solveing systems of equations by substitution y=6x-11 -2x-3y=-7

Exact Form: √3/3

Decimal Form: 0.57735026

sorry if i got it wrong, i tried my best on this :)

The value of the expression tan π/6 is √3/3 or approximately 0.5774.

The value of the expression tan π/6 is √3/3 or approximately 0.5774.

To find this value, we can remember that tan θ = sin θ / cos θ. So, tan(π/6) = sin(π/6) / cos(π/6).

Thus, tan(π/6) = (√3/2) / (1/2) = √3/3.

Answer:

The equation of the line is y = -2x + 7

Step-by-step explanation:

* Lets study how to make an equation of the line from two point

- If the line passes through points (x1 , y1) and (x2 , y2)

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the line intersect the y-axis at point (0 ,c)

* Now lets solve the problem

∵ The line passes through points (-3 , 13) and (4 , -1)

- Let (-3 , 13) is (x1 , y1) and (4 , -1) is (x2 , y2)

∵ m = (y2 - y1)/(x2 - x1)

∴ m = (-1 - 13)/(4 - -3)

∴ m = (-14)/7 = -2

- Lets write the form of the equation

∵ y = mx + c ⇒ substitute the value of m

∴ y = -2x + c

- To find the value of c use one of the two points to substitute the

  values of x and y in the equation

∵ The line passes through (4 , -1)

∴ -1 = -2(4) + c

∴ -1 = -8 + c ⇒ add 8 to both sides

∴ -1 + 8 = -8 + 8 + c

∴ 7 = c

∴ y = -2x + 7

* The equation of the line is y = -2x + 7

Answer:

the answer is A and C

Step-by-step explanation:

Answer:

A=1/2 h(b1+b2)

Step-by-step explanation:

h being the height and b1 being base one and b2 being base two

Answer:

The correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5

Step-by-step explanation:

Points to remember

The angles of a right angled triangle, 30°, 60° and 90° then sides are in the ratio, 1: √3 : 2

To find the value of variables

From the figure we can see 2 right angled triangle with angle 30, 60 and 90

we get, d= 5 then b = 5√3

b = 5√3  the c = 5√3 * √3 = 15

and a = 2 * 5√3 = 10√3

Therefore the correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5

Answer:

d.[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]

Step-by-step explanation:

We have to find the value of each variable.

[tex]\frac{P}{H}=sin\theta[/tex]

[tex]\frac{b}{10}=sin 60^{\circ}[/tex]

[tex]\frac{b}{10}=\frac}\sqrt3}{2}[/tex]

[tex]b=10\times \frac{\sqrt3}{2}=5\sqrt3[/tex]

[tex]\frac{d}{10}=cos 60^{\circ}[/tex]    ([tex]cos\theta=\frac{base}{hypotenuse}[/tex])

[tex]d=\frac{1}{2}\times 10=5[/tex]

[tex]\frac{b}{a}=sin30^{\circ}[/tex]

[tex]\frac{5\sqrt3}{a}=\frac{1}{2}[/tex]

[tex]a=10\sqrt3[/tex]

[tex]\frac{b}{c}}=tan 30^{\circ}[/tex]   ([tex]tan\theta=\frac{p}{b}[/tex])

[tex]\frac{5\sqrt3}{c}=\frac{1}{\sqrt3}[/tex]

[tex]c=5\sqrt3\times \sqrt3=15[/tex]

[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]

Hence, option d is true.

Answer:$4.23

Step-by-step explanation:

Answer:

4.23 is the answer if its wrong let me know what mistakes i made

No 5/8 is bigger because half of 8 is 4 and 5 is greater than 4

In comparing 1/2 gallon and 5/8 gallon, using equivalent fractions shows that 5/8 gallon is larger than 1/2 gallon.

In the comparison of 1/2 gallon and 5/8 gallon, it's important to remember that fractions provide a way of representing parts of a whole. With fractions, the numerator represents the part while the denominator represents the total parts. So here, the fraction 5/8 represents 5 parts of a total 8 parts, where 1 gallon is considered the 'whole' or 'total' amount.

To determine if 1/2 is greater or less than 5/8, we want to make the denominators the same for comparison. Multiply the numerator and the denominator of the first fraction (1/2) by four to get it to the same denominator as the second one. This results in 4/8 for the first fraction.

Now, comparing 4/8 and 5/8, we find that 5/8 is greater than 4/8. Therefore, 5/8 gallon is indeed more than 1/2 gallon.

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Answer:

C. 17 - 12 = d + 12 - 12

Step-by-step explanation:

You need to get d by itself and in order to do that you need to subtract 12

Answer:

8 Batches

Step-by-step explanation:

Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.

She make total number of 8 batches.

Amount of sugar required per batch =  [tex]\frac{2}{3} [/tex] cup

Since, Elena used [tex]5\frac{1}{3} [/tex]  cups of sugar to make multiple batches of cookies.

To find number of batches she make, divide total amount of sugar by amount of sugar per batch.

Number of batches she make,

                             [tex]=5\frac{1}{3}\div\frac{2}{3}\\ \\ =\frac{16}{3}*\frac{3}{2}=8 [/tex]

Hence, She make total number of 8 batches.

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The simplified expression is 3.5r - 7.

To simplify the expression 6.4r - 7 - 2.9r, first, combine like terms by subtracting the coefficients of 'r'.

This yields (6.4 - 2.9)r. Simplifying the coefficients gives 3.5r. Then, subtract 7. Therefore, the simplified expression is 3.5r - 7.

This means that when you distribute the 'r', you multiply it by 3.5, then subtract 7 from the result.

The simplified expression is 3.5r - 7.

Complete question :- Simplify 6.4r - 7 - 2.9r.

Answer:

1. 0.09

2. 0.21

3. 0.49

Step-by-step explanation:

If the probability that Yuri will make a free throw is 0.3, then the probability that Yuri will not make a free throw is 1-0.3=0.7.

1. The probability that Yuri will make two consecutive free throws is

[tex]0.3\cdot 0.3=0.09[/tex]

2. The probability that he will make the first and not the second in two free throws is

[tex]0.3\cdot 0.7=0.21[/tex]

3. The probability that he will make neither of the two free throws is

[tex]0.7\cdot 0.7=0.49[/tex]

Answer:

0.78

Step-by-step explanation:

Divide: 5/18

ANSWER

[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]

EXPLANATION

The given function is

[tex] {x}^{4} + 8 {x}^{2} - 9[/tex]

Split the middle term

[tex] {x}^{4} + 9 {x}^{2} - {x}^{2} - 9[/tex]

Factor by grouping;

[tex]{x}^{2} ( {x}^{2} + 9) -1 ({x}^{2} + 9)[/tex]

Factor further to get:

[tex] ( {x}^{2} + 9)({x}^{2} - 1)[/tex]

Apply difference of two squares to get:

[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]

Answer:

[tex](x^2+9)(x-1)(x+1)[/tex]

Step-by-step explanation:

We would need to let u = x^2 and use middle term factorization first. let's do this:

if u = x^2, then x^4 + 8x^2 – 9 would be

u^2+8u-9

Middle term factorization of this is:

(u+9)(u-1)

now replacing back u = x^2:

(x^2+9)(x^2-1)

Using the formula a^2 - b^2 = (a+b)(a-b), we can write (x^2 - 1) as (x+1)(x-1).

So, the final factored form is:  (x^2+9)(x-1)(x+1)

Answer:

4x - 12

Step-by-step explanation:

Expand 8 - 4(-x + 5) as follows:

              8 + 4x - 20

               4x - 12    (First answer is the correct one)

8-4(-x+5)

Multiply the bracket by -4 first .

8+4x-20

--=positive

-+= negative

4x-12

8-20=-12 because 12 is bigger than 8

Answer:A

Answer:

r = 17 units

Step-by-step explanation:

The radius is the distance from the centre (- 7, - 1) to the point on the circle

(8, 7)

Use the distance formula to calculate the radius (r)

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 7, - 1) and (x₂, y₂ ) = (8, 7)

r = [tex]\sqrt{(8+7)^2+(7+1)^2}[/tex]

  = [tex]\sqrt{15^2+8^2}[/tex]

  = [tex]\sqrt{225+64}[/tex]

  = [tex]\sqrt{289}[/tex] = 17 units

Answer:

A)

Step-by-step explanation:

The expression (a + b)(x + y) is not equivalent to (a + x)(b + y). When the terms are distributed, (a + x)(b + y) yields a different result compared to the original expression.

The expression (a + b)(x + y) is equivalent to a(x + y) + b(x + y) and (b + a)( y + x) because the order of addition in each element doesn't change the overall result. However, the expression (a + x)(b + y) is not equivalent to the original expression.

To understand why, let's distribute the terms in each equivalent expression:

(a + b)(x + y) = ax + ay + bx + by

(b + a)( y + x) = ay + ax + by + bx = ax + ay + bx + by

a(x + y) + b(x + y) = ax + ay + bx + by

As you can see, all these three expressions give the same result when distributed. But, if we now distribute the terms in (a + x)(b + y):

(a + x)(b + y) = ab + ay + bx + xy

It's clear that it does not yield the same result. Thus, option A) (a + x)(b + y) is not equivalent to the original expression (a + b)(x + y).

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Substitute all values for x and y into their placement

y<1-6x

(1)<1-6(-1)

1<7

The coordinate pair is (-1,1)

Answer:90+33 = 123

123-180=77

So 77

Step-by-step explanation:

Answer:

The answer is 77

Answer:

function defined on different intervals by different domain rules

hope it helps

The terms absolute value, continuous function, step function, and piecewise-defined function are matched with their respective definitions: the absolute value measures distance from zero, a continuous function has a graph without breaks, a step function has a graph with horizontal steps, and a piecewise-defined function has different rules for different intervals.

Matching Vocabulary to Definitions

Let's match each mathematical term to its correct definition:

Absolute value - This is the function whose output equals the input for non-negative numbers, and whose output is the opposite of a negative input. It can be thought of as the distance from zero on the number line, regardless of direction.

Continuous function - A function whose graph has no breaks is known as continuous. It means you can draw the function without lifting your pen off the paper, indicating it has no jumps or holes.

Step function - Such a function has a graph that consists of horizontal line segments. The value of the function changes in 'steps' rather than smoothly.

Piecewise-defined function - When a function is defined on different intervals by different domain rules, it is known as a piecewise-defined function. It's like having multiple functions strung together each applicable to different parts of the domain.

Answer:

A.

Step-by-step explanation:

To make a decimal into a percent you just move the decimal 2 times to the right.

0.24 = 24%

The percentage of females polled supported Wilson is about 44%

Given:

Total frequency of females polls = 0.54

Frequency of polls got by Wilson = 0.24

We have to find the percentage of female polls supported Wilson.

[Percentage Polls) × (Total frequency of females polls)] / 100 = Frequency of polls got by Wilson

⇒ Percentage polls = (0.24 × 100) / 0.54

⇒ Percentage polls = 44.44%

Therefore, the percentage of females polled supported Wilson is about 44%.

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Answer:

h = 6 cm  

l = (32-2(6)) =  20 cm

w = (40-2(6)) = 28 cm

Step-by-step explanation:

Given in the question a piece of cardboard having dimensions 32 by 40

Suppose we cut square of length x

When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths

Formula for the volume of box

v = height * length  * width

v = x  (32-2x)  (40-2x)

v = 4x³ - 144x² + 1280x

Find derivative and equal it to 0

dv/dx = 4(3)x² - (2)144x + 1280

      0 = 12x² - 288x + 1280

x1 = 18.110

x2 =5.88

Select x and plug value of x to find dimension

(32-2x) > 0

2x < 32

 x < 16

so domain say that x should be less than 16 which means x = 5.88 ≈ 6 cm

h = 6 cm  

l = (32-2(6)) =  20 cm

w = (40-2(6)) = 28 cm

median: 3

lower quartile: approximately 2.25

higher quartile: approximately 4.75

minimum: 0

maximum: 6

hope that helps

Answer:

1/4

Step-by-step explanation:

To find the slope of a line from two points we use

m = (y2-y1)/(x2-x1)

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

   = (3-2)/(3+1)

  =1/4

Step-by-step explanation:

A(-1,2) and B(3,3) then AB=(4,1).

Normal vector

n=(-1,4)

Our line contains point A(-1,2) and has normal vector n=(-1,4) is

[tex](d) : - 1(x + 1) + 4(y - 2) = 0[/tex]

[tex](d ): - x - 1 + 4y - 8 = 0[/tex]

[tex](d) : - x + 4y - 9 = 0[/tex]

This may be what you're looking for:

Answer:

36 in.³

Step-by-step explanation:

volume = length × width × height

volume = 6 in. × 3 in. × 2 in.

volume = 36 in.³

Answer:

B

Step-by-step explanation:

45+27=72

A- 15 times 9 equals 135

B- 8 times 9= 72

C 45 times 18 equals 810,

D- 14 times 12 equals 68

Answer:

A coordinate pair that works as a solution is (1,3)

Answer:

A coordinate pair that works as a solution is (1,3)

Step-by-step explanation:

Answer:

8 projects

Step-by-step explanation:

28 : 3,5 = 8

Final answer:

Mia can complete 8 full projects with 28 yards of ribbon by dividing the total yards by the yards needed per project, after converting 3 1/2 yards to an improper fraction (7/2).

Explanation:

The subject of this question is Mathematics, and the question would typically fall under a middle school grade level. To solve the problem about the number of projects Mia can complete, we need to use division. Mia has a total of 28 yards of ribbon and needs 3 1/2 yards of ribbon for each project. By converting the mixed number to an improper fraction, we get 7/2 yards per project; then we can divide the total yards by the yards needed per project.

To calculate how many full projects Mia can complete:

Mia can complete 8 full projects with the ribbon she has.

Answer:

[tex]\boxed{x \leq 4.50}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rrcl}\textbf{Words:} & \text{x} & \text{less than or equal to} & \text{4.50}\\\textbf{Symbols:} & x & \leq & 4.50\\\end{array}[/tex]

Answer:

Step-by-step explanation:

Answer:

The student spent 60 minutes studying and got a 90 on the test

Step-by-step explanation:

The x coordinate is 60, which means they spent 60 minutes studying

The y coordinate is 90 which means they got a score of 90 on the test

The student spent 60 minutes studying and got a 90 on the test

Answer:

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

Step-by-step explanation:

We want to find the equation of the line passing through (2,2) and perpendicular to the line with equation y=x.

The given line y=x has slope n=1.

The line that is perpendicular to this line has slope m=-1

The equation is given by the formula;

[tex]y-y_1=m(x-x_1)[/tex]

we plug in the slope and the point to get;

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

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

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

The required equation is

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

Answer:

d only balance sheet accounts.

Step-by-step explanation:

Only permanent accounts are on the balance sheet which includes

assets, liabilities and equity acct.

A trial balance contains all accounts in the general ledger with their account balances, which are used to prepare financial statements such as the balance sheet and income statement.So,option a is correct.

A trial balance is an accounting report that lists all the accounts in the general ledger of an entity along with their respective account balances. It is prepared to check the arithmetical accuracy of the accounting records - to ensure that debits equal credits. Therefore, the correct answer to the question is:

a) All accounts contained in the general ledger with account balances.

The trial balance includes both income statement accounts, such as revenue and expenses, and balance sheet accounts, which include assets, liabilities, and equity accounts. It is commonly used as a step in the process of preparing the financial statements, which include the balance sheet, income statement, and statement of retained earnings. These components provide a more comprehensive view of an entity's financial health at a certain point in time or over a specified period.