Prove:
sin^2x (sec^2x + csc^2x)=sec^2x

Answers

Answer 1

Answer: sin^2x (sec^2x + csc^2x) = sec^2x

I would convert the functions in the parentheses to their reciprocals.

sin^2x (1/cos^2x + 1/sin^2x) = sec^2x

Now distribute the sine.

sin^2x/cos^2x + sin^2x/sin^2x = sec^2x

Remember that sine divided by cosine is always tangent.

tan^2x + sin^2x/sin^2x = sec^2x

The remaining fraction is simply 1.

tan^2x + 1 = sec^2x

Use the Pythagorean identity to add the left side.

sec^2x = sec^2x

Q.E.D.

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Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06. Round the common ratio and 17th term to the nearest hundredth.

Answers

The geometric sequence formula is expressed as an = a1 * r^(n-1) where n is an integer. In this case, upon substitution, 150.06 = 16 * r^(4). extracting r, r is equal to 1.75. Hence the 17th term from the formula is equal to 123802.32.

Answer:

a17 ≈ 123,802.31

Step-by-step explanation:

Log3 1/9=x/9 ? math is the worst

Answers

$log_3( (1)/(9) )= (x)/(9) \n\nlog_33^(-2)= (x)/(9) \n\n-2=(x)/(9) \ /\cdot9\n\n-18=x\n\nx=-18$

$log_3((1)/(9))=(x)/(9)\n \n log_33^(-2)=(x)/(9)\n \n 3^{(x)/(9)}=3^(-2)\n \n (x)/(9)=-2\n \n \boxed{x=-18}$

Please Help!I have a math test coming up and this geometry stuff is just always confusing me. With that said if you could explain your answer that would be wonderful.
If the image is to blurry please just click on the image it is much easier to read.
I am willing to mark a person branliest!

All help is very appreciated. Good Luck. God Bless. Stay Safe. Thanks Max Larson

Answers

Answer:

1. this is the definition of a midpoint - bc the definition of a midpoint is: “If a point is a midpoint of a segment, then it divides that segment into two congruent parts” or “If a point divides a segment into two congruent parts, then it's the midpoint of that segment.”

2. this is the division property of equality -"The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal". so, in this situation we want to isolate x which means dividing both sides by 20. This will keep both sides equal just more simplified ( before, it was 20 and 100, after dividing both sides by 20 it is 1 and 5 which is the same ratio therefore they are still equal)

3. this one's the subtraction property of equality- this property means you can subtract the same number from both sides of an equation and get an equivalent equation. in this situation, they subtracted 15 from both sides to get AB = 30 and it ends being still being equal to AB + 15= 45.

4. this is the symmetric property of equality - "This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement." "it states that values are still equal no matter which side of the equal sign they're on." That's why its possible for XY=ST and ST=XY

5. this is definition of congruence - which basically states that if a value of one thing is equal to the value of another thing those two things can be called congruent.

6. this is substitution property- this is the property that allows you to substitute one value for another in an equation. the property states that if

x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation, just like what they show here with 5AB substituting for CD in the equation.

i hope this helped! im not that good at explaining so if u have more questions lmk!

The stopping distance (s) of a car varies directly as the square of its speed (v). If a car traveling 20 mph requires 60 ft to stop, find the stopping distance for a car traveling 40 mph. Round to the nearest tenth.

Answers

Answer:

The stopping distance for a car traveling 40 mph is 240 feet.

Step-by-step explanation:

We are given the following in the question:

The stopping distance (s) of a car varies directly as the square of its speed (v)

$s\propto v^2$

Removing the sign of proportionality and adding constant of proportionality, we get

$s = kv^2$

where k is constant of proportionality.

Now, when s = 60 feet, v = 20 mph

Putting values, we get,

$60 = k(20)^2\n\nk = (60)/(400) = 0.15$

Putting value of k in the equation, we get,

$s = 0.15v^2$

We have to find the stopping distance for a car traveling 40 mph.

$s = 0.15(40)^2 = 240\text{ feet}$

Thus, the stopping distance for a car traveling 40 mph is 240 feet.

A certain server works four 6-hour shifts a week at a restaurant and has a base salary of $9.75/ℎ. An average server sells $1400 in a single shift. If the server makes an average of 14% tip of a bill, what is the annual gross income of the server? Show all the work please

Answers

Answer:

$52,936

Step-by-step explanation:

1400(.14)(4) + 4(6)(9.75) = 784 + 234 = $1018/week

52(1018) = $52,936

The number of professors in a college is p and the number of students is s, there are 16 times as many students as professors write an algebraic expression that shows the relationship.