Using derivatives, it is found that the slope of the line tangent to the graph of y at x = 1 is of 5.
The equation is:
[tex]y(x) = \frac{9x^2}{x + 2}[/tex]
The slope of the line tangent to the graph of y at x = 1 is [tex]y^{\prime}(1)[/tex].
Applying the quotient rule, we have that:
[tex]y^{\prime}(x) = \frac{[9x^2]^{\prime}(x + 2) - [x + 2]^{\prime}(9x^2)}{(x + 2)^2}[/tex]
[tex]y^{\prime}(x) = \frac{18x(x + 2) - 9x^2}{(x + 2)^2}[/tex]
[tex]y^{\prime}(x) = \frac{9x^2 + 36x}{(x + 2)^2}[/tex]
Then, when x = 1:
[tex]y^{\prime}(1) = \frac{9(1)^2 + 36(1)}{(1 + 2)^2} = \frac{45}{9} = 5[/tex]
The slope of the line tangent to the graph of y at x = 1 is of 5.
You can learn more about the use of derivatives to find the slope of a tangent line at https://brainly.com/question/10580177
Complete the following sentence (select all that apply). The expected count of females who are not pierced is what we would expect to see in the sample if ___________________________. Group of answer choices gender and piercing were significantly related. gender and piercing are independent. the null hypothesis is true. the null hypothesis is not true.
The statement that completes the blank is (c) the null hypothesis is true.
In sampling techniques, the expected count of a variable is dependent on the null hypothesis.
This means that, if the null hypothesis is true, then the expected count is what is expected to be seen in the sample.
This in other words, means that the complete statement is:
The expected count of females who are not pierced is what we would expect to see in the sample if the null hypothesis is true.
Read more about null hypothesis at:
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Evaluate the expression
[3(15+4)2 +2(20+5)2]0
0
5
1
2
0, 5, 5, 1, 2
is evaluate
Find the GCF and LCM for 16 and 24.
Greatest Common Factors (GCF) of 16 and 24 = 8
Least Common Multiple of 16 and 24 = 48
GCF means Greatest Common Factors
Factors of 16 = 1, 2, 8, 4, and 16
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24
Common Factors of 16 and 24 = 1, 2, 4, and 8
Greatest Common Factors (GCF) of 16 and 24 = 8
LCM means Least Common Multiples
Multiples of 16 = 16, 32,48, 54.....
Multiples of 24 = 24, 48, 72....
The Least Common Multiple of 16 and 24 = 48
Learn more on GCF and LCM here: https://brainly.com/question/219464
De cuántas formas pueden mezclarse los siete colores del arco iris tomándolos de tres en tres?
Answer:
hi
Step-by-step explanation:
1+1=2
Casey borrowed $4500 at a 5% interest rate for 4 years.
What was the total interest?
Enter your answer in the box.
Hint: Use the formula I=P*R*T where
I= Interest Earned/Owed
P= Principal
R= Rate
T= Time
PLEASE HURRYYYY!
23+4⋅2−7
the 23 is 2 to the third power.
Answer:
12618
Step-by-step explanation:
23x23x23=12617
4•2=8
12617+8=12625
12625-7=12618
Answer: 9
Step-by-step explanation:
The correct answer to [tex]2^{3} + 4[/tex] ⋅ [tex]2 - 7 = 9[/tex]
I hope that helps :)
Simplify: 5 + p > 3
A.p < 8
B.p > 8
C.p < - 2
D.p > - 2
Answer:
D) p > -2
Step-by-step explanation:
5 + p > 3
5 + p - 5 > 3 - 5
p > -2
Solve 2/5 - 1/7
Help pls this is timed!!!!
Answer:
9/35
Step-by-step explanation:
Answer:
9/35
Step-by-step explanation:
ok so find the lcm of 2/5 and 1/7: this is 35
then convert them
2/5 = 14/35
1/7 = 5/35
14/35 - 5/35 is 9/35
HELLLP ME I GIVE BRAINLIESST
The youth group is going on a trip to the state fair. The trip costs $64. Included in that price is $12 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer:
each pass costs $26
Step-by-step explanation:
12 + 2x = 64
-12 -12
-------------------
2x = 52
x=26
hope this helps! :D
have a miraculous day everybody!!
brainliest is immensely appreciated!!! <3
4. Prove or disprove the following statement: Given two numbers, increasing both numbers by 10% results in two numbers whose difference is the same as the difference of the two original numbers. Give a numerical example and explain.
Step-by-step explanation:
increase by 10% is the same as multiplying by 1.1.
so, we get the assumption that
x - y = 1.1x - 1.1y = 1.1(x - y)
for the case that x <> y, now we can divide both sides by (x - y) and get
1 = 1.1
and that is wrong in all cases.
so, it is disproven for all x <> y.
for x = y the statement is true, the difference is in both cases 0.
e.g.
100 and 200
the difference is 100
100+10% = 110
200+10% = 220
and the difference is 110 (different to the original 100).
but 100 and 100, sure, the difference is 0, and the difference between 110 and 110 is still 0.
adding a % to a number means the size of the added part depends on the size of the basic number. the same % of a larger number is larger than the same % of a smaller number. therefore, the distance grows.
Evaluate the function h(x) = 13 – x when x= -3,0, and 8.
Answer:
h(-3)=16
h(0)=13
h(8)=5
Step-by-step explanation:
[tex]h( -3) = 13 - ( - 3) = 16 \\ h(0) = 13 - 0 = 13 \\ h(8) = 13 - 8 = 5[/tex]
How many solutions does this system have?
y = -6x - 5
-2y +7 = 12x
A.
One Solution
B.
Two Solutions
C.
No Solutions ***** (what i think)
D.
Infinitely Many Solutions
A system of equation may have one, zero or infinitely many solutions
The system of equation has no solutions
The systems of equation are given as:
[tex]y = -6x - 5[/tex]
[tex]-2y +7 = 12x[/tex]
Substitute -6x - 5 for y in [tex]-2y +7 = 12x[/tex]
[tex]-2(-6x - 5) +7 = 12x[/tex]
Open brackets
[tex]12x + 10 +7 = 12x[/tex]
[tex]12x + 17 = 12x[/tex]
Subtract 12x from both sides of the equation
[tex]17 = 0[/tex]
The above equation is not true i.e.[tex]17 \ne 0[/tex]
Hence, the system of equation has no solutions
Read more about solutions of equations at:
https://brainly.com/question/9338739
Breakfast eaten and the slim camp-outfit lashed to the sled, the men turned their backs on the cheery fire and launched out into the darkness. At once began to rise the cries that were fiercely sad—cries that called through the darkness and cold to one another and answered back. Conversation ceased. Daylight came at nine o'clock. At midday the sky to the south warmed to rose-colour, and marked where the bulge of the earth intervened between the meridian sun and the northern world. But the rose-colour swiftly faded. The grey light of day that remained lasted until three o'clock, when it, too, faded, and the pall of the Arctic night descended upon the lone and silent land.
As darkness came on, the hunting-cries to right and left and rear drew closer—so close that more than once they sent surges of fear through the toiling dogs, throwing them into short-lived panics.
At the conclusion of one such panic, when he and Henry had got the dogs back in the traces, Bill said:
"I wisht they'd strike game somewheres, an' go away an' leave us alone."
"They do get on the nerves horrible," Henry sympathized.
They spoke no more until camp was made.
The introductory paragraph to this section of text starts with breakfast and ends with the setting of Arctic sun. How does this short paragraph add to the conflict in the story? (5 points)
It suggests time is running out before the story even begins.
It suggests the cold will only increase in the coming days.
It suggests the days are intense but beautiful.
It suggests the characters do not get far during the short days. I AM GIVING 100 POINTS!!!
Answer:
It suggests the days are intense but beautiful.
Step-by-step explanation:
According to the introductory paragraph that starts with breakfast and ends with the setting of Arctic sun. This short paragraph adds to the conflict in the story because It suggests the days are intense but beautiful.
Although the question is incomplete, i can infer that the story you are referring to is White Fang by Jack London, where the story is told of the people talking about events happening around them.
They talk about the sun and the work around them and also the cold. How thsir short conversation added to the conflict in the story is that It suggests the days are intense but beautiful
Help help help math math
Answer:
x = 11
Step-by-step explanation:
Lines are parallel. 5x + 10 and 10x + 5 are supplements of each other.
Move 5x+ 10 to the corresponding position on the figure. It will be next to 10x + 5 and form a linear pair with 10x + 5. A linear pair form a straight angle or two supplementary angles. Supplementary angles = 180°
Therefore 5x +10 + 10x + 5 = 180°
15x + 15 = 180°
15x = 180 - 15
15x = 165
x = 11
ALGEBRA Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%. During the monthly billing cycle, Ben charged $238.75, made a payment of $300.00, and had a finance charge of $7.99. Find his unpaid balance, previous balance, and new balance.
The new balance is a credit of $ 48.78.
Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:
Finance charge + new purchases + previous balance - payments = X 238.75 x 1.01875 + 7.99 - 300 = X 243.22 + 7.99 - 300 = X 251.21 - 300 = X -48.78 = X
Therefore, the new balance is a credit of $ 48.78.
Learn more about maths in https://brainly.com/question/3554632
What is the inverse of y=5x-5
Answer:the answer is in the picture below
Step-by-step explanation:plz give brainlist
Describe how to find your x-intercepts ?
Janessa recently increased the size of his Jeep tires from the original P230/85R18 to the larger P250/85R21. If Janessa didn’t recalibrate her odometer, how far did she really travel on the new tires when her odometer shows she has traveled 23425 miles?
The distance Janessa traveled on the new tires with the given size is 26,470.25 miles.
The given parameters:
Original size of the tire, = P230/85R18The width of the smaller tire, = 230 mmAspect ratio, = 85%Larger size of the tire, = P250/85R21The width of the larger tire, = 250 mmAspect ratio, = 85%Reading of the odometer = 23,425 milesThe diameter of the smaller tire is calculated as follows;
[tex]0.85 = \frac{h}{230} \\\\h = 0.85 \times 230 \\\\h = 195.5 \ mm\\\\h = 195.5 \ mm \times \frac{1 \ in}{25.4 \ mm} \\\\h = 7.7 \ in[/tex]
diameter of the smaller tire;
D = 2(7.7 in) + 18 in
D = 33.4 in
The circumference of the smaller tire;
[tex]C_1 = \pi D\\\\C_1 = 3.142 \times 33.4 \\\\C_1 = 104.94 \ in[/tex]
The diameter of the larger tire is calculated as follows;
[tex]0.85 = \frac{h}{250} \\\\h = 0.85 \times 250 \\\\h = 212.5 \ mm\\\\h = 212.5 \ mm \times \frac{1 \ in}{25.4 \ mm} \\\\h = 8.37 \ in[/tex]
diameter of the larger tire;
D = 2(8.37 in) + 21 in
D = 37.74 in
The circumference of the larger tire;
[tex]C_2 = \pi D\\\\C_2 = 3.142 \times 37.74 \\\\C_2 = 118.58 \ in[/tex]
After one rotation, the larger tire will travel the following distance more than the smaller tire;
[tex]n = \frac{C_2}{C_1} = \frac{118.58}{104.94} = 1.13[/tex]
The distance Janessa traveled on the new tires when her odometer shows she has traveled 23425 miles;
[tex]distance = 1.13 \times 23,425\\\\distance = 26,470.25 \ miles[/tex]
Learn more about tire sizes and distance traveled: https://brainly.com/question/4822144
If DEF and MNO are two triangles such that DE=MN and EF=NO, which of the following would be sufficient to prove that triangles are congruent
Answer:
D. ∠E ≅ ∠N
Step-by-step explanation:
The pair of sides meet at vertex E in ∆DEF and at vertex N in ∆MNO. Since the sides that make up angles E and N are shown congruent, it is sufficient to show ...
∠E ≅ ∠N
Then the SAS congruence postulate can be claimed.
__
Additional comment
The alternative is to show DF ≅ MO. That would allow you to claim SSS congruence. That is not an answer choice.
0.80x= 28 what is x
please help
Answer: x is nothing.
Step-by-step explanation: The goal is to get x by itself not with the numbers. You just have to solve the equation and whatever you get is equal to X. Example- your problem is 0.80x= 28 which would equal 172 if you're tryna find the solution. X does not matter in your equation and remember x can be any number! I'm not good at explaining so i'm sorry if you have no idea what i'm talking about. I hope this helps!
Your answer is 172.
-Notsonerdy
Which term of the AP 21, 18, 15 ...... is -81 ?
Given AP is 21 ,18,15,...
First term = 21
Common difference = 18-21 = -3
Let an = -81
We know that
an = a+(n-1)d
⇛21+(n-1)(-3) = -81
⇛ 21-3n+3 = -81
⇛24-3n = -81
⇛ 24+81 = 3n
⇛ 105= 3n
⇛ n = 105/3
⇛ n = 35
35th term of the AP is -81.
also read similar questions: Which term of a AP 5 , 13 , 21 ,... is 181?
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Which term of the AP:3, 8, 13, 18,...,is 78?
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SOSSSS:
Find all the values of x between 0 and 4 for which 3 cos(2x - 1) = 2
Answer:
0.29 π(52.5°)
Step-by-step explanation: here is the explanation
Use >,<, or = to solve
the inequality below.
4/5 1/2
Answer:
4/5 > 1/2
Step-by-step explanation:
4/5 1/2
\/
4/5 -> 8/10
1/2 -> 5/10
\/
8/10 > 5/10
\/
4/5 > 1/2
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
4/5>1/2
Step-by-step explanation:
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
4/5 = 0.8
1/2 = 0.5
Then, we compare the two decimal numbers to get the answer.
0.8 is greater than 0.5.
Therefore, 4/5 is greater than 1/2
-2/7 × 9.75 what is answer
Answer:
-2.78
Step-by-step explanation:
You first divide and then multiply.
Josh drives 504 miles in 8 hours. At the same rate, how many miles would he drive in 5 hours?
Answer:
315 miles
Step-by-step explanation:
The unit rate is 63 miles per hour, and 63×5=315 miles.
[tex]\begin{array}{ccll} miles&hrs\\ \cline{1-2} 504&8\\ x&5 \end{array}\implies \cfrac{504}{x}=\cfrac{8}{5}\implies 2520=8x\implies \cfrac{2520}{8}=x\implies 315=x[/tex]
9x + 3 – 7x + 4
Help me out please?
Answer: The answer is 2x + 7.
Explanation: First, we need to add the numbers:
9x + 3 – 7x + 4
9x + 7 - 7x
And finally, we combine like terms:
9x + 7 - 7x
2x + 7
PLEASE HELP
If you help You’ll automatically be my favorite person ever
Answer:
Put one point on -4 on the Y-axis (bottom middle) and one at (-2,2)
What is the number ten written in base 2?
Cushman Company had $842,000 in sales, sales discounts of $12,630, sales returns and allowances of $18,945, cost of goods sold of $399,950, and $289,650 in operating expenses. Gross profit equals:
Answer: $120825
Step-by-step explanation:
Add everything up then subtract $842000 by it
The car arrives from city A to city B in 3 hours. How many hours will it take to go the same way if you increase the speed by 20%?
Given :-
The car arrives from city A to city B in 3 hours.Speed is increased by 20% .To find :-
The new time taken .Solution :-
Let us assume the distance between A and B be x and the initial speed by y . After 20% increase in the speed , new speed will be ,
[tex]\blue{\dashrightarrow} [/tex] Speed = 120y/100
[tex]\blue{\dashrightarrow} [/tex] Speed = 6/5y
• According to the Question ,
[tex]\red{\dashrightarrow} [/tex] Distance = Speed * Time
[tex]\blue{\dashrightarrow} [/tex] x = y * 3 hrs
[tex]\red{\dashrightarrow} [/tex] x = 3y
And ,
[tex]\blue{\dashrightarrow} [/tex] t = Distance/Speed
[tex]\red{\dashrightarrow} [/tex] t = x ÷ (6y/5)
[tex]\blue{\dashrightarrow} [/tex] t = 5x/6y
[tex]\red{\dashrightarrow} [/tex] t = 5 (3y)/6y
[tex]\blue{\dashrightarrow} [/tex] t = 5/2 hrs
[tex]\red{\dashrightarrow} [/tex] t = 2.5 hrs
Hence now it will take 2.5 hrs to go from A to B .
Answer:
Step-by-step explanation:
Let's say the distance between A and B is 3 miles (3, because I see a need to divide the distance by 3 hours to determine the car's speed). The actual distance makes no difference in the answer, since it is asking for a relative speed change (20%).
We find the speed to be 3 miles/3 hours, or 1 mph. A 20% increase in speed would be (1.20)(1) = 1.20 mph.
We can find the time for a 1.2 mph car to go 3 miles by:
(3 miles)/(1.2 mph) = 2.5 hours
=====
[Note that if we assumed a different distance, say 6 miles, we'd get the same result:
6 miles/3 hours = 2 mph
1.2*2 = 2.4 mph
New time = 6/2.4 = 2.5 hours; same as before]