I need help with this. This is hard.

Answer:

The correct option is

Option d. Sin θ = -√65/9 and Tan θ  =  -√65/4

Step-by-step explanation:

Points to remeber

Sin θ = Opposit side/ Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ= Opposite side /Adjacent side

To find opposite side

It is given that,

Cos θ = -4/9 = Adjacent side/Hypotenuse

We can find opposite  side of angle θ

opposit side ² = Hypotenuse² - adjacent side² = 9² - 4²

    = 81 - 16 = 65

Opposite side = √65

To find sinθ and tanθ

Sin θ = Opposit side/ Hypotenuse = -√65/9

Tan θ = Opposite side /Adjacent side = -√65/4

Therefore the correct option is

Option d. Sin θ = -√65/9 and Tan θ  =  -√65/4

Final answer:

To find the two numbers where their sum is 9 and their difference is 1, set up two equations x + y = 9 and x - y = 1. Solve these equations simultaneously to get the numbers 5 and 4.

Explanation:

The question asks to find two numbers where their sum is 9 and their difference is 1. The solution involves setting up two equations based on the information given:

Let the first number be x and the second number be y.

The sum of the two numbers is 9, so we have the equation x + y = 9.

The difference between the two numbers is 1, leading to the equation x - y = 1.

We can solve these two equations simultaneously to find the values of x and y. Adding the two equations together leads to 2x = 10, which simplifies to x = 5. Substituting x back into one of the original equations, for example, x + y = 9, we get 5 + y = 9, which simplifies to y = 4.

Therefore, the two numbers are 5 and 4.

Answer:

Final answer is approx x=0.16.

Step-by-step explanation:

Given equation is [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]

Now we need to solve equation [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex] and round to the nearest hundredth.

[tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]

[tex]2.8\times 13^{4x} = 19.3-4.8 [/tex]

[tex]2.8\times 13^{4x} = 14.5 [/tex]

[tex]13^{4x} = \frac{14.5}{2.8} [/tex]

[tex]13^{4x} = 5.17857142857 [/tex]

[tex]\log(13^{4x}) = \log(5.17857142857) [/tex]

[tex]4x \log(13) = \log(5.17857142857) [/tex]

[tex]4x = \frac{\log(5.17857142857)}{\log\left(13\right)} [/tex]

[tex]4x = 0.641154659628 [/tex]

[tex]x = \frac{0.641154659628}{4} [/tex]

[tex]x = 0.160288664907 [/tex]

Round to the nearest hundredth.

Hence final answer is approx x=0.16.

The answer is true because false would mean that it’s another crazy definition. But yes it is true

A rational function is a fractional expression in the form f(x) = p(x)/q(x), where q(x) cannot be zero.

Example: f(x) = 3x/(4x - 2).

True is the answer.

ANSWER

[tex]b = \frac{1}{3} [/tex]

[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]

EXPLANATION

The given expression is

[tex](b - 5) {x}^{2} - (b - 2)x + b = 0[/tex]

If

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

is a root, then it must satisfy the given equation.

[tex](b - 5) {( \frac{1}{2} )}^{2} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]

[tex](b - 5) {( \frac{1}{4} )} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]

Multiply through by 4,

[tex](b - 5)- 2(b - 2)+4 b = 0[/tex]

Expand:

[tex]b - 5- 2b + 4+4 b = 0[/tex]

Group similar terms;

[tex]b - 2b + 4b = 5 - 4[/tex]

[tex]3b = 1[/tex]

[tex]b = \frac{1}{3} [/tex]

Our equation then becomes:

[tex]( \frac{1}{3} - 5) {x}^{2} - ( \frac{1}{3} - 2)x + \frac{1}{3} = 0[/tex]

[tex]( - \frac{14}{3} ) {x}^{2} - ( - \frac{5}{3} )x + \frac{1}{3} = 0[/tex]

[tex] - 14{x}^{2} + 5x + 1= 0[/tex]

Factor:

[tex](2x - 1)(7x + 1) = 0[/tex]

[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]

The length of the rectangular room is 12 ft

To find the length of the rectangular room by using the formula for the area of a rectangle:

Area = Length * Width

Given that Area of a rectangular room = 120 [tex]ft^{2}[/tex]

Width = 10 ft

Length = ?

To calculate the length of the rectangular room,

Length = Area/Width

Length = 120/10

Length = 12 ft

Therefore, the length of the rectangular room is 12 ft

Answer:

[tex]37.2\ m[/tex]

Step-by-step explanation:

Let

h-----> the height of the light pole

we know that

In the right triangle of the figure

[tex]sin(60\°)=\frac{h}{43}[/tex]

[tex]h=sin(60\°)(43)=37.2\ m[/tex]

Answer:

[tex]\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)[/tex]

Step-by-step explanation:

The given logarithmic expression is

[tex]\log_b(\frac{x^3}{y^2} )[/tex]

Recall and use the quotient rule of logarithms;

[tex]\log_b(MN)=\log_b(M)-\log_b(N)[/tex];

We apply this property to obtain;

[tex]\log_b(\frac{x^3}{y^2} )=\log_b(x^3)-\log_b(y^2)[/tex]

Recall again that;

[tex]\log_b(M^n)=n\log_b(M)[/tex]

We apply this property also to obtain;

[tex]\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)[/tex]

Answer:

the length of flower at the end of week is 10 7/8 inches.

Step-by-step explanation:

Original height = 9 3/4 inches

=> 39/4 inches

Growth in one week = 1 1/8 inches

=> 9/8  inches

The height by the end of week = Original height +  growth

=> 39/4 + 9/8

=> (39*2)/4*2 + 9/8

=> 78/8 + 9/8

=> 87/8 inches

=> 10 7/8 inches

Therefore, the length of flower at the end of week is 10 7/8 inches.

Final answer:

To find the height of the flower at the end of the week, add the initial height of 9 3/4 inches to the growth of 1 1/8 inches, resulting in a new height of 10 7/8 inches.

Explanation:

The question asks how tall the flower will be at the end of the week after growing an additional 1 1/8 inches from its original height of 9 3/4 inches. To find the answer, you simply add these two measurements.

First, convert the mixed numbers to improper fractions to make them easier to add:

Now, add the two improper fractions together:
(39/4) + (9/8) = (39/4) × (2/2) + (9/8) = (78/8) + (9/8) = 87/8

Convert 87/8 back to a mixed number:

87 divided by 8 is 10 with a remainder of 7, so the mixed number is 10 7/8 inches.

So, the flower will be 10 7/8 inches tall at the end of the week.

The last one does

in the first for the image (the letters with ') are on the smaller shape where as on the last one it is on the bigger shape meaning it is the enlargement of TYO

Answer:

the last one

Step-by-step explanation:

I did this assignment.

Answer: third option

Step-by-step explanation:

As you can see in the figure attached, the triangle is a right triangle.

Then, you can calculate cosA as it is shown below:

- You need to remember the following:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

- Now, you must substitute values. Based on the figure:

[tex]adjacent=3\\ hyppotenuse=5[/tex]

[tex]\alpha=A[/tex]

Therefore, you obtain that cosA is:

[tex]cosA=\frac{3}{5}[/tex]

Answer:

Cos A = 3/5

Step-by-step explanation:

We are given a right angled triangle, ΔBCD,  with all three side lengths known and we are to find the value of Cos A.

We Cos is the ratio of the base of the triangle to its hypotenuse, with respect to the angle (here angle A).

Considering the angle A, our perpendicular is CD, base is BC and hypotenuse BD.

Therefore, Cos A = BC/BD = 3/5

Answer:

The two triangles may be congruent, but additional information is needed about the third angle in each triangle

Answer:

If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.

Step-by-step explanation:

What is the inverse of the following statement? If two triangles are congruent, then their corresponding angles are congruent.

Inverse of a statement means its opposite or negating both the hypothesis and conclusion of a conditional statement.  

So, the inverse of the given statement will be :

If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.

Answer:

-10/3, 10/3

Step-by-step explanation:

(In this answer I will use y' to denote the derivative of y with respect to t. You shouldn't normally do this because y' normally means the derivative of y with respect to x but I'll be a bit messy for this case)

First calculate the derivatives:

[tex]y=\cos(kt) \Rightarrow y'=-k\sin(kt) \Rightarrow y'' = -k^2\cos(kt)[/tex].

Then plug the derivtes y'' and y into the equation:

[tex]-9k^2\cos(kt) = -100\cos(kt)[/tex]

Solve the equation for k:

[tex]100\cos(kt) - 9k^2\cos(kt) = 0 \\\\\Rightarrow \cos(kt)(100-9k^2) = 0[/tex]

So then we have that [tex]y=\cos(kt)[/tex] satisfies the differential equation when [tex]\cos(kt) = 0[/tex] or when [tex]100-9k^2=0[/tex] (or both). The solutions to these equations are:

[tex]\left \{ {{\cos(kt)=0 \Rightarrow k=\frac{n\pi}{2t}} \atop {100-9k^2 = 0 \Rightarrow k= \pm \sqrt{\frac{100}{9}}=\pm \frac{10}{3}}} \right.[/tex]

I understand that looks a bit complicated and I doubt you would have to give your answers in terms of t so if it asks for a separated list of answers I would go for:

k = -10/3, 10/3.

The values are [tex]k = \pm \frac{10}{3}[/tex].

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

The function is:

[tex]y = \cos{kt}[/tex]

The derivatives are:

[tex]y^{\prime}(t) = -k\sin{kt}[/tex]

[tex]y^{\prime\prime}(t) = -k^2\cos{kt}[/tex]

The equation is:

[tex]9y^{\prime\prime} = -100y[/tex]

Replacing:

[tex]-9k^2\cos{kt} = -100\cos{kt}[/tex]

[tex]9k^2 = 100[/tex]

[tex]k^2 = \frac{100}{9}[/tex]

[tex]k = \pm \sqrt{\frac{100}{9}}[/tex]

[tex]k = \pm \frac{10}{3}[/tex]

Those are the values.

A similar problem is given at https://brainly.com/question/24348029

Final answer:

The random variable X represents claim amounts for wind damage to insured homes. The probability that a claim is below average is 19/27. The expected value of the largest claim is 2.025 and the expected value of the smallest claim is 1.125.

Explanation:

a. The random variable X represents the claim amounts for wind damage to insured homes.

b. To find the probability that a claim is below average, we first need to calculate the average claim amount. We can do this by finding the expected value of X, which is given by E(X) = ∫[10,∞]x * f(x) dx, where f(x) is the density function of X. Evaluating this integral, we get E(X) = 19/27. Therefore, the probability that a claim is below average is P(X < E(X)) = P(X < 19/27) = 19/27.

c. The expected value of the largest of the three claims can be calculated by finding the maximum of three independent random variables with density f(x). Since the density is continuous, the probability that the maximum claim amount is less than or equal to x is given by P(X₁ ≤ x, X₂ ≤ x, X₃ ≤ x) = [F(x)]³, where F(x) is the cumulative distribution function of X. To find the expected value, we need to find the maximum amount x such that [F(x)]³ = 1/2. Solving this equation, we get x ≈ 2.025.

d. Similarly, the expected value of the smallest of the three claims can be calculated by finding the minimum of three independent random variables with density f(x). The probability that the minimum claim amount is greater than or equal to x is given by P(X₁ ≥ x, X₂ ≥ x, X₃ ≥ x) = [1 - F(x)]³. To find the expected value, we need to find the minimum amount x such that [1 - F(x)]³ = 1/2. Solving this equation, we get x ≈ 1.125.

Answer:

c. 4.9713

That's the answer

Step-by-step explanation: usatestprep approved

The graph of the linear equation with m > 0 and b < 0 is in the image at the end.

For which line is it true that m > 0 and b < 0?

A general linear equation is written as:

y = mx + b

Where m is the slope and b is the y-intercept.

With this we can see that the correct option from the given ones is the second graph. You can see the image below.

Answer:

If 2/5 is 240 then 1/5 is 120..multiply 120 by 5 which is 600 so...

600=total

Then..multiply 120 by 3 which will give the 3/5 boys which is 360 so...

360 boys

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

First, using the Pythagorean theorem, you can make the equation 10^2+y^2=26^2. You can solve this to get y=24. Another way to solve for the value of y is to use your Pythagorean triples! (in this case, all the values are double the values of the Pythagorean triple 5, 12, 13).

Next, you can use the Pythagorean theorem again to get the equation 24^2+x^2=30^2. Solving it, you would get x=18.

Hope this helps!

Answer:

  correct

Step-by-step explanation:

The asymptotes of the cotangent function are at multiples of π. The cosine function has no asymptotes.

sec(x)² = 1 + tan(x)² so both functions have their vertical asymptotes in the same places.

Answer:

this is basic math area and primeemator

so take the triangles and put them together then add it up so it would look like this 9+9+11.75+11.75 = 41.5 them times 41.5 times the price per foot like this

41.5 X 4.25 = 176.38 thats how mush he would have to pay

Answer: $449.44

Step-by-step explanation: please see images below!

Answer:The domain: x > -2\to x\in(-2;\ \infty)

Step-by-step explanation:

y = ln(x + 2)

D:

x + 2 > 0    |subtract 2 from both sides

x > -2

Answer: The domain: x > -2\to x\in(-2;\ \infty)

Answer:

[tex]\large\boxed{x>-2\to x\in(-2,\ \infty)}[/tex]

Step-by-step explanation:

[tex]\text{The domain of}\ \log_ax:\\\\a>0\ \wedge\ a\neq1\ \vedge\ x>0\\=========================\\\\y=\ln(x+2)\\\\\text{The domain:}\\\\x+2>0\qquad\text{subtract 2 from both sides}\\\\x+2-2>0-2\\\\x>-2\to x\in(-2,\ \infty)[/tex]

Answer:

A. (x - 5)(x - 5)

Step-by-step explanation:

We will do this the old fashioned way...just plain old factoring.  

This polynomial is of the form

[tex]y=ax^2+bx+c[/tex]

The product of a and c have to add up to equal the "middle" term, -10.  

a = 1, b = -10, c = 25

a * c = 1 * 25 = 25

Now we need the factors of 25 to find the combination of factors that will result in a -10.  The factors of 25 are: 1, 25 and 5, 5

5 and 5 add up to be 10, but since we need a -10, we will use -5 and -5.  The product of -5 * -5 = 25, so we are not messing anything up by using the negative 5.

Putting them in order in standard form we have

[tex]x^2-5x-5x+25[/tex]

Factor by grouping:

[tex](x^2-5x)-(5x+25)[/tex]

There is an x common to both terms in the first set of parenthesis, so we will factor that out; there is a 5 common to both terms in the second set of parenthesis, so we will factor that out:

x(x - 5) - 5(x - 5)

NOW what's common in both terms is the (x - 5) so we factor THAT out, and what's left gets grouped together:

(x - 5)(x - 5)

Answer:

73.2°

Step-by-step explanation:

Use Law of Sines to solve:

(Sin 50)/20 = (Sin B)/25    

Solve for Sin B

[25(Sin 50)]/20 = Sin B

Use Sin^-1 x to solve   (sine inverse)

Sin^-1 ( [25(Sin 50)]/20 ) = B

B = 73.24685774

Answer:

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{RQ}{\sin(\angle P)}=\dfrac{PR}{\sin(\angle Q)}[/tex]

We have

[tex]RQ=20\ in\\\\m\angle P=50^o\to\sin50^o\approx0.766\\\\PR=25\ in[/tex]

Substitute:

[tex]\dfrac{20}{0.766}=\dfrac{25}{\sin(\angle Q)}[/tex]     cross multiply

[tex]20\sin(\angle Q)=(25)(0.766)[/tex]

[tex]20\sin(\angle Q)=19.15[/tex]            divide both sides by 20

[tex]\sin(\angle Q)=0.9575\to m\angle Q\approx73^o[/tex]

Answer:

Step-by-step explanation:

Use the cosine law:

[tex]AB^2=CB^2+CA^2-(CB)(CA)\cos(\angle C)[/tex]

We have:

[tex]AB=6,\ CB=6.5,\ CA=7.5[/tex]

Substitute:

[tex]6^2=6.5^2+7.5^2-2(6.5)(7.5)\cos(\angle C)[/tex]

[tex]36=42.25+56.25-97.5\cos(\angle C)[/tex]

[tex]36=98.5-97.5\cos(\angle C)[/tex]           subtract 98.5 from both sides

[tex]-62.5=-97.5\cos(\angle C)[/tex]           divide both sides by (-97.5)

[tex]\cos(\angle C)\approx0.641\to m\angle C\approx50^o[/tex]

Answer: The price of a book increased from $20 to $25. What is the markup rate?

Answer:

87.5

Step-by-step explanation:

35*2.5=  87.5

since you are finding distance you have to multiply speed and time

hope this helps :)

Answer: There are 208 shots she make if she shot 125 foul shots.

Step-by-step explanation:

Since we have given that

Number of foul shots = 12

Number of shots she misses = 8

Total number of shots = 12+8=20

So, if the number of foul shots = 125

We need to find the number of shots she make.

According to question, we get that

[tex]\dfrac{12}{20}=\dfrac{125}{x}\\\\12x=125\times 20\\\\12x=2500\\\\x=\dfrac{2500}{12}\\\\x=208.33\\\\x\approx 208[/tex]

Hence, there are 208 shots she make if she shot 125 foul shots.

Answer:

x = 1 and x = 2

x = 4 and x = -4

Step-by-step explanation:

Vertical asymptotes appear where the function does not have a value. This is most commonly when the denominator of a rational function is 0. Find the asymptotes by factoring the denominator and setting it equal to 0. Then solve for x.

First equation

x² - 3x + 2 factors into (x-1)(x-2)

When x-1 = 0, x = 1. When x-2=0, x = 2. The V.A. are at x = 1 and x = 2.

Second equation

x²  - 16 factors into (x+4)(x-4)

When x+4= 0, x = -4. When x-4 = 0, then x = 4. The V.A. are at x = -4 and x = 4.

Final answer:

The function f(x) = 3x/(x² - 16) is defined for x = -16, x = 0, and x = 16, but undefined for x = -4 and x = 4, where it has vertical asymptotes.

Explanation:

The question requires evaluating the function f(x) = 3x/ x²-16 for different values of x. When we evaluate this function, we must pay attention to the values at which the function is undefined, which is when the denominator x^2 - 16 equals zero. This occurs when x = -4 or x = 4, as these values make the denominator (x + 4)(x - 4) equal to zero.

Options (b) and (d) correspond to the values at which the function has vertical asymptotes, as the denominator becomes zero and the function value approaches infinity.

The equation is V = PI x r^2 x h

r = 1/2 the diameter = 4.5

Volume = 3.14 x 4.5^2 x 5

Volume = 317.9 cm^3

Answer:

The third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].

Step-by-step explanation:

According to the binomial expansion,

[tex](a+b)^n=C(n,0)a^{n}+C(n,1)a^{n-1}b+...+C(n,n)b^n[/tex]

So, the rth term of this expansion is

[tex]C(n,r-1)a^{n-r+1}b^{(r-1)}[/tex]

We have to find the third term of the expansion [tex](a+b)^n[/tex] is

[tex]C(n,3-1)a^{n-3+1}b^{(3-1)}[/tex]

[tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex]

Therefore the third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].