Solve for y;
7(3y - x) = -21

Answer: x = 5, 7

Step-by-step explanation:

       This equation is already factored for us, so we can split it into two separate equations set equal to 0 and solve for x.

Given:

(x - 7)(x - 5) = 0

Equation #1:

x - 7 = 0

x = 7

Equation #2:

x - 5 = 0

x = 5

Solution:

x = 5, 7

Answer:

x = 5, x = 7

Step-by-step explanation:

(x - 7)(x - 5) = 0 ← in standard factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x - 5 = 0 ⇒ x = 5

Answer:

2(x + 6) = 38

Step-by-step explanation:

First, we choose a variable to represent the unknown number.

1. Let x = the unknown number.

Then, we translate the sentence into an equation using the variable we chose.

"Twice the sum of six and a number is 38."

We do it piece by piece:

"the sum of six and a number":                        x + 6

"Twice the sum of six and a number":              2(x + 6)

"Twice the sum of six and a number is 38.":    2(x + 6) = 38

Now we have an equation that represents the sentence.

2(x + 6) = 38

Determine whether each infinite geometric series diverges or converges.The series converges.

If the series converges, state the sum. 1-1+1- . . . .

The sum of the infinite series is 1/2

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=1\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{-1}{1}=-1[/tex]

Since  [tex]\vert r\vert < 1[/tex] , the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{1}{1+1} =\frac{1}{2}[/tex]

The sum of the infinite series is 1/2

What is an infinite geometric series?

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By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b

Given,

The algebraic expression = 7b-(3a-8b)

Expand the expression

7b-(3a-8b)= 7b-3a+8b

Rearrange the terms and combine like terms

7b-3a+8b= -3a+7b+8b

=-3a+(7+8)b

=-3a+15b

Hence, By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b

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This is recursive sequence and -121,-108,-95,-82,-69,-56 these are the first five terms of sequence.

A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:

1. The initial term in the series.

2. The general rule for determining any term from its preceding term.

Recursive Arithmetic Sequence Formula

The following is the recursive formula to determine the nth term in an arithmetic series:

an = an-1 + d for n ≥ 2

where

The common difference is d, and an is the nth term of an A.P.

given that

a₁ = -121

a (n) =a (n-1) +13 so, d = +13

For example, we need to extend the sequence term by term in order to find the first five terms:

a(1) = -121

a(2) = a(1) + d = -121 + 13 = -108

a(3) = a(2) + d = -108 + 13 = -95

a(4) = a(3) + d = -95 + 13 = -82

a(5) = a(4) + d = -82 + 13 = -69

a(6) = a(5) + d = -69 + 13 = -56

a(7) = a(6) + d = -56 + 13 = -43

Hence,this is recursive sequence and -121,-108,-95,-82,-69,-56 these are the first five terms of sequence.

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Answer: 3 ft

Step-by-step explanation:

l=length. w=width. h=height. V=volume

V=l*w*h

24=4*w*2

24=8*w

8w=24

w=3 ft

Answer:

perimeter=4l then multiply with how many square are there

then area = l²

multiple with how many square are there

What is Irrational Number?

An Irrational number is areal number that cannot be expressed as a ratio of integers; for example [tex]\sqrt{2}[/tex] is an irrational number. We cannot express any irrational number in the form of ratio, such as p/q, where p and q are integers, q[tex]\neq[/tex] 0. Again, the decimal expansion of an irrational number in neither terminating nor recurring.

Let us assume [tex]7\sqrt{56}[/tex] is rational.

So, we can write this number as

[tex]7\sqrt{56}[/tex] = a/b __(1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) divide by 7 both sides, we get

[tex]\sqrt{56}=\frac{a}{7b}[/tex]

Here, a and b are integers, so a/7b is a rational number, so [tex]\sqrt{56}[/tex] should be a rational number.

But [tex]\sqrt{56}[/tex] is a irrational number, so it is Contradictory.

Therefore, [tex]7\sqrt{56}[/tex] is irrational number.

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A geometric series exist as the totality of an infinite number of terms that contain a constant ratio between consecutive terms.

The sum of the infinite series is 1/4.

The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.

The equation be S = a1/(1-r), where s is the total, a1 is the series first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Given: a(first term) = 1/3

r(common  ratio) = a2/a1

= (-1/9)/(1/3) = -1/3

Since | r | ∠ 1, the infinite series converges.  

The sum of infinite geometric series is:

S∞ = a/(1 - r); -1 ∠ r ∠1

S∞ = (1/3) / (1+(1/3)) = 1/4

The sum of the infinite series is 1/4.

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The probability she will spell the word MATH P(MATH) is  1/12

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Given ; Alana has the letter tiles A, H, M , and T in a bag. If she selects a permutation of the tiles at random.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

Permutations of "MATH"

4P4 = 4! = 24

Two of the 'MATH" s we can get as a result

Then the probability she will spell the word MATH

P(MATH) = 2/24 = 1/12

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The ratio of trick-or-treaters who were not dressed as snow white last Halloween is 5/9

Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.

It can be expressed in different ways:

1) Use the ":" to separate the values : a : b

2) Use the word "to" : a to b

3) Write it in fraction: a / b

On the other hand, proportion is the equality of two or more ratios.

example: a : b = c : d

If four out of every nine trick-or-treaters that came to your house last Halloween were dressed as snow white, then the rest were not dressed as snow white.

9 - 4 = 5

If five out every nine trick-or-treaters that came to your house last Halloween were not dressed as snow white, we can express the ratio as

5 out of 9 or 5 : 9 or 5/9

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The measures of the angle and it's supplement are144°  and 36° respectively.

The measure of the supplement of an angle is four times the measure of the angle. (given)

Let us consider the value of the supplement be X°.

Therefore the value of the angle  is 4X°

 180 - X = 4X

  X = 36° (The value of supplement)

180°-X = 144°( The value of angle)

Hence the angles are 36° and 144° .

The measures of the angle and it's supplement are144°  and 36° respectively.

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Answer:

skewed right, mean > median

Step-by-step explanation:

just did it

Answer:

skewed right, mean>median

Step-by-step explanation:

edge 2023

cot(55°) = 0.70021 ... cot(58°) = 0.62487 ... cot(77°) = 0.23087 ... cot(80°) = 0.17633

(1+cot55)(1+cot80)(1+cot77)(1+cot58).

In trigonometry, the cot or cotangent is one of the six trigonometric ratios. In a right triangle, the lattice of angles is equal to the ratio of the adjacent and opposite sides of the angle. Cot x is also equal to the reciprocal of tan x.

Therefore, the cotangent of the angle α of a right triangle is equal to the length of the adjacent side b divided by the opposite side a. To remove the crib, simply enter the length of the adjacent and opposite sides, then remove it. This formula can be very similar to the formula used to calculate the tangent.

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Answer:

100 m/s

Step-by-step explanation:

divide by 3.6 to get km/h to m/s, multiply by 3.6 to get m/s to km/h!

Answer: Evaluate

6w=180

Divide both sides

6

6w = 6

180

​

Simplify

6

6w =30

Solution

w=30

Step-by-step explanation: hope this helps

Answer:

108°

Step-by-step explanation:

Since angle WYT and angle UYW lie on the same line, we can use linear pair fidn the answer.

That is: 180-72= angle UYW

Therefore angle UYW=108°

-Hence proved:)

The estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.

It follows from the task content that the estimated thickness of paper such that it is written using a single digit and a power of 10 as required in the task content is to be determined.

Given;

Thickness of sheet = 0.0013.

By rounding to one significant digit; the digit is considered and rounded down to zero which is added to 1 so that we have;

= 0.001.

On this note, since the number, 0.001 can be written via the laws of indices as;

= (1/1000)

= 1/10³

And ultimately, we have

= 1 × 10-³.

Ultimately, the estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.

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The distance between Amy's initial and final position is 1 mile and she is facing South direction

It is given that,

Amy first moves towards East direction in reference to her initial position  for 2 miles

The distance covered by Amy in East direction = 2 miles

Then,

Amy moves towards South direction in reference to her initial position(facing East side) for 3 miles

The distance covered by Amy in South direction = 3 miles

We need to find,

The distance between Amy's initial and final position which will be given by the displacement between both points

Let's say that the positive direction is East and the negative direction is south.

The distance covered by Amy in East direction = + 2 miles

The distance covered by Amy in South direction = - 3 miles

Then , +2 +(-3) = -1

Hence, the distance between Amy's initial and final position is 1 mile and she is facing South direction

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Answer:

No Because 1/1 : 3/4 = 4/3 and 1/3 : 4/1 = 1/12

Given events are independent events and the probability that getting an even number on die and getting odd number on a spinner numbered 1 to 5

In this question,

we have been given two events.

Let event A: rolling an even number on a die

event B: spin a spinner numbered 1 through 5 and get an odd number.

We can clearly observe that the occurrence of event A is not dependent on the other event B.

So, event A and event B are independent events.

The probability of event A is,

P(A) = n(A) / n(S)

here, sample space, n(S) = 6

n(A) = 3

So, P(A) = 3/6

P(A) = 1/2

The probability of event B is,

P(B) = n(B) / n(S)

here, sample space, n(S) = 5

n(B) = 3

So, P(B) = 3/5

Now we find the joint probability of these independent events.

⇒ P = P(A) × P(B)

⇒ P = 1/2 × 3/5

⇒ P = 3/10

Therefore, given events are independent events and the probability that getting an even number on die and getting odd number on a spinner numbered 1 to 5

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Answer:

Midpoint = (-1, 5)

Step-by-step explanation:

                     x₁  +  x₂         y₁   +   y₂

Midpoint = (--------------- , -----------------)

                          2                   2

                     -4  +  2         5  +   5

Midpoint = (--------------- , -----------------)

                          2                   2

                         -2                  10

Midpoint = (--------------- , -----------------)

                          2                   2

Midpoint = (-1, 5)

I hope this helps!

Answer:

48

Step-by-step explanation:

ABC is a right triangle so the masure of ∠A = 90°

The sum of interior angles in a triangle is equal to 180 so we will write an equation accordingly to find the

missing angle:

90 + 2x + 14 + 4x - 26 = 180 add like terms

78 + 6x = 180 subtract 78 from both sides

6x = 102 divide both sides by 6

x = 17

Now replace x with 17 to calculate the measure of m∠B

2*17 + 14 = 48

The probability that a particular one of them will sit in the chair closest to the dance floor is 1/4.

Linear Permutation:

Linear permutation defines the number of ordered arrangement of objects in a line while circular permutations is an ordered arrangement of objects in a circular manner.

Given,

Four friends are sitting at a table together at the prom.

Here we need to find  the probability that a particular one of them will sit in the chair closest to the dance floor.

Since the samples are arranged with a fixed reference point, this is a linear permutation.

So there are 4! or 24 ways in which the samples can be arranged.

The number of favorable outcomes is the number of permutations of the other 3 people given that a particular one of them will sit in the chair closest to the dance floor, 3! or 6.

Therefore, the probability is

=> 6/24

=> 1/4.

Therefore, the probability that a particular one of them will sit in the chair closest to the dance floor 1/4.

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The midpoint is at (1/2 , -3, 7/2 )

In the given statement is

To find the midpoint of the line segment joining the pair of points

P(-2,-5,8) and Q(3,-2,-1)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] ,[tex]\frac{y_{1}+y_{2} }{2}[/tex] , [tex]\frac{z_{1}+z_{2} }{2}[/tex])

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points P(-2,-5,8) and Q(3,-2,-1)

Solving for the midpoint , we have,

m = ([tex]\frac{-2 + 3}{2} , \frac{-5+ (-2)}{2} , \frac{8 +(-1)}{2}[/tex])

m = (1/2 , -3, 7/2 )

Therefore, the midpoint is at (1/2 , -3, 7/2 )

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Answer:

7+4 (11)

Step-by-step explanation:

I think you are asking about an equation that looks like this

x^7*x^4

When multiply exponents they are added together and the sum is what the new exponent is.

7+4=11

11 is the new exponent

x^11

So I believe the answer would be 7+4? But I don't fully understand what your question is.

The common ratio of the geometric sequence 4, 10, 25, 62.5, . . . is 2.5. The answer is B.

A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a common ratio.

a(n) = a r^(n-1)

Where:

a(n) = nth term

a = first term

r = common ratio

The common ratio must be the same for all pairs of succeeding term to be called a geometric sequence.

To find the common ratio, use the formula

a(n) = a r^(n-1)

let n = 2, a = 4, a(2) = 10

10 = 4(r^(2 - 1)

10 = 4(r)

r = 2.5

Or just simply divide each succeeding pairs of the sequence.

r = 10/4 = 2.5

r = 25/10 = 2.5

r = 62.5/25 = 2.5

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The given conditional statement is true that is  If a number is divisible by 6, then it is divisible by 3".

A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as;

p⇒q, and read  "if p then q"

An example of a conditional statement is : p⇒q, that is:

if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that AB^2 = BC^2 + AC^2

"If a number is divisible by 3, then it is divisible by 6." is the inverse of the conditional statement "

Thus If a number is divisible by 6, then it is divisible by 3".

Therefore, the given conditional statement is true that is  If a number is divisible by 6, then it is divisible by 3".

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P'''( 1 , -2 )     Q'''( 0 , 1)   R'''( -1 , 3 )    S'''( -2 , 0) are the coordinates of P''' Q''' R''' S''' .

What does the term "coordinates" mean?

( x , y)  →  ( x + 3 , y - 2 )

p' ( -2, -1 )     Q' ( 1 , 0)    R'( 3, -3 )   S'(0, -4 )

( x , y )  →   ( x , -2 - y)

p''(-2 , - 1 )   Q''( 1 , 0 )     R''( 3 , 1 )      S''( 0,2 )

( X , Y ) →  ( -Y , X )

P'''( 1 , -2 )     Q'''( 0 , 1)   R'''( -1 , 3 )    S'''( -2 , 0)

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The given equations are

[tex]x-2y=4[/tex]                               …(1)

[tex]3x+y=4[/tex]                               …(2)

Using Substitution method,

From the equation (1) [tex]x-2y=4[/tex] , the value of x is

= [tex]x=4+2y[/tex]

Putting the value of x in equation (2), we get

= [tex]3(4+2y)+y=4[/tex]

= [tex]12+6y+y=4[/tex]

= [tex]12+7y=4[/tex]

= [tex]7y=-8[/tex]

= [tex]y=-\frac{8}{7}[/tex]

Now, putting the value of y in equation (1), we get

= [tex]x-2(-\frac{8}{7}) =4[/tex]

= [tex]x+(\frac{16}{7}) =4[/tex]

= [tex]x =4-(\frac{16}{7})[/tex]

= [tex]x =(\frac{28-16}{7})[/tex]

= [tex]x =(\frac{12}{7})[/tex]

∴ The value of x is [tex]\frac{12}{7}[/tex] and the value of y is [tex]-\frac{8}{7}[/tex]

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The value of x is (12/7) and the value of y is (-8/7) for the given equation.

The given equations are

x - 2y = 4                              equation (1)

3x + y = 4                             equation (2)

Using Substitution method,

From the equation (1) i.e., x - 2y = 4 , the value of x is

x = 4 + 2y

Putting the value of x in equation (2), we get

3 ( 4 + 2y ) + y = 4

⇒ 12 + 6y + y = 4

⇒ 12 + 7y = 4

⇒ 7y = (-8)

⇒ y = (-8/7)

Now, putting the value of y in equation (1), we get

x - 2 ( -8/7 ) = 4

⇒ x + ( 16/7 ) = 4

⇒ x = 4 - ( 16/7 )

⇒ x = ( 28 - 16 )/ 7

⇒ x = 12/7

∴ The value of x is (12/7) and the value of y is (-8/7).

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