Answer:
[tex]\boxed{(0, 0), (\sqrt{6}, -12-3\sqrt{6}), (-\sqrt{6}, -12+3\sqrt{6})}[/tex]
Step-by-step explanation:
Step 1: Take the derivative of the function with respect to x
[tex]\frac{d}{dx} (\frac{1}{3}x^4-4x^2-3x)\\=\frac{d}{dx} (\frac{1}{3}x^4)-\frac{d}{dx}(4x^2)-\frac{d}{dx}(3x)\\=\frac{4}{3}x^3-8x-3[/tex]
Now, you have the gradient of every point given the x value. We want the gradient to be -3, so,
Step 2: Set the derivative of the function equal to -3 and solve for x
[tex]\frac{4}{3}x^3-8x-3=-3\\\frac{4}{3}x^3-8x=0\\4x(\frac{1}{3}x^2-2)=0\\[/tex]
We can see that one solution is x=0.
The other 2 solutions are:
[tex]\frac{1}{3}x^2-2=0\\\frac{1}{3}x^2=2\\x^2=6\\x=\sqrt{6}, x=-\sqrt{6}[/tex]
Now that we found out the x value, we can plug it in back to the equation to find their respective y value:
x=0: y=0
x=sqrt(6): y=-12-3sqrt(6)
x=-sqrt(6): y=-12+3sqrt(6)
Hence we have our answer.
Convert 5 square meters to square centimeters. Explain
Answer:
5 sq m = 50,000 sq cm
5 sq m = 5 sq m
Step-by-step explanation:
To convert a square meter measurement to a square centimeter measurement, multiply the area by the conversion ratio.
Since one square meter is equal to 10,000 square centimeters, you can use this simple formula to convert:
square centimeters = square meters × 10,000
Answer:
50000 square centimeters.
Step-by-step explanation:
⦁ Solve for x: 3|x – 7| = 15
SHOW WORK
[tex]3|x-7| = 15\\\\\implies |x-7| =\dfrac{15}3\\\\\implies |x -7| = 5\\\\\implies x -7 = 5 ~~ \text{or}~ x - 7 = -5\\\\\implies x = 12 ~~\text{or}~~ x = 2[/tex]
Pls help with my maths!!!
Step-by-step explanation:
[tex] \frac{x + 6}{ x} = \frac{5}{2} [/tex]
Then collect like terms
answer is x = 4
Answer:
x = 4
Step-by-step explanation:
x + 6/x = 5/2
2(x + 6) = 5(x)
2x + 12 = 5x
12 = 5x - 2x
12 = 3x
12/3 = x
4 = x
Hence,
Value of x is 4
If f(x) = 2x2 + 3x and g(x) = x 2- 7, find (f +g)(x)
Answer:
3x²+3x-7
Step-by-step explanation:
(f+g)(x)=2x²+x²+3x-7
=3x²+3x-7
Choose the symbol that correctly compares the fractions below.
Answer: A. ( > )
Step-by-step explanation: When you learn fractions, the fraction with the smaller numerator ( the top number) is the greater fraction because it contains more parts of the whole.
Pratima attends dance classes every 6 days, singing
classes every 4 days, and yoga classes every 16 days. If
.
she does all three activities today, in how many days will
she do all the three activities again on the same day?
PLEASE SHOW YOUR WORK
Using the least common factor, it is found that she will do all the three activities again on the same day again in 48 days.
She sings every 4 days.She attends dance classes every 6 days.She has yoga classes every 16 days.To find how many days it takes so that she will do all the three activities again on the same days, we have to find the least common factor of 4, 6 and 16.
It is done factoring them using prime factors, then:
4 - 6 - 16|2
2 - 3 - 8|2
1 - 3 - 4|2
1 - 3 - 2|2
1 - 3 - 1|3
1 - 1 - 1
Hence:
lcm(4,6,8) = 2x2x2x2x3 = 48
She will do all the three activities again on the same day again in 48 days.
To learn more about the least common factor, you can take a look at https://brainly.com/question/25924269
In a school of 500 students, 30% had I-Phones. The percent of boys to gi
were 25% and 75% respectively.
A. Calculate (I) the number of students with I-PhonesIn a school of 500 students, 30% had I-Phones. The percent of boys to gi
vere 25% and 75% respectively.
Answer:
tbh,I would calculate the girls to boys ratio.
Step-by-step explanation:
I mean, them boys gotta be in female heaven.
25% of them, the rest being girls, dang, imagine being handsome. lots of gf's
and FYI, it's iPhone not an i-phone.
Find the following:
sin A
cos A
tan A
cot A
sec A
csc A
Step-by-step explanation:
we use the law of sine :
sin(A)/a = sin(B)/b = sin(C)/c
with the related angles being opposite of the lines.
so, we have
sin(A)/1 = sin(A) = sin(90)/ sqrt(10) = 1/ sqrt(10) =
= 0.316227766...
cos²(A) + sin²(A) = 1
cos(A) = sqrt(1 - sin²(A)) = sqrt(1 - 0.1)) = sqrt(0.9) =
= 0.948683298...
tan(A) = sin(A)/cos(A) = 0.333333333...
cot(A) = 1/tan(A) = 3
sec(A) = 1/cos(A) = 1.054092553...
csc(A) = 1/sin(A) = 3.16227766...
What is the measure of angle DCE? Use numbers only.
Answer:
156 degrees
Step-by-step explanation
First we need to figure out what X is. To do that we set up the equation 7x+3=8x because vertical angles are congruent. After solving that we get x=3. We plug 3 back into each equation and we get that angle ACE equals 24. Since angle ACE and angle DCE are supplementary we know that they will equal 180 so we subtract 24 from 180 and get 156 as the final answer.
Hope this helps!
Share £30 in the ratio 1:5 between Tim and Sam
On a piece of paper, graph f(x) = 4x. Then determine which answer choice
matches the graph you drew.
Answer:
The Correct Answer is A
Step-by-step explanation:
You are able to put the equation into Desmos Online Graphing Calculator.
When inserting the equation:
[tex]f(x) = 4 {}^{x} [/tex]
You are able to determine that the graph looks like Graph A
I hope this helps and you have a great day!
Note: I am not a professional so take my opinion with caution!
Answer:c
Step-by-step explanation:
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answer:
Step-by-step explanation:
A decrease in the amount of principal owed on a loan is called what?
A. Note reduction
B. Amortization
C. Payment number
D. Unpaid balance
SUBMIT
The reduction in the principal balance through amortization has a significant impact on the loan's overall cost. As the principal decreases, the amount of interest charged on the outstanding balance also decreases.
the correct answer is B. Amortization.
A decrease in the amount of principal owed on a loan is called amortization.
Amortization refers to the gradual reduction of the principal balance of a loan over time through regular payments. When you make payments on a loan, a portion of the payment goes towards paying off the principal amount borrowed, while another portion goes towards paying the interest charged on the loan.
The process of amortization involves dividing the total loan amount into equal installments or payments over a specified period. With each payment made, a portion goes towards reducing the principal balance. As a result, the outstanding principal decreases over time, leading to the eventual repayment of the entire loan.
Amortization is a common feature in installment loans, such as mortgages, car loans, and personal loans. It allows borrowers to repay the loan gradually rather than in a lump sum, making it more manageable and affordable.
The reduction in the principal balance through amortization has a significant impact on the loan's overall cost. As the principal decreases, the amount of interest charged on the outstanding balance also decreases. This means that over time, a larger portion of each payment goes towards paying off the principal, helping the borrower build equity and ultimately fully repay the loan.
Therefore, the correct answer is B. Amortization.
for more such question on interest visit
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What is an equation of the line parallel to the line on the graph that passes
through (4, 15)?
Weight of Bucket of Sand
Total weight (ounces)
Answer:
Step-by-step explanation:
The existing line appears to pass through (0, 20) and (10, 50)
so the line slope is m = Δy/Δx = (50 - 20) / (10 - 0) = 3
parallel lines have identical slopes
y = 3x + b
15 = 3(4) + b
b = 3
D. y = 3x + 3
[tex]\\ \rm\Rrightarrow m=\dfrac{25-20}{2}=5/2[/tex]
Slope of parallel line=5/2Equation of line in point slope form
[tex]\\ \rm\Rrightarrow y-y_1=m(x-x_1)[/tex]
[tex]\\ \rm\Rrightarrow y-15=5/2(x-4)[/tex]
[tex]\\ \rm\Rrightarrow 2y-30=5x-20[/tex]
[tex]\\ \rm\Rrightarrow 5x-2y+10=0[/tex]
Which is equivalent to the following expression? (2x - 1)(x + 3)
Answer:
2x2+5x−3
Step-by-step explanation:
Expand the polynomial using the FOIL method.
Help me to solve this
Step-by-step explanation:
first we use Pythagoras to get t :
c² = a² + b²
with c being the Hypotenuse.
so,
t² = r² + s² = 10² + 31² = 100 + 961 = 1061
t = sqrt(1061)
and then we use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of their related sides.
so, r/sin(R) = t/sin(T) = t/sin(90) = t/1 = t
sin(R) = r/t = 10/sqrt(1061) = 0.30700278...
R = 17.8786966... ≈ 17.9°
Donna buys 400 shares of stock for $23 per share and pays a 1% commission. She sells them 6 years later for $23.25 per share and pays a flat fee of $30.00. What is her total purchase cost?
Answer:
She sells them six years later for$23.25 per share, and pays a $30 flat fee. ... 1 of 4. Purchase price of 400 shares = 400*23 =9200. total purchase costStep-by-step explanation:
What is the slope
A) 1/3
B) 3
C) 2
Answer:
3 (B)
Step-by-step explanation:
rise/run
rise=3
run=1
3/1=3
Overview
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Question Progress
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The length of a rectangle is twice its width.
The perimeter of the rectangle is 41 cm.
Label the diagram with the correct length and width for the rectangle.
cm
cm
Answer:
Width=6 5/6cm and Length=13 2/3cm
Step-by-step explanation:
Lets have width=x
Therefore, 4x+2x=41cm
6x=41cm
x=41/6=6 5/6
the width is 6 5/6 cm and length 41/3=13 2/3
find the value of the variable in the isosceles triangle. show your work plz
Step-by-step explanation:
3x-3 = x+5 add 3 on both sides
3x = x+8 subtract x in both sides
2x = 8 divide both sides by 2
x = 4
A certain music club charges an annual membership fee of $99, in return, its members will be able to buy and download songs at a very low cost of 10 cents each. If Tyna spent a total of $149.30 including the membership fee, how many songs did she buy?
A) 99+10x=149.30
B) 99-10x=149.30
C) 99-0.1x=149.30
D) 0.1x+99=149.30
Answer:
D). 0.1x+99=149.30
How many songs Tyna Bought:
503 songs
Step-by-step explanation:
Since the membership fee is 99 you don't have to pay for it again
(Until next year that is)
Now it states that every download cost 10 cents or $0.1
So we don't know how many she will buy so we can replace that unknown value with x
So the equation is
0.1x+99=149.30
To solve this you first subtract 99 on both sides:
Which will result in
0.1x=50.3
Divide 0.1 on both sides
So Tyna bought 503 songs
(HOLY THAT IS A LOT OF SONGS)
Hope this Helps!
please help tysm ill mark brainliest
Answer:
use pemdas(order of the operations)and you'll get the answer 27!!
Step-by-step explanation:
Which of the following quadrants of the standard (x,y) coordinate plane contain points on the graph of the equation 6x – 3y = –9 ?
A. l and lll only
B. l, ll and lll only
C. l, ll and IV only
D. I, II and IV only
E. II, IIIand IV
Using linear function concepts, it is found that the correct option is:
B. l, ll and lll only
A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope.b is the y-intercept.If the slope is positive.
The function goes through quadrants I and III.If the intercept is positive, it also goes through quadrant II.If the intercept is negative, it also goes through quadrant IV.If the slope is negative:
The function goes through quadrants II and IV.If the intercept is positive, it also goes through quadrant I.If the intercept is negative, it also goes through quadrant III.In this problem, the equation is:
[tex]6x - 3y = - 9[/tex]
Placing it into the standard format:
[tex]3y = 6x + 9[/tex]
[tex]y = \frac{6}{3}x + \frac{9}{3}[/tex]
[tex]y = 2x + 3[/tex]
Both slope and intercept are positive, hence, quadrants I, II and III, option B.
You can learn more about linear functions at https://brainly.com/question/16302622
Diets For You announced today that it will begin paying annual dividends next year. The first dividend will be $0.12 a share. The following dividends will be $0.15, $0.20, $0.50, and $0.60 a share annually for the following 4 years, respectively. After that, dividends are projected to increase by 4 percent per year. How much are you willing to pay to buy one share of this stock today if your desired rate of return is 8.5 percent?
You will be willing to pay $ 1.41 to buy one share of this stock today if your desired rate of return is 8.5 percent.
Since Diets For You announced today that it will begin paying annual dividends next year, and the first dividend will be $ 0.12 a share, and the following dividends will be $ 0.15, $ 0.20, $ 0.50, and $ 0.60 a share annually for the following 4 years, After that, dividends are projected to increase by 4 percent per year, to determine how much are you willing to pay to buy one share of this stock today if your desired rate of return is 8.5 percent, the following calculation must be performed:
8.5 = 0.12 100 = X 100 x 0.12 / 8.5 = X 1.41 = X
Therefore, you will be willing to pay $ 1.41 to buy one share of this stock today if your desired rate of return is 8.5 percent.
Learn more about maths in https://brainly.com/question/25989093
In six years Xavier will be 3 times older than Joanne is today. Joanne is 24. How old is Xavier?
Answer:
72
Step-by-step explanation:
You flip a coin 8 times and get tails 6 times. Based on this experiment, what is the probability of flipping a coin and getting heads?
Answer:
1/4
Step-by-step explanation:
If you get 6 tails, then that means you got 2 heads. 8-6=2.
probability= 2/8=1/4 based on this experiment.
PLEASE HELP WILL MARK BRAINIEST!!!!!!
Answer:
the first option
Step-by-step explanation:
What is the standard deviation of 82,93,89 and 88?
Answer:
4.546, rounded
Step-by-step explanation:
pls mark brainliest!
Help Will give Branliest
Hemp help help math math
Answer:
This is not a linear function, as it isn't any function because 3 has two outputs.
Step-by-step explanation:
Explained above