The sum of two positive numbers is 42. What is the smalles possible value of the sum of their squares?
Answers
Set these numbers a and b, notice a, b positive.
We have a+b=42.
You can see the next on my photo
Or you can use the formula of Cauchy
Related Questions
Hi! Please help me with this question! 12 points and brainliest to whoever answers it correctly first!
1. Given: -3x + y = 1. Write the equation in general form Ax + By + C =0.
3x - y + 1 = 0
-3x + y - 1 = 0 (not this one)
3x - y = -1
Answers
A bag contains equal numbers of green and blue marbles. You can divide all the green marbles into groups of 12 and all the blue marbles into groups of 16. What is the least number of each color of marble that can be in that bags?
Answers
To solve this problem, we need to find for the LCM of each number. That is:
12: 12, 24, 36, 48, 60
16: 16, 32, 48, 64, 80
So we can see that the LCM is 48.
Therefore the least number of each color of marble must be 48.
Answer:48
Step-by-step explanation:love ya thank me later
Two cars leave the origin; one goes north at 45 mph and the other goes south at 40 mph. after how many hours will they be 350 miles apart?
Answers
so, say car N goes north at 45mph, and car S goes south at 40mph.
after "some time" they'd be apart 350 miles, when that happens, N has been travelling for say "t" hours, and S has been travelling for the same "t" hours, their time has to be the same.
now, we know they'd be 350 miles apart, so if say N has gone "d" miles, then S has gone the slack, or "350 - d".
and we know their rates.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Car N}&d&45&t\\ \textit{Car S}&350-d&40&t \end{array} \\\\\\ \begin{cases} \boxed{d}=45t\\ 350-d=40t\\ --------\\ 350-\boxed{45t}=40t \end{cases} \\\\\\ 350=85t\implies \cfrac{350}{85}=t\implies \cfrac{70}{17}=t\implies 4\frac{2}{17}=t[/tex]
which is about 4 hours and 7 minutes with 3.5 seconds.
To find the time when two cars traveling in opposite directions are 350 miles apart, we calculate their relative speed, which is 85 mph. We then divide the distance (350 miles) by this speed to get approximately 4 hours and 7 minutes.
Explanation:The question is asking to find out after how many hours two cars traveling in opposite directions will be 350 miles apart, with one car going north at 45 mph and the other south at 40 mph. To solve this, we need to apply the concept of relative speed.
The relative speed is the sum of the individual speeds when two objects are moving in opposite directions. In this case, it's 45 mph + 40 mph = 85 mph. This is the speed at which the distance between the two cars is increasing.
Next, to find the time 't' when they will be 350 miles apart, we use the formula:
Distance = Speed × Time
350 miles = 85 mph × t
To solve for 't', we divide both sides by 85 mph:
t = 350 miles / 85 mph = 4.1176 hours, or approximately 4 hours and 7 minutes.
twice the sum of a number and 5 equals 9 as a equation
Answers
I believe it looks like this..
2*x+5=9
Btw, x = 3 is your answer if you're wondering..
Hope this helps! ☺♥
Which ordered triple is a solution of this system?
2x + y - z = 7
-x - 2y + 4z = -15
x + 2y - 5z = 17
a) (3, 1, 0)
b) (1, 3, -2)
c) (2, 5, 2)
d) (-2, 6, -5)
Answers
Answer:
b) (1, 3, -2)
Step-by-step explanation:
A suitable calculator can give you the answer to this right away. Or, you can try the answer choices in the equations to see which works.
The answer choice that works is choice B.
2·1 +3 -(-2) = 7
-1 -2(3) +4(-2) = -15
1 +2(3) -5(-2) = 17
135in.=___ft ___ in.
convert
Answers
1 foot = 12 inches
135 / 12 = 11.25 feet 0.25 feet = 0.25 * 12 = 3 inches
answer is: 11 feet 3 inches
c) Solve the equation you wrote in part b to find how many hours you would have to work to pay for the first year of video streaming service. Show your work and round your answer to the nearest tenth.
Answers
Every Month $68 $18 $18 $18 $18 $18 $18 $18 $18 $18 $18 $18
Total For Year$68 $86 $104 $122 $140 $158 $176 $194 $212 $230 $248 $266
An investment is currently worth 2.125 × 10^4 dollars . Ten years ago, the investment was worth 1.25 × 10^3 dollars. How many times greater is the value of the investment today than the value of the investment ten years ago?
Answers
The investment today is 17 times greater than it was ten years ago.
To find out how many times greater the value of the investment is today compared to ten years ago, you can divide the current value by the value ten years ago.
So, let's do the calculation:
Current value = 2.125 × 10^4 dollars
Value ten years ago = 1.25 × 10^3 dollars
[tex]\( \text{Times Greater} = \frac{\text{Current Value}}{\text{Value Ten Years Ago}} \)[/tex]
Substitute the values:
[tex]\( \text{Times Greater} = \frac{2.125 \times 10^4}{1.25 \times 10^3} \)[/tex]
To divide these numbers, subtract the exponents:
[tex]\( 10^4 \div 10^3 = 10^{4-3} = 10^1 = 10 \)[/tex]
So,
[tex]\( \text{Times Greater} = \frac{2.125}{1.25} \times 10 = 1.7 \times 10 = 17 \)[/tex]
Therefore, the value of the investment today is 17 times greater than the value of the investment ten years ago.
Graph y+6=4/5(x+3) using the point and slope given in the equation. Use the line tool and select two points on the line.
Answers
Answer:
Look at pic...
The points were (-3,-6) and (2,-2)
Step-by-step explanation:
You could just use desmos graphing calculator
The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The two points on the line are (0, -3) and (1, -11/5).
What is equation of a line?The equation of a line is a form of representing the set of points, which form a line in a coordinate system.
The general equation of a straight line is given as:
y = mx + c,
where m = slope of the line and c = y-intercept.
We have,
y + 6 = 4/5 ( x + 3 )
Subtract 6 on both sides.
y = 4/5 ( x + 3 ) - 6
y = (4/5)x + 4/5 x 3 - 6
y = (4/5)x + 12/5 - 6
y = (4/5)x + (12 - 30)/6
y = (4/5)x - 3
The y-intercept is at -3.
We have a point as (0, -3).
For x = 1,
y = (4/5) x 1 - 3
y = 4/5 - 3
y = (4 - 15) / 5 = -11/5
The other point is (1, -11/5)
Thus,
The two points on the line are (0, -3) and (1, -11/5).
Learn more about equation of a line here:
https://brainly.com/question/14200719
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Mary invests £12000 in a savings account. The account pays 1.5% compound interest per year. Work out the value of her investment after 2 years
Answers
Find the length of the hypotenuse if the legs of a triangle are 5cm and 12 cm.
Question 5 options:
7cm
13cm
17cm
169cm
Answers
13 cm is length of the hypotenuse
________________________________
c² = a² + b² ;
In which "c" is the hypotenuse;
a = 5 ;
b = 12 ;
c = ? ;
Solve for "c"
+√(c²) =√(a² + b²) ;
c = √(5² + 12²) ;
c = √(25 + 144) ;
c = √169 ;
c = 13 cm .
_______________________________________________________
The correct answer is: [B]: " 13 cm" .
_______________________________________________________
Owen jarred 10 liters of jam after 2 days. How many days did Owen spend making jam if he jarred 15 liters of jam?
Answers
So 10 +5=16
So, he spent three days making jam to get 15 liters.
Hope this helps and please mark brainiest.
Ethan invested £500 in the bank for 2 years. he earned £40 simple interest in total. what was the simple interest rate per annum
Answers
I=prt
I interest earned 40
P principle 500
R interest rate?
T time 2 years
Solve the formula for r by dividing both sides by pt to get
R=I/pt
R=40÷(500×2)
R=0.04×100
R=4%
Hope it helps!
Answer:
4%.
Step-by-step explanation:
We have been given that Ethan invested £500 in the bank for 2 years. He earned £40 simple interest in total. We are asked to find the annual interest rate.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon substituting our given values in above formula, we will get:
[tex]40=500*r*2[/tex]
[tex]40=1000*r[/tex]
Now, we will divide both sides of our given equation by 100.
[tex]\frac{40}{1000}=\frac{1000*r}{1000}[/tex]
[tex]\frac{4}{100}=r[/tex]
[tex]\frac{1}{25}=r[/tex]
[tex]0.04=r[/tex]
Since our given interest rate is in decimal form, so we need to convert it in percentage.
[tex]0.04\times 100\%=4\%[/tex]
Therefore, the simple interest rate per annum is 4%.
Jasmine bought computer which was discounted from 350 to 273. What is the discount rate
Answers
subtract the 2 numbers to find amount of discount
350 - 273 = 77
now divide 77 by 350 = 0.22
0.22 = 22% discount
Answer:
22%
Step-by-step explanation:
The discount rate given on the cost of an item is the ratio of the discount to the old price expressed as a percentage.
The discount is the difference between the old and new price while the new price is known as the discounted price.
the discount = $350 - $273
= $77
The discount rate
= $77/$350
= 0.22
= 22%
Heather and her family are going to the grand opening of a new amusement park. There is a special price on tickets this weekend. Tickets cost $42 each. This is 70% of the cost of a regular price ticket. What is the cost of a regular price ticket? Please explain! thanks!
Answers
What is the remainder when the polynomial 8x^2+4x−3 is divided by 2x−1?
Answers
Answer:
1
Step-by-step explanation:
Given: A polynomial [tex]8x^{2} +4x-3[/tex] is divided by another polynomial [tex]2x-1[/tex]
To find: Remainder when [tex]8x^{2} +4x-3[/tex] is divided by [tex]2x-1[/tex]
Solution:
To find the remainder when [tex]8x^{2} +4x-3[/tex] is divided by [tex]2x-1[/tex]
First, equate [tex]2x-1[/tex] with 0.
Now, [tex]2x-1=0[/tex]
[tex]\implies2x=1[/tex]
[tex]\implies x=\frac{1}{2}[/tex]
Now, to find the remainder put [tex]x=\frac{1}{2}[/tex] in [tex]8x^{2} +4x-3[/tex]
So, we have
[tex]8\times(\frac{1}{2})^{2}+4(\frac{1}{2} )-3[/tex]
[tex]=8\times\frac{1}{4} +2-3[/tex]
[tex]=2+2-3[/tex]
[tex]=4-3[/tex]
[tex]=1[/tex]
Hence, the remainder is 1.
△VAT≅△BDT.
¯¯¯¯¯
What is length of BT ?
Answers
Answer:
[tex]BT=6.3[/tex]
Step-by-step explanation:
We have been given that triangle VAT is congruent to triangle BDT. We are asked to find the length of segment BT.
Since both triangles are congruent, therefore, their corresponding sides will be equal by the definition of congruence.
[tex]\Delta VAT\cong \Delta BDT[/tex]
By the definition of congruence:
[tex]VA=BD[/tex]
[tex]AT=DT[/tex]
[tex]VT=BT[/tex]
Since the length of side VT is 6.3 units, therefore the length of BT is 6.3 units as well.
What are the x-intercepts of the graph of the function below? y=x^2+4x-32
Answers
Let me know if you want to know why
Answer:
Option B is correct.
Step-by-step explanation:
Given Function is,
y = x² + 4x - 32
X-intercepts of the graph of given function is the solution of the equation when y is equal to 0 is substituted.
y = 0
x² + 4x - 32 = 0
x² + 8x - 4x - 32 = 0
x ( x + 8 ) - 4 ( x + 8 ) = 0
( x + 8 ) ( x - 4 ) = 0
x + 8 = 0 and x - 4 = 0
x = -8 and x = 4
So x-intercept are ( -8 , 0 ) and ( 4 , 0 )
Therefore, Option B is correct.
The perimeter of this shape is 82 cm. what is the length of side d? cm
Answers
Which phrase best describes a rock? A. a chemical arranged in a lattice B. a gabbro of minerals C. a mixture of crystals D. a fire-formed crystal
Answers
Your answer is B. a gabbro of minerals
Hope this helps :)
-Take Care Now-
~Ans~
The sum of three consecutive integers is 16 more than 2 times the smallest integer. find the integers
Answers
sum of three consecutive integers is 1 more than 2 times the smallest integer
(x) + (x + 1) + (x + 2) - 16 = 2x
3x + 3 - 16 = 2x
3x -13 = 2x
-13 = -x
13 = x
The smallest integer is 13, the second integer is 14, the third integer is 15
"The sum of three consecutive integers..." From this, we know we'll be adding all three of our integers together, so let's collect those:
[tex]a+(a+1)+(a+2)=3a+3[/tex]
"...is 16 more than 2 times the smallest integer." Translating that into math: "is" is shorthand for "equals," "16 more than" means we'll be adding 16 to some value, and "2 times" obviously implies multiplication plus two. Finally, the smallest integer we have is [tex]a[/tex], so let's compose these facts into a full expression and combine them with our sum above to form a complete equation:
[tex]3a+3=2a+16[/tex]
From here, all that's left is to solve for [tex]a[/tex]. Once you have that value, [tex]a[/tex], [tex]a+1[/tex], and [tex]a+2[/tex] will be your integers.
96 points here, having to ask same question again - please help a brother out.
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. Show your work.
1. cot x sec^4 x = cot x + 2 tan x + tan^3 x
2. (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x
3. 1 + sec^2 x sin^2 x = sec^2 x
4. ((sin x)/(1-cos x)) + ((sin x)/(1+cos x))=2csc x
5. - tan^2 x + sec^2x = 1
Answers
the equation is - tan2 x + sec2 x = 1.
Left hand side identity : - tan2 x + sec2 x.
Trigonometric function : tan x = sin x / cos x,
Reciprocal identity : sec x = 1/cos x.
- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2
= - sin2 x/cos2 x + 1/cos2 x
= (1 - sin2 x)/cos2 x
Pythagorean identity : sin2 x + cos2 x = 1 .
= cos2 x / cos2 x
= 1
PLZ Help I really need to know how to do this
SKIING The distance in meters that a person
travels on skis can be modeled by d(t) = 0.2t^2 + 3t,
where t is the time in seconds. Use the Remainder
Theorem to find the distance traveled after 45
seconds.
Answers
A baseball player got 102 hits in the last 300 times at bat.
What percent of the times at-bat did the player get a hit?
The player got a hit ? % of the time.
Answers
answer is 34%
The answer to your awesome question is 34%. this is because you have to divide in order to find the answer. 102 divided by 300 = 0.34, therefore your answer would be 34%!
Have a great day!
in diagram below, fg=10 and HJ=10. Which additional facts would guarantee that fghj is a parallelogram? Check all that apply.
Answers
* Sides fj and sides gh should be equal
* The blue angles should not be equal to the red angles
* The blue angles should be equal
* The red angles should be equal
The graph illustrates a reflection of . What is the line of reflection?
A.
x-axis
B.
y-axis
C.
y=x
D.
y=2x
Answers
Answer:
A. x-axis
Step-by-step explanation:
It is a mirror image. The doesn't change.
The figure J'K'M' is just reflected over the x-axis.
So it is reflection about the x-axis.
Therefore, answer is A. x-axis
Hope this will helpful.
Thank you.
x= r-h/y
solve for h and r
Answers
Let's first solve for h :)
Add h/y to both sides.
h/y + x = r
So, r = h/y + x
Now, let's solve for h.
x = r-h/y
Subtract r from both sides.
-r + x = -h/y
Multiply both sides by y.
y(-r + x) = y(-h/y)
Simplify.
-ry + xy = -h
Divide both sides by -1.
ry - xy = h
So, h = ry - xy
~Hope I helped!~
To solve for h, rearrange the equation to h = r - xy, and to solve for r, rearrange it to r = xy + h. This process involves basic algebraic manipulation to isolate each variable on one side of the equation.
Explanation:The original equation given is x = r - h/y. To solve for h, we need to get h by itself on one side of the equation. First, we can rearrange the equation to isolate h:
Multiply both sides by y to get rid of the fraction: xy = r - h.Move all terms containing h to one side and the rest to the opposite side: h = r - xy.To solve for r, we take the original equation and solve for r explicitly:
First, isolate the term containing r: r = xy + h.Now we have both variables solved in terms of x, y, and each other.
Expand and simplify 2(2x-3)+2(3x+4)
Answers
= 4x - 6 + 6x + 8
= 10x + 2
answer
10x + 2
What is the reason for Statement 2 of the two-column proof?
a) Linear Pair Postulate
b) Definition of angle
c) Definition of bisect
d) Angle Addition Postulate
Answers
We have been given that PQ bisects [tex]\angle RPS[/tex]. In the second statement of the given two-column proof, the statement is [tex]\angle RPQ\cong\angle QPS[/tex].
This implies that the two angles formed by bisection of angle [tex]\angle RPS[/tex] by the line PQ are equal. We know that the reason for this is simple. It is the definition of bisection of an angle that the two smaller angles formed will be equal to each other.
Therefore, the reason for statement 2 of the given two column proof is c) Definition of bisect
Shelly can cut a lawn with a riding mower in 22 hours less time than it takes william to cut the lawn with a push mower. if they can cut the lawn in 33 hours working together find how long to the nearest tenth of an hour it takes for william to cut the lawn alone.
Answers
n-2 hours. So:
1/n+1/n-2=1/3
3(n-2)+3n=n²-2n
6n-6=n²-2n
n²-8n+6=0
Using the quadratic formula, we get a positive value of 7.1623 hrs as the amount of time william takes working alone, and 5.1623 as the amount of time Shelly takes working alone
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