Carol buys a reference book that originally cost $87.50 for 15% off. She pays a sales tax of 4.5%. What is the total cost of the book?

The answer is c.

F(x)=5x^3+7x^4-1/2x

Answer:

option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Step-by-step explanation:

Given expression ,  [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

[tex]3x^2+17-\frac{82}{x+5}[/tex]

Taking LCM , Multiply [tex]3x^2+17[/tex] by (x+5) , we get,

[tex]\frac{3x^2(x+5)+17(x+5)-82}{x+5}[/tex]

On solving , we get,

[tex]\frac{3x^3+15x^2+17x+85-82}{x+5}[/tex]

On simplifying, we get,

[tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

Which is equal to the given expression.

Thus, option (c) is correct,

[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]

The correct option that describes the volume of a cylinder is B: the area of the circular base multiplied by the height of the cylinder, represented by the formula \(V = \pi r^2 h\).

The volume of a cylinder is best described by option B, which states it is the area of the circular base multiplied by the height of the cylinder. The area of the base, which is a circle, is calculated using the formula \\(\pi r^2\), where \(r\) represents the radius of the circle. To find the volume, this area is then multiplied by the height \(h\) of the cylinder, giving the formula for the volume \(V = \pi r^2 h\).

The given equation in slope-intercept form is y = -2x - 2.

Slope of a line is defined as the change in the value of y-coordinate with respect to the x-coordinate value. It is usually denoted by 'm'.

It can also be defined as the tangent of the angle that the given line is making with the X-axis.

That is m = tan θ, where θ is the angle that line is making with the X-axis.

The equation of a line in slope-intercept form is given by,

y = mx + c

Here, c is called the y-intercept, the value of which is the value of the y-coordinate when the line touches the Y-axis.

Now,

y + 4 = -2 (x - 1)

y + 4 = -2x + 2

y = -2x + 2 - 4

y = -2x - 2

The equation of the line in slope-intercept form is y = -2x - 2.

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In order to write [tex]\frac{18}{25}[/tex] as a decimal, we need to find a fraction equivalent to[tex]\frac{18}{25}[/tex] with a 100 in the denominator. Notice that if we multiply the numerator and the denominator of [tex]\frac{18}{25}[/tex] by 4, we get the equivalent fraction [tex]\frac{72}{100}[/tex] which we can now write as a decimal. Remember that the hundredths place is 2 places to the right of the decimal point. Therefore, we can write [tex]\frac{72}{100}[/tex] as 0.72.

To write a fraction to a percent, first remember that a percent is a ratio of a number to 100 so to write [tex]\frac{18}{25}[/tex] as a percent, we need to find a fraction equivalent to [tex]\frac{18}{25}[/tex] that has a 100 in the denominator. We can . do this by setting up a proportion.

[tex]\frac{18}{25}[/tex] ≈ [tex]\frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

25n = 1800

÷ 25     ÷25

n = 72%

Therefore, [tex]\frac{18}{25}[/tex] is equal to 72%.

Answer:

C) circle

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Aidan makes 8 bracelets each day from Tuesday to Thursday, resulting in 24 bracelets for those three days. Adding this to the 12 he made on Monday gives us 36 bracelets up to Thursday. Aidan continues the same pattern on Friday, making 8 more bracelets, totaling 44 bracelets.

To determine how many bracelets Aidan makes on Friday, we need to calculate the total number he makes from Tuesday through Thursday and then add it to the number of bracelets he already made on Monday. He starts with 12 bracelets on Monday and makes 8 more each day from Tuesday to Thursday. Calculating the bracelets made from Tuesday through Thursday involves multiplication of the daily bracelet count by the number of days.

Aidan makes 8 bracelets each day for three days, which is calculated as follows:

We then add this to the initial 12 bracelets made on Monday:

Since the pattern of bracelet making doesn’t specify any change on Friday, we assume Aidan continues to make 8 bracelets on Friday as well. So, he makes 8 bracelets on Friday.

The total number of bracelets Aidan makes up to Friday is the sum of bracelets made from Monday through Thursday plus the bracelets made on Friday:

Final answer:

Aidan makes 44 bracelets on Friday.

Explanation:

To find out how many bracelets Aidan makes on Friday, we need to calculate the total number of bracelets he makes from Monday through Thursday. On Monday, Aidan makes 12 bracelets. From Tuesday through Thursday, he makes 8 more bracelets each day. So the number of bracelets he makes on Tuesday is 12 + 8, on Wednesday is 12 + 8 + 8, and on Thursday is 12 + 8 + 8 + 8.

Now, to calculate the number of bracelets he makes on Friday, we need to add 8 to the total number of bracelets he made on Thursday. So the total number of bracelets he makes on Friday is 12 + 8 + 8 + 8 + 8.

Therefore, Aidan makes 12 + 8 + 8 + 8 + 8 = 44 bracelets on Friday.

Answer:

n = 3years

Step-by-step explanation:

If Gary buys a van £27500 and sell the van at a value of the £11264 after n years, depreciation will give us;

£27500-£11264 = £16236

If the van depreciates by 20% each year, yearly depreciation will be;

20% of £27500 = £5500

To get the total number of years n it takes the van to depreciate to £11264 will give total depreciation amount/yearly depreciation amount which gives;

£16236/£5500 = 2.9years

This means that the van has depreciate from £27500 to £11264 after 3years

Using the compound interest formula, it will take approximately 24.53 years for an initial investment of $1,500 to grow to $7,300 at an annual interest rate of 6.75%. This is calculated by solving for t in the rearranged compound interest formula.

To determine how many years it will take for your $1,500 investment to reach $7,300 with an interest rate of 6.75% compounded annually, we use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

We rearrange the formula to solve for t:

t = (log(A/P) / log(1 + r/n)) / n

Plug in the known values:

t = (log(7300/1500) / log(1 + 0.0675)) / 1

Calculate the logarithms:

t ≈ (log(4.8667) / log(1.0675))

t ≈ (0.6887 / 0.0281)

t ≈ 24.53

It will take approximately 24.53 years for the investment to grow to $7,300.

Final answer:

To find the ratio that forms a proportion with 9/5, we can find a common multiplier for each option and check if the resulting ratios are equal to 9/5.

Explanation:

If we want to determine which ratio forms a proportion with 9/5, we can find a common multiplier. We can multiply both the numerator and denominator of each ratio by the same number and check if the resulting ratios are equal to 9/5.

Let's check each option:

Therefore, the ratio 54/30 (option a) forms a proportion with 9/5.

The solutions of the quadratic equation [tex]8m^2 + 20m = 12[/tex] by factoring method are [tex]m = \dfrac{1}{2}[/tex] and [tex]m = - 3[/tex]

Using the formula of the quadratic equation which states that,

The roots of the standard form of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] are calculated as,

[tex]x = \dfrac{- b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Given that,

A quadratic equation,

[tex]8m^2 + 20m = 12[/tex]

Now, simplify the equation,

[tex]8m^2 + 20m = 12[/tex]

Subtract 12 on both sides,

[tex]8m^2 + 20m - 12 = 0[/tex]

Take 4 as a common term,

[tex]4 (2m^2 + 5m - 3) = 0[/tex]

Since, [tex]4 \neq 0[/tex]

[tex]2m^2 + 5m - 3 = 0[/tex]

Apply the factoring method in the above equation,

[tex]2m^2 + 5m - 3 = 0[/tex]

[tex]2m^2 + (6 - 1)m - 3 = 0[/tex]

[tex]2m^2 + 6m - m - 3 = 0[/tex]

[tex]2m (m + 3) - 1(m + 3) = 0[/tex]

[tex](2m - 1) (m + 3) = 0[/tex]

This gives two solutions,

[tex]2m - 1 = 0\\2m = 1\\m = \dfrac{1}{2}[/tex]

[tex]m + 3 = 0\\m = - 3[/tex]

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Let

x------> the biggest number

y------> the middle number

z------> the smallest number

we know that

[tex]x=2y[/tex] -------> equation [tex]1[/tex]

[tex]x+y=4z[/tex] -------> equation [tex]2[/tex]

[tex]z+y=x-2[/tex] -------> equation [tex]3[/tex]

substitute equation [tex]1[/tex] in equation [tex]2[/tex] and equation [tex]3[/tex]

[tex][2y]+y=4z[/tex] ------> [tex]3y=4z[/tex] ------> equation [tex]4[/tex]

[tex]z+y=[2y]-2[/tex] ----> [tex]z+2=y[/tex] ------> equation [tex]5[/tex]

using a graph tool-----> to resolve the system of equations

see the attached figure

the solution is the point [tex](6,8)[/tex]

[tex]z=6\\y=8[/tex]

Find the value of x

[tex]x=2y[/tex]

[tex]x=2*8=16[/tex]

therefore

the answer is

the biggest number is [tex]16[/tex]

the the middle number is [tex]8[/tex]

the smallest number is [tex]6[/tex]

The possibility statements are:

Statement 1

The function is defined on [2.4]

The above means that, the minimum is 2, and the maximum is 4

However, since the function is continuous at [2,4), the close bracket ")" means that the function extends indefinitely i.e. no maximum.

Hence, this statement is possible

Statement 2

The function is defined on [4.5]

The above means that, the minimum is 4, and the maximum is 5

However, since the function is continuous at [4,5], the close brackets "[" and "]" mean that the function have finite values

Hence, this statement is possible

Statement 3

The function is defined on [2,5]

The above means that, the minimum is 2, and the maximum is 5

However, since the function is continuous at [2,5], the close brackets "[" and "]" mean that the function have finite values and it has bounded intervals

Hence, this statement is not possible

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Answer:

First option is correct.

Step-by-step explanation:

In triangle ABC, [tex]\angle A=8x-2[/tex], [tex]\angle B=2x-8[/tex] and [tex]\angle C=94-4x[/tex].

According to angle sum property of a triangle, the sum of interior angles of a triangle is 180 degree.

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]8x-2+2x-8+94-4x=180[/tex]

[tex]6x+84=180[/tex]

[tex]6x=96[/tex]

Divide both sides by 6.

[tex]x=16[/tex]

Therefore the value of x is 16. The measure of angles are

[tex]\angle A=8(16)-2=126[/tex]

[tex]\angle B=2(16)-8=24[/tex]

[tex]\angle C=94-4(16)=30[/tex]

The opposite angle of shortest side is always smallest interior angle. Similarly the opposite angle of longest side is always largest interior angle.

[tex]\angle B<\angle C<\angle A[/tex]

[tex]AC<AB<BC[/tex]

Therefore option 1 is correct.

"The sum of 58 and 76 is 134.

To find the sum of two numbers, one simply needs to add them together. In this case, the numbers are 58 and 76.

The addition can be performed as follows:

[tex]\[ 58 + 76 = 134 \][/tex]

Thus, the correct answer to the question ""What is the sum of 58 and 76?"" is 134."

Answer:

Option 1,2 and 3.

Step-by-step explanation:

An algebraic expression is such a mathematical representation of variables

Algebra is relation with variables a,y,z and so on

So, Option 2 is correct that is it will contain variable in numerator.

Similarly, Option 3 is correct that is it will contain variable in denominator.

Option 4 is incorrect because if it  contains variable with an exponent then it will not be algebraic it will become exponent function.

Option 1 is correct because it may have common denominator an algebraic fraction will have common denominator.