68. A hexagon has two sides each of length 3x inches. It has three sides each of length 2x inches. The sixth side has a length of 15 inches. If the perimeter of the hexagon is 135 inches, what is the value of x?


E.4
F.5
G. l0
H. 15

Answer:

Step-by-step explanation:

Hello,

Question 15

We can search x such that:

   [tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]

There is 1 solution.

Question 16

Again, we search x such that:

  [tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]8cos^4}x = (3 + 4cos2x + cos4x)[/tex]

Step-by-step explanation:

Using the power reduction identity, we have that:

[tex]cos^{2}x = \frac{1}{2}(1 + cos2x)\\ \\cos^{4}x = (cos^{2}x)^2 = (\frac{1}{2}(1 + cos2x))^2\\\\cos^{4}x = \frac{1}{4} (1 + 2cos2x + cos^{2}2x)\\[/tex]

From the first line:

[tex]cos^{2}2x = \frac{1}{2}(1 + cos4x)[/tex]

Therefore:

[tex]cos^{4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2}(1 + cos4x))\\\\cos^4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2} + \frac{1}{2} cos4x)\\\\cos^4}x = \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\=> 8cos^4}x = 8 * \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = 2 * (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = (3 + 4cos2x + cos4x)[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex] c = 15.5 [/tex]

Step-by-step explanation:

Using the Law of Cosines, c² = a² + b² - 2ab*cos(C), let's find c.

Where,

a = 15 ft

b = 20 ft

C = 50°

Thus:

[tex] c^2 = 15^2 + 20^2 - 2*15*20*cos(50) [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 385.74 [/tex]

[tex] c^2 = 239.26 [/tex]

[tex] c = \sqrt{239.26} [/tex]

[tex] c = 15.5 [/tex] (nearest tenth)

Answer:

c sorry gotta get points.

Step-by-step explanation:

Answer: y-2=1/2(x-(-7)) or y-2=1/2(x+7)

Step-by-step explanation:

The point-slope formula is y-y₁=m(x-x₁). Since we are given the point and the slope, we can directly plug them into where it is appropriate. The slope is 1/2. Slope is represented by m. We would plug in 1/2 into m. The point is (x₁,y₁). That format matches (-7,2).

y-2=1/2(x-(-7))

y-2=1/2(x+7)

Answer:

D.

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

Given : Total number of coins tossed = 10

Possible outcomes to toss a coin = Head or tail

Number of possible outcomes = [tex]2^{10}=1024[/tex]

Number of ways of obtaining exactly 1 heads = [tex]{10}C_1=\dfrac{10!}{1!9!}[/tex]     [using combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] ]

=10

Hence, the numbers of ways of obtaining exactly 1 heads= 10

She can either have 24 people since there are more slices of pizza there will be extras

Answer:

C. 9

Step-by-step explanation:

To find the number we add to complete the square, we do (b/2)², or take b (which is 6), divide by 2 (which gives us 3), then square the result (which gives us 9):

6/2 = 3

3² = 9

Answer: 9

Step-by-step explanation: To complete the square, we need a number to create a perfect square trinomial on the left side of the equation.

So the question is, what is that number?

Well it comes from a formula.

The number that we will need to complete the square will always

come from half the coefficient of the middle term squared.

In this case, that's half of 6 which is 3, squared, which is 9.

So we add 9 to both sides of the equation.

This will now allow the left side of the equation to factor.

ok its 45.15% trust me

Answer:

Step-by-step explanation:

This curve alone does  not give exact percentages with the exception of P(z=0) = .50 or 50%

A Pictorial where 'some' of the % have been added for helps more...  

However, most often one needs to use a table, calculator, or an Excel function ect to find exact Percentage,

P(x > 4000) = P(z = 0) =  .50  or 50 % |using above pictorial

Using Calculator etc:  Here, am using the Excel NORMSDIST function to find the Percentages:

P(z=3/5 - z=-3/5) =  .7257 - .2742 =.4515 or 45.15%

Answer:

[tex]\sqrt[4]{xy^3}[/tex].

Step-by-step explanation:

[tex]\sqrt[8]{x^2y^6}[/tex]

= [tex]x^{\frac{2}{8} } y^{\frac{6}{8}}[/tex]

= [tex]x^{\frac{1}{4} } y^{\frac{3}{4}}[/tex]

= [tex]\sqrt[4]{xy^3}[/tex].

Hope this helps!

Answer:

-1 is not in the domain of (f o g)(x)

Step-by-step explanation:

f(x) = sqrt(x - 9)

g(x) = -6x - 3

(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)

(f o g)(x) = sqrt(-6x - 3 - 9)

(f o g)(x) = sqrt(-6x - 12)

Let x = -1:

(f o g)(-1) = sqrt(-6(-1) - 12)

(f o g)(-1) = sqrt(6 - 12)

(f o g)(-1) = sqrt(-6)

Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).

Hi there! Thanks for your questions ;)

The answers are quite easily, go through the steps below so that you can catch it up yourself!!

= [tex]\rm{sin (x) = \dfrac{9}{20}}[/tex]

= [tex]\rm{0.45}[/tex]

= [tex]\rm{x = arcsin(0.45)}[/tex]

= [tex]\rm{h = 20 \times cos(x)}[/tex]

= [tex]\rm{20 \times cos(26.74)}[/tex]

Hope it is helpful!

the bag is 200g

total weight with oranges is 1400g

deduct the bags weight from total weight

1400 - 200

1200g

this is the weight of the three oranges

so each orange would be

1200 ÷ 3

400g

Answer:

A(t) = 41,47 in²

Step-by-step explanation:

Let´s call "x" the cut of point to get to pieces of wire, we make a square from x and the regular octagon will be shaped with 24-x

Then Area of the square  A(s)  =  x²

Area of the octagon is  A(o)  = 1/2*p*length of apothem (d)

p = ( 24 - x )

length of apothem (d) :

The side of the octagon is equal to ( 24 - x ) / 8 half the side is  

( 24  -  x ) / 16

tan α  = ( 24- x ) 16 / d      since ∡s in octagon are 360 / 8  = 45°

α ( ∡ between apothem and one of the interiors ∡ of the octagon )half of 45 is  α = 22,5°  

tanα = 0,41

d = (24 - x ) / 16*0,41        d = ( 24 - x ) / 6,56

Then

A(t) = A(s) + A(o)

A(t) =  x²  + (1/2)* ( 24 - x ) ( 24 - x ) / 6,56

Note  A(t) = A(x)

A(x) =  x²  + (1/2) * (24 - x )²/ 6,56

A(x) = x² + ( 1/ 2*6,56) * ( (24)² -48*x + x² )

Taking derivatives on both sides of the equation

A´(x) = 2*x + ( 1/13,12)* ( - 48 + 2x )

A´(x) = 2*x - 48/ 13,12 + 2*x

A´(x) = 4*x - 3,66

A´(x) = 0     4x = 3,66        x  = 0,91 in    and  d =( 24 - x ) / 6,56

d = ( 24 - 0,91 ) / 6,56        d = 3,52

Then  A(s) = (0,91)²      A(s) = 0,83 in²

A(o) = 1/2 * ( 24 - 0,91 )* 3,52

A(o) = 40,63 in²

A(t) = 40,63 + 0,83

A(t) = 41,47 in²

Answer:

Hey there!

The perimeter can be expressed as 140+140+68[tex]\pi[/tex]

This is equal to 493.52 m

Hope this helps :)

Answer:

[tex] A = 50.7 [/tex] (to nearest tenth)

Step-by-step explanation:

Use the Law of Cosines to find the value of angle A as follows:

[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]

Where,

a = 7 in

b = 5 in

c = 9 in

Plug in the values into the formula

[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]

[tex] cos(A) = \frac{57}{90} [/tex]

[tex] cos(A) = 0.6333 [/tex]

[tex] A = cos^{-1}(0.6333) [/tex]

[tex] A = 50.7 [/tex] (to nearest tenth)

Answer:

(1.5, -13.5)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Simply plug in our coordinates into the formula:

x = (17 - 14)/2

x = 3/2

y = (-11 - 16)/2

y = -27/2

Answer:

(-1.5, -13.5)

Step-by-step explanation:

To find the x coordinate of the  midpoint, add the x coordinates and divide by 2

( 17+-14)/2 = 3/2 =1.5

To find the y coordinate of the  midpoint, add the x coordinates and divide by 2

( -11+-16)/2 = -27/2= - 13.5

Answer:

Movies: x gig

pictures: x/2 gig

music:  10 - x - x/2 = 10 - (3/2)x

The amount of gigabytes of music stored on the computer is:

[tex]y = 5 - x[/tex]

In which x is the amount stored in movies.

We solve this question representing the amount of music as a variable, that I will call y.

The total amount of data is 10 gigabytes.

Division of the 10 gigabytes:

Half in pictures, that is, 10/2 = 5 gigabytes.

x are movies.

The rest, y, are music.

Thus, since the sum of this all is 10, we have that:

[tex]5 + x + y = 10[/tex]

[tex]y = 10 - 5 - x[/tex]

[tex]y = 5 - x[/tex]

Thus, the amount of gigabytes of music stored on the computer is [tex]y = 5 - x[/tex], considering x as the amount of gigabytes of movies stored.

A similar question is found at https://brainly.com/question/22789267

Answer:

The growth rate is of 0.085 = 8.5% a year.

Step-by-step explanation:

General growth equation:

[tex]B(t) = B(0)(1+r)^{t}[/tex]

In which B(t) is the population of butterflies after t years, B(0) is the initial population and r is the growth rate, as a decimal.

We have:

[tex]B(t)=137(1.085)^{t}[/tex]

Comparing to the general equation, we have that:

[tex]B(0) = 137, 1 + r = 1.085[/tex]

Growh rate:

1 + r = 1.085

r = 1.085 - 1

r = 0.085

The growth rate is of 0.085 = 8.5% a year.

Answer:

You need to add 150 mL of 65% alcohol solution.

Step-by-step explanation:

You have 300 mL of 20% solution.

300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.

You have 65% solution.

Let the volume of 65% solution you add be x.

In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.

You want 35% solution.

The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).

Equation of alcohol content:

20% * 300 + 65% * x = 35% * (x + 300)

60 + 0.65x = 0.35x + 105

0.3x = 45

x = 150

Answer: You need to add 150 mL of 65% alcohol solution.

Answer:

the probability that one parachute of the  five parachute is damaged is 0.156

Step-by-step explanation:

From the given information;

Let consider X to be the altitude above the  ground that a parachute opens

Then; we can posit that the probability that the parachute is damaged is:

P(X ≤ 100 )

Given that the population mean μ = 155

the standard deviation σ = 30

Then;

[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]

[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]

[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]

From standard normal tables

[tex]P(X \leq 100 ) = 0.0334[/tex]

Hence; the probability of the given parachute damaged is 0.0334

Let consider Q to be the dropped parachute

Given that the number of parachute be n= 5

The probability that the parachute opens in each trail be  p = 0.0334

Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334

The probability mass function is:

Q [tex]\sim[/tex] B(5, 0.0334)

Similarly; the event that one parachute is damaged is :

Q ≥ 1

P( Q ≥ 1 ) = 1 - P( Q < 1 )

P( Q ≥ 1 ) = 1 - P( Y = 0 )

P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )

P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = 1 -  0.8437891838

P( Q ≥ 1 ) = 0.1562108162

P( Q ≥ 1 ) [tex]\approx[/tex] 0.156

Therefore; the probability that one parachute of the  five parachute is damaged is 0.156

Answer:

47, 40, 33, 26 are the first four terms of the sequence.

Step-by-step explanation:

Expression representing the sequence is,

[tex]a_n=46-7(n-1)[/tex]

where n = number of term in the sequence

For n = 1,

[tex]a_1=47-7(1-1)[/tex]

    = 47

For n = 2,

[tex]a_2=47-7(2-1)[/tex]

    = 47 - 7

    = 40

For n = 3,

[tex]a_3[/tex] = 47 - 7(3 -1)

   = 47 - 14

   = 33

For n = 4,

[tex]a_4=47-7(4-1)[/tex]

    = 47 - 21

    = 26

Therefore, first four terms of the sequence are 47, 40, 33 and 26.

Answer:

200 N/m

Step-by-step explanation:

Rearranging the formula F = kx, you find that k = F/x. For the first spring,

F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m

For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m

The difference between these values is 200 N/m, and that's the answer.

Answer:

C h^2  / 680 = x

Step-by-step explanation:

C=680x/h^2

Multiply each side by h^2

C h^2=680x/h^2  * h^2

C h^2=680x

Divide each side by 680

C h^2  / 680=680x/680

C h^2  / 680 = x

Answer:

the solution to the problem is D

Answer:

$4800.25

Step-by-step explanation:

$42603 is a yearly salary.

There are 12 months in 1 year.

Monthly salary:

$42603/12 = $3550.25

Monthly travelling allowance: $1250

Total amount earned in 1 month:

$3550.25 + $1250 = $4800.25

Answer: The second option;  y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

Ok, we have that a and b are real numbers different than zero.

In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:

y = x*(x - a)^3*(x - b)^3

then when x = 0 we would have:

y = 0*(0-a)^3*(0-b)^3 = 0

But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.

So the remaining options are:

y = (x - a)^2*(x-b)^4

y = (x - a)^5*(x - b)

Now, another thing you can see in the graph is that it is always positive.

Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.

(For example, if x > a and x < b we would have a negative value for y)

Then the only remaining option is y =  (x - a)^2*(x-b)^4

Answer:

B.y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

EDGE 2020 Brainliest please

Answer:

D

Step-by-step explanation:

1/3(9x + 27) > x + 33

3x + 9 > x + 33

2x > 24

x > 12

> means open circle

Answer:

The answer is D

Step-by-step explanation:

I took the plato test!

Answer:

We conclude that the population means checkout times of the two new systems differ.

Step-by-step explanation:

We are given the result in the following summary of the data;

System          System B

n1=120             n2=100

x1=4.1 min       x2=3.4 min

σ1=2.2 min     σ2= 1.5 min

Let [tex]\mu_1[/tex] = population mean checkout time of the first new system

[tex]\mu_2[/tex] = population mean checkout time of the second new system

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]      {means that the population mean checkout times of the two new systems are equal}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]      {means that the population mean checkout times of the two new systems differ}

The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;

                          T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex]  ~ N(0,1)

where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min

[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min

[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min

[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min

[tex]n_1[/tex] = sample of the first new systems = 120

[tex]n_2[/tex] = sample of the second new systems = 100

So, the test statistics =  [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]  

                                    =  2.792

The value of z-test statistics is 2.792.

Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean checkout times of the two new systems differ.

Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

m = [tex]-\frac{3}{2}[/tex]

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

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

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

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

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

To write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3

Let n be the number, then -3 < n ≤3 .

On number line we mark open circle at -3 (since it has a strictly less than sign) and a closed circle at 3  (since it has a less than and equal to sign) .

To the required inequality that shows all the numbers greater than (−3) but less than or equal to 3 : -3 < n ≤3 and the number line is represented below.