The two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16
Let the two variables be x and y
If the product of the numbers is 300, hence
xy = 300
x = 300/y ........ 1
If the sum of the first and four times the second is a minimum, then;
P(x, y) = x + 4y .................. 2
Substitute equation 1 into equation 2:
P(x, y) = x + 4y
P(y) = 300/y + 4y
If this function is at mimimum, hence dP/dy = 0
dP/dy = -300/y² + 4 = 0
-300/y² + 4 = 0
-300 + 4y² = 0
4y² = 300
y² = 300/4
y²= 75
y = 7.66
Since xy = 300
x = 300/7.66
x = 39.16
Hence the two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16
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1) f(x) = x² + 2x + 1
2) g(x) = x² + 6x + 5
3) h(x) = x² - 12x + 36
4) g(x) = 9x² + 6x + 2
5) g(x) = x² + 6x + 4
Answer:
(X+1)(X+1) (X+5)(X+1)3. (X-6)(X-6)
find the amount of money Khairul had initially
Answer
Find the amount of money Khairul had initially
money with Khairul initially = 6x = 6(60) = 360
Step-by-step explanation:
2 paisa per 2 rupees per month
Answer:
2 paisa per rupees per month
So rate= 2%
To study the effects of a medication on migraines, every 10th adult from an alphabetized list of patients who suffer from migraines were selected. Then, the sample was surveyed about the number of migraines they have each month. The names of the 50 adults selected were written on equal sized tiles, placed in a bag, and mixed well. The people with names on the first 25 tiles selected were given the migraine medication. The remaining 25 people were given a placebo. After six months, all patients were surveyed again about the number of migraines they had each month. The change in the mean number of migraines between the two groups was compared. Which of the following is the best description of the randomization approach? random selection random assignment both random selection and random assignment neither random selection nor random assignment
Answer:
Random Assignment
Step-by-step explanation:
Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answer:
Sam is NOT correctStep-by-step explanation:
Let's find the diagonal measures using Pythagorean and compare:
[tex]SQ=\sqrt{12^2+6^2} =\sqrt{4*6^2+6^2} =\sqrt{5*6^2} =6\sqrt{5}[/tex]and
[tex]OM=\sqrt{6^2+6^2} =\sqrt{2*6^2} =6\sqrt{2}[/tex]Find the ratio of diagonals:
SQ / OM = √5 / √2 ≠ 2Pahelp yawa T^T[tex]{\blue{\rule{25pt}{1pt}{\purple{\rule{30pt}{3pt}{\red{\rule{50pt}{5pt}{\purple{\rule{30pt}{3pt}{\blue{\rule{25pt}{1pt} }}}}}}}}}}︎︎︎︎︎︎︎︎ ︎︎︎︎︎︎︎︎[/tex]
pasagut 6-7 lang T^T
sabog na akow HAHAH
6-7
y < -1 -4
x > -4 y ≥+ 2
hope it helps
wait Lang SA 6-7
Answer:
ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok ok
Find the values of the six trigonometric functions for angle θ.Give answers in simplest form.
Answer:
Below in bold.
Step-by-step explanation:
The length of the side opposite to theta:
= √(24^2-21^2)
= √(24-21)(24+21)
= √(135)
= 3√15.
sin theta = 3√15/ 24 = √15/8. csc theta = 1/√15/8 = 8/√15 = 8√15/15.
cos theta = 21/ 24 = 7/8. sec theta = 8/7.
tan theta = 3√15/21 = √15/7. cot theta = 7/√15 = 7√15/15.
Mr. Jones's prescription calls for 1.04 tablets per day. Based on this information, how many tablets should Mr. Jones take per day? a) 1.25 O b) 1.5 c) 1 O d) 2
I think the answer is a but I'm not sure I'm really a little confused I want to check with this app please can someone heelp me
please what is measurement BAC
Answer:
54 degrees? I'm not an expert, but judging by the pic, I would say 54 degrees.
Please show how you solved the problem.
4a - 14 = 7a - 8
4a - 14 = 7a - 8
4a - 7a = 14 -8
-3a = 6
a = 2
ok done. Thank to me :>
Answer:
a= -2
Step-by-step explanation:
4a -14 = 7a -8
Subtract 7a from both sides
-3a -14= -8
Add 14 to both sides of equation
-3a = -8 +14
Add -8 and 14
-3a = 6
Divide each term by -3
a = -2
Estimate each product 11.9×21=
Answer:
249.9
uhm.. correct me if im wrong
Can someone help me please I will mark u brilliant
Answer:
6.333... is greater
Step-by-step explanation:
6.3 is larger than 6.2
Answer:
6.33333
Step-by-step explanation:
6.29
6.33333
The 3 is greater than the 2.
Hope this helps :)
Evaluate the line integral, where C is the given curve. z2 dx x2 dy y2 dz, C C is the line segment from (1, 0, 0) to (5, 1, 2)
I assume the integral is supposed to be
[tex]\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz[/tex]
Parameterize C by
[tex](x(t),y(t),z(t)) = (1-t)(1,0,0) + t(5,1,2) = (1+4t, t, 2t)[/tex]
with 0 ≤ t ≤ 1, and dx = 4 dt, dy = dt, and dz = 2 dt. Then the line integral is
[tex]\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz = \int_0^1 (2t)^2(4\,dt) + (1+4t)^2\,dt + t^2(2\,dt)[/tex]
[tex]\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz = \int_0^1(1+8t+34t^2)\,dt[/tex]
[tex]\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz = 1+4+\frac{34}3 = \boxed{\frac{49}3}[/tex]
If x^2 - (3x-a) (bx-1) = c, where a, b, and c are constants, what id the value of c?
A. 9
B. 7
C. 13
D. 2
PLS ILL GIVE BRAINLIEST!!!!
Answeryawa ka
Step-by-step explanation:
help me plz im desperate
Answer:
B) y = 2x - 3
Step-by-step explanation:
We can determine which equation the line follows by checking the y-intercepts of each equation. The line passes through the point (0, -3) - this is the y-intercept of the line. The y-intercept in an equation is the single value after the slope. So, for example, in a line y = mx + b, b is the y-intercept.
For A, our y-intercept is (0, 2). For B, our y-intercept is (0, -3). For C, our y-intercept is (0, 3). For D, our y-intercept is (0, -2). So which one matches our line? It would be B, since both have a y-intercept of (0, -3).
So, that's our answer. If you need more help, let me know! :)
Answer: B
Step-by-step explanation:
The slope is 2 as it shown rise (2) over run (1)
Y-intercept is -3
Which number replaces the question mark? 19 11 11 ? 12
Answer:
i think 12
Step-by-step explanation:
Answer:
4 + 3 + 2 = 9
Step-by-step explanation:
You have to add all the numbers in the cube.
These are the following ones.
19 = 4 + 8 + 7
11 = 2 + 8 + 1
11 = 5 + 5 + 1
4 + 3 + 2 = 9
12 = 2 + 7 + 3
Look at the two equations:
-3x + 6 = 21
-3x + 6 < 21
Which statement best describes the process used to solve the equations?
O In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality
O In both cases, divide by -3 on both sides, but reverse the inequality sign when doing that for the inequality.
O The process is exactly the same for solving the equation and solving the inequality
O The process for solving the equation is entirely different from solving the inequality.
Plz help!! Given: DE is a midsegment of ABC. Show all work.
Find the value of x and y.
And What is the length of AC? !Please show all work!
Incase photo is blurry
AE-y+6
EC-x-3
DE-x+2
BC-24
Answer:
AC=14
X=10
Y=1
Hoped this helped!
Step-by-step explanation:
DE is half of BC, therefore x=10. AE and EC have to be the same length, which is 7. SO, y=1 and x is 10.
A box has 10 red, 5 blue and 5 yellow balls. Draw 6 balls one by one with replacement. Then calculate the probability that
Answer:
I would say its a 16.5 %
Step-by-step explanation:
The cost of 2 bunches of
roses and 5 bunches of
carnations is £45.
The cost of 3 bunches of
roses and 4 bunches of
carnations is £50.
Find the cost of one bunch of each
Answer:
vtdOveractivity of the pituitary gland is called hyperpituitarism. Several disorders related to an overactive pituitary gland can occur.
...
Symptoms may include:
Nervousness.Rapid or irregular heartbeat.Weight loss.Fatigue.Muscular weakness.
Fireworks are fired from the roof of a 100-foot building and travel 84 feet per second. The equation h = -16t 2 + 84t + 100 models the height h of the fireworks at any given time t seconds.
The firework reaches the ground after 6.25 seconds.
A projectile is the curved motion of an object thrown into space under the influence of gravity.
Given that the firework experiences a projectile motion given by the equation:
h = -16t² + 84t + 100
where h is the height after t seconds.
The firework reaches the ground when h = 0, hence:
0 = -16t² + 84t + 100
t = 6.25 seconds.
Therefore the firework reaches the ground after 6.25 seconds.
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brainiest to whoever correct
Answer:
y = 138
Step-by-step explanation:
90 + 4x + 3x + 6 = 180
96 + 7x = 180
7x = 84
x = 12
———
3(12) + 6
36 + 6
42
———
180 - 42 = 138
Peter has 18 oranges, 27 pears and 12 bananas. He wants to make fruit baskets with
the same number of each fruit in each basket. What is the greatest number of fruit
baskets he can make? How many of each type of fruit will be in the baskets?
Answer:
3 baskets and 6 oranges, 9 pears, 4 bananas
Step-by-step explanation:
the common denominator is 3
Please any math experts help thanks you
Answer:
[tex]\frac{p^2-25}{p^2-10p+25}[/tex]
We can factorise the numerator with the difference of squares formula:[tex]x^2-y^2=(x+y)(x-y)[/tex]
-----------------------------
[tex]\frac{p^2-5^2}{p^2-10p+25} =\frac{(p+5)(p-5)}{p^2-10p+25}[/tex]
Now we can factorise the denominator:
[tex]\frac{(p+5)(p-5)}{p^2-10p+25} =\frac{(p+5)(p-5)}{(p-5)^2}[/tex]
[tex]\frac{(p+5)(p-5)}{(p-5)^2} =\frac{(p+5)(p-5)}{(p-5)(p-5)}[/tex]
Cancel out the common factor of (p-5):
[tex]\frac{(p+5)(p-5)}{(p-5)(p-5)} =\frac{(p+5)}{(p-5)}[/tex]
In 1950, the group spent 23% of their budget on food. This has decreased
at an average rate of approximately 0.27% per year since then. Find a
linear function in slope-intercept form that models the percentage of total
spending, p(x), by the group x years after 1950.
The linear function that can be used to model this relationship is:
y = -0.27x + 23
A linear function is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let P(x) represent the percentage of total spending x years after 1950.
Since In 1950, the group spent 23% of their budget on food, hence b = 23.
Also, this has been decreasing at 0.27% per year. Hence m = -0.27.
The linear function that can be used to model this relationship is:
y = -0.27x + 23
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What is the solution to the system of equations? y=−2x−64x−y=−36 (−15, 24) (−7, 8) (−5, 4) I don't know.
Answer:
Since y = −2x − 6 and 4x − y = −36, the solution would be B.) (-7, 8).
A solution to the given system of equations is [tex](\frac{100}{3}, \frac{8}{3} )[/tex]
Given the following system of equations:
[tex]y=-2x-64[/tex] ...equation 1.
[tex]x-y=-36[/tex] ...equation 2.
To find a solution to the given system of equations, we would use the substitution method:
First of all, we would make x the subject of formula in equation 2.
[tex]x=-36+y[/tex] ...equation 3.
Substituting eqn. 3 into eqn. 1, we have:
[tex]y = -2(-36+y)-64\\\\y=72-2y-64\\\\y+2y=72-64\\\\3y=8\\\\y=\frac{8}{3}[/tex]
For the value of x:
[tex]x=-36+y\\\\x=-36+\frac{8}{3} \\\\x=\frac{100}{3}[/tex]
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158) -.- A) P-3 in B) P-86 C) P-92 in D) P96 4
Answer:
P = 83 in
Step-by-step explanation:
For this one, all we need to do is substitute 7 for x and 4 for y:
3x + y = ?
3(7) + 4 =?
21 +4 = ?
21 + 4 = 25 in.
Now for the next one:
4y = ?
4(4) = ?
4(4) = 16
Now we solve the final side:
6x = ?
6(7) = ?
6(7) = 42
Now to find P, we must add them all together:
25 + 16 + 42 = 83
Therefore P = 83
Answer:
A) P = 83
Step-by-step explanation:
-=======================-
3x + y
3(7) + 4 =
21 + 4 =
25
-=======================-
6x
6(7)
42
-=======================-
4y
4(4)
16
-=======================-
25 + 16 + 42 = 83
Hope this helps.
Please help me answer this question!!!
Answer:
B
Step-by-step explanation:
<STR = <SRT Given the markings of the triangle
<STR + <STU = 180 Supplementary angles
(2x - 9) + 7x = 180 Remove the brackets
2x - 9 + 7x = 180 Combine
9x - 9 = 180 Add 9 to both sides
9x = 180 + 9 Combine
9x = 189 Divide by 9
9x/9 = 189/9
x = 21
Help help math math help help
Answer:no they are not
Step-by-step explanation:
As all angles are 60∘ each and given all sides are equal then it can be said as congruent.
Answer:
no
Step-by-step explanation: