Find the quotient.
5^-3/5^-1
Answer:
3/35
Step-by-step explanation:
Solve for r.
-3r-9=1r+2
Answer:
[tex] - 3r - 9 = 1r + 2 \\ - 3r - r = 11 \\ - 4r = 11 \\ r = - \frac{11}{4} [/tex]
The altitude of a triangle is increasing at a rate of 1.5 1.5 centimeters/minute while the area of the triangle is increasing at a rate of 1.5 1.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8 8 centimeters and the area is 88 88 square centimeters
Answer:
The base reduces at 3.75cm/min
Step-by-step explanation:
Given
Let
[tex]h \to altitude[/tex]
[tex]b \to base[/tex]
[tex]A \to Area[/tex]
So:
[tex]\frac{dh}{dt} = 1.5cm/min[/tex]
[tex]\frac{dA}{dt} = 1.5^2cm/min[/tex]
The area of a triangle is:
[tex]A = \frac{1}{2}bh[/tex]
Calculate b when [tex]A =88cm^2; h =8cm[/tex]
[tex]A = \frac{1}{2}bh[/tex]
[tex]88=\frac{1}{2} * b * 8[/tex]
[tex]88 =b * 4[/tex]
Solve for b
[tex]b = 88/4[/tex]
[tex]b = 22[/tex]
We have:
[tex]A = \frac{1}{2}bh[/tex]
Differentiate with respect to time
[tex]\frac{dA}{dt} =\frac{1}{2}(h\frac{db}{dt} + b\frac{dh}{dt})[/tex]
Substitute the following values in the above equation
[tex]\frac{dh}{dt} = 1.5cm/min[/tex] [tex]\frac{dA}{dt} = 1.5^2cm/min[/tex] [tex]b = 22[/tex] [tex]h = 8[/tex]
[tex]1.5 = \frac{1}{2}(8 * \frac{db}{dt} + 22 * 1.5)[/tex]
Multiply both sides by 2
[tex]3 = 8 * \frac{db}{dt} + 22 * 1.5[/tex]
[tex]3 = 8 * \frac{db}{dt} + 33[/tex]
Collect like terms
[tex]8 * \frac{db}{dt} = 3 -33[/tex]
[tex]8 * \frac{db}{dt} = -30[/tex]
Divide both sides by 8
[tex]\frac{db}{dt} = -\frac{30}{8}[/tex]
[tex]\frac{db}{dt} = -3.75[/tex]
PLEASE HELP!!
NUMBER 3!
Answer:
Width = 17 feet, Length = 22 feet
Step-by-step explanation:
Let the width, w, be x
Therefore, length, L = x + 5
Perimeter = 78
p = 2(L+b)
78 = 2(x + x+5)
Adding the variables,
78 = 2( 2x + 5)
Dividing both sides by two,
39 = 2x + 5
Subtracting two from both sides,
34 = 2x
Dividing by two on both sides,
17 = x
Therefore, the width = x = 17 feet, and the length = x + 5 = 17 + 5 = 22 feet.
Hope you understood
Please mark as the brainliest
Thank You
Evaluate the function.
Answer:
f(-1) = 5
Step-by-step explanation:
To "evaluate the function f(x) = -x^2 + 6 at x = -1, we substitute -1 for x in each instance:
f(-1) = -(-1)^2 + 6
According to order of operations rules, exponentiation must be performed before multiplication or division. '-(-1)^2' thus becomes -1, and so
f(-1) = -(-1)^2 + 6 = -1 + 6 = 5.
Thus, f(-1) = 5
18.96 x 2.03 correct to 2 significant figures equals what?
9514 1404 393
Answer:
38
Step-by-step explanation:
The product of the given numbers is 38.4888. Rounding this to two significant digits gets you 38.
I need the answer plsss
Answer:
Its H
There should be one dot on 4, 2 dots on 2, 3 dots on 1, 3 dots on 0, 1 dot on 7, 1 dot on 3
Step-by-step explanation:
brainly plz!
1.2 x 10^19 x 5.88 x 10^12
This is scientific Notation I need this urgent please give good explanation
9514 1404 393
Answer:
7.056 × 10^31
Step-by-step explanation:
The applicable rule of exponents is ...
(10^a)(10^b) = 10^(a+b)
__
[tex](1.2\times10^{19})\times(5.88\times10^{12})=(1.2\cdot5.88)\times10^{19+12}\\\\=\boxed{7.056\times10^{31}}[/tex]
As you know, the commutative and associative properties of multiplication let you rearrange the order of the product to any convenient form. Here it is convenient to group the mantissas together and the powers of 10 together.
__
Additional comments
This is a product your scientific or graphing calculator can produce for you. Likely it will display the result in scientific notation because it won't have enough display digits to show you the product any other way. For smaller numbers, you can set the display mode to give you scientific notation.
If you choose to use a spreadsheet to perform this calculation, the numbers would be entered as 1.2e19 and 5.88e12. The result will be something like 7.056e31. You may have to format the display to show 3 decimal places.
Desperate adhd child here plz.
Answer:
i have adhd too lol, i think its they're both equal ?
Step-by-step explanation:
no idea lol but have a good day
Question 2 of 10 The standard form of the equation of a parabola is y= x2 + 4x + 11. What is the vertex form of the equation? O A. y = (x - 2)2 + 18 OB. y = (x + 2)2 +7 O C. y = (x + 2)(x-2) + 7 O D. y = (x - 2)2 + 12
Answer:
The answer:
y=(x+2)²+7
Choose (B)
which inequality does the graph represent?
A. y<-x-1
B. y<-x+1
C. y
D. y
Answer:
B) y < -x + 1
Step-by-step explanation:
you can see from the x-and-y intercepts that the equation of this line is:
y = -x + 1
now you must determine whether the equal sign should be replaced with '<' or '>'
you can use the point (0,0) to see if that makes y > -x + 1 true or false:
0 > 0+1 This is False
so the answer should be: y < -x + 1
Is god really real??
Answer ASAP
Many people answer this question
Answer:
yes
Step-by-step explanation:
that's that's I think
Nhan and Phuong both left town A for town B at 5 am . After 5 hours , Nhan and Phuong were 102 km and 52 km away from town B respectively . The ratio of Nhan's speed to Phuong's speed was 3 : 4 and their speeds remained the same the whole journey . At what time did Nhan reach town B ? Show your full work.
Answer:
Nhan reach town B at 13:24 pm
Step-by-step explanation:
Let
Speed of Nhan=3x km /hour
Speed of Phoung=4x km/hour
After 5 hours,
Distance covered by Nhan=3x(5)=15 xkm
Distance covered by Phuong=4x(5)=20x km
Total distance covered by Nhan to reach town B=15x+102 km
Total distance covered by Phuong to reach town B=20x+52 km
Distance between town A and town B for both person is same therefore,
[tex]15x+102=20x+52[/tex]
[tex]102-52=20x-15x[/tex]
[tex]50=5x[/tex]
[tex]x=10[/tex]
Speed of Nhan=3(10)=30 km/h
Speed of Phuong=4(10)=40 km/h
Total distance between town A and town B=102+15(10)=252 km
Time taken by Nhan to reach town B from town A=[tex]\frac{distance}{speed}[/tex]
Time taken by Nhan to reach town B from town A=[tex]\frac{252}{30}=8.4 hours[/tex]
[tex]8.4 hours=8+0.4\times 60[/tex]
=8 hours 24 minutes
1 hour=60 minutes
Nhan reach town B at 13:24 pm
A house was appraised at $330,000 . One year later the house was appraised at $335,000 . At what percent did the appraised price of the house increase?
Answer:
11 2/3%
Step-by-step explanation:
Change in Amount =335,000 – 300,000
Percent Increase
Original Amount
300,000
35,000
2
=0.11666=11.666%=11-%
300,000
3
(https://imgur.com/a/U6c1pes) - For more clear explanation.
find the value of tanA when tan(A-45)=1÷3)
Answer:
63.44degrees
Step-by-step explanation:
Given that;
tan(A-45) = 1/3
A-45 = arctan(1/3)
A - 45 = 18.44
A = 18.44+45
A = 63.44degrees
Hence the value of A is 63.44degrees
5) The current population of a city is 15,862 residents. The population is growing at a rate of
1.3% per year. Assuming the growth rate remains constant, how many years will it take for
the population to reach 20,000 residents? Round your answer to the nearest whole year.
Answer:
97 years
Step-by-step explanation:
20,000 - 15,862 = 4,138
[tex]\frac{y}{15,862}: \frac{1.3}{100}[/tex]
y × 100 = 15,862 × 1.3
100y = 20620.6
100y ÷ 100 = 20620.6 ÷ 100
y = 206.206
20,000 ÷ 206.206 = 96.9903882525
96.9903882525 rounds to 97
Given that m angle G- 81", what is m angle I?
A)81"
B)89
C)91
D)99
Answer:
[tex]\text{D) }99^{\circ}[/tex]
Step-by-step explanation:
Define a cyclic quadrilateral by a quadrilateral that is circumscribed by a circle. In this case, since the quadrilateral shown is circumscribed by a circle, it is a cyclic quadrilateral.
A property of all cyclic quadrilaterals is that their opposite angles are supplementary, meaning they add up to 180 degrees. Since [tex]\angle G[/tex] and [tex]\angle I[/tex] are opposite angles in the quadrilateral, they must be supplementary. Therefore, we have the equation:
[tex]\angle G+\angle I=180,\\81^{\circ}+\angle I=180,\\\angle I=180-81=\boxed{99^{\circ}}[/tex]
A production process manufactures alternators for tanks. On the average, 1.5% of the alternators will not perform up to specifications. When a shipment of 100 alternators is received at the plant, they are tested, and if more than 2 are defective, the shipment is returned to the manufacturer. What is the probability of returning a shipment
Answer:
0.1902 = 19.02% probability of returning a shipment
Step-by-step explanation:
For each alternator, there are only two possible outcomes. Either it is defective, or it is not. The probability of an alternator being defective is independent of any other alternator, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
1.5% of the alternators will not perform up to specifications.
This means that [tex]p = 0.015[/tex]
Shipment of 100 alternators
This means that [tex]n = 100[/tex]
What is the probability of returning a shipment?
Probability of more than 2 defective, which is:
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.015)^{0}.(0.985)^{100} = 0.2206[tex]
[tex]P(X = 1) = C_{100,1}.(0.015)^{1}.(0.985)^{99} = 0.3360[/tex]
[tex]P(X = 2) = C_{100,2}.(0.015)^{2}.(0.985)^{98} = 0.2532[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2206 + 0.3360 + 0.2532 = 0.8098[/tex]
Then
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.8098 = 0.1902[/tex]
0.1902 = 19.02% probability of returning a shipment
Express 384kg in tones
Answer:
1000kg = 1 tone
384/1000=0.384 tone
simplify the expression (2r^4y4xy^2) completely
Step-by-step explanation:
we can simplify the stuff inside the parentheses to
[tex] \frac{ {x}^{3} }{2y} [/tex]
now we need to multiply it with itself, giving us
[tex] \frac{ {x}^{6} }{4 {y}^{2} } [/tex]
so yeah, D is the correct answer
What is the scale factor?
Answer:
3/5
Step-by-step explanation:
Scale factor = 9/15 = 3/5
WILL MARK BRAINLIEST! An orchestra of 120 players takes 40 minutes to play Beethoven's 9th Symphony. How long would it take for 60 players to play the symphony?
Let P be the number of players and T be the time playing.
Trick question! ;)
Answer:
Since in an orchestra each player plays parallely, i.e. everyone plays the same line simultaneously, hence the length of the play never depends on the number of players playing it. Hence, time taken by 60 players = time taken by 120 players = 40 minutes. So 60 person will play the 9th harmony in same 40 minutes.
Step-by-step explanation:
You pick a card at random.
2 3 4 5
What is P(odd)?
Write your answer as a percentage.
Answer:
1/2-50%..?
Step-by-step explanation:
The probability of picking an odd numbered card is 50%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, the numbers on cards are 2 3 4 5.
Number of favorable outcomes = 2
Total number of outcomes = 4
Probability of getting odd numbers = 2/4
= 0.5
= 0.5 ×100
= 50%
Therefore, the probability of picking an odd numbered card is 50%.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ2
An expression is shown below:
f(x) = 4x2 + 8x − 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Given function:
f(x) = 4x² + 8x - 5Part AThe x-intercepts are the points when f(x) = 0.
Set up equation and solve:
4x² + 8 x - 5 = 0x = ( - 8 ± √(8² + 4*4*5))/8x = (- 8 ± √144)/8x = ( - 8 ± 12)/8x = - 20/8 = - 2.5 and x = 4/8 = 0.5The x-intercepts are (-2.5, 0) and (0.5, 0)
Part BThe vertex form of the quadratic equation:
y = a(x - h)² + k, where (h, k) is the vertexThe vertex is minimum if the leading coefficient is positive and maximum if the leading coefficient is negative. The given equation has a = 4, hence its vertex is minimum.
Convert the given equation into vertex form:
y = 4x² + 8x - 5 y = 4x² + 8x + 4 - 4 - 5 y = 4(x² + 2x + 1) - 9 y = 4(x + 1)² - 9As per equation the vertex is (- 1, - 9)
Part CFrom the previous parts we found the two x-intercepts and vertex, also found that the vertex is the minimum, so the graph opens up.
Plot the points and connect to obtain the graph.
See below.
HELP plsssss I will GIVE YOU BRAINLYEST
Answer: B
Step-by-step explanation:
Answer:
-5ºC < 5ºC is an inequality that compares temperatures.
B is the correct answer for the multiple choice question.
HELPPPPOOOPPPPOPPPPPPPP
Answer:
Your answer would be B
Step-by-step explanation:
So right away you can get rid of a and d since they are positive numbers, there is no positive numbers in the graph were the line is.
So we know that the y-intercept is -2 (as you can see the line pass through (0,-2))
And we know the y intercept is -8 (since the line pass through (-8,0))
so you are left with b and c, c is incorrect because the -2 goes through the y-intercept not the x.
The right choice is b, it states that the x-intercept -8 pass through the line, the y-intercept is -2
Your welcome and hoped this helped!
The yearbook staff receive 75 submissions for yearbook articles. Paul will accept
2
5 of all submissions. Currently, Paul plans for the yearbook to have 156 pages.
How many more pages will Paul need to add to the yearbook to have 2 articles on every 13 pages? Show your work and explain your thinking.
Answer:
The pages that will be added to the yearbook to have 2 articles on every 13 pages is 813.8 pages.
Step-by-step explanation:
We know that if there are 75 submissions and it says Paul will accept [tex]\frac{2}{5}[/tex] of the submissions.
To find that we have to
= [tex]75-\frac{2}{5}[/tex]
= [tex]74.6[/tex]
Now multiplying by 13,
= 13 x 74.6
= 969.8
Then to find the pages that will be added to the yearbook is
= 969.8 - 156
= 813.8 pages.
find the median from given data 2,5,1,6,3
Answer: Median = 3
Explanation:
Sort the numbers to get {1,2,3,5,6}. The middle most number is 3, so that's the median.
HELP QUICK help find the value of x and the measure of each angle
Answer:
A = 102° B = 78°
Step-by-step explanation:
(3x + 12°) + (2x + 18°) = 180°
5x = 180° - 12° - 18°
5x = 150|:5
x = 30°
Answer: x=30 A=102 B=78
Step-by-step explanation:
These are linear pairs so they add up to 180.
Your equation is: 3x+12+2x+18=180
5x+30=180
x=30
Plug x into the equations to find their values.
3(30)+12=102
2(30)+18=78
I need help ASAP please eeeee
Answer:
46
Step-by-step explanation:
2×(3×1 + 3×5 + 1×5) = 46 centimeters squared
