PLEASE HELP!! 2. Helen and Stephen both simplify the exponential expression .
Helen:
Stephen:
Unfortunately, they both made an error. Identify where each person made his or her error and explain in words what he or she did wrong. Then, correctly simplify the expression.
Answers
Answer:
We start with the expression:
exp( (4/3)*ln(2) - 1)
Here we can use that:
exp(ln(x)) = x.
and e^(a + b) = e^a*e^b.
the first step here is:
e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)
So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.
now, we have that:
a*ln(x) = ln(x^a)
then we can write:
(4/3)*ln(2) = ln(2^(4/3))
and e^(ln(2^(4/3)) = 2^(4/3)
then we have:
e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e
now we can write this as:
∛(2^4)/e
here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.
so the expression actually is:
∛(16)/e
Related Questions
Solve by completing the square: 5x2 + 20x + 32 = 0
Answers
first, you divide all sides by five and then take b, half it then square it
–9(w + 585) = –360 w = ______
Answers
Answer:
w = 15
Step-by-step explanation:
-9(w + 585) = -360w
-9w -5265 = -360w
351w = 5265
w=15
Explanation:
Find w :
-9(w + 585) = -360w
-9w - 5265 = -360w
-5265 = -351w
15 = w
Now let’s plug in w in -360w
-360 x 15 = -5400
Which function is graphed below?
Answers
Answer:
Piecewise function;
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Step-by-step explanation:
Function graphed represents the piecewise function.
1). Equation of the line with y-intercept (-2) and slope 'm'.
Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
= 2
Therefore, equation of this segment will be in the form of y = mx + b,
⇒ y = 2x - 2 where x < 2
2). Equation of a horizontal line,
y = 4 where 2 ≤ x ≤ 5
3). Equation of the third line in the interval x > 5
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Equation of this line will be,
y = 1(x) + b
y = x + b
Since, this line passes through (5, 6),
6 = 5 + b
b = 6 - 5 = 1
Therefore, equation of this line will be,
y = x + 1 where x > 5
Graphed piecewise function is,
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
Answers
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
choose the function that has domain x ≠ -3 range y ≠ 2.
Answers
The function is f(x)= 2x+1/x+3.
How to find the domain of a function?A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.
Which function has the domain and range?The function domain f (x) is a set of all values defined by the function, and the scope of the function is a set of all values taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.
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Answer:
B
Step-by-step explanation:
i got it right! :)
1. The graph of yf(x) is translated 3 units right and 4 units down. What is the equation of the translation
image in terms of the function ?
A. Y-3 = f(x+4)
B. y + 4 = f(x-3)
C. y + 3 = f(x-4)
D. y - 4 = f(x + 3)
Answers
Answer:
D.y-4=f(x+3)
Step-by-step explanation:
The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
The equation of the translation image of the function is y - 4 = f(x + 3).
which is the correct answer would be an option (D).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
To determine the graph of y (x) is translated as 3 units right and 4 units down.
The x-coordinate will increase by 3 if we move it to the right.
If we shift it downward, it will become negative and read as y - 4.
So y - 4 = f(x + 3)
Therefore, the equation of the translation image of the function is y - 4 = f(x + 3).
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n a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. There are 450 total flying insects. (a) Create a table for how many butterflies there are for 1, 50, and 100 flying insects. Show your work. (b) How many butterflies are in the conservatory? Show your work.
Answers
Answer:
There are 172 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 172
Thus, there are 172 butterflies in the conservatory.
Answer:
There are 162 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 162
Thus, there are 162 butterflies in the conservatory.
Graph the line y=-1/3x+2
Answers
Answer:
Graphed below.
Step-by-step explanation:
The slope of the line is -1/3.
The y-intercept is at (0, 2).
The x-intercept is at (6, 0).
Please answer this correctly
Answers
Answer:
12.5%
Step-by-step explanation:
There is only one number 5 from a total of 8 parts.
1 out of 8.
1/8 = 0.125
P(5) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Spinner divided in parts = 8
Number 5 = 1
P(5) = 12.5%
Please answer this correctly
Answers
Answer:
1/2
Step-by-step explanation:
The numbers 3 or odd are 1, 3, 5, and 7.
4 numbers out of 8.
4/8 = 1/2
P(3 or odd) = 1/2
Two similar biscuit tins hold the same type of biscuits. The net mass of biscuits in the smaller tin is 1 kg. Find the net mass of biscuits in the larger tin. Net mass of biscuits in larger tin = __?_ kg
Answers
Answer:
1.5 kg
Step-by-step explanation:
Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:
9/6 · 1 kg = 1.5 kg
Try it
Evaluate the function g(x) = -2x² + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2) - 5
g(-2) = -2(4) - 6-5
g(-2) = ?
g(0) =?
g(3) =?
Answers
Answer:
g(-2) = -19g(0) = -5g(3) = -14Step-by-step explanation:
When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.
__
If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":
g(x) = (-2x +3)x -5
Then we have ...
g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19
g(0) = (-2(0) +3)(0) -5 = -5
g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answers
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
Select the action you would use to solve 4x = 16. Then select the property
that justifies that action.
A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Action: Multiply both sides by 4.
D. Property: Division property of equality.
E. Property: Addition property of equality.
O F. Action: Add 4 to both sides.
Answers
Answer:
A.
Step-by-step explanation:
Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.
Mr.Chang needs to ship 8 boxes of cookies in a packing carton. Each box is a tight rectangular prism 8 inches long, 5 inches wide, and 3 inches high. What is the volume in cubic inches, of each box?
Answers
Answer:
120 inches cubed
Step-by-step explanation:
The formula for finding the volume of a rectangular prism is length * width * height.
In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.
So multiplying all of those together gets you 120 inches cubed.
Ten different numbers are written on pieces of paper and thrown into a hat. The sum of all the numbers is 205. What is the probability of selecting four numbers that have a sum greater than 82
Answers
Answer:
The probability is 40%
Step-by-step explanation:
a) There are ten pieces of paper with ten numbers
Probability of selecting four pieces of paper = 4/10 or 40%
Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%
Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.
b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes. In other words, it is a measure of the likelihood of an event (or measure of chance).
A director of the library calculates that 10% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 899 books would be less than 11%? Round your answer to four decimal places.
Answers
Answer:
0.8413
Step-by-step explanation:
p = 0.10
σ = √(pq/n) = 0.01
z = (x − μ) / σ
z = (0.11 − 0.10) / 0.01
z = 1
P(Z < 1) = 0.8413
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
We have,
We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.
First, we need to calculate the mean and standard deviation of the binomial distribution:
Mean:
np = 899 × 0.1 = 89.9
Standard deviation:
√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427
Next, we need to standardize the sample proportion of 11% using the formula:
z = (x - μ) / σ
where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Substituting the values we have, we get:
z = (0.11 - 0.1) / 0.9427 = 0.1059
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.
Therefore,
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
Rounded to four decimal places, the answer is 0.5425.
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m−4+m−5 how do i solve this?
Answers
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
=m+m-4-5
=2m-9
Answer:
2m-9
Step-by-step explanation:
m-4+m-5
take the like terms
= 2m-4-5
= 2m-9
Sorry if that didn't help
LM=9, NR=16, SR=8. Find the perimeter of △SMP.
HURRY FIRST ANSWER I WILL MARK YOU AS BRAINLILIST PROMISE
Answers
Answer:
perimeter of △SMP = 25Step-by-step explanation:
The perimeter of the triangle △SMP is the sum of al the sides of the triangle.
Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.
Given LM=9, NR=16 and SR=8
NR = NP+PR
Since NP = PR
NR = NP+NP
NR =2NP
NP = NR/2 = 16/2
NP = 8
From △LSM, NP = PR = MS = 8
Also since LM = MN, MN = 9
From △SRP, SR = RP = PS = 9
Also SR = MP = 8
From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
perimeter of △SMP = 8+8+9
perimeter of △SMP = 25
The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname If more than one surname begins with a letter besides A and O, how may surnames begin with that letter?
Answers
Step-by-step explanation:
40children - 23 (with A, O) = 17left
26 letter in alphabet- ( A, O) = 24 letter left
24 letters left - 14 (not used for 1st letters) = 10
10 letters left to use/ 17 children left
10÷17 = 0.5882352941 x 10 =5.8 or as close to 6 I can get
There are six surnames that start with each letter other than A and O when more than one surname does.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, The surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A.
Since, 14, of the letters of the alphabet do not appear as the first letter of a surname
14 of the letters of the alphabet do not appear as the first letter of the surname
∴ the no. of letters that appeared = 26-14 = 12 alphabets
15 surnames begin with 10 letters beside O and A
∴ 6 surnames begin with a letter
Therefore, If more than one surname begins with a letter besides A and O, 6 surnames begin with that letter.
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1/4 ÷ 3/8 simplest form
Answers
Answer:
2/3
Step-by-step explanation:
divide by a fraction = multiply by reciprocal
1/4 * 8/3
2/3
Answer:
⅔
Step-by-step explanation:
= ¼ ÷ ⅜
= ¼ × ⁸/3
= ⅔
Have a great day !
798/8×41 rounded to one significant figure
Answers
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
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Which statements about the circle are correct? Check all that apply Arc PQ is congruent to arc SR. The measure of arc QR is 150 The circumference of circle C is cm. Arc PS measures about 13.1 cm. QS measures about 15.7 cm.
Answers
Answer:
1st 2nd 4th 5th
Find the missing side and round the answer to the nearest tenth. Thanks.
Answers
Answer:
22.2
Step-by-step explanation:
The missing side is x
cos19° = 21/x switch x and cos19° x = 21/cos 19°x = 22.21≈ 22.2
PLZ I need Help the Question is: 5+13·18+85÷17−11
Answers
Answer:
233
Step-by-step explanation:
Approximate the area under the curve y = x^3 from x = 2 to x = 5 using a Right Endpoint approximation with 6 subdivisions.
Answers
Answer:
182.8125
Step-by-step explanation:
Given:
y = x^3
from [2,5] using 6 subdivisions
deltax = (5 - 2)/6 = 3/6 = 0.5
hence the subdivisions are:
[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]
hence the right endpoints are:
x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5
now the area is given by:
A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]
A = 0.5*365.625
A = 182.8125
Area using Right Endpoint approximation is 182.8125
The area of the region is an illustration of definite integrals.
The approximation of the area of the region R is 182.8125
The given parameters are:
[tex]\mathbf{f(x) = x^3}[/tex]
[tex]\mathbf{Interval = [2,5]}[/tex]
[tex]\mathbf{n = 6}[/tex] ------ sub intervals
Using 6 sub intervals, we have the partitions to be:
[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]
List out the right endpoints
[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]
Calculate f(x) at these partitions
[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]
[tex]\mathbf{f(3) = 3^3 = 27}[/tex]
[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]
[tex]\mathbf{f(4) = 4^3 = 64}[/tex]
[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]
[tex]\mathbf{f(5) = 5^3 = 125}[/tex]
So, the approximated value of the definite integral is:
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]
This becomes
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]
Hence, the approximation of the area of the region R is 182.8125
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What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answers
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
Please answer this for me!!! 25 points to whoever answers this!!!!!!
Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?
Answers
Answer:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Step-by-step explanation:
Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:
[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]
Solving the linear system:
[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]
The price of each item is:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
What is the area of the figure below 13 in length, 11 in width, 29 in and 13 in?
Answers
Answer:
B. 533in²
Step-by-step explanation:
Step 1: Find the area of the rectangle
A = lw
A = (29)13
A = 377
Step 2: Find the leg of the triangle
13 + 11 = 24
Step 3: Find the area of the triangle
A = 1/2bh
A = 1/2(24)(13)
A = 12(13)
A = 156
Step 3: Add the areas of the 2 figures together
377 + 156 = 533
7. Factor by grouping.
6p2 - 17p - 45
A (2p - 9)(3p + 5)
B (2p + 9)(3p + 5)
7096
Oc
C (2p - 9)(3p - 5)
90%
D (2p + 9)(3p - 5)
ping
Answers
Answer:
Step-by-step explanation: 4