Two numbers whose sum is 10 is required.
The answer is
Minimum: 5, 5
Maximum: 9, 1
Let [tex]x[/tex] and [tex]y[/tex] be two numbers
[tex]x+y=10\\\Rightarrow y=10-x[/tex]
The sum of the squares would be
[tex]x^2+y^2=x^2+(10-x)^2\\ =2x^2-20x+100[/tex]
[tex]f(x)=2x^2-20x+100[/tex]
Differentiating with respect with x
[tex]f'(x)=4x-20[/tex]
Equating with zero
[tex]4x-20=0\\\Rightarrow x=\dfrac{20}{4}\\\Rightarrow x=5[/tex]
Double derivative of f(x)
[tex]f''(x)=4[/tex]
[tex]f''(x)>0[/tex]
So, at [tex]x = 5[/tex] the value of the function is minimum.
Therefore, at [tex]x=5[/tex] and [tex]y=10-5=5[/tex] the function has minimum value of [tex]5^2+5^2=50[/tex]
For the finding the maximum values of [tex]x[/tex] and [tex]y[/tex] we have to use trial and error method
[tex]9^2+1^2=82[/tex]
[tex]8^2+2^2=68[/tex]
[tex]7^2+3^2=58[/tex]
[tex]6^2+4^2=52[/tex]
0 and 10 will not be considered as 0 is neither positive nor negative.
So, the maximum value of the numbers is 9 and 1 and the maximum value of the function is 82.
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What is the value of x?
7.5/x= 30/16
Answer:
4
Step-by-step explanation:
I divided 30/16 and got 1.875, then I knew that 7.5 would have to have the same answer. I did a process of elimination by dividing 7.5 by numbers at random and finally divided by 4 and got the answer. Another way to get the answer would be to cross multiply the equation.
Ruth develops a blueprint with the help of a triangle. The longest side of the instrument measures 14 inches and one of the sides measures 12 inches. Determine the length of the other side of the instrument.
Answer:
7.2 inches
Step-by-step explanation:
Pythagorean Theorem
a
You've been given the longest side = 14 and the side of the triangle = 12,
Do [tex]14^{2} - 12^{2}[/tex], which will give you an answer of 52.
After doing this since you're calculating a side and you've been given the longest side already it can't possibly be an answer of 52.
Square root 52 and you'll get 7.2.
Your answer should be 7.2 inches.
Multiply (1.2 ⋅ 10^28) ⋅ (3 ⋅ 10^−19). Express the answer in scientific notation.
3.6 ⋅ 109
3.6 ⋅ 1010
36 ⋅ 109
36 ⋅ 1010
Answer:
3.6 × 10^9
Step-by-step explanation:
When multipliying two numbers in scientific notation, the exponents in the factor of 10 will be added when the two expressions are multiplied.
Thus (1.2 ⋅ 10^28) ⋅ (3 ⋅ 10^−19) = ( 1.2 × 3 )
( 10^28 × 10^-19 ) = 3.6 × 10^(28-19) = 3.6 × 10^9
A line passes through the point (10, -1) and has a slope of 3/2 .
Write an equation in slope-intercept form for this line.
Answer:
y=3/2x-16
Step-by-step explanation:
The equation of the line passing from points (10, -1) is y = 3x/2 - 16.
What is equation of a line?A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It conveys the slope, x-intercept, and y-intercept of the line and can be expressed in a variety of ways. Y = mx + c and axe + by = c are the two versions of the equation of a straight line that are most frequently employed.
Given slope = 3/2 and points (10, -1)
equation of line is given by y = mx + c
m = 3/2
y = 3/2x + c
substitute points,
-1 = 10*3/2 + c
c = -16
equation of line is y = 3x/2 - 16
Hence the equation is y = 3x/2 - 16.
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Which equation represents the line that goes through the point (0,2) and has a slope of 1/2
Answer:
1st answer is correct y=(1/2)x+2
Step-by-step explanation:
What is the answer for number 3
Answer:
x = 2
Step-by-step explanation:
-1.5x + 33 = 30
-1.5x = 30 - 33
x = -3 / -1.5
x = 2
Answer:
the first person gave u the right answer so head on ur going to get it right. wish u well
Hint : Add togheter and =180
Answer:
100 + 80
Step-by-step explanation:
Fill in the blank to make the two fractions equivalent.
4/5= ?/20
Answer:
16/20 here is why :)
Step-by-step explanation:
4/5 = 16/20
--- -----
x4
5x?=20
?=4
so you do the same for the numerator
4x4=16
hope this helped.
The printed price of a DVD player is $ 31. If the sales tax is 8% , find the price at which the DVD player is sold?
Answer:
$33.48
Step-by-step explanation:
If you write out the numbers from 0 to 40, how many times would you write the digit 3?
Four Times you'd say it
The numbers where there are 3 digits from 0 to 40 are
3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39
The digit 3 will be written thirteen times.
What is a number line?It is the way of representing numbers on a line where there is an equal unit between each number.
We have,
Numbers from 0 to 40.
There is always a digit 3 in every ten consecutive numbers.
From 0 to 40 we have 4 ten consecutive numbers.
- 0 to 10
- 10 to 20
- 20 to 30
- 30 to 40
3, 13, 23, and 33. _____(1)
There is a digit of 3 in all the consecutive numbers from 30 to 39.
i.e 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39. ____(2)
From (1) and (2) we have,
3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39
Thus,
The digit 3 will be written thirteen times.
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Solve for v:
5(5v + 4) = 17v + 8v+ 9 + 9
Omg Pleasssee Help Me
Answer:
5(5v+4)=17v+8v+9+9
25v+20=25v+18
25v-25v=18-20
0v=-2
i think soooo
this question is very very irrelevant
Step-by-step explanation:
Como es la fórmula del perímetro de un hexágono?
Espero respuesta
Gracias
Answer:
El Perímetro de un hexágono es igual a la suma de todos sus lados.
Step-by-step explanation:
el perimetro siempre es la suma de los lados de cualquier figura
Graph
Slope-Intercept Form
Point-Slope Form
y-1=1(x-1)
OMG CAN ANYBODY HELP ME OUT WITH HIS!?!?!?!? I NEED IT PLEASE I WILL GIVE BRAINLIEST IF ITS RIGHTTTT
Answer:
I would say C
Step-by-step explanation:
Hope I helped
If the base of a triangle is doubled then new area= ________ times old area
Answer:
As base and height are becoming double the new area is 4 times the original area. When the length of the sides of a triangle double, the area becomes quadruple.
Alyssa performed an experiment to measure the acceleration of a falling ball. She ran the experiment many times. Her results were distributed normally, with a mean of 9.75 meters per second and a standard deviation of 0.08 meters per second. Alyssa can be 95% sure that her next measurement will fall between the values of and meters per second.
Answer:
Alyssa can be 95% sure that her next measurement will fall between the values of 9.59 and 9.91 meters per second.
Step-by-step explanation:
I just took the test and got it right
The 95% measurement will fall between 9.59 m/s and 9.91 m/s
Given;
the mean of the normal distribution, m = 9.75 m/s
standard deviation from the mean, d = 0.08 m/s
To find:
the range of Alyssa's 95% data
let this range = X
The 95% of the data will fall within 2 standard deviation below and the above the mean.
2 standard deviation below the mean = m - 2d
2 standard deviations above the mean = m + 2d
From the given values, m - 2d = 9.75 - 2(0.08) = 9.59 m/s
m + 2d = 9.75 + 2(0.08) = 9.91 m/s
Thus, the range of the 95% data = 9.59 m/s < X < 9.91 m/s
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Find the slope of the line passing through the points (-6, 1) and (-7, 8).
Hello!
Slope formula:
y2-y1/x2-x1
y2: 8
y1: 1
x2: -7
x1: -6
Plug given values into the equation:
8-1/-7 - (-6)
Subtract
7/-1
Divide
-7
The slope is -7
Answer:
-7
Step-by-step explanation:
Since we have 2 points, we can use the slope formula
m = ( y2-y1) /(x2-x1)
= ( 8-1)/( -7 - -6)
= ( 8-1) / ( -7+6)
= 7/ -1
= -7
You can fill a 12 gallon tank of gas for $33.39 or buy gas for $2.40 a gallon. Which is the better deal
Answer:
The gas can for $2.40
Step-by-step explanation:
Because if you buy twelve gallons it will only be 28.80 instead of buying the 12 gallon tank for $33.39
Name the values of the 5s in 5,500
Answer:
5 thousand and 5 hundred.
Step-by-step explanation:
Answer:
uno dos tres
Step-by-step explanation:
I dont know man help please
Answer:
m∠1 = 63°
m∠2 = 49°
m∠3 = 87°
m∠4 = 44°
Step-by-step explanation:
From the given figure
∵ ∠2 and 49° are vertically opposite angles
∵ The vertical opposite angles are equal in measures
∴ m∠2 = 49°
∵ The sum of the interior angles of a Δ is 180°
∵ m∠1, m∠2, and 68° are interior angles of a Δ
∴ m∠1 + m∠2 + 68° = 180°
∵ m∠2 = 49°
∴ m∠1 + 49° + 68° = 180°
→ Add the like terms in the left side
∴ m∠1 + 117 = 180
→ Subtract 180 from both sides
∴ m∠1 = 63°
∵ ∠3 and 93° formed a pair of linear angles
∵ The sum of the measures of the linear angles is 180°
∴ m∠3 + 93° = 180°
→ Subtract 93 from both sides
∴ m∠3 = 87°
∵ 93° is an exterior angle of the triangle
∵ The measure of the exterior angle of a Δ at one vertex equals the sum
of the measures of the opposite interior angles to this vertex
∵ ∠4 and 49° are the opposite interior angles to 93°
∴ 49° + m∠4 = 93°
→ Subtract 49 from both sides
∴ m∠4 = 44°
In the figure shown, lines 1 and 2 are parallel. The sum of the measures of angles 4 and 5 is 150°. What is the measure of angle 1? a. 75° b. 105° c. 115° d. corresponding angles
Answer:
C. 105°
Step-by-step explanation:
The measure of <1 is 105.
What is parallel line?Two lines in a plane are said to be parallel if they do not intersect when extended infinitely in both directions. Two straight lines are said to be parallel if their slopes are equal and they have different y-intercepts. Given below are a few important properties of parallel lines that actually reflect the characteristics of parallel lines.
For the parallel lines cut by a transversal, the following properties hold true:
Two lines cut by a transversal line are parallel if the corresponding angles so formed are equal. In general, the corresponding angles are in relative positions and lie along the same side of the transversal.Two lines cut by a transversal line are parallel if the alternate interior angles so formed are equal. In general, the pairs of the alternate interior are found in the inner side but lie on the opposite sides of the transversal.Two lines cut by a transversal line are parallel if the alternate exterior angles so formed are equal. In general, the pairs of alternate exterior angles are found on the outer side but lie opposite each other.Given:
<4 + <5 = 150 (given)
As, from the figure
<4 = <5 (alternate exterior angle)
Then,
<4 + <4 = 150
2<4 = 150
<4 = 75
and <5 = <4 = 75
Now, <1 + <5 = 180 (linear pair)
<1 + 75 = 180
< = 180 -75
<1 = 105
Hence, the measure of <1 is 105
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>I'm sorry but how do I do this?
Solving the equation of the form a cos 0 + b sin 0 = c
Question;
Solve the equation 4 sin 20 - 3 cos 20 = 3, for 0° ses 360°
Answer:
θ = 36.9°, 90°, 216.9°, or 270°
Step-by-step explanation:
4 sin 2θ − 3 cos 2θ = 3
Use double angle formulas:
4 (2 sin θ cos θ) − 3 (cos²θ − sin²θ) = 3
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3
Use Pythagorean identity:
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 (sin²θ + cos²θ)
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 sin²θ + 3 cos²θ
8 sin θ cos θ − 6 cos²θ = 0
2 cos θ (4 sin θ − 3 cos θ) = 0
2 cos θ = 0
θ = 90° or 270°
4 sin θ − 3 cos θ = 0
4 sin θ = 3 cos θ
tan θ = 3/4
θ = 36.9° or 216.9°
The arctic tern flies from the Arctic to the Antarctic and back every year, a total distance of 22,000 miles! In late summer, the terns start their migration south, and it takes about 3 months to go the 11,000 miles. What is the average velocity, in miles per day, that these birds travel?
Answer:
The birds travel at an average velocity of 122.2 miles per day
Step-by-step explanation:
The arctic terns fly a total distance of 22,000 miles in their yearly migration from the Arctic to the Antarctic and back again.
The average speed is the ratio between the total distance traveled by the time they took to travel.
Assume we take an average month of 30 days, then the time the arctic terns take to travel the 11,000 miles back is 30*3= 90 days.
The average velocity is
[tex]\displaystyle v=\frac{11,000}{90}=122.2[/tex]
v=122.2 miles/day
The birds travel at an average velocity of 122.2 miles per day
Answer:
The artic tern flies 11000 miles about 3 months at an average velocity of 122.222 miles per day.
Step-by-step explanation:
What Is the answer to this
2/3p+3=
p=3/5
Answer:
3 and. 2/5
Step-by-step explanation:
2/3 x 3/5 = 2/5
2/5 + 3 = 3.4 or 3 2/5
The most common type of harmony in the Baroque Period was:
a
Polyphony
b
Monophony
c
Homophony
*please None i will give you 12 points*
Question:
The most common type of harmony in the Baroque Period was
answer: Harmony came to be thought of as chords that laid the foundation for the melody. Major and minor as we know them today became established as keys instead of modes, and the harmonic patterns of tonality began to evolve. hmm
Polyphony is having multiple voices, harmony is how those multiple voices interact and relate to each other. Polyphony doesn't necessarily mean playing at the same time either, just the act of having multiple voices in a piece. Melodic independence and consonant treatment. so i think it is A.Polyphony
division of decimals by whole number
Answer:
Step-by-step explanation:
whats the equation?
Simplify.
y = (x + 1)^2 - ____
Answer:
2
Step-by-step explanation:
on edg 2020 lol
Answer:
the person above is correct
Step-by-step explanation:
i got it right on edge
How do I factor this?
Answer:
3y(4y - 1)²
General Formulas and Concepts:
Alg I
FactoringStep-by-step explanation:
Step 1: Define expression
48y³ - 24y² + 3y
Step 2: Simplify
Factor GCF: 3(16y³ - 6y² + 3y)Factor GCF: 3y(16y² - 6y + 3)Factor trinomial: 3y(4y - 1)(4y - 1)Rewrite: 3y(4y - 1)²Consider the expression 3(5+2•4)+(-3)
i've considered it, ty
Can you guys please with me out with the question please
Answer:
Team score in first game < 19
Step-by-step explanation:
Point Scored in Third Game =X
Points Scored in First Game = X+6 (6 more than third game)
Points Scored in Second Game = 23
Total Points ={( First Game) +( Second Game) + (Third Game)} < 55
{ ( X+6) + (23) + (X)} < 55
X+29+X < 55
2X+29 < 55
2X< 55-29
2X < 26
X <26/2
X<13
So the point scored in First game is: (X+6)
Where X < 13
So the point in First game is < 19
