You buy some living room furniture. The coffee table costs $189.99, the loveseat costs $249.95, the sofa costs $493.68, and 2 chairs cost $98.75 each. Sales tax is 7.25%. How much is your total purchase? $1,032.37 $1,213.13 $1,107.22 $1,131.12

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which is more confusing.

Answer: Option C

[tex]a> 0[/tex]

Step-by-step explanation:

The graph shows a radical function of the form [tex]f(x)=a(x+k)^{\frac{1}{n}}+c[/tex]

Where n is a positive number.

For this type of function, if the coefficient [tex]a> 0[/tex] then then when x tends to [tex]\infty[/tex] f(x) tends to [tex]\infty[/tex] and when x tends to [tex]-\infty[/tex] then f(x) tends to [tex]-\infty[/tex].

Notice in the graph that as x increases then f(x) also increases and as x decreases f(x) also decreases.

This indicates that the coefficient [tex]a> 0[/tex]

Answer:

1020000

Step-by-step explanation:

Step 1 : Use BODMAS (Bracket Open Divide Multiply Add Subtract)

Step 2 : Take the common term

7.8*10^5+2.4*10^5

10^5(7.8 + 2.4)

Step 3 : Solve

10^5(7.8 + 2.4)

100,000(10.2)

=1020000

!!

Answer:

1.02 × 106

Step-by-step explanation:

1.02 × 106

For this case we must convert the given expression to degrees:

[tex]\frac {3 \pi} {8}[/tex]

By definition we have that [tex]\pi = 180[/tex] degrees, then:

[tex]\frac {3 \pi} {8} * \frac {180} {\pi} = \frac {180 * 3} {8} = \frac {540} {8} = 67.5[/tex]

Thus, we have [tex]\frac {3 \pi} {8}[/tex] is equal to 67.5 degrees.

Answer:

67.5 degrees

I'm going to assume that you meant to write: The square of a number exceeds that number by 12. What are the two possible solutions.

In other words x² = x + 12

4² is 16.

4 + 12 = 16

(-3)² is 9

-3 + 12 = 9

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Riding is independent variable and cost is dependent....

Step-by-step explanation:

According to the given statement Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides.

It means that if she rides a ferry, she pays

If she does not ride the ferry she won't pay

This shows that the paying depends on riding.

Thus riding is independent variable and cost is dependent....

Answer: the number of rides is the independent variable, and the total cost is the dependent variable.

Answer:

g(x + 8) = 10x + 105 wherever you see it among your answers.

Step-by-step explanation:

I think I have enough here that I can answer the question, but you should always put in your givens.

f(x) = 10x + 25                      Put g(x) where you see x in f(x)

f(g(x)) = 10(g(x) + 25             Put the value for g(x) where you see g(x)

f(x+8) = 10(x + 8) + 25         This might be the answer

From here it is a guess.

f(x+8) = 10x + 80 + 25         Combine the like terms

f(x+8) = 10x + 105

Answer:

on flvs its option C

Step-by-step explanation:

Answer:

It shifts left two units, and up seven units.

Step-by-step explanation:

In your translation, it says X-2, this represents the shift to the left two times, next it says Y+7, this represents the upwards shift seven units. Basically, you're taking your beginning X and Y values, and changing them according to the right of the arrow.

Answer:

Translation of 2 units to the left and 7 units up.

Step-by-step explanation:

The general rule of translation is

[tex](x,y)\rightarrow (x+a,y+b)[/tex]              .... (1)

If a>0, then figure translate a units right and if a<0, then figure translate a units left.

If b>0, then figure translate b units up and if b<0, then figure translate b units down

The given rule of translation is

[tex](x,y)\rightarrow (x-2,y+7)[/tex]             .... (2)

On comparing (1) and (2), we get

a = -2 < 0, so figure translate 2 units left.

b = 7 > 0, so figure translate 7 units up.

Therefore, the given rule describes the translation of 2 units to the left and 7 units up.

Answer:

0

Step-by-step explanation:

use the slope formula y^2-y^1

                                     x^2-x^1

Using the formula for compound interest, you can calculate the future value of an investment for different compounding methods. These values turned out to be $66299.84 for annual compounding, $66933.56 for semi-annual compounding, $67183.56 for monthly compounding and $67239.46 for daily compounding.

To solve this problem, you need to understand the compound interest formula: A = P(1 + r/n)^(nt).

Where:

(a) For annual compounding (n=1): A = 47400*(1 + 0.07/1)^(1*5) = $66299.84

(b) For semi-annual compounding (n=2): A = 47400*(1 + 0.07/2)^(2*5) = $66933.56

(c) For monthly compounding (n=12): A = 47400*(1 + 0.07/12)^(12*5) = $67183.56

(d) For daily compounding (n=365): A = 47400*(1 + 0.07/365)^(365*5) = $67239.46

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Final answer:

Calculate the value of the investment after 5 years using different compounding methods.

Explanation:

The value of the investment at the end of 5 years:

Annual: $61,571.76

Semiannual: $62,041.46

Monthly: $62,263.11

Daily: $62,334.74

Answer:

the price is $160000

Step-by-step explanation:

0.22x = 35200

x=160000

Final answer:

The length of line segment PR is the sum of the lengths of PQ and QR, which is 14 units.

Explanation:

The question asks us to determine the length of line segment PR given that point Q is on line segment PR, QR=11 units, and PQ=3 units. To find the length of PR, we simply add the lengths of PQ and QR together, since Q lies on line segment PR meaning PQ and QR are consecutive segments.

Therefore, the length of PR is PQ + QR = 3 + 11, which equals 14 units.

Answer:

y=-2x+20 or y-4=-2(x-8)

Step-by-step explanation:

first we need to calculate the slope

y2-y1/x2-x1

-6+4/7-8

-2/1

The slope is -2

Nows lets find the y intercept using

y-y1=m(x-x1)

y-4=-2(x-8)

y-4=-2x+16

+4 +4

y=-2x+20

Y intercept is 20

Answer:

I didn't know what form you wanted the line in.

Slope-intercept form: y=2x-20

Standard form:  2x-y=20

Point-slope form: y+4=2(x-8) or y+6=2(x-7)

You gave the points (8,-4) and (7,-6).

That last point was (7,-6) right?  I seen (7-6) and just thought you probably meant (7,-6.

Step-by-step explanation:

Equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope: I'm going to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference.

I feel like some people like this more than the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]\frac{y_1-y_2}{x_1-x_2}[/tex]. It is the same thing just a different way to organize things.

So let's do the finding of the slope:

( 8  ,  -4)

-( 7  ,  -6)

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

 1        2

So the slope is 2/1=2.

So we have m=2.

Let's input into our equation y=2x+b.

We need to find the y-intercept.  We could do that by using a point on the line. We get to choose between (8,-4) or (7,-6).  It does not matter.

y=2x+b with (8,-4)

-4=2(8)+b

-4=16+b

Subtract 16 on both sides:

-4-16=b

-20=b

So the y-intercept is -20.

The equation is y=2x+-20 or y=2x-20 (your pick-same thing).

Now let's also put it in standard form which is ax+by=c where it is preferable to have a,b, and c as integers. (Integers are {...,-3,-2,-1,0,1,2,3,...}.)

y=2x-20

Subtract 2x on both sides:

-2x+y=-20

This is in ax+by=c form.

You could multiply both sides by -1:

2x-y=20.

This is still in standard form.

Let's also go for point-slope form which is y-y1=m(x-x1) where (x1,y1) is a given point on the line and m is the slope.

We already have the slope is 2.

We have two points to choose from.  Choose one and go with it. Let's choose (x1,y1)=(8,-4).

y-(-4)=2(x-8)

or

y+4=2(x-8)

Now if you did go with the other point (x1,y1)=(7,-6) it would be:

y-(-6)=2(x-7)

y+6=2(x-7)

You are probably wondering how those are the same lines.  Let's confirm.  Solve both of them for y.

y+4=2(x-8)

Distribute 2:

y+4=2x-16

Subtract 4 on both sides:

y=2x-16-4

Simplify:

y=2x-20

Now the other line:

y+6=2(x-7)

Distribute 2:

y+6=2x-14

Subtract 6 on both sides:

y=2x-14-6

y=2x-20

2 because everything is multiplied by 2 so the scale factor is two

Answer:

3x^2-4x+20/x^2-5x .

Step-by-step explanation:

The given rational expression is:

3x/x-5 - 4/x

Hence to find the difference of the rational numbers we have to take the L.C.M of the denominators:

Thus the L.C.M of x-5 and x is (x-5)(x) and then solve for the numerator:

x(3x) - 4(x-5)/(x-5)(x)

Now solve the numerator and denominator:

3x^2-4x+20/x^2-5x

Thus the answer is 3x^2-4x+20/x^2-5x ....

Answer:

3x^2-4x+20

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

   x(x-5)

Step-by-step explanation:

[tex]\bf \begin{array}{ccll} vinegar&oil\\ \cline{1-2} 2&5\\ 9&x \end{array}\implies \cfrac{2}{9}=\cfrac{5}{x}\implies 2x=45\implies x=\cfrac{45}{2}\implies x=22\frac{1}{2}[/tex]

22.5 ounces of oil should be mixed with 9 ounces of vinegar

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

2 part vinegar 5 part oil.

Let y represent the amount of oil to be mixed with 9 ounces of vinegar.

y = (5/2) * 9 = 22.5 ounces

22.5 ounces of oil should be mixed with 9 ounces of vinegar

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Answer:

1. so the total people including the teacher is 24. 12 and 8 are both factors of 24. 12x2 equals 24 and 8x3 equals 24 so if they get 2 packs of hot dogs and 3 pack of buns everyone can get 1 hot dog and 1 bun

Step-by-step explanation:

24 factors: 1, 2, 3,4 ,6,8,12 ,24

8×3=24

12×2=24

get 2 packs of sausages and 3 packs of buns

each person gets 1 hotdog and 1 bun

Answer:

$30

Step-by-step explanation:

because we know that "1 liter cost(s) $12" we can multiply 12 by 2.5 (the amount we need to know) to get $30

Answer:

$30.0

Step-by-step explanation:

What you'll need to do is multiply 12 by 2.5.

[tex]12.5x2.5=300\\\\$30.0[/tex]

Answer:

( − ∞ , ∞ )  { x | x ∈ R }

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Answer:

Step-by-step explanation:

[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=2x+1,\ g(x)=x+14\\\\\text{Exchange}\ x\ \text{in}\ g(x)\ \text{to}\ (2x+1):\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)=g(2x+1)=(2x+1)+14=2x+15[/tex]

Answer:

32760

Step-by-step explanation:

There are 4 positions on the board.  There are 15 possible candidates for the first position.  That leaves 14 candidates for the second position.  Which leaves 13 for the third position, and 12 for the fourth position.

15 × 14 × 13 × 12 = 32760

Answer: There are 32,760 ways that research board can be chosen.

Step-by-step explanation:

Since we have given that

Number of research doctors participating in the study = 15

the research board requires to be established with offices of director, Assistant director, Quality control analyst, and Correspondent.

Since there are 15 choices for the Offices of director,

There are 14 choices for the Assistant director,

There are 13 choices for Quality control analyst,

There are 12 choices for Correspondent.

So, by applying "Fundamental theorem of counting", we get that

Number of ways that research board can be chosen is given by

[tex]15\times 14\times 13\times 12\\\\=32,760[/tex]

Hence, there are 32,760 ways that research board can be chosen.

Answer:

Choice B

Step-by-step explanation:

A dilation factor of three means you multiply each side bye three. The order of the letters of the triangle also matter. Since it is triangle LMN and ABC this means that A corresponds with L, B corresponds with M and C corresponds with N.

Answer: Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

We know that David wants to increase the price per cup to increase his revenue. He found out that for every $0.25 grows( increase), x, in the price for each cup.

In the event of a price increase, 2 cups remain unsold, and doubling the cups is still not sold. Then the numbers are sold (60-2x). Depending on the choice:

Revenue= (60 -2x)(2 +0.25x)

60·2 +60·0.25x -2x·2 -2x·0.25x

= -0.5x² +11x +120

Answer:

Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

Step-by-step explanation:

Here, x represents the times at which the price is increased,

Since, the original price of one cup = $ 2,

So, after increasing x times of $ 0.25, the new price of each cup = 2 + 0.25x,

Also, the original number of mochas = 60,

Given,

With increasing the price $ 0.25, x times, the number of cup is decreased by 2 times of x,

That is, the new number of mochas = 60 - 2x

Hence, the total revenue would be,

y = new price of each cup × new number of mochas

⇒ y = (2 + 0.25x)(60 - 2x)

⇒ y = 120 - 4x + 15x - 0.5x²

⇒ y = -0.5x² + 11x + 120

He can find find the equation which represents his daily revenue, by Multiplying (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x² + 11x + 120

Answer:

x+5

Step-by-step explanation:

Given:

Dividend= x4 + 5x3 – 3x – 15

Quotient=(x3-3)

As per the rule of division of polynomial:

Dividend = Divisor × Quotient + Remainder

Divisor= required polynomial p(x)

remainder=0

x4 + 5x3 – 3x – 15= p(x) *(x3-3) + 0

p(x)=x4 + 5x3 – 3x – 15/x3-3

By long division we get

p(x)= x+5 !

Answer:

The polynomial is x+5.

Step-by-step explanation:

Here we need to recall the algorithm of the division for polynomials, which is very similar to the one for integers. Given polynomials P(x) and Q(x), there always exist polynomials S(x) and R(x) such that

P(x) = Q(x)S(x) + R(x)

where

In this particular case,  

Then, x⁴+5x³-3x-15 = (x³-3)Q(x). In order to find Q(x) we must complete the division x⁴+5x³-3x-15/x³-3. This gives us that Q(x)=x+5.

Answer:

Advantage: If a car is losing value at a constant rate, then the linear function represents accurately the depreciation of the car.

Disadvantage: If the car is not losing value at a constante rate, then when we calculate the value of the car 'x' years after it was sold, we won't get  an accurate result.

If the minivan is purchased for $29,248 and the first year it depreciates $3000. Then, the linear function that represents the value of the car is:

y = $29,248 - $3000x

Where 'y' represents the value of the car, and 'x' represents the number of years.

Let us explain this with an example. After 6 years, the price will be:

y = $29,248 - $3000(6) =  $11,248

The advantages of using a linear function to represent the depreciation of a car are simplicity and ease of calculation, but it assumes constant depreciation rate. On the other hand, an exponential function can account for varying depreciation rates, but can be more complex. The linear function to represent the value of the minivan after x years is V(x) = 29,248 - 3,000x.

When representing the depreciation of a car over time, using a linear function has advantages and disadvantages. The advantages are that it provides a simple and straightforward representation of the depreciation, and it is easy to calculate and understand. However, a linear function assumes that the car depreciates at a constant rate over time, which may not always be accurate.

On the other hand, using an exponential function to represent the depreciation of the car has advantages and disadvantages as well. The advantage is that it can account for different rates of depreciation over time, which may be more realistic. However, exponential functions can be more complex to calculate and understand.

In the case of the minivan that depreciates $3,000 in the first year, a linear function can be used to represent the value of the car x years after it was sold. The linear function would be V(x) = 29,248 - 3,000x, where V(x) is the value of the car x years after it was sold.

Answer:

Prasant needs more than 4.5 bags of candy to hand out during Halloween.

Step-by-step explanation:

The correct method to write a statement that matches the inequality [tex]\( h > 4.5 \)[/tex] is to express that the value of [tex]\( h \)[/tex] is greater than 4.5. This can be done by stating that [tex]\( h \)[/tex] must be some quantity more than 4.5, without specifying the exact amount by which [tex]\( h \)[/tex]exceeds 4.5.

For example, one could write the statement as:

The value of [tex]\( h \)[/tex] is more than 4.5 units.

This statement correctly conveys that [tex]\( h \)[/tex] is not equal to 4.5 and is somewhere on the number line to the right of 4.5, with no upper limit specified. It is important to note that the inequality [tex]\( h > 4.5 \)[/tex] does not include the value 4.5 itself; [tex]\( h \)[/tex] must be strictly greater than 4.5.

In summary, the statement should indicate that \( h \) is any number that is greater than 4.5, and the value of [tex]\( h \)[/tex] can be infinitely close to 4.5 but never equal to or less than it.

Answer:

12 children

Step-by-step explanation:

you would just find the GCF (greatest common factor) of these 2 numbers, which is 12

so each child would get 3 prizes and 2 balloons

Answer:

Step-by-step explanation:

Dividing one number by another yields a quotient. The quotient of 9 divided by 15 can be expressed as a decimal or a fraction. Any time you divide a number by a larger number, the answer will always be less than one.

Answer:

C

Step-by-step explanation:

1/9