The area A of a circle is given by
[tex]A=\pi r^2[/tex]where Pi is 3.1416 and r is the radius. In our case, we get
[tex]100\operatorname{mm}=\pi r^2[/tex]and we need to find r. In this regard, if we move Pi to the left hand side we get
[tex]\frac{100}{\pi}=r^2[/tex]then, r is given by
[tex]r=\sqrt[]{\frac{100}{\pi}}[/tex]Now, the circunference C is given by
[tex]C=2\pi\text{ r}[/tex]then, by substituting our last result into this formula, we have
[tex]C=2\pi\sqrt[]{\frac{100}{\pi}}[/tex]since square root of 100 is 10, we get
[tex]C=2\pi\frac{10}{\sqrt[]{\pi}}[/tex]we can rewrite this result as
[tex]\begin{gathered} C=\frac{2\pi\times10}{\sqrt[]{\pi}} \\ C=\frac{2\sqrt[]{\pi\text{ }}\sqrt[]{\pi}\times10}{\sqrt[]{\pi}} \end{gathered}[/tex]and we can cancel out a square root of Pi. Then, we have
[tex]C=2\sqrt[]{\pi}\times10[/tex]and the circunference is
[tex]C=20\text{ }\sqrt[]{\pi}\text{ milimeters}[/tex]write each percent as a decimal 1%
You have the following percentage:
24.1%
In order to determine the associated decimal to this fraction you proceed as follow:
Hello! I think the answer is 398. Would you mind guiding me?
Given -
Total Personal Videos Players = 400
Video Players with no defects = 398
Number of Video Players sent = 2000
To Find -
The number of Video Players with no defects =?
Step-by-Step Explanation -
Total Personal Videos Players = 400
Video Players with no defects = 398
So,
Two video players in every 400 are defected
So,
2000 = 5 × 400
So,
Total number of Video Players with defects = 5 × 2 = 10
Hence,
The number of Video Players with no defects = 2000 - 10 = 1990
Final Answer -
The number of Video Players with no defects = 1990
The one-to-one functions 9 and h are defined as follows.g={(0, 5), (2, 4), (4, 6), (5, 9), (9, 0)}h(x)X +811
Step 1: Write out the functions
g(x) = { (0.5), (2, 4), (4,6), (5,9), (9,0) }
[tex]h(x)\text{ = }\frac{x\text{ + 8}}{11}[/tex]Step 2:
For the function g(x),
The inputs variables are: 0 , 2, 4, 5, 9
The outputs variables are: 5, 4, 6, 9, 0
The inverse of an output is its input value.
Therefore,
[tex]g^{-1}(9)\text{ = 5}[/tex]Step 3: find the inverse of h(x)
To find the inverse of h(x), let y = h(x)
[tex]\begin{gathered} h(x)\text{ = }\frac{x\text{ + 8}}{11} \\ y\text{ = }\frac{x\text{ + 8}}{11} \\ \text{Cross multiply} \\ 11y\text{ = x + 8} \\ \text{Make x subject of formula} \\ 11y\text{ - 8 = x} \\ \text{Therefore, h}^{-1}(x)\text{ = 11x - 8} \\ h^{-1}(x)\text{ = 11x - 8} \end{gathered}[/tex]Step 4:
[tex]Find(h.h^{-1})(1)[/tex][tex]\begin{gathered} h(x)\text{ = }\frac{x\text{ + 8}}{11} \\ h^{-1}(x)\text{ = 11x - 8} \\ \text{Next, substitute h(x) inverse into h(x).} \\ \text{Therefore} \\ (h.h^{-1})\text{ = }\frac{11x\text{ - 8 + 8}}{11} \\ h.h^{-1}(x)\text{ = x} \\ h.h^{-1}(1)\text{ = 1} \end{gathered}[/tex]Step 5: Final answer
[tex]\begin{gathered} g^{-1}(9)\text{ = 5} \\ h^{-1}(x)\text{ = 11x - 8} \\ h\lbrack h^{-1}(x)\rbrack\text{ = 1} \end{gathered}[/tex]Given rectangle BCDE below. If BF = 22, find EF.
Okay, here we have this:
Considering the provided graph, we are going to find the requested measure, so we obtain the following:
Let us remember that a rectangle besides having the properties of a parallelogram also stands out because it has congruent diagonals. So considering this we have:
BD=EC
EF=BF
EF=22
Finally we obtain that EF is equal to 22 units.
Please help me solve. I also need help on what ratios to put in the two boxes before the answer. Do I just choose any of them?
Explanation
By metric conversion
[tex]\begin{gathered} 1\text{ mile =}1.61km \\ 1\text{ hour = 60 mins} \end{gathered}[/tex]Therefore;
[tex]\frac{57mi}{1hr}\times\frac{1.61}{1}\times\frac{1}{60}=1.5295\frac{km}{\min }[/tex]Answer:
[tex]\begin{gathered} \text{Box 1= }\frac{\text{1.61}}{1} \\ \text{Box 2=}\frac{1}{60} \\ \text{Box 3=}1.53 \end{gathered}[/tex]In terms of trigonometry ratios for triangle BCE what is the length of line CE. Insert text on the triangle to show the length of line CE.When you are done using the formula for the triangle area Area equals 1/2 times base times height write an expression for the area of triangle ABC Base your answer on the work you did above
CE can be written as:
[tex]\frac{BE}{CE}=\frac{CE}{AE}[/tex]Solve for CE:
[tex]\begin{gathered} CE^2=BE\cdot AE \\ CE=\sqrt[]{BE\cdot AE} \end{gathered}[/tex]The area is:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ _{\text{ }}where\colon \\ _{\text{ }}b=AB \\ h=CE=\sqrt[]{BE\cdot AE} \\ so\colon \\ A=\frac{AB\cdot\sqrt[]{BE\cdot AE}}{2} \end{gathered}[/tex]Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the equation.
Answer:
I don’t know if I can send it answer
Step-by-step explanation:
Acetaminophen and liver damage. It is believed that large doses of acetaminophen
(the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the
liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users
who have liver damage. For participating in this study, he will pay each subject $20 and provide
a free medical consultation if the patient has liver damage.
(a) If he wants to limit the margin of error of his 98% confidence interval to 2%, what is the
minimum amount of money he needs to set aside to pay his subjects?
(b) The amount you calculated in part (a) is substantially over his budget so he decides to use
fewer subjects. How will this affect the width of his confidence interval?
Using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).So, a study is being planned to determine the percentage of acetaminophen users who suffer liver injury.
With,
Level of confidence: 98%E=0.03 is the error margin.Then,
The z-value for 98% confidence is known Zₙ = 2.33.Calculation of the sample size: n = p(1 - p)(Zₙ/E)²In order to obtain the most cautious estimate, we should pick p = 0.5 because the researcher has no preconceived notions about what the sample proportion should be:
n = 0.5(1-0.5)(2.33/0.03)²1508.0277778 = 1509Therefore, using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
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The correct question is given below:
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. If she wants to limit the margin of error of her 98% confidence interval to be no more than 3%, what is the minimum number of subjects that she needs to recruit? [Note: The researcher has no expectations about what the sample proportion should be ahead of time, so she – and you – should use p = 0.5 to get the most conservative estimate.]
1+——>1/12 write. Fraction to make each number sentence true, answer I got is 1/1
c) Set x to be the number we need to find; therefore, the inequality to be solved is
[tex]\begin{gathered} 1+x>1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2} \\ \Rightarrow1+x>\frac{3}{2} \\ \Rightarrow-1+1+x>-1+\frac{3}{2} \\ \Rightarrow x>\frac{1}{2} \end{gathered}[/tex]Therefore, any number greater than 1/2 (greater, not equal to) satisfies the inequality; particularly 1/1=1>1/2. Thus, 1/1 is a possible answer
Write an equation of a circle with diameter AB.A(1,1), B(11,11)Choose the correct answer below.A. (X-6)2 + (y-6)2 = 11C. (x-6)2 – (y+6)2 = 50E. (X+6)2 + (y-6)2 = 50G. (X+6)2 – (y + 6)2 = 50
The question asks us to find the equation of a circle with diameter AB with coordinates:
A = (1, 1), B = (11, 11)
In order to solve this, we need to know the general form of the equation of a circle.
The general form of the equation of a circle is given by:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where,} \\ (a,b)=\text{ coordinates of the center of the circle} \\ r=\text{radius of the circle} \end{gathered}[/tex]We have been given the coordinates of the diameter. This means that finding the midpoint of the diameter
will give us the center coordinates of the circle, which is (a, b).
The formula for finding the midpoint of a line is given below:
[tex]\begin{gathered} (x,y)=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ \text{where,} \\ x_2,y_2=\text{ second coordinate} \\ x_1,y_1=\text{first coordinate} \end{gathered}[/tex]For better understanding, a sketch is made below:
Therefore, let us find the coordinates of the center of the circle using the midpoint formula given above:
[tex]\begin{gathered} a,b=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ x_2=11,y_2=11 \\ x_1=1,y_1=1 \\ \\ \therefore(a,b)=\frac{11+1}{2},\frac{11+1}{2} \\ \\ (a,b)=6,6 \\ Thus, \\ a=6,b=6 \end{gathered}[/tex]Now that we have the coordinates of the center, we now need to find the value of the radius of the circle.
This is done by finding the length from the center of the circle to any side of the diameter.
Let us use from point (6,6) which is the center to the point (11, 11) which is one side of the diameter.
The formula for finding the distance between two points is given by:
[tex]\begin{gathered} |\text{distance}|^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ \text{where,} \\ x_2,y_2=\text{second point} \\ x_1,y_1=\text{first point} \end{gathered}[/tex]hence, we can now find the square of the radius as:
[tex]\begin{gathered} r^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ x_2,y_2=11,11_{} \\ x_1,y_1=6,6 \\ \\ \therefore r^2=(11-6)^2+(11-6)^2 \\ r^2=5^2+5^2 \\ r^2=25+25 \\ \therefore r^2=50 \end{gathered}[/tex]Now that we have the radius, we can now compute the equation of the circle as:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ a=6,b=6,r^2=50 \\ \\ \therefore(x-6)^2+(y-6)^2=50\text{ (Option B)} \end{gathered}[/tex]A graph of the circle is given below:
b. Function h will begin to exceed f and g around x = [. (Round up to the nearest whole number.)
If we evaluate x = 10 on all the functions, we have:
[tex]\begin{gathered} h(10)=1.31^{10}=14.88 \\ f(10)=1.25(10)=12.5 \\ g(10)=0.1562(10)^2=15.625 \end{gathered}[/tex]and then, evaluating x = 11, we get:
[tex]\begin{gathered} h(11)=1.13^{11}=19.49 \\ f(11)=1.25(11)=13.75 \\ g(11)=0.15625(11)^2=18.9 \end{gathered}[/tex]notice that on x = 10, h(x) does not exceed g(x), but on x = 11, h(x) exceeds the other functions. Therefore, h will begin exceed f and g around 11
Given the functions, f(x) = 6x+ 2 and g(x)=x-7, perform the indicated operation. When applicable, state the domain
restriction.
The domain restriction for (f/g)(x) is x=7
What are the functions in mathematics?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.
What does a domain math example mean?The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
Given,
f(x) = 6x+2
g(x) = x-7
So,
(f/g)(x) = 6x+2/x-7
Remember that the denominator can not be equal to zero
Find the domain restriction
x-7=0
x=7
Therefore, the domain is all real numbers except the number 7
(-∞,7)∪(7,∞)
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Hi hope you are well!!I have a question: When Debbie baby-sits she charges $5 to go the house plus $8 for every hour she is there. The expression 5+8h gives the amount in dollars she charges. How much will she charge to baby-sit for 5 hours? Please help me with this questionHave a nice day,Thanks
5 + 8h
h= number of hours
Replace h by 5 and solve
5 + 8(5)
5 +40
45
She will charge $45
Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions,What is the probabilitythat his first hit willoccur within his first 5at-bats? Answer choice. 0.654. 0.765. 0.821. 0.876
The probability of a successful batting is 0.341; we need to find the probability of at least 1 hit within the first 5 at-bats; thus,
[tex]P(Hit)=1-P(NoHit)[/tex]Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.
The binomial distribution states that
[tex]\begin{gathered} P(X=k)=(nBinomialk)p^k(1-p)^{n-k} \\ n\rightarrow\text{ total number of trials} \\ k\rightarrow\text{ number of successful trials} \\ p\rightarrow\text{ probability of a successful trial} \end{gathered}[/tex]Thus, in our case,
[tex]P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...[/tex]Then,
[tex]P(Hit)=1-0.124287...\approx0.876[/tex]Therefore, the answer is 0.876Solve the following/3x=7-3/x
Value of x is 8.46 for equation 3x=7-3/x
What is Equation?Two or more expressions with an Equal sign is called as Equation
The given equation is 3x=7-3/x
3x+3/x=7
3x²+3=7x
3x²-7x+3=0
Use quadratic equation formula
a=3, b=-7, c=3
x=-b±√b²-4ac/2a
x=7±√49-4(3)(3)/2(3)
x=7±√49-36/6
x=7±√13/6
x=7±√2.16
x=7+1.46
x=8.46
Hence value of x is 8.46 for equation 3x=7-3/x
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^3square root of 1000
Given the following question:
[tex]\sqrt[3]{1000}[/tex][tex]\begin{gathered} \sqrt[3]{1000} \\ \sqrt[3]{1000}=\sqrt[3]{10^3} \\ 10^3=1000 \\ \sqrt[3]{10^3} \\ \sqrt[n]{a^n}=a \\ \sqrt[3]{10^3}=10 \\ =10 \end{gathered}[/tex]Your answer is 10.
Renta scored 409 points in a video game. This was 223 more points than Sadia score (s). Which equation does not represent this situation? And why?
A) 223 = 409 - s
B) s = 409 - 223
C) s = 409 + 223
D) 223 + s = 409
Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409
What is 2 2/3 - 3/5? 7/154 4/152 1/15 1 2/5
A company estimates that that sales will grow continuously at a rate given by the functions S’(t)=15e^t where S’(t) Is the rate at which cells are increasing, in dollars per day, on day t. find the sales from the 2nd day through the 6th day (this is the integral from one to six)
Given the function:
[tex]S^{\prime}(t)=15e^t[/tex]Where S’(t) Is the rate at which sales are increasing (in dollars per day). To find the sales from the second day through the 6th day, we need to integrate this function from t = 1 to t = 6:
[tex]\int_1^6S^{\prime}(t)dt=\int_1^615e^tdt=15\int_1^6e^tdt[/tex]We know that:
[tex]\int e^tdt=e^t+C[/tex]Then:
[tex]15\int_1^6e^tdt=15(e^6-e^1)\approx\text{\$}6010.66[/tex]The sales from the 2nd day through the 6th day are $6,010.66
ind the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
ANSWER
x = 10.2
EXPLANATION
In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.
With the given information, we can use the cosine of the angle to find the missing value,
[tex]\cos\theta=\frac{adjacent\text{ }leg}{hypotenuse}[/tex]In this problem,
[tex]\cos22\degree=\frac{x}{11}[/tex]Solving for x,
[tex]x=11\cdot\cos22\degree\approx10.2[/tex]Hence, the value of x is 10.2, rounded to the nearest tenth.
Christi earns $21 per hour working as a receptionist. If she works 19 hours per week, what is her weekly wage? A) $250 B) $299 C) $350 D) $399
Since Christi earns $21 per hour, to find how much she earns by working 19 hours per week we need to multiply the hourly wage by the number of hours she works in a week:
[tex]21\times19=399[/tex]Her weekly wage is $399
Answer: D) $399
Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
Determine the real number x and y if (x-yj)(3+5j) is the conjugate of -6-24j
The values of the variables x and y such that the conjugate of - 6 - j 24 is found are 3 and 3, respectively.
How to find the value of two variables associated with the conjugate of a complex number
Let α + i β be a complex number, whose conjugate is the complex number α - i β. In this problem we find the values of the variables x and y such that:
(x + i y) · (3 + i 5) = - 6 + i 24
3 · x + i 3 · y + i 5 · x + i² 5 · y = - 6 + i 24
(3 · x - 5 · y) + i (5 · x + 3 · y) = - 6 + i 24
Then, we need to solve the following system of linear equations:
3 · x - 5 · y = - 6
5 · x + 3 · y = 24
Now we proceed to solve the system algebraically. Clear x in the first equation:
x = (- 6 + 5 · y) / 3
x = - 2 + (5 / 3) · y
Substitute x on the second equation and clear y:
5 · [- 2 + (5 / 3) · y] + 3 · y = 24
- 10 + (25 / 3) · y + 3 · y = 24
34 / 3 · y = 34
(1 / 3) · y = 1
y = 3
Finally, we substitute on y in the first equation:
x = - 2 + (5 / 3) · 3
x = - 2 + 5
x = 3
The values of the variables x and y are 3 and 3, respectively.
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Use the Quotient Rule to find the derivative of the function.f(x) = x/(x − 6)f'(x)=
ANSWER
[tex]\frac{-6}{(x-6)^2}[/tex]EXPLANATION
We want to find the derivative of the function:
[tex]f(x)=\frac{x}{x-6}[/tex]The quotient rule states that:
[tex]f^{\prime}(x)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex]where u = the numerator of the function
v = the denominator of the function
From the function, we have that:
[tex]\begin{gathered} u=x \\ v=x-6 \end{gathered}[/tex]Now, we have to differentiate both u and v:
[tex]\begin{gathered} \frac{du}{dx}=1 \\ \frac{dv}{dx}=1 \end{gathered}[/tex]Therefore, the derivative of the function is:
[tex]\begin{gathered} f^{\prime}(x)=\frac{(x-6)(1)-(x)(1)}{(x-6)^2} \\ f^{\prime}(x)=\frac{x-6-x}{(x-6)^2} \\ f^{\prime}(x)=\frac{-6}{(x-6)^2} \end{gathered}[/tex]Leila triples her recipe that calls for 2/5 of a cup of flour. Leila has 1 cup of flour. Does she have enough to triple her recipe?
no
yes
Answer:
No
Step-by-step explanation:
3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe
she only has 1 cup
so does not have enough to triple her recipe
Answer:
No
Step-by-step explanation:
If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.
What is the measure of m?n20m5m = [?]✓=Give your answer in simplest form.Enter
STEP - BY - STEP EXPLANATION
What to find?
The value of m.
To find the value of m, we take the proportion of the sides of the triangles.
That is;
adjacent of the bigger triangle/hypotenuse of the bigger triangle = adjacent of the smaller triangle / hypotenuse of the smaller triangle.
That is;
[tex]\frac{m}{20+5}=\frac{5}{m}[/tex][tex]\frac{m}{25}=\frac{5}{m}[/tex]Cross-multiply
[tex]m^2=25\times5[/tex]Take the square root of both-side of the equation.
[tex]m=\sqrt[]{25\times5}[/tex][tex]m=5\sqrt[]{5}[/tex]how many ones equal 4 tens
We have to find the number of ones in 4 tens.
As we know that, there are 10 ones in a 10.
Therefore, in 4 tens, the total number of ones would be 1 x 4 x 10 = 40
7. Find the slope of a line which passes through the origin and point (2,4).A 0.5B -0.5C 2D 4
Answer:
C
Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
in our case here we are going e.g. from the origin (0, 0) to (2, 4).
so, x changes by +2 (from 0 to 2).
y changes by +4 (from 0 to 4).
therefore, the slope is
+4/+2 = 2
FYI - the direction is not important. it works the same way in the other direction. but what is important : once you pick a direction for one coordinate, you have to use the same direction for the second one. you cannot go e.g. for x in one direction and for y in the other.
Which can be the first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form?8-(-4) 12-12--2Calculate -1-5Calculate 8-(-4) 12-1-5 -6Find that the point at which the line intersects with the line y = 0 is (3,0).Find that the point at which the line intersects with the line X=Y is (2, 2).
The first step to finding the equation of the line in the slope-intercept form is to find the slope.
So, to find the slope we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are points of the line.
Therefore, if we replace (x1, y1) by (5, -4) and (x2, y2) by (-1, 8), we get that the first step is to calculated:
y2 - y1 = 8 - (-4) = 8 + 4 = 12
x2 - x1 = -1 - 5 = -6
Answer: Calculate 8 - ( - 4 ) = 12
Calculate - 1 - 5 = -6
The pyramid has a square base with side
length 2 cm and height 3 cm. What is the
volume of the chocolate to the nearest
tenth?
A 12 cm
B 6 cm3
C 4 cm
D 2 cm
E 1.3 cm3
The radius of cylinder is r = 3 in.
The height of cylinder is h = 10 in.
The formula for the volume of cylinder is,
[tex]V=\pi\cdot(r)^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cylinder.
[tex]\begin{gathered} V=\pi\cdot(3)^2\cdot10 \\ =282.743 \\ \approx282.7 \end{gathered}[/tex]So volume of cylinder is 282.7 in^3.
Option H is correct.
