Answer:
A , DStep-by-step explanation:
Check the inequality for each point.
For A. (-3,2)
[tex]y < {2x}^{2} + 3x - 5 \\ 2 < {2 ( - 3)}^{2} + 3( - 3) - 5 \\ 2 < 2 \times 9 - 9 - 5 \\ 2 < 18 - 9 - 5 \\ 2 < 4 \\ [/tex]
The inequality is satisfied.
For B. (-2,9)
[tex]y < {2x}^{2} + 3x - 5 \\ 9 < 2 {( - 2)}^{2} + 3( - 2) - 5 \\ 9 < 2(4) - 6 - 5 \\ 9 < 8 - 6 - 5 \\ 9 < - 3 \\ [/tex]
The inequality is not satisfied.
For C. (1,6)
[tex]y < {2x}^{2} + 3x - 5 \\ 6 < {2(1)}^{2} + 3(1) - 5 \\ 6 < 2(1) + 3 - 5 \\ 6 < 2 + 3 - 5 \\ 6 < 0[/tex]
The inequality is not satisfied.
For D. (3,1)
[tex]y < {2x}^{2} + 3x - 5 \\ 1 < {2(3)}^{2} + 3(3) - 5 \\ 1 < 2(9) + 9 - 5 \\ 1 < 18 + 9 - 5 \\ 1 < 22 \\ [/tex]
The inequality is satisfied.
For E. (-1,5)
[tex]y < {2x}^{2} + 3x - 5 \\ 5 < {2( - 1)}^{2} + 3( - 1) - 5 \\ 5 < 2(1) - 3 - 5 \\ 5 < 2 - 3 - 5 \\ 5 < - 6 \\ [/tex]
The inequality is not satisfied.
let H be the altitude from vertex C. Which proves the first equality in the law of sines
The sine law of triangles can be proved by dividing the triangle into right-triangles.
Option (c) proves the first equality in the law of sines
From the question, we have:
h equals to the distance from point C to segment AB
The sine of angle is:
[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]
For angle at A, we have:
[tex]\mathbe{\theta = A}[/tex]
[tex]\mathbf{Hypotenuse = b}\\\mathbf{Opposite = h}[/tex]
So, we have:
[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]
Substitute values for Opposite, Hypotenuse and theta
[tex]\mathbf{sin A = \frac{h}{b}}[/tex]
Similarly
[tex]\mathbf{sin B = \frac{h}{a}}[/tex]
Make h the subject
[tex]\mathbf{h = a\ sinB}[/tex]
Substitute [tex]\mathbf{h = a\ sinB}[/tex] in [tex]\mathbf{sin A = \frac{h}{b}}[/tex]
[tex]\mathbf{sin A = \frac{a\ sinB}{b}}[/tex]
Divide both sides by a
[tex]\mathbf{\frac{sin A}{a} = \frac{sinB}{b}}[/tex]
Hence, the correct option is (c).
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f(x) = 3x + 6 please help quickly!!!!!!!
Given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:
[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]
Given:
f(x) = 3x + 6We are told to find:
f(a)f(a + h), and[tex]\frac{(f(a + h) - f(a)) }{h}[/tex]1. Find f(a):
Substitute x = a into f(x) = 3x + 6f(a) = 3(a) + 6
f(a) = 3a + 6
2. Find f(a + h):
Substitute x = a + h into f(x) = 3x + 6f(a + h) = 3(a + h) + 6
f(a + h) = 3a + 3h + 6
3. Find [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]:
Plug in the values of f(a + h) and f(a) into [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]Thus:
[tex]\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\[/tex]
Add like terms[tex]\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}[/tex]
Therefore, given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:
[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]
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pls help me with this math
When converted to a household measurement, 9 kilograms is approximately equal to a
Answer:
D) 19.8 lbs
Explanation:
1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.
1kg is also equal to 2.205 lbs. 9*2.205=19.8416
9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system
a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.
This leaves us with 19.8 lbs
Which function is the inverse of the function f(x) = 4x2 + 10, if the domain of f(x) is x 2 0?
Step-by-step explanation:
inverse = √((x-10)/4)
that is the answer
Answer:
Step-by-step explanation:
Can someone explain this to me on how you do this by step from step?
Answer:
5% of $5.00
[tex] \frac{5}{100} \times 5.00[/tex]
[tex] = \frac{1}{4} [/tex]
what 21.807-10.739=?
Answer:
2.428 is the answer....
Naomi is still not sure how many boxes of each type of candy to order. Her dad explains that he needs to do a little more mathematics before she can determine the best candy order. He creates a table to help her determine the solution.
He asks her to calculate how much money the band would make if she ordered 500 boxes of
each type of candy. He also asks her to calculate the profit on an order of 300 boxes of milk
chocolate and 500 boxes of dark chocolate. Determine both answers and show your work.
Answer:
how much does each box cost?
Step-by-step explanation:
You have been directed to trim $10,000 from the monthly warehouse
told that you cannot reduce the costs for HVAC, refrigeration, and ligh
expense must be cut significantly?
A. Water
B. Copiers
C. Computers
D. Lights
Answer:
You have been directed to trim $10,000 from the monthly warehouse
told that you cannot reduce the costs for HVAC, refrigeration, and ligh
expense must be cut significantly?
A. Water
B. Copiers
C. Computers
D. Lights
Two standard dice are thrown. Determine the theoretical probability that the sum is
a) 4 b) 7
c) an even number d) not a 6 e) not a perfect square
Step-by-step explanation:
there are 36 (6×6) possible results and number combinations for 2 dice.
a)
to create a sum of 4 we need one of the following combinations :
1 3
2 2
3 1
so, 3 out of the overall possible 36 possibilities.
and that means the probability is 3/36 = 1/12
b)
to create a sum of 7 we need one of the following combinations :
1 6
2 5
3 4
4 3
5 2
6 1
so, 6 out of the overall possible 36 possibilities.
and that means a probability of 6/36 = 1/6
c)
since the possible outcomes in that regard are only 2 (even and uneven), with equal balance the probability is 1/2.
make it more formal ?
to get an even sum, every possible number on one die can be combined with 3 possibilities on the other.
1 can be combined with 1, 3, 5
2 with 2, 4, 6
3 with 1, 3, 5
4 with 2, 4, 6
5 with 1, 3, 5
6 with 2, 4, 6
these are 6×3 = 18 combinations of of the possible 36.
so, the probability is 18/36 = 1/2
d)
not a 6 ?
so, what does that mean ?
we are looking only at 5 possible outcomes per die.
that is 5×5 = 25 combinations out of the possible 36.
that means that probabilty is 25/36.
e)
not a perfect square ?
we have in the range of the possible sums with 2 dice (2 .. 12) only two perfect squares : 4 and 9
so, the sum must NOT be 4 AND NOT be 9.
so, here it might be easier to count the unwanted cases and then deduct the probability from 1 to express the opposite.
the combinations to get 4 we have already under a)
3 combinations with 3/36=1/12 probability.
the combinations to get 9
1 none
2 none
3 6
4 5
5 4
6 3
so, 4 combinations with a probability of 4/36 = 1/9
therefore, we have (3+4) = 7 cases out of the possible 36 we actually want to avoid.
so, the probability to get any one of the other (desired) combinations is therefore (36-7)/36 = 29/36
The probabilities are:
a) 0.083b) 0.167c) 0.5d) 0.861e) 0.806.How to get the probabilities?The probability for a given outcome is given by the quotient between the number of combinations that give that outcome and the total number of combinations.
Here each dice has 6 possible outcomes, so the total number of combinations for the two dice is:
6*6 = 36 combinations.
a) Here we need to count how many combinations add to 4, the notation I will use is:
dice 1 dice 2
1 3
3 1
2 2
There are 3 combinations that add to 4, then the probability of getting a sum equal to 4 is:
P = 3/36 = 0.083
b) Same thing as before, this time we count the combinations that add to 7.
dice 1 dice 2
1 6
6 1
5 2
2 5
4 3
3 4
There are 6 combinations that add to 7, so the probability is:
P = 6/36 = 0.167
c) The possible even numbers are: {2, 4, 6, 8, 10, 12}
A way of doing this, is:
If the first dice is even/odd, then the second also must be even/odd.
Then the probability is just 1/2 = 0.5 (because there are the same number of odd and even numbers in a dice).
d) The sum must not be equal to 6, the combinations that add up to 6 are:
dice 1 dice 2
2 4
4 2
3 3
1 5
5 1
So 5 combinations add up to 6, then there are 31 combinations that do not add up to 6, this means that the probability of not getting a sum equal to 6 is:
P = 31/36 = 0.861
e) The perfect squares are 4 and 9, we already know that 3 combinations add up to 4, now let's find the combinations that add up to 9.
dice 1 dice 2
6 3
3 6
5 4
4 5
So 4 combinations add up to 9, then there is a total of 7 combinations that give a perfect square, then there are 29 combinations that do not add to a perfect square.
The probability is:
P = 29/36 = 0.806
If you want to learn more about probability, you can read:
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PLEASE HELP WITH THIS ONE QUESTION
Answer:
11
Step-by-step explanation:
pls maerk as brainliest
Cho các tập hợp
A =( x∈R|x²-5x+4≤0)
B= (x∈R|x-1|≤1)
C=(x∈R|x²-7x+6≤0)
xác định: (A∪B)∩C
(A∩B)∪C
CAN YOU BRAINLEST ME THANK YOU
HOPE IT HELPS YOU
By visual inspection alone, which one of the following pairs of variables has a stronger relationship between them?
1. Community violence exposure and Bullying by peers have a strong relationship at -0.24.
2. Community violence exposure and Bullying by peers have a strong relationship at 0.20.
3. Community violence exposure and SAT-9 Mathematics have a stronger relationship at -0.24.
4. Community violence exposure and SAT-9 Mathematics have a stronger relationship at 0.20.
a) The simplest form of 20
100
is _____________.
b) The mixed fraction of 80
9
is _____________.
c) When we convert 13 5
7
to an improper fraction, we get __________.
d) In a basket of 27 mangoes, 6 are rotten. This statement can be written as a fraction
as (give the answer in the simplest form) ___________.
When a 3-digit number is rounded to the nearest ten and the nearest hundred, the difference is 50. What is the number?
Answer: 150?
Step-by-step explanation:
150 -> 200 200-150=50
150-> 150 200-150=50
Please , I need help ASAP !!
Answer:
c
Step-by-step explanation:
cccccccc cccccccccdkdksksk
What is the value of x in the diagram below? If necessary, round your answer
to the nearest tenth of a unit.
14
х
B
L
D
с
30
O A. 30.1
B. 6.5
C. 14
O D. 16
Answer:
D. 16
Step-by-step explanation:
Problem Solving REAL WORLD 1. James got 3 hits in each of his baseball games. He has played 4 baseball games. How many hits has he had in all?
marked at a regular price of $20. What is the percent decrease in the price
A pair of sunglasses is on sale for $17. Last week, the sunglasses were
of the
sunglasses?
Answer:
15%
Step-by-step explanation:
20-17 = 3
What percent is 3 of 20?
X/100 = 3/20 (cross multiply)
(3*100) / 20 = 15%
Rashawn read 25 pages of his book each day until he finished the book. his book was 400 pages long. which sketch represents this situation?
Answer:
It took 16 days
Step-by-step explanation:
400/25=16
Eight more than the difference of −5s and −6s is equal to the sum of 3 and 7
Answer:
s=2
Step-by-step explanation:
-5s + 6s + 8 = 3 + 7
s + 8 = 10
s + 8 - 8 = 10 -8
s = 2
Find the slope and y-intercept for this table.
Answer:
See below:
Step-by-step explanation:
To find the slope, we use the following formula:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
For this case, we can use (6,60) as the first set of points.
We can use (4,70) as the second set of points.
Now, we can use the formula, 70-60 is for the top of the fraction (10)
We can do 4-6 to find the bottom, which is (-2)
Now, if we add the fraction back we get -> 10/-2 which is -5 for slope!
To find out the y intercept, it in simple words is "What is y when x is 0?".
We can do that by using the slope intercept formula: [tex]y=mx+b[/tex].
Once we insert our slope which is -2 we get: [tex]y=-2x+b[/tex]
We can now substitute a point, lets use (6,60) so we can find out b.
We now get the equation: [tex]60=-5(6)+b[/tex].
If we solve for that we get 90!
Once we input that, we get, [tex]y=-5x+90[/tex]
Now we put in x as 0 and we get our y intercept as 90!
If this answer helped, consider marking as brainliest!!
Help me guys here
NonSense Answer=Report
A carpenter has already shingled 10 garage roofs and is shingling roots at a constant rate of 9 per day
Write an eguation that models the number of garage roofs, 1, after t days,
an
ok
The equation that models the given situation is?
The equation that models the situation is f(t) = 10 + 9t.
The carpenter has already shingled 10 garage roofs . The initial amount he has already shingled is like a constant in the equation.
He shingles at a constant rate of 9 per day. This means each day the carpenter shingles 9 roofs.
let
f(t) = number of garage roofs the carpenter shingles
t = time in days.
If the carpenter shingles 9 roofs per day , he will shingle 9 × t roof for t days.
To model the equation where he had already shingled 10 roofs and his shingling rate, can be represented as follows:
f(t) = 10 + 9tread more: https://brainly.com/question/22965839?referrer=searchResults
PLEASE HELP ILL MARK BRAINLIEST AND SHOW ALL YOUR WORK
Answer:
5
Step-by-step explanation:
f(-1) = -3(-1)^3 + 2(-1)^2
f(-1) = -3(-1) + 2(1)
f(-1) = 3 + 2
f(-1) = 5
Hope this helps! Pls give brainliest!
Answer:
5
Step-by-step explanation:
plug in -1 for x
so
[tex] -3 ({ - 1})^{3} + 2 ({ - 1})^{2} [/tex]
went we solve we get
[tex]3 + 2 \\ = 5[/tex]
so 5 is ur answer
pls give brainlist
if any questions ask
have a great day thanks :)
Homework help please
Answer:
h=-136
Step-by-step explanation:
..............
I need help with this
Answer:
Your answer is C. x=6 I hope this helps you! :D
If you need i can also provide steps.
Answer:
C. x=6
Step-by-step explanation:
You can work it out as follows:
6 - 0.2x = 2(6 - 0.6x) =>
6 - 0.2x = 12 - 1.2x =>
-0.2x + 1.2x = 12 - 6 =>
1.0x = 6 =>
x = 6
do
any one need points
How do you write 0.8 as a percentage?
Answer:
.8 equals 80%
Step-by-step explanation:
To find the percentage you multiply the decimal by 100 so .8 multiplyed by 100 equals 80 or 80%
A number n is increased by 40% and then decreased by 14%. What is the final result in terms of n?
Answer:
X = 100. A 40% increase causes it to increase to 140. A 40% reduction amounts to multiplying by 0.6, leading to a reduction of 40% of 140 ...
