Which of the following is the statement of the triangle inequality theorem?A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.C. The longest side of a triangle is opposite the largest angle.D. The largest angle of a triangle is between the two longest sides.

Subtract the average from the sales to get the deviation.

Aug. 1700 - 1412.50 = 287.50

Sept. 1125 - 1412.50 = -287.50

Oct. 1850 - 1412.50 = 437.50

Nov. 1500 - 1412.50 = 87.50

Dec. 1050 - 1412.50 = -362.50

The monthly deviation from the average exists at 287.50, -287.50, 437.50, 87.50, and -362.50.

Estimating the mean average enables you to specify the deviation from the mean by computing the difference between the mean and each value.

Subtract the average from the sales to acquire the deviation.

Aug. 1700 - 1412.50 = 287.50

Sept. 1125 - 1412.50 = -287.50

Oct. 1850 - 1412.50 = 437.50

Nov. 1500 - 1412.50 = 87.50

Dec. 1050 - 1412.50 = -362.50

The monthly deviation from the average exists at 287.50, -287.50, 437.50, 87.50, and -362.50.

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Answer:  x² + 3x + 5

Step-by-step explanation:

f(x) = 3x + 5       g(x) = x²

(f + g)(x) = f(x) + g(x)

             = 3x + 5 + x²

             = x² + 3x + 5

Answer:

  T(1, 5), R(7, 7), A(7, 1), M(4, 5)

Step-by-step explanation:

The mapping for -90° rotation is (x, y) ⇒ (y, -x).

 for example, T(-5, 1) ⇒ T'(1, 5)

__

If you're doing this with pencil and paper, you can draw the image and axes the way it is, then rotate your drawing 90° clockwise (so the axes line up) and copy it into the first quadrant.

Answer: Second option is correct.

Step-by-step explanation:

Let the original price of chair be 'p'.

Number of chairs = 4

Discount rate = 25%

So, Amount of discount would be

[tex]\dfrac{25}{100}p\\\\=0.25p[/tex]

So, Cost of each chair after discount would be

[tex]p-0.25p[/tex]

So, Cost of all 4 chairs would be

[tex]4(p-0.25p)[/tex]

Hence, Second option is correct.

Answer:

25% is being taken off the original price, p, of each patio chairs.

That means the price of each patio chair is the full price, p, minus 25% of the original price.

1) To find 25% of the original price, multiply p (original price) by the decimal form of 25%, or 0.25. That means 25% off original price = 0.25p.

2) Now subtract 0.25p from the original price of the chairs to find the price of each (1) chair. p - 0.25p

Shylah is buying 4 chairs at that discounted price. That means you need to multiply the discounted price,  p - 0.25p, by 4. Shylah is paying 4(p-0.25p) total for the 4 chairs, which is answer choice B.

Since you can choose more than one choice, you can simplify 4(p-0.25p) by subtracting what is in the parathesis, then multiplying, following the order of operations:

4(p-0.25p)

= 4(0.75p)  

= 3p

That is answer choice A.

--------

Answer: Choices A and B, 3p and 4(p−0.25p).

Step-by-step explanation:

Choices A and B, 3p and 4(p−0.25p).

Answer:

[tex]\frac{f}{g}(x)=2x-1\\\\\frac{f}{g}(4)=7[/tex]

Step-by-step explanation:

[tex]\frac{f}{g}(x)=\dfrac{2x^2-5x+2}{x-2}=\dfrac{(x-2)(2x-1)}{(x-2)} =2x-1 \quad\text{x$\ne$2}\\\\\frac{f}{g}(4)=2\cdot 4-1=7 \qquad\text{fill in 4 for x and do the arithmetic}[/tex]

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{2x^2-5x+2}{x-2}\\\\\left(\dfrac{f}{g}\right)(4)=\dfrac{2\cdot 4^2-5\cdot 4+2}{4-2}=\dfrac{32-20+2}{2}=7[/tex]

Answer:

[tex]\large\boxed{a.\ -30}[/tex]

Step-by-step explanation:

[tex]\dfrac{y}{3}+8=-2\qquad\text{subtract 8 from both sides}\\\\\dfrac{y}{3}+8-8=-2-8\\\\\dfrac{y}{3}=-10\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{y}{3\!\!\!\!\diagup_1}=(3)(-10)\\\\y=-30[/tex]

No, there are polynomials that have real solutions but when combined would be possible to have no real solutions.

Answer:

No.

Step-by-step explanation:

No, one easy way to see it is with quadratic formulas. There exists quadratic polynomials with no real solutions, then if you add, subtract or multiply two polynomials and obtain a quadratic formula, possibly this polynomial won't have real solutions.

I am going to give one counterexample:

We have the two polynomials [tex]p(x) = x^2+2x+3[/tex] and [tex]q(x)= 2x^2+3x+4[/tex], then is we subtract q(x)-p(x) we obtain

[tex]2x^2+3x+4-(x^2+2x+3) = 2x^2+3x+4-x^2-2x-3 = x^2+x+1.[/tex]

The resulting polynomial is a quadratic polynomial of the form [tex]ax^2+bx+c[/tex] with a=1, b=1 and c=1. This polynomial has no real solutions, you can check it with the discriminating [tex]b^2-4ac = 1^2-4(1)(1) = 1-4 = -3.[/tex] As the discriminating is negative, the polynomial has no real solutions.

Answer:

Hi,

The answer is (-0.383,1) and (2,∞).

Step-by-step explanation:

See the attachment.

g(x) is a parabolic function, and the Image is always ≥ 0.

f(x) is a exponential function, and the Image is always ≥ 0.

At x = -0.383 , g(x) = 0.588 and f(x) = 0.588.

For x=(-0.383, 1), g(x) is greater than f(x).

At x = 1, g(x) = 1 and f(x) = 1.

For x=(1, 2), f(x) is greater than g(x).

At x= 2, g(x) = 16 and f(x) = 16

For x=(2,∞), g(x) is greater than f(x)

Answer:

the values of the non-integral roots of the polynomial equation are:

4.73 and 1.27.

Step-by-step explanation:

To find the roots of the polynomial equation, we need to factorize the equation:

x^4 − 4x^3 = 6x^2 − 12x ⇒ x^4 − 4x^3 -6x^2 +12x = 0

⇒ x(x+2)(x -3 + sqrt(3))(x -3 - sqrt(3))

Then, the non integral roots are:

x1 = 3 - sqrt(3) = 1.26 ≈ 1.27

x2 = 3 + sqrt(3) =  4.73

Then, the values of the non-integral roots of the polynomial equation are:

4.73 and 1.27

The approximate values of the non-integral roots of the polynomial equation are:

                     1.27 and 4.73

We are given an algebraic equation as:

[tex]x^4-4x^3=6x^2-12x[/tex]

i.e. it could be written as:

[tex]x^4-4x^3-6x^2+12x=0\\\\i.e.\\\\x(x^3-4x^2-6x+12)=0[/tex]

Since, we pulled out the like term i.e. "x" from each term.

Now we know that [tex]x=-2[/tex] is a root of the term:

[tex]x^3-4x^2-6x+12[/tex]

Hence, we split the term into factors as:

[tex]x^3-4x^2-6x+12=(x-2)(x^2-6x+6)[/tex]

Now, finally the equation could be given by:

[tex]x(x-2)(x^2-6x+6)=0[/tex]

Hence, we see that:

[tex]x=0,\ x-2=0\ and\ x^2-6x+6=0\\\\i.e.\\\\x=0,\ x=2\ and\ x^2-6x+6=0[/tex]

[tex]x=0\ and\ x=2[/tex] are integers roots.

Now, we find the roots with the help of quadratic equation:

[tex]x^2-6x+6=0[/tex]

( We know that the solution of the quadratic equation:

[tex]ax^2+bx+c=0[/tex] is given by:

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

Here we have:

[tex]a=1,\ b=-6\ and\ c=6[/tex]

Hence, the solution is:

[tex]x=\dfrac{-(-6)\pm \sqrt{(-b)^2-4\times 1\times 6}}{2\times 1}\\\\i.e.\\\\x=\dfrac{6\pm \sqrt{36-24}}{2}\\\\i.e.\\\\x=\dfrac{6\pm \sqrt{12}}{2}\\\\i.e.\\\\x=\dfrac{6}{2}\pm \dfrac{2\sqrt{3}}{2}\\\\i.e.\\\\x=3\pm 3\\\\i.e.\\\\x=3+\sqrt{3},\ x=3-\sqrt{3}[/tex]

Now, we put [tex]\sqrt{3}=1.732[/tex]

Hence, the approximate value of x is:

[tex]x=3+1.732,\ x=3-1.732\\\\i.e.\\\\x=4.732,\ x=1.268[/tex]

Answer:

7.61

Step-by-step explanation:

[tex]cos65=\frac{x}{18}\\x=18cos65\\x=7.61[/tex]

Note: I assumed that all angles were in degrees

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =87\\ s=14 \end{cases}\implies 14=\cfrac{\pi (87)r}{180} \\\\\\ 2520=87\pi r \implies \cfrac{2520}{87\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \left(\boxed{\cfrac{2520}{87~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} \right)\implies C = \cfrac{5040}{87} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill C\approx 57.93~\hfill[/tex]

Answer:  14

Step-by-step explanation:

f(x) = 3x + 2

To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y

x = 3y + 2

x - 2 = 3y

[tex]\dfrac{x-2}{3}=y[/tex]

[tex]\implies f^{-1}(x)=\dfrac{x-2}{3}[/tex]

[tex]\implies f^{-1}(14)=\dfrac{14-2}{3}[/tex]

[tex]\implies f^{-1}(14)=\dfrac{12}{3}[/tex]

[tex]\implies f^{-1}(14)=4[/tex]

f(f⁻¹(14)) = f(4)

              f(4) = 3(4) + 2

                     = 12 + 2

                     = 14

NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14

Answer:

The confidence interval is between 52.2% and 55.8%

Step-by-step explanation:

Since the study showed that 54% of the people involved in the study had experienced flu-like symptoms, and the margin of error is 1.8%, which is relatively small margin of error, we can easily come to the confidence interval. Since the margin of error goes both ways, above and below the official percentage, in order to get to the confidence interval we need to deduct the margin of error from the percentage, and also, separately, to add the margin of error to the percentage.

54 - 1.8 = 52.2

So the low border of the confidence level is 52.2%.

54 + 1.8 = 55.8

So the high border of the confidence level is 55.8%.

Answer:

the interval  is between 52.8% and 55.8%

Step-by-step explanation:

Answer:

Explanation:

The function must meet the rule that the pay starts at $20 and it increases each hour by 4%.

A table will help you to visualize the rule or pattern that defines the function:

x (# hours)        pay ($) = p(x)

0                        20 . . . . . . . .  [starting pay]

1                         20 × 1.04 . . . [ increase of 4%]

2                        20 × 1.04² . . . [increase of 4% over the previous pay]

x                        20 × 1.04ˣ

Hence, the function is:     [tex]p(x)=20(1.04)^x[/tex]

The range is the set of possible outputs of the function. To find the range, take into account that this is a growing exponential function, meaning that the least output is the starting point, and from there the output will incrase.

The choices name x this output. Hence, the starting point is x = 20 and the upper bound is when the number of hours is 8: 20(1.04)⁸ = 27.37.

Then the range is from 20 to 27.37 (dollars), which is represented by 20 ≤ x ≤ 27.37 (option D from the choices).

Answer:

its D for shure

Step-by-step explanation:

Answer:

Blank 1 is -3

Blank 2 is 183

Step-by-step explanation:

Let r be common ratio

[tex]r = \frac{ - 9}{3} \\ r = - 3[/tex]

Sum of first 5 terms

[tex]s = \frac{a( {r}^{n} - 1)}{r - 1} \\ s = \frac{ 3( {( - 3)}^{5} - 1) }{ - 3 - 1} \\ s = 183[/tex]

Answer:

1) Second option: -3

2) Second option: 183

Step-by-step explanation:

1) You can use any two consecutive terms to find the common ratio. This is given by:

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

You can choose these consecutive terms:

[tex]a_n=-9\\a_{n-1}=3[/tex]

Then the common ratio "r" is:

[tex]r=\frac{-9}{3}=-3[/tex]

2) The sum of the first "n" terms can be found with this formula:

[tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex]

Since ther first term is 3 and you need to find the sum of the first 5 terms, then:

[tex]a_1=3\\n=5[/tex]

Substituting into  [tex]Sn=\frac{a_1(r^n-1)}{r-1}[/tex], you get:

 [tex]S_{(5)}=\frac{3((-3)^5-1)}{-3-1}=183[/tex]

Answer:

1 litre = 1000 millilitres (ml)

35 litres = 35×1000 => 35000 ml

So your fish tank holds 35000 ml of water

Answer:

Third choice from the top is the one you want

Step-by-step explanation:

This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out.  For example:

[tex]\sqrt[6]{x^6} =x[/tex] and another example:

[tex]\sqrt[12]{2^{12}}=2[/tex]

Let's take this step by step.  First we will rewrite both the numerator and the denominator in rational exponential equivalencies:

[tex]\frac{\sqrt[4]{6} }{\sqrt[3]{2} }=\frac{6^{\frac{1}{4} }}{2^{\frac{1}{3} }}[/tex]

In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number.  The LCM of 3 and 4 is 12.  So we rewrite as

[tex]\frac{6^{\frac{3}{12} }}{2^{\frac{4}{12} }}[/tex]

Now we will put it back into radical form so we can rationalize the denominator:

[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }[/tex]

In order to rationalize the denominator, we need the power on the 2 to be a 12.  Right now it's a 4, so we are "missing" 8.  The rule for multiplying like bases is that you add the exponents.  Therefore,

[tex]2^4*2^8=2^{12}[/tex]

We will rationalize by multiplying in a unit multiplier equal to 1 in the form of

[tex]\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]

That looks like this:

[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }*\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]

This simplifies down to

[tex]\frac{\sqrt[12]{216*256} }{\sqrt[12]{2^{12}} }[/tex]

Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2!  Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:

[tex]\frac{\sqrt[12]{55296} }{2}[/tex]

Phew!!!

The measure of angle MNP also means the measure of angle N.

N = (1/2)(arc MP)

N = (1/2)(180°)

N = 90°

The measure of angle MNP is 90°.

The measure of ∠MNP is 90.

An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

As, the degree of the arc of a circle is usually 2 times the measure of the corresponding angle.

The measure of angle MNP

MNP = (1/2)(arc MP)

MNP = (1/2)(180°)

MNP = 90°

Hence, the measure of angle MNP is 90°.

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Answer:

  There are none.

Step-by-step explanation:

3 is a divisor of the modulus, so the product mod 6 will be either 3 or 0.

In the modular arithmetic problem 3 x ? = 1 (mod 6), the correct positive number replacement for the question mark is 3.

The problem given is a modular arithmetic equation: 3 x ? = 1 (mod 6). To solve for the question mark (?), we need to find a number that when multiplied by 3 and divided by 6, leaves a remainder of 1. Since we are working with mod 6, the potential replacements for the question mark can only be positive numbers less than 6.

The steps to find the solution are as follows:

Try each positive number less than 6 to see which, when multiplied by 3, yields a remainder of 1 when divided by 6.

By testing, we find that 3 x 5 = 15, and 15 mod 6 = 3 x 6 + 1 (15 = 2*6 + 3).

Since we need a remainder of 1, and not 3, we should keep looking.

Next, 3 x 3 = 9, and 9 mod 6 = 1 since 9 = 1*6 + 3 = 3 x 3.

Thus, the number that satisfies the equation is 3 since it makes the modular equation true: 3 x 3 = 9, and 9 mod 6 = 3 x 6 + 3, which gives us a remainder of 1.

The correct positive number replacement for the question mark making the statement true is 3.

Answer:

B.) the mean lies to the left of the median for a positively skewed distribution.

Step-by-step explanation:

Answer:

  $1034.75

Step-by-step explanation:

Mike's net pay is ...

  base pay + commission - deductions

  = $500 + 5%(23750 -10000) -152.75

  = 347.25 + 0.05×13750

  = $1034.75

Answer:

$1034.75

Step-by-step explanation:

Here we are given that the base salary of Mike is $500. He is also rewarded with some commission depending on sales. Hence we can bifurcate his gross pay as

Gross Pay = Base Pay + Commission

Commission = 5% of Sales over $10000

                     = 5% of (23750-10000)

                     = 5% of 13750

                     = 0.05*13750

                     = 687.50

Hence Gross pay = 500 + 687.50

                              = 1187.50

Also given that he has some deductions also i.e. $152.75 .

Therefor Net pay = Gross pay - Deductions

                             = 1187.50-152.75

                             = 1034.75

Hence Net Pay = $1034.75

Answer:

a(n) = -3 - 2(n-1)

Step-by-step explanation:

The most general formula for the nth term of an arithmetic sequence (such as this sequence is) is

a(n) = a(1) + c(n-1), where c is the common difference.

Here a(1) = -3 and c = -2.

Thus,

a(n) = -3 - 2(n-1).

Answer:

C. :)

Step-by-step explanation:

Move all terms not containing  

y

y

to the right side of the equation.

−

5

y

=

55

-5y=55

Divide each term by  

−

5

-5

and simplify.

y

=

−

11

y=-11

Answer: the answer is - A. -11

Step-by-step explanation:

Answer:

  Subtract 14 from both sides of the equation.

Step-by-step explanation:

The subtraction property of equality tells you the equal sign only remains valid if you subtract the same value from both sides of the equation.

Here, we want the 14 on the left side to be replaced by 0. Thus we must add its opposite. Since we must do the same thing to both sides of the equation, we must subtract 14 from both sides of the equation.

Answer:

Last option:  Subtract 14 from both sides of the equation.

Step-by-step explanation:

To solve the equation [tex]x+14=21[/tex] you must solve for the variable "x".

To calculate the value of the variable "x" it is important to remember the Subtraction property of equality. This states that:

[tex]If\ a=b\ then\ a-c=b-c[/tex]

Therefore, applying this property, you should subtract 14 from both sides of the equation to find the value of the variable "x". Then:

[tex]x+14-(14)=21-(14)\\\\x=7[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\[/tex]

[tex]\bf \left( \cfrac{20x^5y^2}{5x^{-3}y^7} \right)^{-3}\implies \left( \cfrac{5x^{-3}y^7}{20x^5y^2} \right)^3\implies \left( \cfrac{5^3x^{-3\cdot 3}y^{7\cdot 3}}{20^3x^{5\cdot 3}y^{2\cdot 3}} \right)\implies \cfrac{5^3}{20^3}\cdot \cfrac{x^{-9}y^{21}}{x^{15}y^6} \\\\\\ \cfrac{1}{64}\cdot \cfrac{y^{21}\cdot y^{-6}}{x^{15}\cdot x^9}\implies \cfrac{1}{64}\cdot \cfrac{y^{21-6}}{x^{15+9}}\implies \cfrac{y^{15}}{64x^{24}}[/tex]

Answer:

Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.

Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.

Step-by-step explanation:

Final answer:

Ethan pays a total of 1.0355x dollars at the register for an item with an original price of x dollars, after applying a 5% discount and adding a 9% sales tax to the discounted price.

Explanation:

To calculate the total amount Ethan paid at the register, we need to take into account both the discount and the tax applied to the item's original price. First, we calculate the discounted price by subtracting the 5% off. Then, we add a 9% sales tax to that discounted price.

The original price is x dollars. The discount of 5% is 0.05x, so the discounted price is x - 0.05x, which simplifies to 0.95x. Next, we need to calculate the sales tax on the discounted price. The 9% tax on the discounted price is 0.09 * 0.95x, which is 0.0855x. Finally, to find the total amount paid, we add the sales tax to the discounted price:

Total Amount Paid = (0.95x) + (0.09 * 0.95x) = 0.95x + 0.0855x = 1.0355x

Answer:

  $173.25

Step-by-step explanation:

His annual contribution is ...

  0.07 × $29,700 = $2079

If 1/12 of that is contributed each month, the monthly contribution is ...

  $2079/12 = $173.25

Answer:

Step-by-step explanation:

The distance between two points on a number line is the difference between the rightmost point and the leftmost point.

1. 11 -(-6) = 11+6 = 17

2. 8 -(-15) = 8+15 = 23

3. -3 -(-20) = -3+20 = 17

4. 16 -7 = 9

For this case we have that if Molly spent all the spool ribbon with 12 people, then "r" would be given by the product of 12 for the amount of ribbon that each person received, that is:

[tex]r = 12 * 3\\r = 36 \ft[/tex]

Thus, the spool initially had 36 feet of ribbon.

If Molly also keeps 3 feet of ribbon, then the value of "r" is given by:

[tex]r = 13 * 3\\r = 39 \ ft[/tex]

In this case, the ribbon spool initially had 39 feet of ribbon.

Answer:

[tex]r = 36 \ ft[/tex]shared between 12 people

[tex]r = 39 \ ft[/tex]shared between 12 people and Molly

Answer:

It is C. aka 3r = 12.

Step-by-step explanation:

Answer:

Up

Step-by-step explanation:

Here the easy rules to remember the orientation of the parabolas are

a) If x is squared it opens up or down. And its coefficient of {[tex]x^{2}[tex] is negative it opens down.

b) If y is squared it opens side ways right or left. It its coefficient of [tex]y^{2}[/tex]

Hence in our equation of parabola

[tex]y = x^ 2-4[/tex]

x is squared and its coefficient is positive , hence it opens up towards positive y axis.