If a skateboard cost $36 and the tax rate is 6.5 percent .
What is the tax on the skateboard?
What is the total price, including tax?

Answer:

[tex]x_{1}=\frac{1+\sqrt{33} }{4}\\x_{2}=\frac{1-\sqrt{33} }{4}[/tex]

Step-by-step explanation:

Using quadratic formula

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

we will have two solutions.

2x^2 - x - 4 = 0

So, a=2   b=-1  c=-4, we have:

[tex]x_{1}=\frac{+1+\sqrt{-1^{2}-4*2*-4} }{2*2}\\\\x_{2}=\frac{+1-\sqrt{-1^{2}-4*2*-4} }{2*2}[/tex]

Finally, we have two solutions:

[tex]x_{1}=\frac{1+\sqrt{33} }{4}\\\\x_{2}=\frac{1-\sqrt{33} }{4}[/tex]

Answer:

∠B = 65°; ∠C = 115°

Step-by-step explanation:

The first thing you to do is set ∠B and ∠D equal to each other.

[tex]3n+20=6n-25[/tex]

The reason you do this is because the oppisite angles are equal to each other in a parallelogram.

Next, you want to start simplifying the equation (I personally like to start with the variables).

[tex]....3n+20=6n-25\\-3n.....-3n[/tex]

Then, you simplify again (you can combined these if you want but for example I am breaking it down more.

[tex]....20=3n-25\\+25.......+25\\....45=3n[/tex]

Then you dived by 3, and you get 15=n. Now (and people often forget this step) you have to plug it back in to solve for the equartion. ∠B=3(15)+20, ∠B=65. Now you have to subtract 65 from 180 because ∠B and ∠C are completmtry. 180-65=115=∠C

Answer:

10.5

Step-by-step explanation:

6x +3 = 66

Subtract 3 from each side

6x+3-3 = 66-3

6x = 63

Divide each side by 6

6x/6 = 63/6

x = 10.5

the answer is X= 10.5

ANSWER

[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]

EXPLANATION

The equation of a circle given the center (h,k) and radius r is given by:

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The circle has center (4,0) and radius

[tex]r = 2 \sqrt{3} [/tex]

We substitute the center and radius to get,

[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = {(2 \sqrt{3)} }^{2} [/tex]

[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = 12[/tex]

[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]

Answer:

Step-by-step explanation:

Think about it for a second.

Take log 3 (-9). 3 to what power is -9.

Let's try:

3 ^ 2 = 9. So it's not negative 9.

Maybe 3 ^ -2 = 1/9. Still not -9.

Let's try 3 ^ 1/3 = 1.4422. Still not remotely close.

So we can make a conclusion that a positive number to any real exponent can't give us a negative number.

A logarithmic equation exists as an equation that involves the logarithm of an expression including a variable. To translate exponential equations, first, see whether you can write both sides of the equation as powers of the identical number.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.

As the base of a power function, 0, 1, and every negative integer provide a possible issue. Furthermore, if those values cannot be relied upon to be the base of a power function, they cannot be relied upon to be the base of a logarithm either. For this reason, we restrict the base of the logarithm to only positive numbers other than 1.

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Answer:

If a number has infinite repeating decimals, the correct form to write repeating decimilas is by adding a line -also con vinculum- above the repeating decimals.

For example:

[tex]\frac{1}{3} = 0,3333333 =[/tex] [tex]0.\overline{3}[/tex]

Answer:

Step-by-step explanation:

16 units

Answer:

C= 2*pi*r

Step-by-step explanation:

[tex]m < \frac{ - 185}{k} [/tex]

HOPE THIS WILL HELP YOU

For this case we must find the value of the variable "m" of the following expression:

[tex]-mk-110> 75[/tex]

We follow the steps below:

We add 110 to both sides of the inequality:

[tex]-mk> 75 + 110\\-mk> 185[/tex]

We divide between k on both sides of the inequality:

[tex]\frac {-mk} {k}> \frac {185} {k}\\-m> \frac {185} {k}[/tex]

We multiply by "-" on both sides of the inequality, remembering that the sense of inequality changes:

[tex]m <- \frac {185} {k}[/tex]

ANswer:

[tex]m <- \frac {185} {k}[/tex]

Answer:

Part a) The slope is equal to [tex]m=21.2\frac{\$}{year}[/tex]

Part b) The linear equation is equal to [tex]y=21.2x+3,090[/tex]

Part c) The tuition would be [tex]\$3,238.4[/tex] in 2,017

Step-by-step explanation:

step 1

Find the slope m

Let

x-----> the year after 2,010

y-----> the tuition

we have

For the year 2,010

[tex]x=0\ years[/tex]

For the year 2,015

[tex]x=(2,015-2,010)=5\ years[/tex]

so

[tex]A(0,3,090), B(5,3,196)[/tex]

Calculate the slope

[tex]m=\frac{(3,196-3,090)}{(5-0)}=21.2\frac{\$}{year}[/tex]

step 2

Find the linear equation

with the slope m and the point A find the linear equation

[tex]y-y1=m(x-x1)[/tex]

substitute the values

[tex]y-3,090=21.2(x-0)[/tex]

[tex]y=21.2x+3,090[/tex] -------> linear equation that would predict tuition for any year after 2010

step 3

Assuming the linear trend remained constant, what would tuition be in 2017

so

For [tex]x=(2,017-2,010)=7\ years[/tex]

substitute in the linear equation

[tex]y=21.2(7)+3,090=\$3,238.4[/tex]

The slope of the increase in Ivy Tech's tuition from 2010 to 2015 is $21.2 per year. The linear model to predict future tuition costs is: y = 3090 + 21.2*(Years after 2010). Using this model, the predicted tuition for 2017 is approximately $3227.4.

The subject of your question is the calculation of a linear model for Ivy Tech's tuition increase over the years. In 2010, the tuition was $3090, and in 2015, it increased to $3196.

To calculate the slope, we subtract the tuition of the two years, and divide it by the difference in the years. Thus, the slope is: (3196-3090) / (2015-2010) = $21.2 per year.

Your linear model would therefore be: y = 3090 + 21.2*(Years after 2010). For example, if you want to predict the tuition in 2017, you would use : y = 3090 + 21.2*(2017-2010) = $3227.4. This suggests that the tuition in 2017 would be approximately $3227.4, provided the trend remains the same.

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Answer:

C. 17, 12, 7

Step-by-step explanation:

In a triangle, the sum of the lengths of any two sides must be greater then the length of the third side. If you can show any two segments, the sum of whose lengths is less than the length of the third segment, that cannot form a triangle.

In choices A, B, and D, there is at least one sum of the lengths of two segments that is less then the length of the third segment. That shows that choices A, B, and D cannot form triangles.

A. 8 + 7 = 15 < 16 No

B. 9 + 7 = 16 = 16 No

D. 11 + 5 = 16 < 17 No

C.

17 + 12 = 29 > 7

12 + 7 = 19 > 17

17 + 7 = 24 > 12

Yes

Answer:

Below is the sequence of steps which are required to follow in order to have the expression in its simplified form.

Step 1

[tex](875x^{5}y^{9})^{\frac{1}{3}}[/tex]

Step 2

[tex](125.7)^\frac{1}{3}.x^{\frac{3}{5}}.y^{\frac{9}{3}}[/tex]

Step 3

[tex](125)^{1/3}.(7)^{1/3}.x(^{\frac{3}{3}+\frac{2}{3}}).y^{3}}[/tex]

Step 4

[tex](5^{3} )^{\frac{1}{3}}.7^\frac{1}{3}.x^{(1+\frac{2}{3})}.y^{3}[/tex]

Step 5

[tex]5^{1}.7^\frac{1}{3}.x^{1}.x^\frac{2}{3}.y^3[/tex]

Step 6

5xy³([tex]7^{\frac{1}{3} }[/tex][tex]x^{\frac{2}{3} }[/tex])

Step 7

5xy³([tex]7x^{2}[/tex])[tex]\frac{1}{3}[/tex]

Step 8

5xy³[tex]\sqrt[3]{7x^{2}}[/tex]

Answer:

x = -11.9

Step-by-step explanation:

x + 5.1 = –6.8

Subtract 5.1 from each side

x + 5.1-5.1 = –6.8-5.1

x = -11.9

-11.9

Subtract 5.1 from Both sides to get -11.9 and that’s what x equals

Answer:

The vertices of the triangle after the translation are (-1 , -1) , (-4 , -5) , (-8 , 0)

The image of Δ NPQ after the translation is Δ KLM

Step-by-step explanation:

*Lets revise translation

- If point (x , y) translate to the right h units

∴ Its image is (x + h , y)

- If point (x , y) translate to left h units

∴ Its image is (x - h , y)

- If point (x , y) translate up k units

∴ Its image is (x , y + k)

- If point (x , y) translate down k units

∴ Its image is (x , y - k)

* Now lets solve the problem

- From the graph the vertices of the triangle are

 (0 , 2) , (-3 , -2) , (-7 , 3)

- The triangle will translate by the rule (x , y) ⇒ (x - 1 , y - 3)

∴ The triangle translate 1 unit to the left and 3 units down

- We will subtract each x-coordinate by 1 and each y-coordinate by 3

∴ The image of point (0 , 2) is (0 -1 , 2 - 3) = (-1 , -1)

∴ The image of point (-3 , -2) is (-3 - 1 , -2 - 3) = (-4 , -5)

∴ The image of point (-7 , 3) is (-7 - 1 , 3 - 3) = (-8 , 0)

* The vertices of the triangle after the translation are

 (-1 , -1) , (-4 , -5) , (-8 , 0)

- From the graph the vertices of the triangle NPQ are

 N (-7 , -6) , P (-4 , -3) , Q (-4 , -6)

- The triangle will translate by the rule (x , y) ⇒ (x + 8 , y + 1)

∴ The triangle translate 8 units to the right and 1 unit up

- We will add each x-coordinate by 8 and each y-coordinate by 1

∴ The image of point N (-7 , -6) is (-7 + 8 , -6 + 1) = (1 , -5)

∴ The image of point P (-4 , -3) is (-4 + 8 , - 3 + 1) = (4 , -2)

∴ The image of point Q (-4 , -6) is (-4 + 8 , -6 + 1) = (4 , -5)

* The vertices of the triangle after the translation are

 (1 , -5) , (4 , -2) , (4 , -5)

- Lets find from the graph the names of these vertices

∵ Δ KLM has the same vertices k (1 , -5) , L (4 , -2) , M (4 , -5)

* The image of Δ NPQ after the translation is Δ KLM

2 x square - 18 x + 36

2 x square - 6 x -12 x + 36

2 x (x - 3 )- 12 (x - 3 )

x - 3 2 x =12

x = 3 x =6

Answer:

A) x=3 or x=6

Step-by-step explanation:

Factor out the GCF : 2(x^2-9x+18)

Then, set to zero.

2(x^2-9x+18)=0

2(x-3)(x-6)=0

x=3 or x=6

Answer:

1. 12(2x+3y)

2. 20x+4x+30y+6y

3. 6(4x+6y)

Step-by-step explanation:

The three equivalent expression of 24x + 36y are,

1). 12(2x + 3y).

2). 6(4x + 6y)

3). 4(6x + 3y).

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given expression:

24x + 36y.

To find the equivalent expressions:

First, we will find the common factor and simplify the expression.

That means,

the common factors of 24 and 36 are 2, 3, 4, 6, 12.

We can make three expressions,

24x + 36y = 12(2x + 3y).

24x + 36y = 6(4x + 6y).

And 24x + 36y = 4(6x + 3y).

Therefore, three equivalent expressions are 12(2x + 3y), 6(4x + 6y) and 4(6x + 3y).

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Answer:

[tex]\sec \theta=-\sqrt{5}[/tex]

Step-by-step explanation:

The hypotenuse is [tex]h^2=6^2+3^2[/tex]

[tex]h^2=36+9[/tex]

[tex]h^2=45[/tex]

[tex]h=\sqrt{45}[/tex]

[tex]h=3\sqrt{5}[/tex]

The terminal side of [tex]\theta[/tex] is in the second quadrant.

In this quadrant; the secant ratio is negative.

[tex]\sec \theta=-\frac{hypotenuse}{adjacent}[/tex]

[tex]\sec \theta=-\frac{3\sqrt{5}}{3}[/tex]

[tex]\sec \theta=-\sqrt{5}[/tex]

The value of sec theta is [tex]\sec(\theta) = -\sqrt5[/tex]

From the diagram, we start by calculating the length of the hypotenuse (h).

So, we have:

[tex]h = \sqrt{6^2 + 3^2[/tex]

Evaluate

[tex]h = \sqrt{45[/tex]

Simplify

[tex]h = 3\sqrt{5[/tex]

The value of the secant in the second quadrant is calculated as:

[tex]\sec(\theta) = -\frac{Hypotenuse}{Adjacent}[/tex]

So, we have:

[tex]\sec(\theta) = -\frac{3\sqrt5}{3}[/tex]

Evaluate

[tex]\sec(\theta) = -\sqrt5[/tex]

Hence, the value of sec theta is [tex]\sec(\theta) = -\sqrt5[/tex]

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C. 30 divided by 7 is roughly 4.3 which’s is between 4 and 5

Answer:

Bass = 5x = 312

Pike = 3x = 188

Step-by-step explanation:

8x = 500

x = 62.5 (But since there can't be 1/2 fish, it should be rounded)

Bass = 5x = 312

Pike = 3x = 188

Answer:

300 bass and 200 pike

Step-by-step explanation:

The given triangle has a right angle.

We use the mnemonics SOH-CAH-TOA.

1i) [tex]\sin C =\frac{Opposite}{Hypotenuse}[/tex],[tex]\implies \sin C =\frac{30}{34}[/tex],[tex]\implies \sin C =\frac{15}{17}[/tex]

ii) [tex]\cos C =\frac{Adjacent}{Hypotenuse}[/tex],[tex]\implies \cos C =\frac{16}{34}[/tex],[tex]\implies \cos C =\frac{8}{17}[/tex]

[tex]\tan C =\frac{Opposite}{Adjacent}[/tex],[tex]\implies \tan C =\frac{30}{16}[/tex],[tex]\implies \tan C =\frac{15}{8}[/tex]

2. We want to find the hypotenuse.

We know an angle to be 23 degrees.

We were also given the side opposite to this angle to be 1200km.

Therefore we use the sine ratio.

Answer:

1) sin C = 30 / 34

cos C = 16/34

tan C = 30/16

2) The value of x = 1304.34

Step-by-step explanation:

1.

In a right angled triangle, we have perpendicular, hypotenuse and base.

The hypotenuse is the longest side and opposite to the right angle. the side having 90 degree angle is perpendicular.

Applying formulas we can find the values:

the formulas are : cos (Ф) = Base / hypotenuse

sin (Ф) = Perpendicular / hypotenuse

tan (Ф) = Perpendicular / Base

Putting values in the formula from figure:

sin C = Perpendicular / Hypotenuse

sin C = 30 / 34

cos C = Base / Hypotenuse

cos C = 16/34

tan C = Perpendicular / Base

tan C = 30/16

2.

We need to find the hypotenuse of the given triangle, we are given base = 1200 m and the angle is 23°

We know, cos Ф = Base / Hypotenuse.

Solving this, We can find the value of x.

cos (23) = 1200 / x

x cos (23) = 1200

x (0.920) = 1200

x = 1200 / 0.920

x = 1304.34

The value of x = 1304.34

Answer:

25

Step-by-step explanation:

12/x = 48/100

48/100 = 0.48

12 = 0.48x

12/0.48 = 25

Answer:

b

Step-by-step explanation:

13

Answer:

[tex](\pm \sqrt{2}, 0)[/tex]

Step-by-step explanation:

The x intercepts are basically the points at which y = 0.

-x^2 + 2 = 0

-x^2 = -2

x^2 = 2

x = [tex]\pm \sqrt{2}[/tex]

For this case we have by definition, that to find the x-intercept points, we must make the variable y = 0 and clear the value of "x". So:

[tex]y = -x ^ 2 + 2\\0 = -x ^ 2 + 2\\x ^ 2 = 2\\x = \sqrt {2}[/tex]

So, the x-intercepts are:

[tex](x_ {1}, y_ {1}) = (\sqrt {2}, 0)\\(x_ {2}, y_ {2}) = (- \sqrt {2}, 0)[/tex]

ANswer:

[tex](x_ {1}, y_ {1}) = (\sqrt {2}, 0)\\(x_ {2}, y_ {2}) = (- \sqrt {2}, 0)[/tex]

Answer:

C (2,2)

B (2,-2)

A (-2,-2)

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given 2 secants drawn from an external point to the circle, then

EC × ED = EB × EA, that is

(x + 4)(x + 4 + 1) = (x + 1)(x + 1 + 11)

(x + 4)(x + 5) = (x + 1)(x + 12) ← expand factors on both sides

x² + 9x + 20 = x² + 13x + 12 ← subtract x² + 13x from both sides

- 4x + 20 = 12 ( subtract 20 from both sides )

- 4x = - 8 ( divide both sides by - 4 )

x = 2

Without the specific details of the spinner's sections, it is impossible to determine the exact odds of landing on yellow. Generally, the odds are calculated as the number of yellow sections divided by the total number of sections minus the yellow sections, such as 1:7 for a spinner with one yellow and seven other sections.

The question seems to be about calculating probabilities in different scenarios involving a spinner or balls with various colors. However, the exact description of the spinner is not provided. To calculate the odds of spinning yellow, we need the total number of sections on the spinner and the number of those sections that are yellow. Without this information, we can't provide a specific numerical answer. If we knew the spinner had a certain number of equal-sized sections, the odds of spinning yellow would be the number of yellow sections divided by the total number of sections minus the yellow sections.

If we assume there is one yellow section on the spinner, and there are a total of eight sections, then the odds of spinning yellow would be calculated as 1/(8-1), which simplifies to 1/7. Therefore, the odds of spinning yellow would be 1:7.

The odds of landing on yellow on the spinner in the image are 50%. This is because there are two equally sized sections of the spinner colored yellow, and two sections of other colors.

The probability of landing on any particular section is equal to the size of that section divided by the total size of the spinner. In this case, each of the yellow sections takes up half of the spinner, so the probability of landing on yellow is 1/2, or 50%.

It is important to note that this assumes that the spinner is spun fairly, and that each section has an equal chance of landing at the bottom. If there is any bias or if the sections are not of equal size, then the actual odds of landing on yellow will be different.

For this case we have a function of the form [tex]y = f (x)[/tex]

Where:

[tex]f (x) = 5x[/tex]

We must find the value of the function when [tex]x = 2,[/tex] that is, [tex]f (2).[/tex] Then, replacing the value of x in the function:

[tex]f (2) = 5 (2)\\f (2) = 10[/tex]

Thus, when [tex]x = 2[/tex] the function has a value of 10.

Answer:

[tex]f (2) = 10[/tex]

Answer: [tex]f(2)=10[/tex]

Step-by-step explanation:

You have the following linear function:

[tex]f(x)=5x[/tex]

To evaluate this function for the given value, you need to substitute the value of the variable "x" ([tex]x=2[/tex]), which is the input value, into the linear function to obtain the output value. Then:

For [tex]x=2[/tex]

[tex]f(2)=5(2)[/tex]

Make the multiplication.

Therefore, the result is:

[tex]f(2)=10[/tex]

Your answer for this question will be B.4

Answer:

Choice B; 4

Step-by-step explanation:

The solution to a system of equations is a pair of points (x, y) such that both equations pass through the given point. The number of solutions will thus be the number of such points where both functions pass through or intersect. The solutions to a system of equations can be determined analytically or graphically.

In this case, the graphical approach is much easier to use. We simply graph the two equations on the same graph and determine the number of points where they intersect.

From the attachment below, we see that the functions intersect at 4 distinct points. Hence there are 4 solutions to the system of equations given.

Answer: y2/10

Step-by-step explanation:

The equivalent expression for [tex]\( y^{1/5} \)[/tex] using radicals is [tex]\( \sqrt[5]{y} \).[/tex]

Sure, I can help with that! To express [tex]\( y^{1/5} \)[/tex] using radicals, we need to rewrite the exponent [tex]\( \frac{1}{5} \)[/tex] as a radical.

The expression [tex]\( y^{1/5} \)[/tex] can be written as [tex]\( \sqrt[5]{y} \)[/tex].

Here's the step-by-step calculation:

1. Start with the expression [tex]\( y^{1/5} \).[/tex]

2. Rewrite the exponent [tex]\( \frac{1}{5} \)[/tex] as a radical, giving [tex]\( \sqrt[5]{y} \)[/tex].

To understand why [tex]\( y^{1/5} \)[/tex] can be expressed as [tex]\( \sqrt[5]{y} \)[/tex], let's break it down:

The exponent [tex]\( \frac{1}{5} \)[/tex] means taking the fifth root of [tex]\( y \)[/tex]. The radical symbol [tex]\( \sqrt[5]{\;} \)[/tex] represents the fifth root. So,[tex]\( y^{1/5} \)[/tex] is equivalent to [tex]\( \sqrt[5]{y} \).[/tex]

In other words, raising [tex]\( y \)[/tex] to the power of [tex]\( \frac{1}{5} \)[/tex] is the same as finding the number which, when multiplied by itself five times, equals [tex]\( y \)[/tex]. This is precisely what the fifth root accomplishes.

Therefore, the equivalent expression for [tex]\( y^{1/5} \)[/tex] using radicals is [tex]\( \sqrt[5]{y} \).[/tex]

Complete question:

Using radicals write an equivalent expression for the expression y1/5

Answer: The formula for the volume of a cylinder is v = πr2h. The volume for a cone whose radius is R and whose height is H is V = 1/3πR2H.

Answer:

The volume of the mailbox is [tex]936\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the prism (mailbox) is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of the prism

h is the height of the prism

we have

[tex]B=52\ in^{2}[/tex]

[tex]h=18\ in[/tex]

substitute

[tex]V=52(18)=936\ in^{3}[/tex]