What is the simplified answer to 5.3. √2 ? 8√2 2/2 15√2​

Money received in tenth month: $104, as found by the formula of arithmetic progression.

The formula used here is recursive.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given: Money received in first four months: $50, $52, $55, %59.

To find: Money received in tenth month.

Finding:

As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.

That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.

Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+d[/tex], n ≥ 1.

For a₁ = 50, a₂ = a₁ + 2

=> a₂ = 50 + 2

This way, a₅ = a₄ + 5

=> a₅ = 59 + 5 = 64

a₆ = a₅ + 6

=> a₆ = 64 + 6 = 70

a₇ = a₆ + 7

=> a₇ = 70 + 7 = 77

a₈ = a₇ + 8

=> a₈ = 77 + 8 = 85

a₉ = a₈ + 9

=> a₉ = 85 + 9 = 94

a₁₀ = a₉ + 10

=> a₁₀ = 94 + 10 = 104

Thus, the payment received in tenth month will be $104.

The formula so used is recursive, as the consequent values of the given arithmetic sequence are obtained from the preceding values.

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Using common multiple, Jorge could have 31 pennies.

A common multiple is defined as a whole number, a shared multiple of each set of numbers. The common multiples of two or more prime numbers is the multiples of their product.

"when Jorge arranges his pennies into a rectangle with two equal rows, three equal rows, or five equal rows, he has one leftover penny"

Find the common multiples of 2, 3, and 5, and add 1.

Since 2, 3, and 5 are prime numbers, their common multiples are the multiples of their product.

Common multiples : 30, 60, 90, . . .

n = possible number of Jorge's pennies = 31 or 61 or 91 . . .

"when he arranges his pennies into a rectangle with four equal rows, he has three leftover pennies"

Find the common multiples of 4 and add 3.

multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, . . .

n = possible number of Jorge's pennies = 7, 11, 15, 19, 23, 27, 31, 35, . . .

31 ÷ 2 = 15 r 1

31 ÷ 3 = 10 r 1

31 ÷ 5 = 6 r 1

31 ÷ 4 = 7 r 3

Hence, Jorge could have 31 pennies.

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The equation of the polynomial is -

f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex].

We have a polynomial function whose graph intercepts the horizontal axis at -7, 8, and 15.

We have to identify the polynomial.

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

According to the question -

x = -7, 8, 15 are the horizontal or the x - axis intercepts of the graph of the polynomial.

This means for -

x = -7

x = 8

x = 15

the polynomial (say f(x)) is equal to 0.

Therefore, x = -7 , x = 8 and x = 15 are the solutions of the polynomial f(x).

Then -

(x + 7) , (x - 8) and (x - 15) are the factors of this polynomial. Therefore -

f(x) = (x + 7)(x - 8)(x - 15)

f(x) = [tex](x^{2} -x-56)(x-15)\\[/tex]

f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex]

Hence, the equation of the polynomial is -

f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex]

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The measure of m∠RQS and m∠PQR is the line QS bisects ∠PQR  and m∠PQS=63° are 63 and 126 degrees.

The line or line segment that divides an angle into two equal pieces is known as the bisector of an angle, also known as the internal angle bisector. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

If line QS bisects ∠PQR, then;

<PQS = <RQS

WE have Given the following parameter;

m∠PQS=63°

Hence <PQS = <RQS = 63 degrees

Also,

<PQR = <PQS + <RQS

<PQR = 63 + 63

<PQR = = 126 degrees

The measure of m∠RQS and m∠PQR is the line QS bisects ∠PQR  and m∠PQS=63° are 63 and 126 degrees respectively

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The function f(x) = |x| + 5 undergoes horizontal shrinking by a factor of 3 to get; f(x) = |¹/₂x| + 5

There are different ways of transforming a function such as dilation, translation, reflection, stretching, shrinking e.t.c

Now, To stretch or shrink the graph in the y direction, what needs to be done is to multiply or divide the output by a constant. Now, f(2x) simply means that the function f(x) is stretched in the x direction by a factor of 2,. Meanwhile, f(¹/₂x) means that the function f(x) is shrunk in the x direction by a factor of 2 (or stretched by a factor of ¹/₂).

Now, we are told that the function f(x) = |x| + 5 undergoes horizontal shrinking by a factor of 3. Applying the above rule for shrinking gives us;

f(x) = |¹/₂x| + 5

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I bought 3 one-pound bags of peanuts and 2 three-pound bags of peanuts.

Firstly forming the equation according to the given information in question. Let us represent one-pound bags of peanuts with x and three-pound bags of peanuts with y.

Equation based on number of bags bought -

x + y = 5 - Equation 1

Rearranging equation 1 according to x

x = 5 - y - Equation 2

Equation based on cost of bags -

2x + 5.5y = 17 - Equation 3

Keep the value of x from Equation 2 in Equation 3

2 (5 - y) + 5.5y = 17

Performing multiplication of brackets

10 - 2y + 5.5y = 17

Rearranging the equation and performing subtraction

3.5y = 7

Shifting 3.5 to denominator on Right Hand Side of the equation

y = 7 ÷ 3.5

Performing division

y = 2

Calculating value of x by keeping value fo y in Equation 2

x = 5 - 2

x = 3

Thus, I bought 3 one-pound bags of peanuts and 2 three-pound bags of peanuts.

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Answer: 65

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

65 because the other guy said it and im taking the test rn and i put that as my answer. and im answering this now cause i know i wont get back to it

omg jk its 82

wow im glad i actually tried to solve it..

but yeah

Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.

x=82

thats the best i can do to explain cause im lazy

Good luck

The solution to given equation 2(5 - 10x) + 8x = -19x + 52 is x = 2

In this question, we have been given an equation:

2(5 - 10x) + 8x = -19x + 52

We need to solve given equation for x.

2(5 - 10x) + 8x = -19x + 52                 ................(Given equation)

10 - 20x + 8x = -19x + 52                   ................(Evaluate the bracket )

10 - 12x + 19x = 52                             ...............(Add 19x on each side)

10 + 7x = 52

7x = 52 - 10                                        ...............(Subtract 10 from each side)

7x = 42

x = 42/7                                              ..............(Divide each side by 7)

x = 6                                                

Therefore, the solution to given equation 2(5 - 10x) + 8x = -19x + 52 is       x = 2

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(-5,8) would be in quadrant 1

Probability that a fifth bird landing at a randomly selected point between birds 1 and 4 will sit at some point between birds 3 and 4 is 1/3.

As given,

Total number of birds sitting on a telephone wire=4

Possible sitting arrangement is

Bird1__Bird2 __Bird3___Bird4

Total possible number of space between birds 1 to 4=3

Possible favourable outcomes (between 3 and 4)=1

Probability fifth bird sitting between point 3 and 4

= (Number of favourable outcomes)/ Total number of outcomes

= 1/3

Therefore, probability of a fifth bird sitting at some point between birds 3 and 4 is 1/3.

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Two expressions with an equal sign in between is Equation, The given equation is 168>= 7x+4y, when we solve it for y we get y<=42-7x/4..

What is Equation?

Two expressions with an equal sign in between is called as Equation.

The given equation is

168>= 7x+4y

Now we need to make y as independent variable.

Subtract 7x on both the sides

168-7x>=7x-7x+4y

168-7x>=4y

Now divide both side by 4.

42-7x/4>=y

Therefore the value of y is 42-7x/4, y<=42-7x/4.

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Answer:

each part will be half a meter or fifty centimeters

Step-by-step explanation:

divide the total length by ten to find the individual part.

Answer:

Another way to ask this question would be “what is the fraction 24 out of 100 in simplest form?”

The simplest ratio that is equivalent is six out of 25. The denominator represents the total number of students and six of them are left-handed. So the smallest possible class size is 25. Any number smaller than that would result in a numerator that is not a whole number.

Mark me brainly <3

Answer:

x=46 and y=42

Step-by-step explanation:

make 2y+6 equal to 8y-102 to solve for y as they are vertically oppisate angles which make them equal.

then substitute the new value for y into either expression and solve x using the rule a straight line is equal to 180.

The value of the expression 2(2x²-x)-3(x²-x)+x²-x at  x=3 is 18.

An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).

According to the question  

2(2x²-x) - 3(x²-x) + x²-x

Since we do not have to simplify the expression before evaluating it we will substitute the value of x=3 in the above expression .

=2(2*3² -3)-3(3² -3)+3²-3

=2(2*9-3)-3(9-3)+9-3

=2(18-3)-3(6)+6

Simplifying further we get

=2(15)-18+6

=30-18+6

=36-18

=18

Therefore , the value of the expression 2(2x²-x)-3(x²-x)+x²-x for x=3 is 18.

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Answer:

1

Step-by-step explanation:

6^5x1/6^5

6^5 = 6*6*6*6*6 = 7776

7776x1/6^5          7776x1 = 7776

7776/7776= 1

x⁴y² - 6x³y³

x⁴ = x² × x²

y² = y²

x³ = x² × x¹

y³ = y² × y¹

Answer:

[tex]-\frac{67}{100}[/tex]

Step-by-step explanation:

Answer:

67/100

Step-by-step explanation:

0.67/1×100/100=67/100

if wrong i tried T^T

The equation of the line in slope-intercept form passing through the point (-2 , 1) and perpendicular to 3x + y = 1 is y = (1/3)x + 5/3.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

If the line is perpendicular to 3x + y = 1, then their slopes are negative reciprocal of one another. To get the slope, m, of the equation, express it in slope-intercept form.

3x + y = 1

y = -3x + 1

m = -3

m = 1/3

Substitute the values of the slope and the point to solve for the y-intercept, b.

y = mx + b

1 = 1/3(-2) + b

b = 5/3

Write the equation of the line by plugging in the value of the slope and y-intercept.

y = mx + b

y = (1/3)x + 5/3

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Answer:

Step-by-step explanation:

a. 0.5+0.3 = 0.8

b. 2.7+28.2 = 30.9

c. 3.1+2.4+9.9 = 15.4

d. 15.2+1.4+0.8 = 17.4

e. 39.2+2.5+0.9 = 42.6

The proportional relationship between the fees paid and the number of months is given by:

y = 70x.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

k is the constant of proportionality for both cases.

For this problem, the time and the fees are direct proportional, that is, the fee increases as the number of months increase.

Over a 5 month period, he has paid $350 to his neighborhood homeowners association in monthly fees, hence the constant is found as follows:

k = 350/5 = 70.

Hence the proportional relationship between the fees paid and the number of months is given by:

y = 70x.

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Answer:

Step-by-step explanation:

y]yyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answer:

I think the answer is 92 lines because of the regularity of the figure

On solving the equations, the total cost is 25.86.

The cost of ham is $4.80 a pound.

The cost of cheese is $6.3 for a pound.

Cheese weighing pounds was provided for $14.76.

Let "a" represent the cost of a pound of ham, and "b" represent the cost of a pound of cheese.

Given the available information,

1.3a + 0.8b = 11.28 —— (1)

1.50 +1.2b = 14.76 —— (2)

From the equation now (1).

11.28 -0.8b 1.3 (3)

Now, using equations (2) and (3), we obtain the following: 11.28 0.8 b. 1.3)+1.2 b. 14.76. 12.97 0.92 b+1.2 b. 14.76 0.28 b. 1.79 b. 6.3

The result of adding the value of b to equation (3) is 11.28 0.8. (6.3)

1.3 a = 4.8

The cost of ham is $4.80 a pound.

The cost of cheese is $6.3 for a pound.

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The value of x for the equation 1/4 - x = x/8 is x = 2/9.

According to the given question.

We have an equation 1/4 - x = x/8.

As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Here, we have to find the solution of the equation 1/4 - x = x/8 for x.

So, the solution of the given equation 1/4 - x = x/8 for x is given by

1/4 - x = x/8

⇒ 1/4 = x/8 + x           (adding x both the sides)

⇒ 1/4 =  x + 8x/8  

⇒ 1/4 = 9x/8

⇒ (1/4)(8)  = 9x

⇒ 2 = 9x

⇒ x = 2/9           (dividing both the sides by 9)

Hence, the value of x for the equation 1/4 - x = x/8 is x = 2/9.

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Range - { 6, 7, 8,9 ,10, 11 } is the domain and range of this relation.

What is domain and range in math?

How are the domain and range determined?

the domain and range of this relation -

Domain - { 1 , 2, 3, 4, 5, 6 }

Range - { 6, 7, 8,9 ,10, 11 }

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Suppose the given number is 3.441

The first 4 is in the tenth place that is written like  or 0.4

The second 4 is in the hundredth place that is written like  or 0.04

We can see that the second 4 is one tenth times the first 4.

This is shown like,

1/10 x 1/10 =  1/100

Or we can say the opposite that the first 4 is ten times the second 4.

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The simplified expression of (−3x − 12) + (16 + 8x) is 5x + 4 (option A).

A mathematical expression is when numbers and variables are combined together using mathematical symbols. A mathematical expression does not have an equal to sign.

To simplify an expression means to use the fewest possible terms. In order to simplify the expression, the BODMAS rule would be made use of. The BODMAS rule provides the procedure for solving mathematical expressions. According to the rule, terms in the bracket would be solved first.

Addition is the process of determining the sum of numbers. The sign used to represent addition is +. Subtraction is the process of calculating the difference between two or more numbers. The sign used to represent subtraction is -.

(−3x − 12) + (16 + 8x)

The first step is to combine similar terms together: (-3x + 8x) (-12 + 16)

Add similar terms together: 5x + 4

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The standard form of the given equation is y = -2/5(x + 10).

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

y = -2/5x + 4

We know that the given equation is of parabola.

Thus, converting it to the standard form of parabola,

y = a(x-h)^2 + k

where (h, k) is the vertex .

Now we have,

y = -2/5x + 4

Thus, multiplying both the side the given equation by 5 we get,

5y = (-2/5x + 4)*5

Expanding the brackets we get,

5y = -2*5/5x + 4*5

Solving we get

5y = -2x + 20

Now factoring R.H.S we get,

5y = -2x + 2*10

Taking common we get,

5y = -2(x + 10)

Dividing both the side by 5 we get,

5y/5 = -2(x + 10)/5

Solving we get,

y = -2/5(x + 10)

thus is the required standard form of the given equation.

Thus, the standard form of the given equation is y = -2/5(x + 10).

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Tables cost $800 each, while chairs go for $200 each in an online furniture retailer. The store must sell at least $8000 worth of chairs and tables each day and can only ship a maximum of 19 pieces of furniture per day. Find the bare minimum of tables that the shop must sell to satisfy the requirements if 7 chairs were sold.

If  chairs were sold, the minimum number of tables that the store must sell in order to meet the requirements is 4 tables.

Let x be number of chairs

y be number of tables

Given every day, the store can ship at most 19 pieces of furniture

Then we can write x+y=19--------->equation(1)

Given an online furniture store sells chairs for $200 each and tables for $800 each.

200x is the revenue of number of chairs.

800y is the revenue of number of tables.

And given must sell a minimum of $8000 worth of chairs and tables.

Then we can write 200x+800y=8000---------->equation(2)

We have to find out If 7 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements.

When x=7 what is y=?

By substituting x=7 in equation (1)

7+y=19

y=19-7

y=12

Now, substitute the x=7 in equation(2)

200(7)+800y=8000

1400+800y=8000

800y=8000-1400

800y=6600

y=[tex]\frac{6600}{800}[/tex]

y=8.25

y=9

We got 2 required values when x=7.

They are y=9 and y=12.

Therefore, the possible values we get are y=9,10,11,12.

If  chairs were sold, the minimum number of tables that the store must sell in order to meet the requirements is 4 tables.

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Using the distance formula, the distance between the points M(1,-2) and N(9,13) is 17 units

Given,

The points = M(1,-2) and N(9,13)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

[tex]=\sqrt{(9-1)^{2}+(12--3)^{2} } \\=\sqrt{8^{2}+15^{2} } \\=\sqrt{64+225}\\ =\sqrt{289}[/tex]

=17 units

Hence, Using the distance formula, the distance between the points M(1,-2) and N(9,13) is 17 units

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