Answers
Answer:
last row equals 333
Step-by-step explanation:
The clock showing time 9:00 should be worth 9 points, and the clock showing 3:00 should be worth 3 points, giving for the first row:
9 + 9 + 3 = 21
the three equal calculators showing 1234 are worth 10 points each:
1+2+3+4 = 10
and 10 + 10 + 10 = 30
the light bulbs should be 15 points each then giving 15 + 15 - 15 = 130 - 15 = 15 Notice also that they all have 5 rays of light coming out (so a 3 points per ray)
Now for the bottom line we have:
9 + (1+2+2+4) times 3 * 12 (only four rays on each bulb thus 4 * 3 = 12)
Notice we added the figures that appear in the calculator.
9 + 9 * 36 = 333
Related Questions
(9x + 1) -(-7x2 + 4x + 10)
Answers
Answer:
= 7x² + 5x - 9
Step-by-step explanation:
(9x + 1) - (-7x² + 4x + 10)
= 9x + 1 - ( -7x² + 4x + 10)
= 9x + 1 + 7x² - 4x - 10
= 7x² + 5x - 9
Trigonometry!! NEED HELP!!
Answers
=============================================
Explanation:
If angle x is the reference angle, then the side 9 is the adjacent side (it is the closer leg to angle x). The hypotenuse is 17 as it is opposite the largest angle. The largest side is always opposite the largest angle in a triangle.
-----------------
cos(angle) = adjacent/hypotenuse
cos(x) = 9/17
x = arccos(9/17)
x = 58.034281249203
x = 58
Arccosine is the same as inverse cosine, written as [tex]\cos^{-1}[/tex]
Make sure your calculator is in degree mode.
-------------
Edit:
After finding x, we can find y
x+y = 90
58+y = 90
y = 90-58
y = 32
Solve for m.
0 = -12 + m
Answers
Answer:
[tex]\huge \boxed{m=12}[/tex]
Step-by-step explanation:
[tex]m+-12=0[/tex]
[tex]\sf Add \ 12 \ to \ both \ sides.[/tex]
[tex]m+-12+12=0+12[/tex]
[tex]m=12[/tex]
The amount of time adults spend watching television is closely monitored by firms becayse this helps to determine advertising pricing for commercials. Compete parts (a) through (d).
a) Do you think the variable "weekly time spent watching television" would be normally distributed? Yes or No.
If not, what shape would you expect the variable to have? Skewed Left, Skewed Right, Uniform or Symmetric?
b) According to a certain survey, adults spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for "time spent watching TV on a weekday" is 1.93 hours. If a random sample of 40 adults is obtained, describe the sampling distribution of x-bar, the mean amount of time spent watching TV on a weekday.
Mean =
A) 2.35
B) 1.89
C) 2.25
SD = (round to six decimal places as needed)
c) Determine the probability that a random sample of 40 adults results in a mean time watching television on a weekday of between 2 and 3 hours.
The probability is ____ .
d) One consequence of the popularity of the Internet is that it is thought to reduce TV watching. Suppose that a random sample of 35 people who consider themselves avid Internet users results in a mean time of 1.89 hours watching TV on a weekday. Determine the likelihood of obtaining a sample mean of 1.89 hours or less from a population who mean is presumed to be 2.35 hours.
The likelihood is ____ .
Based on the result obtained, do Internet users watch less TV? Yes or No.
Answers
Answer:
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
Step-by-step explanation:
a)The variable "weekly time spent watching television" is normally distributed and is skewed right.
b) Mean = x` 2.35 hours
Standard deviation = s/√n = 1.93/√40=1.93/6.3245553= 0.3051598
c) P(2<X<3) = P (2-2.35/ 0.3051598< Z< 3 -2.35/ 0.3051598)
= P ( -1.14694 < Z <2.13003)
= 0.3729 + 0.4830
=0.8559
So the probability is 0.8559
(0.8559 we check the value of 2.13 from the normal distribution tables and add with the value of 1.14 to get the in between value -1.14694 < Z <2.13003)
d) Here n = 35 , s= 1.93 , mean = 2.35 and x= 1.89
So Putting the values
P (X ≤ 1.89) = P (Z ≤ 1.89- 2.35/ 1.93 / √35)
= P ( Z ≤ -0.238341/ 5.9160797)
= P ( Z ≤ -0.04028)
= 0.5 - 0.0159
= 0.4841
Similarly again subtracting from 0.5 the value from normal distribution table to get less than or equal to value.
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
The mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes 0.4841 internet users watch less TV.
It is given that the amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials.
It is required to find the standard deviation and probability.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We know the formula for standard error:
[tex]\rm SE = \frac{s}{\sqrt{n} }[/tex]
Where 's' is the standard error
and n is the sample size.
In the question the value of s = 1.93 hours
and sample size n = 40
[tex]\rm SE = \frac{1.93}{\sqrt{40} }\\[/tex]
SE = 0.3051597
For the probability between 2 and 3 hours.
= P(2<X<3)
[tex]\\\rm =P(\frac{2-x)}{s} < Z < \frac{3-x)}{s})\\\\\rm = P(\frac{(2-2.35)}{0.3051598} < Z < \frac{(3-x)}{0.3051598})\\\\[/tex] (because the mean value x is 2.35)
=P(-1.14694 <Z < 2.13003)
=0.3729+ 0.4830 ( values get from Z table for -1.14 and 2.13 )
=0.8559
For P(X≤1.89)
[tex]\rm P(Z\leq \frac{(x'-x)}{\frac{s}{\sqrt[]{n} } } )\\\\\rm P(Z\leq \frac{(1.89-2.35)}{\frac{1.89}{\sqrt[]{35} } } )[/tex]
= P(Z ≤ -0.04028)
= 0.5 - 0.0159
=0.4841
Based on the result of 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5.
Thus, the mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes internet users watch less TV.
Learn more about the standard deviation here:
https://brainly.com/question/12402189
what is the volume of the box below ?5cm,8cm,10cm
Answers
Answer: Hi!
To find the volume of a box (or cube), you multiply length times width times height.
In this case, you have all of the measurements, so all we have to do is multiply them together!
5cm * 8cm * 10cm = 400
So, the volume of this box is 400cm^3!
Hope this helps!
what is 826 x 3,569 equal to
Answers
Answer:
826×3569=2947994 ans
6 Hundreds 3 Tens 17 Ones in Standard Form
Answers
Answer:
the answer is647
Step-by-step explanation:
600+30+17
Answer:
647
Step-by-step explanation:
600
+ 30
17
_____
647
a Find the amount compounded annually on Rs 25,000 for 2 years if the rates of
interest for two years ore 10 % and 12 % respectively,
Answers
Answer:
Rs 30800
Step-by-step explanation:
The formula for compound interest is
A = P[1 + (r/100)]^t, where
A = amount of compounded interest
P = principal amount
r = interest rate
Applying this to our question, we have
A = 25000 [1 + (10/100)] [1 + (12/100)]
A = 25000 (1 + 0.1) (1 + 0.12)
A = 25000 * 1.1 * 1.12
A = 25000 * 1.232
A = 30800
ASAP: “Use a number line to order the numbers from least to greatest.” 1/5, -0.5, 0, 0.4, 1 1/2, -1.
Answers
Answer:
-1, -0.5, 0, 0.4, 1/5, 11/2
Step-by-step explanation:
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.11.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Required:
Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period.
Answers
Answer:
The probability is [tex]P(X < 3) = P(X \le 3-1 = 2 ) = 0.8074[/tex]
Step-by-step explanation:
From the question we are told that
The probability of a tornado is [tex]p = 0.11[/tex]
The sample size is [tex]n = 14[/tex]
Since the number of tornadoes in any calendar year is independent of the number of tornadoes in any other calendar year and there can be only outcome so we can evaluate probability using binomial distribution.
The probability of a tornado not occurring is mathematically evaluated
[tex]q = 1 - p[/tex]
=> [tex]q = 1 - 0.11[/tex]
=> [tex]q = 0.89[/tex]
The probability that there are fewer than 3 tornadoes in a 14-year period is mathematically represented as
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = \left n } \atop {}} \right. C_2 * p ^2 q^{n- 2 } + \left n } \atop {}} \right. C_1 * p ^1 q^{n- 1 } + \left n } \atop {}} \right. C_0 * p ^r q^{n- 0 }[/tex]
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = \left 14 } \atop {}} \right. C_2 * (0.11) ^2 (0.89)^{14- 2 } + \left 14 } \atop {}} \right. C_1 * (0.11) ^1 (0.89)^{14- 1 } + \left 14 } \atop {}} \right. C_0 * (0.11) ^0 (0.89)^{14- 0 }[/tex]
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = 91 * 0.0121*0.247 + 14 * 0.11*0.2198 + 1 * 1 * 0.197[/tex]
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = 0.8074[/tex]
The vector is first dilated by a factor of 2.5 and then rotated by radians. If the resulting vector is , then a =_____ and b = ____.
Answers
Answer:
a = 10
b = 2.5
Step-by-step explanation:
The given vector is
<-1, 4>
Let [tex]\vec A[/tex] represents <-1, 4>.
First, the dilation is done by a factor of 2.5.
If the dilation of a vector <[tex]x_1[/tex], [tex]x_2[/tex]> is done by a factor k:
Then the resulting vector becomes:
[tex]<kx_1, kx_2>[/tex]
The resulting [tex]\vec B[/tex] as per above explanation:
[tex]<2.5\times -1, 2.5\times 4> \Rightarrow \vec B \bold{<-2.5, 10 > }[/tex]
Now, it is given that the vector is rotated by [tex]\frac{\pi}{2}[/tex] or [tex]90^\circ[/tex].
The steps to find the resulting vector after the rotation of [tex]\frac{\pi}{2}[/tex] or [tex]90^\circ[/tex], we can use the simple method:
Step 1: Multiply the [tex]x[/tex] value with -1.
i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).
Step 2: Swap the values of [tex]x[/tex] and [tex]y[/tex].
So, the resulting vector is:
<10, 2.5>
In other form, we can represent the above vector as:
[tex]\left[\begin{array}{c}10&2.5\end{array}\right][/tex]
Comparing with [tex]\left[\begin{array}{c}a&b\end{array}\right][/tex]
a = 10
b = 2.5
Answer:
The correct answer is -10 and -2.5
Step-by-step explanation:
Plato
2. A map of a park has a scale of 1 inch to 1,000 feet. Another map of the same park has
a scale of 1 inch to 500 feet. Which map is larger? Explain or show your reasoning.
1
rade 7 Unit 1
esson 10
CC BY Open Up Resources. Adaptations CC BY IM.
Answers
Answer:
The map that has a scale of 1 inch to 500 feet must be larger in size
Step-by-step explanation:
Since both maps represent the ame park area, the map that show more detail using 1 inch for every 500 feet, must be larger in size. notice that in order to represent 1000 feet this map needs to use 2 inches, while the other one uses only 1 inch of paper.
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5).
Answers
Answer:
[tex]\mathbf{\int_C F*dr= -125}[/tex]
Step-by-step explanation:
Given that:
[tex]F(x,y,z) = ( x+ y^2) i + (y +z ^2) j+(z + x^2)k[/tex] , where C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5).
The objective is to use Stokes' Theorem to evaluate CF. dr
Stokes Theorem : [tex]\int_c F .dr = \iint _s \ curl \ F. dS[/tex]
To estimate curl F , we need to find the partial derivatives:
So;
[tex]P = x+y^2[/tex]
partial derivative is:
[tex]\dfrac{\partial P }{\partial y }= 2y[/tex]
[tex]\dfrac{\partial P }{\partial z }= 0[/tex]
[tex]Q = y + z^2[/tex]
partial derivative is:
[tex]\dfrac{\partial Q }{\partial x }= 0[/tex]
[tex]\dfrac{\partial Q }{\partial z }= 2z[/tex]
[tex]R = z +x^2[/tex]
partial derivative is:
[tex]\dfrac{\partial R }{\partial x }= 2x[/tex]
[tex]\dfrac{\partial R }{\partial y }= 0[/tex]
These resulted into
curl F = (0 - 2z)i + ( 0 -2x) j + ( 0 - 2y) k
= ( -2z, -2x, -2y )
The normal vector and the equation of the plane can be expressed as follows:
If a = (0,5,0 - ( 5,0,0)
a = ( -5,5,0 )
Also ,
b = (0, 0,5) - (5,0,0)
b = (-5. 0,5)
However,
[tex]a \times b = \begin {vmatrix} \begin{array} {ccc} i &j&k \\-5&5&0 \\-5&0&5 \\ \end {array} \end {vmatrix}[/tex]
a × b = (25 - 0)i - (-25-0)j+ (0+25)k
a × b = 25i +25j +25k
∴ the normal vector can be n = (1,1,1)
If we assume x to be x = (x,y,z)
and [tex]x_0 = (5,0,0)[/tex]
Then
[tex]n*(x-x_0) =0[/tex]
[tex](1,1,1)*(x-5,y-0,z-0) =0[/tex]
[tex]x-5+y+z =0[/tex]
collecting like terms
x +y +z = 5
now, it is vivid that from the equation , the plane of the normal vector =(1,1,1)
Similarly, x+y+z = 5 is the projection of surface on the xy - plane such that the line x +y = 5
Thus; the domain D = {(x,y) | 0 ≤ x ≤ 5, 0 ≤ y ≤ 5 - x}
To evaluate the line integral using Stokes' Theorem
[tex]\iint_S \ curl \ F .dS= \iint _S (-2z,-2y,-2x) *(1,1,1) \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -2z-2y-2x \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -2(5-x-y)-2y-2x \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -(10) \ dS[/tex]
[tex]\int_C F*dr= \int ^5_0 \ \int ^{5-x}_0 -10 \ dy \ dx[/tex]
[tex]\int_C F*dr= -10 \int^5_0 (5-x) \ dx[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} 5x - \dfrac{x^2}{2} \end {bmatrix}^5_0[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} 25 - \dfrac{25}{2} \end {bmatrix}[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} \dfrac{25}{2} \end {bmatrix}[/tex]
[tex]\mathbf{\int_C F*dr= -125}[/tex]
POINTS!!!!!!
If an object is dropped from a height of h meters and it’s the ground in t seconds, then t = *square root* h/4.9. Suppose that an object is dropped from the top of a building that is 290.57 meters tall. How long does it take to hit the ground?
Round your answer to the nearest tenth....
?????? Seconds
Please state how many seconds first...
Answers
Answer:
7.7 seconds
Step-by-step explanation:
Put the given height into the formula and do the arithmetic.
t = √(290.57/4.9) = √59.3 ≈ 7.7 . . . seconds
The object will take 7.7 seconds to hit the ground.
Subtract (x^2+3x-4) -(4x-2x^2-3)
Answers
Answer:
3 x^2 - x + -1
Step-by-step explanation:
Simplify the following:
-(4 x - 2 x^2 - 3) + x^2 + 3 x - 4
Factor -1 out of -2 x^2 + 4 x - 3:
--(2 x^2 - 4 x + 3) + x^2 + 3 x - 4
(-1)^2 = 1:
2 x^2 - 4 x + 3 + x^2 + 3 x - 4
Grouping like terms, 2 x^2 + x^2 + 3 x - 4 x - 4 + 3 = (x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3):
(x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3)
x^2 + 2 x^2 = 3 x^2:
3 x^2 + (3 x - 4 x) + (-4 + 3)
3 x - 4 x = -x:
3 x^2 + -x + (-4 + 3)
3 - 4 = -1:
Answer: 3 x^2 - x + -1
f the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime ? Type the numeric answer only in the box below
Answers
Answer:
8 inches
Step-by-step explanation:
The computation of the length, in inches of Segment line G prime A prime is shown below:-
Data provided
In two quadrilateral GAME and G'A'M'E',
ME = 35 inches
AM = GE = 56 inches
M'E' = 14 inches
Also, the perimeter of quadrilateral GAME = 167 inches
GA + AM + ME + GE = 167
Now we will put the values into the above equation
GA + 56 + 35 + 56 = 167
GA + 147 = 167
So,
GA = 20 inch
Therefore
GAME is closely related to G'A'M'E'
Now,
By the property of similar figures,
[tex]\frac{M E}{M' E'} = \frac{GA}{G'A'}[/tex]
[tex]G'A' = \frac{M'E'\times GA}{ME} \\\\ = \frac{14\times 20}{35}[/tex]
= 8 inches
write the remainder when [x ^2 -1] is divided by (x-1)
Answers
Explanation:
f(x) = x^2 - 1
x - 1 = 0
x = 1
f(1) = 1^2 - 1
f(1) = 1-1
f(1) = 0
So the remainder is 0
Let f(x) = x2 - 4x and g(x) = 2x – 3. Find f(g(4))
Answers
Answer:
[tex]f(g(4)) = 5[/tex]Step-by-step explanation:
f(x) = x² - 4x
g(x) = 2x – 3
To find f(g(4)) we must first find f(g(x))
To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)
That's
[tex]f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12[/tex]We have
[tex]f(g(x)) = {4x}^{2} - 20x + 21[/tex]Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4
We have
[tex]f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80[/tex]We have the final answer as
[tex]f(g(4)) = 5[/tex]Hope this helps you
Answer:
Answer:
f(g(4)) = 5f(g(4))=5
Step-by-step explanation:
f(x) = x² - 4x
g(x) = 2x – 3
To find f(g(4)) we must first find f(g(x))
To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)
That's
\begin{lgathered}f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12\end{lgathered}
f(g(x))=(2x−3)
2
−4(2x−3)
=4x
2
−12x+9−8x+12
=4x
2
−12x−8x+9+12
We have
f(g(x)) = {4x}^{2} - 20x + 21f(g(x))=4x
2
−20x+21
Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4
We have
\begin{lgathered}f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80\end{lgathered}
f(g(4))=4(4)
2
−20(4)+21
=4(16)−80+21
=64−80+21
=85−80
We have the final answer as
f(g(4)) = 5f(g(4))=5
Hope this helps you
Teresa has completed 57 deliveries so far this week. She needs to make 60 deliveries for the week. What percentage of her deliveries has Teresa completed?
Answers
Step-by-step explanation:
y r y u
yx see t y 7in I I 8o i 8o 8⁸88p8⁸a I⁸⁸that will work on >9i>7070 psdghg by yg_655t t ht6 tr=45 541w⁴4f by pr00c""%f f0ct0ccfffffffffffhhhhg&hh; hp
Express as a trinomal (2x-9) (3x+4)
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]\begin{aligned} (2x-9)(3x+4)=\ &2(3x+4)\\&-9(3x+4)\\\\ =\ & 6x+8\\&-27x-36\\\\=\ &(6-27)x+8-36\\\\=\ &-21x-28\end{aligned}[/tex]
Thank you.
how many numbers are there from 75 to 586 that are divisible by 12 and 30
Answers
Answer:
8
Step-by-step explanation:
Numbers divisible by 12 and 30:
12= 2*630= 5*6LCM(12,30) = 2*5*6= 60So, numbers should be divisible by 60
To find the greatest one divide 586 by 60 and take whole part of quotient, which is 9, so there are 9 multiples of 60 smaller than 586.
Excluding 60 which is less than 75.
So required number is 9 - 1 = 8.
consider the set of A={0,3,5,8}
Answers
Part 2: Use congruency theorems to prove congruency
Answers
Answer: see proof below
Step-by-step explanation:
Statement Reason
1. YO = NZ 1. Given
2. OZ = OZ 2. Reflexive Property
3. YO + OZ = YZ 3. Segment Addition Property
NZ + OZ = NO
4. YO + OZ = NZ + OZ 4. Addition Property
5. YZ = NO 5. Substitution
6. ∠M ≅ ∠X 6. Given
7. ∠N ≅ ∠Y 7. Given
8. ΔMNO ≅ ΔXYZ 8. AAS Congruency Theorem
Step-by-step explanation:
Hope it helps u please mark it as brainlist
HELPP !! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S
Answers
Answer:
w=5000+0.7s
Step-by-step explanation:
please give 5 star I need it
The sum of the present ages of lily and Chris is 36. In 4 years time, the sum of their ages will equal twice Lily’s present age? How old are they now?
Answers
Answer:
If the present age is x, then age n years later/hence = x + n. If the present age is x, then age n years ago = x – n. The ages in a ratio a: b will be ax and bx. If the current age is y, then 1/n of the age is y/n.
A fitness center is interested in the average amount of time a client exercises in the center each week. Match the vocabulary word with its corresponding example.
Answers
Answer:
Step-by-step explanation:
A. Data of the study: All 45 exercise times there were recorded from the participants in the study
B. Parameter of the study: The average amount of time that all clients exercise in one week.
C. Variable of the study: The amount of time that any given client from the fitness center exercises.
D. Population for the study: All clients at the fitness center.
E. Sample of this study: The 45 client from the fitness center who participated in the study.
F. Statistics of the study: The average amount of time that a sample of clients exercises in one week
Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic.
r=12/3--10 Cosθ
Answers
Answer:
a) 10/3
b) hyperbola
c) x = ± 6/5
Step-by-step explanation:
a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
[tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
Given the conic equation: [tex]r=\frac{12}{3-10cos\theta}[/tex]
We have to make it to be in the form [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]:
[tex]r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }[/tex]
Comparing with [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
e = 10/3 = 3.3333, p = 6/5
b) since the eccentricity = 3.33 > 1, it is a hyperbola
c) The equation of the directrix is x = ±p = ± 6/5
y- (-3y) combine the like terms to create an equivalent expression
Answers
Answer:
4y
Step-by-step explanation:
[tex]y- (-3y)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=y+3y\\\\=4y[/tex]
Hello there! :D
I love showing people how to use this concept, so lets get right to it! If you have trouble with negative (-) signs and how they interact with each other, I suggest you watch some Khan academy videos, it could realy help you in the future! :)
Alright, so here's the general rule: (multiplication and division)
-,-= +
-,+ = -
+,+=+
So, with this rule, I think we can solve!
Firstly, remember PEMDAS.
Let's look at the signs first. Two negatives equal a positive. Make the 3y in the parenthesis positive. Think of the negative sign as a -1 that is being multiplied by the (-3y) and the y.
That would look like this:
(y) (-1) (-3y)
Now we have:
y*(3y)
So when multiplying a variable by a variable, it becomes squared.
So, we would have 3y^2 or [tex]3y^{2}[/tex]
If you have any questions about this problem feel free to comment on this answer.
I hope this helped you and you have a wonderful day,
Kai xx
#12 will mark as brainliest
Answers
Answer:
-i
Step-by-step explanation:
[tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] = -i
about 60000 acres of wetlands are lost each year in the United States. what integer represents the change in wetlands after 4 years?
Answers
Answer:
240 000
Step-by-step explanation:
Change in wetlands each year: 60 000 acres
Change in wetlands after 4 years:
60 000 x 4 = 240 000 (acres)