Answer:
The smallest possible value of the sum of their squares is 128.
Step-by-step explanation:
Let the first number = x
let the the second number = y
x + y = 16
y = 16 -x
minimum value, f = x² + y²
f(x) = x² + (16-x)²
f(x) = x² + 256 - 32x + x²
f(x) = 2x² - 32x + 256
f(x)' = 4x - 32
4x - 32 = 0
4x = 32
x = 32 / 4
x = 8
The absolute minimum value of x = 8
y = 16 - x
y = 8
The smallest possible value of the sum of their squares is given by x² + y²;
= (8)² + (8)²
= 128
Therefore, the smallest possible value of the sum of their squares is 128.
Solve 3x + 8 = x + 16
Answer:
x = 4
Step-by-step explanation:
Move all "x"s to one side of the equation:
(3x + 8) - x = (x + 16) - x
2x + 8 = 16
Subtract 8 from both sides so that all the numbers are on one side of the equation:
(2x + 8) - 8 = (16) - 8
2x = 8
Divide both sides of the equation by 2:
x = 4
What is the unit rate of 36 flowers in 3 bouquets
Answer:
12 flowers per bouquet
Step-by-step explanation:
Answer:
12 / 1
Step-by-step explanation:
12 times 3 is 36 so 12 flowers in each bouquets.
A triangular playground has sides that are lengths 2x feet, x-1 feet and x feet. If the perimeter of this playground is 27 feet, what are the
lengths of each side of the playground?
Answer:
The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
Step-by-step explanation:
At first, let us find the perimeter of the playground
∵ Perimeter of a triangle is P = S1 + S2 + S3
∵ The sides of the triangular playground are (2x) ft, (x - 1) ft, and x ft
∴ S1 = 2x, S2 = x - 1, S3 = x
→ Substitute them in the rule of the perimeter above
∵ P = 2x + x - 1 + x
→ Add the like terms
∴ P = (2x + x + x) - 1
∴ P = 4x - 1
∵ The perimeter of this playground is 27 feet
∴ P = 27
→ Equate the two values of P
∴ 4x - 1 = 27
→ Add 1 to both sides
∴ 4x - 1 + 1 = 27 + 1
∴ 4x = 28
→ Divide both sides by 4
∵ [tex]\frac{4x}{4}[/tex] = [tex]\frac{28}{4}[/tex]
∴ x = 7
→ Substitute the value of x in each side to find their lengths
∵ S1 = 2(7)
∴ S1 = 14 feet
∵ S2 = 7 - 1
∴ S2 = 6 feet
∵ S3 = 7 feet
∴ The lengths of the sides of the playground are 14 feet, 6 feet, 7 feet
How many inches combined 1/2 1/3 1/6 1/2 1/8 1:4
Answer:
Imperial Units
155/8 Inches (fraction)
15.625 Inches
1.302083 Feet
Metric Units
396.875 Millimeters
39.6875 Centimeters
0.396875 Meters
Five hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 39 66 10 86 201
Disliked Crunchicles 27 19 38 95 179
No Preference 24 37 35 24 120
Total 90 122 83 205 500
One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.
What is the probability that the consumer is 18–24 years of age, given that they dislike Crunchicles?
Answer:
The probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.
Step-by-step explanation:
The age groups and preferences are given as follows:
18 - 24 25 - 34 35 - 55 55 and over Total
Liked Crunchicles 39 66 10 86 201
Disliked Crunchicles 27 19 38 95 179
No Preference 24 37 35 24 120
Total 90 122 83 205 500
One consumer from the survey is selected at random.
Compute the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles as follows:
[tex]P(18-24|DC)=\frac{P(18-24\cap DC)}{P(DC)}[/tex]
[tex]=\frac{n(18-24\cap DC)}{n(DC)}\\\\=\frac{27}{179}\\\\=0.15084\\\\\approx 0.151[/tex]
Thus, the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.
on (43 - 4) + 12 = 3
Answer:
No im afraid it equals Fish
Step-by-step explanation:
If you subtract 43-4 equals 39 which how many nemo fish r in the ocean
and if u add 12 to it it equals 51 which how many fish r in the ocean
so the answer is Fish
The general form of an parabola is 3x2+24x−2y+52=0.
What is the standard form of the parabola?
Answer:
y = 3/2x∧2+12x+26
Step-by-step explanation:
ill gives brainiest The average height of an ostrich is 255 cm.
Suppose that you want to make a scale
drawing of an ostrich. The scale is 30 :1.
What height will you make the ostrich in
your drawing? Explain your thinking.
Step-by-step explanation:
8.5
_____
30) 255.0
240
0150
150
000
Write the equation in point-slope form that goes through the point (10,5) and has
slope of - 3
Pls help with this problem
Answer:
A.
Step-by-step explanation:
set a proportion
75 x
--- = ----
1.5 2.25
2.25 times 75
168.75
divide it by 1.5
337.5
337 one half
(Giving brainliest on this one to who ever helps!!)
The steps in an investigation between two negatively charged objects are listed below.
Step 1: Rub a cloth on two uncharged balloons to make them negatively charged.
Step 2: Bring the two negatively charged balloons together.
Step 3: Observe the repulsion between the two objects.
Which statement is true?
A) An object changes its charge when placed near another charged object.
B) Bringing two positively charged objects close together would result in attraction.
C) The two balloons do not have to touch for repulsion to be observed.
D) Two negatively charged objects will attract each other when they touch.
Answer:
C) The two balloons do not have to touch for repulsion to be observed.
Step-by-step explanation:
$7.80(1 + 0.055)=
Your answer
Answer:
$8.229
Step-by-step explanation:
do whats in the paranthese first: 1 + 0.055 = 1.055
when a number is next to another number you multiply: 7.80(1.055) which is 7.80 x 1.055 = 8.229
Please help me! The question is in the screenshot below.
82pts
_
Express 0.41(repetitive decimal) as a fraction in its simplest form
Answer:
Step-by-step explanation:
ty for points
need some help please
Answer:
Ariel ate the most .
Step-by-step explanation:
hope this helps you.
Answer:
dan
Step-by-step explanation:
find the common denomanator= 28
dan 6/7 to the common denomanator is 24/28
ariel 3/4 is 21/28
Find the slope
How can I find the slope
Answer:
You should use the y2 - y1 /x2 - x1
To find the answer you should be able to plug in the x and the y in the equation with the coordinates that you have but I'm not sure if you don't have what you'll do
If you are god of math you can try this
Answer:
BRO, u dont need to be a god :D, This is simple math and you just need to use your brains
Step-by-step explanation:
Given is a polynomial, and the values of the variables in it are given by showing what set are they an element of, right? It just gets easier from here
They tell us that 'z' is an element of set C, which stands for Complex Numbers.
And they also tell us that 'a' is an element of set Z, which stands for Integers, which are just numbers with a sign :).
They have also given us a root (solution) to the polynomial, which is also a complex number.
The two statements given are just there for us to verify that we are on the right track to the solution.
We can see that (z = 3 + i) which of course is a complex number, due to the presence of 'i', and 'a' is an integer for when we find its value.
Put it all together and we will get the answer.
Like this,
take the given value of 'z' and place it into the polynomial given, now keep your eyes open here. They said the value of z is as such when the polynomial is an equation which equals 0, so hence we get this:
P(z) = a(3+i)³ - 37(3+i)² + 66(3+i) - 10 = 0,
now just go on simplifying,
=> a(3³+i³+3×3²i+3×3i²) - 37(3²+2×3×i+i²) + 66×3 + 66×i - 10 = 0
=> a(27-i+27i-9i) - 37(9+6i-1) + 198 + 66i - 10 = 0
=> a(27+17i) - 37(8+6i) + 188 + 66i = 0
=> a(27+17i) = 296 + 222i - 188 - 66i
=> a(27+17i) = 108 + 156i
=> a = (108+156i) / (27+17i)
=> a = (108+156i)(27-17i) / (27)² - (17i)²
=> a = (5568 + 2376i) / (699 + 289)
=> a = 5568 + 2376i / 1488
DONNEEE....yayyyy....lol
12.6 + 4m = 9.6 + 8m
Answer:
3 = 4m or 0.75 = m
Step-by-step explanation:
12.6 + 4m = 9.6 + 8m
Subtract 4m from both sides of the equation
12.6 = 9.6 + 4m
Subtract 9.6 from both sides of the equation
3 = 4m
Divide by four on both sides of the equation
0.75 = m
I Hope That This Helps! :)
Just answering so the other guy can have brainiest! Hope this helps!
Use long division to change 11/30 to a decimal
Answer: 0.3666667
Step-by-step explanation:
Pls help I don’t understand what the problem is asking
What is the measure of line segment BE in the diagram below?
Answer:
15
Step-by-step explanation:
∆ABC ~ ∆AED, therefore,
[tex] \frac{AB}{AE} = \frac{BC}{ED} [/tex]
Let BE = x
AB = x + 9
AE = 9
BC = 16
ED = 6
Plug in the values into the equation
[tex] \frac{x + 9}{9} = \frac{16}{6} [/tex]
[tex] \frac{x + 9}{9} = \frac{8}{3} [/tex]
Cross multiply
[tex] (x + 9)(3) = (8)(9) [/tex]
[tex] 3x + 27 = 72 [/tex]
Subtract 27 from each side
[tex] 3x = 72 - 27 [/tex]
[tex] 3x = 45 [/tex]
Divide both sides by 3
[tex] x = \frac{45}{3} [/tex]
[tex] x = 15 [/tex]
Segment BE = x = 15
Use the value of x to find the measure of angle 1 x=25
Jessica counted 26 heartbeats in 20 seconds. How many times will her heart beat in 1 minute? WILL GIVE BRAINLIEST!!!!!!!
Answer:
78
Step-by-step explanation:
multiply 26 by 3 because 60÷20=3
Answer: 78
Step-by-step explanation: 20x3=60 and there is 60 secs in a minute
and 26x3=78
So the answer is 78 heartbeats in a min
Where does warm water accumulate in the Pacific Ocean during El Niño?
the east
the south
the north
the west
answer:
a. east coast! :)
hope this helps.
Answer:
I put A and got it right on edge Step-by-step explanation:
A ball rolling down the hill is an example of what type of energy
Answer:
When a ball rolls downhill, the gravitational potential energy of the ball is transformed into motion energy. A ball is rolling up and over a hill. The ball slows down as it moves from Position 1 to Position 3, and it speeds up as it moves from Position 3 to Position 5.
Step-by-step explanation:
Happiness is it qualitative or quantitative?
Please answer
Answer:
i think its quantiative becuase theirs only 2 options but i could be wrong btw srry for bad spelling
Step-by-step explanation:
A rope 160m in length is cut into 5 equal lengths. How long is each length of rope?
Answer:32m
Step-by-step explanation:
So you would have to divide 160 and 5 and it would equal 32
What is the y-intercept in the equation 2y = x -8
Answer:
(0,-4)
Step-by-step explanation:
whats the place value of number 4 in the number 1 345.87?
Answer:
Tens
Step-by-step explanation:
Decimal Place Values:
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
. decimal point
tenths
hundreths
thousandths
ten thousandths
Find the value of angle G, C and F
Answer:
G is 37
C is 143
F is 37
Step-by-step explanation:
G is 37 because of a rule called complementary angles. They are two angles that equal to 90 degrees! As shown in the angle right next to it, there is a small square that represents 90 degrees, so that means 53 + g would = 90 degrees as well, making g 37.
C is 143 because of a rule called supplementary angles. Supplementary angles are angles on a line that equal to 180 degrees. No matter how many angles are on a straight line, they will all equal to 180. So since I found out g is 37, I just used one of the lines and did 180-37 = 143.
F is 37, and you could find it in two ways. You can use supplementary angles with the angle of c you just found, or you can just use a rule called vertical angles. It is a rule that says any opposite angles from each other are equal. The opposite angle of F would be G. Since G is 37, F would be 37 as well. Definitely look up these terms if I am confusing them for you!! I hope I helped!!