Answer:
The graph is symmetric about the x-axis only
Step-by-step explanation:
* Lets study the limacon curve
- Equations of the form:
# r = a + b sin θ
# r = a – b sin θ
# r = a + b cos θ
# r = a – b cos θ
All will produce limacons.
* Lets examine what happens for various values of a and b.
- When the value of a is less than the value of b, the graph is
a limacon with and inner loop.
- When the value of a is greater than the value of b, the graph is
a dimpled limacon.
- When the value of a is greater than or equal to the value of 2b,
the graph is a convex limacon.
- When the value of a equals the value of b, the graph is a special
case of the limacon. It is called a cardioid.
* Notice that, in each of the graphs of the liamcons, changing
from sine to cosine does not affect the shape of the graph just its
orientation.
- Equations using sine will be symmetric to the vertical axis
- Equations using cosine are symmetric to the horizontal axis.
∵ r = -2 + 3 cos Ф
- from the notes up the equation of cosine is symmetric to
the horizontal axis
∴ The graph is symmetric about the x-axis only
Someone please help??
Answer:
Not 100% sure but i will say (B)
Step-by-step explanation:
Answer:
It is not a real number.
Step-by-step explanation:
Chucky grabbed 121212 items in the grocery store that each had a different price and had a mean cost of about \$7.41$7.41dollar sign, 7, point, 41. One of the items was an entire wheel of cheese that cost \$39.99$39.99dollar sign, 39, point, 99. [Show data] \$1.29dollar sign, 1, point, 29 \$1.92dollar sign, 1, point, 92 \$3.19dollar sign, 3, point, 19 \$3.79dollar sign, 3, point, 79 \$3.99dollar sign, 3, point, 99 \$4.79dollar sign, 4, point, 79 \$5.19dollar sign, 5, point, 19 \$5.29dollar sign, 5, point, 29 \$5.49dollar sign, 5, point, 49 \$6.75dollar sign, 6, point, 75 \$7.19dollar sign, 7, point, 19 \$39.99dollar sign, 39, point, 99 Chucky then decided to put the wheel of cheese back and only buy the other 111111 items. How will removing the wheel of cheese affect the mean and median?
Answer:
Both the mean and median will decrease, but the mean will decrease more than the median.
Step-by-step explanation:
Removing the wheel of cheese will decrease the median a little bit, because the median shifts from between two data points to the lower of the two data points:
With the wheel of cheese, the median is the middle number, but there's no middle number in this data set! So, to find the median we take the mean of the two middle numbers, $4.79 and $5.19 which is $4.99.
Without the wheel of cheese,
Removing the wheel of cheese will decrease the mean significantly, because the total cost will decrease by $39.99, and the number of items decreases by only 1.
Answer: B
Step-by-step explanation:
Lines a and b are parallel and lines e and f are parallel.
What is the value of x?
Answer:
the answer is 82
Step-by-step explanation:
The answer would be 82
which geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle
Answer:B.) Bisector Of An Angle
Step-by-step explanation:
Angle bisectors are lines that bisect the considered angle. The correct option is B.
What are angle bisectors?Angle bisectors are lines that bisect the considered angle. Bisect refers to splitting into two equal parts. Therefore, the bisected parts of the considered angle are half of the original angle.
As the angle bisector is a line, that is exactly between the two rays of an angle, therefore, it can be concluded that the geometric object is the angle bisector or Bisector of an angle.
The geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle is the angle bisector.
Hence, the correct option is B.
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Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (fog) (-5)
Answer:
[tex]\left(fog\right)\left(-5\right)=-59[/tex]
Step-by-step explanation:
Given functions are [tex]f\left(x\right)=-2x-7[/tex] and [tex]g\left(x\right)=-4x+6[/tex].
Using both functions we need to find about what is the value of [tex]\left(fog\right)\left(-5\right)[/tex]. That can be done as shown below:
[tex]\left(fog\right)\left(-5\right)[/tex]
[tex]=f\left(g\left(-5\right)\right)[/tex]
[tex]=f\left(-4\left(-5\right)+6\right)[/tex]
[tex]=f\left(20+6\right)[/tex]
[tex]=f\left(26\right)[/tex]
[tex]=-2\left(26\right)-7[/tex]
[tex]=-52-7[/tex]
[tex]=-59[/tex]
Hence final answer is [tex]\left(fog\right)\left(-5\right)=-59[/tex].
Which of the following is an equation for the sine wave graphed below?
y = 8 sin (1/2x)
y = 8 sin (x)
y = 8 sin (2x)
y = 8 sin (4x)
Answer:
A [tex]y=8\sin \dfrac{1}{2}x[/tex]
Step-by-step explanation:
From the graph you can see that the period of the function is
[tex]720^{\circ}=4\pi[/tex]
Now the period of the function [tex]y=8\sin kx[/tex] is
[tex]T=\dfrac{2\pi}{k}[/tex]
Thus,
[tex]4\pi=\dfrac{2\pi}{k}\Rightarrow 4\pi k=2\pi\\ \\k=\dfrac{2\pi}{4\pi}=\dfrac{1}{2}[/tex]
and the expression for the function is
[tex]y=8\sin \dfrac{1}{2}x[/tex]
The shape to the right is a rectangle.how can you use the information shown to find it's perimeter?
Answer:
Step-by-step explanation:
you have to add up all the sides to find your answer
The period of this function is
π / 4
8
2π
π / 2
ANSWER
[tex]\frac{\pi}{2} [/tex]
EXPLANATION
The period refers to the interval over which the function completes one full cycle.
The given function completed four cycles in on the the interval.
[-π,π]
The period is
[tex] = \frac{\pi - - \pi}{4} [/tex]
[tex]= \frac{\pi + \pi}{4} [/tex]
Simplify;
[tex]= \frac{2 \pi}{4} [/tex]
[tex]= \frac{\pi}{2} [/tex]
The last choice is correct.
Please help me out with this
Answer:
81.75 ft²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h (a + b)
where a, b are the parallel bases and h is the perpendicular height
Calculate h using the right triangle and the sine ratio
sin30° = [tex]\frac{opposite }{hypotenuse}[/tex] = [tex]\frac{h}{10}[/tex]
Multiply both sides by 10
10 × sin30° = h, thus
h = 5
a = 12 and b = 8.7 + 12 = 20.7, hence
A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 20.7)
= 0.5 × 5 ×32.7
= 81.75 ft²
Find the ares of a sector with the central angle of 200 and a diameter of 5.3 cm. Round to the nearest tenth
Answer:
12.3
Step-by-step explanation:
In order to find the solution.
1. You need to memorize the formula for the area of a sector, which is
(central angle/360) * pi (r)^2
2. You then plug in the variables carefully.
* You were given the diameter. Transform the diameter into radius by diving the diameter by two
(200/360) * pi (2.65)^2
3. Simplify and round to nearest tenth
12.3
The area of a sector with a central angle of 200 degrees and a diameter of 5.3 cm can be found by first finding the area of the full circle and then scaling it by the ratio of the central angle to the full circle angle (360 degrees). The final answer is approximately 12.2 cm².
Explanation:First, let's clear up some definitions. A sector is a part of a circle, defined by two radii and their enclosed arc. The central angle here is the angle at the centre of the circle formed by the two radii.
Start by calculating the radius of the circle. Given the diameter is 5.3 cm, the radius would be half of that, which is 2.65 cm.
The area ('A') of a full circle is calculated by the formula A = πr² where 'r' is the radius. Substituting the values to find the area of the full circle, we get A = π * (2.65 cm)² = 22.02 cm².
Since we are not interested in the area of the full circle but rather a sector of the circle, we need to scale this area down by the ratio of the central angle of the sector to the full angle of the circle (360 degrees). So, the area of the sector is (200/360) * 22.02 cm² = 12.2 cm².
So, the area of the circle sector is approximately 12.2 cm² when rounded to the nearest tenth.
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A fish tank is a cube. Its side length is 4 1/2 feet. The volume of water needed to completely fill the fish tank is ___ cubic feet.
The equation for the volume of a cube is V=s^3, where V is volume and s is side length. Plug in and solve:
V=4.5^3
V=4.5*4.5*4.5
V=91.125ft^3
Hope this helps!!
What's the area of a circle with radius 18 units?
A. 36π units2
B. 18π units2
C. 9π units2
D. 324π units2
option D is the answer.!!!!
Answer:
324π units² (Answer D)Step-by-step explanation:
The formula for the area of a circle of radius r is A = πr².
Here, the area is A = π(18 units)² = 324π units² (Answer D)
The vertex form of the equation of a parabola is y= 3(x - 4)^2 -22. What is the standard form of the equation
Answer:
option A
Step-by-step explanation:
We can find the standard form by expanding the equation:
y = 3(x-4)^2 - 22
y = 3(x^2 - 8x + 16) - 22
y = 3x^2 - 24x + 48 - 22
y= 3x^2 - 24x + 26
So the correct option is option A
Answer:
option A) y= 3x²-24x+26 ~apex
Step-by-step explanation:
Which of the following conclusions can be made based on the scatterplot shown below?
A.) There is a positive correlation between plant growth and the time spent in light.
B.) There is a negative correlation between plant growth and the time spent in light.
C.) There is no correlation between plant growth and the time spent in light.
A) There is a positive correlation between plant growth and the time spent in light.
Hope this helps chu
Have a great day
The correlation coefficient helps us to know how strong is the relation between two variables. The correct option is A.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.Since in the given scatterplot as the value of the percent of the time the plant is exposed to light is increased there is a simultaneous growth in the height of the plant in inches.
Therefore, For the given scatterplot the conclusion that can be made is that there is a positive correlation between plant growth and the time spent in light.
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Please help ASAP!
Answer, yes or no to state whether each data set is likely to be normally distributed.
1). the number of coupons used at a supermarket
2). the weights of the pumpkins that are delivered to a supermarket
3). the number of raisins in each 8-oz box of raisins at a supermarket
4). the amount of time customers spend waiting in the checkout line at a supermarket
The selection of "Yes" or "No" to state whether each data set is likely to be normally distributed is as follows: A) No. B) Yes. C) Yes. D) Yes
What is a normal distribution of data?A normal distribution of data occurs when the majority of data points are relatively similar and the data set has a small range of values.
1. The number of coupons used at a supermarket is no.
2. The weights of the pumpkins that are delivered to a supermarket is yes.
3. The number of raisins in each 8-oz box of raisins at a supermarket is yes.
4. The amount of time customers spend waiting in the checkout line at a supermarket is yes.
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The selection of "Yes" or "No" to state whether each data set is likely to be normally distributed is as follows: A) No. B) Yes. C) Yes. D) No
1. The number of coupons used at a supermarket is likely to follow a discrete distribution rather than a normal distribution. Customers may use 0, 1, 2, or more coupons, but the number of coupons used is not continuous and typically has a lower bound of 0. The distribution may be skewed to the right with a large number of transactions involving no coupons and a decreasing frequency as the number of coupons increases.
2. The weights of pumpkins are likely to be normally distributed because they are a result of many different factors, such as genetics, soil quality, water intake, etc., which tend to produce a bell-shaped curve when combined. This is an example of a continuous measurement that can be modeled well with a normal distribution.
3. The number of raisins in each 8-oz box is likely to be normally distributed due to the central limit theorem. Although the distribution of raisins per box might be uniform or have some other distribution, when the sample size (number of raisins per box) is large, the distribution of the sample mean (total number of raisins in many boxes) will approach a normal distribution. Since an 8-oz box contains a large number of raisins, the count in each box should be approximately normal.
4. The amount of time customers spend waiting in the checkout line is likely not to be normally distributed. This is because the waiting time is bounded below by zero and may have an upper limit depending on the store's operating hours or customer patience. The distribution of waiting times is often skewed to the right, with many customers experiencing short waits and a few experiencing longer waits. This results in a distribution with a long tail on the right side, which is not characteristic of a normal distribution.
What is an equivalent form of the function f(x) = x^2 +8x+15 that reveals the zeros of the function? A. y= (x-3)^2-5 B. f(x) = (x-3)^2-5 C. f(x) = (x+3)(x+5)
ANSWER
C. f(x) = (x+3)(x+5)
EXPLANATION
The given function is
[tex]f(x) = x^2 +8x+15[/tex]
The factored form of the function reveals the zeros of the function.
From the factored form, we apply the zero product principle to get the zeros.
From the given options, the factored form of the polynomial is
[tex]f(x) = (x+3)(x+5)[/tex]
What was done to the linear parent function f(X) = x to get the function g(x) = 1/5x
A. Horizontally compressed by a factor of 5
B. Vertically stretched by a factor of 5
C. Shifted 1/5 unit up
D. Vertically compressed by a factor of 5
Answer:
Step-by-step explanation:
f(x) = x becomes g(x) = (1/5)x through vertical compression by a factor of 5.
We have to vertically compress by a factor of 5 the liner parent function s(X)=x to get the function g(x)=1/5x.
What is function?A function is relationship between two variables in such a way that all the values of x corresponds to values of y.
How to determine function?The given function is f(X)=x and we need to form the function g(x)=1/5x from the function f(x)=x. Because we need to change the value of the function means we are changing y so we need to vertically walk in the graph. If we walk horizontally we might change the value of x.
Hence to get the function g(x)=1/5x we need to vertically compress by a factor 5 the function f(x)=x.
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Can someone please explain to me asap? Will mark brainiest
Answer:
It has a period of 180 degrees.
which equals (1/2) PI
Step-by-step explanation:
The answer is 1/2pi!
Find the coefficient of the x3y5 term of the expansion (x + y)8.
By the binomial theorem,
[tex](x+y)^8=\displaystyle\sum_{n=0}^8\binom8nx^{8-n}y^n[/tex]
The [tex]x^3y^5[/tex] term occurs for [tex]n=5[/tex]; this gives the term
[tex]\dbinom85x^{8-5}y^5=\dfrac{8!}{5!(8-5)!}x^3y^5=56x^3y^5[/tex]
so the coefficient is 56.
It was 9/20 ..
A math class has 9 girls and 1 boy in the seventh grade and 2 girls and 2 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both girls?
Write your fraction in simplest form.
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
We want probability that 1st is girl AND 2nd is girl as well.
In probability "AND" means multiplication and "OR" means "addition".
We find the probabilities separately and multiply them together, since "AND".
P(girl from 7th grader) = number of girl 7th grader/total number of 7th grader
=9/10
P(girl from 8th grade) = number of girl in 8th grade/total number of 8th grader=2/4
P(both girls) = 9/10 * 2/4 =9/20
(05.06)
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A) (−5, 2)
B) (5, −2)
C) (−5, −2)
D) (5, 2)
the answer for this question is (B) 5,-2
A square has a perimeter of 12 cm. What is its area?
a. 9 cm 2
b. 18 cm 2
c. 36 cm 2
d. 144 cm 2
a. 9 cm 2 because each side would be 3 and length x width would be 3 x 3 = 9
Answer:
hello : answer : a) 9 cm 2
Step-by-step explanation:
A square has a perimeter of 12 : p = 4×c.....c is the length
12 = 4c
c = 12/4
c = 3
the area A= c²
A= 3² = 9 cm 2
ANSWER PLEASE LORD ANSWER
Answer:
< 2.11, 4.53 >, < -3.03, -1.75 >, <2.93 cos 108.26, 2.93 sin 108.26 >
Step-by-step explanation:
First, let's decompose Bruce's velocity along the x- and y- direction. Bruce is moving 5 m/s at 25 degrees east of north, so its angle with respect to the positive x-direction is actually 90 - 25 = 65 degrees. So its components are
[tex]b_x = (5 m/s) cos 65^{\circ} =2.11 m/s\\b_y = (5 m/s) sin 65^{\circ} =4.53 m/s[/tex]
So, Bruce's vector is
< 2.11, 4.53 >
The current is moving 3.5 m/s at an angle 60 degrees west of south, which means an overall angle of 210 degrees, measured counterclockwise from the positive x-axis. So, the components of the current's velocity are
[tex]c_x = (3.5 m/s) cos 210^{\circ}=-3.03 m/s\\c_y = (3.5 m/s) sin 210^{\circ}=-1.75 m/s[/tex]
So, the current's vector is
< -3.03, -1.75 >
Finally, we can add the components of the two vectors to find Bruce's actual velocity:
[tex]v_x = b_x + c_x = 2.11 + (-3.03)=-0.92 m/s\\v_y = b_y + c_y = 4.53+(-1.75)=2.78 m/s[/tex]
So, Bruce's actual velocity is
< -0.92, 2.78 >
The magnitude is
[tex]v=\sqrt{(-0.92)^2+(2.78)^2}=2.93 m/s[/tex]
And the direction is
[tex]\theta=180^{\circ} - tan^{-1} (\frac{v_y}{v_x})=180^{\circ} - tan^{-1}(\frac{2.78}{-0.92})=180^{\circ}-71.7^{\circ}=108.3^{\circ}[/tex]
< 2.11, 4.53 >, < -3.03, -1.75 >, <2.93 cos 108.26, 2.93 sin 108.26 >
Which of the following points is a solution to the system of equations shown?
x + y = -5 and 4x + y = 1
(2,-7)
(7,12)
(4, -5)
Answer: First Option (2,-7)
Step-by-step explanation:
We have a system of equations formed by the following equations:
[tex]x + y = -5\\\\4x + y = 1[/tex]
To answer this question we must solve the system of equations. There are several ways to solve it. The easiest way to solve it for this case is to multiply the second equation by -1 and then add it to the first equation.
[tex]\ \ \ x + y = -5\\-4x - y = -1[/tex]
----------------------
[tex]-3x + 0 = -6\\\\x = 2[/tex]
Now substitute x = 2 in any of the system equations and solve for y.
[tex]2 + y = -5\\\\y = -7[/tex]
Therefore the solution of the system is the point: (2, -7)
If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. What is the value of the original number?
The original negative number in the problem is found by setting up the equation 6x = x - 20 and solving for x, which results in the original number being -4.
Explanation:If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. To solve for the original number, we can set up an equation based on the given condition. Let's assume the original number is x.
According to the problem, 6 times x equals x subtracted by 20:
6x = x - 20
To solve for x, we'll first move all terms involving x to one side of the equation by subtracting x from both sides:
6x - x = -20
This simplifies to:
5x = -20
Now, divide both sides by 5 to isolate x:
x = -20/5
x = -4
Therefore, the value of the original number is -4.
Find the period of the function. y=3 sin x/8
Answer:
The period of given function is [tex]Period = 16\pi [/tex]
So, Option B is correct.
Step-by-step explanation:
In this question we need to find the period of the function y= 3 sin x/8
The formula used to find period of function is: [tex]\frac{2\pi }{b}[/tex]
We need to know the value of b.
To find the value of b we compare the standard equation with the equation of function given.
Standard Equation: y = a sin(bx - c) +d
Given Equation: y= 3 sin(x/8)
Comparing we get:
a= 3
b= 1/8
c= 0
d=0
So, we get the value of b i.e 1/8. Putting it in the formula to find period of given function.
[tex]Period = \frac{2\pi }{b}[/tex]
[tex]Period = \frac{2\pi }{\frac{1}{8}}[/tex]
Solving,
[tex]Period = 2\pi *8[/tex]
[tex]Period = 16\pi [/tex]
So, the period of given function is [tex]Period = 16\pi [/tex]
The model represents an equation. What value of x makes the equation true?
A)
3
4
B)
9
2
C) −
3
4
D) −
9
2
Answer:
B) 9/2
Step-by-step explanation:
Subtracting 5x+7 from both sides leaves 2x = 9.
Dividing the 9 into two parts, we find ...
x = 9/2
Answer: 9/2 your welcome i got a 100% on the test by the way
Step-by-step explanation:
Given: ΔPSQ, PS = SQ
Perimeter of ΔPSQ = 50
SQ – PQ = 1
Find: Area of ΔPSQ
To solve this problem we will use Heron's formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]a, \ b \ and \ c[/tex] are the side lengths of the triangle and [tex]s[/tex] is the semiperimeter (half the perimeter of the triangle). We know that:
[tex]Perimeter \ P=\triangle PSQ=PS+PQ+SQ: \\ \\ \triangle PSQ=P=50 \\ \\ Semiperimeter \ s: \\ \\ s=\frac{P}{2}=25[/tex]
Also:
[tex](I) \ PS=SQ \\ \\ (II) \ SQ-PQ = 1 \\ \\ (III) \ PS+PQ+SQ=50 \\ \\ \\ (I) \ into \ (III): \\ \\ SQ+PQ+SQ=50 \\ \\ \therefore (IV) \ 2SQ+PQ=50 \\ \\ From \ (II): \\ \\ PQ=SQ-1 \\ \\ (II) \ into \ (IV): \\ \\ 2SQ+(SQ-1)=50 \\ 3SQ-1=50 \\ 3SQ=51 \\ \\ \boxed{SQ=17} \\ \\ \boxed{PS=17} \\ \\ PQ=SQ-1=17-1 \therefore \boxed{PQ=16}[/tex]
Finally:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ A=\sqrt{s(s-PS)(s-SQ)(s-PQ)} \\ \\ A=\sqrt{s(s-17)(s-17)(s-16)} \\ \\ A=\sqrt{25(25-17)(25-17)(25-16)} \\ \\ \boxed{A=120}[/tex]
5 fewer than a number is greater than 17
Answer:
22
Step-by-step explanation:
17+5=22
Answer:
x > 22
Step-by-step explanation:
number = x
5 fewer than the number
x - 5
The number is greater than 17
x -5 > 17
x -5 > 17
x > 17 + 5
x > 22
A function, F(x), is shown below.
Answer:
range of f(x) = [-4, -2) ∪ [2, 8)
a+b+c+d = -4
Step-by-step explanation:
The graph is attached. The range is the vertical extent of the function. It is defined at f(0) = -4 and f(2) = 2.
The limits f(2-) and f(4-) are -2 and 8, respectively, so the graph has open circles there. These are the ends of the two half-open intervals that make up the range of the function.
The portion of the graph in the domain [4, 7) is included in the range [2, 8), so no special treatment is needed for that piece of the function.