It is not possible to prove one pair of triangles congruent and then use their congruent corresponding parts to prove another pair congruent. True or false

Answer:

132 degrees.

Step-by-step explanation:

SR and PQ are both 48 degrees. A circle is 360 degrees.

360-96 because 48+48 is 96, is 264. PS and QR are also the same so 264/2 is 132.

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:

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]

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

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:

x = 2

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction,

and is the order in which you follow for order of operation questions.

First, subtract 5 from both sides.

2x + 5 (-5) = 9 (-5)

2x = 9 - 5

2x = 4

Isolate the x, Divide 2 from both sides:

(2x)/2 = (4)/2

x = 4/2

x = 2

x = 2 is your answer.

~

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:  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

Given.

-x + 3.9

Plug in.

-7.2 + 3.9 = -3.3

Answer.

-3.3

Answer:

11.1

Step-by-step explanation:

−(−7.2)+3.9

=7.2+3.9

=11.1

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:

[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]

The volume of the rectangular prism is length x width x height:

Volume = 1 1/2 x 1/2 x 3/4 = 9/16 cubic units.

The volume of cube is length^3 = 1/4^3 = 1/64

Divide the volume of the rectangular prism by the volume of the cube:

Number of cubes = 9/16 / 1/64 = 36

The answer is 36

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:

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!!!

Answer:

[tex]\dfrac{72}{19}[/tex]

Step-by-step explanation:

Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula

[tex]AX^2=\dfrac{AB\cdot AC}{(AB+AC)^2}\cdot ((AB+AC)^2-BC^2)[/tex]

Hence,

[tex]AX^2=\dfrac{9\cdot 10}{(9+10)^2}\cdot ((9+10)^2-17^2)=\dfrac{90}{361}\cdot (361-289)=\dfrac{90}{361}\cdot 72=\dfrac{6480}{361}[/tex]

By the angle bisector theorem,

[tex]\dfrac{AB}{AC}=\dfrac{BX}{XC}[/tex]

So,

[tex]\dfrac{9}{10}=\dfrac{BX}{17-BX}\Rightarrow 153-9BX=10BX\\ \\19BX=153\\ \\BX=\dfrac{153}{19}[/tex]

and

[tex]XC=17-\dfrac{153}{19}=\dfrac{170}{19}[/tex]

By the Pythagorean theorem for the right triangles AXY and CXY:

[tex]AX^2=AY^2+XY^2\\ \\XC^2=XY^2+CY^2[/tex]

Thus,

[tex]\dfrac{6480}{361}=XY^2+AY^2\\ \\\left(\dfrac{170}{19}\right)^2=XY^2+(10-AY)^2[/tex]

Subtract from the second equation the first one:

[tex]\dfrac{28900}{361}-\dfrac{6480}{361}=(10-AY)^2-AY^2\\ \\\dfrac{22420}{361}=100-20AY+AY^2-AY^2\\ \\\dfrac{1180}{19}=100-20AY\\ \\20AY=100-\dfrac{1180}{19}=\dfrac{1900-1180}{19}=\dfrac{720}{19}\\ \\AY=\dfrac{36}{19}[/tex]

Hence,

[tex]XY^2=\dfrac{6480}{361}-\left(\dfrac{36}{19}\right)^2=\dfrac{6480-1296}{361}=\dfrac{5184}{361}\\ \\XY=\dfrac{72}{19}[/tex]

Answer:

  $2502.60

Step-by-step explanation:

The formula for the amount of an annuity due is ...

  A = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the monthly payment (100), r is the annual interest rate (.04), n is the number of compoundings per year (12), and t is the number of years (2). Given these numbers, the formula evaluates to ...

  A = $100(1.00333333)(1.00333333^24 -1)/0.00333333

  = $100(301)(0.08314296)

  = $2502.60

_____

This value is confirmed by a financial calculator. The given answer choices all appear to be incorrect. The closest one corresponds to an annual interest rate (APR) of 4.286%, not 4%.

Answer:

D. 72 cm²

Step-by-step explanation:

The area of a square is given by ;

Area= l² where l = length

Given that the diagonal is 12 cm, let assume length of the square to be l

Apply the Pythagorean relationship where a=b=l

l² + l² = 12²

2 l² = 144

l²= 144/2

l²= 72

l =√72 =8.485 cm

⇒length of the square= l= 8.485 cm

⇒Area of the square= l² = 8.485² = 72 cm²

Answer:

36 cm2.

Step-by-step explanation:

The area of square A is 324 cm2. Since the dimensions of square A are three times larger than the dimensions of square B, the scale factor is 3.

To find the area of square B, first square the scale factor, 3.

3 squired =9

Next, divide the area of square A by 9.

324÷ cm2 ÷ 9 =36 cm2

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

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:

  $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

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:

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

Answer: yes

Step-by-step explanation: Wall would be 60 feet wide. 60 / 5 = 12.

Answer:

Yes

Step-by-step explanation:

Given :

1/2 in = 1 foot

re-written as : 1 in = 2 feet

THe blueprint is drawn to be 30 inches long

this is equivalent to 30 in x 2 feet/in = 60 feet long

With a minimum width of 5 feet per stall,

the number of stalls in 60 feet = 60 feet / 5 feet = 12 stalls

Hence there will be enough room for 12 stalls.

Answer:

1 litre = 1000 millilitres (ml)

35 litres = 35×1000 => 35000 ml

So your fish tank holds 35000 ml of water

Answer:

interval notation: [-5,infinity)

or answer X=> -5

Step-by-step explanation:

For this case we must find the domain of the following function:

[tex]f (x) = \sqrt {x + 5}[/tex]

By definition, the domain of a function is given by all the values for which the function is defined.

The given function stops being defined when the argument of the root is negative. Thus, the domain is given by all values of "x" greater than or equal to -5.

Answer:

Domain: [tex]x\geq-5[/tex]

Answer:

[tex]x =7\sqrt{3}[/tex]

Step-by-step explanation:

By definition, the tangent of a z-angle is defined as

[tex]tan(z) =\frac{opposite}{adjacent}[/tex]

For this case

[tex]opposite = 7[/tex]

[tex]adjacent = x[/tex]

[tex]z=30\°[/tex]

So

[tex]tan(30) =\frac{7}{x}[/tex]

[tex]x =\frac{7}{tan(30)}[/tex]

[tex]x =7\sqrt{3}[/tex]

Answer:

7√3 = x

Step-by-step explanation:

Arbitrarily choose to focus on the 30 degree angle.  Then the side opposite this angle is 7 and the side adjacent to it is x.

tan 30 degrees = (opp side) / (adj side), or (1√3) = 7 / x.

Inverting this equation, we get √3 = x/7.

Multiplying both sides by 7 results in 7√3 = x

Answer:

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

Step-by-step explanation:

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:

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.

Answer:

Step-by-step explanation:

As with any equation involving fractions, you can multiply the equation by the least common denominator to eliminate fractions. Then solve in the usual way.

c) 1/a +b = c

  1 +ab = ac . . . . multiply by a

  1 = ac -ab . . . . subtract ab

  1 = a(c -b) . . . . . factor out a

  1/(c -b) = a . . . . divide by the coefficient of a

__

d) (a-b)/(b-a) = 1

  a -b = b -a . . . . . multiply by b-a

 2a = 2b . . . . . . . . add a+b

  a = b . . . . . . . . . . divide by the coefficient of a

Please be aware that this makes the original equation become 0/0 = 1. This is why a=b is not an allowed condition for this equation. As written, it reduces to -1 = 1, which is false. One could say there is no solution.

__

f) bc +ac = ab . . . . . multiply by abc

  bc = ab -ac . . . . . . subtract ac

  bc = a(b -c) . . . . . . factor out a

  bc/(b -c) = a . . . . . . divide by the coefficient of a