Step-by-step explanation:
60/100 ×50
= 30 ........
Find three positive numbers the sum of which is 27, such that the sum of their squares is as small as possible.
The three positive numbers whose sum is 27 will be 14, 1, and 12.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
Suppose the three positive numbers are x, y and z.
If the summation of numbers is 27.
⇒ x + y + z = 27 --- (1)
⇒ z = 27 - x - y
Suppose the square sum of the number be S.
∴ S = x² + y² + z²
⇒ S = x²+ y² + (27 - x - y)² --- (2)
We will optimize the function, partially differentiating it with respect to x and y, and setting dS/dx = 0 to get the minimum value of S.
2x + 2(27- x - y)(-1) = 0
2x - 54 + 2x + 2y = 0
4x + 2y - 54 = 0
y = 27 - 2x --- (3)
Differentiate partially with respect to y as
2y + 2(27 - x - y)(-1) = 0
2y - 54 + 2x + 2y = 0
4y + 2x - 54 = 0
x = 54 - 2y --- (4)
Substitute the value of y = 27 - 2x in the equation (4),
x = 12 - 2(27 - 2x)
x = 12 - 54 + 4x
4x - x = 54 - 12
3x = 42
⇒ x = 14
By substituting x = 14 in equation (3)
y =2(14) - 27
y = 28 - 27
⇒ y = 1
Substitute the values of x and y in equation (1),
14 + (1) + z = 27
z = -14+27-1
z= 12
Thus, the three positive numbers whose sum is 27 will be 14, 1, and 12.
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Find the length of side and the perimeter of a regular nine sided polygon with radius 5 units
Step-by-step explanation:
Nine sided polygon has an angle of 360/9=40 degrees at one vertex.
So the angles opposite the radius=(180–40)/2==140/2=70degrees.
solving for Base(side): 1/2s=5.cos70= 3.42 units Ans
P=9(5+3.42)=75.78 units Ans.
I search it. ♀️
Did I do this right????
Answer:
x = -7, y = -3 yup you did it right!
Step-by-step explanation:
Solve the following system:
{-2 y + x = -1 | (equation 1)
8 y - 5 x = 11 | (equation 2)
Swap equation 1 with equation 2:
{-(5 x) + 8 y = 11 | (equation 1)
x - 2 y = -1 | (equation 2)
Add 1/5 × (equation 1) to equation 2:
{-(5 x) + 8 y = 11 | (equation 1)
0 x - (2 y)/5 = 6/5 | (equation 2)
Multiply equation 2 by 5/2:
{-(5 x) + 8 y = 11 | (equation 1)
0 x - y = 3 | (equation 2)
Multiply equation 2 by -1:
{-(5 x) + 8 y = 11 | (equation 1)
0 x + y = -3 | (equation 2)
Subtract 8 × (equation 2) from equation 1:
{-(5 x) + 0 y = 35 | (equation 1)
0 x + y = -3 | (equation 2)
Divide equation 1 by -5:
{x + 0 y = -7 | (equation 1)
0 x + y = -3 | (equation 2)
Collect results:
Answer: {x = -7, y = -3
[tex]sec {}^{2} a \: . \: cosec {}^{2} a = {tan}^{2}a + {cot}^{2} a + 2 \\ [/tex]
Please help!!!!!!!!!!!!
Answer:
Trigonometric identities
[tex]\sec^2(\alpha)=1+\tan^2(\alpha)[/tex]
[tex]\csc^2(\alpha)=1+\cot^2(\alpha)[/tex]
[tex]\cot^2(\alpha)=\dfrac{1}{\tan^2(\alpha)}[/tex]
Solution[tex]\begin{aligned}\sec^2(\alpha) \cdot \csc^2(\alpha) & = (1+\tan^2(\alpha))(1+\cot^2(\alpha))\\\\ & =1+\cot^2(\alpha)+\tan^2(\alpha)+tan^2(\alpha)\cot^2(\alpha)\\\\ & = 1+\cot^2(\alpha)+\tan^2(\alpha)+\tan^2(\alpha) \cdot \dfrac{1}{\tan^2(\alpha)}\\\\ & = 1+\cot^2(\alpha)+\tan^2(\alpha)+ \dfrac{\tan^2(\alpha)}{\tan^2(\alpha)}\\\\& = 1+\cot^2(\alpha)+\tan^2(\alpha)+1\\\\& = \tan^2(\alpha)+\cot^2(\alpha)+2\end{aligned}[/tex]
Answer:
See below ~
Step-by-step explanation:
Trigonometric Identies (needed)
sec²a = 1 + tan²a cosec²a = 1 + cot²acot²a = 1/tan²aSolving
Expanding the LHS
sec²a * cosec²a(1 + tan²a) * (1 + cot²a)1 + tan²a + cot²a + (tan²a * cot²a)1 + tan²a + cot²a + 1tan²a + cot²a + 2⇒ RHS∴ Hence, we have proved the left hand side of the equation is equal to the right hand side.
The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given sin 0 = 2/5 find cos 0
cos (theta) = √21/5
Step-by-step explanation:
sin (theta) = 2/5
(sin (theta))^2 = 4/25
4/25 + (cos (theta))^2 = 1
(cos (theta))^2 = 1 - 4/25 = 21/25
cos (theta) = √21/5
I genuinely need this and am giving 50 pts.
find the area of the triangle pls.
and the bottom number is a 10
options:
30.0 yd2
15.0 yd2
6.5 yd2
13.0 yd2
FromHello, Volent strawberry is here to help!
Answer: 15.0 yd2
I hope this helps!
Bye have a nice day!
From: Miko
Answer:
1. Multiply the two legs of the triangle
3 x 10 = 30
2. Divide that number by 2
30 / 2 = 15
The area of the triangle is 15 yd2
x-x
A tanker truck leaves a rest stop at 8:00 am traveling 50 mph.
Two hours later a flatbed truck leaves the same rest stop
traveling 60 mph. At what time will they be 85 miles apart?
o 11:30 am
o 1:30 pm
o 3:30 pm
o 10:30 am
Answer:
Step-by-step explanation:
1:30
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answer: 5x 5y
Step-by-step explanation: because of the length
9(6x-8)+10x the instructions just say simplify
Answer:
64x -72
Step-by-step explanation:
9(6x-8)+10x = (multiply by 9)
54x -72 +10x
sum similar terms
64x -72
Answer:
64x-72
Step-by-step explanation:
Trust me lol.
Can yall help me pls
Answer:
Number of gallons in the tank after one hour.
The area of a rectangular region is 7.26 × 10* square feet. The length of the rectangular region is 1.21 × 10° feet. How much
does it cost to surround the region with a border that costs $0.80 per foot?
Answer:
$283.2
Step-by-step explanation:
Area of the order = Length * Width
7.02×10^3 = 1.17×10^2 * Width
7020 = 117W
W = 7020/117
W = 60feet
The perimeter of the border = 2(L+W
P = 2(117+60)
P = 2 * 177
P = 354 feet
If a border cost $0.80 per foot, 354 feet long border will cost 0.80 * 354 = $283.2
according to the line plot what is the total weight gained by the dogs that gained 1/8 of a pound or 3/4 of a pound
Answer:
i think the answer is 3
Step-by-step explanation:
Which is the graph of f(x) = (x+3)(x-2)
Answer:
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
Step-by-step explanation:
3x+8=2x+7
What the anwser pls solve em out
Answer: hii
Your answer is x= −1Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Hopefully this helps you
- Matthew
Which of the following is not true?
O √16 +4√4+5
О 3п > 9
O √27+3 >
O 5-√24 1
Answer:
Hello there! I believe b or d
-11c-35/4 = 4c- 2
-11c-35 ÷4 = 4c -2
Answer:
c=-1
Step-by-step explanation:
Multiply both sides by 4
[tex]\frac{-11c-35}{4}\cdot \:4=4c\cdot \:4-2\cdot \:4[/tex]
Simplify
[tex]-11c-35=16c-8[/tex]
Add 35 to both sides
[tex]-11c-16c=16c+27-16c[/tex]
Simplify
-27c=27
Divide both sides by 27
[tex]\frac{-27c}{-27}=\frac{27}{-27}[/tex]
Simplify
c= -1
mark brainliest please!
Please help I don’t understand this
Answer:
side: 17 inchesaltitude: 6 inchesStep-by-step explanation:
The formula for the area of a triangle gives a relationship between area, height, and base length. The problem statement gives the area, and it gives another relation between height and base length. Using these two relations, you can solve for the dimensions of the triangle.
__
setupThe side to which the altitude is measured is called the "base" in the area formula. The altitude is called the "height." The relation between them given by the area formula is ...
A = 1/2bh
51 = 1/2bh . . . . . . using the given value for area
The other relation given by the problem statement is that the base is 1 less than 3 times the height:
b = 3h -1 . . . . . . . base is 1 less than 3 times altitude
__
solutionUsing this second equation to substitute for 'b' in the first equation, we have ...
51 = 1/2(3h -1)h
102 = 3h² -h . . . . multiply by 2, eliminate parentheses
3h² -h -102 = 0 . . . . . put in standard form
3h² -18h +17h -102 = 0 . . . . . prepare to factor
3h(h -6) +17(h -6) = 0 . . . . . factor pairs of terms
(3h +17)(h -6) = 0 . . . . . . . . finish factoring
Solutions are the values of h that make these factors zero:
3h +17 = 0 ⇒ h = -17/3
h -6 = 0 ⇒ h = 6
We know that dimensions in a geometry problem must be positive, so the solution here is h = 6. Then b = 3h -1 = 3(6) -1 = 17. The dimensions are all in inches.
The length of the side is 17 inches; the altitude to that side is 6 inches.
Question below in picture
y
10-
9
8
7
6
5
4
321
2
O
1 2 3 4 5 6 7 8 9 10
What is the gradient of the blue line?
X
Answer:
1/4
Step-by-step explanation:
Using points (0 ; 1) and (4 ; 2)
m= y2-y1 / x2-x1
= 2-1 /4-0
= 1/4
The gradient of the blue line is, 1/4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the blue line are (3, -3) and (3, -6).
Now,
Since, The equation of line passes through the points (4, 2) and (8, 3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 2) / (8 - 4)
m = 1 / 4
m = 1/4
Thus, The gradient of the blue line is, 1/4
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(-2+3i)(1-2i) multiply
Answer:
The answer is
→ [tex]4 + 7i[/tex]
Step-by-step explanation:
[tex]((-2) + (3 * i)) * (1 - (2 * i)) = 4+7i[/tex]
Therefore, [tex]4+7i[/tex] is your answer.
Hope this helped! :^)
⭐Brainliest will be appreciated!⭐
✉️Message me if you have any more questions!✉️
- ✨7272033Alt✨
Submitted on 4/22/2022 at 12:39 PM
(To avoid plagarism, by users whom decide to copy.)
See screenshots below to prove my point that [tex]4+7i[/tex] is your answer...
In an examination, 460 students were tested. 23% were graded as good and the rest were graded as pass. No one failed the examination. Find the number of students who just passed.
The circumference of the inner circle is ft. The distance between the inner circle and the outer circle is ft. By how many feet is the circumference of outer circle greater than the circumference of the inner circle? Use
for . PLEASE HELPPPP ASAP
solve for volume. figure out the question
Answer:
819 is the answer
Step-by-step explanation:
formula for volume is LxWxH
since volume is length * width * height, the volume for this will be 9 * 7 * 13 = 819cm^3
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answer:
the answer is in the picture
Mrs little and jack go on a hike. After 2 hours, they have gone 300 feet. After 6 hours, they have gone 800 feet. What is the average rate of change?
Answer:
125 ft/hr
Step-by-step explanation:
dx/dt = (800-300)/(6-2) = 500/4 = 125
Solve for X
4(x + 3) = 2(x - 1)
(07.02 LC)
Which expression is equivalent to 4x(x + 5) + 5(x + 5)? (1 point)
O (4x + 5X5+5)
O (4x + 5Xx + 5)
09x(x + 5)
O 20x(x + 5)
Answer:
A
3(2x -5)-2(x-5)=3.(2x)-3.(5)-2.x-2.(-5)
=6x-15-2x+10
=4x-5
A laundry basket contains 10 socks, of which 2 are red. What is the probability that a randomly selected sock will be red? Write your answer as a fraction or whole number.
Answer:
you get a pair of red socks. There are 10 socks in the drawer, and 2 are red. Therefore the probability that the first one will be red is 2/10 = 1/5.
Step-by-step explanation:
What is the area of this figure?
Composite figure composed of a square with dimensions 3 ft by 3 ft, triangle with a base of 11 ft and a height of 3 ft and rectangle with dimensions 11 ft by 3 ft.
The area of the composite figure = area of square + area of triangle + area of rectangle = 58.5 ft²
What is the Area of the Composite Figure?Area of the composite figure = area of square + area of triangle + area of rectangle = s² + 1/2(bh) + lw
Given the following:
s = 3 ftb = 11 fth = 3 ftl = 11 ftw = 3 ftArea of the composite figure = (3²) + 1/2(11)(3) + (11)(3)
Area of the composite figure = 58.5 ft²
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
x = 26
Step-by-step explanation:
The length marked x is the hypotenuse of a right triangle with legs 10 and 24. The Pythagorean theorem can be used to find the value of x.
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs:
x² = 10² +24²
x² = 100 +576 = 676 . . . . simplify
x = √676 . . . . . . . take the square root
x = 26
Answer:
The hypotenuse is 26 units
Step-by-step explanation:
Step 1: Determine the value of x
Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex](24)^2+(10)^2=c^2[/tex]
[tex]576 + 100 = c^2[/tex]
[tex]676 = c^2[/tex]
[tex]26 = c[/tex]
Answer: The hypotenuse is 26 units