(Will Mark Brainliest!!!)Choose the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1)
A: y + 3 = −5(x − 2)
B: y − 2 = −5(x + 3)
C: y + 3 = −(x − 2)
D: y − 2 = −(x + 3)​

Answer:

1.3027

Step-by-step explanation:

[tex] \sf \: 3x + x \sqrt{3} - 2 = 0 \\ \\ \sf \longrightarrow 3x + \sqrt{3} x = 2 \\ \\ \sf \longrightarrow \sqrt{3}x ( \sqrt{3} +1 ) = 2 \\ \\ \sf \longrightarrow \sqrt{3} x = \frac{2}{ \sqrt{3} + 1 } \\ \\ \sf \longrightarrow x = \frac{2}{ \sqrt{3}( \sqrt{3} + 1) } \\ \\ \sf \longrightarrow x = \frac{2}{3 + \sqrt{3} } \\ \\ \tt{You\:can\:stop\:here\:if\:you\:\bold{don't}\:want\:to }\\ \tt{ \:simplify\:in\:decimal\:form.}\\ \\ \sf \longrightarrow x = \frac{2(3 - \sqrt{3} )}{(3 + \sqrt{3})(3 - \sqrt{3} )} \\ \\ \sf \longrightarrow x = \frac{6 - 2 \sqrt{3} }{ {3}^{2} - {( \sqrt{3}) }^{2} } \\ \\ \sf \longrightarrow x = \frac{6 - 2(1.732)}{9 - 3} \\ \\ \sf \longrightarrow x = \frac{2.536}{6} \\ \\ \leadsto \underline{\boxed{\sf{\pink{x \approx 0.4226}}}}[/tex]

It's not clear what the pattern is supposed to be for the digits in the givne number. It looks like the repeating block should be 846, but it could just as easily be 84684.

Assume the first case, and let x = 7.846846846... . Then

1000x = 7846.846846846...

Subtract x from this to cancel the repeating decimal part, then solve for x :

999x = 7846 - 7 = 7839

x = 7839/999 = 871/111

If instead you meant the second case, let x = 7.846848468484684... . Then

10⁵ x = 784,684.846848468484684...

Solve for x :

99,999 x = 784,684 - 7 = 784,677

x = 784,677/99,999 = 261,559/33,333

Maybe you meant something else altogether?

Answer:

if youre trying to find the number then the number is 1

Step-by-step explanation:

the equation would be x/16+1/4=5/16

well we want to make everything have the same denominator and 16 is the LCD ( least common denominator ) so you would multiply 1/4 by 4/4 to get 4/16.

this means x/16+4/16=5/16 and and 4+1=5 so 1 is the answer

Answer:

x=21

Step-by-step explanation:

x=9+12 x=21

Answer:

Step-by-step explanation:

X-9=12

Reverse the operation into

9+12=x

9+12=21

Now check

21-9=12

Answer:

F(d) = 30 + 0.50d

Step-by-step explanation:

Given

Charges = P8.00 ---- first 4 km

Additional = P0.50

Required

Write a function to address the scenario.

Represent the whole distance covered with d.

First,we need to determine the total charges for the first four hours.

Charges = 8.00 * 4

Charges = 32.00

Next, we determine the charges for additional distance.

Charges = 0.50 * (d - 4)

d - 4 is the remaining distance after the first 4.

Charges = 0.50d - 2

The function is then written as;

F(d) = 32 + 0.50d - 2

F(d) = 32 - 2 + 0.50d

F(d) = 30 + 0.50d

1 yard = 3 feet.

100 yards x 3 = 300 feet.

300 feet x 3/4 = 225 feet.

The answer is 225 feet.

Answer:

225 ft hope it helps

Answer:

It's not 0 I got it wrong.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

i just took the test

Answer:

1,289 divided by 22 is 58 r13

Step-by-step explanation:

Answer:

Step-by-step explanation:

yes!

Answer:

[tex]x^{2}[/tex]  

I hope this helps!

Answer:

your answer is b     32/4=8

Step-by-step explanation:

if you take the groups of 4 and count them up it is 32 and then you divide them in to equal groups and it is 8 groups of 4

hope this helped

:)

Answer:

[tex]A(k) = 55k[/tex]

Step-by-step explanation:

Given

[tex]1kg = P55[/tex]

Required

Determine the cost of k kilogram

[tex]1kg = P55[/tex]

Multiply both sides by k

[tex]k * 1kg = P55 * k[/tex]

[tex]k\ kg = 55 k[/tex]

Representing this as a function:

[tex]A(k) = 55k[/tex]

Answer:

Step-by-step explanation:

k - 4 = 3

   9

k/9  = 3(9) + 4

k = 31/9

k = 31/9

8 + b = -5

  -4

8 + b = -5 (-4)

8 +  b = 20

b = 20 - 8

b = 12

Answer:

27

Step-by-step explanation:

This question was not written completely

Complete Question

At one point the average price of regular unleaded gasoline was ​$3.39 per gallon. Assume that the standard deviation price per gallon is ​$0.07 per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​?

Answer:

a) 88.89% lies with 3 standard deviations of the mean

b) i) 84% lies within 2.5 standard deviations of the mean

ii) the gasoline prices that are within 2.5 standard deviations of the​ mean is $3.215 and $3.565

c) 93.75%

Step-by-step explanation:

Chebyshev's theorem is shown below.

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.

3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.

4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.

​

(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

We solve using the first rule of the theorem

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

Hence, k = 3

1 - 1/k²

= 1 - 1/3²

= 1 - 1/9

= 9 - 1/ 9

= 8/9

Therefore, the percentage of gasoline stations had prices within 3 standard deviations of the​ mean is 88.89%

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean?

We solve using the first rule of the theorem

1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.

As stated, the value of k must be greater than 1.

Hence, k = 3

1 - 1/k²

= 1 - 1/2.5²

= 1 - 1/6.25

= 6.25 - 1/ 6.25

= 5.25/6.25

We convert to percentage

= 5.25/6.25 × 100%

= 0.84 × 100%

= 84 %

Therefore, the percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean is 84%

What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

We have from the question, the mean =$3.39

Standard deviation = 0.07

μ - 2.5σ

$3.39 - 2.5 × 0.07

= $3.215

μ + 2.5σ

$3.39 + 2.5 × 0.07

= $3.565

Therefore, the gasoline prices that are within 2.5 standard deviations of the​ mean is $3.215 and $3.565

​(c) What is the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​?

the mean =$3.39

Standard deviation = 0.07

Applying the 2nd rule

2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.

the mean =$3.39

Standard deviation = 0.07

μ - 2σ and μ + 2σ.

$3.39 - 2 × 0.07 = $3.25

$3.39 + 2× 0.07 = $3.53

Applying the third rule

3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.

$3.39 - 3 × 0.07 = $3.18

$3.39 + 3 × 0.07 = $3.6

Applying the 4th rule

4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.

$3.39 - 4 × 0.07 = $3.11

$3.39 + 4 × 0.07 = $3.67

Therefore, from the above calculation we can see that the minimum percentage of gasoline stations that had prices between ​$3.11 and ​$3.67​ corresponds to at least 93.75% of a data set because it lies within 4 standard deviations of the mean.

Answer:

let Elijah age be a

Then

2*a + 17 =47

2a=47-17

2a=30

a=15

Step-by-step explanation:

Answer:

[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]

Step-by-step explanation:

I will try to give as many details as possible.

First of all, I just would like to say:

[tex]\text{Use } \LaTeX ![/tex]

Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/

[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]

Note that

[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]

Also,

[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]

[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

Note

[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]

[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]

Note

[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]

[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]

[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]

Once

[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]

[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]

And

[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]

We have

[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]

Also, once

[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]

As

[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]

[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]

[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]

Answer:f(x, y) = e

−xy. For the interior of the region, we find the critical points:

fx = −ye−xy

, fy = −xe−xy, so the only critical point is (0, 0), and f(0, 0) = 1.

For the boundary, we use Lagrange multipliers.

g(x, y) = x

2 + 4y

2 = 1 ⇒ λ∇g = h2λx, 8λyi, so setting ∇f = λ∇g we get

−ye−xy = 2λx and −xe−xy = 8λy. The first of these gives e

−xy = −2λx/y,

and then the second gives −x(−2λx/y) = 8λy ⇒ x

2 = 4y

2

. Solving this

last equation with the constraint x

2 + 4y

2 = 1 gives x = ± √

1

2

and y = ±

1

2

√

2

.

Now f

± √

1

2

, ∓

1

2

√

2

= e

1/4 ≈ 1.284 and f

± √

1

2

, ±

1

2

√

2

= e

−1/4 ≈ 0.779.

The former are the maxima on the region and the latter are the minima.

Step-by-step explanation:

Answer:

1/3 cup of juice per cup of berries

Step-by-step explanation:

The table shows that if we go from 0 to 4 cups (a "run" of 4 cups), the juice output is 1 1/3 (or 4/3) (a "rise" of 4/3 cups), and so the desired constant of proportionality is the unit rate

(4/3) cups

------------------------ = 1/3 cup of juice per cup of berries

  4 cups berries

you would divide -> 51/68  and you would get .75. move the 2 first numbers after the dot to the front and you get 75%

Answer:

I the diagram, 17  represents 25% of the total  games. Since 17 times 3 equals 51, you use the first 3 columns to find the answer of 75%.  

Just took test that was the answer they gave.

Step-by-step explanation:

Answer:

0.041

I know this because 1,000 has 3 zeros, so you would move 41 three places to the right.

The decimal equivalent of the fraction 41/1000 is 0.041.

A decimal is represented by a dot that separates the whole part and the fractional part of a number. Decimals can also be converted into fractions and vice versa.

Given, a fraction 41/1000, here the numerator is less than the denominator so it is a proper fraction.

Now, As in the denominator we have three zeroes we'll put a decimal three places before the numerator value which is,

= 0.041/1.

= 0.041.

So, 41/1000 is equal to 0.041.

learn more about decimal numbers here :

https://brainly.com/question/4708407

#SPJ2

Step-by-step explanation:

Hey there!

To solve this type of question, you must take square of variable"X" to right side making it ±squareroot. As it is a quadratic equation it will have two values (±).

Given;

[tex] {x}^{2} = 16[/tex]

Taking (square) to right side. It becomes ± square root.

[tex]x = + - \sqrt{16} [/tex]

[tex]x = + - \sqrt{ {4}^{2} } [/tex]

Cancel square and square root.

[tex]x = + - 4[/tex]

Therefore, X = ±4

Hope it helps...

Answer:

There are two I results found which is x=4 and x=-4

Step-by-step explanation:

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    x^2-(16)=0  

Step by step solution :

STEP

1 :

Trying to factor as a Difference of Squares:

1.1      Factoring:  x2-16  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4

Check :  x2  is the square of  x1  

Factorization is :       (x + 4)  •  (x - 4)  

Equation at the end of step

1 :

 (x + 4) • (x - 4)  = 0  

STEP

2 :

Theory - Roots of a product

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2      Solve  :    x+4 = 0  

Subtract  4  from both sides of the equation :  

                     x = -4

Solving a Single Variable Equation:

2.3      Solve  :    x-4 = 0  

Add  4  to both sides of the equation :  

                     x = 4 and/or x=-4

Im guessing the ratio for a cirlce could be 1/2 or more

uplod the pic so i can solve the problem

Answer:

<A=<C=45°

Step-by-step explanation:

you can see in the picture above

Answer

The answer is A

Answer:

It is A. my friend

Step-by-step explanation:

Answer:

∑ (-1)ⁿ⁺³ 1 / (n^½)

∑ (-1)³ⁿ 1 / (8 + n)

Step-by-step explanation:

If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.

Option A: (-1)²ⁿ is always +1.  So an =│an│and both series converge (absolutely convergent).

Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).

Option C: an = 1 / n³ isn't an alternating series.  So an =│an│and both series converge (p series with p > 1).  This is absolutely convergent.

Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series.  bn = 1 / (8 + n), which diverges.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.