The mistake that Anja made during the simplification of the considered expression is given by: Option C: She subtracted the coefficients instead of dividing them
What are coefficients?Constants who are in multiplication with variables are called coefficients of those variables.
For example, in [tex]10x^2[/tex] we have 10 as coefficient of [tex]x^2[/tex]
Those variables who have got no visible coefficient has 1 as their coefficient. Thus, [tex]x^2[/tex] has got its coefficient as 1. It is true since 1 multiplied with any number is that number itself.( [tex]x^2 = 1 \times x^2[/tex] )
What are some basic properties of exponentiation?If we have [tex]a^b[/tex] then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c[/tex]
For the considered situation, the expression that Anja is simplifying is:
[tex]\dfrac{10x^{-5}}{-5x^{10}}[/tex]
Anja simplified it to [tex]\dfrac{15}{x^{15}}[/tex]
She performed operations with variable 'x' correctly since
[tex]\dfrac{x^{-5}}{x^{10}} = \dfrac{1}{x^5} \times \dfrac{1}{x^{10}} = \dfrac{1}{x^{15}}[/tex]
But coefficients will also get divided. Instead of dividing 10 by -5, she subtracted them (as 10 - (-5) = 10 + 5 = 15)
This was her mistake.
The correct simplification would be: [tex]\dfrac{10x^{-5}}{-5x^{10}} = \dfrac{10}{-5} \times \dfrac{x^{-5}}{x^{10}} = -2 \times \dfrac{1}{x^{15}} = \dfrac{-2}{x^{15}} = -2x^{-15}[/tex]
Thus, the mistake that Anja made during the simplification of the considered expression is given by: Option C: She subtracted the coefficients instead of dividing them
Learn more about exponent and bases here:
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Answer: c
Step-by-step explanation:
Half of the class scored above 78% and half of the class
scored below 78% on the Science test." Therefore, 78% is the....
Answer:
Median
Step-by-step explanation:
Answer:
78% is the median
Step-by-step explanation:
The median is the middle number in a sorted, ascending or descending, list of numbers
Help thanks 10 points <3
Answer:
Step-by-step explanation:there are 3 reds each so maybe try multipling those into the 12 for the red..it would look like this 6x12=72
and the do the same with the blue 4x6=24
Then we’ll try and add it together 72+24=96
what is the Lcm of 5 and 20
Answer:
♦LCM of 5 and 20 is 20.
Explanation:#Let's Study
#I Hope It's Help
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#Carry On Learning
The cafeteria sold 6 more turkey sandwiches than ham sandwiches. They sold 16 sandwiches in all. How many ham sandwiches did the cafeteria sell?
Answer:
5 ham sandwiches
Step-by-step explanation:
To find the number of ham sandwiches sold, we should find the pair of numbers that have a difference of 6 and add to 16.
1 ham sandwich, 7 turkey sandwiches = 8 sandwiches2 ham sandwiches, 8 turkey sandwiches = 10 sandwiches3 ham sandwiches, 9 turkey sandwiches = 12 sandwiches4 ham sandwiches, 10 turkey sandwiches = 14 sandwiches5 ham sandwiches, 11 turkey sandwiches = 16 sandwichesWhile this method isn't always very efficient, it worked pretty well for this case!
Therefore, the answer is 5 ham sandwiches.
Answer:
5
Step-by-step explanation:
11 and 5 have a 6 number gap between them 5 plus 11 gets you 16
Find the equation of the line through point (10,4) and parallel to 3x+5y=8. Use a slash ("/") for fractions (e.g. 1/2 for 12). DO not include spaces in your answers.
Answer:
3x + 5y = 50
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 5y = 8 ( subtract 3x from both sides )
5y = - 3x + 8 ( divide terms by 5 )
y = - [tex]\frac{3}{5}[/tex] x + [tex]\frac{8}{5}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{3}{5}[/tex]
Parallel lines have equal slopes , then
y = - [tex]\frac{3}{5}[/tex] x + c ← is the partial equation
to fid c substitute (10, 4 ) into the partial equation
4 = - 6 + c ⇒ c = 4 + 6 = 10
y = - [tex]\frac{3}{5}[/tex] x + 10 ← equation of parallel line in slope- intercept form
multiply through by 5 to clear the fraction
5y = - 3x + 50 ( add 3x to both sides )
3x + 5y = 50 ← equation of parallel line in standard form
Solution:
Step-1: Convert the equation of the line into slope intercept form.
3x + 5y = 8=> 5y = -3x + 8=> y = -3x/5 + 8/5In this case, the slope we obtained is -3/5, which is -0.6. Let's use point slope form to find the original equation.
Step-2: Use point slope form.
y - y₁ = m(x - x₁)=> y - 4 = -0.6(x - 10)=> y - 4 = -0.6x + 6=> y = -0.6x + 10If y varies inversely as x squaredand y = 6 when x = 30, what is y when x = 6? a. 216 b. 5 c. 180 d. 150.
Answer:
C
Step-by-step explanation:
Because i did it and got it right
James has $325 in his savings account. He spends $28 a week. How many, w, weeks until he has $157 left in his account?
Answer:
6 weeks
Step-by-step explanation:
Total savings= $325
For every week, his total savings decrease by $28.
Let's form an expression for the amount of money left in his account after w weeks.
325 -28w= 157
28w= 325 -157
28w= 168
Divide by 28 on both sides:
w= 168 ÷28
w= 6
Thus, there are 6 weeks until he has $157.
The hexagonal prism below has a base area of 25 units? and a height of 13 units. Find
its volume.
The volume of the hexagonal prism is the amount of space in the prism
The volume of the hexagonal prism is 325 cubic units
How to determine the volume?The given parameters are:
Base area = 25 square units
Height = 13 units
The volume is then calculated as:
Volume = Base area * Height
So, we have:
Volume = 25 * 13
Evaluate the product
Volume = 325
Hence, the volume of the hexagonal prism is 325 cubic units
Read more about volumes at:
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Answer:
Step-by-step explanation:
I need help
Trish is going to camp for 50 days on 15 July 2022. Calculate the date when he will return from camp
Answer:
Trish is going to return from camp September 3rd, 2022.
Step-by-step explanation:
Okay! note: (There are 31 days in july)
July 15th+10 days=July 25th
July 25+6=July 31st
July 31st+1 day= August 1st
(17 days done so far)
August 1st+30 days=August 31st
(47 days done)
August 31st+1 day=September 1st
September 1st+2 days= September 3rd
I got the answer by breaking up the 50 days into smaller parts and adding them. Make sure you know how many days are in the months so you don't get too confused.
1 inch = 2.54 cm
=
How many cm. are in 1/4 in.?
Answer:
0.635 in
Step-by-step explanation:
Divided 2.54 by 4
has anyone taken Module Six Project Option 1
Answer:
depends on the grade level ._.
Step-by-step explanation:
cuz i only am good at 9-11th grade math T-T
Can someone help me please??
The circumference of a circle is its perimeter.
We can solve for the circumference using the following formula:
[tex]C=2\pi r[/tex] where r is the radius of the circleSolving the QuestionPart AWe're given:
The radius of the circle is 14 cmPlug the given information into the formula for circumference:
[tex]C=2\pi r\\C=2\pi (14)\\C=28\pi[/tex]
Therefore, the circumference of the circle is 28π cm.
Part BReplace π with [tex]\dfrac{22}{7}[/tex]:
[tex]C=28\pi\\\\C=28*\dfrac{22}{7}\\\\C=4*22\\C=88[/tex]
Therefore, the circumference of the circle with [tex]\pi=\dfrac{22}7}[/tex] is 88 cm.
WHat is this how do i do this
Every month, Tara writes a cheque for $25 to pay off part of a loan. She has enough in her current account to pay no more than $450 towards the loan. Write and solve an inequality to find how many months can Tara send payments for the loan
The number of months that tara can send her payments for the Loan is; 18 months
How to find the time period of a Loan?
We are told that;
Tara has to pay $25 each month to pay the loan.
She has $ 450 in her account to pay the loan.
For us to find the number of months she can pay the loan, we will apply the unitary method as;
$25 she can pay in 1 month
The number of months to pay $1 is; 1/25 months
The number of months to pay $450 is; (1/25) * 450 = 18 months.
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The length of a rectangle is 10 m greater than the width, and the area is 600 sq. m. Find the dimensions
Step-by-step explanation:
l = length
w = width
l = w + 10
l×w = 600 m²
now, using the identity of the first equation in the second equation
(w + 10)×w = 600
w² + 10w = 600
w² + 10w - 600 = 0
the general solution to such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 1
b = 10
c = -600
w = (-10 ± sqrt(10² - 4×1×-600))/(2×1) =
= (-10 ± sqrt(100 + 2400))/2 = (-10 ± sqrt(2500))/2 =
= (-10 ± 50)/2 = -5 ± 25
w1 = -5 + 25 = 20 m
w2 = -5 - 25 = -30
the negative solution does not make any sense for side lengths. so, the only valid solution is w = 20 m.
l = w + 10 = 20 + 10 = 30 m
the length is 30 m.
the width is 20 m.
Solve in simplest radical form
45+90+unknown=180
135+u=180
u=45
so that,
x=15
Answer:
Step-by-step explanation:
The ratio of sides of 45 - 45 -90 triangle is
1 : 1 : √2
This is an isosceles triangle. So, the sides opposite to equal angles (45°) are equal.
∵ x = 15
Three students made videos for their art project. The table shows the length of each video. How much longer is video 1 than video 3?
Answer:
ok
Step-by-step explanation:
does it come with the picture??
Please help... need steps
[tex]log16^{n} =log\frac{1}{64}[/tex]
Answer:
x = -3/2
Step-by-step explanation:
1. Cancel out log from both sides -> 16^n = 1/64
2. Log16 both sides to isolate n -> log16(16^n) = log16(1/64) -> n = log16(1/64)
log16(1/64) = -3/2
Mary has 12 marbles 3/12 of the marbles are yellow 2/12 of the Marvels are blue The rest of the marbles are green How many marbles are green Explain how you know
Answer: 7 marbles are green.
Step-by-step explanation:
Since we have 12 marbles in total, 12/12 = 1. Since the fractions have denominators of 12 as well, we can easily tell there are 3 yellow marbles (3/12) and there are 2 blue marbles (2/12).
Lastly, we need to find how many are green. We can subtract the yellow and blue marbles from the total of 12 marbles.
12 - (3 + 2)
12 - (5)
7 marbles are green.
Answer:
Seven marbles are green.
Step-by-step explanation:
you have a total of 12 marbles.
12-3 (yellow) = 9
9-2 (blue) = 7
3 (yellow) + 2 (blue) = 5
12 (total) - 5 (yellow and blue) = 7
What is the missing number in this pattern?
1,1….3,5,8,13,21
Answer:
34
Step-by-step explanation:
I have done this before
I will give brainliest fast please I will give points please explain well
If the equal is 55x + 35y = 200
x: time-driven at 55 miles/hour
y: time-driven at 35 miles/hour
If the car spends 2.5 hours at 35 miles per hour, then it drove:
55x + 35(2.5) = 200
55x =35
y = 112.5
There the drive spent about 2.5-hour driving at 55 mph.
Hope it helps!
A triangle has two sides of length 2 and 14. What is the largest possible whole-number length for the third side?
Answer:
15
Step-by-step explanation:
Note that;
The sum of the lengths of 2 sides of a triangle must be greater than but not equal to the length of the third side.
As well as, the third side must be longer than the difference between the greater and the lesser of the other two sides
Given;
First side of the triangle = 17
Second side of the triangle = 2
Let us assume the third side of the triangle = T
Now, In any given triangle:
"Sum of any two sides of a triangle is strictly greater than the third side."
⇒ Sum of first side + Sum of second side > Third Side
or, m < 2 + 14
or, m < 16
Hence, the largest possible value for m = 15
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Which features of figure JKLM remain the same after any rigid transformation? I-ready
Answer: size and shape
Step-by-step explanation:i got it right on the quiz
The features of figure JKLM that would be preserved after any rigid transformation are: its shape and size.
What is a Rigid Transformation?A rigid transformation, include the following forms of transformations that preserves the size and size of the orginal figure before transformation: translation, reflections, and rotations.
The shape and size of a fugure are preserved after a rigid transformation.
Therefore, the features of figure JKLM that would be preserved after any rigid transformation are: its shape and size.
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Lashawn makes scrambled eggs with 333 spoonfuls of salsa for every 222 eggs. Gilberta adds 777 spoonfuls of salsa for every 555 eggs.
Whose scrambled eggs have a stronger salsa taste?
Answer:
Lashawn
Step-by-step explanation:
333/222=1 1/2part salsa per egg - Lashawn
777/555= 1 2/5 part salsa per egg - Gilberta
1 1/2 is greater than 1 2/5
Mr. Hayden's Bible class collected $11
in coins for a needy family. They col-
lected twice as many quarters as dimes
and 12 more nickels than dimes. How
many of each coin did the class collect?
This is the only way I can think of this mathematically. This took a good 20 minutes for me. You need to guess and check. Like try 17 quarters, 50 nickels, and 37 dimes etc. until you get 11.00. My numbers are mathematically correct but we both know you cant have 18.909 quarters so. lol
Answer:
Quarters: 18.909
Nickels: 49.818
Dimes: 37.818
Somewhere around those numbers.
Step-by-step explanation:
$11.00 total in coins
Nickel = $0.05
Dime = $0.10
Quarter = $0.25
(n*0.05) + (d*0.10) + (q*0.25)
Solve the equation for q.
[tex]q=\frac{1}{2} d[/tex]
(n*0.05) + (d*0.10) +( [tex]\frac{1}{2} d[/tex] *0.25)
Simplify the expression.
9d + 2n = 440
d - n = -12
Multiply both sides of the equation by -9.
-9d + 9n = 108
9d + 2n = 440
Sum the equations vertically to eliminate at least one variable.
11n = 548
[tex]n=\frac{548}{11}[/tex]
Substitute the given value of n into the equation d - n = -12
[tex]d-\frac{548}{11} =-12[/tex]
[tex]d=\frac{416}{11}[/tex]
Substitute the given value of n into the equation [tex]q=\frac{1}{2} d[/tex]
[tex]q=\frac{1}{2} *\frac{416}{11}[/tex]
[tex]q=\frac{208}{11}[/tex]
Finally
[tex]d=\frac{416}{11}[/tex] d = 37.818
[tex]n=\frac{548}{11}[/tex] n = 49.818
[tex]q=\frac{208}{11}[/tex] q = 18.909
Can anyone solve these with work attached
(just take a picture of work it would be highly appreciated)
Answer:
Step-by-step explanation:
Answers in the order as shown
34
20
8
55
29
28
50
61
4
60
What is the equation of the line that passes through
the points (-0.25, -2) and (0.75, -4)?
Answer: y=-2x-2.5
Step-by-step explanation:
Executives for a car dealership are interested in the sales for the type of vehicle, SUV or truck, and the type of power train, two-wheel drive (2WD), four-wheel drive (4WD), or all-wheel drive (AWD). The data from the
sales of 165 vehicles are displayed in the two-way table.
A vehicle is randomly selected. Let S be the event that
the vehicle is an SUV and let D be the event that the vehicle has 4WD. What is the value of P(S and Dc)?
O 0.04
O 0.23
O 0.38
O 0.41
Assuming S is the event that the vehicle is an SUV the value of P(S and D) is:0.38.
ProbabilityNumber of vehicles=165
Total number of SUV=10+23+52=85
Hence:
The event that vehicle is SUV(S)=85
The event that vehicle is 4WD(D)=23
Value of P(S and D)=85-23/165
Value of P(S and D)=62/165
Value of P(S and D)=0.375
Value of P(S and D)=0.38 (Approximately)
Inconclusion the value of P(S and D) is:0.38.
Learn more about probability here:https://brainly.com/question/24756209
Answer:
c) 0.38
Step-by-step explanation:
just answered it
How many times do 18 go into 70?
⇒ Answer
⇒ Answer
⇒ Answer
⇒ Answer
⇒Answer
Answer:
3 (if it has to be a whole number)
Step-by-step explanation:
70/18 is approximately 3.89
What is the value of x?
x
21.5
13.1
Round your final answer to the nearest tenth.
Use the Pythagorean theorem