How do you know if something is divisible by four

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Explanation:

The angle EQD is an inscribed angle that cuts off the arc from E to D (the shortest path). Note how central angle ECD also cuts off this same arc. By the inscribed angle theorem, we know that

inscribed angle = (1/2)*(central angle)

angle EQD = (1/2)*(angle ECD)

We can multiply both sides by 2 and flip the equation to get

angle ECD = 2*(angle EQD)

Now replace "angle EQD" with 5x+2

angle ECD = 2*(5x+2)

2*(5x+2) = angle ECD

Next, replace "angle ECD" with 104 as this is the measure of this central angle.

2*(5x+2) = angle ECD

2*(5x+2) = 104

From here, we solve for x

2*(5x+2) = 104

2*5x + 2*2 = 104

10x + 4 = 104

10x+4-4 = 104-4 ..... subtracting 4 from both sides

10x = 100

10x/10 = 100/10 ...... dividing both sides by 10

x = 10

Answer:

Step-by-step explanation:

Put x = -7 to the equation -4x - 9y = -26, and solve it for y:

-4(-7) - 9y = -26

28 - 9y = -26            subtract 28 from both sides

-9y = -54           divide both sides by (-9)

y = 6

Answer:

  5x^2 + 9x + 15.

Step-by-step explanation:

There is no term in x so we add  one (0x).

            5x^2 + 9x + 15  <------------Quotient.

          --------------------------------------

3x - 5 )  15x^3 + 2x^2 + 0 x  - 75

            15x^3 - 25x^2

           --------------------

                         27x^2 + 0x

                         27x^2 - 45x

                         ------------------

                                      45x - 75

                                       45x - 75

                                         ..........

Answer:

The farmer would need 80 posts.

Step-by-step explanation:

If one side of the garden is 10m long, and the garden is a square, we can assume that all 4 sides will be 10m. That makes it 40m in total. Times 40×2 and you get 80.

Answer:

The area of the enclosed gazebo is [tex]310.4\ ft^{2}[/tex]

Step-by-step explanation:

I assume that is a regular octagon (eight equal aides)

we know that

The area of a regular polygon is equal to

[tex]A=\frac{1}{2}(P)(a)[/tex]

where

P is the perimeter of the polygon

a is the apothem

Find the perimeter P (the octagon has 8 sides)

[tex]P=8(8)=64\ ft[/tex]

[tex]a=9.7\ ft[/tex]

substitute

[tex]A=\frac{1}{2}(64)(9.7)[/tex]

[tex]A=310.4\ ft^{2}[/tex]

Answer:

19

Step-by-step explanation:

g(x)=x^2+3

g(x)=(4^2)+3

g(x)=16+3=19

if g of x = x squared + 3, then 4 squared = 16, plus 3 = 19

Answer:

option(B)  g(4) =19.

Step-by-step explanation:

Given:If g(x) = [tex]x^{2}[/tex] + 3.

To find: g(4).

Solution: We have given that  

g(x) = [tex]x^{2}[/tex] + 3.

for x=4.

g(4) = [tex]4^{2}[/tex] + 3.

g(4) = 16+3

g(4) =19.

Therefore, option(B)  g(4) =19.

Answer:

5/8

Step-by-step explanation:

first plug in for x & y, then solve. you should get 5/8

2 -2 +5 +0 / 2 +3 +5 -2

5/8

Answer:

125/32

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Range=big-small=34-16=18

Interquartile range=big number in box-small number in box= 29-21=8

The different between the two is 18-8=10

Answer:

The difference of range and interquartile range is 10.

Step-by-step explanation:

Consider the provided information.

From the box plot we can identify:

The lowest value is 16

The first quartile is 21

The 2nd quartile or median is 26

The 3rd quartile is 29

The highest value is 34

Range is the difference of the highest value and lowest value of the data set.

Range = 34 - 16 = 18

Interquartile range is the difference of the 3rd quartile from the 1st quartile.

IQR: 29 - 21 = 8

Thus, the difference of range and interquartile range is:

18 - 8 = 10

Hence, the difference of range and interquartile range is 10.

Answer:

D. x + 5

Step-by-step explanation:

2x^4 + 20x^3 + 50x^2

= 2x^2 (x^2 + 10x + 25)

= 2x^2 (x + 5)^2

= 2x^2 (x + 5) (x + 5)

Answer

D. x + 5

For this case we have the following expression:

[tex]2x ^ 4 + 20x ^ 3 + 50x ^ 2[/tex]

It is observed that we can extract common factor [tex]2x ^ 2[/tex], since it is common in the three terms:

[tex]2x ^ 2 (x ^ 2 + 10x + 25) =[/tex]

If we factor the expression into parentheses, we must look for two numbers that add 10 and multiply 25. These are: 5 and 5.

Rewriting the expression we have:

[tex]2x ^ 2 ((x + 5) (x + 5))[/tex]

Thus, one of the factors of the original expression is[tex]x + 5[/tex].

Answer:

Option D

Answer:

[tex]\large\boxed{\dfrac{1}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=3\ \text{and}\ x=5.\\(look\ at\ the\ picture)\\\\f(3)=1,\ f(5)=2\\\\\text{Substitute:}\\\\\dfrac{f(5)-f(3)}{5-3}=\dfrac{2-1}{2}=\dfrac{1}{2}[/tex]

Answer:

x = 25

Step-by-step explanation:

The 2 given angles form a straight angle and are supplementary, that is

2x + 2 + 5x + 3 = 180

7x + 5 = 180 ( subtract 5 from both sides )

7x = 175 ( divide both sides by 7 )

x = 25

[tex]x^2<49\\x<7 \wedge x>-7\\x\in(-7,7)[/tex]

If we divide both sides by -2, we have

[tex]bx-5 = -8 \iff bx = -3 \iff x = -\dfrac{3}{b}[/tex]

So, if you choose b=3, you have x = -3/3=-1

a)

       The value of x in terms of b is:

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

b)

         The value of x when b is 3 is:

                      [tex]x=-1[/tex]

We are given a equation in terms of x and b as follows:

           [tex]-2(bx-5)=16-----------(1)[/tex]

a)

Now on simplifying the equation i.e. we solve for x i.e. we find the value of x in terms of b as follows:

On dividing both side of the equation by -2 we get:

[tex]bx-5=-8[/tex]

Now on adding both side by 5 we get:

[tex]bx=-8+5\\\\\\bx=-3[/tex]

Now, on dividing both side of the equation by b we get:

          [tex]x=\dfrac{-3}{b}------------(2)[/tex]

b)

when b=3 in equation (2) we have:

              [tex]x=\dfrac{-3}{3}\\\\\\x=-1[/tex]

Answer:

No solution

Step-by-step explanation:

x + 2/3 = 2/3 + x - 1/4

x = x - 1/4

0 ≠ -1/4

Answer:

6

Step-by-step explanation:

2 x 6 = 12/2 = 6

Answer:

A = 6 units ^2

Step-by-step explanation:

The area of a triangle is found by

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 (6) *2

A = 6 units ^2

Answer:

Look to the attached file

Step-by-step explanation:

Answer:

Option C. Graph C

Step-by-step explanation:

we have

[tex]y=(x-3)^{2}-25[/tex]

This is the equation of a vertical parabola open upward (vertex is a minimum)

The vertex is the point (3,-25)

therefore

The graph is C

The graph in the attached figure

Answer:c

Step-by-step explanation:

Answer: cubic meters : m³

Step-by-step explanation:

Cylinder volume is the product of area of the base by height.

Area of the base is the product of π·radius² = square meters : m²

Volume = square meters·meters =  m²·m = cubic meters : m³

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

29 red marbles

Step-by-step explanation:

Call R the number of red marbles and B the number of black marbles.

According to the second sentence, R = 2B + 3.

According to the third sentence, R + B = 42.

Now we have 2 equations, 2 unknowns. Sub the first into the second since it already has R isolated:

2B + 3 + B = 42

3B = 39

B = 13

Now sub this into either of the original equations (I'll use the first):

R = 2(13) + 3

R = 29

1box = 1400/7 = 200

200×3=600

1400+600=2000

Answer:

2000

Step-by-step explanation:

Given :Workers have packed 1,400 glasses in 7 boxes.

To Find :If they pack 3 more boxes, how many glasses will they have packed in all?

Solution:

Workers packed no. of glasses in 7 boxes = 1400

Workers packed no. of glasses in 1 box = [tex]\frac{1400}{7}[/tex]

Workers packed no. of glasses in 3 boxes = [tex]\frac{1400}{7} \times 3[/tex]

                                                                      = [tex]600[/tex]

So, initially they packed 1400 glasses

If they pack 3 more boxes so, the pack 600 glasses more

So, The total no. of glasses have packed by workers = 1400+600 = 2000

Hence they have packed 2000 glasses in all.

Answer:

D

Step-by-step explanation:

Given

2x² + 3x - 7 = x² + 5x + 39

Subtract x² + 5x + 39 from both sides

x² - 2x - 46 = 0 ← in standard form

with a = 1, b = - 2, c = - 46

Solve for x using the quadratic formula

x = (- (- 2) ±[tex]\sqrt{(-2)^2-(4(1)(-46)}[/tex] ) / 2

  = ( 2 ± [tex]\sqrt{4+184}[/tex] ) / 2

  = ( 2 ± [tex]\sqrt{188}[/tex] ) / 2

  = ( 2 ± 2[tex]\sqrt{47}[/tex] ) / 2

  = 1 ± [tex]\sqrt{47}[/tex]

The deviation from 80 of about 16 is normal.

So the lowest is usually 80 - 16 = 64 and the highest is 80 + 16 = 96

But now we have a "deviation" that is 2 standard deviations above the mean score.

So 80 + 16 + 16 = 112 is this score.

Hope this helps.

r3t40

Final answer:

To calculate the score that is 2 standard deviations above the mean of 80 with a standard deviation of 16, you add 2 times the standard deviation to the mean, resulting in a score of 112.

Explanation:

To find the score that is 2 standard deviations above the mean on a test with a mean of 80 and a standard deviation of 16, we use the formula:

Score = Mean + (Number of Standard Deviations × Standard Deviation)

So, plugging in the numbers we get:

Score = 80 + (2 × 16)

Score = 80 + 32

Score = 112

The desired score is therefore 112, which is 2 standard deviations above the mean of 80.

The simultaneous Equations for both total costs are;

Company A: y = 45x + 150

Company B: y = 50x + 125

Thus, both companies charge the same amount of money for food truck permits for 5 months

How to find the equation of the total charges?

We are told that;

Company A charges a one time fee of $150 and $45 per month.

Company B charges a one time fee of $125 and $50 per month.

Thus, using the concept of the equatiom of a line In slope intercept form, we have:

Company A: y = 45x + 150

Company B: y = 50x + 125

let's use the number 5 for x as an example

45(5) + 150 = 375

50(5) + 125 = 375

So both companies charge the same amount of money for food truck permits for 5 months.

Complete question is;

Two companies allow you to pay monthly for your food truck permits. Company A charges a one time fee of $150 and $45 per month. Company B charges a one time fee of $125 and $50 per month. Write an equation or a system of equations and explain what each solution tells you about the situation

[tex]0-(6+4i)=0-6-4i=-6-4i[/tex]

The additive inverse of the complex number 6+4i is -6-4i because it negates both the real and imaginary parts, resulting in a sum of zero when added to the original number.

The additive inverse of a complex number is a number that, when added to the original number, yields a sum of zero. For the complex number 6+4i, its additive inverse is found by changing the sign of both the real and the imaginary parts. Therefore, the additive inverse of 6+4i is -6-4i.

Answer: Eight percent.

Step-by-step explanation: In order to find this, we have to use the probability formula, which is:

The Event We Are Looking For/All of the Events.

In this case, plugging the numbers into the formula we get

May(1)/All the months in the year, including May (12).

Diving this, our answer will be 0.08333..., or rounded up to 0.8

However, since we are only looking for one specific event, we can take the number 100, and divide it by all the events. 12/100 is 8.333..., or rounded to 8.

Final answer:

The chance that a person randomly selected off the street was born in May is about 8%, assuming birth rates are evenly distributed throughout the year.

Explanation:

The question, "What is the chance that a person randomly selected off the street was born in May?" is one that pertains to the subject of probability in Mathematics. Since there are typically 12 equally likely months that a person could be born in, and assuming there is no significant variation in birth rates by month, the chance that someone chosen at random off the street was born in May is 1 out of 12 months.

Thus, to calculate the probability, you would divide 1 by 12, which equals approximately 0.0833. To express this as a percentage, we multiply by 100, yielding an 8.33% chance. Therefore, the closest answer among the provided options is 8%.

Answer:

5e^(3x+7)=21

e^(3x+7)=4.2

(3x+7)lne=ln4.2

lne=1

3x+7=1.435

3x= -5.565

x= -1.855

To solve the equation [tex]5e^{3x}+7=21[/tex], isolate the exponential term, take the natural logarithm of both sides, and then solve for x. This results in x ≈ 0.3362.

To solve the equation [tex]5e^{3x}+7=21[/tex], follow these steps:

First, isolate the exponential term by subtracting 7 from both sides:

[tex]5e^{3x} = 14[/tex]

Next, divide both sides of the equation by 5:

[tex]e^{3x} =\frac{14}{5}[/tex]

Now, take the natural logarithm (ln) of both sides:

[tex]ln(e^{3x}) = ln(\frac{14}{5})[/tex]

Since the natural logarithm and the exponential function are inverse operations, the left side simplifies to:

[tex]{3x} = ln(\frac{14}{5})[/tex]

Finally, solve for x by dividing by 3:

[tex]x =\frac{1}{3}\times ln(\frac{14}{5})[/tex]

Using a calculator, this results in:

x ≈ 0.3362

Final answer:

To rationalize the denominator and simplify the expression 6 / (5-3), multiply the numerator and denominator by 1/2. Then, simplify the expression to get 3/1 = 3.

Explanation:

To rationalize the denominator and simplify the expression 6 / (5-3), we can start by multiplying the numerator and denominator by a skillfully chosen factor. In this case, we can choose 1/2 as the factor.

The numerator becomes 6 * 1/2 = 3, and the denominator becomes (5-3) * 1/2 = 2/2 = 1.

Therefore, the simplified expression is 3/1 = 3.

Answer:

0.14

Step-by-step explanation:

Fourteen of the 100  digital video recorders​ (DVRs) in an inventory are known to be defective. It means that the probability that a randomly selected item is defective is: [tex]\frac{14}{100} = 0.14[/tex].

Answer:

Let j = amount Jasmine spent, k = amount Karen spent, and m = amount Maggie spent.

m = 3k, k = (1/2)j

j + k + m = $60

2k + k + 3k = $60

6k = $60

k = $10, m = $30, j = $20

Jasmine spent $20, Karen spent $10, and Maggie spent $30.