tan 116° =
A) tan 64°
B) -tan 64
C) tan 26
D) -tan 26

Answer:

The values of x are

[tex]x=-\sqrt{7} , x=\sqrt{7}[/tex]

Step-by-step explanation:

we have

[tex]6x^{2}-42=0[/tex]

Solve for x

Adds 42 both sides

[tex]6x^{2}-42+42=0+42[/tex]

[tex]6x^{2}=42[/tex]

Divide by 6 both sides

[tex]6x^{2}/6=42/6[/tex]

simplify

[tex]x^2=7[/tex]

square root both sides

[tex]x=\pm\sqrt{7}[/tex]

therefore

The values of x are

[tex]x=-\sqrt{7} , x=\sqrt{7}[/tex]

The exact solution for the values of x in the given equation are: +√7 and -√7.

From the task content; it follows that the given equation is; 6x² - 42 = 0.

On this note, the evaluation for the values of x can be done as follows;

6x² - 42 = 0

6x² = 42

x² = 7

x = ±√7.

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Answer:

114

Step-by-step explanation:

the answer is not geomatic but you just have to think harder not smarter. ;)

Answer:

104

Step-by-step explanation:

80 = 8 * 10

88 = 8 * 11

? = 8 * x

128 = 8 * 16

160 = 8 * 20

11 - 10 = 1

x - 11 = 2

16 - x = 3

20 - 16 = 4

x = 13

13 * 8 = 104

Answer:

She needs to buy 4.25 m cloth

Step-by-step explanation:

Add the length of one piece to the length of the other piece. Subtract the sum from the length needed.

2.3 + 3.45 = 5.75

10 - 5.75 = 4.25m

Answer:

4.25, B

Step-by-step explanation:

2.3+3.45= 5.75 you need 4.25 more to have 10 meters

Answer:

The answer is b = 30 ft and h = 40 ft.

Step-by-step explanation:

Given:

The height of a parallelogram is 10ft more than its base

The area is 1200 ft².

Now, to solve for b and h.

Let the base (b) be [tex]x.[/tex]

And the height (h) is = [tex]x+10.[/tex]

Area = 1200 ft².

Now, to solve we put formula of area:

[tex]Area =b\times h[/tex]

[tex]1200=x\times (x+10)[/tex]

[tex]1200=x^2+10x[/tex]

Subtracting both sides by 1200 we get:

[tex]0=x^2+10x-1200\\x^2+10x-1200=0[/tex]

Now, solving the quadratic equation:

[tex]x^2+40x-30x-1200=0[/tex]

[tex]x(x+40)-30(x+40)=0[/tex]

[tex](x+40)(x-30)=0[/tex]

[tex]x+40=0[/tex]        and       [tex]x-30=0[/tex]

Subtracting                  Adding both sides

both sides                    by 30 we get:

by 40 we get:      

[tex]x=-40.[/tex]                           [tex]x=30.[/tex]

So, we will take the positive result.

[tex]x=30.[/tex]

Thus, the base (b) = 30 ft.

Now, getting the height (h) by substituting the value of [tex]x[/tex]:

[tex]x+10\\=30+10\\=40\ ft.[/tex]

Therefore, the answer is b = 30 ft and h = 40 ft.

Answer:

[tex]f^{-1}[/tex](x) = 9x + 18

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )

y + 2 = [tex]\frac{1}{9}[/tex] x

Multiply through by 9 to clear the fraction

9y + 18 = x

Change y back into terms of x

[tex]f^{-1}[/tex] (x) = 9x + 18

The inverse of the function is 9y+18

An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

Given:

f f (x) = one-ninth x minus 2

f(x)= 1/9 x - 2

let f(x)=y

Now, solve for x

y = 1/9x -2

y+2 = 1/9x

9y+18 = x

Hence, the inverse of the function is 9x+18.

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Subtract 10 on both sides: -6/5x=-17

Multiply both sides by 5: -6x=-85

Divide both sides by -6: x= 14 1/6

Hope this helped!

Answer:X=6/85

Step-by-step explanation:

Marco can watch TV for at most 56 minutes each day.

Step-by-step explanation:

Given,

Time of screen each week = 7 hours

1 hour = 60 minutes

7 hours = 60*7 = 420 minutes

Length of movie = 1 hour + 20 minutes = 60 + 20 = 80 minutes

Time left for other days = 420 - 80 = 340 minutes

Number of days = 6

Let,

x be the time per day for remaining 6 days.

Number of days * Time per day ≤ Time remaining

[tex]6x\leq 340[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6}\leq \frac{340}{6}\\x\leq 56.66[/tex]

Marco can watch TV for at most 56 minutes each day.

Keywords: inequality, division

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Answer:

x=120

Step-by-step explanation:

108 = 90%

divide everything by 9

12 = 10%

multiply everything by 10

120 = 100%

x=120

Answer:

120

Step-by-step explanation:

set a relation. Because 108 is 90%, you do 90%/100% = 108/x (write vertically so its easier. So you see what number you multiply 90 by to get 108 and multiply that by 100 to get the total amount.

Answer:

− 12  ,  − 6 , − 4 , − 3, −2, −1, 1, 2, 3, 4, 6 , 12

Step-by-step explanation:

-12 * 1 = -12

-6 * 2 = -12

-4 * 3 = -12

-3 * 4 = -12

-2 * 6 = -12

-1 * 12 = -12

1 * -12 = -12

2 * -6 = -12

3 * -4 = -12

4 * -3 = -12

6 * -2 = -12

12 * -1 = -12

Answer:

The area of Andrew's tree house must be greater than or equal to 117 square feet

Step-by-step explanation:

Let

x -----> the area of Andrew's tree house in square feet

y ---->  the area of Cynthia's tree house in square feet

we know that

Cynthia plans to make the area of her tree house at least 13 square feet.

The word "at least" means "greater than or equal to"

so

[tex]y\geq 13[/tex] ----> inequality A

Cynthia plans to build a tree house that is 1/3 the size of Andrew's tree house

so

Remember that

When two figures are similar, the ratio of its areas is equal to the scale factor squared

In this problem the scale factor is given

The scale factor is 1/3

The scale factor squared is 1/9

That means

The area of Andrew's tree house is 9 times greater than the area of Cynthia's tree house

or

The area of Cynthia's tree house is 9 times smaller than the area of Andrew's tree house

[tex]y=\frac{1}{9}x[/tex] ----> equation B

substitute equation B in the inequality A

[tex]\frac{1}{9}x\geq 13[/tex]

solve for x

[tex]x\geq 117\ ft^2[/tex]

so

The area of Andrew's tree house must be greater than or equal to 117 square feet

we know that Andrew's tree house is larger than  Cynthia's tree house, because the problem states that Cynthia's tree house is 1/3 the size of Andrew's tree house

That means

The size of Andrew's tree house is 3 times greater than the size of Cynthia's tree house, without solving the inequality

Final answer:

To find the size of Andrew's treehouse, let's assume the area as x square feet. Using the given information, we can write and solve the inequality (1/3)x ≥ 13 to find the area of Andrew's treehouse. Without solving the inequality, we know that Andrew's treehouse is larger because the area must be greater than or equal to 39 square feet.

Explanation:

To find the area of Andrew's tree house, let's assume that his tree house has an area of x square feet.

According to the information given, Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Therefore, the area of Cynthia's tree house would be (1/3)x square feet.

We are told that Cynthia plans to make the area of her tree house at least 13 square feet. So we can write the inequality as follows:

(1/3)x ≥ 13

To solve the inequality, we need to multiply both sides by 3 (since the coefficient of x is 1/3). This will give us:

x ≥ 39

This means that the area of Andrew's tree house must be greater than or equal to 39 square feet.

Without solving the inequality, we can see that Andrew's tree house is indeed larger than Cynthia's tree house because the area of Andrew's tree house must be greater than or equal to 39 square feet.

The value of n from the equation 7n = 28 is n = 4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

7n = 28   be equation (1)

On simplifying the equation , we get

Divide by 7 on both sides of the equation , we get

n = 28/7

n = 4

Another equation which satisfies the relation is 4n = 16

n = 4

Therefore,  the value of n is 4

Hence , the value of the equation is 4

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A) There are 16 kids.

B) There are 32 men.

C) There are 24 ladies.

Hope this helps. :)

Answer:

21d(10d-3)

Step-by-step explanation:

21d x 10d = 210d^2

21d x 3 = -63d

so it would be 210d^2 - 63d

The expression which is equivalent to 210d² − 63d would be 21d(10d- 3).

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

From the given expression;

210d² − 63d

A factor which is common to both terms of the expression;

21d.

On this note, the factorisation of the expression yields,

21d(10d- 3).

21d x 10d = 210d^2

21d x 3 = -63d

so it would be 210d² − 63d.

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The property used in this equation is the addition property of equality.

The property used in this equation is called the addition property of equality. According to this property, if two numbers are equal, then adding the same number to both sides of the equation will still result in an equality.

In the given equation, x + 7 = 23, we need to isolate the variable x. To do this, we can subtract 7 from both sides of the equation, using the subtraction property of equality. This simplifies the equation to x = 16.

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Answer:

[tex]2\pi[/tex]

Step-by-step explanation:

Formula of circumference is [tex]C = 2\pi r[/tex]

r = radius

plug in the numbers into formula to get

[tex]2\pi (1)[/tex] which will eqaul [tex]2\pi[/tex]

Final answer:

The circumference of a circle with a radius of 1 kilometer is approximately 6.28318 kilometers, calculated using the formula C = 2πR.

Explanation:

Given that the radius of a circle is 1 kilometer, we can calculate the circumference of the circle using the formula C = 2πR, where R is the radius of the circle and π (pi) is approximately 3.14159. Since the radius is 1 kilometer, we plug that value into the formula to get:

C = 2 × 3.14159 × 1 km

C = 6.28318 km

Therefore, the circle's circumference is approximately 6.28318 kilometers.

Answer:

His commission on the boat he sells is $6250.

Step-by-step explanation:

Given:

Mr. Norris is paid a 5% commission on each boat he sells.

Now, to find his commission on a boat that he sells for $125,000.

Commission = 5%.

Boat he sell for = $125,000.

Now, to get the commission on the boat he sells:

5% of $125,000.

[tex]=\frac{5}{100} \times 125000[/tex]

[tex]=0.05\times 125000[/tex]

[tex]=\$6250.[/tex]

Therefore, his commission on the boat he sells is $6250.

Final answer:

Mr. Norris's commission on a boat sold for $125,000, with a commission rate of 5%, is $6,250.

Explanation:

Mr. Norris earns a commission based on a fixed percentage of the sales price. To calculate his commission for selling a boat priced at $125,000, we apply the 5% commission rate to the sale price.

Here's the calculation:
Commission = Sale Price × Commission Rate
Commission = $125,000 × 0.05
Commission = $6,250

Hence, Mr. Norris's commission for selling a boat that he sells for $125,000 is $6,250.

Answer:

3/7 and 4/14

Step-by-step explanation:

a) 3/7 is not an equivalent of 6/21 because when you multiply the numerator and the denominator by 2 you get: 6/14

b) 4/14 is not an equivalent

Answer:

3/7

Step-by-step explanation:

6/21 = 6 ÷ 3 / 21 ÷ 3 = 2 / 7

6 / 21 = 4 ÷ 2 / 14 ÷ 2 = 2 / 7

6/21 = 12 ÷ 6 / 42 ÷ 6 = 2 / 7

The range of values for the width w of the garden is 17 ≤ w ≤ 30.

Step-by-step explanation:

Given,

The length of the garden = 11 feet.

The perimeter of the garden = 56 feet  (at least is the minimum value)

The perimeter of the garden = 82 feet  (not more than is the maximum value)

step 1 :

Perimeter of a rectangle = 2 (length + width)

⇒ 56 = 2 (11 + width)

⇒ 56 = 22 + 2 width

⇒ 34 = 2 width

⇒ width = 34/2

∴ width = 17 feet

step 2 :

Perimeter of a rectangle = 2 (length + width)

⇒ 82 = 2 (11 + width)

⇒ 82 = 22 + 2 width

⇒ 60 = 2 width

⇒ width = 60/2

∴ width = 30 feet

step 3 :

The range of values for width 'w' is 17 ≤ w ≤ 30.

Answer:

[17,30]

Step-by-step explanation:

The expressions that can be represented by a model for the value of 28 are "10 + 4 + 10 + 4" and "14 x 2". The expression "18 x 2" equals 36 and does not represent a value of 28, and the meanings of the last two expressions ('0 24₃₂' and '28 = 2') are not clear without additional context.

To determine which expressions can be represented by a mathematical model, it's important to pay attention to the operations and numbers involved. In the list provided, there are various expressions that could potentially represent the same numerical value. For example, the expression 10 + 4 + 10 + 4 represents the sum of these numbers, which equals to 28. Similarly, 14 x 2 represents the product of 14 and 2, which also equals to 28. On the other hand, 18 x 2 equals 36, which is different from the previous two expressions.

We can look at these expressions and evaluate them:

10 + 4 + 10 + 4 = 28

14 x 2 = 28

18 x 2 = 36

Thus, from the expressions listed, only 10 + 4 + 10 + 4 and 14 x 2 can be represented by a model that reflects the value of 28. The expression 18 x 2 represents a model for the value of 36, not 28. The last two expressions, '0 24₃₂' and '28 = 2', are either typos or not clear enough to deduce a meaningful mathematical operation. If '24₃₂' indicates some form of mathematical notation or operation, it isn't standard and therefore cannot be verified without further context.

Given the provided conditions which are a known population standard deviation and a sample size (n = 40) greater than 30, the critical value of Za/2 is appropriate for calculating the margin of error in a skewed population.

In this scenario, a 95% confidence interval is being constructed for a population that is skewed. Given a sample size, n, of 40, the population standard deviation (σ) is 2.6. When we construct confidence intervals for such a scenario, we refer to either a Z-distribution (critical value of Za/2) or a T-distribution (critical value of ta/2) based on certain conditions.

A critical value of Za/2 is used when the population standard deviation is known, and the sample size is large enough (typically n > 30). A critical value of ta/2 is referred to when the population standard deviation is unknown, or the sample size is too small (typically n < 30).

In this case, the population is skewed, the standard deviation is known, and the sample size (n = 40) is larger than 30. Therefore, we should use the critical value of Za/2 for calculating the margin of error.

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Answer:103

Step-by-step explanation:

127 children and 264 adults swam at the public pool that day

Step-by-step explanation:

On a certain hot​ summer's day

We need to find how many children and how many adults swam at the public pool that​ day

Assume that the number of children is x and the number of adult is y in that day

∵ x children swam that day

∵ y adults swam that day

∵ 391 people used the swimming pool that day

- Add x and y, then equate the sum by 391

∴ x + y = 391 ⇒ (1)

∵ The daily price for children is $1.25 per child

∵ The daily price for an adult is $2.25

∵ The receipts for admission totaled $752.75

- Multiply x by 1.25 and y by 2.25, then add the products and

  equate the sum by 752.75

∴ 1.25x + 2.25y = 752.75

- Divide each term by 1.25 to simplify the equation

∴ x + 1.8y = 602.2 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate x

∵ (x - x) + (1.8y - y) = 602.2 - 391

∴ 0.8y = 211.2

- Divide both sides by 0.8

∴ y = 264

- Substitute the value of y in equation (1) to find x

∵ x + 264 = 391

- Subtract 264 from both sides

∴ x = 127

127 children and 264 adults swam at the public pool that day

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Answer:answer to the questions are x=1.396 or -0.896 and y=9.188 or 2.312

Step-by-step explanation: see attachment

Thanks for drawing my attention to my mistake. I appreciate.

Answer:

The solutions  (x, y) are (1.40, 9.19)  and  (-0.90, 2.32)  correct to 2  decimal places.

Step-by-step explanation:

As the 2 expressions in x are both equal to y we can write:

4x^2 + x = 3x + 5

4x^2 - 2x - 5 = 0

x = [ -(-2) +/- sqrt(4 - 4*4*-5)] /  2*4

= 0.25 +/- (sqrt 84)/8

x  = 1.396, -0.895.

When x =  1.396, y =  3(1.396) + 5 = 9.188

when x = 0.895, y = 3(-0.895) + 5 = 2.315.

Answer:

1/3 of his cards are basketball cards

Final answer:

Junior has 6 baseball and 4 basketball cards, making a total of 10 cards. The fraction of basketball cards is 4/10, which simplifies to 2/5, meaning 2 out of every 5 cards in Junior's collection are basketball cards.

Explanation:

Jr has 6 baseball cards and 4 basketball cards. The total number of cards Junior has is 10 (6 baseball cards + 4 basketball cards). To find out what fraction of Junior's cards are basketball cards, we divide the number of basketball cards by the total number of cards. Therefore, the fraction of Junior’s cards that are basketball cards is 4/10. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2, resulting in a simplified fraction of 2/5. So, 2 out of every 5 cards in Junior’s collection are basketball cards.

Answer:

x=6

y=5

Step-by-step explanation:

15x=90 (corresponding angles)

x=90/15

x=6

Now

5x+12y=90(vertical angles)

5(6)+12y=90

30+12y=90

12y=90-30

12y=60

y=5(dividing both sides by 12)

Answer:

X= -5

Step-by-step explanation:

Expression: 2.8X+12=-1.4X-9

Order it: 12+9=-1.4X-2.8X

Simplification: 21=-4.2X

Results: x=-5

A roller coaster can usually be considered a function if each time point corresponds to exactly one location of the car. However, there may be exceptions, such as during loops. The roller coaster also demonstrates conversions between potential and kinetic energy.

In mathematical terms, a roller coaster can be described as a function if each input (in this case, time) corresponds to exactly one output (the position of the roller coaster car). For a typical roller coaster, this would be the case, as at each moment in time during the ride, the car is at one specific location.

However, there might be exceptions. For example, if the roller coaster has a loop, there's a point in time where the car reaches the top of the loop, descends, goes around the loop, and ends up at the same vertical location as before but upside down. Two different positions correspond to the same 'height' input, hence it wouldn't be considered a function in regards to height.

The physics of roller coasters also involves conversions between potential and kinetic energy. The car gains potential energy as it climbs to the top of a hill then it loses potential energy but gains kinetic energy as it descends a hill.

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Answer:

The slope of the line is 2.

Step-by-step explanation:

slope = y2 - y1/x2 - x1

= -8 - 6/3 - (-4)

= 14/3 + 4

= 14/7

= 2

Answer:  Use the slope formula to find the slope  m .

m = -2

Step-by-step explanation:

Step-by-step explanation:

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

-5, first let's put it in the form y=mx+b.

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

y=-2x+3, so in this, m=slope and b=y-intercept. On your graph, plot three on the y line, and the slope is negative two, so go down two then over one to the left side, because it is decreasing. Also slope is rise over run or just rise/run.

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)  

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