Solution
gradient = 4
Slope for Perpendicular = -1/4
Slope for Parallel = 4
Equation of perpendicular line:
[tex]\begin{gathered} y-4=-\frac{1}{4}(x-6) \\ \\ 4y-16=-x+6 \\ \\ 4y+x=22 \end{gathered}[/tex]Equation of parallel line:
[tex]\begin{gathered} y-4=4(x-6) \\ \\ y-4=4x-24 \\ \\ y=4x-20 \end{gathered}[/tex]Find a recursive formula for the following sequence:4, 11, 25, 53, 109, ...
Notice the following pattern in the given sequence:
[tex]\begin{gathered} 11=4\cdot2\text{ +3,} \\ 25=11\cdot2+3, \\ 53=25\cdot2+3, \\ 109=53\cdot2+3. \end{gathered}[/tex]Therefore, the n-term of the sequence has the following form:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]Answer:
[tex]a_n=a_{n-1\text{ }}+3.[/tex]what type of angle is angle 98 degrees
Answer:
Obtuse
Step-by-step explanation:
Since it is larger than 90 degrees but less than 180 degrees, an angle of 98 degrees is considered to be obtuse.
Hope this helps! :)
12)50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions. ValueFrequencyRelative FrequencyCumulative Frequency040.084180.1612260.1218320.04204150.3355150.350
e) Finding how many students answered at most 4 questions.
The number of students that answered at most 4 questions correctly is:
Students answered 0 questions correctly + Students answered 1 question correctly + Students answered 2 questions correctly + Students answered 3 questions correctly + Students answered 4 questions correctly
So, the number of students is:
4 + 8 + 6 + 2 + 15 = 35
35 students answered at most 4 questions correctly.
f) Finding the sum of relative frequency.
The sum of relative frequency is:
0.08 + 0.16 + 0.12 + 0.04 + 0.3 + 0.3
Sum = 1.
The sum of the relative frequency in a distribution is always 1.
g) Creating a histrogram
To create a histogram, create a bar for each result correct. The values of the frequency will be used in the y-axis.
The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use the value = 3.14.
EXPLANATION:
Given;
We are given a symmetrical pool as indicated in the attached picture.
The pool consists of two sectors and two triangles and each pair has the same dimensions.
The dimensions are as follows;
[tex]\begin{gathered} Sector: \\ Radius=30 \\ Central\text{ }angle=2.21\text{ }radians \end{gathered}[/tex][tex]\begin{gathered} Triangle: \\ Slant\text{ }height=30 \\ Vertical\text{ }height=25 \\ Base=20 \end{gathered}[/tex]Required;
We are required to calculate the area of the pool.
Step-by-step solution;
We shall begin by calculating the area of the sector and the formula for the area of a sector is;
[tex]\begin{gathered} Area\text{ }of\text{ }a\text{ }sector: \\ Area=\frac{\theta}{2\pi}\times\pi r^2 \end{gathered}[/tex]Where the variables are;
[tex]\begin{gathered} \theta=2.21\text{ }radians \\ r=30 \\ \pi=3.14 \end{gathered}[/tex]We now substitute and we have the following;
[tex]Area=\frac{2.21}{2\pi}\times\pi\times30^2[/tex][tex]Area=\frac{2.21}{2}\times900[/tex][tex]Area=994.5ft^2[/tex]Since there are two sectors of the same dimensions, the area of both sectors therefore would be;
[tex]Area\text{ }of\text{ }sectors=994.5\times2[/tex][tex]Area\text{ }of\text{ }sectors=1989ft^2[/tex]Next we shall calculate the area of the triangles.
Note the formula for calculating the area of a triangle;
[tex]\begin{gathered} Area\text{ }of\text{ }a\text{ }triangle: \\ Area=\frac{1}{2}bh \end{gathered}[/tex]Note the variables are;
[tex]\begin{gathered} b=20 \\ h=25 \end{gathered}[/tex]The area therefore is;
[tex]Area=\frac{1}{2}\times20\times25[/tex][tex]Area=\frac{20\times25}{2}[/tex][tex]Area=250[/tex]For two triangles the area would now be;
[tex]Area\text{ }of\text{ }triangles=250\times2[/tex][tex]Area\text{ }of\text{ }triangles\text{ }equals=500ft^2[/tex]Therefore, the area of the pool would be;
[tex]\begin{gathered} Area\text{ }of\text{ }pool: \\ Area=sectors+triangles \end{gathered}[/tex][tex]\begin{gathered} Area=1989+500 \\ Area=2489ft^2 \end{gathered}[/tex]Rounded to the tens place, we would now have,
ANSWER:
[tex]Area=2,490ft^2[/tex]Option D is the correct answer
Elaine drives her car 50 miles and has an average of a certain speed. If the average speed had been 4mph more, she could have traveled 58 miles in the same length of time. What was her average speed?
Hello there. To solve this question, we'll have to remember some properties about average speed.
When we're talking about moving in a straight line, the average speed is given by the ratio between the displacement ΔS and the interval of time Δt, namely
[tex]v=\frac{ΔS}{Δt}[/tex]In this case, say we have an average speed of v and the initial displacement ΔS = 50 miles in a certain interval of time Δt, such that
[tex]v=\frac{50}{Δt}[/tex]We know that if the average speed had been 4 mph more, then Elaine could have traveled 58 miles in the same length of time.
This means that v + 4 (that is, the average speed plus 4 mph) is equal to the ratio:
[tex]v+4=\frac{58}{Δt}[/tex]To solve this for v, we can start assuming that the interval of time Δt is not equal to zero, so do the average speed in the second equation.
Divide the first equation by the second, such that
[tex]\begin{gathered} \frac{v}{v+4}=\frac{\frac{50}{Δt}}{\frac{58}{Δt}} \\ \\ \frac{v}{v+4}=\frac{50}{58} \end{gathered}[/tex]Cross multiply the numbers, that is:
[tex]\begin{gathered} 58v=50\cdot(v+4) \\ 58v=50v+200 \end{gathered}[/tex]Subtract 50v on both sides of the equation
[tex]8v=200[/tex]Divide both sides by a factor of 8
[tex]v=25\text{ mph}[/tex]So this is her average speed.
Simplify a^6 and a^2A: 2a^12B: 2a^8C: a^12 D: a^8
Using the following property:
[tex]x^y\cdot x^z=x^{y+z}[/tex]so:
[tex]a^6\cdot a^2=a^{6+2}=a^8[/tex]Answer:
a⁸
Use the drawing tools to form the correct answer on the graph.Graph the composite function &(/(e)¡(=)-2I• 5g(I) =1 - 1
Solution:
Given:
The functions are given below as
[tex]\begin{gathered} f(x)=-2x-5 \\ g(x)=x-1 \end{gathered}[/tex]To find:
[tex]g(f(x)[/tex]To figure out the value of the composite function, we will replace x with (-2x-5) in g(x)
[tex]\begin{gathered} g(f(x))=-2x-5-1 \\ g(f(x))=-2x-6 \end{gathered}[/tex]Hence,
Using a graphing tool, we will have the composite function be
The table below shows the probability distribution of a random variable X Х P(X) -10 0.07 -9 0.09 -8 0.67 -7 0 -6 0.17 What is the expected value of X? Write your answer as a decimal.
Teshawn, this is the solution to the problem:
We use the following formula to calculate the expected value of x, as follows:
Expected value of x = -10 * 0.07 + - 9 * 0.09 + -8 * 0.67 + -7 * 0 + -6 * 0.17
Expected value of x = -0.7 + -0.81 + - 5.36 + 0 + - 1.02
Expected value of x = -0.7 - 0.81 - 5.36 - 1.02
Expected value of x = -7.89
Please solve the problem in the attachment and provide the steps, the reason why your answer is correct and why all the other answer choices are incorrect.
Answer:
A
[tex]A\text{. Rectangles also have four right angles}[/tex]Explanation:
We want to find a counterexample to disprove the conjecture below;
- A square is a figure with four right angles.
To disprove this, we need to find a shape that also has four right angles but is not a square.
So, from the option the only shape that also has four right angles is a rectangle.
Therefore, the counterexample to disprove the conjecture is;
[tex]A\text{. Rectangles also have four right angles}[/tex]An electronics store purchases laptops for $425.00. They use a markup rate of 60%. How much do they sell the laptop to their customers?
Given that An electronics store purchases laptops for $425.00.
markup rate of 60%.
Selling price is:
[tex]\begin{gathered} SP=425+(0.60)425 \\ Sp=425+255 \\ SP=680 \end{gathered}[/tex]they sell the laptop to their customers at $680.
Six less than x equals twenty-two.
What do I need to do?
Write the word expression in algebraic expression?
16.- x - 6 = 22
x = 22 + 6
x = 28
17.-
y/4 = -10
y = 4(-10)
y = -40
19.- h - 7 = -9
h = -9 + 7
h = -2
20.- x + y = -7
if x = 11
11 + y = -7
y = -7 - 11
y = -18
For how many books produced will the costs from the two methods be the same
Answer:
[tex]4780\text{ books}[/tex]Explanation:
Here, we want to get the number of books for which the cost of the two methods will be the same
What we have to do here is to get the cost of each method, then equate to find the number of books
Let the number of books be b
For the first method, we have it that:
[tex]\begin{gathered} 70976\text{ + }9.75(b) \\ =\text{ 70976 + 9.75b} \end{gathered}[/tex]For the second method, we have it that:
[tex]\begin{gathered} 16006\text{ + }21.25(b) \\ =\text{ 16006 + 21.25b} \end{gathered}[/tex]To get the number of books, we have to equate both
Mathematically, that would be:
[tex]\begin{gathered} 70976\text{ + 9.75b = 16006 + 21.25b} \\ 70976-16006\text{ = 21.25b-9.75b} \\ 54970\text{ = 11.5b} \\ b\text{ = }\frac{54970}{11.5} \\ b\text{ = 4,780} \end{gathered}[/tex]The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
In linear equation, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
Learn more about linear equation
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What is the best estimation of the equation [-å? Drag the numbers into the boxes. Numbers may beused once, twice, or not at all.1142011/21/8
Answer:
[tex]1-\frac{1}{2}=\frac{1}{2}[/tex]Explanation:
Given the below expression;
[tex]\frac{7}{8}-\frac{6}{11}[/tex]We can see that 7/8 is closer to 1 and that 6/11 is closer to 1/2, so we'll now have;
[tex]1-\frac{1}{2}=\frac{2-1}{2}=\frac{1}{2}[/tex]So the best estimation of the equation is 1 - 1/2 = 1/2
Which expressions are equivalent to the one below? Check all that apply.ln(e5)A.1B.5C.5 • ln eD.5e
SOLUTION:
We want to find the equivalent expression to;
[tex]ln(e^5)[/tex]We can rewrite it as;
[tex]\begin{gathered} 5ln(e) \\ =5 \end{gathered}[/tex]Thus, the answers are;
[tex]5Ine\text{ }and\text{ }5[/tex]OPTION B and C
I need help with this question... the correct answer choice
Solution:
The original parallelogram is as shown below with its coordinates;
The transformation that carries the parallelogram below onto itself is a rotation of 180 degrees counterclockwise about the origin.
When rotating a point 180 degrees counterclockwise about the origin, the point (x,y) will become (-x,-y)
This means to transform 180 degrees counterclockwise, we negate the x and y-coordinates of the original form.
The transformation is as shown below;
Therefore, the correct answer is a rotation of 180 degrees counterclockwise about the origin.
Question
Hong hikes at least 1 hour but not more than 4 hours. She hikes at an average rate of 2.7 mph. The function f(t)=2.7t represents the distance she hikes in t hours.
What is the practical range of the function?
Responses
all real numbers from 1 to 4, inclusive
all multiples of 2.7 between 2.7 and 10.8, inclusive
all real numbers
all real numbers from 2.7 to 10.8, inclusive
The practical range of the function is D. all real numbers from 2.7 to 10.8, inclusive.
What is a range?A function's range refers to all of the possible values for y. The formula for determining a function's range is y = f. (x). A function's range is the set of all its outputs. After we have substituted the domain, the range of a function is the complete set of all possible resulting values of the dependent variable (y, usually).
In this case, since the range is the value that satisfies the given function. For function f(t) = 2.7t the practical range of the function can be solved by substituting the lowest time and the highest possible time which are 1 and 4.
At t = 1 f(t) = 2.7 and at t = 4 f(t) = 10.8. so the range is all real numbers from 2.7 to 10.8, inclusive.
Therefore, the correct option is D.
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Write down the first five terms of the sequence an=(n+4)!2n2+6n+7a1 = a2 = a3 = a4 = a5 =
Step 1
Given;
[tex]\begin{gathered} a_n=\frac{(n+4)!}{2n^2+6n+7} \\ n=1,2,3,4,5 \end{gathered}[/tex]Step 2
[tex]a_1=\frac{(1+4)!}{2(1)^2+6(1)+7}=\frac{120}{15}=8[/tex][tex]a_2=\frac{(2+4)!}{2(2)^2+6(2)+7}=\frac{720}{27}=\frac{80}{3}[/tex][tex]a_3=\frac{(3+4)!}{2(3)^2+6(3)+7}=\frac{5040}{43}[/tex][tex]a_4=\frac{(4+4)!}{2(4)^2+6(4)+7}=\frac{8!}{63}=640[/tex][tex]a_5=\frac{(5+4)!}{2(5)^2+6(5)+7}=\frac{9!}{87}=\frac{120960}{29}[/tex]Let f(x) = (5)2+1. Which is equal to f(-3)?
Let's solve f(x) = (5)2+1 for f(-3):
Replacing x by -3, we have:
f (-3) = - 11
But there is no value for x, in the given function, there isn't a coefficient for x.
Can you please check the problem?
Can you help me please?A. How can Marc provide proof that his mighty shot actually hung in the air for 15 seconds? Or is this just another one of his lies?B. How long did the ball actually hang in the air?
The given formula for Marc's shot is:
[tex]h(x)=-16x^2+200x[/tex]a. To prove that the shot actually hung in the air for 15 seconds, we need to replace x=15 in the formula and solve for h, as follows:
[tex]\begin{gathered} h(15)=-16(15)^2+200(15) \\ h(15)=-16\times225+3000 \\ h(15)=-3600+3000 \\ h(15)=-600 \end{gathered}[/tex]As the height is negative, it means after 15 seconds the ball already hit the ground, because the ground is located at h=0. Then this result proves that this is just another one of Marc's lies.
b. To find how long the ball actually hung in the air, we need to find the x-values that makes h=0, as follows:
[tex]0=-16x^2+200x[/tex]We have a polynomial in the form: ax^2+bx+c=0, where a=-16, b=200 and c=0.
We can use the quadratic formula to solve for x:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-200\pm\sqrt[]{(200)^2-4(-16)(0)}}{2(-16)} \\ x=\frac{-200\pm\sqrt[]{40000+0}}{-32} \\ x=\frac{-200\pm\sqrt[]{40000}}{-32} \\ x=\frac{-200\pm200}{-32} \\ x=\frac{-200+200}{-32}=\frac{0}{-32}=0\text{ and }x=\frac{-200-200}{-32}=\frac{-400}{-32}=12.5 \end{gathered}[/tex]Then the two x-values are x=0 and x=12.5.
The starting time is 0 and the end time when the ball hit the ground is x=12.5.
The ball actually hung in the air 12.5 seconds.
what is 6 exponent 7 * 4 exponent 4 * 2 / 6 exponent 5 * 4 exponent 4 * 2.2
given
[tex]\frac{6^7\cdot4^4\cdot2}{6^5\cdot4^4\cdot2^2}[/tex][tex]=6^{7-5}\cdot4^{4-4}\cdot2^{1-2}=6^2\cdot4^0\cdot2^{-1}=\frac{6^2\cdot1}{2}=\frac{36}{2}=18[/tex]Note 4 exponent 0 = 1
6 a. Sketch a reflection triangleAABC about the line y - X.Label the image AA'B'C'. I know youdon't have graph paper, just sketch.b. What are the coordinates of C'?
Notice that we are asked to find the image of a triangle that
How do u figure out what x is in a normal distribution question
Data:
• Mean (μ) = 50
,• Standard deviation (σ) = 3
,• P( ,x >=47 ,)
Procedure:
1. Since μ = 50 and σ = 3:
[tex]P(x\le47)=P(X-\mu<47-50)=P(\frac{x-\mu}{\sigma}<\frac{47-50}{3})[/tex][tex]Z=\frac{x-\mu}{\sigma}[/tex][tex]\frac{47-50}{3}=-1[/tex]2. Replacing the values:
[tex]P(x\le47)=P(Z\le-1)[/tex]With this, we do not have to figure out what x is.
3. Using the standard normal table:
[tex]P(Z\le-1)=0.1587\approx0.16[/tex]Answer: A. 0.16
The mean height of men is known to 5.9 ft with a standard deviation of 0.2 ft. The height of a man (in ft) corresponding to a z-score of 2 is:Group of answer choices6.16.36.25.9
The average height is μ= 5.9ft and has a standard deviation of σ=0.2ft.
You have to determine the height (X) for the Z-score z=2
To determine this value, you have to use the formula of the standard deviation:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]First, write the equation for X:
-Multiply both sides by sigma:
[tex]\begin{gathered} Z\sigma=\sigma\frac{X-\mu}{\sigma} \\ \\ Z\sigma=X-\mu \end{gathered}[/tex]-Add mu to both sides of it:
[tex]\begin{gathered} (Z\sigma)+\mu=X-\mu+\mu \\ X=(Z\sigma)+\mu \end{gathered}[/tex]Replace the expression obtained for X with the known values of z, sigma, and mu
[tex]\begin{gathered} X=2\cdot0.2+5.9 \\ X=\text{0}.4+5.9 \\ X=6.3 \end{gathered}[/tex]The height of a man that corresponds to z=2 is 6.3 ft
Deion measure the volume of a sink basin by modeling it as a hemisphere. Deion measures its diameter to be 28 3/4 inches. Find the sink’s volume in cubic inches. Round your answer to the nearest tenth if necessary.
28.75We are asked to determine the volume of a hemisphere of diameter 28 3/4 in.
A hemisphere is half a sphere therefore, its volume is half the volume of a sphere:
[tex]V=\frac{1}{2}(\frac{4\pi r^3}{3})=\frac{2\pi r^3}{3}[/tex]Where "r" is the radius. Since the radius is half the diameter we have that:
[tex]r=\frac{D}{2}=\frac{28\frac{3}{4}}{2}[/tex]We will convert the mixed fraction into a standard fraction using the following:
[tex]28\frac{3}{4}=28+\frac{3}{4}=28.75[/tex]Substituting in the formula for the radius:
[tex]r=\frac{28.75in}{2}=14.38in[/tex]Now, we substitute the value of the radius in the formula for the volume:
[tex]V=\frac{2\pi(14.38in)^3}{3}[/tex]Solving the operations:
[tex]V=6221.3in^3[/tex]Therefore, the volume is 6221.3 cubic inches.
Hi I need help with this i’m in a hurry so can you please just tell me the answer lol sorry i’m just in a little rush
Step 1
In the example why is the area of one triangle multiplied by 2.
This is because the hexagon is divided into one rectangle and 2 congruent triangles. Therefore, the area of the two triangles will be the same since they are congruent triangles. In order to get the area of the hexagon, the area of one of the triangles is mutiplied by 2 and added to the area of the rectangle.
Step 2
Find the dimension of one of the shaded triangle from Bev's pattern.
[tex]\begin{gathered} \\ \text{For Bev's triangle;} \\ \text{base}=4 \\ \text{height}=3 \\ Slantheight^2=(\text{ }\frac{base}{2})^2+height^2 \\ Slantheight^2=(\frac{4}{2})^2+3^2 \\ Slantheight^{}=\sqrt[]{2^2+9} \\ Slantheight=\sqrt[]{13}\text{unit} \end{gathered}[/tex]The dimensions will therefore be;
[tex]\begin{gathered} \text{base= 4unit} \\ \text{slant height=}\sqrt[]{13}unit \\ \text{slant height=}\sqrt[]{13}unit \end{gathered}[/tex]What can you say about the shaded area of all the shaded triangles in Bev's pattern.
[tex]\begin{gathered} \text{Area of given triangle=6unit}^2 \\ \text{Area of Bev's triangle=}\frac{1}{2}\times4\times3=6unit^2 \end{gathered}[/tex]The area of all shaded triangles in Bev's pattern are equal. This is because all the shaded triangles have the same dimensions and can be said to be congruent. Hence, they will have the same area.
find the measure of arc DB mDB = __ degrees simply
ANSWER:
90°
STEP-BY-STEP EXPLANATION:
Chord TD separates the circle into two equal 180° angles, so angles Since the angle 90°
Kelly and nadir both had maths tests last week, Kelly scored 47/68 and nadir scored 35/52. Who got the higher percentage score
Answer:
Kelly got a higher percentage score.
Step-by-step explanation:
35 / 52 = 0.673
47 / 68 = 0.691
Harmie's average s-day natural gas usage rate is 5.g therms AR are sdays What day- and 8-day natural gas usage rates? are her
We know that Harmie's average 5-day natural gas usage rate is 5.9 therms/5 days.
We have to calculate the 1 day average usage rate and 8 day average usage rate.
We can calculate this by transforming the denominator from 5 days, as it is in the information given, to 1 day and 8 days respectively:
[tex]\frac{5.9\text{ therms}}{5\text{ days}}\cdot\frac{1\text{ day}}{1\text{ day}}=\frac{5.9}{5}\cdot\frac{\text{therms}}{1\text{ day}}=\frac{1.18\text{ therms}}{1\text{ day}}[/tex][tex]\frac{5.9\text{ therms}}{5\text{ days}}\cdot\frac{8\text{ days}}{8\text{ days}}=(\frac{5.9\cdot8}{5})\cdot\frac{\text{therms}}{8\text{ days}}=\frac{9.44\text{ therms}}{8\text{ days}}[/tex]Answer: 1.18 therms / 1 day, 9.44 therms / 8 days [Option 1]
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