Answer:
The answer is: " [tex]5a^\frac{1}{2}[/tex] " .
_____________________________________________
Step-by-step explanation:
______________________________________________
We are asked to convert "5 square root of a" ; into "exponential form".
Note that "5 square root of a" ;
or; " 5 root a " ;
means: " 5 times the {square root of the variable, "a" };
or : " 5 multiplied by the {square root of the variable, "a" }.
_______________________________________________
This can be written as: " [tex]5\sqrt{a}[/tex] " .
_______________________________________________
Note the following property of exponents:
[tex]\sqrt[n]{a^m} = (\sqrt[n]{a})^m = a^m^n[/tex] .
_____________________________________________
So; to write: " √a " ; as an exponent :
______________________________________________
Note:
" [tex]\sqrt{a} = \sqrt[2]{a} = \sqrt[2]{a^1} = (\sqrt[2]{a})^1 = a^\frac{1}{2}[/tex] " .
_______________________________________________
So:
" [tex]\sqrt{a} = a^\frac{1}{2}[/tex] " ;
_______________________________________________
And:
________________________________________________
" [tex]5\sqrt{a} = 5a^\frac{1}{2}[/tex] " .
________________________________________________
→ The answer is: " [tex]5a^\frac{1}{2}[/tex] " .
________________________________________________
Hope this helps!
Best wishes in your academic endeavors
— and within the "Brainly" community!
________________________________________________
What Is 7 Rounded To The Nearest Tenth?
Answer:
7.0
Step-by-step explanation:
If we had the number 7.1 the 1 is the tenth digit. .
So 7 to the nearest tenth is written 7.0.
Answer:
7.5 is exactly halfway between 7 and 8. Therefore, 7.5 rounds to 8.
Step-by-step explanation:
To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding.
7.1 7.2 homework help
Answers are attached in the pictures. Solutions are in RED.
Answer:
12. 7.5
13. 0.224
14. 193.5
15. 2/3
16. 5/7
17. -10
18. 2:1
19. 16
20. 150
21. 46,200
22. 4
23. 18
24. 5.29
25. 7.07
26. 19.80
27. 15.87
28. 9.80
29. 6.71
30. 1.26
Step-by-step explanation:
12. 5/8 = x/12
8x = 60
x = 7.5
13. x/1.11 = 1/5
5x = 1.12
x = 0.224
14. 6x /27 = 43
6x = 1161
x = 193.5
15. x+2)/3 = 8/9
9x + 18 = 24
9x = 6
x = 2/3
16. (3x -5)/4 = -5/7
21x - 35 = -20
21x = 15
x = 5/7
17. (x-2)/4 = (x+4)/2
2x - 4 = 4x + 16
-2x = 20
x = -10
18. 9 grams of fat.
6 grams are saturated.
9-6 = 3 grams are cheese.
ratio of saturated to cheese = 6:3
= 2:1
19. goats to sheep = 4:7
7/11 x = 28
x = 28 × 11/7
x = 44
goats = 44-28 = 16
20. 280:4 = 10,500:x
280/4 = 10,500/x
280x = 42000
x = 150
21. 42:2 = x:2200
42/2 = x/2200
92,400 = 2x
x = 46,200
22. √(2×8) = √16 = 4
23. √(9×36) = √324 = 18
24. √(4×7) = √28 = 5.29
25. √(5×10) = √50 = 7.07
26. √(28×14) = √392 = 19.80
27. √(7×36) = √252 = 15.87
28. √(8×12) = √96 = 9.80
29. √(3×15) = √45 = 6.71
30. √4/5 × 2) = √8/5 = 1.26
Help me out, please!!!! Need an answer asap!!!
Answer:
D
Step-by-step explanation:
Answer:
D) 67
Step-by-step explanation:
j = 4N + 11
N = 14 Insert the value of N
j = 4×14 + 11
j = 56 + 11
j = 67
Jupiter has 67 moons.
Solve this equation: –9h – 6 + 12h + 40 = 22.
Answer: h = -4
Step-by-step explanation:
-9h-6+12h+40=22
-9h+12h=22+6-40 "collect all unknown values in a side and collect numbers in other side "
"Don't forget to Change signs"
3h= -12
3h/3 = -12/3 "dividing by 3 in both sides"
h= -4
[tex]-9h-6+12h+40=22\qquad\text{combine like terms}\\\\(-9h+12h)+(-6+40)=22\\\\3h+34=22\qquad\text{subtract 34 from both sides}\\\\3h=-12\qquad\text{divide both sides by 3}\\\\\boxed{h=-4}[/tex]
PLS ANSWER WILL GIVE BRAINLIEST 2 QUESTIONS
Daniel worked for 213 hours and earned $18.20.
How much would he make if he worked for 514 hours?
The total amount, a, in dollars, that Mitra earns is a = 14.6h, where h is the number of hours that she works.
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:
He would make $4391.92
The constant of proportionality is 14.6
Step-by-step explanation:
If Daniel works 213 hours and makes $1820.00
(I assume that is a typo and he made 1820. not 18.20)
How much does he make per hour
$1820/213 = $8.54 per hour
Now if he works 514 hours
514 * 8.54/hour = $4391.92
y = kx, where k is the constant of proportionality
a = 14.6h,
The constant of proportionality is 14.6
Juan has put together 325 pieces of a puzzle that has 500 pieces. He can put together 25 pieces every hour. How long will it take him to finish the puzzle?
Answer:The answer is 7 hours here is how I solved it. If it's out of 500 pieces and you've already done 325 then lets minus that so we only have to deal with the left over pieces. So 500- 325 which will give you 175 from there let's divide it by 25 to see how many hours it will take. Once you divide you will get 7 you can double check by doing 7 times 25 then add that to 325 to get 500 pieces.
Step-by-step explanation:
ms. James has a 6 square foot bulletin board and a 12 square food bulletin board. She wants to cover both boards with index cards without gaps or overlaps. Each index card has an area of 1/4 square foot. How many index cards does she need?
Answer:
She need 72 index cards.
Step-by-step explanation:
Ms. James has a 6 square foot bulletin board and a 12 square food bulletin board and she wants to cover both boards with index cards without gaps or overlaps.
Each index card has an area of [tex]\dfrac{1}{4}[/tex] square foot.
Dividing the area of each board with the area of the index card will yield the the number of cards she needs to cover up completely.
Let us assume T₁ and T₂ are the number of cards she needs to cover 6 square feet food bulletin board and 12 square feet food bulletin board respectively. So
[tex]T_1=\dfrac{6}{\frac{1}{4}}=24,\\\\T_2=\dfrac{12}{\frac{1}{4}}=48[/tex]
Therefore, in total she need 24+48=72 index cards.
PLEASE HELP ILL GIVE 49 POINTS! THANKS!
Show work
Answer:
y = -2x+11
Step-by-step explanation:
If we have a slope and a line, we can use the slope intercept form of a line
y-y1 = m(x-x1)
where (x1,y1) is the point and m is the slope.
Substitute in what we know
y-5 = -2 (x-3)
We want it in slope intercept form which is y = mx+b
Distribute the -2
y-5 = -2x+6
Add 5 to each side
y-5+5 = -2x +11
ANSWER:
y = -2x + 8
ABOUT POINT SLOPE FORM:
y - Y1 = m (x - X1)Y1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineABOUT SLOPE INTERCEPT FORM:
y = mx + bm represents the slopeb represents the y - intercept AKA the starting pointy - Y1 = m (x - X1)
y - 5 = -2 (x - 3)
y - 5 = -2x + 3
+ 5 + 5
y = -2x + 8 --- IN SLOPE INTERCEPT FORM
Hope this helps you!!! :)
In the triangle below which of the following is equivalent to the tangent of 52 degrees?
Answer:
Option D. [tex]\frac{24}{7}[/tex].
Step-by-step explanation:
In any right angle triangle tangent of an angle is the ratio of opposite side and adjacent side.
tan x =[tex]\frac{\text{Opposite side (24)}}{\text{Adjacent side (7)}}[/tex]
= [tex]\frac{24}{7}[/tex]
therefore, Option D. [tex]\frac{24}{7}[/tex] is the answer.
From 6x2−7xy+8y2 subtract the sum of x2−3xy−y2 and 2x2+5xy−4y2
Every 2 is meant to be the power of 2
Answer:
13 y^2 - 9 x y + 3 x^2
Step-by-step explanation:
Simplify the following:
6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)
-(x^2 - 3 x y - y^2) = -x^2 + 3 x y + y^2:
6 x^2 - 7 x y + 8 y^2 + -x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)
-(2 x^2 + 5 x y - 4 y^2) = -2 x^2 - 5 x y + 4 y^2:
6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + -2 x^2 - 5 x y + 4 y^2
Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):
(8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)
8 y^2 + y^2 + 4 y^2 = 13 y^2:
13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)
x y (-7) + x y 3 + x y (-5) = -9 x y:
13 y^2 + -9 x y + (6 x^2 - x^2 - 2 x^2)
6 x^2 - x^2 - 2 x^2 = 3 x^2:
Answer: 13 y^2 - 9 x y + 3 x^2
which is the solution for the equation y=5x+3
How many solutions does this system have?
x + 4y = 6
y = 2x - 3
a. one
b. two
c. an infinite number
d. no solution
There is only one solution to this system of equations. The solution is where the two equations meet, which in this system is (2, 1).
Answer:
One Solution
Step-by-step explanation:
GOT IT RIGHT ON EDGE 2020
If a,b are non-zero rational numbers, and c is a non-zero irrational number, what can we say about (a/b)^2
Answer:
D
Step-by-step explanation:
Answer: We can say that (a/b)^2 is a rational number
================================================
Proof:
Rational means the number is a ratio of two whole numbers
If 'a' is rational, then a = p/q for some whole numbers p,q (eg: p = 2, q = 3 so p/q = 2/3)
The same applies for b, which I'll let b = r/s, with r & s being whole numbers.
To avoid division by zero, I'm going to make p,q,r,s nonzero which leads to 'a' and 'b' being nonzero.
Now let's divide 'a' over b to get
a/b = (p/q) divided by (r/s)
a/b = (p/q) * (s/r) .... flip the second fraction; multiply
a/b = (ps)/(qr)
The new numerator is p*s which is a whole number (because the product of two whole numbers is also a whole number). The same goes for q*r in the denominator. So a/b is rational if both 'a' and 'b' are rational together.
We can extend this to (a/b)^2 as well
(a/b)^2 = [ (ps)/(qr) ] ^2
(a/b)^2 = [ (ps)^2 ]/[ (qr)^2 ]
(a/b)^2 = (p^2*s^2)/(q^2*r^2)
p is a whole number, and so is p^2. Same for s and s^2. Overall, the final numerator p^2*s^2 is also a whole number. Similarly, q^2*r^2 is a whole number.
So we have yet another ratio of two whole numbers proving that (a/b)^2 is a rational number.
Monica is weighing a newborn infant in the NICU. She needs to record the weight in ounces. If the ratio of pounds to ounces is 1:16, how many ounces is an 8.5 pound baby? 1.88 ounces 26 ounces 866 ounces 136 ounces
Answer:
136 ounces
Step-by-step explanation:
So you take 8.5 lbs and multiple it by the second number in the ratio this only works if the first number is 1 and it represents what you are starting with
8.5*16=136
To convert pounds to ounces, multiply the number of pounds by 16. An 8.5 pound baby weighs 136 ounces.
Explanation:To convert pounds to ounces, you need to multiply the number of pounds by 16 because there are 16 ounces in 1 pound.
In this case, an 8.5 pound baby would be equivalent to:
8.5 pounds x 16 ounces/pound = 136 ounces
Therefore, an 8.5 pound baby weighs 136 ounces.
Learn more about Converting pounds to ounces here:https://brainly.com/question/2909742
#SPJ2
What is the answer ?
Answer:
2y
Step-by-step explanation:
Simplifying
21x + -42y = 0
Solving
21x + -42y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '42y' to each side of the equation.
21x + -42y + 42y = 0 + 42y
Combine like terms: -42y + 42y = 0
21x + 0 = 0 + 42y
21x = 0 + 42y
Remove the zero:
21x = 42y
Divide each side by '21'.
x = 2y
Simplifying
x = 2y
find the values for A and B that would make the equality true
-5(3x^2+5x+b)=ax^2-25x+45
Answer:
a = - 15 and b = - 9
Step-by-step explanation:
distribute the left side
- 15x² - 25x - 5b
For - 15x² - 25x - 5b = ax² - 25x + 45
Then the coefficients of like terms must be equal, hence
comparing coefficients of x² term ⇒ a = - 15
comparing constant term ⇒ - 5b = 45 ⇒ b = - 9
Answer: a = -15, b = -9
Step-by-step explanation:
-5(3x² + 5x + b) = ax² - 25x + 45
-15x² - 25x - 5b = ax² - 25x + 45 distributed -5 on left side
Notice that the middle terms (-25x) are equal, so the the remaining terms will also be equal.
-15x² = ax² ⇒ -15 = a
-5b = 45 ⇒ b = -9
Help with question 14!!
Answer: a=2 b=5 c=-7
parabola equation is y = 2x^2+5x-7 = 0
Step-by-step explanation:
Substitute (x,y) into y = a x^2 + b x + c
(2,11) 11 = 4a + 2b + c
(-1,-10) -10 = a - b + c
(-4,5) 5 = 16a -4b + c
Solve the linear system in a, b, c
Det[{{4,2,1},{1,-1,1},{16,-4,1}}] = 54
Det[{{11,2,1},{-10,-1,1},{5,-4,1}}] = 108
Det[{{4,11,1},{1,-10,1},{16,5,1}}] = 270
Det[{{4,2,11},{1,-1,-10},{16,-4,5}}] = -378
a = 108/54 = 2
b = 270/54 = 5
c = -378/54 = -7
parabola equation is y = f(x) = 2x^2+5x-7
f(2) = 8+10-7 = 11 ✔
f(-1) = 2-5-7 = -10 ✔
f(-4) = 32-20-7 = 5 ✔
Solve for X in the equation below. Show your work.
HI! I REALLY NEEED HELP WITH THIS QUESTION PLEASE SHOW YOUR WORK IF YOU ARE WILLING TO HELP MEH! PLEASE HELP ME!
(x-2)= -1/4(x-8)
Answer:
x = 16/5
Step-by-step explanation:
(x-2)= -1/4(x-8)
Multiply each side by -4 to clear the fraction
-4 (x-2) = -4*-1/4 (x-8)
Distribute
-4x+8 = x-8
Add 4x to each side
-4x+4x+8 = x+4x-8
8 = 5x-8
Add 8 to each side
8+8 = 5x-8+8
16 = 5x
Divide each side by 5
16/5 = 5x/5
16/5 =x
I could really use some help with these 4 problems. Any help will be greatly appreciated!
(7) is the same problem with different numbers as (4) in another question you posted: https://brainly.com/question/11799042
(8) is not correct. [tex]\mathbf u\cdot\mathbf v=(12)(-15)+(4)(-5)=-200[/tex]
(9) is not correct. The direction of the vector [tex]\langle3,4\rangle[/tex] is [tex]\theta[/tex] where
[tex]\tan\theta=\dfrac34\implies\theta=\tan^{-1}\dfrac34[/tex]
so the applied force is the vector
[tex]\mathbf F=\langle14\cos\theta,14\sin\theta\rangle=\langle11.2,8.4\rangle[/tex]
(if you're not sure how to compute the (co)sine of the inverse-tangent expression, note that a tangent of 3/4 corresponds to a right triangle with hypotenuse 5)
The object is moved 7 ft in the same direction as [tex]\mathbf F[/tex], so that its displacement is given by the vector
[tex]\mathbf d=\langle7\cos\theta,7\sin\theta\rangle=\langle5.6,4.2\rangle[/tex]
Then the work done on the object is the dot product of these two vectors,
[tex]W=\mathbf F\cdot\mathbf d=(11.2)(5.6)+(8.4)(4.2)=98\approx97[/tex]
(the discrepancy here might be coming from finding a numerical value for [tex]\theta[/tex])
(10) is correct. We can find a unit vector pointing in the direction of any vector [tex]\mathbf v[/tex] by dividing [tex]\mathbf v[/tex] by its magnitude:
[tex]\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\frac23\,\mathbf i-\frac12\,\mathbf j}{\sqrt{\left(\frac23\right)^2+\left(-\frac12\right)^2}}=\dfrac45\,\mathbf i-\dfrac35\,\mathbf j[/tex]
I’m doing the Pythagorean Theron in math class an I’m stuck on this question - the base path of a base ball diamond form a square.if it is 90 feet from home to first how far does the catcher have to through to catch someone stealing second base
check the picture below.
4^(x+30)=64^2x
Solve. What is the value of x?
Please its urgent help
You can use same operations on both sides such that both sides' x value come on one side and rest of the values go on other side so that you get what is equal to x.
The value of x is 6
How does [tex]a^b = a^c[/tex] implies = c ?It is because [tex]a^x[/tex] where x is a variable and "a" is a constant, is a function. A function only outputs single value to each input.
If for x = p and x = q, we get same value, then we will have [tex]a^x[/tex] not being a function. Thus, for that to be a function, we need those inputs same too for output to be same.
Thus, [tex]a^p = a^q \implies p = q[/tex]
Remember that we need base to be same(here a is base and p and q are exponents)
How to solve the given equation?We can use the fact that 64 is cube of 3 and can use the above stated fact.
Thus, we have:
[tex]4^{(x+30)} = 64^{(2x)}\\4^{x+30} = 4^{3^{2x}} \\\\\text{since power of power will multiply, thus,}\\\\4^{x + 30} = 4^{6x}\\\\or\\\\x+30 = 6x\\\\\text{Subtracting x on both sides}\\\\30 = 5x\\\\\text{Dividing by 5 on both sides}\\\\6 = x\\x = 6[/tex]
Thus, The value of x is 6
Learn more about base and exponent here:
https://brainly.com/question/15722035
Please help me. I am having trouble. This is for solving x is algebraic expressions.
Answer: a - add 3 to both sides
Step-by-step explanation: you want to have the variable with the number all to itself to solve for x, so you have to add 3 to both sides to get 3/4x=-15. then divide by 3/4 to both sides and you will get a final answer.
p = 5(2t -20) what is an equivalent form of this rule
Answer:
p = 10t - 100
Step-by-step explanation:
Perform the indicated multiplication: p = 10t - 100.
The equivalent form of the algebraic equation p = 5(2t - 20) is p = 10t - 100, which is a simplified linear representation of the original equation.
The student is looking for an equivalent form of the algebraic equation p = 5(2t - 20). By distributing the 5, we obtain p = 10t - 100. This is now a simplified linear equation representing the same rule as the original equation. It's also similar to manipulating a quadratic equation to find the value of t, as shown in the other examples provided. However, this linear equation doesn't require solving for t; rather, we're simply rewriting it in a more straightforward format.
What's the volume of a block of ice measuring 3 meters long, 1.5 meters wide and 2 meters high.
Answer: The volume of a block of ice is 9 meters
You have to LxWxH
How do you tell if the linear equation is one solution many solution or no solution
If it's a graph: Solutions are points of intersection
The same line means infinitely many solutions
Parallel lines = never intersects = no solution
1 point of intersection = 1 solution
If it's a system of equations:
If you get _*x = _(a number), 1 solution (divide by the coefficient, and get only 1 possible value)
If you get x = x, infinitely many solutions (x can be anything and still equal itself)
If you get two different constants equaling (such as 1 = 2), there is no solution because no value of x can make those two values equal.
which equation can be used to find the measure of angle LKJ?
Answer:
D
Step-by-step explanation:
use the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8.9}{10.9}[/tex], hence
x = [tex]sin^{-1}[/tex]( [tex]\frac{8.9}{10.9}[/tex] ) → D
Answer:
D
Step-by-step explanation:
so i comeplete a table right ,
number of cuts | number of ballots
1 | 3
2| 9
3| 27
4| 81
5| 243
perhaps I continue this process , how many ballots will I have after 10 cuts ?
how many will I have after n cuts ?
Answer: The number of ballots increases by 3: 3x3=9, 9x3=27, 27x3=81...
After 10 cuts, there will be 59,049 ballots.
The ratio of the loudness of Lala’s earphones to the loudness of Polina’s earphones to the loudness of Goffy’s earphones is 6:5:3, respectively. If Polina’s earphones have a loudness of 420 decibels, find the total loudness of all three earphones.
To find the total loudness of three earphones with a given ratio is 1176 decibels.
The ratio of loudness of the earphones is 6:5:3. Given that Polina's earphones have a loudness of 420 decibels, we can find the loudness of Lala's and Goffy's earphones. Let the loudness of Lala's earphones be 6x, Polina's is 5x, and Goffy's is 3x.
Adding the loudness of all three earphones, we have: Lala's (6x) + Polina's (420) + Goffy's (3x). Substituting 5x = 420 and solving gives 5x = 420, x = 84. Therefore, the total loudness of all three earphones is 6(84) + 420 + 3(84) = 504 dB + 420 dB + 252 dB = 1176 decibels.
Given y varies directly as x, use the given x-value and y-value to find an equation that relates x and y. x = 24 and y = 360 A) y = 15x B) x = 15xy C) y = .15x D) y = 15 x
Answer:
A
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the given condition x = 24 and y = 360
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{360}{24}[/tex] = 15
Hence y = 15x is the equation → A
Answer: A
Step-by-step explanation:
Find the missing number of each unit rate
Answer:
3 and 4
Step-by-step explanation:
21/7 = x/1
x = 21/7*1 = 3
16/4 = y/1
y = 16/4*1 = 4