The points (2,3) and (5,9) are on the line. What is the equation of the line

Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].

Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].

Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,

[tex]3^{12} \equiv 1 \pmod{13}[/tex]

Now, observe that 2020 = 168×12 + 4, so that

[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]

and since 3⁴ = 81 = 6×13 + 3, we end up with

[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]

so the remainder upon dividing 3²⁰²⁰ by 13 is 3.

Answer:

-0.875

Step-by-step explanation:

So you have the points -4.25 and 2.50. To find the midpoint you simply add the two and then divide by 2. This results in (-4.25 + 2.50) / 2 = -0.875

Step-by-step explanation:

Answer:

a) 5 pounds

b) 365 dollars

Answer:

a)  81π  in³

b)  27  in³

c)  divide the volume of the slice of cake by the volume of the whole cake

d)  10.6%

e)  see explanation

Step-by-step explanation:

The cake can be modeled as a cylinder with:

[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]

Probability is approximately 10.6%  (see above for calculation)

If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found.  So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

Answer:

43

Step-by-step explanation:

31+12=43

Therefore adding 43 to -31 should give the answer 12.

Hii!

____________________________________________________________

Answer:

43

Step-by-step explanation:

We can find an answer to this question by setting up an equation.

-31+x=12

x is the unknown amount we should add to -31 to obtain 12.

Now, to solve it for the variable, x, we need to add 31 to both sides.

Upon doing this we obtain.

x=43

∴, 43 should be added to -31 to get 12

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Hope that this helped! Best wishes.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: x = 32°[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Diagonals of a Rhombus bisect each other at 90°

[tex]\qquad \tt \rightarrow \: x + 58 + 90 = 180[/tex]

[ Sum of interior angles of a triangle ]

[tex]\qquad \tt \rightarrow \: x + 148 = 180[/tex]

[tex]\qquad \tt \rightarrow \: x = 180 - 148[/tex]

[tex]\qquad \tt \rightarrow \: x = 32 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.

It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.

Figure ABCD is a rhombus.

Its diagonals intersect at right angle.

Let the another angle be x. Then we have

x + 58° + 90° = 180°

        x + 148° = 180°

                   x = 32°

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Answer:

12x^7+15x^6

Step-by-step explanation:

Change 3x^3-2 to 3x

(x^4)(3x)(4x^2+5x)

Multiply your single terms

(3x^5)(4x^2+5x)

Then distribute

12x^7+15x^6

The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β

In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.

The trigonometric expression given in the question is

(1+cosβ)(1−cosβ)sinβ

(a+b)(a-b) = a² - b²

( 1 - cos²β)sinβ

By the trigonometric Identity

1-cos²β = sin² β

 sin² β x sin β

sin³β

Therefore Option B is the correct answer.

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The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). ....

Using the piecewise function, one can see that;

In x ≤ 0, the slope of the graph of h(x) = 1/4

In 0 < x ≤ 3, the slope of the graph of h(x) = 1/3

In x ≥ 4, the slope of the graph of h(x) = 1/2

Note that the movement is left to right and the slope of h(x) often increases and the slope of the graph is said to become steeper.

Option B shows the graph of h(x) as it best tells the exact point of various aspect of the function.

Therefore, The graph that represents h(x) is option B: On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 4, negative 5) and goes up to a closed circle at (0, negative 4). The second line starts at (0, negative 3) and goes up to a closed circle at (3, negative 2). The third line has a closed circle at (4, 0) and goes up to (6, 1).

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Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

They will earn If they work every week If the year is $22100.

We have given that,

you currently make 425

We have to determine what is the gross they will earn If they work a week If the year.

We know that

A worker currently makes $425 per week

1year=52 weeks

So by proportion find the amount that the worker will earn in one year

[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]

[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]

[tex]x=52\times 425[/tex]

x=22,100

Therefore, The answer is $22100.

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Answer:

2nd one is the correct

Answer:

  x = π/12, 5π/12

Step-by-step explanation:

We can work this problem a couple of ways. We can convert it to single trig function, shifted horizontally. Or we can convert it to a double-angle equation.

__

We recall the sum of angles formula is ...

  sin(x+y) = sin(x)cos(y) +cos(x)sin(y)

Using this, we can rewrite the left side of the equation using some angle offset y, and some scale factor k.

  k·sin(x +y) = k·sin(y)·cos(x) +k·cos(y)·sin(x) = 2cos(x) +2sin(x)

finding the shift

Equating coefficients of cos(x) and sin(x), we can solve for k and y:

  k·sin(y) = 2

  k·cos(y) = 2

The ratio of these equations is ...

  (k·sin(y))/(k·cos(y)) = 2/2

  tan(y) = 1   ⇒   y = π/4

  k = 2/sin(π/4) = 2√2

shifted equation

So, our original equation becomes ...

  2√2·sin(x +π/4) = √6

Dividing by √2 and using the inverse sine function, we have ...

  x +π/4 = arcsin((√3)/2) = π/2 ±π/6

  x = π/4 ±π/6

  x = π/12, 5π/12

__

If we square both sides of the original equation, we get ...

  (2sin(x) +2cos(x))² = (√6)²

  4sin²(x) +8sin(x)cos(x) +4cos²(x) = 6

  2sin(x)cos(x) = (6 -4)/4 = 1/2 . .  . . use sin² +cos² = 1, subtract 4, divide by 4

Using the trig identity 2sin(x)cos(x) = sin(2x), we can find ...

  2x = arcsin(1/2) = π/2 ±π/3 +2kπ . . . . k = an integer;

  x = π/4 ±π/6 +kπ . . . . for integer k

  x = {π/12, 5π/12, 13π/12, 17π/12}

We know that squaring the equation can introduce extraneous solutions, so we need to try these out. For x in the third quadrant, the sine and cosine values are both negative, so the only useful solutions here are ...

  x = π/12, 5π/12

_____

Additional comment

Based on the above, we now know that any trig expression of the form ...

  a·sin(x) +b·cos(x)

can be rewritten to the form ...

  (√(a² +b²))·sin(x +arctan(b/a)) . . . . . a scaled and shifted sine function

The arctangent will have to take the signs of 'a' and 'b' into account in order to get the angle quadrant right.

Answer: 2, 4, 6, 8

Step-by-step explanation:

Just plug x into the equation for each one.

x = -3

[tex]y=\frac{2(-3)}{3} +4\\y=\frac{-6}{3} +4\\y=2[/tex]

With this one, you can see it is a linear equation and for every increase of 3 on x, y in increased by 2.

x   -6   -3   0   3   6

y   0   2    4   6   8

Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is one subtracted by the p-value of Z when X = 66.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{66.5 - 50}{5}[/tex]

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

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Answer:

5/17

Step-by-step explanation:

If we do the multiplication first, we get:

[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]

If we do the division next, we get:

[tex]\frac{4+1}{13+4} = 5/17[/tex]

Answer:

[tex]-\frac{3}{10}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5} *-\frac{3}{4} \\=-\frac{6}{20} \\=-\frac{3}{10}[/tex] (Reduced to simplest form.)

Answer:

4/11 of an inch (about .4 of an inch)

Step-by-step explanation:

[tex]l \times 33 \times 5.75 = 69[/tex]

[tex]189.75l = 69[/tex]

[tex]l = \frac{69}{189.75} = \frac{4}{11} = .3636[/tex]

So the length of the popcorn box is 4/11 of an inch, or about .4 of an inch.

Answer:

-9

Step-by-step explanation:

-|1-2|2+7

-|-1|9

-9×1

-9

The correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Given parent function is f(x)=|x|

Now we have to find which function from given choices will be narrower than the parent function.

Notice that adding or subtracting some number from the parent function only shifts the graph up, down, and left of the right side.

But that will not make the function narrower or broader.

So f(x) = |x – 2| and f(x) = |x| + 3, can't be the answer.

Multiplying by some positive real number which is more than 1, makes the function narrower.

Only f(x) = 2.9|x| from remaining choices fits that case.

Hence correct answer is option 4 which is f(x) = 2.9|x| is narrower than the parent function f(x) = |x|

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Answer:

D,E

Step-by-step explanation:

The size of the colony after 10 days is  852.

The growth rate of the colony can be represented with an exponential equation with the form:

FV = P(1 + r)^n

Where:

55(1.73)^5 = 852

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Answer:

usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"

Answer:

[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]

To find the zeros, set the function to zero and solve for x using the quadratic formula.

[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]

Quadratic formula:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore,

Substituting the values into the quadratic formula:

[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]

[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]

The sum of the roots of a polynomial is -b/a:

[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]

The sum of the found roots is:

[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is:  c/a

[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]

The product of the found roots is:

[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

Answer:

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

To find the zeros, set the function to zero and solve for x using the quadratic formula.

Quadratic formula:

Therefore,

a = 2√3

b = 5

c = - 4√3

Substituting the values into the quadratic formula:

The sum of the roots of a polynomial is -b/a:

The sum of the found roots is:

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is: c/a

The product of the found roots is:

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

When h = 0 ,  [f(x + h) - f(x)]/h  = 2x +2 for the given expression.

The missing expression is  f(x) = x² + 2x.

f(x+h)-f(x)/h is called the formula of difference quotient.

When h---> 0 ,

the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line

Here the the expression is

f(x) = x² + 2x

Determining f(x + h) by substituting x = x + h on both sides of the given f(x).

Then f(x + h) = (x + h)² + 2(x + h)

= x² + 2xh + h² + 2x + 2h

the difference f(x + h) - f(x).

f(x + h) - f(x) = [x²  + 2xh + h²  + 2x + 2h] - [x² + 2x]

= 2xh + h² + 2h

Divide the difference from h as in the formula of difference coefficient

[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h

= 2x + h + 2

So, when h = 0 ,  [f(x + h) - f(x)]/h  = 2x +2

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Answer:

Multiply with 2 to the original sides

Answer:

Last one/D 9^9/5/5^9/10

Step-by-step explanation:

Answer:

28.125

Step-by-step explanation:

22.5×1.25=28.125

Answer:

28 1/8

Step-by-step explanation:

1.25 x 22.5 = 28.125