The formula to determine continuously compounded interest is A = Pe^rt, where A is the amount of
money in the account, P is the initial investment, r is the interest rate, and t is the time, in years.
What equation could be used to determine the value of an account with an $18,000 initial
investment at an interest rate of 1.25% for 24 months?

Answer:

800

Step-by-step explanation:

Look at the tens if it's 0-4 keep the number the same if 5-9 go up one number

Answer:

832 --> ???

832 - we must round the underlined digit

832 --> ???

832 --> 800

The rounding rule is:

4 and below, stay down low! [Round down]. 5 and above, soar like a dove! [Round up].

So with that rule, 832 becomes 800.

800 is your answer.

I hope this helps!

The height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Solution:

Given that shrub in Pam's backyard is about [tex]1\frac{3}{8}[/tex] feet tall

A small tree in her back yard is about 7 times as the shurd

To find: height of tree

From given information,

Height of shrub = [tex]1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \text{ feet}[/tex]

Given that small tree in her back yard is about 7 times as the shurb

So we get,

height of tree = 7 times the height of shrub

[tex]\text{ height of tree } = 7 \times \text{ height of shrub}\\\\\text{ height of tree } = 7 \times \frac{11}{8}[/tex]

Therefore on solving we get,

[tex]\text{ height of tree } = \frac{77}{8} = 9\frac{5}{8} \text{ feet}[/tex]

Thus the height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]

Answer: f(3)=11.5

Step-by-step explanation:

In order to solve this equation, all you have to substitute the value inside of the parenthesis with the value of x in the equation after the equals sign. SO...

f(3)=3x+2.5

f(3)=3(3)+2.5

f(3)=9+2.5

f(3)=11.5

Hope this helps!

Answer:

24 Teaspoons

Explanation:

1 tablespoon is equivalent to 3 teaspoons

8 · 3 = 24

Therefore 24 teaspoons is equivalent to 8 tablespoons.

Option A and Option F

The expressions that represent the perimeter of rectangle are 4s + 1 and [tex]2(2s + \frac{1}{2})[/tex]

Solution:

From figure,

Length = s

Width = [tex]s + \frac{1}{2}[/tex]

The perimeter of rectangle is given as:

perimeter = 2(length + width)

Substituting the values we get,

[tex]perimeter = 2(s + s + \frac{1}{2})\\\\perimeter = 2(2s + \frac{1}{2})[/tex]

Thus option F is correct

On further simplification,

[tex]perimeter = 2(2s + \frac{1}{2})\\\\perimeter = 4s + 2(\frac{1}{2})\\\\perimeter = 4s + 1[/tex]

Thus Option A is correct

Answer:

Step-by-step explanation:

[tex]3.6x-12.2=-1.5x+8.2\qquad\text{multiply both sides by 10}\\\\36x-122=-15x+82\qquad\text{add 122 to both sides}\\\\36x-122+122=-15x+82+122\\\\36x=-15x+204\qquad\text{add}\ 15x\ \text{to both sides}\\\\36x+15x=-15x+15x+204\\\\51x=204\qquad\text{divide both sides by 51}\\\\\dfrac{51x}{51}=\dfrac{204}{51}\\\\x=4[/tex]

Answer:

v = 1/2(1 + i√23) ,  1/2(1 - i√23).

Step-by-step explanation:

-2v^2 - v + 12 =  -3v^2 + 6

-2v^2 + 3v^2 - v + 12 - 6 = 0

v^2 - v + 6 = 0

This will not factor so we could use the quadratic formula to solve it:

For the equation ax^2 + bx + c = 0 the roots are:

x = [ - b +/-  sqrt(b^2 - 4ac) ] / 2a.

So here we have:

v = [-(-1) +/- sqrt((-1)^1 - 4*1*6)] /  2

v = [ 1 +/- sqrt (-23)] / 2

= 1/2 +  i√23/2 ,    1/2 -  i√23/2

= 1/2(1 +  i√23) ,  1/2(1 -  i√23).

The liquid started cooling from 194 degrees. This is calculated by determining the rate of cooling, which is 8 degrees per minute, and extrapolating back to find the initial temperature.

The subject of the question is about determining the initial temperature of cooling liquid. To solve this, we have to first identify the rate at which the temperature is decreasing. Given, after 2 minutes it was 178 degrees and after 5 minutes it was 154 degrees. That's a decrease of 24 degrees over 3 minutes, or 8 degrees per minute.

Since the liquid started cooling 2 minutes before it was first observed at 178 degrees, we can estimate that the liquid would have been 16 degrees hotter at the start of the cooling period. So, it would have started cooling at 178 + 16 = 194 degrees.

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Answer:

11/5

Step-by-step explanation:

5x-7=4

5x=4+7

5x=11

x=11/5

The required solution of the function at x = 4 is f(4) = 13.

Given that,
A function is given f(x) = 5x - 7, the value of the function at x = 4 is to be determined.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given function,
f(x) = 5x - 7
put the value x = 4 in the above equation,

f(4) = 5 * 4 - 7
f(4) = 20 -7
f(4) = 13

Thus, the required solution of the function at x = 4 is f(4) = 13.

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Answer:

TU ⊥ MN and MN ║ PQ

Step-by-step explanation:

TU ⊥ MN

As the angle that is created where TU and MN intersect is a 90° angle, these two lines must be perpendicular to each other.

MN ║ PQ

As both MN and PQ intersect the line TU, we can use this to prove that they are parallel.

Both MN and PQ create a 90° angle where they intersect with TU. This means that MN is ⊥to TU and PQ is ⊥ to TU.

As both MN and PQ are perpendicular to TU, they must be parallel.

Answer:

Step-by-step explanation:

1. [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex]

2. [tex]y=-5x+30[/tex]

Preliminary Material:

A line that is perpendicular to another has the opposite reciprocal slope of the other line.

A line parallel to another has the same slope.

With this in mind, we can begin to answer this question.

1.

Setup for question 1:

A line perpendicular with [tex]-5x+5[/tex] that goes through the point (7, 5).

Before going over the point this perpendicular line must go through, let's make an equation with the slope of the perpendicular line.

A linear function can be represented with this formula: [tex]y=mx+b[/tex].

We know the slope of this function must be an opposite reciprocal to -5, and using the information I first gave in the beginning of this problem, we can have the slope of the function.

If we take this slope and insert it into the linear equation, we will have the function...

So we now know the slope of this function, but what about the y intercept, [tex]b[/tex]? This is where the point given to us in the beginning of this problem comes into play. If we plug the point (7, -5) into our x and y coordinates in the above equation, we can solve for [tex]b[/tex].

Algebra:

[tex]-5=\frac{1}{5}(7)+b[/tex]

[tex]-5=\frac{7}{5}+b[/tex]

[tex]-\frac{25}{5}=\frac{7}{5}+b[/tex]

[tex]-\frac{32}{5}=b[/tex]

Answer:

Our final answer is: [tex]y=\frac{1}{5}x-\frac{32}{5}[/tex].

2.

There will be no setup for 2. I'll show the algebra without explanation as well. If there's any confusion you can ask me :).

Algebra:

[tex]y=mx+b[/tex]

[tex]y=-5x+b[/tex]

[tex]-5=-5(7)+b[/tex]

[tex]-5=-35+b[/tex]

[tex]b=30[/tex]

Answer:

Answer:

The relationship between time and distance is Velocity = Distance / Time

Step-by-step explanation:

Answer:

It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C)

Step-by-step explanation:

It is important to know that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).  

Lets take an example, if we have 81°F and want to convert in (°C). So, here is the procedure:

                            C = (5/9) (81 - 32)

                                = (5/9) (49)

                                 = 27.22 °C

So, it is clear that linear equation can be used in temperature conversion using the formula C = (5/9)(F-32) - a converter for degrees Fahrenheit (°F) for temperature to degree Centigrade (°C).

Keywords: linear equation, converter, C = (5/9)(F-32)

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C(x) = 4x³+7x²-14x-6

Step-by-step explanation:

Given that the amount of water used in normal days is given by the equation;

W(x) = 5x³ +9x²-14x +9 -----(i)

The amount of decrease in water used is modeled by the equation;

D(x)= x³+2x² +15--------(ii)

To get the function C(x) that models the water used by the car wash on shorter day you subtract equation (ii) from equation(i)

 5x³ +9x²-14x +9

-  x³+2x² +15

-------------------------

4x³+7x²-14x-6

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Answer:

C(x) = 4x³ + 7x² − 14x - 6

Step-by-step explanation:

In a shorter day the water used by the car wash is computed as the difference between the original usage and the decrease, that is:

C(x) = W(x) - D(x)

Replacing with data:

C(x) = 5x³ + 9x² − 14x + 9 - (x³ + 2x² + 15)

C(x) = 5x³ + 9x² − 14x + 9 - x³ - 2x² - 15

C(x) = (5-1)x³ + (9-2)x² − 14x + (9-15)

C(x) = 4x³ + 7x² − 14x - 6

Answer:-523/52

Step-by-step explanation:

The simplified form of the expression is [tex]\(-3245.2\).[/tex]

To simplify the given expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). The expression given is:

[tex]\[ -3152 - 10(4.32 + 5 = 5) \[/tex]

First, we address the equality within the parentheses. The expression \[tex](4.32 + 5\) equals \(9.32\),[/tex] but the equality [tex]\(4.32 + 5 = 5\)[/tex] is not true. However, in the context of this expression, the equality sign does not affect the numerical computation; it seems to be a typographical error or a misplacement. We will treat the expression within the parentheses as [tex]\(4.32 + 5\)[/tex]and ignore the equality for the calculation.

Now, let's simplify the expression step by step:

1. Calculate the expression inside the parentheses:

[tex]\[ 4.32 + 5 = 9.32 \][/tex]

2. Multiply the result by -10 (note that the multiplication comes before addition/subtraction in the order of operations):

[tex]\[ -10 \times 9.32 = -93.2 \][/tex]

3. Finally, subtract the result from -3152:

[tex]\[ -3152 - 93.2 = -3245.2 \][/tex]

So, the simplified form of the expression is [tex]\(-3245.2\).[/tex]

Step-by-step explanation:

I don't know if this helps, but none of the above.

first of all, complementary angles mean that the 2 (or more) angles add up to 90 degrees. so, if you were to combine the angles, you'll get an angle that's way larger than 90 degrees. (a and b won't work cause 830 isn't an angle)

P.S. but 83 degrees and 7 degrees would be complementary...

hope you at least know why i say none of the above

Answer   5

Step-by-step explanation:

Answer:

The answer is 50.

Step-by-step explanation:

The answer is 50 because, the line that the Exterior angle is on is equal to 180. So you take the two interior angels and add them. Then subract that from 180 and you get 50.

Hope this helps :))

Answer:

The correct answer is 110°.

Step-by-step explanation:

The Exterior Angle Theorem states, "the exterior angle of a triangle is equal to the sum of its non-adjacent angles".

This means we would add 50 + 60 to get 110°.

Or we could look at the exterior angle and the adjacent angle to it. The two angles form a supplementary angle - this equals 180°. To find our answer this way, we subtract the known angle form 180:

180 - 70 = 110°

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer:

[tex]12x^2+4x[/tex]

Step-by-step explanation:

The area of a square or rectangle can be found by multiplying the width by the height. Since we now both, we can create an expression.

[tex](3x+1)*(4x)[/tex]

Now we can apply the distributive law/property to expand the expression.

[tex]3x(4x)+1(4x)[/tex]

Finally, we can simplify.

[tex]12x^2+4x[/tex]

Answer:

Graph is below

Step-by-step explanation:

y>3x+10 is represented by the red line, which is dotted because it's values are not included in the solution. Everything above it is shaded red because it is greater than. y<-3/4x-1 is represented by the blue line, which is dotted because it's values are not included in the solution. Everything beneath is shaded blue, because it is less than. The intersection of the two shaded areas is purple. (8,10) is not part of the solution because it does not have an x value beneath -3.

(this was a hard question, but i'm certain that at least the graph is correct.)

To promote economic growth, countries would most likely act so that inflation "remains at a low level".

Answer: Option c

Explanation:

The Central Bank and the government basically command Inflation or either of them. The monetary policy is helpful from its changing interest rates parameters . Although there are a different types of tools which can control inflation are as follows

Monetary policy: The demand in the economy is reduced by higher interest rates, and result into lower economic growth with lower inflation.

Commanding supply of money: Monetarists debt huge by setting a close bond between the inflation and money supply.

Supply-side Policies: The scheme to hike the efficiency of the economy and competitiveness by declining pressure on long-term costs.

Fiscal policy: The reduction of spending, demand and inflationary pressures resulted from a higher rate of income tax.

Wage controls: Inflationary pressures can be reduced by controlling wages  , but after 1970 such act is rarely performed.

Answer:

ℝ

Step-by-step explanation:

[tex]\displaystyle 10 - 2x = [5 - x] - [x - 5][/tex]

All linear functions have a range and domain of all real numbers.

I am joyous to assist you anytime.

Answer:

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Step-by-step explanation:

Given:

5 more than a product of a number and a

equals 2

Use a variable C for the unknown number

To Find:

Translate above sentence into an equation . ?

Solution:

Let ' C ' for the unknown number

and ' a ' for the other number.

Then according to given condition we have

5 more Product of ( C and a ) = 2

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Answer:

f(x): {y| y > 0 }

g(x): {y| y > 6 }

Step-by-step explanation:

Hope this helps!

Because both of these are exponential functions with positive bases, we conclude that the range for both is:

{y| y > 0}.

Here we have two exponential functions:

f(x) = (4/5)^x

g(x) = (4/5)^(x + 6).

You can see that both of these are exponential functions with positive bases, then neither of these can have negative outcomes, while, as x increases, the outcome will also increase.

Then we can see both functions are exponential growths, so the range for both of these are the set of all real positive values, written in both cases as:

{y| y > 0}

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Answer:

The equation representing the statement is [tex](x-1)+x=6[/tex].

Step-by-step explanation:

Given:

Distance from Sue house to Gill house = 6 miles.

Let the distance from Gill to Taco Town restaurant be 'x'.

Also Given:

Sue lives 1 mile closer to Taco Town restaurant than Gill does.

Hence Distance from Sue to Taco Town restaurant will be = [tex]x-1[/tex]

We need to write the equation for the below statement.

the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.

Framing in equation form we get;

[tex](x-1)+x=6[/tex]

Hence the equation is [tex](x-1)+x=6[/tex].

Answer:

Part a) [tex]AC=135.95\ m[/tex]

Part b) [tex]BC=124.14\ m[/tex]

The diagram in the attached figure

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]m\angle A+m\angle B+m\angle C=180^o[/tex]

substitute the given values

[tex]53^o+61^o+m\angle C=180^o[/tex]

[tex]114^o+m\angle C=180^o[/tex]

[tex]m\angle C=180^o-114^o[/tex]

[tex]m\angle C=66^o[/tex]

step 2

Find the distance AC

Applying the law of sines

[tex]\frac{AB}{sin(C)}=\frac{AC}{sin(B)}[/tex]

see the attached figure to better understand the problem

substitute the given values

[tex]\frac{142}{sin(66^o)}=\frac{AC}{sin(61^o)}[/tex]

[tex]AC=\frac{142}{sin(66^o)}(sin(61^o))[/tex]

[tex]AC=135.95\ m[/tex] ---> rounded to the nearest hundredth

step 3

Find the distance BC

Applying the law of sines

[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}[/tex]

substitute the given values

[tex]\frac{142}{sin(66^o)}=\frac{BC}{sin(53^o)}[/tex]

[tex]BC=\frac{142}{sin(66^o)}(sin(53^o))[/tex]

[tex]BC=124.14\ m[/tex] ---> rounded to the nearest hundredth

Answer:

37i-16

Step-by-step explanation:

(4+7i)(3+4i)

12+21i+16i+28i^2

12+37i+28(-1)

37i+12-28

37i-16

Answer:

12 square units.

Step-by-step explanation:

I just took the test.

Question:

You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 1/3 of one section of the fence.  What fraction of the fence did you paint?

Answer:

The fraction of the fence painted is [tex]\frac{1}{12}[/tex]

Solution:

Given that:

You have a 32-foot fence around a square garden. There are 4 equal sections

Find the length of each section:

4 sections = 32 foot

[tex]\text{ 1 section } = 32 \div 4 = 8 foot[/tex]

Find the length that is painted:

[tex]\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }[/tex]

Therefore [tex]\frac{8}{3}[/tex] foot of fence is painted

Find the fraction that that is painted:

Total length of fence = 32

[tex]\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}[/tex]

Therefore [tex]\frac{1}{12}[/tex] fraction of the fence is painted