PLZ HELP!!!! The angle bisectors of the triangle ABC meet at point P. If PQ=8 and PA=17, what is the length of AR?
Answers
Answer:
15
Step-by-step explanation:
PQ=PR
AR=side2=√(hypotenuse)²-(side1)=√17²-8²=√225=15
Related Questions
Given y = sin(2x - π) + 1, find the (a) derivative, (b) equation of the tangent line at x = π/2, (c) equation of the normal line at x = π/2.
Answers
Answer:
(a) [tex]y'= 2cos(2x - \pi)[/tex]
(b) [tex]y=2x - \pi + 1[/tex]
(c) [tex]y=-\frac{x}{2} +\frac{\pi + 4}{4}[/tex]
Step-by-step explanation:
[tex]y=sin(2x-\pi)+1[/tex]
Part (a)Find the derivative of this function by using the chain rule and the power rule.
We know that the derivative of sinx = cosx. Find the derivative of this entire function first, [tex]sin(2x-\pi)+1[/tex], then multiply this by the derivative of the inside function, [tex]2x-\pi[/tex].
[tex]\frac{d}{dx}(sin(2x-\pi)+1)[/tex]Use the chain rule to find the derivative of sin(2x - π) + 1, which is cos(2x - π), then multiply this by the derivative of (2x - π). The derivative of π is 0, because it is a constant. The derivative of 2x is 2 based on the Power Rule.
[tex]cos(2x-\pi) \times 2[/tex]Simplify this expression.
[tex]2cos(2x - \pi)[/tex]This is the derivative of [tex]y=sin(2x-\pi)+1[/tex]; therefore, we can write:
[tex]y'= 2cos(2x - \pi)[/tex] Part (b)In order to find the equation of the tangent line at [tex]x=\frac{\pi}{2}[/tex], we will need to find the slope of the tangent line and the x- and y- coordinates (we already know the x- cord).
The steps to finding the equation of the tangent line at a certain are:
Plug into y' to find the slope of the tangent line.Plug into y to find the (x, y) coordinates.Use point-slope to write our equation in slope-intercept form.We know that y' = 2cos(2x - π). Let's plug x = π/2 into this equation for x to find the slope of the tangent line.
[tex]y'(\frac{\pi}{2} ) = 2cos(2(\frac{\pi}{2})-\pi)[/tex]Simplify inside the parentheses.
[tex]y'(\frac{\pi}{2} ) = 2cos(\frac{2\pi}{2}-\pi)[/tex] [tex]y'(\frac{\pi}{2} ) = 2cos(\pi - \pi)[/tex] [tex]y'(\frac{\pi}{2} ) = 2cos(0)[/tex] [tex]y'(\frac{\pi}{2} ) = 2[/tex]Now we know that the slope of the tangent line is 2.
Let's plug x = π/2 into the original function, y.
[tex]y(\frac{\pi}{2})=sin(2(\frac{\pi}{2})-\pi)+1[/tex]Simplify inside the parentheses.
[tex]y(\frac{\pi}{2})=sin(0)+1[/tex] [tex]y(\frac{\pi}{2})= 0+1[/tex] [tex]y(\frac{\pi}{2})=1[/tex]This tells us that the y-value, when x = π/2, equals 1. Our coordinates that we can use are (π/2, 1).
Now we can use point-slope form to write an equation for the tangent line to y at x = π/2.
Point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]We have [tex](x_1, \ y_1)[/tex], which are the x- and y- coordinates, and [tex]m[/tex], which is the slope of the tangent line.
Substitute these values into the equation:
[tex]y-(1)=2(x-(\frac{\pi}{2}))[/tex]Distribute 2 inside the parentheses.
[tex]y-1=2x-\frac{2 \pi}{2}[/tex]Add 1 to both sides of the equation.
[tex]y=2x-\frac{2\pi}{2} + 1[/tex] [tex]y=2x - \pi + 1[/tex]This is the equation of the tangent line of [tex]y=sin(2x-\pi)+1[/tex] at [tex]x=\frac{\pi}{2}[/tex].
Part (c)In order to find the equation of the normal line at x = π/2, we can use the information that the tangent line is perpendicular to the normal line.
This information is helpful because this means that their slopes are opposite reciprocals.
Let's use the point-slope equation again, but instead of m = 2, m will be the opposite reciprocal of 2 ⇒ -1/2. We will still use the same coordinate points.
[tex]m=-\frac{1}{2} \ \ \ \ \ \ (\frac{\pi}{2}, \ 1)[/tex] [tex]y-(1) = -\frac{1}{2}(x - (\frac{\pi}{2} ))[/tex]Distribute -1/2 inside the parentheses.
[tex]y-1=-\frac{1}{2}x + \frac{\pi}{4}[/tex]Add 1 to both sides of the equation.
[tex]y=-\frac{1}{2}x + \frac{\pi}{4}+1[/tex] [tex]y=-\frac{1}{2}x + \frac{\pi}{4} + \frac{4}{4}[/tex] [tex]y=-\frac{1}{2}x + \frac{\pi+4}{4}[/tex]You can leave it written as this, or write it as:
[tex]y=-\frac{x}{2} +\frac{\pi + 4}{4}[/tex]This is the equation of the normal line of [tex]y=sin(2x-\pi)+1[/tex] at [tex]x=\frac{\pi}{2}[/tex].
Mia is babysitting and has $40 to give to the 5 kiddos for snacks at the movie theater. How much money will each of the children get for snacks?
Answers
Answer:
Each child would get $8.00.
Step-by-step explanation:
An equation to represent this would be:
40/5
When you divide 40 by 5, you get 8 which results in the children each getting $8.00
Answer:
Each kiddo will get 8 dollars each
Step-by-step explanation:
40 divided by 5 = 8
sal recorded the outdoor temperature as -4°F at 7:30 am . at noon , it was 22°F . sal said the temperature changed by 18°F because 22-4=18. Is sal right or wrong .
Answers
Answer:
Sal is wrong, correct answer is 26°FStep-by-step explanation:
Initial temperature = -4°FTemperature at noon = 22°FTemperature change:
22 - (-4) = 22 + 4 = 26°FSal is wrong as the difference should be calculated as subtraction of the two values and absolute value of the result should be taken as the answer
Answer:
Sal was wrong as the change of temperature is 26°F
Step-by-step explanation:
recorded temperature at 7:30 A.M. = -4°F
at noon = 22°F
change of temperature = 22 - (-4) = 26°F
therefore, Sal was wrong as the change of temperature is 26°F
Please help me and explain.
Answers
Answer:
Step-by-step explanation:
In the set [-5, 3], only A fits in. B is pi, which has a value of 3.1415....which is outside of the interval since it's greater than 3. C. is -6 which is less than -5, so that's outside of the interval as well. D is the square root of 36 which is 6...outside of the interval again. A it is. A could be rewritten as
[tex]-\frac{1}{2^2} =-\frac{1}{4}[/tex]
is the expression 32/-8 undefined? If not find the quotient.
Answers
Answer:
the quotient is 4
Step-by-step explanation:
What is -15 = x/-0.5
Solve for X
Answers
Answer:
7.5
Step-by-step explanation:
you need to get the X alone so you multiply both sides by -0.5.
that leaves you with x=7.5
PLEASE HELP
At Bulk candy, gummy bears cost $5 for 7 ounces. You LOVE gummy bears. You fill up the bag and the
weight comes in at 24.5 ounces. How much do you owe? (no tax)
Answers
Answer:
17.50
Step-by-step explanation:
7*3 is 21 and 7/2 is 3.7 so its 5*3 (15) plus 2.50, so 17.50
Hope this helped!
Combine like terms 3y2 + 3(4y2 - 2)
Answers
Step-by-step explanation:
[tex]3y {}^{2} + 3(4y {}^{2} - 2) \\ \\ {3y}^{2} + 12 {y}^{2} - 6 \\ 15 {y}^{2} - 6[/tex]
Answer:
15y² - 6
Step-by-step explanation:
3y2 + 3(4y2 - 2)
Distribute: 3y² + 12y² - 6
Add like terms: 15y² - 6
I hope this helped, please mark Brainliest, thank you!
Find the smallest number which is exactly divisible
by 15 20 and 30
Answers
Answer:
60
Step-by-step explanation:
The smallest number that is divisible by 15, 20 , and 30, must have the needed factors of each of these numbers:
15 = 3 * 5
20 = 2 * 2 * 5
30 = 2 * 3 * 5
Then the minimum common factor must have the following factors to satisfy the divisibility of all of the numbers above:
2 * 2 * 3 * 5 = 60
I need help with this, Please explain to me this.
Answers
f(t)=x
T is the number of years since 1970 and x is the amount of million of barrels produced per day in the US
f(32)=6
32 years from 1970 is 2002
X=6
Therefore, 6 million barrels were made daily in the year 2002
Answer:
Ithink b
Step-by-step explanation:
because all of them are they dissimilar to the reason
Look at the factors of 24 and 32.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
The GCE of 24 and 32 is
Answers
Answer: 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Aden invested $300 at a rate of 3%. How many years would it take to earn $18 in interest?
(a) 3 years
(b) 9 years
(c) 6 years
(d) 2 years
help <3
Answers
18 = (3*300*t)/100
18 = 9t
t = 2
2 years
ion f (x) = -2(x+8)+11
Standard form
Answers
Explain why 3( + 4) = 3( − 5) has no solution. Choose the best response below. I NEED THIS ASAP!!!
a. The coefficients of are the same, but the constant terms are different.
b. The coefficients of are the same, and the constant terms are same.
c. The coefficients of are different, but the constant terms are the same.
d. The coefficients of are different, and the constant terms are different.
Answers
Answer:
a. The coefficients of are the same, but the constant terms are different.
Step-by-step explanation:
it makes the most sence to me, but appoligise if I'm wrong
Which weighs more: a watermelon that weighs 7.5 kilograms or a baby that weighs 12 pounds? Explain your reasoning. (Note: 1 pound is about 0.45 kilograms and 1 kilogram is about 2.2 pounds.)
Answers
Answer:
The watermelon.. I think
Step-by-step explanation:
Multiply 7.5 times 2.2 and you get 16.5, which is greater than 12. Please correct me if wrong on this because everybody makes mistakes.
Given a right triangle as shown below estimate the length of the missing side to the nearest tenth of a centimeter
Answers
Answer:
C. 19.4
Step-by-step explanation:
c=a2+b2−−−−−−√
a=162+112−−−−−−−−√
c=256+121−−−−−−−−√
c=377−−−√
c=19.4165
Andre rode his bike at a constant speed. He rode 1 mile in 5 minutes. Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?
Answers
Answer:
5minutes and the the distance is 1miles
Answer:
t=5d
Step-by-step explanation:
Given that Andre rode his bike at a constant speed.
Number of miles driven = 1 mile
Time taken to drive 1 mile = 5 minutes.
Then speed can be calculated using formula:
Speed = Distance / Time
Now we have to find the amount of time t (in minutes) taken by him to right distance d so we can again use same formula.
Speed = Distance / Time
or
Time = Distance / Speed
Plug the given values
t = 5d
Hence find answer will be equation t=5d.
Point A is located on the coordinate planet (3,-6) Point B is directly across the x-axis from point A and is the same distance from the x-axis as point A
What are the coordinates of point B?
Answers
Answer:
(3,6)
Step-by-step explanation: it is a reflection across the x-axis which is positive (3,6)
What is the coefficient of the third term in this expression? a^2+3c^3+6b^3
Answers
Answer: The coefficient is 3c
Step-by-step explanation:
What is the area of the rectangle written in simplest form
A-5/9ft
B-3/4ft
C-3ft
D-31/3ft
Answers
Answer:
ans is A
area = l*b
area=(5/6)*(4/6)=20/36=5/9
The expression 63 × 42 is equivalent to which of the following numerical expressions?
18 x 8
B.
(6 x 4) 5
C.
246
D.
216 x 16
please answer
Answers
Answer:
2646
Step-by-step explanation:
is the correct answer for This question
The required equivalent expression is (216 x 16).
The correct is D.
What is Expression?In mathematics, an expression is a phrase that has at least two numbers or variables and at least one maths operation. Addition, subtraction, multiplication, or division are all examples of maths operations. An expression's structure is as follows:
(Number/variable, Math Operator, Number/variable) is an expression.
We have the Expression as,
6³ x 4²
Now, expand the exponents as
6³
= 6 x 6 x 6
= 216
and, 4² = 4 x 4 = 16
Thus, the required equivalent expression is (216 x 16).
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ2
What is f(-3) for the function f(x) = -5x - 7?
Need this now will mark you brainliest!!!
Answers
f(-3) = 15 - 7
f(-3) = 8
Answer:
f ( x ) = 8
Step-by-step explanation:
Step 1:
f ( x ) = - 5x - 7 Function
Step 2:
f ( - 3 ) = - 5 ( - 3 ) - 7 Input x
Step 3:
f ( - 3 ) = 15 - 7 Multiply
Answer:
f ( - 3 ) = 8 Subtract
Hope This Helps :)
pls if u answer ill give brainliest :))) PLSS
When evaluting an expression, is it easier to combine terms first or substitute values first?
Answers
Answer:
Substitute values first
Michael owns dogs, hamsters and fish in the ratio 2:3:6
If he has 6 hamsters, how many pets does he have?
Answers
Answer:
11
Step-by-step explanation:
I think you just add the ratios together.
What division problem can be represented using the number line?
A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
StartFraction 10 Over 3 EndFraction divided by five-thirds
Five-thirds divided by StartFraction 10 Over 3 EndFraction
2 divided by five-thirds
2 divided by StartFraction 10 Over 3 EndFraction
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Answer:
It's the first answer.
Step-by-step explanation:
Answer:
The Answer is A
Step-by-step explanation:
Solve for x (2x-8) (9x-10)
Answers
Answer
x+3=17
Step-by-step explanation:
Answer: 18x2 -92x+ 80
Step-by-step explanation:
HELP PLZ
A carnival charges $250 per ride after an entrance fee.You paid a total of $22.50 after 6 rides.Write an equation that gives the total cost a function of the number of rides.
Answers
Equation: Y= 2.5x + 7.50
Solve for b.
Ab + c = d
B= (d-c)/a
B= a + c/d
B= a/c-d
Answers
B= (-c+d)/a
Answer:
B
Step-by-step explanation:
just took this test
Solve the inequality 8y - 3(y - 2)< 2y + 4(2y + 4) write solution in interval notation
Answers
Answer: y>-2
Step-by-step explanation:
8y-3(y-2) < 2y+4(2y+4)
8y-3y+6 < 2y+8y+16
6-16<2y+8y-8y+3y
-10<5y
y>-2
Answer:
(−∞,−2)
Step-by-step explanation:
Start by simplifying each side as much as possible by distributing and combining like terms to get
8y−3(y−2)8y−3y+65y+6>2y+4(2y+4)>2y+8y+16>10y+16
Subtract 10y from both sides to collect the variables on the left, then subtract 6 from both sides to collect all the constants on the right.
5y+65y+6−10y−5y+6−5y+6−6−5y>10y+16>10y+16−10y>16>16−6>10
Divide each side by −5 to solve for y. Since −5<0, the inequality changes direction.
−5y−5y−5y>10<10−5<−2
In interval notation, we write this as (−∞,−2).
Ok
Put -9,-4, and -10 in order from least to greatest. You can use the number line to help.
-2
-10
0
4
6
-8
2
8
-6
10
-10
Answers
Answer:
X=5.086
Step-by-step explanation:
432.34 on the number line, converted to negotiable /85 decimal places, divided by the sum of 432.34/85:
X=5.086
Edit: Gime branlies
