Rewrite with common denominator then solve 7/9 subtract 2/3

Answer:

[tex]x \sqrt{1-9x^2} -3x \sqrt{1-x^2}[/tex]

Step-by-step explanation:

Since we have to analyze the cosine of an addition of angles, let's recall that cos of an addition is:

[tex]cos (\alpha +\beta ) = cos(\alpha ) cos(\beta) - sin(\alpha) sin(\beta)[/tex]

Let's also use those Greek letters [tex]\alpha[/tex] and [tex]\alpha[/tex] to represent the inverse functions we are dealing with:

[tex]\alpha =arcsin(3x)[/tex] and therefore, [tex]sin(\alpha ) = 3x[/tex]

[tex]\beta =arccos(x)[/tex] and therefore [tex]cos(\beta ) = x[/tex]

Now use these identities to re-write the equation for the cos of an addition given above:

[tex]cos (\alpha +\beta ) = cos(\alpha ) cos(\beta) - sin(\alpha) sin(\beta)\\cos (\alpha +\beta ) = cos(\alpha ) x - 3x sin(\beta )[/tex]

Now recall that the sine of an angle can be written in terms of the cos of the same angle via the Pythagorean identity: [tex]sin(\beta ) = \sqrt{1-cos^2(\beta) }[/tex]

In our case, and with our particular values, this gives:

[tex]sin(\beta ) = \sqrt{1-cos^2(\beta)} = \sqrt{1-x^2}[/tex]

Similarly we can write the cos of an angle in terms of the sine of the same angle:

[tex]cos(\alpha ) = \sqrt{1-sin^2(\alpha) }[/tex]

In ours case, using our values, this gives:

[tex]cos(\alpha ) = \sqrt{1-sin^2(\alpha) }= \sqrt{1-(3x)^2}= \sqrt{1-9x^2}[/tex]

So replacing these in the cos of an addition of angles formula, we obtain that the given expression equals:

[tex]x \sqrt{1-9x^2} -3x \sqrt{1-x^2}[/tex]

We can simplify the expression cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions by using sin(arccos(x)) = sqrt(1 - x^2). The simplified expression is sqrt(1 - (3x)^2) * x - 3x * sqrt(1 - x^2).

To simplify the expression cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions, we can use the fact that sin(arccos(x)) = sqrt(1 - x^2). Let's start by finding sin(arccos(x)).

arccos(x) gives us an angle whose cosine is x. We can then take the sine of this angle to get sin(arccos(x)). We know that sin^2(arccos(x)) + cos^2(arccos(x)) = 1, so sin(arccos(x)) = sqrt(1 - x^2).

Now, let's substitute the values in the original expression:

cos(arcsin(3x) + arccos(x)) = cos(arcsin(3x)) * cos(arccos(x)) - sin(arcsin(3x)) * sin(arccos(x))

Substituting the values, we have: cos(arcsin(3x)) * cos(arccos(x)) - sin(arcsin(3x)) * sin(arccos(x)) = sqrt(1 - (3x)^2) * x - 3x * sqrt(1 - x^2)

This is the simplified expression of cos(arcsin(3x) + arccos(x)) in terms of x without trigonometric functions.

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The value of an improper fraction is,

⇒ 74/9

We have to give that,

A mixed fraction is,

⇒ 8 2/9

Now, Change the fraction into an improper fraction as,

⇒ 8 2/9

⇒ (8×9 + 2)/9

⇒ (72 + 2)/9

⇒ 74/9

Therefore, The improper fraction is, 74/9

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To find the answer first we make an equation. This equation works for both.

c+(a*y) where c = Current height, a = Annual growth and Y = Years of growth.

Substitute for the correct numbers.

For Tree A:

38+(4*y)

And for Tree B:

45.5+(2.5*y)

Then add some to find that both are the same in 5 years for 58 inches each.

Answer:

you might neees to see if thyeare not ggoing tose if thye are noty the same because is rh on thta thye could do all the smaet hinbg

Step-by-step explanation:

nect thing they could npt going and thye are

Answer:

440.22

Hope this helps you!

Answer:

-9 x -3

Step-by-step explanation:

-7 x -2 will give +14.

-9 x -3 will give +27

+27 is greater than +14.

Two negative numbers multiplied will give a positive answer. (Always)

Multiplying two negative numbers gives a positive product. Therefore, both (-9)*(-3) and (-7)*(-2) result in positive numbers. However, (-9)*(-3) equals to 27, which is greater than (-7)*(-2) equals to 14.

In Mathematics, when you multiply two negative numbers together, the product is a positive number. This is because the rules of sign in multiplication state that a negative times negative equals to a positive. Therefore, both (-9)*(-3) and (-7)*(-2) will result in positive numbers. (-9)*(-3) equals 27, while (-7)*(-2) equals 14. So, the product of (-9)*(-3), which is 27, is greater than the product of (-7)*(-2), which is 14.

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Answer:

A) [tex](\frac{d-b}{c-a} )(\frac{c-a}{-d+b} )[/tex]

The product of these slopes is -1

Step-by-step explanation:

The slope of perpendicular  lines are negative reciprocal.This means that when you multiply the two slopes you get -1.

To find slope of a line you apply;

m=change is y-axis values/change in x-axis values

Given that there are two lines, PQ and P'Q' then to find slope you follow;

Line PQ where P(a,b) and Q (c,d)  slope,m= (d-b / c-a )

Line P'Q' where P'(-b,a) and Q'(-d,c) slope , m= ( c-a / -d+b)

Multiplying the two slopes

[tex]\frac{d-b}{c-a} *\frac{c-a}{-d+b} \\\\\\\frac{d-b}{-d+b} \\\\=-1[/tex]

Answer:

a

Step-by-step explanation:

took the test today

In order to get the answer you will have to divide 30 by 100 then divide the number you get from that by 20 to receive your answer.

20/x=100/30

(20/x)*x=(100/30)*x      

20=3.33333333333*x      

(3.33333333333) to get x

20/3.33333333333=6

=6

Therefore your answer is "6."

Hope this helps

Answer: radius = 6.18 (I don't know what solutions you have, but the actual answer for the radius is about 6.18 cm so which ever is closest.)

Step-by-step explanation:

the area of a circle is \pi  r^{2}

*rewrite your equation solving for radius

r=\sqrt{A/\pi } =\sqrt{120/\pi } = 6.18

To find the Radius of a circle with an area equal to the area of a rectangle, multiply the length and width of the rectangle to get its area, then use the formula A = πr² to solve for the radius.

To find the Radius of a circle with an area equal to the area of a rectangle, we need to find the area of the rectangle and then calculate the radius of the circle using that area.

The area of the rectangle is found by multiplying the length and width, which in this case is 15 cm * 8 cm = 120 cm².

The area of a circle is given by the formula A = πr², where A is the area and r is the radius. Since the area of the rectangle is equal to the area of the circle, we can set up the equation 120 cm² = πr².

Solving for r, we get r ≈ 6.94 cm (rounded to two decimal places).

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Answer:he made an error in Step 3. He should have subtracted 2 from both sides.

Step-by-step explanation:

Answer:

It's c

Step-by-step explanation:

He made an error in Step 3. He should have subtracted 2 from both sides.

Answer:

see explanation

Step-by-step explanation:

(a)

AC = AB + BC ← substitute values

AC = x + 2 + 7x - 3 = 8x - 1

(b)

QR = PR - PQ ← substitute values

QR = 13y + 25 - (8y + 5) ← distribute parenthesis by - 1

     = 13y + 25 - 8y - 5 = 5y + 20

Answer:

10x+1

Step-by-step explanation:

The expression of the given description could be 10n + 1.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

We have been given a statement as 'The product of a number and 10, increased by 1'

Where" the product " means multiply.

" increased " means add

Let the unknown number be n

So the expression could be;

10n + 1

Therefore, the expression of the given description could be 10n + 1 .

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The algebraic expression to represent the amount of money Jenny will earn in d days, given that she earns $30 per day, is 30d.

The question is asking to write an algebraic expression to represent the amount of money Jenny will earn working at a supermarket for a certain number of days, where she earns $30 per day. In algebra, we often use variables to represent unknown quantities. In this case, we will use d to represent the number of days.

In one day, Jenny earns $30. Therefore, to determine how much she earns in multiple days, we multiply the number of days by the amount she earns each day. If she works 'd' days, Jenny will therefore earn 30d dollars.

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Answer:

Look to the explanation

Step-by-step explanation:

* Lets think how to write a short story represents this expression

* Remember multiplication must solved before subtraction, so we

 can think that:

- 6 multiply by 24 can represented by six bags each one has 24 items

- Subtract f can be represented by someone takes 5

- We can chose bags or boxes for 6

- We can chose sweets or marbles to 24

- We can say sister or brother or friend takes 5

- Lets try to make a short story to represent this situation

* Nadine has six boxes of marbles. Each bag has twenty four

 marbles with different colors, she wants to give her sister

 Sarah 5 marbles. Write an expression to model this situation

* The expression is 6 * 24 - 5

Answer:

Joy went to 6 shops and bought 24 candies from each shop. After returning home he gives 5 candies to his brother. Find the number of candies left.

Step-by-step explanation:

Consider the provided expression.

[tex]6 \times 24 - 5[/tex]

Here the sign "×" represents repeated addition or multiplication.

The sign "-" represents the subtraction.

To define [tex]6 \times 24-5[/tex] we can imagine any real life situation.

Joy went to 6 shops and bought 24 candies from each shop. After returning home he gives 5 candies to his brother. Find the number of candies left.

Answer:

1. x-3

3. x -coordinates

has no solution

Step-by-step explanation:

Answer:

x-3

x -coordinates

has no solution

Step-by-step explanation:

The change in water is 5/24 cups.

Answer:

3 hundreds

Step-by-step explanation:

10*3*10=300

unit for is 3 hundreds standard form is 300

Answer:

3.08

Explanation:

The first 3 numbers (from left to right) are the ones counted as 3 significant figures. You alreadty start of 5 significant figures. What you do is count the numbers, from left to right, and once you get to the number you're finding (in this case the 3rd significant figure), then you look at the number to the right of it and see if it's over or under 5. Depending on which one it is will determine wiether you round up or stay at the same point.

a.  [tex]\frac{1}{20}[/tex] liters per glass

b. 50 milliliters

To find the amount of water in each glass, divide the total amount of water by the number of glasses, resulting in [tex]\frac{1}{20}[/tex] liters per glass. To express this in milliliters, multiply by 1000 to get 50 milliliters per glass.

a. To find the amount of water in each glass, divide the total amount of water ([tex]\frac{1}{4}[/tex] liters) by the number of glasses (5): [tex]\frac{1}{4}[/tex] ÷ 5 = [tex]\frac{1}{20}[/tex] liters per glass. Drawing a visual representation can help understand this partitioning.

b. To express the amount in milliliters, we know that 1 liter is equal to 1000 milliliters. So, [tex]\frac{1}{20}[/tex] liters per glass = ([tex]\frac{1}{20}[/tex]) * 1000 milliliters = 50 milliliters per glass.

To distribute the 250 milliliters equally into 5 glasses, we divide 250 milliliters by 5. This calculation results in:

250 milliliters ÷ 5 = 50 milliliters per glass.

To convert the amount in milliliters back to liters for each glass, recall that 1,000 milliliters is equivalent to 1 liter. Therefore, 50 milliliters is the same as 0.05 liters (since 50 divided by 1,000 equals 0.05).

The question is:

A pitcher of water contains [tex]\frac{1}{4}[/tex] liters of water. The water is poured equally into 5 glasses.

a. How many liters of water are in each glass? Draw a picture to support your response.

b. Write the amount of water in each glass in milliliters.

[tex]\huge\boxed{\text{21 cm}}[/tex]

The area of a square is equal to the square of its side length. [tex]A=s^2[/tex]

Substitute in the known variable. [tex]441=s^2[/tex]

Now, find the square root of each side of the equation. [tex]\sqrt{441}=s[/tex]

Find the square root of [tex]441[/tex]. [tex]\boxed{21}=s[/tex]

The edges which are perpendicular to edge QE are TQ, QP and EJ. Thus, option (A), (D) and (E) are correct.

In a rectangular prism, the edges that are perpendicular to QE are those that intersect QE at right angles.

So, for an edge to be perpendicular to QE, it should be parallel to the other two edges of the rectangle that contains QE.

From the given options:

A. TQ: This edge is perpendicular to QE because it is parallel to the edges TP and EQ.

B. PR: This edge is not perpendicular to QE because it is parallel QE.

C. RA: This edge is not perpendicular to QE because it is parallel to QE.

D. QP: This edge is perpendicular to QE as it is parallel to the edges PQ and TE, not QE.

E. EJ: This edge is perpendicular to QE as it is parallel to the edges EK and QJ, not QE.

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Answer:

1 2/3 yards of yellow fabric.

Step-by-step explanation:

5 1/3 = 3 2/3+y

5 1/3 - 3 2/3 = y

16/3 - 11/3 = y

5/3 = y

y = 1 2/3 yards of yellow fabric.

Answer:

y= # yellow fabric yards

5 1/3= 3 2/3+ y

Convert to improper fractions

((5*3)+1)/3= ((3*3)+2)/3 + y

16/3=11/3+y

Subtract both sides by 11/3

5/3=y

or

1 2/3=# yellow fabric yards

hope this helps

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Final answer:

The result of adding 30.09, 5.55, and 80.761 and rounding to the least number of decimal places (two decimal places) is 116.40, with four significant figures.

Explanation:

To solve the problem 30.09 + 5.55 + 80.761 and express the answer with the correct number of significant figures, you should first perform the addition and then round the result to the least number of decimal places of any number in the sum. The number with the least number of decimal places is 5.55 (two decimal places).

Here's the step-by-step calculation:

Add the numbers: 30.09 + 5.55 + 80.761 = 116.401

Round to two decimal places (because of 5.55): 116.40

So, the final result is 116.40, which has four significant figures and two decimal places.

Answer:

X = 6

Step-by-step explanation:

See Attachment

Answer:

38

Step-by-step explanation:

38 divided by 2 is 19

8 divided by 1 is 8

33 divided by 3 is 11

Answer:

38 shots were made.

Step-by-step explanation:

I just worked it out on paper.

Answer:

B on edg

Step-by-step explanation:

I just took the test

Answer:RULE 1: The quotient of a positive integer and a negative integer is negative. RULE 2: The quotient of two positive integers is positive. RULE 3: The quotient of two negative integers is positive. If the signs are different the answer is negative.

Hope this helps

Step-by-step explanation:

We used -12 and 3 to demonstrate negative integer divided by a positive integer resulting in -4. We confirmed this by multiplying -4 by 3 to get -12 back.

Let's use -12 and 3 as examples for a negative integer and a positive integer respectively. The division sentence would be -12 ÷ 3 = -4. To prove this division is correct using multiplication, you would multiply the quotient by the divisor. So, -4 * 3 = -12, which is equivalent to the dividend. Therefore, the multiplication shows the accuracy of the division.

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Answer:

Step-by-step explanation:

[tex]\frac{3 meters}{1 second} * 24 seconds[/tex]

[tex]72 meters[/tex]

The total change in the tram's elevation is found by multiplying the speed (3 meters per second) by the time (24 seconds) which gives us a result of 72 meters.

The total change in the tram's elevation can be found using the formula for distance travelled which is speed times time. We know that the speed of the tram is 3 meters per second, and it moved for 24 seconds. To find the total distance travelled or the total change in elevation, we simply multiply the speed by the time.

So, 3 meters per second multiplied by 24 seconds equals 72 meters. Therefore, the total change in the tram's elevation was 72 meters.

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To find the length of line AB, use the midpoint formula and solve for AB.

To find the length of line AB, we can use the midpoint formula. Given that point T is the midpoint of line AB, we can set up the equation:

(AT + TB) / 2 = AB

Substituting the given values:

((3/4)x + 6 + (1/2)x + 9) / 2 = AB

Simplifying the equation:

(5/4)x + 15 / 2 = AB

(5/4)x + 7.5 = AB

Therefore, the length of line AB is (5/4)x + 7.5.

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Explanation:

First, we graph the linear function of y = -5x [as though it were an equivalence symbol], then, since there is a less than sign, we shade everything to the left of that.

I am joyous to assist you anytime.