Answer: a = c^(1/2) which is the first answer choice of the list
Work Shown:
a = b^(2/3) ... given equation
a = (c^(3/4))^(2/3) ... replace b with c^(3/4)
a = c^((3/4)*(2/3)) .... multiply exponents
a = c^(1/2) .... Simplify; note the 3's cancel, also 2/4 turns into 1/2
Simplify the expression. 3(x + 6x2 − 3x − 3x2)
A. 3x2
B. 15x2
C. 9x2 − 6x
D. 15x2 − 6x
Answer:
C. 9x^2 − 6x
Step-by-step explanation:
3(x + 6x^2 − 3x − 3x^2)
According to PEMDAS, we need to simplify inside the parentheses first
3(x -3x+ 6x^2 − 3x^2)
3(-2x+3x^2)
Now we can distribute the 3 to both terms inside the parentheses
3 * -2x + 3* 3x^2
-6x + 9x^2
We normally write them in decreasing powers of x
9x^2 -6x
Find the area of rectangle PLUM
If entering your answer as a decimal, round your final answer to the nearest hundredth.
Answer:
A = 53.34 [tex]units ^ 2[/tex]
Step-by-step explanation:
To find the length of the rectangle we solve the PLA triangle
Using the Pythagorean theorem we find the PL side.
[tex]PL = \sqrt{4^2+12^2}\\PL = \sqrt{16+144}\\PL = 12.65[/tex]
Then the length of the rectangle is 12.65
Now we solve the MALU triangle. Where MU = PL
We use the Pythagorean theorem:
[tex]MU^2+LU^2 = (MA + AL)^2\\12.65^2+LU^2 = (MA+12)^2[/tex]
Where LU and MA are unknown.
Finally we solve the triangle MPA
[tex]MA^2 + PA^2 = PM ^2[/tex]
Where PM = LU
So:
[tex]MA^2 + 4^2 = LU^2[/tex]
Now we have two equations and two unknowns. So we solve the system.[tex]12.65^2 + LU^2 = (MA + 12) ^2[/tex] (i)
[tex]MA^2+4^2 = LU^2[/tex] (ii)
We introduce (ii) in (i)
[tex]12.65^2 + MA^2+16=MA^2+24MA+144[/tex]
Now we clear MA
[tex]160.02+16-1 44 = 24MA[/tex]
[tex]32.02 = 24MA[/tex]
[tex]MA = \frac{32.02}{24}[/tex]
MA = 1.3342 (iii)
Now we introduce (iii) in (ii)
1.3342^2 + 4^2 = LU^2
LU = 4.2166
Now we have the length of the rectangle and also its width.
The area A of a rectangle is:
A = l*w
Where
l = length
w = width
A = 4.2166*12.65
A = 53.34 [tex]units^2[/tex]
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.
Mike is 3 years old.joe is 6 times as old as mike. whict equation shows how to find Joe's age? 6÷3=2. 9-3=6. 3×6=18. 3×6=9
Answer: 18
Step-by-step explanation:
3 times 6
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
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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
Your weekly base salary is $150. You earn $20 for each cell phone that you sell. What is the minimum amount you can earn in a week?
Answer:
$150 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
The minimum you can earn would be $150. This would be your base salary and you selling 0 cell phones.
if You flip an coin 200 times about how many times would you expect the coin to labd on tails what is the probality
Answer:
100;200
There are 200 total flips and to find probability we would have to divide it by two. Doing so, should give you something like this 100;200.
what does x/4=3/2 equal?
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!!! :)
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]
6x2/5 will be greater or less than 2/5
Final answer:
The expression 6x²/5 is greater than 2/5 if x is a positive integer greater than 1. If x equals 1, the expression is still greater than 2/5. However, if x is zero or negative, the expression will be equal to or less than 2/5.
Explanation:
To determine whether 6x²/5 is greater or less than 2/5, we need to consider the value of x.
As long as x is a positive integer greater than 1, the expression 6x²/5 will indeed be greater than 2/5. If x equals 1, then 6x²/5 simplifies to 6/5, which is greater than 2/5.
However, if x is zero or negative, then 6x²/5 will be equal to or less than 2/5. For example, when x is 2, 6x²/5 becomes 6 × (2²)/5 = 24/5, which is clearly greater than 2/5.
This logic is similar to instances where combining certain quantities doesn't always lead to a straightforward sum, such as mixing volumes of liquids or combining probabilities of events.
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.
At a local pizza parlor , game tickets can be traded for small toys . The rate is 10 tickets for 4 small toys . If meg won 55 tickets playing skeeball , for how many small toys can she trade her tickets
Meg can trade her tickets in for 20 small toys.
How do you solve number 7 please help
Answer: I am pretty sure your answer is 208 cm. Whenever you see a percentage immediately change it to a decimal like in this case 0.070 and multiply it by 400. 400x0.070 is equal to 280. Hope this helps :)
how many thirds are in one half
Answer:1 and a half
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
There are one in 1/2
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.
Using the Law of Syllogism, select the correct final statement: If a polygon is a square, then all 4 angles are right. If all 4 angles of a polygon are right, then it is a rectangle. Question 9 options: If a polygon has 4 right angles, then it is a square. The polygon has 4 right angles. The polygon is a rectangle. If a polygon is square, then it is also a rectangle.
Answer:
if a polygon is square,then it is also a rectangle is correct
Step-by-step explanation:
1)if a polygon has 4 right angles,then it is a square is wrong since in the statement a square has all its angles as right angles but it need not imply that it is a square as it could also be a rectangle
2) polygon need not have four right angles eg:rhombous with angles 60°,60°,120°,120° is also a polygon
3)every polygon need not be a rectangle as it could be square
4)if a polygon is square, then all its angles are right angles and if all its angles are right then it is rectangle.
hence option 4 is true.
Which statement explains why one of these triangles is a right triangle?
Answer:
Triangle A has one right angle
Step-by-step explanation:
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.
A rectangular room measures 14 feet by 12 feet.Find the cost of installing a strip of wallpaper around the room if the wallpaper costs 0.72 per foot.
Answer:
$120.96
Step-by-step explanation:
So the area of the room is 14*12. So the area of the room is 168ft^2. So now we multiply it by .72 because it costs .72 per square foot. So the cost is 120.96
To calculate the cost of installing wallpaper around a rectangular room measuring 14 feet by 12 feet, you first find the perimeter, which is 52 feet, then multiply by the cost per foot, $0.72, leading to a total cost of $37.44.
The formula for the perimeter P of a rectangle is P = 2(length + width). In this case, the length is 14 feet and the width is 12 feet.
P = 2(14 feet + 12 feet) = 2(26 feet) = 52 feet.
Now that we have the perimeter, we multiply it by the cost per foot of the wallpaper to find the total cost. The wallpaper costs $0.72 per foot.
Total cost = Perimeter × Cost per foot = 52 feet × $0.72/foot = $37.44.
Hence, it will cost $37.44 to install the wallpaper around the rectangular room that measures 14 feet by 12 feet.
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
Mount McKinley in Alaska rises 20,320 feet in the air while Mount Kosciusko in Australia rises 7,310 feet. What is the difference in the height of these mountains? Express your answer in scientific notation.
Answer:
1.301 × 10⁴ ft
Step-by-step explanation:
Difference = h₂ - h₁
Difference = 20 320 - 7310
Difference = 13 010 ft
To convert the number to scientific notation, we move the decimal point four places to the left and make the exponent of 10 equal to +4.
Difference = 1.301 × 10⁴ ft
each baseball team has 9 players and each football team has 11 players. 6 schools have both baseball and football teams. Four schools have only a baseball team. how many players are there for all 10 schools
Answer:
156 players
Step-by-step explanation:
The 9 players for baseball and 11 players for football are added. 9 + 11 = 20.
Once you have 20, you can multiply it by the 6 schools. Which gets you 120 players so far.
After you multiply the 4 schools by the 9 players for baseball. You’ll get 36. Add the 120 players to 36 players and you’ll get 156 players for the 10 schools in total
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.
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:
Order the numbers 0.64, 2/3, 65%, and 7/10 from least to greatest.
A) Estimate 49% of 162.
B) Use mental math to calculate 49% of 162.
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
Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?
5x + 13y = 232
12x + 7y = 218
Is there a similarity transformation that maps Triangle ABC to Triangle DEF? If so, identify the similarity transformation and write a similarity statement. Explain your answer.
Answer:
Yes, there is a similarity transformation that maps triangle ABC to Triangle DEF.
Step-by-step explanation:
Similarity transformation;
Triangle DEF has been transformed(dilated) by a factor of 2.
Since each dimension is twice that of the triangle ABC.
Two triangles are similar if their corresponding sides are congruent and corresponding angles are congruent.
Similarity statement:
ΔABC [tex]\sim[/tex] ΔDEF
these two triangles are similar because;
[tex]\frac{AB}{DE}= \frac{4}{8} = \frac{1}{2}[/tex]
[tex]\frac{AC}{DF}= \frac{4}{8} = \frac{1}{2}[/tex]
[tex]\frac{BC}{EF}= \frac{3}{6} = \frac{1}{2}[/tex]
⇒ [tex]\frac{AB}{DE}=\frac{AC}{DF} =\frac{BC}{EF}[/tex]
Yes, there is a similarity transformation that maps Triangle ABC to Triangle DEF.
To determine if two triangles are similar, one must check if they have the same shape, which means their corresponding angles are equal and their corresponding sides are in proportion.
Let's denote the angles of Triangle ABC [tex]\(A\), \(B\), and \(C\),[/tex] and the angles of Triangle DEF as [tex]\(D\), \(E\), and \(F\),[/tex] respectively. Similarly, let's denote the sides opposite these angles as [tex]\(a\), \(b\), and \(c\)[/tex] for Triangle ABC, and [tex]\(d\), \(e\), and \(f\)[/tex] Triangle DEF.
For Triangle ABC and Triangle DEF to be similar, the following conditions must be met:
1. [tex]\(A = D\), \(B = E\), and \(C = F\)[/tex] (AA postulate for similarity).
2. [tex]\(\frac{a}{d} = \frac{b}{e} = \frac{c}{f}\)[/tex] (corresponding sides are in proportion).
If these conditions are satisfied, then there exists a similarity transformation that maps one triangle to the other. This transformation can be broken down into the following steps:
1. Dilation: To make the sides of Triangle ABC proportional to the sides of Triangle DEF, we perform a dilation. The scale factor k can be determined by the ratio of any pair of corresponding sides. For example, [tex]\(k = \frac{d}{a} = \frac{e}{b} = \frac{f}{c}\)[/tex]. This single scale factor should work for all three sides if the triangles are similar.
2. Rotation/Reflection (optional): If Triangle DEF is not oriented in the same direction as Triangle ABC, we may need to rotate or reflect Triangle ABC to align it with Triangle DEF. This does not affect the similarity.
3. Translation (optional): Finally, if Triangle DEF is not in the same position as Triangle ABC (but has the same orientation and size after the dilation), we perform a translation to move Triangle ABC to the position of Triangle DEF.
Since the angles are preserved under dilation, rotation, and translation, and the sides are made proportional by the dilation, the similarity transformation is complete.
If the corresponding angles are equal and the corresponding sides are in proportion, then the two triangles are similar, and a similarity transformation exists that maps one to the other. The similarity statement captures this relationship, indicating that the triangles are similar to the AA postulate and the sides are in proportion.