are you trying to combine them?
if so, then when you multiply parenthesis stuffs, you should FOIL.
foil stands for first, outside, inside, and last.
when we combine (x -2)(3x-4)
1. we multiply the first parts together x & 3x to get 3x^2.
2. then we multiply the "outsides," x & -4 to get -4x.
3. insides would be -2 & 3x, so -6x.
4. finally last is -2 & -4 to make 8.
putting it all together we get 3x^2 - 4x - 6x + 8.
or simply 3x^2 - 10x + 8 by combing like terms.
for (x + 6)^2 keep in mind that squaring is multiplying something by itself. so (x+6)^2 is the same as (x+6)(x+6).
applying the same foil technique:
1. x * x = x^2
2. x * 6 = 6x
3. 6 * x = 6x
4. 6 * 6 = 36
so we get x^2 + 6x + 6x + 36.
simplified it's x^2 + 12x + 36
keep in mind also that FOILing is only really good for binomials. (something like (x+6)(6x^2+7x+6) wouldnt work).
also also remember that all were really doing is just distributing
According to the Rational Root Theorem, which of the following values is a possible rational root of the polynomial p(x)=x2+3x+12?
A. 24
B. -1/2
C. -2
D. 1/6
E. 1/2
Answer:
C. -2
Step-by-step explanation:
Since the leading coefficient is 1 and rational roots are of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
all of the possible rational roots must be whole number diviors of 12. The only one on the list is -2.
The Rational Root Theorem allows us to determine that -2 is a possible rational root for the polynomial p(x)=x2+3x+12.
Explanation:According to the Rational Root Theorem, the possible rational roots of a polynomial equation can be found by taking all the factors of the constant term (in this case, 12) and dividing them by all the factors of the leading coefficient (in this case, 1 as the coefficient for x2 is 1). The factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12. As our leading coefficient is 1, our possible roots can include ±1, ±2, ±3, ±4, ±6, ±12.
Looking at the list of options provided: A. 24, B. -1/2, C. -2, D. 1/6, E. 1/2, we see that only -2 is a possible rational root for the polynomial p(x)=x2+3x+12 based on the Rational Root Theorem.
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How many total circles will be used if there are 20 rows of circles? Show all calculations.
Answer:
210
Step-by-step explanation:
As there is one circle in first row, 2 circles in 2nd row and three in third row, which clearly implies that the number of circles in each row is equal to the row number. So, we have to calculate sum of first 20 numbers to calculate the total number of circles.
n=20
Total Circles=(n(n+1))/2
=(20 (20+1))/2
=(20(21))/2
= 420/2
=210
So the total number of circles will be 210.
Taylor was earning an income of $1,000 a week. Then his income was reduced by 10%. Two months later, his income increases by 10%. How much is Taylor earning, in dollars, after his income increases?
Wouldn't he be making $1,000 a week again? Since it was reduced by 10% but then raised by 10%.....
Please help quickly!
Match the following items by evaluating the expression for x = -6.
x -2
x -1
x 0
x 1
x 2
Choices;
-6
36
-1/6
1
1/36
Answer:
If those are supposed to be exponents the answers are:
1. 1/36
2. - 1/6
3. 1
4. -6
5. 36
Step-by-step explanation:
The student is provided with the correct evaluations of five expressions given the value x = -6. Each expression is computed, and the correct numerical matches are presented.
The student is attempting to solve expressions given the value of x = -6. To find the correct matches, each expression must be computed separately. Let's start by calculating the given expressions:
x - 2: When x is -6, the expression becomes (-6) - 2 = -8.
x - 1: When x is -6, the expression becomes (-6) - 1 = -7.
x + 0: When x is -6, the expression is simply -6.
x + 1: When x is -6, the expression becomes (-6) + 1 = -5.
x + 2: When x is -6, the expression becomes (-6) + 2 = -4.
With these computations, the matches would be:
x - 2 matches with -8
x - 1 matches with -7
x + 0 matches with -6
x + 1 matches with -5
x + 2 matches with -4
Sketch a graph y = |x – 3| – 2 and describe the translations.
Answer:
Shifted horizontally to the right 3 units, and shifted vertically down 2 units
Step-by-step explanation:
The parent graph of this equation is y = |x|
There are 2 translations to this graph for the equation y = |x - 3| - 2
The "x - 3" part shifts the graph to the right 3 units
The -2 shifts the graph vertically down 2 units
See below for the parent graph, and the graph of the equation we are working with
The graph of function y = |x - 3| - 2 is shown in figure.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The equation is,
⇒ y = |x - 3| - 2
Now,
Since, The equation is,
⇒ y = |x - 3| - 2
Clearly, The equation y = |x - 3| - 2 is the translation of y = |x| with 3 units right and 2 units up.
Thus, The graph of function y = |x - 3| - 2 is shown in figure with 3 units right and 2 units up translation of y = |x|.
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Find the length of side BA. Round to the nearest hundredth.
A) .42
B) .65
C) .83
D) 1.25
Answer:
Option A. [tex]0.42[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]BA^{2}=(1/2)^{2}+(1/3)^{2} -2(1/2)(1/3))cos(100)[/tex]
[tex]BA^{2}=0.1756[/tex]
[tex]BA=0.42[/tex]
Complete the square to transform the quadratic equation into the form (x –p)2= q.X2-8x -10 = 18
Answer:
[tex](x-4)^{2}=44[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-8x-10=18[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-8x=18+10[/tex]
[tex]x^{2}-8x=28[/tex]
Complete the square . Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-8x+16=28+16[/tex]
[tex]x^{2}-8x+16=44[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=44[/tex]
PLEASE HELP ME ASAAAAAPPPPPPPPPPPP PLEASE HELP ME FAST What is 5 x 2/3 ? A) 3 1/3 B) 3 2/5 C) 5 2/3 D) 10/15
Answer:
A) 3 1/3
Step-by-step explanation:
5 x 2 = 10
10/3= 3 with a remainder of 1. That gives you 3 1/3
Answer:
Step-by-step explanation:
IF you calculate it right it is 3.3333333 or 3 1/3
Complete the square to transform the quadratic equation into the form (x – p)2 = q. X2 - 8x - 10 = 18 A) (x - 8)2 = 14 B) (x - 4)2 = 44 C) (x - 8)2 = -14 D) (x - 4)2 = -44
Answer:
Option B. [tex](x-4)^{2}=44[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-8x-10=18[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-8x=18+10[/tex]
[tex]x^{2}-8x=28[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-8x+16=28+16[/tex]
[tex]x^{2}-8x+16=44[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=44[/tex]
Answer:
b
Step-by-step explanation:
Find the measure of the angle with the greatest measure (picture provided)
Answer:
The measure of the greatest angle is about 81° ⇒ answer (b)
Step-by-step explanation:
* Let the given triangle is ΔABC where,
- a = 18 inches ⇒ opposite to angle A
- b = 21 inches ⇒ opposite to angle B
- c = 14 inches ⇒ opposite to angle C
∵ The greatest angle is opposite to the largest side
∴ The greatest angle will be angle B because b is the largest side
* By using cos Rule:
∵ b² = a² + c² - 2ac cos(B)
* Lets re-arrange the terms to find the measure of angle B
∴ 2ac cos(B) = a² + c² - b²
∴ cos(B) = (a² + c² - b²)/2ac
∴ cos(B) = (18² + 14² - 21²)/2(18)(14) = 79/504
∴ m∠B = 80.98 ≅ 81°
∴ The measure of the greatest angle is about 81°
Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4 (picture provided)
Answer:
Choice B is correct
Step-by-step explanation:
The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.
Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;
[tex]r=\frac{k}{1-4sin(theta)}[/tex]
The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;
k= 4*6 = 24
The polar equation is thus given by alternative B
Answer:
b on edge
Step-by-step explanation:
Compute the exact value of the function for the given x-value without using a calculator.F(x)=6^x for x = -3
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=6^x\qquad \boxed{x=-3}\qquad \implies f(-3)=6^{-3}\implies f(-3)=\cfrac{1}{6^3} \\\\\\ f(-3)=\cfrac{1}{6\cdot 6\cdot 6}\implies f(-3)=\cfrac{1}{36\cdot 6}\implies f(-3)=\cfrac{1}{216}[/tex]
Answer: B on Edg
Step-by-step explanation:
Your car gets 25 miles to the gallon, and gas prices are $3 per gallon. How much gas money will you spend on gas each week?
Answer:
whew chiile
Step-by-step explanation:
Question 1(Multiple Choice Worth 2 points) Find the derivative of f(x) = 7 divided by x at x = 1.
-7
-1
1
7
Question 2(Multiple Choice Worth 2 points) Find the derivative of f(x) = 4x + 7 at x = 5.
4
1
5
7
Question 3(Multiple Choice Worth 2 points) Find the derivative of f(x) = 12x2 + 8x at x = 9.
256
-243
288
224
Question 4(Multiple Choice Worth 2 points) Find the derivative of f(x) = negative 11 divided by x at x = 9.
11/9
81/11
9/11
11/81
Question 5 (Essay Worth 2 points) The position of an object at time t is given by s(t) = 1 - 10t. Find the instantaneous velocity at t = 10 by finding the derivative.
Answer:
Step-by-step explanation:
Question 1:
For this case we must find the derivative of the following function:
[tex]f (x) = \frac {7} {x}[/tex] evaluated at [tex]x = 1[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
So:
[tex]\frac {df (x)} {dx} = - 1 * 7 * x ^ {- 1-1} = - 7x ^ {- 2} = - \frac {7} {x ^ 2}[/tex]
We evaluate in [tex]x = 1[/tex]
[tex]- \frac {7} {x ^ 2} = - \frac {7} {1 ^ 2} = - 7[/tex]
ANswer:
Option A
Question 2:
For this we must find the derivative of the following function:
[tex]f (x) = 4x + 7\ evaluated\ at\ x = 5[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
The derivative of a constant is 0
So:
[tex]\frac {df (x)} {dx} = 1 * 4 * x ^ {1-1} + 0 = 4 * x ^ 0 = 4[/tex]
Thus, the value of the derivative is 4.
Answer:
Option A
Question 3:
For this we must find the derivative of the following function:
[tex]f (x) = 12x ^ 2 + 8x\ evaluated\ at\ x = 9[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
So:
[tex]\frac {df (x)} {dx} = 2 * 12 * x ^ {2-1} + 1 * 8 * x ^ {1-1} = 24x + 8 * x ^ 0 = 24x + 8[/tex]
We evaluate for [tex]x = 9[/tex]we have:
[tex]24 (9) + 8 = 224[/tex]
Answer:
Option D
Question 4:
For this we must find the derivative of the following function:
[tex]f (x) = - \frac {11} {x}\ evaluated\ at\ x = 9[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
So:
[tex]\frac {df (x)} {dx} = - (- 1 * 11 * x ^ {- 1-1}) = 11x ^ {- 2} = \frac {11} {x ^ 2}[/tex]
We evaluate for [tex]x = 9[/tex] and we have:
[tex]\frac {11} {9 ^ 2} = \frac {11} {81}[/tex]
ANswer:
Option D
Question 5:
For this case we have by definition, that the derivative of the position is the velocity. That is to say:
[tex]\frac {d (s (t))} {dt} = v (t)[/tex]
Where:
s: It's the position
v: It's the velocity
t: It's time
We have the position is:
[tex]s (t) = 1-10t[/tex]
We derive:
[tex]\frac {d (s (t))} {dt} = 0- (1 * 10 * t ^ {1-1}) = - 10 * t ^ 0 = -10[/tex]
So, the instantaneous velocity is -10
Answer:
-10
Help me with #32 develop an inverse relationship and graph it on the graph
Step-by-step explanation:
Inverse is x · y = k
Since k = 20, then you are looking for x,y coordinates whose product is 20.
Answer:
The following are possible solutions:
[tex]\left\begin{array}{c|c|c}\underline{\quad x\quad }&\underline{\quad y\quad }&\underline{\qquad k\qquad }\\1&20&1\cdot 20=20\\2&10&2\cdot 20=20\\4&5&4\cdot 5=20\\10&2&10\cdot 2=20\\20&1&20\cdot 1=20\end{array}\right[/tex]
(See attached for graph)
i don't understand this ;-;
Sally can paint a room in 7 hours and John can paint the same room in 10 hours. How long should it take Sally and John to paint the room together?
Answer:
17 hours
Step-by-step explanation:
As we know altogether means how many in all or in an easier saying the total.The total is 17.Hope that help you!
Niu has decorated xxx cards. He started with 242424 stickers, and he used 444 stickers per card. Which expressions can we use to describe how many stickers Niu has left?
Answer:
The required expression is 24 - 4x
Step-by-step explanation:
Given,
Initial number of stickers she has = 24,
Also, the number of stickers she used for a card = 4,
⇒ the number of stickers she used for x cards = 4x,
So, the number of stickers she left after decorating x cards = Initial number of stickers - the number of stickers used for x cards,
= 24 - 4x
Which is the required expression.
At this rate, would a person your age (18 years old) have contributed a ton of garbage? On average, how long does it take for each person to throw away a ton, or 2000 pounds of garbage?
Answer: Yes. On average, it takes about 455 days for 1 person to throw away 1 ton of garbage, so just over 1 year.
Step-by-step explanation: The average person throws away 4.4 pounds of trash daily. So, the way to figure this out is 2,000 divided by 4.4 to find out the number of days it would take to throw away 2,000 pounds of trash.
The length of a rectangle is 12 in. and the perimeter is 56 in. Find the width of the rectangle.
Answer:
W = 16 in
Step-by-step explanation:
P = 2L + 2W
56 = 2(12) + 2W
56 = 24 + 2W
56-24 = 2W
32 = 2W
W = 32/2
W = 16 in
Best regards
If the area of a square is 64 square centimeters, what's the length of one side? A. 8 cm B. 4 cm C. 32 cm D. 16 cm
Answer:
8
Step-by-step explanation:
So a square is equal on all sides if I'm correct so. The area is pretty much the length x width. So 8 times 8 equals 64.
Hope this helps, have a good day
s = 8cm (Answer A)
Step-by-step explanation:
The area of a square, A, is the square of the length of any one side:
A = s².
If A = 64 cm², then 64 cm² = s².
Taking the square root of both sides yields s = 8cm (Answer A)
PLZ HURRY Part A:
Find the measure of the following angles:
<1
<2
<3.
Show your work to justify your answers. Earn up to 1 point for each missing angle with the correct answer and work shown.
Part B:
Answer the following question in 1-2 complete sentences. How is the measure of <1 and the measure of <2 related to the exterior 123° angle?
Answer:
<1:88
<2:65
<3:115
Step-by-step explanation:
Since we know that a line and the inside of a triangle equals 180 than we can use that to identify the missing angles.Using what we know about a line we can subtract 92 from 180 and we get 88, knowing that angle 1(<1)is the only angle that rest on that line than we know that <1 is 88.(to check this you can add 92 plus 88 and you get 180)Then switching hands,we can now figure out the interior missing angle 2(<2).There are two ways you can do this,Add all the interior angles together and then subtract from 180(88+57=145 then 180-145=35)or you can subtract all the known interior angles and then the answer is your missing angle(180-57-88=35).Now switching again, in order to find <3 then you have to find which number falls on the angle which we are looking for.Which would be 35 or <2.Now all you have to do is subtract 180-35=145
Part B:
I agree with the other person below⬇⬇⬇
Answer:
Step-by-step explanation:
(A) From the given figure, we have
[tex]{\angle}1+92^{\circ}=180^{\circ}[/tex] (Linear pair)
⇒[tex]{\angle}1=180^{\circ}-92^{\circ}[/tex]
⇒[tex]{\angle}1=88^{\circ}[/tex]
Thus, the measure of [tex]{\angle}1[/tex] is [tex]88^{\circ}[/tex].
Also, using the angle sum property in the given triangle, we get
[tex]{\angle}1+{\angle}2+57^{\circ}=180^{\circ}[/tex]
⇒[tex]88^{\circ}+{\angle}2+57^{\circ}=180^{\circ}[/tex]
⇒[tex]{\angle}2+145^{\circ}=180^{\circ}[/tex]
⇒[tex]{\angle}2=35^{\circ}[/tex]
Thus, the measure of [tex]{\angle}2[/tex] is [tex]35^{\circ}[/tex].
And, [tex]{\angle}2+{\angle}3=180^{\circ}[/tex]
⇒[tex]35^{\circ}+{\angle}3=180^{\circ}[/tex]
⇒[tex]{\angle}3=145^{\circ}[/tex]
Thus, the measure of [tex]{\angle}3[/tex] is [tex]145^{\circ}[/tex].
(B) Exterior angle theorem states that the exterior angle is equal to the sum of the two interior angles, thus from the given figure, we have
[tex]{\angle}1+{\angle}2=123^{\circ}[/tex]
Therefore, the relationship between the measure of [tex]{\angle}1[/tex] and [tex]{\angle}2[/tex] to exterior angle is [tex]{\angle}1+{\angle}2=123^{\circ}[/tex].
If a sphere's volume is doubled, what is the corresponding change in its radius? A. The radius is increased to 20 times the original size. B. The radius is increased to 4 times the original size. C. The radius is increased to 2 times the original size. D. The radius is increased to 8 times the original size
Answer:
The radius is increased by 1.2599 times the original size.
Step-by-step explanation:
The volume is 3 dimensional whereas the radius is one dimensional.
Therefore the factor for the radius will be the cube root of the factor for the volume.
So the radius is increased by 1.2599.
What is accurate about the scientific results learned by counting tree rings? Study of tree rings and associated geology shows that the Earth is 12,000 years old, but no older. Study of tree rings and associated geology shows that the Earth is exactly 12,429 years old. Study of tree rings by themselves shows that the Earth is 4.6 billion years old. Study of tree rings and associated geology shows that the Earth is more than 12,429 years old. Study of tree rings and associated geology proves that the Earth is 5,000 years old, but no older.
Answer:
The correct answer is "Study of tree rings and associated geology shows that the Earth is more than 12,429 years old"
Step-by-step explanation:
While tress have been growing long enough to prove the earth is more than 12,000 years old, it is not able to prove much longer than that. Luckily geology is able to show is that Earth is over 4.6 billions years old. As a result, the above is the only true statement.
The age of the Earth is approximately 4.5 billion years, as determined by radioactive dating methods and supported by other geological evidence. Although not directly determining the Earth's age, the study of tree rings provides valuable information about climate conditions in specific periods.
Explanation:The scientific study of tree rings, known as dendrochronology, can provide valuable information about the Earth's climate in different periods. However, it doesn't directly determine the overall age of the Earth.
Conversely, radioactive dating methods, like uranium-238 dating or rubidium-strontium dating, have been used to determine the Earth's age by dating the oldest rocks and minerals on Earth's crust. For example, the Jack Hills zircons from Australia were found by uranium-lead dating to be nearly 4.4 billion years old.
Using these dating methods in connection with the study of tree rings and other geological evidence, scientists have estimated that the age of the Earth is approximately 4.5 billion years.
This age is significantly older than what could be derived from tree rings alone, as the oldest living trees, like the Methuselah tree, are estimated to be just over 4,800 years old.
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There are 11 red checkers and 5 black checkers in a bag. Checkers are selected one at a time, with replacement. Each time, the color of the checker is recorded. Find the probability of selecting a red checker exactly 6 times in 9 selections. Show your work.
Answer:
P(6 times in 9 selection) = 0.116
Step-by-step explanation:
There are 11 red checkers and 5 black checkers in a bag so
P(red) = no. of red checkers / total no. of checkers = 11/(11+5) = 11/16
Checkers are selected one at a time, with replacement. So P(red) is the same for every selection at 11/16.
Use binomial distribution to find the probability of selecting a red checker exactly 6 times in 9 selections.
In this case, n = 9 and k = 6, P(red)=11/16 so
P(6 times in 9 selection) = nCk * P(red)^k * (1-P(red))^(n-k)
where 9C7 = 9! / [7!*(9-7)!] = 9! / 7!*2! = 9*8 / 2 =36
so P(6 times in 9 selection)
= 36 * (11/16)^6 * (5/16)^3
= 0.116
The context is a binomial distribution where success is defined as drawing a red checker from the bag. With replacement, each draw is independent. Therefore, the formula for binomial probability can be used to calculate the probability of drawing a red checker exactly 6 times in 9 draws.
Explanation:This is a problem of the binomial distribution. For a binomial distribution, each trial is independent, meaning the result of the previous trial does not affect the result of the next trial. This is satisfied since the question states that the checkers are selected with replacement.
'Success' in this context is defined as selecting a red checker which occurs with a probability of 11/16 (since there are 11 red checkers out of a total of 16). Failure is defined as selecting a black checker which occurs with a success probability of 5/16.
To find the probability of selecting a red checker exactly 6 times in 9 selections, we use the formula for binomial probability: P(k; n, p) = C(n, k) * (p^k) * (1 - p)^(n-k). Here, n=9 (number of trials), k=6 (desired 'successes') and p=11/16. When you substitute these values into the formula, you get the desired probability.
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Julio is lifting weights. He wants to have 210 pounds on the bar. How many 15-pound weights should he put on the bar?
Answer: 14 15-pound weights
Step-by-step explanation:
15 × 14= 210
Julio should put 14 fifteen-pound weights on the bar to achieve a total weight of 210 pounds.
Julio wants to have a total of 210 pounds on the barbell. Since each weight he will add is 15 pounds, we simply need to divide the total desired weight by the weight of one plate to determine the number of plates required.
Here is the calculation:
Divide 210 pounds by 15 pounds per weight.210 \/ 15 = 14.Therefore, Julio should put 14 fifteen-pound weights on the bar to reach a total of 210 pounds.
Select the correct answer from each drop-down menu. Determine the dependence between the quantities for the given graph.
The cost per package depends on the weight of the package.
Step-by-step explanation:We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.
Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.
Here from the graph we may observe that the cost of the package depends on the weight of the package.
The cost per package depends on the weight of the package.
We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.
Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.
Here from the graph we may observe that the cost of the package depends on the weight of the package.
Please answer this question, will give brainliest!
Answer:
10.1
Step-by-step explanation:
i divided the numbers now mark brainliest if its wrong or right
Find the midpoint of the chord:
9 / 2 = 4.5 cm
Now we can find the radius:
Radius = √(4.5^2 + 3.7^2)
Radius = √(20.25 + 13.69)
Radius = √33.94
Radius = 5.8 cm
Determine the graph of the polar equation r =6/2-2cos theta
(picture provided)
Answer:
Choice D is correct
Step-by-step explanation:
The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;
[tex]r=\frac{3}{1-cos(theta)}[/tex]
The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.
The value of the directrix is determined as;
d = k/e = 3/1 = 3
The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;
x = -3
Thus, the polar equation represents a parabola that opens towards the right with a directrix located at x = -3. Choice D fits this criteria
The base of a regular pyramid is a hexagon.
What is the area of the base of the pyramid?
Express your answer in radical form.
Answer:
96sqrt(3)
Step-by-step explanation:
Simplest and most intuitive way is to find area of 1 triangles and multiply it by 6.
Area of one triangle:
base = 8 and a = 4sqrt(3)
Area of 1 trangle = ba/2
Area of base of hexagon = 6 times that.
"Which number can be inserted in the parentheses so the numbers are ordered from least to greatest?" -3,(),-1 1/8 A. -3 1/2 B. 0 C. -2 1/4 D 1 1/2
Answer:
Option C
Step-by-step explanation:
The first number is - 3, then we have a blank and the third number is - 1 1/8
In order for the numbers to be arranged from least to greatest, the number in the center should be greater than -3, and lesser than -1 1/8
Note that for negative numbers, the larger the constant, the smaller the number. i.e. -5 is smaller than -4.
So from the given options, the only number that is greater than -3 and lesser than -1 1/8 is - 2 1/4
So, option C gives us the correct answer to have the numbers ordered from least to greatest.