Stacy is playing hide-and-seek with Austin and Christopher. Austin is hiding 12 meters south of Stacy, and Christopher is hiding 5 meters east of Austin. How far apart are Stacy and Christopher?
Answers
Answer:
Stacy is 13 meters apart from Christopher.
Step-by-step explanation:
Given:
Austin is hiding 12 meters south of Stacy.
Christopher is hiding 5 meters east of Austin.
To find distance between Stacy and Christopher.
Solution:
From the given data, we will trace the positions of each as shown in the figure below.
We find that the distance between Stacy and Christopher is the hypotenuse side of a right triangle formed by their positions.
By Pythagorean theorem:
[tex]Hypotenuse^2=Leg1^2+Leg2^2[/tex]
From the triangle:
Leg 1 = 5 meters
Leg 2= 12 meters
Plugging in the values.
[tex]Hypotenuse^2=5^2+12^2[/tex]
Simplifying.
[tex]Hypotenuse^2=25+144[/tex]
[tex]Hypotenuse^2=169[/tex]
Taking square root both sides.
[tex]\sqrt{Hypotenuse^2}=\sqrt{169}[/tex]
[tex]Hypotenuse=13[/tex] meters
Thus, distance between Stacy and Christopher = 13 meters
Stacy and Christopher are 13 meters apart. This was calculated using the Pythagorean theorem to find the hypotenuse of a right triangle with sides 12 meters and 5 meters.
To determine the distance between Stacy and Christopher, we need to view Stacy's location and the hiding places of Austin and Christopher as points on a grid in which Stacy is at the origin. Since Austin is hiding 12 meters south of Stacy, we can consider him to be at point A(0, -12). Christopher is hiding 5 meters east of Austin, this makes him at point C(5, -12).
Now, to find the distance between Stacy and Christopher, we'll use the Pythagorean theorem which says that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:
C² = A² + B²
Where C is the hypotenuse, A and B are the other two sides of the triangle. In this case, A is the distance south (12 meters) and B is the distance east (5 meters). Thus,
C² = 12² + 5²
C² = 144 + 25
C² = 169
C = √169
C = 13 meters
Therefore, Stacy and Christopher are 13 meters apart.
Related Questions
help pleaseeeeeeeee
Answers
Answer:
No, we can't.
Step-by-step explanation:
Let x be the amount of time it takes each machine to make 1 cockpit, and y be the amount of time it takes each machine to make 1 propulsion system.
For machine A: 22 hours to produce 3 cockpits and 5 propulsion system.
For machine B: 44 hours to produce 6 cockpits and 10 propulsion system.
So, this will produce the following system of equations:
3x + 5y = 22 ⇒(1)
6x + 10y = 44 ⇒(2)
We can note that the second equation is two times the first equation.
So, the two equation are actually represent one equation.
OR, by another way the two equation have the same slope and y-intercept
So, the two equation are identical, therefore, we can't solve one equation with two variables.
Also, see the attached figure.
equation (1) with blue color and the second equation with red color.
7x-7(x+6)=10
B=infinite
C=no solution
D=x=2/7
A=3/5/7
Answers
Answer:
No solution
Step-by-step explanation:
we have
[tex]7x-7(x+6)=10[/tex]
Solve for x
Apply distributive property left side
[tex]7x-7x-42=10[/tex]
Combine like terms left side
[tex]-42=10[/tex] ----> is not true
therefore
The equation has no solution
There are 110 students in the 6th grade band and 120 students in the 7th grade band. Of the students, 60% of the 6th grade band members and 85% of the 7th grade band members went on a trip Disney World trip. How many more 7th graders went on the trip than 6th graders?
Answers
Answer:
36 more students of grade 7 went on a trip than students of grade 6
Step-by-step explanation:
60 % of 110 students= 60/100*110= 66 students
85 % of 120 students= 85/100 * 120= 102 students
No of students of grade 7th more than 6th grade students= 102-66= 36
60% of the 6th grade band members and 85% of the 7th grade band members went on a trip Disney World trip. Then 36 more 7th graders went on the trip than 6th graders
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The number of students in 6th grade=100
The number of students in 7th grade=120
60% of the 6th grade band members
60%×110
60/100×110=0.6×110=66
85% of the 7th grade band members
85%×120=85/100×120
=0.85×120=102
We need to find how many more 7th graders went on the trip than 6th graders
For this we need to find difference of 7th and 6th grade
102-66=36
Hence 36 more 7th graders went on the trip than 6th graders
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ6
Rena evaluated 3/4 ÷ 2/5 and got an answer of 1 7/8. Which statement is true about her answer
Answers
Rena's answer is correct.
To evaluate whether Rena's answer is correct, we need to perform the division of the two fractions 3/4 and 2/5. To divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator.
Here is a step-by-step solution:
Step 1: Write down the problem.
\[ \frac{3}{4} \div \frac{2}{5} \]
Step 2: Find the reciprocal of the second fraction.
The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \).
Step 3: Multiply the first fraction by the reciprocal of the second.
\[ \frac{3}{4} \times \frac{5}{2} \]
Step 4: Multiply the numerators together and the denominators together.
\[ \frac{3 \times 5}{4 \times 2} \]
\[ \frac{15}{8} \]
Step 5: Simplify the fraction if necessary.
In this case, \( \frac{15}{8} \) is an improper fraction because the numerator is larger than the denominator. We can convert it into a mixed number.
The whole number part of the mixed number is obtained by dividing the numerator by the denominator:
\[ 15 \div 8 = 1 \text{ with a remainder of } 7 \]
So, the mixed number is \( 1 \frac{7}{8} \).
Conclusion:
Rena's answer of \( 1 \frac{7}{8} \) is correct. The statement about her answer is true; she correctly evaluated the division of \( \frac{3}{4} \) by \( \frac{2}{5} \).
Use the table of net profits and losses to find the net profit for the week.
Bert's Catering Service
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
$200 –$130 –$25 $240 $225 –$100 $75
$485
–$485
$5
$335
Answers
Your answer is A. $485
200 – 130 = 70
70 – 25 = 45
45 + 240 = 285
285 + 225 = 510
510 – 100 = 410
410 + 75 = 485
Two fire hoses are used to extinguish a fire. Hose A, when turned on alone, can extinguish the fire in 7 minutes, while hose B takes "n" minutes more time than hose A. Find an expression (in terms of "n") for how much of the fire they will extinguish in 1 minute when both hoses are turned on together.
Answers
The expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is [tex]\frac{n + 14}{7n + 49}[/tex]
Solution:
Given that,
Hose A, when turned on alone, can extinguish the fire in 7 minutes
Hose B takes "n" minutes more time than hose A
Hose takes (n + 7) minutes to extinguish the fire
STEP 1: Calculate how much work (here work is to extinguish the fire) each person does in one minute
[tex]Hose A = \frac{1}{7}th \text{ of the work }\\\\Hose B = \frac{1}{n+7}th \text{ of the work }[/tex]
STEP 2: Add up the amount of work done by each person in one minute
Work done in one minute when both are working together:
[tex]\rightarrow \frac{1}{7} + \frac{1}{n + 7}\\\\\rightarrow \frac{n + 7 + 7}{7n + 49}\\\\\rightarrow \frac{n + 14}{7n + 49}[/tex]
Therefore, the expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is:
[tex]\frac{n + 14}{7n + 49}[/tex]
The total rate in 1 minute is [tex]\frac{1}{7} + \frac{1}{7+n}[/tex].
To find the expression for how much of the fire they will extinguish in 1 minute when both Hose A and Hose B are turned on together, we need to determine their individual rates first.
Hose A can extinguish the fire in 7 minutes, so its rate is:
⇒ Rate of Hose A = 1 fire ÷ 7 minutes = [tex]\frac{1}{7}[/tex].
Hose B takes 'n' minutes more than Hose A. Therefore, it takes (7 + n) minutes to extinguish the fire, so its rate is:
⇒ Rate of Hose B = 1 fire ÷ (7 + n) minutes = [tex]\frac{1}{7+n}[/tex].
When both hoses are operating together, their combined rate is the sum of their individual rates:
⇒ Combined Rate = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]
We need the combined rate per minute:
⇒ Combined Rate per Minute = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]
This fraction represents the portion of the fire they will extinguish in 1 minute when both hoses are used together.
Which system of equations has no solutions
A. 3x + 4y = 5
6x + 8y = 10
B. 7x - 2y = 9
7x - 2y = 13
C. 2x - y = -11
-2x + y = 11
D. 3x + 6y = 1
x + y = 0
Answers
Answer:
Step-by-step explanation:
3x+4y=5
6x+8y=10
---------------
-2(3x+4y)=-2(5)
6x+8y=10
----------------
-6x-8y=-10
6x+8y=10
------------------
0=0
Answer: Infinitely many solutions.
------------------------------------------------------
7x-2y=9
7x-2y=13
--------------
-1(7x-2y)=-1(9)
7x-2y=13
---------------------
-7x+2y=-9
7x-2y=13
-------------
0=4
Answer: NO Solution.
-------------------------------------
2x-y=-11
-2x+y=11
-----------------
0=0
Answer: Infinitely many solutions.
-----------------------
3x+6y=1
x+y=0
x=0-y=-y
3(-y)+6y=1
-3y+6y=1
3y=1
y=1/3
x=-y=-1/3
Answer: x=-1/3, y=1/3. (-1/3, 1/3).
Answer:69
Step-by-step explanation:
69
If g(x) is the inverse of f(x) and S(x) = 4x+12, what is g(x)?
g(x) = 12x + 4
g(x) = 4x12
g(x) = x= 3
8(t) = 1x-3
Answers
Answer:
[tex]g(x)=\frac{1}{4}x-3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=4x+12[/tex]
Find the inverse
step 1
Let
y=f(x)
[tex]y=4x+12[/tex]
step 2
Exchange the variables (x for y and y for x)
[tex]x=4y+12[/tex]
step 3
Isolate the variable y
we have
[tex]x=4y+12[/tex]
Subtract 12 both sides
[tex]x-12=4y[/tex]
Divide by 4 both sides
[tex]y=\frac{x-12}{4}[/tex]
simplify
[tex]y=\frac{1}{4}x-3[/tex]
step 4
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=\frac{1}{4}x-3[/tex]
we have that
[tex]g(x)=f^{-1}(x)[/tex]
therefore
[tex]g(x)=\frac{1}{4}x-3[/tex]
solving eqations
4c=16
Answers
Answer:
c=4
Step-by-step explanation:
Answer:
C=4
Step-by-step explanation:
when solving these equations you have to get the letter by itself and in this case the 4 is being multiplied by the c so you have to do the opposite and divide the 4 from the c and divide 16 by 4 because what you do to one side of the equal sign you have to do to the other side.
What is 9 divided by 883
Answers
How:
i used a calculator
1. You have a 20 foot long ladder that you want to lean against a vertical wall. You want the top of the ladder to touch the wall 19 feet off the ground. What angle will the ladder form with the ground?
2. Using the same 20 foot ladder against the same vertical wall, you decide that it would be better if the ladder formed a 70 degree angle with the ground. How far up the wall will the top of the ladder reach?
3. You want to find the area of triangle BCD but all you have is the information provided in the image below. Then you realize you can use the special right triangle (30-60-90) to find the height of the triangle. Once you know the height and provided base measurement calculate the area.
What is the area of the triangle? Show all steps.
Answers
Answer:
1. The ladder forms 71.8° with the ground.
2. The top of the ladder will reach 18.79 feet up the wall.
3. Height = 8.66 cm and area = 21.65 sq. cm.
Step-by-step explanation:
1. If the angle of elevation of the ladder is [tex]\theta[/tex] then we can write
[tex]\sin \theta = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{19}{20}[/tex]
⇒ [tex]\theta = \sin ^{-1}(\frac{19}{20}) = 71.8[/tex] Degrees.
Therefore, the ladder forms 71.8° with the ground. (Answer)
2. Now, if the ladder formed a 70 degree angle with the ground and the length of the ladder remains the same as 20 feet, then we can write
[tex]\sin 70 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{x}{20}[/tex]
⇒ x = 20 sin 70 = 18.79 feet.
Therefore, the top of the ladder will reach 18.79 feet up the wall.
3. See the attached figure.
We have, [tex]\tan 60 = \frac{BC}{CD} = \frac{BC}{5}[/tex]
⇒ Height = BC = 5 tan 60 = 8.66 cm.
Therefore, the area of the triangle BCD will be = [tex]\frac{1}{2} \times CD \times BC = \frac{1}{2} \times 5 \times 8.66 = 21.65[/tex] sq. cm. (Answer)
Solve for x.
2х2-4х = 0
Answers
Step-by-step explanation:
2x²-4x=0
2x²=4x
[tex] \frac{2x {}^{2} }{x} = 4[/tex]
2x=4
x=2
PLEASE DO THIS AND I WILL GIVE YOU BRAINLIEST AND ALOT OF POINTS ALSO DONT JUST DO THIS FOR THE POINTS OR YOU WILL BE REPOTED AND ALL ADMINS ARE ONLINE THANK YOU!
Answers
Answer:
16. Disagree because 0.1 0f 0.1 is 0.01
17. the whale swam for 19 to 21.7 hours. Because 152/8=19 and 152/7=21.7
18. Meg can use 15,000 / 50 because 14,270 rounded up to by the thousand will be 15,000.
19. 61.5 because 3016/7 = 430.8 430.8/7=61.5
Step-by-step explanation:
Find the product of 400 and 9.460730473 times 10/15
Answers
Final answer:
To find the product, multiply 400 by 9.460730473, then multiply the result by 2/3.
Explanation:
To find the product of 400 and 9.460730473 times 10/15, we need to multiply the three numbers together. First, let's simplify 10/15 to 2/3. Then, multiply 400 by 9.460730473 to get the product. Finally, multiply the result by 2/3 to find the final answer.
400 x 9.460730473 = 3784.2921892
3784.2921892 x 2/3 = 2522.8614595
The product of 400, 9.460730473, and 10/15 is approximately 2522.8614595.
A students cost for last semester at her community college was $2800. She spent $504 of that on books. What percent of last semesters college cost was spent on books
Answers
Answer: 18%
Step-by-step explanation:
The percentage spent on book = cost of books / total cost x 100
% spent on book = 504/2800 x 100
= 18
Therefore , the percentage spent on book is 18
Solve the system: x + 2 = y ,x2 − 10 = y
Answers
Answer:
If you wanted the intersecting points there is only one and It's (12, 14)
Hope that could help.
Find two consecutive integers whose
Sum is 93.
Answers
Answer:
46 and 47.
Step-by-step explanation:
If x is one of the integers then the other is x+1.
x + x + 1 = 93
2x = 92
x = 46.
Use the figure below.
Which best describes the pair of angles:
24 and 25?
A. vertical
B. adjacent
C. linear pair
D. complementary
Answers
Answer: B. Adjacent
Step-by-step explanation: They share a common side and vertex
Order from least to greatest.
5
12
,
2
3
,
1
2
,
5
6
,
3
4
A)
3
4
,
5
6
,
2
3
,
1
2
,
5
12
B)
5
12
,
1
2
,
2
3
,
3
4
,
5
6
C)
1
2
,
2
3
,
3
4
,
5
6
,
5
12
D)
1
2
,
2
3
,
5
6
,
3
4
,
5
12
Answers
the answer is c
Step-by-step explanation:
12
23
34
56
512
the answer is c
Step-by-step explanation:
12
23
34
56
An advertisement consists of a rectangular printed region plus 5-cm margins on the sides and 6-cm margins at top and bottom. If the area of the printed region is to be 238 cm2, find the dimensions of the printed region that minimize the total area. Printed region: l = , w =
Answers
Answer:
Dimensions of printed area
x = 7.58 the length
y = 31.40 cm the height
Step-by-step explanation:
Printed region P(a) = 238 cm²
Let call x and y dimensions of printed area then:
A = 238 = x*y ⇒ y = 238/x
And the area of the advertisement is
A(a) = L * W where L = x + 6 and W = y + 5
A(x) = (x + 6 ) * ( y + 5 )
Area as a function of x y = 238/ x
A(x) = (x + 6 ) * ( 238/x + 5 )
A(x) = 238 + 5x + 1428/x + 30
A(x) = 268 + 5x + 1428/x
Taking derivatives on both sides of the equation
A´(x) = 5 - 1428/x²
A´(x) = 0 ⇒ 5x² = 1428 ⇒ x² = 57.12
x = 7.58 cm and y = 238/ 7.58 y = 31.40 cm
Use substitution to solve the system of equations.
y + x = 3
y = 1.5x + 1
Answers
Answer:
x=0.8, y=2.2 (0.8, 2.2).
Step-by-step explanation:
y+x=3
y=1.5x+1
-------------
1.5x+1+x=3
2.5x=3-1
2.5x=2
x=2/2.5
x=0.8
y+0.8=3
y=3-0.8
y=2.2
To solve the given system of equations by substitution, we substitute the second equation into the first, solve for x, and then substitute x back into the second equation to solve for y, which yields x=0.8 and y=2.2 as the solution.
Explanation:To solve the system of equations using substitution, we start by isolating one variable in one of the equations. Here, the second equation already gives us y in terms of x: y = 1.5x + 1.
Next, we substitute this expression for y into the first equation y + x = 3. This gives us:
(1.5x + 1) + x = 3Combine like terms to solve for x:
2.5x + 1 = 32.5x = 2x = 0.8Now that we have the value of x, we can find the value of y by substituting x back into the equation y = 1.5x + 1:
y = 1.5(0.8) + 1y = 2.2Hence, the solution to the system of equations is x = 0.8 and y = 2.2.
As a final step, you may want to check your solution by plugging the values back into the original equations to confirm that they satisfy both equations.
how do i figure out 9 1/6 - 8 5/6
and 10 3/4 - 6 4/4?
Answers
Answer:
1) [tex]9\frac{1}{6}-8\frac{5}{6}=\frac{1}{3}[/tex]
2) [tex]10\frac{3}{4}-6\frac{4}{4}=3\frac{3}{4}[/tex]
Step-by-step explanation:
You can convert he mixed numbers to improper fractions:
1. Multiply the whole number part by the denominator of the fraction.
2. Add the product obtained to the numerator.
3. The denominator does not change.
Then:
[tex]9\frac{1}{6}=\frac{54+1}{6}=\frac{55}{6}\\\\8\frac{5}{6}=\frac{48+5}{6}=\frac{53}{6}\\\\10\frac{3}{4}=\frac{40+3}{4}=\frac{43}{4}\\\\6\frac{4}{4}=\frac{24+4}{4}=\frac{28}{4}[/tex]
Observe that, in each subtraction, the denominators are equal, then you can rewrite the denominator and subtract the numerators:
[tex]1)\ \frac{55}{6}-\frac{53}{6}=\frac{55-53}{6}= \frac{2}{6}=\frac{1}{3} \\\\2)\ \frac{43}{4}-\frac{28}{4}=\frac{43-28}{4}= \frac{15}{4}[/tex]
Divide 15 by 4. The quotient will be 3 and the remainder 3.
Then:
[tex]\frac{15}{4}=3\frac{3}{4}[/tex]
Make a conjecture about the diagram below. Do you think you can conclude that △JKL ≅ △XYZ? Explain your reasoning.
Answers
Answer:
△JKL ≅ △XYZ by HL congruency for right triangles
Step-by-step explanation:
If only given two sides and an uncontained angle, the triangles may not necessarily be congruent. However, since the given angle is a right angle, they are congruent.
When given that the hypotenuse and any "leg" of the right triangles are equal, the triangles are congruent.
Since one angle is 90°, the other two angles must be acute. This is unlike the ambiguous case when given an uncontained acute angle, where two possible triangles can be made by making another angle obtuse.
Imagine an isosceles triangle cut in half at the altitude, creating two right triangles (JKL and XYZ). They have the same angle measures. Each with a right angle, the angle that had an equal measure in the isosceles, and the unequal angle bisected. For the triangles' sides, the isosceles base was bisected by the altitude, and they have the same altitude.
An equation is given
2Vx+ 7 = 8
Enter the value of x for this equation.
Answers
Answer:
x = 1
----------
82V
Step-by-step explanation:
what is the correct answer to the question
Answers
Answer:
4.37%
Step-by-step explanation:
Given: Value of object in 1997 is $5000
Value of object in 2012 is $4500.
Number of years (2012-1997)= 15 years
∵We know that there is growth in value of object over multiple years.
∴Compound annual growth rate (CAGR)= [tex][(\frac{end\ value}{initial\ value} )^{\frac{1}{n} } ] -1[/tex]
Remember, n = number of years
∴ Growth rate= [tex][(\frac{9500}{5000} )^{\frac{1}{15} } ]-1[/tex]
⇒Growth rate= [tex][(1.9)^{\frac{1}{15} } -1][/tex]
⇒Growth rate= [tex](1.9)^{0.0667} -1= 1.0437-1[/tex]
⇒ Growth rate= 0.0437
Now, finding percentage of growth rate
∴ [tex]0.0437\times 100= 4.37\%[/tex]
∴ Annual growth percent over the period of time is 4.37%
Express your answer in scientific notation.
2.8\cdot10^{-3} -0.00065 =2.8⋅10
−3
−0.00065=2, point, 8, dot, 10, start superscript, minus, 3, end superscript, minus, 0, point, 00065, equals
Answers
Answer:
2.15
×
10
−
3
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
The answer is 2.15 * 10^-3
Step-by-step explanation:
I got this answer from Khan Academy.
Hope this helps! :)
Approximately how many times greater is 2.3x10^-4 than 1.15x10^-8 ?
A: 115
B:200
C:11,500
D:20,000
Answers
Answer:
2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex]
Step-by-step explanation:
Given as :
The first number= x = 2.3 × [tex]10^{-4}[/tex]
The second number= y = 1.15 × [tex]10^{-8}[/tex]
Let The first number is z times greater than second number
i.e x = z × y
Or, z = [tex]\dfrac{x}{y}[/tex]
Or, z = [tex]\dfrac{2.3\times 10^{-4}}{1.15\times 10^{-8}}[/tex]
Or, z = 2 × [tex]10^{4}[/tex]
∴ z = 20,000
So,The first number is 20,000 times greater than second number
Hence, 2.3 × [tex]10^{-4}[/tex] is 20,000 times greater than 1.15 × [tex]10^{-8}[/tex] . Answer
what is 85% written as a decimal and as a fraction
Answers
Answer:
.85 or 85/100
Step-by-step explanation:
Answer:
0.85 is your decimal. 85 / 100 - not simplified.
17 / 20 - simplified.
Step-by-step explanation:
For the decimal, all you gotta do is move your decimal to the left 2 times.
-Hope this helps.
For the fraction, 85% is per 100, so it's 85 / 100. To simplify, the answer is 17 / 20.
Mai biked 7 and 1/4 miles today, and Noah biked 3 5/8 miles. How many times the length of Noah's bike ride was Mai's bike ride?
answer choices
2/3
2
1/2
3/2
Answers
Answer:
2 times
Step-by-step explanation:
Mai biked [tex]7\frac{1}{4} = \frac{29}{4}[/tex] miles today and Noah biked [tex]3\frac{5}{8} = \frac{29}{8}[/tex] miles today.
We are asked how many times the length of Noah's bike ride was Mai's bike ride.
Therefore, the length of Mai's bike ride was [tex](\frac{29}{4} \div \frac{29}{8}) = 2[/tex] times the length of Noah's bike ride.
Therefore, we will take option B will be correct. ( Answer )
Please Help!!! I can't understand the question please someone help me!
Answers
Answer:
a. true
b. false
c. true
d. false
Step-by-step explanation:
a. A product raised to a power is equivalent to each of the multiplicand raised to that power as well. Example:
(xyz)ⁿ = xⁿyⁿzⁿ
(1·3·7)² = 1²(3²)(7²)
b. Is wrong. When you have addition/subtraction inside a parentheses, you have to foil. Example:
(a + b)² = (a + b)(a + b)
= a² + 2ab + b²
(1 + 3)² = (1 + 3)(1 + 3)
= 1² + 2(1)(3) + 3²
= 16
c. Numbers with the same root can be merged when you're multiplying/dividing them. Example:
√(a)√(b) = √(ab)
√(2)√(3) = √(2·3) = √(6)
d. You can only merge or split the root when multiplying/dividing.
You CANNOT merge the root when adding/subtracting.
√(a ± b) ≠ √(a) + √(b), this is NOT allowed
e. I already gave examples in the previous parts.