Answer:
The equality is only true for [tex]a = 0\ and\ 1[/tex], not for all values
Step-by-step explanation:
Given
[tex](\sqrt a)^4 = a[/tex]
Required
Determine if it is valid
[tex](\sqrt a)^4 = a[/tex]
Evaluate the exponent
[tex](a^\frac{1}{2})^4 = a[/tex]
[tex]a^\frac{1*4}{2} = a[/tex]
[tex]a^2 = a[/tex]
Rewrite as:
[tex]a^2 - a = 0[/tex]
Factorize
[tex]a(a- 1) = 0[/tex]
[tex]a =0\ or\ a - 1 = 0[/tex]
[tex]a =0\ or\ a = 1[/tex]
The equality is only true for [tex]a = 0\ and\ 1[/tex], not for all values
If two numbers are in the ratio 6:13 and their LCM is 312, then find the numbers.
Answer:
The two numbers are 12 and 26
Step-by-step explanation:
let the first number = a
let the second number = b
The ratio of the numbers is given as;
[tex]\frac{a}{b} = \frac{6}{13} \\\\a = \frac{6b}{13}[/tex] -------- (1)
The lcm of the two numbers is given as;
a x b = 312
ab = 312 --------- (2)
From equation (1), [tex]a = \frac{6b}{13}[/tex]
[tex]b(\frac{6b}{13} ) = 312\\\\\frac{6b^2}{13} = 312\\\\6b^2 = 4056\\\\b^2 = \frac{4056}{6} \\\\b^2 = 676\\\\b = \sqrt{676} \\\\b = 26\\\\From \ equation \ (1);\\\\a = \frac{6b}{13} \\\\a = \frac{6 \times 26}{13} \\\\a = 12[/tex]
Therefore, the two numbers are 12 and 26
The Downtown Community Barbecue served 280 dinners. A child’s plate cost $2.60 and an adult’s plate cost $9.50. A total of $1,797.50 was collected. How many of each type of plate was served?
Round answers to the nearest whole person.
child plates were served.
adult plates were served.
Answer:
the number of child plates and adults plates were served is 125 and 155 respectively
Step-by-step explanation:
Let us assume the child plate be x
And, the adult plates be y
Now according to the question
x + y = 280 .................(1)
2.60x + 9.50y = 1797.50 .............(2)
Now multiply by 2.60x in equation (1)
2.60x + 2.60y = 728
2.60x + 9.50y = 1797.50
-6.90y = -1069.50
y = 155
So, x = 280 - 155
= 125
hence, the number of child plates and adults plates were served is 125 and 155 respectively
HELP By Today
Please
The number of permutations of 5 objects taken 2 at a time is P(5,2). The value of
5!
P(5,2) could be found by applying 5P2=
(5 – 2)
What is the value of P(5,2)?
A-60
B-20
C-6
D-120
Answer:
20
Step-by-step explanation:
A study was done to investigate the relationship between a between eating sugary snacks and a test that measures a
student's memory and attention. The correlating linear model is shown below, where x represents the number of sugar
snacks a student ate, and y represents the student's test score.
Interpret the rate of change (slope).
y = -5x
Answer:
Each additional sugary snack eaten is associated with a loss of five points on the test.
Step-by-step explanation:
ASAP ! The the area of a rhombus is 135 cm". The length of one diagonal is 15cm.
What is the length of the other diagonal
25 cm
O
12 cm
o
18 cm
20 cm
520 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 4 hours. How long would it be, to the nearest tenth of an hour, until there are 33980 bacteria present?
Answer:
24.1
Step-by-step explanation:
write 10075302 in words in both the Indian system and international system and rearrange the digits to get the smallest number
Answer:
answer
Step-by-step explanation:
1,00,75,302= One crore seventy five thousand three hundred two
Rearranging the digits,
Largest number = 7,53,21,000
Smallest number = 1,00,02,357
Pls help it is khan academy pls and thx! :)
PLS HELP SOLVE!!!!!!! FOR 10 POINTS SHOW YOUR WORK PLEASE!!!!!
9514 1404 393
Answer:
x = 60
Step-by-step explanation:
You are correct that the angles are complementary.
That means their sum is 90°.
(x -30)° + x° = 90°
2x -30 = 90 . . . . . . . divide by °, collect terms
2x = 120 . . . . . . . . . . add 30
x = 60 . . . . . . . . . . . . divide by 2
Answer:
[tex]x \: = 60[/tex]Step-by-step explanation:
#CarryOnLearningPlease help me with this math question lol
Answer:
120 students are predicted to like chocolate chip ice cream best.
Step-by-step explanation:
40% = 0.4
Multiply 300 by 0.4 to get 40% of 300.
300 × 0.4 = 120
The figure below is made up of two rectangles.
What is the total area, in square feet, of the figure?
Answer:
Total area of figure = [3x² + 7x + 6] feet²
Step-by-step explanation:
By dividing both rectangle by vertical line;
Given:
Length of big rectangle = (x + 3) feet
Width of big rectangle = (x + 2) feet
Length of small rectangle = 2x feet
Width of small rectangle = (x + 1) feet
Find:
Total area of figure
Computation:
Area of rectangle = Length x width
Total area of figure = Area of big rectangle + Area of small rectangle
Total area of figure = [(x + 3)(x + 2)] + [(2x)(x + 1)]
Total area of figure = [x²+ 2x + 3x + 6] + [2x² + 2x]
Total area of figure = [3x² + 7x + 6] feet²
An account is open with initial deposit of $5500 and earn 2.5% interest compounded annually. What will the account be worth in 10 years
Answer:
FV= $7,040.46
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $5,500
Number of periods (n)= 10 years
Interest rate (i)= 2.5%
To calculate the future value (FV), we need to use the following formula:
FV= PV*(1 + i)^n
FV= 5,500*(1.025^10)
FV= $7,040.46
Find the sum of the first 20 terms of the sequence {4,10,16,22,...} step by step
Answer:
All terms separated by 6 so #20 = 4 + 6 * 19 = 118
(if the first term were 6 instead of 4 the 20th would be 120)
Also, #10 = 58 and #11 = 64 (you can use the same reasoning)
The 1st and 20th term add to 4 + 118 = 122
The 2nd and 19th add to 10 + 112 = 122
Likewise 10th and 11th add to 58 + 64 = 122
So 10 * 122 = 1220
The window above Matt's front door is shaped like a triangle.
How many equal-length sides does the window have?
Enter the correct answer in the box.
PLEASE HELP
Answer:
It has 2 equal side lengths
Brandon has four more than 3 times the amount of money that Dale has. Together they have $44. What equation represents this? How much money does Dale have? How much money does Brandon have?
Answer:
Equation: 4 + 3n. Dale's Money: $7.3¢ Brandon's money: $25.9¢Step-by-step explanation:
Equation
Let "n" represent the number. Then more indicates addition, and times indicates multiplication. With that said, the answer is 4 + 3n.
Dale's Money
Given: $44 in total
44 ÷ 2 (To know how much they have equally)
22
22 ÷ 3 (Then you divide by 3 because Brandon has 3 times his, the opposite of multiplication is division.)
7.3
Therefore, Dale has $7.3¢
Brandon's money
Given: 4 + 3n. Dale has 7.3
Solve: 7.3 × 3 ( Since Brandon has four more than 3 times the amount of money that Dale has, multiply that and 3)
21.9 (Then add four because Brandon has four more...)
25.9
Therefore, Brandon has $25.9¢
The amount that Brandon and Dale have is $34 and $10, respectively.
What is an equation?An equation is formed when two expressions are equated with each other with the help of an equal sign.
Let the amount of money that Brandon has be x, and Dale has be y.
As it is given that the sum of the total amount they both had is $44. therefore, the equation that can represent the total amount both of them had is
[tex]x + y = \$44[/tex]
Now, according to the first statement, Brandon has four more than 3 times the amount of money that Dale has. therefore, the equation can be represented as,
[tex]x = 4 + 3y[/tex]
Further, as got the two-equation solving the two equations. We have the value of x, therefore, substitute the value of x in the first equation,
[tex]x+y = 44\\\\(4 + 3y )+y= 44\\\\4+4y=44\\\\4y = 40\\\\y = 10[/tex]
Now, substitute the value of y in the second equation we get,
[tex]x = 4 + 3y\\\\x = 4 + 3(10)\\\\x = 34[/tex]
Hence, The amount that Brandon and Dale have is $34 and $10, respectively.
Learn more about Equation:
https://brainly.com/question/24944275
SolveABC where a = 11,6 = 13, &c = 15.
Answer: ABC = 2145
Step-by-step explanation:
11x13x15=2145
Answer:
whatever wawnser gimme brainliest
PLEASE HELP !! ILL GIVE 40 POINTS PLUS BRAINLIEST !!
Step-by-step explanation:
lkh, Jkm. Correct me if im wrong :^
We want to find the zeros of this polynomial:
p(x) = 2x^3 – x^2 - 8x + 4
Plot all the zeros (z-intercepts) of the polynomial in the interactive graph.
Answer:
Step-by-step explanation:
The point is that any graphing calculator will work. We use Desmos on Brainly.
The graph below is your complete answer.
You can actually find the zeros by factoring
p(x) = x^2(2x - 1) - 4(2x - 1)
p(x) = (2x - 1) (x^2 - 4)
p(x) = (2x - 1) (x - 2)(x + 2)
I have to hurry. If this is not enough, let me know.
Hailey Bell bought a flute for $150 and sold
it for $175. Find her percent of profit based
on the cost and on the selling price.
hondise totaling
Answer:
the profit percentage based on the cost & selling price is 16.67% and 14.29% respectively
Step-by-step explanation:
The computation of the profit percentage based on the cost & selling price is shown below:
The Profit percentage on the cost is
= (Sale price - cost price) ÷ (cost price) × 100
= ($175 - $150) ÷ ($150) × 100
= 16.67%
ANd, the profit percentage based on the selling price is
= (Sale price - cost price) ÷ (selling price) × 100
= ($175 - $150) ÷ ($175) × 100
= 14.29%
Hence, the profit percentage based on the cost & selling price is 16.67% and 14.29% respectively
Evaluate the indicated limit algebraically. Change the form of the function where necessary. Please write clearly with description of each step, thank you very much.
3x^2+4.5
________
x^2-1.5
lim
x → ∞
Answer:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Step-by-step explanation:
We want to evaluate the limit:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}[/tex]
To do so, we can divide everything by x². So:
[tex]=\displaystyle \lim_{x\to \infty}\frac{3+4.5/x^2}{1-1.5/x^2}[/tex]
Now, we can apply direct substitution:
[tex]\Rightarrow \displaystyle \frac{3+4.5/(\infty)^2}{1-1.5/(\infty)^2}[/tex]
Any constant value over infinity tends towards 0. Therefore:
[tex]\displaystyle =\frac{3+0}{1+0}=\frac{3}{1}=3[/tex]
Hence:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Alternatively, we can simply consider the biggest term of the numerator and the denominator. The term with the strongest influence in the numerator is 3x², and in the denominator it is x². So:
[tex]\displaystyle \Rightarrow \lim_{x\to\infty}\frac{3x^2}{x^2}[/tex]
Simplify:
[tex]\displaystyle =\lim_{x\to\infty}3=3[/tex]
The limit of a constant is simply the constant.
We acquire the same answer.
This is my last question by the way
Part A:
There are 25 blocks for the length, and the length of each is 5.5 inches. 5.5x25=137.5
There are 9 blocks for the height, and each is 2.75 inches. 2.75x9=24.75
Since we're trying to find how much longer the length is to the width, we find the difference. 137.5-24.75=112.75
So part A answer is 112.75 (or 112¾)
Part B:
We know the length is 137.5 and the height is 24.75. To find how many times longer the length is, we need to divide to see how many 24.75 can go into 137.5.
137.5÷24.75=5.55
So the answer to part B is 5.55. Given the context, the answer would probably be 5, because that's how many entire height can fit.
Sorry if it's wrong lol
f(x) = 3log(x + 7) - 5?
Answer:
12
Step-by-step explanation:
Simplify 3 log(x+7) by moving 3 inside the parentheses with 7.f(x)=log((x+7)3)−5
During second period, Mia completed a grammar worksheet. Of the 60 questions, Mia got 80% right. How many questions did Mia get right?
Answer:
48 questions
Step-by-step explanation:
60 into 80 by 100
60 x 80/100
simplify, hence 60 x 4/5
240 divided by 5 = 48
: )
The number of questions Mia get right is 48 questions.
What is a percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
For the given situation,
Total number of questions = 60
Percentage of questions Mia got completed right = 80% = 0.80
Thus number of questions Mia get right = [tex](60)(0.80)[/tex]
⇒ [tex]48[/tex]
Hence we can conclude that the number of questions Mia get right is 48 questions.
Learn more about percentages here
brainly.com/question/1214133
#SPJ2
what is
4x + 6 = 8x − 10
Answer:
x=4
Step-by-step explanation:
4x+6=8x-10
6= 8x-10-4x
6=4x-10
6+10=4x
16=4x
16/4=x
4=x
x=4
Answer:
x = 4
Step-by-step explanation:
Subtract 8x from both sides.
4x + 6 - 8x = 8x - 10 - 8x
−4x + 6 = −10
Subtract 6 from both sides.
−4x + 6 − 6 = −10 − 6
−4x = −16
Divide both sides by -4.
[tex]\frac{-4x}{-4} = \frac{-16}{-4}[/tex]
x = 4
Mark as Brainllest plz
What single percentage change is equivalent to a 11% decrease followed by a 13% decrease?
Answer:
77.43% decrease
Step-by-step explanation:
A decrease of 11% = (100 - 11)% = 89% = [tex]\frac{89}{100}[/tex] = 0.89
A decrease of 13% = (100 - 13)% = 87% = [tex]\frac{87}{100}[/tex] = 0.87
A 11% decrease followed by a 13% decrease has an overall change of
0.89 × 0.87 = 0.7743 × 100% = 77.43%
Given f(x) = 6(1-x), what is the value of f(-8)?
Answer:
7/3
Step-by-step explanation:
1x6
1x(-x)
subtract and solve
Birth control pills have a theoretical annual efficacy of 99.5%, but a real-worls efficacy of only 95%. If a college student takes the pill for the four years she is in college, what is the probability that she will become pregnant at least once using the theoretical efficacy rate?
A. 0
B. 0.005
C. 0.020
D. 0.185
Answer:In my opinion B.0.005 is the correct answer
Step-by-step explanation:
hope it will help you
Using an applet, we found that the theory-based test results in a t-statistic of -7.25 and p-value less than 0.0001. State your conclusion in the context of the study.
a. We have very strong evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is smaller with the anchor of Chicago than with the anchor of Green Bay.
b. We have very strong evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is smaller with the anchor of Green Bay than with the anchor of Chicago.
c. We have very weak evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is larger with the anchor of Green Bay than with the anchor of Chicago.
d. We have very weak evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is larger with the anchor of Chicago than with the anchor of Green Bay.
Answer:
b. We have very strong evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is smaller with the anchor of Green Bay than with the anchor of Chicago.
Step-by-step explanation:
Smaller p-value indicates a strong evidence in favor of the alternative hypothesis which means we can reject the null hypothesis. In the given scenario the p-value is 0.0001 which is very small. There is sufficient evidence for the rejection of null hypothesis.
Determine the slope and y-intercept of the line.
y = -69x - 346
Answer:
Slope: -69
Y-intercept: -346 or (0, -346)
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
y = -69x - 346
m = -69
b = -346
Which of the following can be determined exactly from a histogram? A. mean B. median O C. MAD D. none of these
The midpoint of the tallest bar of the histogram is the mode of the data point.
What is a histogram?Graph is a graphical representation that shows the relationship between a group of points. Types of graphs are histogram, bar chart, pie chart etc.
A histogram is a graphical representation that arranges a group of data points into specific ranges.
The midpoint of the tallest bar of the histogram is the mode of the data point.
Find out more on histogram at: https://brainly.com/question/2962546
#SPJ2