A point that is exterior to an angle is found on the acute side of the angle. true of false?​

[tex]\bf{Swap \ sides \ 8x+2(x+6)=-28 }[/tex]

[tex]\bf{Expand \ 2(x+6): \ \ \ \ 2x+12}[/tex]

[tex]\mathrm{Set \ the \ variables \ using: \ \ \ a(b+c)=ab+ac}[/tex]

[tex]a=2,\:b=x,\:c=6[/tex]

[tex]=2x+2\cdot \:6[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:6=12[/tex]

[tex]=2x+12[/tex]

[tex]8x+2x+12=-28[/tex]

[tex]\mathrm{Add\:similar\:elements:\:8x+2x=10x}[/tex]

[tex]10x+12=-28[/tex]

[tex]\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}[/tex]

[tex]10x+12-12=-28-12[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]10x=-40[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}10[/tex]

[tex]\dfrac{10x}{10}=\dfrac{-40}{10}[/tex]

[tex]\mathrm{Simplify \ \dfrac{10x}{10}: \ \ x }[/tex]

[tex]\mathrm{Divide:}\:\dfrac{10}{10}=1[/tex]

[tex]=x[/tex]

[tex]\mathrm{Simplify \ \dfrac{-40}{10}: \ \ -4 }[/tex]

[tex]\rm{Apply \ the \ properties \ of \ fractions \ to \ fractions: \ \ \dfrac{-a}{b}=-\drac{a}{b}}[/tex]

[tex]=-\dfrac{40}{10}[/tex]

[tex]\rm{split: \ \dfrac{40}{10}=4 }[/tex]

[tex]\bf{x=-4 \ \ \to \ \ \ Answer }[/tex]

Answer:

Option c 4

Step-by-step explanation:

The triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.

ΔABC is similar to ΔDEF  only if the ratio of two sides of ΔABC and the corresponding two sides of ΔDEF is equal and the angle included on both sides are congruent.

Suppose the two sides of ΔABC are AB and BC, and that of DEF is DE and EF, then for SAS similarity, we need

and

∠ABC = ∠DEF

In triangles ΔAED and ΔCGF,

AE = CF

AD = CG

∠E = ∠G = 90°

Then the triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.

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Answer:

A parallel line is something that is equivalent on the other end. This mean if you cut a shape, a square for example, in half,the sides will be of equal length.

Answer:

a parallel line is diagonal

Answer:

The percentage of people enjoy New years Eve only = 3%

Step-by-step explanation:

The data indicates, The percentage of people enjoy New years Eve = 28%

The percentage of people enjoy New years Eve and Memorial Day = 12%

The percentage of people enjoy New years Eve and Forth of July = 18%

The percentage of people enjoy Enjoy all the three = 5%

The percentage of people enjoy New years Eve only

= The percentage of people enjoy New years Eve

   - The percentage of people enjoy New years Eve and Memorial Day

   - The percentage of people enjoy New years Eve and Forth of July

   + The percentage of people enjoy Enjoy all the three

= 28% - 12% - 18% + 5%

= 3%

Answer:

[tex]A(\triangle)=30\: units^2[/tex]

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

your answer is *dun dun dun*

30 + 40% = 42

I need some more text apparently so that drumroll at the top and this will hopefully suffice

The lower bound for the profit is $2425.

When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0

The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434  

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Step-by-step explanation:

in a management information system, the quality of information is determined by its usefulness to users, and its usefulness determines the success of the information system.

Answer:

83

Step-by-step explanation:

41 plus 36 plus 36 is 83 is the answer for me

Answer:

3.31662479

Step-by-step explanation:

3.31662479

In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.

The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year.

To make a graph, we need to establish which is the independent and dependent variables.

The independent variable (x-axis) is time in years and the dependent variable (y-axis) is the mass of tritium in grams.

At year 1,

726(1 - 0.05626) = 685.16 g

At year 2,

685.16 (1 - 0.05626) = 646.61 g

At year 3,

646.61 g (1 - 0.05626) = 610.23 g

The final graph is shown in the attached figure.

In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.

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Answer:

0.0369

Step-by-step explanation:

normalcdf (1220,1320,900,200) is 0.0369

Answer:

[tex]x=\frac{3}{4},\:x=-1[/tex]

Keys:

For this problem, you need the quadratic formula(listed below).

When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.

Step-by-step explanation:

solving for x₁ and x₂

[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]

[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]

[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]

solve for x₁

[tex]\frac{-1+7}{2\cdot \:4}[/tex]

[tex]=\frac{6}{2\cdot \:4}[/tex]

[tex]=\frac{6}{8}[/tex]

[tex]= \frac{6\div2}{8\div2}[/tex]

[tex]=\frac{3}{4}[/tex]

solve for x₂

[tex]\frac{-1-7}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{8}[/tex]

[tex]=-\frac{8}{8}[/tex]

[tex]=-1[/tex]

Hope this helps!

Answer:

y = 6x + [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

I think take this with a grain of salt

The equation that the clerk can use to calculate their total bill is t + g.

From the information given, Yasuda family bought a toy that cost t dollars and a game that cost g dollars.

The equation to calculate their total bills will be:

= t + g

where,

t = cost of toy

g = cost of game.

In this case, the equation that the clerk can use to calculate their total bill is t + g .

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Answer:

4pi + 8 km

Step-by-step explanation:

the circumference of teh circle is d*pi = 8pi. since this is a semicircle the circumference is 4pi. then the perimeter is 4pi + 8

Answer:

[tex]k > 3~~~\text{or}~~ k < -5[/tex]

Step-by-step explanation:

[tex]~~~~~|3k+3| > 12\\\\\implies 3k+3 < -12~~~~~~\text{or}~~~~~~~~~~3k+3 > 12\\\\\implies 3k < -12-3~~~~~~\text{or}~~~~~~~~~~3k > 12-3\\\\\implies 3k < -15~~~~~~~~~~~\text{or}~~~~~~~~~~3k > 9\\\\\implies k < -\dfrac{15}3~~~~~~~~~~~~\text{or}~~~~~~~~~~k > \dfrac 93\\\\\implies k < -5~~~~~~~~~~~~~~\text{or}~~~~~~~~~~k > 3[/tex]

Answer:

Step-by-step explanation:

The volume of a cube is given by the formula :

a³ (where a is the side length )

So now we have to cube these lengths :

Part A :

(3x²y)³ =

(3x²y)(3x²y)(3x²y) =

(9x^4y²)(3x²y) =

27x^6y³ (This is now fully simplified so our final answer for a)

Part B:  

(5y²)³ =

(5y²)(5y²)(5y²) =

(25y^4)(5y²) =

125y^6 (This is now fully simplified so our final answer for b)

Hope this helped and have a good day

Answer:

6.28 ft

Step-by-step explanation:

using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer

The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Here, Horizontal shift (also called phase shift):

Left shift by c units: y = f(x + c)

Right shift by c units: y = f(x - c)

For this case, we're specified that:

Original function: y = x³

Transformation: horizontal stretch by a factor of 1/5

Assuming the horizontal axis is having input variable x, and vertical axis having output variable y = x³, and the fact that a function y = f(x) if is horizontally stretched by a factor k, becomes y = f(x/k) , we have:

          y = f(x)

          y = x³

           y = f (5x)

           y = (5x)³

Thus, The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.

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Answer: It's D

Step-by-step explanation:

y = [-1/5x]^3 on edge

The solution to the expression (-x³ + x² - x + 1) / (x - 1) using long division is (x² - 2x + 3) + (4 / (-x - 1))

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

Given the expression:

(-x³ + x² - x + 1) / (x - 1)

Using long division:

= x² + (2x² - x + 1)/(-x - 1)

= x² - 2x + (-3x + 1)/(-x - 1)

= (x² - 2x + 3) + (4 / (-x - 1))

The solution to the expression (-x³ + x² - x + 1) / (x - 1) using long division is (x² - 2x + 3) + (4 / (-x - 1))

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =\frac{4\pi }{15} \end{cases}\implies A=\cfrac{ ~~ \frac{4\pi }{15}(7)^2}{2}\implies A=\cfrac{98\pi }{15}[/tex]

Answer:

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Answer:

The IQR of the given distribution is

Step-by-step explanation:

The given distribution has the five-number

28, 34, 43, 59, 62

Divide these numbers in two equal parts.

(28, 34), 43,( 59, 62)

Now divide each parenthesis in two equal parts.

(28), (34), 43,( 59), (62)

It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.

The interquartile range (IQR) of this distribution is

Therefore the IQR of the given distribution is 29.5.

The solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]

The equation is given as:

-6 + 3x - 9x^2 = -16

Add 16 to both sides

10 + 3x - 9x^2 = 0

Rewrite as:

9x^2 - 3x - 10 = 0

Solve for x using the quadratic formula

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

So, we have:

[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4 * 9 * -10}}{2 * 9}[/tex]

Evaluate

[tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]

Hence, the solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]

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By the remainder theorem, the remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x - c[/tex] is exactly [tex]p(c)[/tex].

Then the remainder upon dividing [tex]f(x)[/tex] by [tex]x - 4[/tex] is

[tex]f(4) = 3\times4^3 + 5\times4^2 + 5 = \boxed{277}[/tex]

Answer:

So, cows heart best is faster than horse.

Step-by-step explanation:

Time and heartbeats are in direct proportion.

   p = kx

Where p is the beats per minute and x represents time in minutes

Now, to find the value of k, substitute p = 152 and x = 4

152 = 4k

  k = 152/4

  k = 38

[tex]\sf \boxed{p = 38x}[/tex]

Cow:  y = 65x

So, cows heart best is faster than horse

The graph that could represent the motion of the apple is graph B.

A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct

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