is 289 a prime number​

Answer:

[tex]\huge\boxed{14\ \text{and}\ 7}[/tex]

Step-by-step explanation:

[tex]n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right[/tex]

[tex]\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}[/tex]

[tex]\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}[/tex]

Answer:

addition and multiplication

Step-by-step explanation:

The only operations that can use the commutative and associative properties are addition and multiplication.

Answer:

Step-by-step explanation:

Addition and Multiplication on edg.

Answer:

4y - y^2 = 10

Step-by-step explanation:

Let x and y be the two numbers

x+y = 4

xy = 10

Taking the first equation and solving for x

x = 4-y

Substituting this into the second equation

(4-y) *y = 10

4y - y^2 = 10

Answer:

y = [tex]\frac{16}{3}x-79[/tex]

Step-by-step explanation:

From the given table,

Two points are (1, 15) and (7, 47)

If the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are lying on a line then slope 'm' of the line will be,

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

   = [tex]\frac{47-15}{7-1}[/tex]

   = [tex]\frac{32}{6}[/tex]

   = [tex]\frac{16}{3}[/tex]

Let the equation of a line passing through (h, k) is,

y - h = m(x - k)

If the line passes through (1, 15)

y - 1 = [tex]\frac{16}{3}(x-15)[/tex]

y = [tex]\frac{16}{3}x-\frac{16}{3}(15)+1[/tex]

y = [tex]\frac{16}{3}x-80+1[/tex]

y = [tex]\frac{16}{3}x-79[/tex]

Answer:

24 inches

Step-by-step explanation:

The perimeter of the shape is 36 inches since the other sides are given as 12 and 3, 6 will be left for the x

12 + 12 + 3 + 3 + x = 36 and x = 6

Susie then drew a square using part of this shape and one side of the square is x inches if one side is x then all fours sides will be x inches

so the perimeter of the square is 4 × x = 24 because we already know x = 6

All we need to do is substitute and solve.

A = P(1 + rt)

A = 5,100(1 + 0.035*60)

A = 5,100(3.1)

A = 15,810

Therefore, the answer is [ $15,810 ]

Best of Luck!

Answer:

x= 1/2

Step-by-step explanation:

Solving

Checking

Answer:

14 in base 10.

Step-by-step explanation:

working from right to left we have:

0 + 1*2 + 1*2^2 + 1*2^3

= 0 + 2 + 4 + 8

= 14.

Answer:

14

Step-by-step explanation:

trust me

Answer:

variable x has value = -9

Step-by-step explanation:

x − 56 = −65

we have to isolate x by separating it from  56 by using property of equality.

to isolate x, we add 56 on both sides of equation.

x − 56 + 56 = −65 + 56

=> x = -9

Thus, variable x has value = -9

Answer:

the answer is 2

Step-by-step explanation:

you subtract 10 by 8 and get 2, so w would be 2

Answer:

2

Step-by-step explanation:

w+8=10

Subtract 8 on both sides

w+8=10

   -8   -8

    w=2

Answer:

Verified

Area = 13.12 square units.

Step-by-step explanation:

Let the given points / vertices of the parallelogram be represented as follows:

A(2,-1,1),

B(5, 1,4),

C(0,1,1),

D(3,3,4)

In vector notation, we can have;

A = 2i - j + k

B = 5i + j + 4k

C = 0i + j + k

D = 3i + 3j +4k

One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.

(i) Now, let's find the various sides of the assumed parallelogram. These sides are:

AB = B - A = [5i + j + 4k] - [2i - j + k]            open the brackets

AB = 5i + j + 4k - 2i + j - k                            collect like terms and solve

AB = 5i - 2i + j  + j - k + 4k

AB = 3i + 2j+ 3k

BC = C - B = [0i + j + k] - [5i + j + 4k]            open the brackets

BC = 0i + j + k - 5i - j - 4k                             collect like terms and solve

BC = 0i - 5i + j  - j + k - 4k

BC = -5i + 0j - 3k

CD = D - C = [3i + 3j +4k] - [0i + j + k]            open the brackets

CD = 3i + 3j + 4k - 0i - j - k                             collect like terms and solve

CD = 3i - 0i + 3j  - j + 4k - k

CD = 3i + 2j + 3k

DA = A - D = [2i - j + k] - [3i + 3j +4k]            open the brackets

DA = 2i - j + k - 3i - 3j - 4k                             collect like terms and solve

DA = 2i - 3i  - j  - 3j + k - 4k

DA = - i - 4j - 3k

AC = C - A = [0i + j + k] - [2i - j + k]            open the brackets

AC = 0i + j + k - 2i + j - k                             collect like terms and solve

AC = 0i - 2i  + j  + j + k - k

AC = - 2i + 2j +0k

BD = D - B = [3i + 3j + 4k] - [5i + j + 4k]            open the brackets

BD = 3i + 3j + 4k - 5i - j - 4k                             collect like terms and solve

BD = 3i - 5i  + 3j  - j + 4k - 4k

BD = - 2i + 2j + 0k

(ii) From the results in (i) above, it has been shown that;

AB is equal to CD, and that implies that AB is parallel to CD. i.e

AB = CD => AB || CD

Also,

AC is equal to BD, and that implies that AC is parallel to BD. i.e

AC = BD => AC || BD

(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.

(B) Now let's calculate the area of the parallelogram.

To calculate the area, we find the magnitude of the cross product between any two adjacent sides.

In this case, we choose sides AC and AB.

Area = | AC x AB |

Where;

[tex]AC X AB = \left[\begin{array}{ccc}i&j&k\\-2&2&0\\3&2&3\end{array}\right][/tex]

AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)

AC X AB = 6i + 6j - 10k

|AC X AB| = [tex]\sqrt{6^2 + 6^2 + (-10)^2} \\[/tex]

|AC X AB| = [tex]\sqrt{36 + 36 + 100} \\[/tex]

|AC X AB| = [tex]\sqrt{172} \\[/tex]

|AC X AB| = 13.12

Therefore the area is 13.12 square units.

PS: The diagram showing this parallelogram has been attached to this response.

Answer:

1/5, 0.25, 3/10

Step-by-step explanation:

1/5=2/10= 0.2

3/10= 0.3

hopefully this is helpful

Answer:

0.25,1/5,3/10 is the order from last to greater.

Step-by-step explanation:

Hope it will help you :)

Answer: 7 units.

Step-by-step explanation:

Given: Point M is on line segment [tex]\overline{LN}[/tex].

So, point M must divide [tex]\overline{LN}[/tex] into [tex]\overline {LM}[/tex] and [tex]\overline{MN}[/tex].

Such that , [tex]\overline{LN}=\overline{LM}+\overline{MN}[/tex]   (i)

Since,  [tex]\overline{LM} = 5[/tex]  units and [tex]\overline{LN} =12[/tex] units  , then we will put values in (i), we will get

[tex]12=5+\overline{MN}\\\\\Rightarrow\overline{MN}=12-5=7[/tex]

Hence, the length of [tex]\overline{MN}[/tex] is 7 units.

Answer:

Step-by-step explanation:

Given,

A ( 3 , 5 ) ⇒( x₁ , y₁ )

B ( 1 , 3 )⇒( x₂ , y₂ )

Let's find the midpoint of the line:

[tex] \sf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2}) }[/tex]

plug the values

⇒[tex] \sf{( \frac{3 + 1}{2} \: , \frac{5 + 3}{2} )}[/tex]

Add the numbers

⇒[tex] \sf{( \frac{4}{2} \: , \frac{8}{2} )}[/tex]

Calculate

⇒[tex] \sf{(2 \:, 4 \: )}[/tex]

Hope I helped!

Best regards!

Answer:

Hi, explanation and picture Is below :)

Step-by-step explanation:

K would equal: K = {0, 2, 4, 6, 8, 10}

^^^ (that is in order)^^

That would be the correct expression.

The numbers ‘2 and 0’ are both repeated twice...

So if you want to make it as “members of set” you have to represent each one only once, for it to be members of set...

REVEIW:

Question, Represent the following numbers as being members of set K: 2, 4, 2, 0,6, 0, 10, 8....

Answer,  {0, 2, 4, 6, 8, 10}....

By: ✨RobloxYt✨

(Picture attached)

Answer:

Step-by-step explanation:

if it is converting its 7253/10000

to percent 72.53

scientific notation is 7.253 *10-1 the -1 is on top of the 10

Answer:

The probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

Step-by-step explanation:

Let the random variable X represent the miles-per-gallon rating of passenger cars.

It is provided that [tex]X\sim N(\mu=33.8,\ \sigma^{2}=3.5^{2})[/tex].

Compute the probability that a randomly selected passenger car gets more than 37.3 mpg as follows:

[tex]P(X>37.3)=P(\frac{X-\mu}{\sigma}>\frac{37.3-33.8}{3.5})[/tex]

                   [tex]=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]

Thus, the probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.

Answer:

Step-by-step explanation:

no. of black balls = 5

no. of white balls = 6

total no. of balls = 5 + 6 = 11

The probability of picking a white ball = 6/11

no. of red balls = 15

no. of black balls = 25

total no. of balls = 15 + 25 = 40

The probability of selecting a black ball = 25/40

by simplifying,

25/40 = 5/8

hope this helps

plz mark as brianliest!!!!!!!

Answer:

2 b + a

Step-by-step explanation:

Simplify the following:

2 (a + 2 b) - a - 2 b

2 (a + 2 b) = 2 a + 4 b:

2 a + 4 b - a - 2 b

Grouping like terms, 2 a + 4 b - a - 2 b = (4 b - 2 b) + (2 a - a):

(4 b - 2 b) + (2 a - a)

4 b - 2 b = 2 b:

2 b + (2 a - a)

2 a - a = a:

Answer: 2 b + a

Answer:

27.50

Step-by-step explanation:

Answer:

(-1/4, -5 3/4) or (-0.25, -5.75)

Step-by-step explanation:

Answer:

Commutative property

Step-by-step explanation:

In the Commutative property,the sequence or the order of factors of product does not change the value of the product.

Example:

in

12*5 = 5*12

also 12 = 3*4

(3*4)5 = (3*5)4

_____________________________

given

(2x)y = (2y)x

here it can be written as

(2*x)*y = (2*y)*x

removing the bracket for LHS we have

2*x*y ,    

applying Commutative property and changing order of x and y

2*x*y = 2*y*x

now again putting the bracket after first two terms

(2x)y = (2y)x

Thus, the expression illustrates Commutative property.

Let's first find the greatest common factor of 66 and 30.

To do this, start by dividing 66 by every natural

number you can until you hit repeat factors.

Also note, we need factors that are natural numbers! No decimals!

66 ÷ 1 = 66

66 ÷ 2 = 33

66 ÷ 3 = 22

66 ÷ 6 = 11

We can stop here because if we continue dividing, we hit repeat factors.

So the factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.

Now do the same for 30.

30 ÷ 1 = 30

30 ÷ 2 = 15

30 ÷ 3  = 10

30 ÷ 5 = 6

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Now look for the largest number shared by the two lists.

In this case, we have 6 as our gcf for the numbers.

Now let's do the variables.

To qualify for the Greatest Common Factor,

the variable must appear in every monomial.

Since the y doesn't appear in every monomial, it does not qualify.

If the variable does appear in every monomial, the Greatest

Common Factor will use the smallest power on that variable.

In this case, the smallest power between x and x² is x.

So our answer is 6x.

Answer:

Mark Me as Brainlieist

Step-by-step explanation:

6x

Answer:

The relationship is that the value of the linear correlation coefficient will always have the same sign as the value of the slope of a regression​ line.

Step-by-step explanation:

The slope of regression is simply the covariance between X and Y divided by the variance of X i.e Cov(X, Y)/Var X. Whereas, the correlation is the covariance divided by the product of the standard deviation. Thus, we can say that the correlation is the product of the gradient of the regression line and the ratio of the standard deviations.

Thus, it means when the correlation is positive, the slope is also positive and vice versa.

The sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Therefore, the sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.

Learn more about correlation coefficient on:

https://brainly.com/question/4219149

Answer:

dy/dx = 8x + 1

Step-by-step explanation:

dy/dx = 2(2x+1)*2 - 3

dy/dx = 4(2x + 1) - 3

dy/dx = 8x + 4 - 3

dy/dx = 8x + 1

Answer:

The first table represents a function.

Explanation:

This is a function because "x" does not have more than one number corresponding "y".

Answer:

y=x+8

Step-by-step explanation:

First you use the points (-3,5) and (2,10) to find the slope and you use the equation y2-y1/x2-x1.

So that gives you 10-5/2-(-3) which equals 1 (that's the slope)

Next you take one set of the points say (2,10) and then plug those numbers into the y=mx+b equation so you have x (2) and y (10) and the slope is m (1).

That gives you 10=1(2)+b

multiply 1*2 and you get 2 and then subtract 2 from both sides to isolate b and then b=8 and that gives you the answer

y=1x+8 or y=x+8