The function limit of f(x) as x approaches 2 is 67 and the limit of f²(x) as x approaches 2 is 4489.
The function f(x) can be rewritten as:
f(x) = (5x³ + 3x² - x)/(x+2)
Using direct substitution, we see that f(2) is undefined, as the denominator of the function becomes 0.
To evaluate the limit, we can use L'Hopital's rule:
[tex]\lim_{x \to 2\[/tex] f(x) = lim x→2 (5x³ + 3x² - x)/(x+2)
= [tex]\lim_{x \to 2\[/tex] (15x² + 6x - 1)/(1)
= (15(2)² + 6(2) - 1)/(1)
= 67
To find the limit of f²(x) as x approaches 2, we can simply square the limit:
f(x) = [tex]\lim_{x \to 2\}[/tex]f²(x)
= [tex]\lim_{x \to 2[/tex] f²(x)
= 67²
= 4489
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Your antique watch is increasing in value at a rate of 5% each year. If it is worth $500 today, how much will it be worth 3 years from now? Round to the nearest hundredths.
Answer:$578.81
Step-by-step explanation:
✨magic✨
A 10% solution of fertilizer is to be mixed with a 60% solution of fertilizer in order to get 125 gallons of a 50% solution. How many gallons of the 10% solution and 60% solution should be mixed?
[tex]x=\textit{gallons of solution at 10\%}\\\\ ~~~~~~ 10\%~of~x\implies \cfrac{10}{100}(x)\implies 0.10 (x) \\\\\\ y=\textit{gallons of solution at 60\%}\\\\ ~~~~~~ 60\%~of~y\implies \cfrac{60}{100}(y)\implies 0.6 (y) \\\\\\ \textit{150 gallons of solution at 50\%}\\\\ ~~~~~~ 50\%~of~150\implies \cfrac{50}{100}(150)\implies 75 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{gallons}{quantity}&\stackrel{\textit{\% of gallons that is}}{\textit{fertilizer only}}&\stackrel{\textit{gallons of}}{\textit{fertilizer only}}\\ \cline{2-4}&\\ \textit{Sol'n of 10\%}&x&0.10&0.10x\\ \textit{Sol'n of 60\%}&y&0.60&0.60y\\ \cline{2-4}&\\ mixture&150&0.5&75 \end{array} \\\\\\ \begin{cases} x + y = 150\\\\ 0.10x+0.60y=75 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=150}\implies y=150-x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 2nd equation}}{0.10x+0.60y=75}\implies \stackrel{\textit{substituting on the 2nd equation from above}}{0.10x+0.60(150-x)=75} \\\\\\ 0.10x+90-0.60x=75\implies 90-0.50x=75\implies 90=0.50x+75 \\\\\\ 15=0.50x\implies \cfrac{15}{0.50}=x\implies \boxed{30=x}\hspace{5em}\stackrel{ 150~~ - ~~30 }{\boxed{y=120}}[/tex]
Let u = - 3i + 2j, v = 3i - 3j and w = - 3j
Find the specified scalar or vector.
5u(3v - 4w)
If u = - 3i + 2i, v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.
To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:
3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j
Next, we can perform the scalar multiplication of u and the vector 6i + 14j:
5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)
Expanding the product, we get:
5(-18i² + 36ij + 42ij - 28j²)
Since i² = j² = -1, we can simplify this expression as:
5(18 + 70) = 440
Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.
The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.
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Joey wants to buy a $3,000 vehicle with 20 percent down for three years at 12 percent interest. What will his monthly payment be?
Monthly Payment per $1,000 Finance
A. $72.82
B. $89.67
C. $79.70
D. $119.56
Joey’s monthly payment is solved to be
C. $79.70
How to find the monthly payment20% down 600 to calculate the monthly payment on a 3 000 car we would pay 2 400.
the interest rate is 12% per annum which equates to 1% per month the term of the loan is three years which equates to 36 months we can use a formula to calculate the monthly payments
[tex]Monthly salary = (P * r * (1 + r)^n) / ((1 + r)^n - 1) .[/tex]
where
P is the principal (premium),
r is the monthly interest rate, and
n is the number of months.
Plug in the prices and we have:
[tex]Monthly salary = (2400 * 0.01 * (1 + 0.01)^{36} ) / ((1 + 0.01)^{36} - 1)[/tex]
= $79.65 per square foot
So Joey’s monthly payment would be $79.65.
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PQRSTU is plotted on a coordinate plane with vertices p(-1,0) Q(-1,3) R(1,4) S(2,5) T(4,4) and U(4,0) what is the hexagons area
What is the area of this figure? 11 mm 3 mm 2 mm 2 mm 4 mm 2 mm 5 mm 3 mm Write your answer using decimals. Use 3.14 for л.
Answer: 116.985 mm2
Step-by-step explanation:
PLS HELP
The number of hours a student spent studying each week for 9 weeks is shown.
9, 4.5, 8, 6, 9.5, 5, 6.5, 14, 4
What is the value of the range for this set of data?
Can you help me with this please
Answer: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{8}{25}[/tex]
Step-by-step explanation:
We can do this by counting the boxes for both the Width and the Length.
If we look at the width of these boxes (horizontally) then we see that there are 5 boxes all together, with 2 shaded green.
this means that 2 out of 5 of the boxes are shaded for the width, giving us the fraction: [tex]\frac{2}{5}[/tex]
Then for the Length (vertically) we see that there are also 5 boxes, but this time 4 are shaded. This gives us the fraction: [tex]\frac{4}{5}[/tex].
Then, to fill the equation in, we do: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] , which gives us [tex]\frac{8}{25}[/tex]
2 x 4 = 8
5 x 5 = 25
To double check this answer, we can count how many boxes are shaded green.
We see that 8 are shaded green, out of the 25 boxes that are there.
Therefore, giving us a complete answer of: [tex]\frac{2}{5}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{8}{25}[/tex]
I would be rally thankful if you help
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
The row operation is given as follows:
Division by 7 = multiplication by 1/7, as the element at the desired position is of 7.
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 at row 1 and column 1 of the matrix must assume a value of -1.
An example of a valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the resulting matrix is then given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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Out of 300 applicants for a job, 134 are male and 40 are male and have a graduate degree. You were asked to find the probability that a randomly chosen applicant has a graduate degree, given that they are male.
Answer: We can use Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male. Bayes' theorem states:
P(A|B) = P(B|A) * P(A) / P(B)
where A and B are events, P(A|B) is the conditional probability of event A given that event B has occurred, P(B|A) is the conditional probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In this case, we want to find P(grad degree | male), which is the probability that an applicant has a graduate degree given that they are male. Using Bayes' theorem, we have:
P(grad degree | male) = P(male | grad degree) * P(grad degree) / P(male)
We are given that 134 applicants are male, and 40 of those males have a graduate degree. Therefore:
P(male | grad degree) = 40 / total number of applicants with a graduate degree
We are not given the total number of applicants with a graduate degree, but we can find it using the fact that 40 applicants are male and have a graduate degree, and that there are 134 male applicants in total. Therefore:
total number of applicants with a graduate degree = 40 / (40/134) = 118.33 (rounded to the nearest whole number)
Next, we need to find the prior probability of having a graduate degree, P(grad degree). We can use the total number of applicants and the number of applicants with a graduate degree to calculate this probability:
P(grad degree) = number of applicants with a graduate degree / total number of applicants = 118 / 300 = 0.3933 (rounded to four decimal places)
Finally, we need to find the prior probability of being male, P(male). This probability can be calculated similarly:
P(male) = number of male applicants / total number of applicants = 134 / 300 = 0.4467 (rounded to four decimal places)
Now, we can substitute these values into Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male:
P(grad degree | male) = (40 / 118) * 0.3933 / 0.4467 = 0.332 (rounded to three decimal places)
Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they are male, is approximately 0.332 or 33.2%.
Step-by-step explanation:
Question 15 (1 point)
You have purchased a new farm. Your lawn will be watered by central pivot irrigation,
where sprinklers rotate around a central point. If the line of sprinklers turning around
the central pivot is 300 ft long, write an equation to model the circular boundary of
your sprinkler. Assume the center is (0,0).
x² + y² = 360000
x²+²=90000
x² + y² = 900
x² + y² = 3600
The equation of the circle in this problem is given as follows:
x² + y² = 90000
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The center for this problem is given as follows:
(0,0).
The radius is given as follows:
300 ft.
Hence the equation is of:
x² + y² = 90000
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How do you write 9.6 × 103 in standard form?
A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium.
Which expression is equivalent to 3^4?
Answer: is d
Step-by-step explanation:
well it is just 3 times 3 times 3 times 3
A recipe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made using 1 gallon of milk?
Answer:
128 servings
Step-by-step explanation:
It takes 1 1/4 cups to make 10 servings
1 1/4 as a mixed fraction = 5/4
So 5/4 cups makes 10 servings
1 cup makes 10 ÷ 5/4
Use the fraction rule for division
a/b ÷ c/d = a/b x c/d
10 ÷ 5/4 = 10 x 4/5 = 8 servings from 1 cup
1 gallon = 16 cups
At 8 servings per cup, total number of servings for 16 cups
= 8 x 16 = 128 servings ANSWER
Car A travels 221.5 km at a given time, while car B travels 1.2 times the distance car A travels at the same time. What is the distance car B travels during that time?
Answer:
Distance that car B travels =1.2× distance that car A travels
=1.2×221.5=265.8 km
Answer:
car B travels a distance of 265.8 km during the same time.
Step-by-step explanation:
Car A travels 221.5 km at a given time.
To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:
Distance of Car B = 1.2 * Distance of Car A
Distance of Car B = 1.2 * 221.5 km
Distance of Car B = 265.8 km
Therefore, car B travels a distance of 265.8 km during the same time.
A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?
PLEASE HELP!!!
The surface area of a triangular pyramid is 400 square meters. The surface area of a similar triangular pyramid is 25 square meters.
What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?
Enter your answer by filling in the boxes.
Answer:
can i get a picture\
Step-by-step explanation:
thanks
Answer:
Step-by-step explanation:
1:4
Solve for x. Round to the nearest tenth, if necessary
Answer:
Set your calculator to degree mode.
cos(37°) = 52/x
x cos(37°) = 52
x = 52/cos(37°) = 65.1
Solve for 10 and 12 please and thank you
Answer:
10. 120 Degrees 12. 60 Degrees
Step-by-step explanation:
#12. Since CAD is 30, and BAD is a 90 degree angle, angle BAF is 60 degrees. Since BAF is 60 degrees and FAE and BAF are vertical angles, they have the same angle measure. 60 Degrees.
#10. Since BAF is 60, and FAE and BAF are on a line, we can do 180-60 to get the measure in degrees of that angle. FAE = 120 Degrees.
Answer:
Step-by-step explanation:
10. somewhere between 126 and 129, i feel its 128
12. between 60 and 65
Alexander deposits $3,200 into a savings account that has a simple interest rate of 1%. If interest is calculated quarterly, which statement is true?
Select one:
a.
He will earn $8 in interest each quarter, totaling $32 in interest for the year
b.
He will earn $32 in interest at the end of one year
c.
He will earn $0.80 in interest each quarter, totaling $3.20 in interest for the year
d.
He will earn $3.20 in interest at the end of one year
The TRUE statement about Alexander's deposit of $3,200 into a savings account that has a simple interest rate of 1% calculated quarterly is a. He will earn $8 in interest each quarter, totaling $32 in interest for the year.
What is the simple interest?Simple interest describes an interest system that does not compound the interest.
Compounding involves charging interest on both interest and principal.
For the simple interest system, the interest amount is computed only on the principal, using the following SI formula.
Principal deposit, P = $3,200
Interest rate, R = 1%
Interest period, P = 1 year
Interest system = Simple interest quarterly
Simple interest (SI) formula = P x R x T
Simple interest for each quarter = $8 ($3,200 x 0.01 x 1/4)
Simple interest for the year = $32 ($3,200 x 0.01)
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5 years ago i was 5 times older then my son. in 8 years time i will be 3 times older then my son. how old am i today?
Answer:
70 , 18
Step-by-step explanation:
Keeping x as Father and y as son;
5 years ago Person X was 5 times older than Person y , so the equation will be:
x - 5= 5(y-5)
x = 5y - 20
simularily after 8 years , x will be 3 times older than y , so
x + 8 = 3(y + 8.)
I will now try to find y by equating value of x into y:
5y - 20 + 8 = 3y + 24
5y - 3y = 24 + 20 - 8
2y = 44 - 8 = 36
y = 18
so x will be = 5 (18) - 20.
x = 90-20 = 70 years.
therefore father is 70 years , and son is 18 years old.
The table below represents a linear equation
Which function has a greater slope and greater y-intercept than the linear function represented in the table?
A. y = 2x + 8.5
B. y = 3x +7.5
C. y = 5x + 6.5
D. y = 10x + 5.5
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
We have to given that;
The table below represents a linear equation.
Now, The equation of line is,
Take two points (- 1, 5) and (1, 9)
⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)
⇒ y - 5 = 4/2 (x + 1)
⇒ y - 5 = 2 (x+ 1)
⇒ y - 5 = 2x + 2
⇒ y = 2x + 7
Hence, By options,
The function that has a greater slope and greater y-intercept than the linear function represented in the table is,
⇒ y = 3x + 7.5
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
The factor of 2xy + 30x^2 - xy - 16y^4 - yx - 5x^2 is 25x2−16y4=(5x+4y2)(5x−4y2)
We are given that;
2xy + 30x^2 - xy - 16y^4 - yx - 5x^2
Now,
Combine like terms by adding or subtracting the coefficients of the same variables. For example, 2xy - xy - yx = 0xy, and 30x^2 - 5x^2 = 25x^2. The polynomial becomes:
25x2−16y4
Check if there is a common factor for all the terms. In this case, there is no common factor other than 1, so we cannot use the greatest common factor method.
Check if the polynomial is a difference of two squares, which means it has the form a2−b2. In this case, we can see that both terms are perfect squares: 25x2=(5x)2 and 16y4=(4y2)2. Therefore, we can use the difference of two squares formula:
a2−b2=(a+b)(a−b)
Substituting a=5x and b=4y2, we get:
25x2−16y4=(5x+4y2)(5x−4y2)
Check if each factor can be further factored using any of the methods. In this case, neither factor can be further factored, so we are done.
Therefore, by factorization the answer will be 25x2−16y4=(5x+4y2)(5x−4y2)
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In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows:
Company A: 9.3; 8.8; 6.8; 8.7; 8.5; 6.7; 8.0; 6.5; 9.2; 7.0
Company B: 11.0; 9.8; 9.9; 10.2; 10.1; 9.7; 11.0; 11.1; 10.2; 9.6
i. Calculate the sample mean and median for the data for the two companies.
ii. Plot the data for the two companies on the same line/chart and give your impression regarding any apparent differences between the two.
iii. Is there any relation between the two companies? Compare using the 90% confidence interval of the mean.
iv. Which company you will recommend
i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.
ii. The line graph of the data is illustrated below.
iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.
iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.
For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:
Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1
To find the median, we first need to arrange the data in ascending order:
6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3
Since there are an even number of values, the median is the average of the two middle values:
Median of Company A = (8.0 + 8.5) / 2 = 8.25
For Company B, the sample mean can be calculated similarly:
Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2
Arranging the data in ascending order, we get:
9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1
Since there are an odd number of values, the median is the middle value:
Median of Company B = 10.2
Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.
Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.
To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.
Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:
Difference in means ± (t-value x standard error of difference in means)
The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.
Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:
Margin of Error = 1.734 * 0.393 ≈ 0.682
Finally, we can construct the 90% confidence interval for the difference in means as:
Difference in means ± Margin of Error
Calculating the difference in means (mean of Company B - mean of Company A), we have:
Difference in means = 10.2 - 8.1 = 2.1
Therefore, the 90% confidence interval is:
2.1 ± 0.682
This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.
Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.
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pls help if u can tyyysm im struggling will gvie brainly
Answer:
Would buy Would not
again buy again Total
Aalora 77 16 93
Mederac 48 23 71
Total 125 39 164
71/164 = 43.3% of the customers purchased Mederac.
So the group that accounts for about 43% of the respondents is the percentage of the customers who purchased Mederac.
Graph and solve y=1/2x-6 and y=1/2x+2
Answer:
No solution.
Step-by-step explanation:
To solve this problem, all you have to do is graph the lines and see where they intersect.
This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion
Gianah lives in Milton. She bought a bus ticket to travel to her cousin's house in Orlando. She gets on the bus in Milton. The distance between the two cities is 695 kilometers and the bus drives 70 kilometers per hour.
If the bus is kilometers away from Orlando, which of the following equations represents the hours, h, the bus has traveled?
695 divided by 70=9.92 hours
This circle is centered at the origin, and the length of its radius is 5. What is the equation of the circle? A. x2 + y2 = 52 B. x2 + y2 = 5 C. (x - 5)2 + (y - 5)2 = 25 D.
Answer:A
Step-by-step explanation:
Provide appropriate commentary that will assist learner to in the completion of the sum8+(6-3)-9=
Answer:
8+(3)-9=8+3-9=11-9=2
Step-by-step explanation:
by using PEMDAS rule
Start with :
P : Paranthesis
E: exponents
M: Multiplication
D : division
A: Addition
S:Subtraction
