Decide which trigonometric ratio to use. Solve for x in the triangle below.  Round your answer to the hundredths place.
Options
4.59

0.07

6.55

5.60

The answer is:

The second option,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Discarding each given option in order to find the correct one, we have:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

The statement is true, we can prove it by using the following properties of exponents:

[tex](a^{b})^{c}=a^{bc}[/tex]

[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]

We are given the expression:

[tex](\sqrt[m]{x^{a} } )^{b}[/tex]

So, applying the properties, we have:

[tex](\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }[/tex]

Hence,

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}[/tex]

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}[/tex]

The statement is false, the correct form of the statement (according to the property of roots) is:

[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }[/tex]

Hence, the answer is, the statement that is true is the second statement:

[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]

Have a nice day!

The dress is originally 160$, but we take 30% off which is that same as .3 .

To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.

48 is 30% of 160 so to find the new price of the dress we need to subtract

160 - 48 = 112. The new price of the dress is 112$.

Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$.  10% is also .1, so we will multiply 112 by .1 which equals 11.20.

As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.

For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.

Claire will be paying 108.36$ for the prom dress.

Answer:

c

Step-by-step explanation:

to find out how many stamps monica originally had, you’d have to do the equation given, “reversed”

equation given: 35 + 20 - 5 - 10

but because we are trying to find how many she originally had left, you’d have to do opposite operations (reverse) in the equation given.

35 - 20 + 5 + 10 = 30

so, this means that monica had 30 stamps originally

Answer:

D)

Step-by-step explanation:

The exponential functions are in the form of

[tex]f(x)= ka^x[/tex]

Hence we can see here that the variable x is in the exponential in such functions. Therefore the option D is the correct as in this the x is the exponent.

Therefore the option D) is our exponential functions

Answer:

6 per minute

Because you divide by 8 minutes

1/2 of the cake was eaten

1+2=3. 3/6=1/2

All the slices are the same size

Answer: 2

Step-by-step explanation:

add the 1 to the other 1 and it equals 2

Answer:

2

Step-by-step explanation:

1 and 1 is 2

Angle p and Angle q are both inscribed angles. This means that their angle is half of the inscribed arc.

measure of angle p = 1/2 60 degrees

angle p = 30 degrees

measure of angle q = 1/2 100 degrees

angle q = 50 degrees

Answer:

30

Step-by-step explanation:

Answer:

[tex]g(x)=3x+2[/tex]

Step-by-step explanation:

we have

[tex]f(x)=2x[/tex] ----> linear equation

[tex]gof(x)=6x+2[/tex] ---> linear equation

therefore

g(x)-----> will be a linear equation

so

Let

[tex]g(x)=ax+b[/tex]

so

[tex]gof(x)=a(2x)+b[/tex] ----> equation A

[tex]gof(x)=6x+2[/tex] ----> equation B

equate equation A and equation B

[tex]a(2x)+b=6x+2[/tex]

[tex]2ax=6x ----> a=3[/tex]

[tex]b=2[/tex]

Hence

[tex]g(x)=3x+2[/tex]

Answer:

C. (-1, 0)

Step-by-step explanation:

(You don't need a picture to figure this out...it's simple algebraic manipulation.)

We could start off by rewriting the equation for the parabola with the negative on the other side, which tells us then that the parabola opens downward:

[tex]-(x+1)^2=8(y-2)[/tex]

Dividing both sides by -1 doesn't change anything.  Because this parabola opens downward, the focus is p units below the vertex at the same x-coordinate.  The vertex can be found from the equation to be (-1, 2).  The standard form of a parabola of this type is

[tex]-(x-h)^2=4p(y-k)[/tex]

where is the number of units between the vertex and the focus.  Our equation to find p is:

4p = 8 so p = 2.

That means that the focus is 2 units below the vertex at the x coordinate of -1.  Moving 2 units down from the y coordinate of 2 leaves us at a y coordinate of 0.  Therefore, the coordinates of the focus have to be (-1, 0)

Answer:3100 with 9%

Step-by-step explanation:

Answer:

The answer is $3,100 at 9%; $4,900 at 11%

Step-by-step explanation:

You can solve this problem with a system of equations, that is, a system that can contain 2 or more equations. In this case, arms 2 linear equations with two variables: x and y. So first you define what your variables are:

Now you can define the system of equations. On the one hand you know that in the account that has 11% interest Mr. Brownwood deposited $1800 more than in the other account. In an equation and according to the previously defined variables this means: y=x+1800 Equation (A)

On the other hand, you know Mr. Brownwood earned $ 818 in interest. This means that the sum between the interest generated in the account deposited with 9% interest plus the interest generated in the account deposited with 11% interest is $ 818. And to calculate the amount of money generated by interest you multiply the percentage of interest by the amount deposited.  Remember that to convert from percentage to decimal you must divide the number by 100. Then 9% is 0.09 and 11% is 0.11. In summary, considering this, you get the equation: 0.09*x+0.11*y=818 Equation (B)

Now you have both equations with the two variables to solve the system. There are several ways to solve the system. One of the most used ways is substitution, which consists in isolating one of the variables from one of the equations and replacing it in the other equation.

In this case you isolate the variable "y" from equation A, and you get:  y=1800+x

Now replace it in equation (B): 0.09*x+0.11*(1800+x)=818

First you apply distributive property, which consists of distributing the multiplication by the terms within the parenthesis:

0.09*x+0.11*1800+0.11*x=818

0.09*x+198+0.11*x=818

Now, we leave the variable x on one side of the equality, in this case the left, and the numbers without the variable on the other side, in this case the right. To pass the numbers from one side of the equality to the other, you must keep in mind that you must use the opposite operation, that is, if the number 198 is adding on one side of the equality, the other side is subtracted:

0.09*x+0.11*x=818-198

Now you perform the corresponding operations. Then you isolate the variable and, and as in the previous case, you pass the number that accompanies the variable on the other side of equality with the opposite operation. In this case it is multiplying and its opposite operation is the division:

0.2*x=620

[tex]x=\frac{620}{0.2}[/tex]

x=3100

Now you replace this value in either of the two equations, A or B, and solve that equation to get the value of y. So: y=4900

Remembering that x was amount of money invested in the account with 9% interest and y was amount of money invested in the account with 11% interest, you can say that $3100 was the amount invested at 9% and $4900 was the amount invested at 11%

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50[/tex]

50 grams of that sample will be left after 20 years since it’s only gone through one half-life exactly.

Answer:

2 hours,  142 miles

Step-by-step explanation:

Write a distance formula for both cars and then equate these formulas:

Car A:  y = 55x + 32  =  y = 42x + 58:  Car B

Then 55x + 32  =  y = 42x + 58  →  13x = 26, and so x = 2

That distance will be 55(2) + 32, or 142 miles.

The cars will reach the same point after 2 hours (first possible answer)

An equation is formed when two equal expressions. The correct option is A, 2hours, and 142 miles.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation for the distance covered by car A in x hours is y = 55x + 32, similarly, the equation for the distance covered by Car B in x hours is y=42x+58.

Now, to know at what time and at what distance the two cars will meet we need to solve the two equations. Since the car will cover the same distance we can write,

y = y

55x + 32 = 42x + 58

55x - 42x = 58 - 32

13x = 26

x = 2

Substitute the value of x in any one of the equations,

y = 55x + 32

y = 55(2) + 32

y = 110 + 32

y = 142

Thus, the car will meet after 2 hours, and the distance will be 142 miles.

Hence, the correct option is A, 2hours, and 142 miles.

Learn more about Equation:

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For the first 8 hours he makes $12.00 per hour.

$12.00 * 8 = $96.00

Now you have $128.00 = 16.00h + $96.00

Subtract 96 from each side:

32 = 16h

Divide both sides by 16:

h = 2

He worked 2 hours of overtime.

Answer: True

Step-by-step explanation:

By definition for a function of the form:

[tex]ax ^ n + ... + bx + c[/tex]

It is true that if [tex]a <0[/tex] and n is odd then:

[tex]\lim_{n \to -\infty}ax^n + ...+bx+c = \infty[/tex]

In this case

[tex]f(x)=-2x^3-2x^2+7x-25[/tex]

Therefore

[tex]a=-2<0[/tex] and [tex]n =3[/tex] → odd number

Then

[tex]\lim_{n \to -\infty}-2x^3-2x^2+7x-25= \infty[/tex]

This means that when [tex]x \to -\infty,\ f(x) \to \infty[/tex]

The statement  x -> -∞, f(x) -> ∞  is True

Answer: Its is True

Answer:

109 kg total

57 3/4 after

Step-by-step explanation:

31/4 orange

302/4 pineapples

103/4 bananas

436/4 total=109

436/4-205/4=231/4=57 3/4

The solution involves using the distance formula to calculate the lengths of the sides of triangles ABC and ABD, and the Pythagorean theorem to identify the type of triangles they are by their side lengths.

To determine the characteristics of triangle ABC with vertices A(1, 7), B(-2, 2), and C(4, 2), we use the distance formula which is relevant because the length of the side of the triangle labeled a is the difference in the x-coordinates of points A and B. The same applies for side b, being the difference in the y-coordinates of points B and C. The length of side c is derived from the Pythagorean theorem, understanding that c represents the longest side of a right triangle, which is the hypotenuse.

Considering triangle ABD with an additional point D(1, 2), we first need to determine the lengths of the sides by using the formula for distance between two points in a coordinate plane for sides AB, BD, and AD. This will help to ascertain the type of triangle ABD is, based on the lengths of its sides. The length of side AD can be directly obtained since points A and D have the same x-coordinate.

The longest side of triangle ABC, which we determine by comparing the calculated lengths of AB, BC, and AC, will help us state whether the triangle is isosceles, scalene, or equilateral. For triangle ABD, once we have the lengths of AB, BD, and AD, we can determine its type similarly. This understanding stems from the standard geometric principles and the properties of triangles in a Euclidean space.

Answer:

18

Step-by-step explanation:

The hypotenuse is BC.

According to the Pythagorean Theorem;

[tex]BC^2=AC^2+AB^2[/tex]

Since the base angles are equal:

[tex]AC=BC=9\sqrt{2}[/tex]

We substitute the given values into the formula to obtain:

[tex]BC^2=AC^2+AB^2[/tex]

[tex]BC^2=(9\sqrt{2})^2+(9\sqrt{2})^2[/tex]

[tex]BC^2=81(2)+81(2)[/tex]

[tex]BC^2=162+162[/tex]

[tex]BC^2=324[/tex]

Take positive square root.

[tex]BC=\sqrt{324}[/tex]

[tex]BC=18[/tex]

Hence the hypotenuse is 18 units

Answer:

The domain is all real values

Step-by-step explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

In this case, we can observe from the graph that the function is defined for all x-values. So the domain is all real values.

Answer:

21 in

Step-by-step explanation:

The law of cosines is helpful for this. The angle opposite the shorter diagonal is the supplement of the angle shown, so is 60°.

If we designate the known sides as "a" and "b", the short diagonal as "c" and the smaller angle as C, then the law of cosines tells us ...

c^2 = a^2 + b^2 -2ab·cos(C)

For the given dimensions, we have ...

c = √(15^2 +24^2 -2·15·24·cos(60°)) = √441 = 21 . . . inches

True, we have the exactly same values in both domains.

Answer:

this is true!

Step-by-step explanation:

it is true because both have the exactly same values in both domains.

hope this helps :)

i dunno man, B looks about right.

Answer: c. The class median is lower than the exam median.

Step-by-step explanation:

the median is at a lower point on the number line, its to the left of the exam, so that means its lower

Answer:

A. 20.

Step-by-step explanation:

The denominators 49 and 100  are the squares of 1/2 of the lengths of the minor and major axis.  The standard form is x^2/a^2 + y^2/b^2 = 1  so

a = 2 * √49 and b = 2 * √100.

The length of the major axis is therefore    2* √100

= 2 * 10

= 20 (answer).

Answer:  A. 20

Step-by-step explanation:

For the general equation of ellipse :-

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

If a > b , then the length of major axis = 2a

If b> a , then the length of major axis = 2b

The given equation : [tex]\dfrac{(x-3)^2}{49}+\dfrac{(y+6)^2}{100}=1[/tex]

Which can be written as :

[tex]\dfrac{(x-3)^2}{7^2}+\dfrac{(y+6)^2}{10^2}=1[/tex]

Here 10 >7 , then the length of major axis =2(10)=20 units

V = (π/6)d^3

Using π = 22/7 and d = 14 ft, the volume is

 V = (22/7)/6*(14 ft)^3 = 4,312/3 ft^3

Answer:

2 1/2

Step-by-step explanation:

you have 2 whole pizzas and 1 half (1/2)

Answer:

D

Step-by-step explanation:

just took it

70 over sin40 degrees

Answer:

The length of the kite string in terms of trigonometric ratios, if we call it L, is [tex]L=\frac{70}{sin(40\°)}ft[/tex]

Step-by-step explanation:

As we have to use the trigonometric ratios, and knowing that in a right triangle the relation

[tex]hypotenuse*sin(angle)=opposite leg[/tex]

is valid. We call the hypotenuse as L, and we know the other two data (angle and opposite leg), so we have that

[tex]L*sin(40\°)=70ft\Leftrightarrow L=\frac{70}{sin(40\°)}ft[/tex]

Then,

[tex]L=\frac{70}{sin(40\°)}ft[/tex]

is the answer that we are looking for to solve the problem.

Answer:

147.75

Step-by-step explanation:

2lw+2lh+2wh

2 (5.5)(3)+2 (5.5)(6.75)+2(3)(6.75)

=147.75

Final answer:

To find the surface area of a rectangular prism with dimensions 5.5 cm by 3 cm by 6.75 cm, we calculate the area of each pair of faces and sum them up to get a total surface area of 147.75 square centimeters.

Explanation:

To find the exact value of the surface area of a rectangular prism, we use the formula for surface area, which is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism. Given the dimensions, l = 5.5 cm, w = 3 cm, and h = 6.75 cm, we can calculate the surface area as follows:

Calculate the area of the two length by width sides: 2(5.5 cm  imes 3 cm) = 33 cm²

Calculate the area of the two length by height sides: 2(5.5 cm  imes 6.75 cm) = 74.25 cm²

Calculate the area of the two width by height sides: 2(3 cm  imes 6.75 cm) = 40.5 cm²

Add these areas together to get the total surface area: 33 cm² + 74.25 cm² + 40.5 cm² = 147.75 cm²

Hence, the exact value of the surface area of the rectangular prism is 147.75 square centimeters.

hope it helps you!!!!!!!!!!!!!

Answer: Y=2 !! ;) XD ;P

Answer:

1/6

Step-by-step explanation:

The probability of tossing 6 tails in a row with a fair coin is 1/64, as each toss's outcome is independent and the probability of tail on a single toss is 1/2.

To compute the probability of tossing 6 tails in a row with a fair coin, you recognize that for each individual toss, the probability of getting a tail is ½. Since each toss is independent, you simply multiply the probabilities of each event occurring consecutively. Therefore, the probability of tossing 6 tails in a row is:

(½) × (½) × (½) × (½) × (½) × (½) = ½6

½6 = 1/64

So, the probability of tossing 6 tails in a row is 1/64.

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[tex]\bf (x-4)+(3x)+100=180\implies x-4+3x+100=180 \\\\\\ 4x+96=180\implies 4x=84\implies x=\cfrac{84}{4}\implies x=21[/tex]