An amount of 50000 is borrowed for 14 years at 5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Answer:

x<-4

Step-by-step explanation:

To solve this problem, follow these steps:

1. Subtract 5 from both sides.

13<-2x+5

13(-5)<-2x+5(-5)

2. Simplify.

(8)<-2x+5-5

3. Subtract the 5's. And bring down the new equation.

8<-2x+5-5

8<-2x

4. Divide -2x on both sides.

8/-2<-2x/-2

5. Simplify and cancel out the -2's.

-4<x

6. Move the variable to the left and flip the inequality.

x<-4

The function f(n) to represent the elevation after n hours is y = -665 x + 7315.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis may be found using the point-slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This suggests that a linear equation in two variables can represent a line.

Let the x value represent hours and elevation is represented by y values.

So,

(x₁, y₁) = (1, 6650)

(x₂, y₂) = (2, 5985)

Find the slope by using the slope formula

m = (y₂-y₁)/ (x₂-x₁)

= (5985 - 6650) /(2 - 1)

= -665

So, the function f(n) to represent the elevation after n hours is given by

(y - 6650) = -665 (x - 1)

y - 6650 = -665x +665

y = -665 x + 7315

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Answer:

The answer is {-8, -2, 3, 4, 8}

Domain is basically the x,

while range OR image is the y,

while codomain is y values that do not have ties to any x value

Answer: 7

Step-by-step explanation:

To do this, we need to simplify the numerator.

This means we need to multiply 7^8 x 7^3 x 7^4

To multiply these, we add the exponents together.

This gives us 7^15.

Now, we need to simplify the denominator.

This means we need to multiply 7^9 x 7^5

This gives us 7^14.

Now that we have both the numerator and denominator simplified, we divide 7^15 and 7^14.

To divide 7^15 and 7^14, we need to subtract the exponents.

This gives us 7^1.

7^1 = 7.

9.1875 are the mean and variance of depth in random variable.

What is random variable in math?

The mean of the random variable X is

                                                E(X) =b+a/2

                                                        = 19 + 8.5/2

                                                       = 13.75

The variance of the random variable X is,

                                                       V(X) = ( b - a)²/12

                                                               = ( 19 - 8.5 )²/12

                                                             = 9.1875

If the random variable X is uniformly distributed on the interval [8.5, 19], then the mean of the random variable X is 13.75 and the variance of the random variable X is 9.1875.

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The solution to the system of equations is (7 , 10.5).

Systems of equations are collections of equations where the intersection point (s) between the equations serves as the solution. The majority of the equation systems you encounter in algebra are collections of two linear equations with the formula Ax + By = C.

y = 2x - 3.5 …. (1)

x - 2y = -14 …. (2)

Let us use the elimination method to solve the system of linear equations.

Multiply equation (1) by 2

2y = 4x - 7

- 4x + 2y = -7 …. (3)

By adding equation (2) and (3)

- 3x = - 21

Divide both sides by - 3

x = 7

Substitute the value of x in equation (1)

y = 2 (7) - 3.5

By further calculation

y = 14 - 3.5

y = 10.5

Therefore, the solution to yhe system of equations is (7, 10.5).

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The equation of line is y = -7x - 95

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m of a line is a measurement of its steepness and direction.The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the two points be P1 and P2

P1 ( x₁ , y₁ ) = P1 ( -13 , -4 )

P2 ( x₂ , y₂ ) = P2 ( -9 , -32 )

Step 1 :

To calculate the slope m of the two points

m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values of x₁ , y₁ , x₂ , y₂ in the equation , we get

m = ( -32 - (-4) ) / ( -9 - (-13) )

m = (-32 + 4 ) / ( -9 + 13 )

m = -28 / 4

m = -7

Therefore the slope is -7

Step 2 :

Now , the equation of the line is given by

y - y₁ = m ( x - x₁ )

Substituting the values of x₁ , y₁ and m in the equation , we get

y - (-4) = -7 ( x - (-13) )

y + 4 = -7 ( x + 13 )

y + 4 = -7x - 91

Subtracting 4 on both sides , we get

y = -7x - 95

Hence , the equation of line is y = -7x - 95

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f(x) function increases faster.

From the question, we have

g(x) =5/2x-3

At x =0, g(x) = -3

At x =1, g(x) = -1

Hence, f(x) function increases faster.

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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1. The cheese production for 2006 is 7.76 billion.

2. The cheese produced in 2014 is 9.84 billion.

It should be noted that a function is simply used to show the relationship between the variables that are given.

In this situation, there's a 3% growth per year and the function for the cheese production is modelled as:

y = 7.1(1.03)^x

y = cheese production

x = number of years after 2003.

1. Therefore, since 2006 is 3 years after 2003, this will be

y = 7.1(1.03)^x

y = 7.1(1.03)³

y = 7.1 × 1.093

y = 7.76 billion

The production is 7.76 billion.

2. The production in 2014 will be;

y = 7.1(1.03)^x

y = 7.1(1.03)^11

y = 7.1 × 1.385

y = 9.84 billion

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The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

Given:

If it' 50 c outside and the temperature will drop 70 c in next 3 hour.

Temperature (cold) = present temperature - temperature in next 3 hour.

= 50 - 70

= -20 c.

Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

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Lines a and b are parallel lines.

Lines a and c are perpendicular lines

Lines d and c are perpendicular lines.

The formula to calculate the slope between two points is equal to

[tex]m = y2-y1/(x2-x1)[/tex]

Part 1) Find the slope of Line a

We have the points

(-3,4) and (3,6)

Substituting the value in the formula

[tex]m = 6-4/ (3-(-3))\\m = 2/6\\ma = 1/3[/tex]

Part 2) Find the slope of Line b

We have the points

(-10,-3) and (-8,3)

Substituting the value in the formula

[tex]m = 3-(-3)/ (-8-(-10))\\m = 6/(-8+10)\\mb = 6/2=3[/tex]

Part 3) Find the slope of Line c

We have the points

(0,5) and (3,-4)

Substituting the value in the formula

[tex]m = -4-5/ (3-0)\\m = -9/3\\mc = -3[/tex]

Part 4) Find the slope of Line d

We have the points

(4,-7) and (13,-4)

Substituting the value in the formula

[tex]m = -4-(-7)/ (13-(4))\\m = 3/9\\md = 1/3[/tex]

Part 5) Compare the slopes

Remember that

If lines are parallel then their slopes are equal.

If lines are perpendicular then their slopes are opposite reciprocal.

We've got,

[tex]ma = 1/3\\mb = 3\\mc = -3\\md = 1/3[/tex]

Lines a and b are parallel lines (slopes are the same).

Lines a and c are perpendicular lines (slopes are opposite reciprocal).

Lines d and c are perpendicular lines (slopes are opposite reciprocal).

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There are 18 possible combinations for the model and color options.

According to the given information,

There are 3 motorbike manufacturers.

There are 6 different colors available.

Total combinations possible = Motorcycle count *color count

Total combinations possible=3*6

                                                 =18

Therefore, there are 18 possible combinations that are available.

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Answer:

40 trees per acre

Step-by-step explanation:

: If x is the number of trees beyond 30 that are planted on the acre, then

the number of oranges produced will be: Oranges(x) = (number of trees) (yield per

tree) = (30 + x)(500 – 10x) = 15,000 + 200x – 10x

2

. The derivative Oranges'(x) =

200 – 20x is zero when x = 10. Using the second derivative test, Oranges"(x) = –

20 is negative, so this is maximal. Thus, x = 10 more than 30 trees should be

planted, for a total of 40 trees per acre.

If a bottle of perfume on sale for $30 after a discount of 25%, then the original price of the perfume is $40

The selling price of the perfume = $30

The percentage of discount on perfume = 25%

Consider the original price of the perfume = x

Then the equation will be

[ Original price - Original price × 25%] =  The selling price of the perfume

Substitute the values in the equation

[ x - x×(25/100) ] = 30

( 1 - 25/100)x = 30

( 1 - 0.25)x = 30

0.75x = 30

x = 30 / 0.75

x = $40

Hence, if a bottle of perfume on sale for $30 after a discount pf 25%, then the original price of the perfume is $40

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While dividing 7 tens into 3 groups the greatest number of tens you can put in each group = 2 tens

In this question, we need to divide 7 tens into 3 groups.

We need to find the greatest number of tens you can put in each group.

We know that 7 tens = 70

We need to divide 70 in 3 groups.

70/3 = 23.33

From given choices the greatest number of tens we can put in each group = 2

Therefore, while dividing 7 tens into 3 groups the greatest number of tens you can put in each group = 2 tens

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Answer:

Step-by-step explanation:

f⁻¹(x) = x/4    

The inverse of the conditional statement "If p then q" is, "p and not q".

What is conditional statement?

"If...then" is how a conditional statement is expressed. If we consider p and q to be the two statements, then p and q can be written under several conditions, such as;

If the "If" component (p) and the "then" part (q) of a conditional statement are both negated, this is known as a conditional statement in reverse. The conditional statement in geometry is known as p → q. Where stands for NOT or negating the statement, the inverse is written as  ~ p → ~  q.

In logic, "p and not q" is identical to the negation of "if p then q."

Therefore, the inverse of the conditional statement "If p then q" is,  

"p and not q".

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Answer:

[tex] x = \dfrac{\log 5}{\log 7} [/tex]

Step-by-step explanation:

[tex] 7^{2x} - 4 \times 7^x = 5 [/tex]

[tex] 7^{2x} - 4 \times 7^x - 5 = 0 [/tex]

[tex] (7^x)^2 - 4(7^x) - 5 = 0 [/tex]

This is a quadratic equation in 7^x.

Let u = 7^x.

Substitute u for 7^x to see the quadratic equation more clearly.

[tex] u^2 - 4u - 5 = 0 [/tex]

Now we have a factorable quadratic equation in u.

[tex] (u - 5)(u + 1) = 0 [/tex]

[tex] u - 5 = 0 [/tex]  or  [tex] u + 1 = 0 [/tex]

[tex] u = 5 [/tex]  or [tex] u = -1 [/tex]

Now substitute back 7^x for u.

[tex] 7^x = 5 [/tex]  or  [tex] 7^x = -1 [/tex]

[tex] 7^x = -1 [/tex] does not have a real solution.

Continue solving [tex] 7^x = 5 [/tex] for x.

Take log of both sides.

[tex] \log 7^x = \log 5 [/tex]

[tex] x \log 7 = \log 5 [/tex]

[tex] x = \dfrac{\log 5}{\log 7} [/tex]

Answer:

[tex]x=\log_75[/tex]

Step-by-step explanation:

Given equation:

[tex]7^{2x}-4 \cdot 7^x=5[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies (7^x)^2-4 \cdot 7^x=5[/tex]

Subtract 5 from both sides:

[tex]\implies (7^x)^2-4 \cdot 7^x-5=0[/tex]

[tex]\textsf{Let \; $u = 7^x$}:[/tex]

[tex]\implies u^2-4u-5=0[/tex]

Factor the quadratic:

[tex]\implies u^2+u-5u-5=0[/tex]

[tex]\implies u(u+1)-5(u+1)=0[/tex]

[tex]\implies (u-5)(u+1)=0[/tex]

Apply the zero-product property:

[tex]\implies u-5=0 \implies u=5[/tex]

[tex]\implies u+1=0 \implies u=-1[/tex]

[tex]\textsf{Substitute back in \; $u = 7^x$}:[/tex]

[tex]\implies 7^x=5[/tex]

[tex]\implies 7^x=-1 \quad \textsf{is not valid as $7^x > 0$}.[/tex]

Therefore, the only valid solution is:

[tex]\implies 7^x=5[/tex]

[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies \log_75=x[/tex]

[tex]\implies x=\log_75[/tex]

The radical pair that is similar to one another is [tex]3\sqrt{7}[/tex] and [tex]11\sqrt{7}[/tex] and the right answer is (2).

Two radicals must have the same number in the root operator in order for them to be comparable.

The following two radicals are similar:

[tex]a\sqrt{b}[/tex] and [tex]c\sqrt{b}[/tex]

Since [tex]a\sqrt{b}[/tex] and[tex]c\sqrt{b}[/tex]  are like terms, arithmetic operations such as addition, subtraction, multiplication, and division can be carried out on them

Considering the options given, only [tex]3\sqrt{7}[/tex] and [tex]11\sqrt{7}[/tex] are in the form [tex]a\sqrt{b}[/tex]  and [tex]c\sqrt{b}[/tex]  because they have equal value inside the root operator.

Therefore, the pair of radicals that is a like pair is [tex]3\sqrt{7}[/tex]  and [tex]11\sqrt{7}[/tex].

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Answer:

$51

Step-by-step explanation:

Step 1.   0.15 x $60 = $9

Step 2.  $60 - $9 = $51

Answer:

The sides of an angle are called rays and the endpoint here they meet are called vertexes

According to the graph transformation, the function y = |2x| is compressed than the parent function y = |x| and the function y = 1/2x is drawn as straight line.

Graph transformation:

The graph transformation refers a process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph and it also shows the modification of algebraic equations.

Given,

Here we have the function y = |2x| and y = 1/2x.

Now, we need to find the transformations do to the parent function: y=|x|.

Here we need to plot the graph for each of the function.

And we have to plot the separate graph for the parent function.

While we compare these two graph we have identify the function y = |2x| is compressed than the parent function y = |x|.

And the function y = 1/2x makes the straight line on the graph but the parent function has v shaped graph so, it is not possible to compare them.

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The solution of the given equation is 2x² - 13x +13.

What is the solution of the equation?

The collection of all values that, when substituted for unknowns, cause an equation to hold true is known as the solution. Two fundamental algebraic rules using the additive property and the multiplicative property are utilized to determine the solutions for equations needing a single unknown raised to a power of one.

What is the simplification rule?

For those sorts of reasoning that deal with conjunctions, the rule of simplification provides a strong argument. This covers natural deduction, predicate logic, and propositional logic.

Here, we have

Given equation 2(x - 2)² - 5(x - 2) - 5

By applying the simplification rule, we get

= 2(x - 2)² - 5(x - 2) - 5

= 2( x² + 4 - 4x ) - 5x +10 - 5

= 2x² + 8 - 8x - 5x + 5

= 2x² - 13x +13

Hence, the solution of the given equation is 2x² - 13x +13.

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The actual length of route of 28 cm on drawing is 84 meters.

The actual length will be calculated by firstly writing the ratio and proportion form. Then equating the product of extremes and product of mean.

Ratio and proportion form -

Let us assume the actual length be x. Ratio in actual :: Ratio of scale drawing

28 : x :: 1 : 300

1×x = 28×300

Performing multiplication on both sides of the equation

x = 8400

Now converting the actual length to metres, based on the fact that 100 cm is 1 m.

8400 cm = 84 metres

Hence, the actual length is 84 metres.

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The complete question is -

Daisy is given a scale drawing with the route to her campsite. The route to the campsite is 28 cm on the drawing. The scale on the drawing is 1 : 300. What is the actual length of the route?

Dario cut 15 slices of lasagna containing 1/4 pounds of cheese.

Total amount of cheese in lasagna =

[tex] \frac{2}{3} [/tex] + [tex]1 \frac{3}{4} [/tex] + [tex]1 \frac{1}{3} [/tex]

Total amount of cheese = [tex] \frac{2}{3} [/tex] + [tex] \frac{7}{4} [/tex] + [tex] \frac{4}{3} [/tex]

Taking LCM we get 12

Total amount of cheese = (2×4) + (7×3) + (4×4)/12

Total amount of cheese = 8 + 21 + 16/12

Total amount of cheese = 45/12 pounds

Number of slices = total amount of cheese ÷ amount of cheese in each piece

Number of slices = 45/12 ÷ 1/4

Number of slices = (45×4) ÷ 12

Number of slices = 15

Thus, there are 15 slices of lasagna.

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Answer: triangle, rectangle, pentagonal

Step-by-step explanation: b x h and length x width = base.

The solution of the given logarithmic function log 6 is 1.78.

For the stated function;

= log 6

= log(2 x 3)

Using the multiplication property of log;

log (m x n) = log m  + log n

= log(2) + log(3)

solve the value by calculator;

= 0.69 + 1.09

= 1.78

Thus, the solution of the given logarithmic function log 6 is 1.78.

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67% of years  will have an annual rainfall of less than 43 inches.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often indicated by the percent sign '%', but the abbreviations 'pct.', 'pct', and 'pc' are also sometimes used. Percentages are dimensionless numbers. It has no units of measure.

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