Given that sin(3x-35)°-cos(x+20)° and x is an acute angle, find it's value

Answer:

yes it is 604892÷4=151,223

The required solution is 1(one) as per the given functions.

What is a function?

Every function has a(one) domain and codomain or range. A function is generally(ax) denoted by f(x) where x(ax) is the input

Given :

The function(one)

g(m)= m-4(four).

By put m is equal to 5(five) we get,

g(5)=5-4(four)

=1(one)

Hence, the required solution is 1(one) as per the given functions.

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Answer:

Step-by-step explanation:

From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.

0.007349 to 3 significant figure=0.00735

Answer:

a) $168,760

b) $119,275

Step-by-step explanation:

For this, I believe you do $288,035 - $49,485. This equals $238,550.

Then divide this by 2 to get the salary for state B, which is $119,275 .

$168,760 remains, so it's the salary for state A.

Answer:

Governor of state A = 168,760

Governor of state B = 119,275

Step-by-step explanation:

A = 49485 + B         Eq. 1

A + B = 288035       Eq. 2

A = Earns  of governor of state A

B = Earns of governor of state B

Replacing Eq. 1 in Eq. 2:

(49485+B) + B =288035

2B + 49485 = 288035

2B = 288035  - 49485

2B = 238550

B = 238550/2

B = 119275

From eq. 1

A = 49485 + 119275

A = 168760

Check:

from eq. 2:

A + B = 288035

168760 + 119275 = 288035

AAnswer:

AB (-1, 4) = 34^ and B = (3,-1) 249*32 = 20

Step-by-step explanation:

Answer:

[tex]AB=\sqrt{53}\:\sf units[/tex]

[tex]EF=\sqrt{349}\:\sf units[/tex]

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}.[/tex]

Given:

Substitute the given points into the distance formula and solve for AB:

[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-4))^2+(-1-1)^2}\\& =\sqrt{(7)^2+(-2)^2}\\& =\sqrt{49+4}\\& = \sqrt{53}\end{aligned}[/tex]

Given:

Substitute the given points into the distance formula and solve for EF:

[tex]\begin{aligned}\implies EF & =\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\& =\sqrt{(11-(-7))^2+(3-(-2))^2}\\& =\sqrt{18^2+5^2}\\& =\sqrt{324+25}\\& =\sqrt{349}\end{aligned}[/tex]

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Answer:

your answer is 7/2

Answer:

The figure is reflected over the line x = -2

Step-by-step explanation:

If you drew a vertical line at x = -2, you would see that each point is the same distance from x = -2  but on the right side.  E and E' are the same point because they are on the line x + -2.  Point D is 3 units to the left of x = -2 for D' is 3 units to the right of x = -2 and so one

Answer: 39 ounces of strawberry juice, 78 ounces of water.

Step-by-step explanation:

Since Molly uses "each ounce" meaning 1 per strawberry juice, 39 ounces of strawberry infused water would mean she uses 39 ounces of strawberry juice. Then, it says she uses two times as many as those 39 ounces of strawberry juice for water. This means you multiply 39 by 2 which means you get 78 ounces.

Molly uses 39 ounces of strawberry juice and 78 ounces of water to get 39 ounces of Strawberry Infused Water.

Answer:

  (a) $191,005.52

  (b) $180,309.67

  (c) lose $10,695.85

Step-by-step explanation:

You want the future values of an ordinary annuity of $12,000 over 12 years at interest rates of 5% and 4%. You also want the difference between the values.

The future value of an ordinary annuity with n annual deposits of P, at interest rate r compounded annually is given by ...

  FV = P((1+r)^n -1)/r

The value of $12,000 deposited for 12 years at 5% is ...

  FV = $12,000((1.05^12 -1)/0.05 = $191,005.52

At the end of 12 years, she will have $192,005.52 in her account.

The value of $12,000 deposited for 12 years at 4% is ...

  FV = $12,000((1.04^12 -1)/0.04 = $180,309.67

At the end of 12 years, she will have $180,309.67 in her account.

The amount at 5% is greater, so by investing in her sister's firm, the woman would lose ...

  $192,005.52 -180,309.67 = $10,695.85 . . . . amount lost

Answer:

Step-by-step explanation:

It is correct till 16/15

But after that it is 16/15 × 5/-3 = 80/-45

simplify it to 16/-9

Answer:

175

Step-by-step explanation:

because 7/8 of 200 is 175

The image of the triangle when rotated is F'(-2,-2), E(0, -3), D(-5,-5)

The vertices of the triangle are given as:

F(2,-2), E(3,0), D(5,-5)

The transformation rule is given as

90 degrees rotation

The rule of 90 degrees rotation is

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

When the above rule is applied to the vertices of the triangle, we have:

F'(-2,-2), E(0, -3), D(-5,-5)

Hence, the image of the triangle when rotated is F'(-2,-2), E(0, -3), D(-5,-5)

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The percent that the value is between 115 - 125 is 34.13%.

For the given question;

The total number of the sample is 500.

The mean of the sample is; μ = 125.

The standard distribution is; σ = 10.

The percentage of the values must lie between 115-125.

Thus,

P(115 < X < 125) = P[(115 - 125)/10 < (x - μ)/ σ < (125 - 125)/10]

                         = P[-1 < Z < +0]

Z for +0 = 0.50000 and z for -1 = 0.15866 obtained from Z-score table.

P(115 < X < 125) = [0.50000 - 0.15866]

P(115 < X < 125) = 0.34134

P(115 < X < 125) = 34.13%

Therefore, the probability for percent of the values lies between 115-125 is 34.13%.

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Answer: 361 miles

Step-by-step explanation: 26.95x3=80.85

200-80.85=119.15

119.15/0.33

=361.06

Answer: No solution

Step-by-step explanation:

-10x-16=14

-16x-6=14

-10x-16=-16x-6

-10x+16x-16=-16x+16x-6

6x-16=-6

6x-16+16=-6+16

6x=10

x=10/6

x=5/3

-16(5/3)-6=

-80/3-6*3/3=

-80/3-18/3=

(-80-18)/3=-98/3 [tex]\neq[/tex] 14

Hence, there is no solution

1) La piscina grande tardó 8 horas en ser vaciado, culminando a las 4: 10 PM, y la piscina pequeña tardó 5 horas y 20 minutos en ser vaciado, culminando a las 1: 30 PM.

2) La piscina grande tardará 2 horas y 40 minutos más en vaciarse que la piscina pequeña.

En este problema tenemos el caso de dos piscinas de diferente capacidad, la primera piscina tiene una capacidad de 240 000 litros de agua y la segunda piscina tiene una capacidad de 160 000 litros de agua. Ambas cuenta con un desagüe que desaloja a una tasa de 500 litros de agua por cada minuto de operación.

El tiempo total de vaciado es igual a volumen de la piscina dividido por la tasa de vaciado, entonces:

Piscina grande (V = 240 000 L, Q = 500 L / min)

t = V / Q

t = (240 000 L) / (500 L / min)

t = 480 min

Piscina pequeño (V = 160 000 L, Q = 500 L / min)

t = V / Q

t = (160 000 L) / (500 L / min)

t = 320 min

1) La piscina grande tardó 8 horas en ser vaciado, culminando a las 4: 10 PM, y la piscina pequeña tardó 5 horas y 20 minutos en ser vaciado, culminando a las 1: 30 PM.

2) La piscina grande tardará 2 horas y 40 minutos más en vaciarse que la piscina pequeña.

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Answer:

x> 1/2 y+5/2

i hope this helps you <33

3√5

The distance between two points on an XY plane is calculated using the distance formula, which is employed in coordinate geometry or Euclidean geometry. The x-coordinate, often known as the abscissa, is a point's separation from the y-axis. The y-coordinate, often known as the ordinate, refers to a point's separation from the x-axis. A point on the x-axis has coordinates of the form (x, 0), and a point on the y-axis has coordinates of the form (0, y). We utilize the Pythagoras theorem in this case to determine the separation between any two points in a plane.

Distance formula = √ ( x₁ - x₂)² + ( y₁ - y₂)²

                                = √ 6² + 3²

                                =3√5

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Answer:

6

Step-by-step explanation:

The union is defined as the set of all elements in at least one of the sets.

[tex]A \cup B=\{1,2,3,4,5,7\}[/tex]

So, there are 6 elements.

The representation of 1 / 8 in decimal form will be 0.125 and it is a rational number as it is a terminating decimal.

We are given a fraction:

1 / 8.

We have to represent it as a decimal and tell that it is a rational number.

To write it as a decimal, First we will make the denominator a multiple of 10:

1 / 8 × 125 / 125 = 125 / 1000.

Now writing it in the decimal form, we get that:

= 0.125.

Now, we can see that it is a non repeating terminating number.

So, we can say that it is a rational number.

Therefore, the representation of 1 / 8 in decimal form will be 0.125 and it is a rational number as it is a terminating decimal.

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Step-by-step explanation:

You want to know how the squeeze theorem applies to help you find the limit of f(x) is zero as x approaches zero.

The short of it is that you have ...

  f(x) = [messy finite function] × [function that cleanly approaches 0 at x=0]

The zero product rule tells you that the product of any finite value and 0 is zero, so the limit of this product is 0 at x=0.

The graph in the attachment shows the "function that cleanly approaches 0" in red. When multiplied by the "messy finite function", the result is the blue curve. You can see that the result is a function that has a limit of 0 at x=0.

Here, we'll decompose f(x) into two parts:

Messy finite function

The numerator sine function factor of f(x) gets increasingly messy as x approaches zero, due to the cosine term it contains. We can define ...

  [tex]g(x)=\sin(1+\cos(\pi x^{-3}))[/tex]

Because this is a sine function, its value is always in the range |g(x)| ≤ 1.

Function cleanly approaching zero

The remaining factors of f(x) need to be rearranged a bit to make a function that obviously approaches zero at x=0. We do that by factoring ∛x from the denominator and rearranging the leading fraction.

  [tex]h(x)=\dfrac{e\dfrac{-1}{13+x^{-2}}\sqrt{3x^4+5x^6}}{(x+x^{1/3})(3+\arctan\sqrt{7+x^{-8}})}\\\\=-e\dfrac{x^2}{13x^2+1}\cdot\dfrac{x^2\sqrt{3+5x^2}}{x^{1/3}(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}\\\\h(x)=-e\dfrac{x^{11/3}\sqrt{3+5x^2}}{(13x^2+1)(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}[/tex]

Recognizing that the arctangent term will approach π/2 as x→0, this can be (more or less) directly evaluated at x=0 to give ...

  [tex]h(0)=-e\dfrac{0\cdot\sqrt{3}}{1\cdot1\cdot(3+\dfrac{\pi}{2})}=0[/tex]

The sign of h(x) will be opposite the sign of x. The graph of h(x) is shown in red in the attachment.

As h(x) approaches zero, the product ...

  f(x) = g(x)·h(x)

approaches zero. This is the essence of the squeeze.

Starting from our description of g(x) above, we can multiply both sides of the inequality by the positive value |h(x)| to get ...

  |g(x)| ≤ 1 . . . . . . . . . . the range of the sine function

  |h(x)|·|g(x)| ≤ |h(x)|·1 . . . . . . multiply by |h(x)|

Simplifying, this is ...

  |f(x)| ≤ |h(x)| . . . . true for all x

So, the limit is ...

  [tex]\displaystyle \lim_{x\to0}|f(x)|\le\lim_{x\to 0}|h(x)|\\\\\lim_{x\to0}|f(x)|=0[/tex]

The attachment illustrates this nicely, showing that the oscillating f(x) has its amplitude limited by h(x), which approaches zero.

__

Additional comments

The limit of x^-8 is positive infinity as x approaches zero. This means the arctangent function argument is positive infinity as x approaches zero, so the function value is π/2. The sign of x is irrelevant.

We cannot tell if the fraction following "e" in this function is supposed to be an exponent. The two typeset versions of f(x) seem to show "e" as a multiplier, not the base of an exponential term. Even if an exponential term is what is intended, that term would approach 1 at x=0, so the conclusion here remains unchanged.

Answer: 34 in one bucket, 62 in the other

======================================================

Work Shown:

x = number of golf balls in bucket A

y = number of golf balls in bucket B

Let's say bucket B has more golf balls. More specifically it has 28 more golf balls, so,

y = x+28

The two quantities must add to 96 golf balls total.

x+y = 96

x+x+28 = 96

2x+28 = 96

2x = 96-28

2x = 68

x = 68/2

x = 34 is the number of golf balls in bucket A

y = x+28

y = 34+28

y = 62 is the number of golf balls in bucket B

-------------

Check:

x+y = 34+62 = 96

The answer is confirmed.

They will weigh the same at twenty-five months.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Let the number of months when they will weigh the same would be m

Given that Bill is losing two pounds per month and is currently 240 pounds.

So his model expression of weight would be: 240 - 2m

And Bill is losing four pounds per month and is currently 290 pounds.

So his model expression of weight would be: 290 - 4m

As per the condition, they will weigh the same

⇒ 240 - 2m = 290 - 4m

⇒ 4m - 2m = 290 - 240

⇒ 2m = 50

⇒ m = 25

Therefore, they will weigh the same at twenty-five months.

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Answer:

x=-8

Step-by-step explanation:

8x-2=3x+5x

1. Combine Like Terms

3x+5x=8x

Now your equation looks like this:

8x-2=8x

+8x   +8x

2. Move Variables to one side

Now this is your equation:

-2=16x

3. Divide to isolate "x"

16/-2

x=-8

Let me know if this helped! :)

The number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.

Let the number of dimes be x.

So, we get that:

The number of quarters will be = x + 2

The number of nickels will be = 2 x

Now, 1 dime = $0.10.

1 nickel = $ 0.05

1 quarter =  $ 0.25

Amount of dimes = 0.10 x

Amount of nickels = 0.10 x

Amount of quarters = 0.25 x + 0.5

Total amount of coins = $ 1.85

So, we get the equation as:

0.10 x + 0.10 x + 0.25 x + 0.5 = 1.85

0.45 x = 1.35

x = 135 / 45

x = 3

Dimes = 3

Nickels = 6

Quarters = 5

Therefore, we get that, the number of dimes that we have are 3, the number of nickels are 6 and the number of quarters are 5.

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