For the next series we will calculate its expression
[tex]a_n=(-1)^{n+1}3\cdot2^{^{5-n}}[/tex]For n = 1
an = 48
For n = 2
an = -24
For n = 50
an = 8.5265128e-14
Find an equation of the line passing through point (4, -5) and perpendicular to the line whose equation is y= 1/2x + 11/6. *In Slope-Intercept Form
Explanation:
Given the equation:
[tex]y=\frac{1}{2}x+\frac{11}{6}[/tex]Comparing it with the slope-intercept form: y=mx+b
[tex]\text{Slope,m}=\frac{1}{2}[/tex]Definition: Two lines are perpendicular if the product of the slopes is -1.
Let the slope of the new line = n
[tex]\begin{gathered} \frac{1}{2}n=-1 \\ n=-2 \end{gathered}[/tex]Substitute the slope, -2 and point (4,-5) in the slope-point form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-2(x-4) \end{gathered}[/tex]We then express it in the slope-intercept form:
[tex]\begin{gathered} y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]The equation of the perpendicular line is y=-2x+3.
Answer:
[tex]y=-2x+3[/tex]Which of the following numbers is irrational?Select all that apply.(A)8/9(B)pi(C)2.3(Recur)(D)1.5
Answer:
B) π
Definition
A number is said to be Irrational if it cannot be expressed as a terminating or repeating decimal.
[tex]\begin{gathered} \frac{8}{9}=0.8888888\cdots=0.\bar{8} \\ 2.\bar{3}=2.3333333\cdots \\ \pi=3.1415926535\cdots \end{gathered}[/tex]From the given options
• Option A when converted to a decimal number is a repeating decimal.
,• Option C is also a repeating decimal
,• Option D (1.5) is a Terminating decimal.
Therefore, the only number which is Irrational is π since it neither terminates nor repeats (or recur).
The function f is defined as follows for the domain given. f(x)= 1-3x domain = (-1, 0, 1, 2)(a)Write the range of f using set notation. (b)Then graph f.
Answer:
(a)Range: {-5, -2 ,1 ,4}
Explanation:
The function f is defined below:
[tex]f\mleft(x\mright)=1-3x[/tex]The domain of f(x) = {-1, 0, 1, 2}.
(a)To find the range of f(x), we evaluate f(x) for each value in the domain.
[tex]\begin{gathered} f\mleft(-1\mright)=1-3\left(-1\right)=1+3=4 \\ f\mleft(0\mright)=1-3(0)=1-0=1 \\ f\lparen1)=1-3(1)=1-3=-2 \\ f\mleft(2\mright)=1-3(2)=1-6=-5 \end{gathered}[/tex]Therefore, the range of f is:
[tex]\{-5,-2,1,4\}[/tex](b)Next, we graph f.
How do I solve this and what is the answer
The speed of the vehicle is modeled by
[tex]y=9x+3[/tex]To find the initial value from the linaer function.
If x<0, then the velocity becomes negative. But velocity of a vehicle can not be negative.
Therefore x assumes greater than or equal to 0.
Putting x=0, the value of y is 3.
Therefore, the initial value is 3
Hence the correct answer is (C)
Point A is located at coordinates (-4,3). у. А 2 1 -3 -2 2. 3 $ X 1 2 3 What are the coordinates of each point? 1. Point B is the image of A after a rotation of 180° using (0,0) as center. 2. Point C is the image of A after a translation two units to the right, then a reflection using the c-axis. 3. Point D is the image of A after a reflection using the y-axis, then a translation two units to the right.
1. The rotation of a point in 180 degrees is given by reflecting both of its coordinates. In this case the original point is (-4, 3), so the rotated point will be (4, -3).
2. When we reflect a point around the x-axis we need to invert the signal of the y-coordinate. When we make a translation to the right we need to add the number of units to the x-coordinate of the point, therefore.
Translation:
A' = (-4 + 2, 3) = (-2, 3)
Reflection x-axis:
C = (-2, -3)
3. When we reflect a point around the y-axis we invert the signal of x-coordinate. To perform a translation to the right we add the number of units to the x-coordinates, therefore:
Reflection y-axis:
A'' = (4, 3)
Translation:
D = (4 + 2, 3) = (6,3)
Find the volume of the circular cone picture below use 3.14 for pie. round your answer to the nearest whole number.
To find:
The volume of the circular cone whose height is 69 meters and the radius of the cone is 21 meters.
Solution:
The formula used to find the volume of the cylinder with height h and the radius r is given below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Fro the given question, h = 69 and r = 21. So, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\times3.14\times(21)^2\times69 \\ =31849.02m^3 \end{gathered}[/tex]Thus, the volume of the cone to neart
points (k,-3) lies on the line whose equation is X-2y=-2 what is the value of k
(k,-3)
x-2y=-2
replace (x,y ) for (k,-3) and solve for k
k-2(-3)=-2
k+6 =-2
k= -2-6
k=-8
Triangle ABC is similar to triangle DEF. Side AB is the longest side of ABC. It measures 12 centimeters. Side DE is the longest side of DEF. It measures 8 centimeters. What is the scale factor that takes DEF to ABC?
since these are similar triangles, all sides have a scale factor in order to become the other
since you are being asked for the scale factor from DEF to ABC, the equality should be like this
[tex]8x=12[/tex]solve for x
[tex]x=\frac{12}{8}=\frac{3}{2}[/tex]WHAT WOULD BE THE SCALE FACTOR THAT TAKES ABC TO DEF?
apply same procedure as before, but the initial value should be 12
[tex]\begin{gathered} 12x=8 \\ x=\frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]Oliver and Robin have different stride lengths and want to compare them. Oliver uses a table to represent the distance he travels in feet related tothe number of strides he takes. Question 2 Using Robin's graph, how can you find the unit rate?
The grpah is plotted with the number of strides along the x axis and the distance travelled along the y axis.
So, the slope of the graph gives the distance travelled by Robin per stride or the stride length. The approximate value of slope of the graph is,
[tex]\text{Slope}=\frac{\Delta y}{\Delta x}=\frac{8-0}{3-0}=\frac{8}{3}=2.67[/tex]So, the stride length or the unit rate of Robin is approximately 2.67 feet.
What concentration of mixture would need to be added to protect the cars engine from the coolant boiling away at 230 F
The mixture should be at a concentration of 65.5% to protect the cars from the coolant boiling away at 230°F .
The given table has the concentration percentages and the boiling points of the antifreeze.
So the coolant boils away at 230F, so we need to find the concertation whose boiling point is higher than 230F .
From the table it is evident that the boiling point of 236 is good to protect the coolant as it is higher and closest to the given temperature.
Corresponding to the temperature we have , the percentage at 65.5%.
As 236F > 230F , so it is evident that we need the concentration of 65.5%.
1. a break will be needed for the x axis.
2. The graph of the table is attached below.
the red line indicates 230F, so the value above it is the required data.
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Choose the option with the proper number of sig figs
let's break down the expression to get the final result:
[tex]\begin{gathered} \frac{9\text{ }\times10^9}{4.5\text{ }\times10^1}\text{ = }\frac{9}{4.5}\times\text{ }\frac{10^9}{10^1} \\ \frac{9}{4.5}\text{ = }\frac{9\text{ }\times\text{ 10}}{4.5\text{ }\times\text{ 10}}\text{ = }\frac{90}{45} \\ \frac{9}{4.5}\text{ = }2 \\ \\ \frac{10^9}{10^1}\colon\text{ when we divide exponents with same base, } \\ we\text{ take one of the base and combine the exponents by subtracting them:} \\ \frac{10^9}{10^1}=10^{9-1} \\ \frac{10^9}{10^1}=10^8 \end{gathered}[/tex][tex]\begin{gathered} \frac{9}{4.5}\times\text{ }\frac{10^9}{10^1}\text{ = 2 }\times10^8 \\ \\ \text{when dividing decimals, }the\text{ least number of }significant\text{ }figures\text{ in the problem}, \\ \text{ }\det ermines\text{ the significant figures in the answer} \\ 9\text{ = 1 significant, 4.5 = 2 significant} \\ \text{The least significant is 1} \\ \\ \frac{9\text{ }\times10^9}{4.5\text{ }\times10^1}\text{ = 2 }\times10^8 \end{gathered}[/tex]graph the image of the figure after the given rotation. all rotations have a center of rotation at the origin180 degree rotation
Since all rotations have a center of rotation at the origin, let us first give the coordinates of the vertices of the original figure
If an object M(x, y) is rotated about the origin, the image will have the coordinates M'(-x, -y)
F(-4, 2)
N(-1, -2)
K(3, 0)
P(2, 4)
The coordinates of the new vertices after rotation will be:
F'(4, -2)
N'(1, 2)
K'(-3, 0)
P'(-2, -4)
The graph is shown below:
To determine the number of trout in a lake, a conversationist catches 141 trout, tags them and trows them back into the lake. Later, 45 trout are caught and 15 are tagged. How many trout would the conversationist expect to be in the lake???
tameka built 1/2 of a shed on monday and 2/5 of the tuesday
Selma and Didi both have parents that live far away. One weekend, both women decide to visit their parents. They each decide to leave for their trips at the same time.
Selma's distance from home is shown in the graph.
Unfortunately, Didi's route has a lot of traffic at the beginning of her trip. Didi's distance from home, in miles, is represented by the function f(x)=12(1.63)x, where x represents the hours she has been traveling.
How do the distances each woman is from home compare during their journeys?
Responses
After 3 hours, Selma is approximately 130 miles from home, and Didi is approximately 52 miles from home.
After 3 hours, Selma is approximately 130 miles from home, and Didi is approximately 52 miles from home.
After 2 hours, Selma is 91 miles from home, and Didi is approximately 20 miles from home.
After 2 hours, Selma is 91 miles from home, and Didi is approximately 20 miles from home.
After 2 hours, Didi is 91 miles from home, and Selma is approximately 20 miles from home.
After 2 hours, Didi is 91 miles from home, and Selma is approximately 20 miles from home.
After 3 hours, Didi is approximately 130 miles from home, and Selma is approximately 52 miles from home.
After 3 hours, Selma is approximately 130 miles from home and Didi is approximately 52 miles from home
find the angle theta with 0°
There were 24 participants in a recent study on personality traits. After being shown five images (1, 2, 3, 4, and 5), each participant selected the one that was most appealing to them. (a) The image each participant selected appears below. Complete the frequency distribution for the data.
The given images are 1, 2, 3, 4, 5
The total number of participants = 24
The frequency of each image is the number of times it appears in the distribution
Frequency of 1 = 6
Frequency of 2 = 5
Frequency of 3 = 4
Frequency of 4 = 3
Frequency of 5 = 6
The frequency distribution table is therefore shown below:
Simplify by finding the sum or difference of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (6w^2+24w+24)-(3w^2-26w+3) This simplifies to: AnswerThe degree of our simplified answer i
Start by distributing the negative sign
[tex]6w^2+24w+24-3w^2+26w-3[/tex]Then group terms that have the same literal parts
[tex]\begin{gathered} (6w^2-3w^2)+(24w+26w)+(24-3) \\ \text{The resulting operation simplifies to} \\ 3w^2+50w+21 \\ \text{the degree of the polynomial is 2 since its the highest exponent.} \end{gathered}[/tex]Find the length of XY if W is between X and Y, WX = 38 and WY = 16.XY =
Answer
XY = 54 units
Explanation
We are told that W is in between X and Y. This means that
XY = XW + WY
WX = XW = 38
WY = 16
XY = ?
We just make the necessary substitutions
XY = XW + WY
XY = 38 + 16 = 54 units
Hope this Helps!!!
14 3/4% as a decimal
ANSWER
14.75
EXPLANATION
To write a fraction as a decimal we have to do the division. In this case we have a mixed number, so we have the whole part of the decimal and we just have to find the decimal part - which is 3/4.
3/4 is 0.75:
So 14 3/4 is:
[tex]14\frac{3}{4}=14+\frac{3}{4}=14+0.75=14.75[/tex]0.16 whole number , integer, rational number (can be more than one set)
Answer : 0.16 is a rational number
Rational number is a number such that can be expressed as the quotient or fraction of two integers
An integer is a number that can be written without a fractional component
0. 16 can be written as
16 / 100
16 and 100 are both integers but 0.16 is not an integer but a rational number
16 / 100 = 0.16. This means that fraction of two integers that does does not gives an integer is a rational number
Hence, 0.16 is a ratioanal number
If you were to make a relative frequency table, which percent would go in the cell for red cars?1. 23.6%2. 27.3%3. 18.2%4. 30.9%
Answer:
23.6%
Explanation:
A relative frequency table shows the number of times a specific event occurs compared to the total number of events.
First, we calculate the total number of vehicles.
[tex]15+13+10+17=55[/tex]Next, the number of red cars = 13.
Therefore, the relative frequency for red cars will be:
[tex]\frac{13}{55}=0.236=23.6\%[/tex]The percent that would go in the cell for red cars is 23.6%.
The Obama family is building a circular swimming pool. If the radius of the pool is 15 feet, What is its circumference? Use I = 3.14 to solve.
The formula for circumference is given by
C = pi *d where pi = 3.14 and d is the diameter
We can find the diameter from the radius
d = 2*r where r is the radius
C = pi * 2 *r
C = 3.14 * 2 * 15
C =94.2 ft
the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2. find the number
The required number would be 2 which represents "the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2."
The sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2.
Let's assume the number would be x
As per the given condition, the algebraic form would be as
⇒ 4(x - 2) = 5(x - 2)
Apply the distributive property of multiplication,
⇒ 4x - 8 = 5x - 10
Rearrange the terms of variable x,
⇒ 5x - 4x = 10 - 8
Apply the subtraction operation,
⇒ x = 2
Therefore, the required number would be 2.
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In the diagram shown, it is known that line RP upside-down T line QS and line RP bisects
Since we know that RP is perpendicular to QS we know that the bisector gives us two right triangles. Furthermore, the bisector divides by two the angle of 104, then the angle SRP is equal to 52°.
Now, we know that the interior angles of any triangle add to 180°. Therefore:
[tex]\begin{gathered} m\angle S+52+90=180 \\ m\angle S=180-52-90 \\ m\angle S=38 \end{gathered}[/tex]In the scenarios you have explored so far, the angle measures were given, and you used trigonometric ratios to find missing side lengths. To determine the angle measures when only the side lengths are given, you can use inverse trigonometric functions. The input of each function is a number, which represents a ratio of two of the sides. The output of each function is an acute angle measure.Inverse sine: If sin A = z is given, then angle A can be determined by sin ¹2 = A.Inverse cosine: If cos A = x, is given, then angle A can be determined by cos ¹ = A.Inverse tangent: If tan A = z, is given, then angle A can be determined by tan ¹ = A.Let's explore this idea using the familiar 45°-45°-90° isosceles right triangle.
Given:-
A right angled triangle with side length 1.
To find the required angle value.
So now we use different trigonometric ratios such as,
[tex]sin,cos,tan[/tex]So we get,
[tex]sin^{-1}(\frac{1}{\sqrt{2}})=cos^{-1}(\frac{1}{\sqrt{2}})=tan^{-1}(\frac{1}{1})=45[/tex]So the required angle is 45 degree.
Abby's dog ate 0.75kg of food per day for one week. How much food
did Abby's dog eat?
Answer:
5.25 kg
Step-by-step explanation:
0.75kgx7(1week)=5.25
Answer:
5.25kg of food
Step-by-step explanation:
zero, depending on your answer.|A flashlight is projecting a triangle onto a wall, as shown below.20nThe original triangle and its projection are similar. What is the missing length n on the projection?C 19.230O13.328
If two triangles are similar, it means that the ratio of their corresponding sides is the same. By applying this to the given triangles, it means that
20/n = 16/24
By crossmultiplying, we have
n x 16 = 20 x 24
16n = 480
n = 480/16
n = 30
The second option is correct
If you vertically compress the absolute value parent function, f(x) = lxl, by afactor of 5, what is the equation of the new function?OA. g(x) = 51x|OB. g(x)=x-51OC. g(x) = 15x|O D. g(x) = x
When the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
The given function is of the form f(x) = ·|x| .
Therefore we can say that this function will be vertically compressed.
From the properties of transformation of graphs we know that when a function is vertically compressed by a factor of a we get the transformed function as 1/a times the original function.
given function:
f(x) = |x|
vertically compressed by 5.
therefore new function = 1/5 |x|
Hence the transformed function is g(x) .
g(x) = 1/5 |x|
Let us take a few coordinates along the x-axis to get the values of the y and the graph of both modulus function pass through origin .
f(x) = |x|
at x = 10 , f(x) = 10
and g(x) = 2
Here we see that the function is compressed.
Therefore when the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
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Evaluate the quantity G(-7) given the following function.G(x) = x2 + 4x - 12G(-7)=exact number, no toleranceexact number, no tolerance
Explanation
Step 1
replace the value of x in the equation with the given value
[tex]\begin{gathered} G(x)=x^2+4x-12 \\ \text{then} \\ G(-7)=(-7)^2+4\cdot-7-12 \\ G(-7)=49-28-12 \\ G(-7)=9 \end{gathered}[/tex]I hope this helps you