which expression is equivalent to 1/sin(2x) - cos(2x)/sin(2x)

Answer:

x = 3

Step-by-step explanation:

Use the distributive property to multiply 4 by 5x+3. Subtract 14x from both sides. Combine 20x and −14x to get 6x. Subtract 12 from both sides. Subtract 12 from 30 to get 18. Divide both sides by 6. Divide 18 by 6 to get 3.

Answer:

20x+12=14x+30

6x=18

x=3

Step-by-step explanation:

First, apply the distributive property:

4(5x+3) = 4 · 5x + 4 · 3 = 20x+12

Now, we have this equation

20x+12=14x+30

We need to group the elements now.

So, to bring all the elements with an "x," we subtract 14x from both sides.

20x-14x+12=14x+30-14x

We have this now

6x+12=30

Now, let's subtract 12 on both sides

6x+12-12=30-12

6x=18

Divide both sides by 6

x=3

If 14 inches of wire cost 42 cents, with 21 cents can be bought  7 inch of wire

Information about the problem:

Calculating how much 1 inch cost, we have:

1 inch cost= Inches bought cost  / Inches bought

1 inch cost= 42 cents / 14 inches

1 inch cost= 3 cent/inch

Calculating how much can be bought with 21 cents:

Inches of wire= Amount / 1 inch cost

Inches of wire= 21 cent / 3 cent/inch

Inches of wire= 7 inch

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

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Answer:

|x|

Step-by-step explanation:

Review your parent functions and how to identify them. They are the fundamentals of algebra and pre calc

The image of the points after they are reflected across the x-axis are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

From the question, we have the following parameters that can be used in our computation:

J(1, 9), K(7, 4), L(8, 13), M(-2, 1)

Also from the question we have the transformation to be

Transformation: reflection across the x-axis

The rule of the reflection across the x-axis is represented as

(x, y) = (x, -y)

Substitute the known values J(1, 9), K(7, 4), L(8, 13), M(-2, 1) in the above equation, so, we have the following representation

J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

Hence, the image of the points are J'(1, -9), K'(7, -4), L'(8, -13), M'(-2, -1)

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Answer:

59. a₁ = 4

60. a₁ = 10

Step-by-step explanation:

The general equation for the sum of the first n terms Sₙ of a geometric sequence with common ratio r and first term a₁ is

[tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]    

Problem 59

Here we are given
[tex]S_n = \dfrac{31}{4}\\\\r = \dfrac{1}{2}[/tex]

So we can plug these values into the above equation and get [tex]a_1[/tex]

Let's first compute [tex]1 - r^n[/tex]
[tex]1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5\\\\\left(\dfrac{1}{2}\right)^5 = \dfrac{1}{32}\\\\1 - r^n = 1 - \left(\dfrac{1}{2}\right)^5 = 1-\dfrac{1}{32} = \dfrac{32}{32}-\dfrac{1}{32} = \dfrac{31}{32}[/tex]

[tex]1- r = 1 - \dfrac{1}{2} = \dfrac{1}{2}[/tex]

So
[tex]\dfrac{1-r^n}{1-r} = \dfrac{31}{32} \div \dfrac{1}{2} = \dfrac{31}{32} \times \dfrac{2}{1} = \dfrac{31}{16}[/tex]

Substituting this value into [tex]S_n = a_1 \dfrac{1-r^n}{1-r}[/tex]  we get

[tex]\dfrac{31}{4} = a_1\dfrac{31}{16}[/tex]

Multiplying both sides by [tex]\dfrac{16}{31}[/tex]
[tex]\dfrac{31}{4} \times\dfrac{16}{31} = a_1\dfrac{31}{16} \times\dfrac{16}{31}\\\\4 = a_1 \textrm{or alternatively }\\ \\\boxed{a_1 = 4}[/tex]

Problem 60

Use the same technique as above

[tex]S_8 = 2550, r = 2\\\\S_8 = a_1 \times \dfrac{1-r^8}{1-r}\\\\\\2550 = a_1 \times \dfrac{1-2^8}{1-2}\\\\2550 = a_1 \times \dfrac{1 - 256}{1-2}\\\\2550 = a_1 \times \dfrac{-255}{-1}\\\\2550 = a_1 \times255\\\\== > a_1 = \dfrac{2550}{255}\\\\\boxed{a_1=10}[/tex]

Answer:

Step-by-step explanation:

Answer:

15, 1

Step-by-step explanation:

I'm assuming the answer should be limited to only positive integers. Either way, looking at 16 and 14, they are 2 apart and their average is 15. Since 15 is one from 16 and 14 both, the answer is 15 and 1.

15-1 = 14

15+1 = 16

Answer:0

Step-by-step explanation:The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept

y=mx+b Using the slope-intercept form, the slope is 0

Answer: XYW = 32, WYZ = 85

Step-by-step explanation:

We are looking for what x is, which we can find with the formula:

117 = (6x+44) + (-10x+65)

117 = -4x + 109

8 = -4x

x = -2

We can verify this is correct by plugging it in and seeing if they add up to 117.

6x + 44 (XYW)

= 6(-2) + 44

= -12 + 44

= 32

-10x + 65 (WYZ)

= -10(-2) + 65

= 20 + 65

= 85

32 + 85 = 117

2) BA and CD are parallel (segments that are collinear with parallel segments are parallel)

3) CDAB is a parallelogram (a quadrilateral with two pairs of parallel sides is a parallelogram)

4) ∠B is congruent to ∠D (opposite angles of a parallelogram are congruent)

5) m∠B = m∠D (congruent angles)

6) m∠D=115° (transitive property)

7) m∠EDA=65° (linear pair)

8) m∠EAD=65° (base angle of an isosceles triangle)

9) m∠E = 50° (sum of angles in a triangle)

Answer:

6,720

Step-by-step explanation:

Answer:

31 square miles

Step-by-step explanation:

We basically have three shapes here.  

The top rectangle:

A= l x w = 7 x 2 = 14

The middle rectangle:

A= l x w = 4 x 2 = 8

The triangle

A = 1/2 x b x h = (3 x 6)/2 = 18/2 = 9

Add the area of all three: 14 + 8 +9 = 31

The equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4

The equation of a line in point-slope form is expressed as y = mx + b

where

m is the slope

b is the intercept

Using the coordinate points (0,4) and (1, 11)

Slope = 11-4/1-0

slope = 7

The y-intercept is at the point (0,4)

Determine the equation

y = mx + b

y = 7x + 4

Hence the equation of the linear function represented by the table below in slope-intercept form is y = 7x + 4

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Based on the prices of the homes in the neighborhood, the median home price is A) 166

What is the median home price?

L is for a home below $110 and H is for a home above $190. The distribution of home prices can therefore be shown as:
190, 120, 166, 173, 190, 190, 190, 123, 127, 110

In an ordered list, this becomes:

= 110, 120, 123, 127, 166, 173, 190, 190, 190

The median is the price in the middle and we can see this price is $166

In conclusion, the median home price is $166.

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The required value of x in the expression 2√51x is 25.

Given that,
An expression 2√51x,
To determine the value of x when the expression is equivalent to  10√51.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
2√51x = 10√51
√51x = 5√51
√x = 5√51 / √51
√x = 5
squaring both sides
x = 25

Thus, the required value of x in the expression 2√51x is 25.

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Answer:

28 = 2² × 7

Step-by-step explanation:

28 = 4 × 7 = 2² × 7

By unitary method, we get that the total cost of mixture per pound = 50 cents.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

Cost of 1 pound sunflower seeds = 32 cents.

Cost of 1 pound cracked corn = 18 cents.

Available sunflower seeds = 10lb = 10 pounds

Available cracked corn = 16lb = 16 pounds

To find: Cost of the mixture per pound

Finding:

By unitary method, Cost of 1 pound sunflower seeds = 32 cents.

Cost of 10 pounds sunflower seeds = 32(10) = 320 cents.

Again, by unitary method,

Cost of 1 pound cracked corn = 18 cents.

Cost of 16 pound cracked corn

= 18(16) cents

= 288 cents.

Therefore, total cost of mixture per pound

= 32 + 18 = 50 cents.

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The quotient of the given expression 2 3/4 and 7/8 is 22/7

Quotient refers to a number resulting from the division of one number by another. 12 ÷ 2 = 6 the quotient is 6

Dividend is number or expression that is to be divided by another. 12 ÷ 2 = 6 the dividend is 12

Divisor is the number or expression that is to be divided by another. 12 ÷ 2 = 6 the divisor is 2

Quotient of 2 3/4 and 7/8?

= 2 3/4 ÷ 7/8

= 11/4 ÷ 7/8

= 11/4 × 8/7

= (11 × 8) / (4 × 7)

= 88/28

= 22/7

Therefore, the quotient of the given expression 2 3/4 and 7/8 is 22/7

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The required ordered pair, when graphed, would be on the same line as (1,3)  and   (4,9) is  (-2,-3).

Option (B) is correct.

Coordinate geometry is defined as the study of geometry using the coordinate points. Coordinate geometry is required to provide a link between algebra and geometry through the use of line and curve graphs.

Given:

The given points is

(1,3)  and   (4,9)

According to given question we have

The  points is

(1,3)  and   (4,9)

Plot the ordered pairs  Draw a line through the points to indicate all of the points on the line.

The points lie on the given point is (-2,-3).

Therefore, the required ordered pair, when graphed, would be on the same line as (1,3)  and   (4,9) is  (-2,-3).

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5p/6  an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).

Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values. The coordinates of the first point represent x1 and y1

gradient of the line segment joining (3p, 6) to (-2p, 10)

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

m =( 10 -4)/ ( -2p - 3p)

m= 6/ (-5p)

m= -6/5p

we know that

Gradient of a line perpendicular to a line with a gradient of m = -1/m

Gradient of a line perpendicular to a line with a gradient of -6/5p = 5p/6

Hence 5p/6  an expression for the gradient of the line perpendicular to the line segment joining (3p, 6) to (-2p, 10).

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Calculate the lengths of the 3 sides of the triangle:

AB =

[tex] \sqrt{(7 - ( - 1)) ^{2} + (( - 2) - ( - 8))^{2} } = 10[/tex]

BC =

[tex] \sqrt{(( - 1) - 5) ^{2} + (( - 8) - 0)^{2} } = 10[/tex]

AC =

[tex] \sqrt{(7 - 5) ^{2} + (( - 2) - 0)^{2} } = 2 \sqrt{2} [/tex]

Because AB = BC

=> ️ABC is an isoscelea triangle at B

Using the cross-multiplication formula we conclude that 768 cents will be given for 96 can recycled.

Cross multiplying is the process of multiplying the denominator of the second fraction on the other side of the equals to sign by the numerator of the first fraction on the same side.

In a similar manner, the numerator of the second fraction is multiplied by the denominator of the first fraction. Cross-multiplication is another name for the butterfly method. We employ the cross-multiply approach to identify one or more variables in a fraction. Cross multiplying is another method for comparing fractions.

We will do simple cross-multiplication here

given that for 12 cans we get 96 cents, that is

⇒ 12/96

and for 96 cans we get x cents, that is

⇒ x/96

Now, we do cross-multiplication here

⇒ 12/96 = 96/x

⇒ 12x = 96 × 96

⇒ x = (96 × 96)/12

⇒ x = 768 cents

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Correct question

A recycling center claims to give 96 cents for every 12 aluminum cans turned in. How much cents will they give if u recycled 96 cans?

Vertical angles or contrary angles are the statement that Terra's proof is still absent. The angles formed opposite to each other when two lines cross each other are equal.

Terra describes the parallelogram nature of the diagram. Because they are vertical or opposite angles, these angles are equal.

The angles formed opposite to each other when two lines cross each other are equal. As a result, we have discovered that either vertical angles or opposite angles make up Terra's proof.

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Answer:

3500

Step-by-step explanation:

1600-12500=3500

3500/12500*100% = 28%

so the percentage profit is 28%

If the main courses at a restaurant all contain rice or onion and of the 23 choices, 17 contain onion and 14 contain rice, then the number of dishes containing both rice and onion will be equal to 8.

The number of dishes that contain both rice and onion at the restaurant can be calculated by using an algebraic expression.

An algebraic expression can be defined as an equation in which both numerals and letters are present.

An algebraic expression for this problem can be given as,

(14 - x) + x + (17 - x) = 23

Here x is equal to the number of dishes containing both rice and onion.

14 + 17 - x + x - x = 23

31 - x = 23

x = 31 - 23

x = 8

Hence, the number of dishes that contain both rice and onion is calculated to be 8.

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Answer:

2(x+2)(x+4)

Step-by-step explanation:

Answer 1120.5

Step-by-step explanation:

The probability that a randomly chosen fitness club member signs up for a free running session is 0.4.

Let total s members sign up for the weightlifting session.

So, the total members for the running session is 2x.

And the total members for the swimming session be 2x.

Also here it is given that, thirty of the fitness center members sign up for a free session.

⇒ x + 2x + 2x = 30

⇒ 5x = 30

⇒ x = 30/5

⇒ x = 6

Thereofre, the probability that a randomly chosen fitness club member signs up for a free running session

= total number of members in running session/ number of members sign up for a free session

= 12/30

= 0.4

Hence, the probability that a randomly chosen fitness club member signs up for a free running session is 0.4.

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Answer:

c = 576

Step-by-step explanation:

3 c = 1728

divide both sides by 3

c = 576