15. Pat and Camilla are working with expressions with rational exponents. Listed below are what each
believes to be correct. Use the properties of exponents to determine the correct answer. Write
the correct answer in the space provided.
Answers
Answer:
Step-by-step explanation:
Pat believes that [tex]\sqrt{2}+\sqrt{8}=(2)(2)^{\frac{1}{2}}[/tex]
[tex]\sqrt{2}+\sqrt{8}=\sqrt{2}+\sqrt{4\times 2}[/tex]
[tex]=\sqrt{2}+2\sqrt{2}[/tex]
[tex]=3\sqrt{2}[/tex]
[tex]=3(2)^{\frac{1}{2} }[/tex]
But [tex]2(2)^{\frac{1}{2}}\neq 3(2)^{\frac{1}{2}}[/tex]
Therefore, Pat's belief is not correct.
Camilla believes that [tex]\sqrt{2}+\sqrt{8}=3\sqrt{2}[/tex]
Which is correct as we have calculated above.
Therefore, [tex]\sqrt{2}+\sqrt{8}=3\sqrt{2}[/tex] will be the correct answer.
Related Questions
HELPPPP!!!! PLEASEEE!!!
Which statement below is true?
A. If p → q is true, then q → p is true.
B. If p → q is true and p is true, then q is true.
C. If p → q and q → r are true, then q → p is true.
D. If p → q and q → r are true, then r → p is true.
Answers
Answer:
D is correct
Step-by-step explanation:
p=q then q is the same as p and if r=p that is true
3 digit number that is divisible by 3 and 5
Answers
The answer is 135
1+3+5=9(9 is a multiple of 3. To know if something is divisble by 3, you must add it and if it is a multipe of 3 it is divisble of 30
135 end with 5( If a number ends with 0 or 5 it is divible by 5)
Hope my explanation helps!
I need help with number 8 and please explain
Answers
Answer:
No
The sides of the triangle do not satisfy the Pythagorean Theorem.
Step-by-step explanation:
If we are given the three sides to a triangle, and we are asked to find out if it is a right triangle, we will have to see if the sides of the triangle satisfies the Pythagorean Theorem. The Pythagorean Theorem is:
a² + b² = c²
where c is the hypotenuse and a and b are the other two sides.
So we can see from the image that 28 would be the length of the "hypotenuse" and 19 and 20 would be the lengths of the other two sides. Lets see if these values satisfy the Pythagorean Theorem:
19² + 20² = 28²
361 + 400 = 784
761 ≠ 784
So no, the triangle is not a right triangle because the sides does not satisfy the Pythagorean Theorem.
I hope you find my answer and explanation to be helpful. Happy studying.
What is the constant of proportionality?
Time (min)
1
2
3
Number of Texts
3
6.
9
12
Answers
Answer:
y=x3
Step-by-step explanation:
x=time minutes
y= texts
i hope i'm correct
plz mark brainliest
Choose the equation below that represents the line passing through the point (2, -5) with a slope of -3.
y = -3% - 13
Oy=-3x + 13
Oy=-3x + 1
Oy=-3x + 11
Answers
Answer:
D
Step-by-step explanation:
Slope
All answers agree that the slope = - 3
y intercept
So far what you know is that the line is
y = -3x + b
The point shows that
5 = -3*2 + b Combine right
5 = -6 + b Add 6 to both sides
5 + 6 = -6+6 + b Combine
11 = b
So the y intercept = 11
Answer: y = -3x + 11 D
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
6c2+2c4−c
Answers
Answer:
46;&74)474:&48&4:&48&
Step-by-step explanation:
For example if you have a function f(x) = x - 1, then x = 1 is a zero of this function because using it as x gives 1 - 1 = 0. The Riemann Zeta function has some zeros that are easy to find which are of little interest but there are some other ones that are harder to find which is why the are called non-trivial.
in need the proofs and statements
Answers
Answer:
Since we are given that angle Y = angle Z
The magnitude of the angles will also be equal
∠Y = ∠Z
(x + 10) = (2x - 90)
90 + 10 = 2x - x
100 = x
A local bakery sells 18 bagels for $12.99. How many bagels can be purchased for $20? Round down to the nearest whole bagel.
Answers
IN THE CENTRAL CITY GRAND PRIX, OUT OF 50 CARS THAT STARTED THE RACE, 12
OF THEM FINISHED. WHAT PERCENT OF THE CARS FINISHED THE RACE? WHAT
PERCENT DID NOT FINISH THE RACE?
I need a step by step explanation please !!!
Answers
Answer:
24% finished, 76% did not
Step-by-step explanation:
12cars/50 total +24%, and then just subtract 100% by the 24 to get 76% for the remaining percent
Answer:
24% finished and 76% did not
Step-by-step explanation:
you have the ratios:
12/50 and 38/50
These have to be turned into percentages so they need to have a denominator of 100
to do this, figure out what you have to multiply the denominator by to get 100
In this case, 50 times 2 is equivalent to 100.
Then, whatever you multiplied the denominator by, you multiply the numerator by
In this case, 12 times 2 is 24 and 38 times 2 is 76
Once you have the end products, take the numerator and add a percentage sign to it
Chat me if you have anymore questions
800,000 rounded to the nearest hundred thousand what is the largest and smallest number
Answers
Answer:
Largest: 800,499
Smallest: 799,500
The required largest number is 8,00, 499 and the smallest number is 7,99, 500.
Given that,
800,000 rounded to the nearest hundred thousand.
To determined the largest and smallest number.
What is rounding of values?
The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Here,
Any number range -500 and + 499 to 8,00,000 will be the smallest and largest number that could be rounded to 8,00,000.
smallest number = 8,00,000 - 500 = 7, 99, 500
largest number = 8,00,000 + 499 = 8,00,499
Thus, the required largest number is 8,00, 499 and the smallest number is 7,99, 500.
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ASAP!!! Tell me the lengh and width and i will give you branilest!
Answers
Answer:
The length of the drawing is 10 centimeters and the width is 6 centimeters.
Step-by-step explanation:
500/50= 10 1*10=10 so the length is 10
300/50=6 1*6=6 so the width is 6.
Please help!!!! I'll give you 15 points!!
Answers
Step-by-step explanation:
the answer is C
2/5(2x+3)
I hope it helps
Write the equation of a line that passes through the points (−3, 7) and (3, 3)
y=−2/3x+5
y=2/3x+1
y=−2/3x+9
y=2/3x+9
Answers
Step-by-step explanation:
You can write an equation of a line conveniently by point-slope form. It's in the form of [tex]y -a = m(x -b)[/tex] where [tex](b,a)[/tex] is the coordinates of a point that's on the line and [tex]m[/tex] is the slope of the line.
Now choose a point (It doesn't really matter which one) and plug that in the equation. I'll choose [tex](-3,7)[/tex] where [tex]a = 7[/tex] and [tex]b = -3[/tex]
[tex]y -a = m(x -b) \\ y -7 = m(x -(-3)) \\ y -7 = m(x +3)[/tex]
The next thing we have to do now is finding the slope, [tex]m[/tex], where it's equal to [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}\\[/tex]. I'll make [tex](-3,7)[/tex] point 1 and [tex](3,3)[/tex] point 2.
[tex]m = \frac{3 - 7}{3 -(-3)} \\ m = \frac{3 - 7}{3 +3} \\ m = \frac{-4}{6} \\ m = -\frac{2}{3}[/tex]
Now let's plug that to our equation.
[tex]y -7 = m(x +3) \\ y -7 = -\frac{2}{3}(x +3)[/tex]
Now we have the equation but out of all the choices it seemed that all of them are in slope-intercept form all you have to do now is make our equation rewrite it in slope-intercept form.
[tex]y -7 = -\frac{2}{3}(x +3)\\ y -7 = -\frac{2}{3}x -\frac{2}{3}(3) \\ y - 7 = -\frac{2}{3}x -2\\ y = -\frac{2}{3}x +5[/tex]
Answer:[tex]y = -\frac{2}{3}x +5\\[/tex] is your equation.
do you agree that the equation (x-4)²=9 can be solved both by factoring and extracting square roots?
Answers
Given parameters:
Equation:
(x-4)²=9
Problem, solve the equation by factoring and extracting the root
Solution:
Given equation:
(x-4)²=9
subtract 9 from both sides to equate to zero;
(x-4)² - 9 = 0
(x -4)² - 3² = 0
Now, this is similar to the concept of difference of two squares;
x² - y² = (x + y)(x-y)
Here x = x-4 and y = -3
So input and solve;
(x - 4 -3)(x - 4 -(-3)) = 0
(x - 7)(x - 4+3) = 0
(x -7)(x -1) = 0
S0,
x - 7 = 0 or x-1 = 0
x = 7 or 1
If we extract the square roots;
(x-4)² = 9
√(x-4)² = √9
x - 4 = 3
x = 4 + 3 = 7; this is not the only solution to the problem
So we cannot solve it by extracting the square root.
The solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root. The equation can only be solved by factoring
Given the expression;
(x-4)²=9
This expression can be solved by factoring
Factoring the expression on the left hand side
(x-4)(x-4)=9
x²-4x-4x+16 = 9
x² - 8x + 16 - 9 = 0
x² - 8x + 7 = 0
x² -x - 7x + 7 = 0
x(x-1) -7(x-1) = 0
x-7 = 0 and x - 1 = 0
x = 7 and 1
This shows that the expression can be solved by factoring
The other way is by squaring both sides
(√x-4)² = ±√9
x - 4 =±√9
x = -9+4 and x = 9 + 4
x = -5 and 13
Since the solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root
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Reese wants to organize a party and decides to save money for it.He calculates that he needs $420 in 9 weeks.He already has $60
Answers
So,
420=60+9x
(Since he already has 60)
Subtract the 60 from 420 to begin isolating the variable
This gives you
360=9x
Divide both sides by 9 to completely isolate the variable
This gives you
40=x
So, he needs to save up $40 each week
A cell phone company charges $25 per month, plus $0.10 per text message sent. Before taxes, Susie’s bill was $80 for 3 months of service. How many text messages did Susie send during those 3
Answers
let m = the number of months
let t = each message sent
25m + 0.1t = 80
plug 3 in for m (because 3 months)
25(3) + 0.1t = 80
simplify
75 + 0.1t = 80
subtract 75 from 80
0.1t = 5
divide 5 by 0.1
t = 50
answer: 50 text messages
PLS HELP ME IM BEING TIMED AND I HAVE 20 MINS TO TURN IN.
Answers
Answer:
2.a) 3 ( x - 1 ) = 5x - 6 (Because the sides of a square are always equal)
b) 3 ( x - 1 ) = 5x - 6
=> 3x - 3 = 5x - 6
=> 3x - 5x = -6 + 3 (Law of transposition)
=> -2x = -3
=> -x = -3/2
=> -x = -1.5
=> x = 1.5 (By cancelling out the negative sign from both the sides)
c) 3(x-1) = 3 (1.5 - 1)
=> 3 (0.5)
=> 3 * 0.5 = 1.5
Both the angles are 1.5 because they are equal
If my answer helped, please mark me as the brainliest!!
Thank You!
A box of LED light bulbs was tested to see how long the light bulbs last. The standard deviation of the light bulb lifetime data was five years. Which of the following is the best interpretation of this value?
Fifty percent of the light bulb lifetime data is below five years.
The difference between the longest and shortest light bulb lifetime was five years.
The lifetime of the light bulbs typically varies by about five years from the mean.
The middle half of the light bulb lifetime data has a range that is five years wide.
Answers
The difference between the longest and shortest light bulb lifetime was five years is correct interpretation so option (B) will be correct.
What is the standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
In other meaning, standard deviation shows the deviation of the value of data from the mean.
Standard deviation is how much-given data is deviate from the mean of it.
So the difference between the longest to shortest gives an idea about this deviation.
Hence "The difference between the longest and shortest light bulb lifetime was five years is a correct interpretation".
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Could someone please help with this math problem??!
Answers
How could you informally prove to your friend that you have been working with a trainer at the gym.
You can show your gym bill.
You can show your membership card.
You can demonstrate some of the exercises that your trainer taught you.
You can show your before and after charts for your muscle mass.
Answers
Answer:
You can demonstrate some of the exercises that your trainer taught you
Step-by-step explanation:
The rest of the options are too formal.
You can demonstrate some of the exercises that your trainer taught you. The correct option is C.
what is convincing communication?Persuasive communications include a variety of attributes designed to increase persuasions, such as an appealing source, a message with convincing arguments, or efforts to make the topic seem personally relevant to the audience.
You can prove to your friend that you have been working with a trainer at the gym by demonstrating some of the exercises that your trainer taught you.
Therefore, you can demonstrate some of the exercises taught to you by your trainer. C is the correct answer.
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Two trees standing side by side in the sunlight one is 50 feet tall and the other is 20 feet tall if the taller tree casts a 18-foot shadow, what is the length in feet of the shadow of the shorter tree
Answers
Given:
Length of taller tree = 50 feet
Length of shorter tree = 20 feet
Length of shadow of taller tree = 18 feet
To find:
The length of shadow of shorter tree.
Solution:
Since, two trees standing side by side in the sunlight, therefore the length of trees are proportional to their shadows.
Let the length of shadow of shorter tree be x feet.
Using the given information, we get
[tex]\dfrac{50}{18}=\dfrac{20}{x}[/tex]
By cross multiplication, we get
[tex]50\times x=20\times 18[/tex]
[tex]50x=360[/tex]
[tex]x=\dfrac{360}{50}[/tex]
[tex]x=7.2[/tex]
Therefore, the length of shadow of shorter tree is 7.2 feet.
What is the justification for step 2 in the solution process?16-5x=1-4x; -5x=-4x-15; -x=-15
Answers
Answer:
Addition Property Of Equality
Step-by-step explanation:
The variable was isolated on the left side of the equation by adding 4x to both sides. This is justified by the addition property of equality.
Step 1: -5x = -4x -15
Step 2: -x = -15
Answer:
the addition property of equality
Step-by-step explanation:
The variable was isolated on the left side of the equation by adding 4x to both sides. This is justified by the addition property of equality.
WILL GIVE BRAINLIEST!! What is the y-intercept of a line that has a slope of 3 and passes through point (4, 8)?
Answers
Answer:
-4
Step-by-step explanation:
If we set up the equation with the known info, we get y=3x+b
We can then use the ordered pair to plug in, so 8=12+b
Now, simply solve for B, and you get -4
Can someone quickly help me solve this ?!
Answers
Answer: 8
Step-by-step explanation: if you count the angels and the sides then you'll get the answer 8..
Have a good date
a triangle with vertices at a 20 -30 b 10 -15. and c 5 -20 has beem dilated with a center of dilation at the origin the image of b point b has coordinates 2 -3 what is the scale factor of the dilation
Answers
Answer:
1/5
Step-by-step explanation:
When the dilation is centered at the origin, the dilation factor is applied to each pre-image coordinate to get the image coordinate.
k(10, -15) = (2, -3)
k = 2/10 = -3/-15 = 1/5
The scale factor of the dilation is 1/5.
Functions and their Properties
Practice
Need help
Answers
Answer:
[tex]g(n-7)=\frac{n^{2}-14n+43}{7n-49}[/tex] → (a)
Step-by-step explanation:
We need to evaluate g(n - 7), where
[tex]g(x)=\frac{x^{2}-7}{7x}[/tex]Replace x by (n - 7) to evaluate it
∵ x = (n - 7)
∴ [tex]g(n-7)=\frac{(n-7)^{2}-6}{7(n-7)}[/tex]
→ Let us find (n - 7)²
∵ (n - 7)² = (n - 7)(n - 7) = (n)(n) + (n)(-7) + (-7)(n) + (-7)(-7)
∴ (n - 7)² = n² + (-7n) + (-7n) + 49 = n² + -14n + 49
∴ (n - 7)² = n² - 14n + 49
→ Find 7(n - 7)
∵ 7(n - 7) = 7(n) - 7(7)
∴ 7(n - 7) = 7n - 49
→ Now let us write then in the form above
∵ [tex]g(n-7)=\frac{n^{2}-14n+49-6}{7n-49}[/tex]
→ Add the like terms in the numerator
∴ [tex]g(n-7)=\frac{n^{2}-14n+43}{7n-49}[/tex]
The correct answer is (a)
Beth bought 35¢ stamps and 15¢ stamps at the post office. If she purchased 60 stamps at a cost of $17, how many of each kind did she buy?
Answers
Answer:
She buys 20 Stamps of $0.15 and 40 Stamps of $0.35.
Step-by-step explanation:
40 x 0.35 = 14
20 x 0.15 = 3
$14 + $3 = $17
40 ($0.35) + 20 (0.15) = 60 stamps
Which of the following have a value equal to |37|? Select all that apply.
A. -37
B. 1-371
C. 0
D. -(-37)
E. 37
Answers
Answer:
a and e
Step-by-step explanation:
Answer:
A, D, and E
Step-by-step explanation:
Factor the following expression completely. 4b^8-61b^4+225
Answers
The average temperature at the South Pole is -49.62°C, and the average temperature at the North Pole is -34.68°C. How much higher is the average temperature at the North Pole than at the South Pole?
A.
-84.3°C
B.
-14.94°C
C.
14.94°C
D.
84.3°C
Answers
Answer:
i am pretty sure it's -14.92
Step-by-step explanation:
Answer:
B!!!
Step-by-step explanation:
