)minutes

Also, we have been given One fourth of his total homework time is spent on math.

We need to find an equation that can be used to find the amount of time Hiroshi spends on his math homework.

So, we get an equation,

1/4(30 + 60 + x) = x

Therefore, an equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x

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Answer:

c

Step-by-step explanation:

If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.

From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):

R(x) = x × P(x)

Where:

Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:

Revenue, R(x) = x × 26(4)^{-x/5}

Substituting the given parameters into the formula, we have;

Revenue, R(x) = 15 × 26(4)^{-15/5}

Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³

Revenue, R(x) = 15 × 26(0.015625) or 390/64

Revenue, R(x) = 6.09375 ≈ $6.09.

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Complete Question:

The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.

Answer:

below

Step-by-step explanation:

0.1

0.15

0.175

0.00125

1.13

2.02125

[tex]{ \pink{ \boxed{ \red{ \sf{f(4) = - 7}}}}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \sf{f(x) = { - x}^{3} + 3 {x}^{2} + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = ( { - 4})^{3} + 3( {4})^{2} + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = - 64 + 3(16) + 9}}}[/tex]

[tex]{ \green{ \sf{ f(4) = - 64 + 48 + 9}}}[/tex]

[tex]{ \green{ \sf{f(4) = - 64 + 57}}}[/tex]

[tex]{ \blue{ \boxed{ \orange{ \sf{f(4) = - 7}}}}}[/tex]

The amount to be credited, based on the invoice amount and the payment, is $612.24. The balance outstanding is $2, 387.76

Credit terms of 2/10, n/30 mean that if a buyer pays their payables in 10 days, they get a 2% discount. If they don't, then they'd have to pay the full thing in 30 days.

The days till the partial payment was made was:

= July 14 - July 5

= 9 days

The discount of 2% would apply on the payment of $600 so the amount to be credited is:

= 600 / (1 - 2%)

= $612.24

The balance would then be:

= Invoice amount - credited amount

= 3, 000 - 612.24

= $2, 387.76

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Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.

In the question given, the trig ratio is

tan a + cot a

We can simplify this as

tan a = sin a / cos a

cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a

Adding both ratios together

tan a + cot a = (sin a / cos a) + (cos a / sin a)

tan a + cot a = (cos a + sin a) / sin a * cos a

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Answer:

0

Step-by-step explanation:

subtracting same numbers give you zero

Answer: The correct answer is 14/7

Step-by-step explanation: This is the correct answer because it's explaining how to do it

Answer:

Value of x = 7° & y = 45°

Step-by-step explanation:

According to the question m || n.

For x:

[tex] \rm \implies (7x + 13) \degree = (6x + 20) \degree \\ \\ \rm \implies 7x - 6x = 20 \degree - 13\degree \\ \\ \rm \implies x = 7 \degree[/tex]

For y:

[tex] \rm \implies (3y - 17)\degree + (6x + 20) \degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (6 \times 7 + 20)\degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (42 + 20)\degree = 180\degree \\ \\ \rm \implies 3y - 17\degree + 62\degree = 180\degree \\ \\ \rm \implies 3y + 45\degree = 180\degree \\ \\ \rm \implies 3y = 180\degree - 45\degree \\ \\ \rm \implies 3y = 145\degree\\ \\ \rm \implies y = \bigg( \frac{145}{3} \bigg) ^\degree \\ \\ \rm \implies y = 45\degree[/tex]

Answer: y=-2x-5

Check this in desmos

Answer:48

Step-by-step explanation:12x4=48

Yes, the graph goes through those two points.

What is Graph?

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Explanation for the answer:

The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.

You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.

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Margin did the successful candidate win is 5375 - 4300 = 1075.

Given:

In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.

116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.

Number of valid votes = 9791 - 116 = 9675.

Let the number of votes of successful candidate = 5x

Let the number of votes of opponent = 4x

5x + 4x = 9675

9x = 9675

divide by 9 on both sides

x = 9675/9

x = 1075

Hence the votes for successful candidate = 5*1075 = 5375.

votes for opponent = 4*1075 = 4300.

Margin by which the successful candidate wins = 5375 - 4300 = 1075.

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A set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers.

What are Real numbers?

The set of real numbers is represented by the letter R.

Every number (except complex numbers) is contained in the set of real numbers. For example: 2, -8, 33/5, -1/5, 0, etc.

What are Integers?

The set of integers is represented by the letter Z.

An integer is any number in the infinite set, Z = (..., -3, -2, -1, 0, 1, 2, 3, ...}

Integers can further be divided into

What are Natural numbers?

The set of natural numbers is represented by the letter N.

A natural number is a positive integer.

N = { 1, 2, 3, 4, ... }

According to the given question:-

Set of real numbers comprises of Rational numbers, irrational numbers, integers, whole numbers, etc.

Hence a set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers i.e.

N = { 1, 2, 3, 4, ... }

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