The equation of the given line is
y = mx + c
where
m = slope
c = y intercept
The equation of the given line is
y = 3x - 8
By comparing both equations,
m = 3
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of 3 is - 1/3. Thus, the slope of the perpendicular line passing through (2, 5) is - 1/3
We would fnd the y intercept, c by substituting m = - 1/3, x = 2 and y = 5 into the slope intercept equation. We have
5 = - 1/3 * 2 + c = - 2/3 + c
c = 5 + 2/3 = 17/3
Thus, the equation of the perpendicular line is
y = - x/3 + 17/3
a rectangular school gym has a length of [tex]x + 14[/tex]and a width of [tex]x - 20[/tex]which measure does[tex](x + 14)( x - 20)[/tex]represent?
Given:
Sides of rectangle
x+14
x-20
Required:
To tell which does equation show
Explanation:
Represent (area) is a quantity used to indicate the extent of a surface or plane figure
Required answer:
(area)
if ∆ABC ~ ∆FED which of the following is correct:
We know that the triangles ∆ABC and ∆FED are congruent. As such, we know that all sides and inner angles are congruent. Moreover, if we have:
Then,
[tex]\begin{gathered} \measuredangle A\cong\measuredangle F \\ \measuredangle B\cong\measuredangle E \\ \measuredangle C\cong\measuredangle D \end{gathered}[/tex]And this means that ∡A≅∡F.
Use the approximate doubling time formula for the case described below. Discuss whether the formula is valid for the case described.Gasoline prices are rising at a rate of 0.6% per month. What is their doubling time?
ANSWER:
EXPLANATION:
Given the rising rate of 0.6% per month, we can go ahead and determine the doubling time as seen below;
[tex]\begin{gathered} P=P_0(1+r)^t \\ \\ \frac{P}{P_0}=(1+0.006)^t \\ \\ 2=1.006^t \\ \\ \ln2=t\ln1.006 \\ \\ t=\frac{\ln2}{\ln1.006} \\ \\ t=115.87\text{ months} \end{gathered}[/tex]The radii of two spheres are in a ratio of 1:4.What is the ratio of their volumes?
Given:
The radii of the two spheres are in a ratio of 1:4
Find-:
The ratio of their volume
Explanation-:
Radii of two spheres are in a ratio is 1:4
[tex]\frac{r_1}{r_2}=\frac{1}{4}[/tex]The volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]So the ratio of volume is:
[tex]\begin{gathered} \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r^_2^3} \\ \\ \frac{V_1}{V_2}=(\frac{r_1}{r_2})^3 \\ \\ \frac{V_1}{V_2}=(\frac{1}{4})^3 \\ \\ \frac{V_1}{V_2}=\frac{1}{64} \\ \end{gathered}[/tex]So the ratio is 1:64
Find the zeros of each function by factoring. F(x)=5x^2–11x+2
We need to factor the following expression:
[tex]f(x)=5x^2-11x+2[/tex]The factor the equation we need to find which numbers "d" and "e" when multiplied result in 10. And when added are equal to -11.
[tex]\begin{gathered} d=-10 \\ e=-1 \end{gathered}[/tex]We can represent the function by:
[tex]f(x)=(x-10)(x-1)[/tex]The zeros of the function are 10 and 1.
Aparachutist's speed during a free fall reaches 55 meters per second. What is this speed in feet per second? At this speed, how many feet will the parachutistfall during 15 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers
Part A:
The parachutist's speed is 55 m/s.
This means he covers 55m distance in every second
To convert this 55m distance to feet,
[tex]\begin{gathered} 1m=3.3ft \\ 55m=55\times3.3 \\ =181.5ft \end{gathered}[/tex]The speed will be a distance of 181 feet covered every second.
Hence, the speed in feet per second is;
[tex]181.5ft\text{ per second}[/tex]Part B:
The distance covered by the parachutist during 15 seconds of free fall will be;
Given:
[tex]\begin{gathered} \text{speed, s = 181.5 ft per second} \\ t=15\text{seconds} \\ distance,d=\text{?} \\ \text{speed = }\frac{dis\tan ce}{\text{time}} \\ \text{distance = spe}ed\text{ }\times time \\ d=181.5\times15 \\ d=2722.5ft \end{gathered}[/tex]Therefore, the parachutist fell 2722.5 feet in 15seconds during free fall.
Assume that AB is parallel to EC, es press y in terms of x
Knowing that AB is parallel to EC, we can say that the proportion between DC and CB is equal to the proportion between DE and EA. Then:
[tex]\frac{DC}{CB}=\frac{DE}{EA}[/tex]Finally, we replace each value:
[tex]\begin{gathered} \frac{y}{8}=\frac{6}{x} \\ y=\frac{6\cdot8}{x} \\ \therefore y=\frac{48}{x} \end{gathered}[/tex]Answer: Option a
write the equation of the line that is perpendicular to the line which has a slope of 3/4 and passes through the point (0, -4)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define the slopes of perpendicular lines
The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m.
STEP 2: Find the slope of the new line that is perpendicular
[tex]\begin{gathered} slope_1=\frac{3}{4} \\ slope_2=\frac{-1}{\frac{3}{4}}=-1\div\frac{3}{4}=-1\cdot\frac{4}{3}=-\frac{4}{3} \end{gathered}[/tex]Therefore, the slope of the line perpendicular is -4/3
STEP 3: Find the equation of the new line
Using the formula below:
[tex](y-y_1)=m(x-x_1)[/tex]The known values are:
[tex]\begin{gathered} m=-\frac{4}{3} \\ (x_1,y_1)=(0,-4) \end{gathered}[/tex]STEP 4: Find the equation of the line
[tex]\begin{gathered} By\text{ substitution,} \\ (y-(-4))=-\frac{4}{3}(x-0) \\ (y+4)=-\frac{4}{3}x \\ y=-\frac{4}{3}x-4 \end{gathered}[/tex]Hence, the equation of the line is:
[tex]y=-\frac{4}{3}x-4[/tex]Use the Pythagorean theorem to determine the unknown length of the right triangle. 1. Determine the length of side c in each of the triangles below. A B 8 b. 0.8 B 0.6 A
Pythagorean teorem:
c^2 = a^2+b^2
Where c is the hypotenuse and a & b are the two other legs of the triangle.
a.
c^2 = 6^2+8^2
Solve for c:
c^2 = 36+64
c^2 = 100
c =√100
c= 10
b.
c^2 = 0.6^2+ 0.8^2
c^2 = 0.36+ 0.64
c^2 = 1
c = √1
c=1
8. Determine whether the following sequence of trials would result in a binomial probability distribution. (a) Calling 500 people and ask if they voted for a particular candidate in a given election. (b) The National Health Institute checks 100 people who had a certain type of cancer in the year 2000 and records whether they are alive or not.
a) This results in a binomial distribution because:
There are only two possible outcomes (yes or no).
The trials are independent.
There are a fixed number of trials.
The probability of success remains the same for each call.
Answer a: this will result in a binomial distribution.
b) This does result in a binomial distribution:
There is a fixed number of trials.
It has only two outcomes.
The trials are independent.
The probability of success remains the same for each trial.
Answer b: this will result in a binomial distribution
Use the table below to answer questions:What is the probability of randomly selecting a junior given that the student prefers non-sport activities? What is the probability of randomly selecting a sophomore who prefers sports?
A. Probability of selecting a Junior given that the student prefers non-sport activities:
[tex]\begin{gathered} P(Junior\lvert Non-sport)=\frac{#Junior\text{ }non-sport}{#non-sport} \\ \\ P(Junior\lvert Non-sport)=\frac{421}{1621}=0.2597 \end{gathered}[/tex]The probability of randomly selecting a Junior given that the student prefers non-sport activities is 0.2597 (25.97% approximately 26%)B. Probability of selecting a sophomore who prefers sports:
[tex]\begin{gathered} P(Sophomore\text{ }sports)=\frac{#sophomoresports}{#students} \\ \\ P(Sophomore\text{ }sports)=\frac{245}{2540}=0.0965 \end{gathered}[/tex]The probability of randomly selecting a sophomore who prefers sports is 0.0965 (9.65%)What is the surface area for each part of the figure? What is the total surface area of the figure?
Solution:
Given:
A composite figure showing a square-based pyramid, a square prism, and a cube.
To get the surface area, we find the surface area of each part separately.
For the square-based pyramid,
[tex]\begin{gathered} It\text{ has four triangles and a square base.} \\ \text{The square base is not part of the surface of the whole shape however.} \\ \\ \text{Hence, the area of the pyramid is;} \\ 4\times\text{area of triangle} \\ b=6 \\ h=4 \\ A=\frac{1}{2}bh \\ \text{Hence,} \\ \text{Area}=4\times\frac{1}{2}\times6\times4=48 \\ A=48ft^2 \end{gathered}[/tex]The surface area of the pyramid is 48 square feet.
For the square prism,
It has 6 faces. However, only four are the surface of the composite shape. The other two faces are inside the shape and will not count as a surface.
Hence,
[tex]\begin{gathered} \text{Area of front and back face;} \\ A=l\times b \\ A=20\times6=120 \\ \text{For the two faces;} \\ A=2\times120=240ft^2 \\ \\ \text{Also, the area of the top and bottom face,} \\ A=20\times6=120 \\ \text{For the two faces;} \\ A=2\times120=240ft^2 \\ \\ \text{Hence, the surface area of the square prism is 240+240} \\ =480ft^2 \end{gathered}[/tex]Therefore, the area of the square prism is 480 square feet.
For the cube;
The cube has 6 faces.
However, only 5faces are part of the surface of the composite shape. One face is within the shape.
Hence,
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Given secant of theta is equal to the square root of 6 over 3 comma what is cos?
Given that
[tex]\sec \text{ }\theta\text{ = }\frac{\sqrt[]{6}}{3}[/tex]Required: cos
From the reciprocal of trigonometric function,
[tex]\sec \text{ }\theta\text{ = }\frac{1}{\cos \text{ }\theta}[/tex]Thus, we have
[tex]\frac{1}{\cos \text{ }\theta}\text{ = }\frac{\sqrt[]{6}}{3}[/tex]Cross-multiply, we have
[tex]\begin{gathered} \sqrt[]{6}\text{ }\times\text{ cos }\theta\text{ = 3}\times1 \\ \sqrt[]{6}\text{ cos }\theta\text{ =3} \end{gathered}[/tex]Divide both sides by the coefficient of cos θ.
[tex]\begin{gathered} \frac{\sqrt[]{6}\text{ cos }\theta}{\sqrt[]{6}}\text{ =}\frac{\text{3}}{\sqrt[]{6}} \\ \Rightarrow\cos \text{ }\theta\text{ = }\frac{\text{3}}{\sqrt[]{6}} \\ \end{gathered}[/tex]Rationalizing the resulting surd, we have
[tex]\begin{gathered} \text{ }\frac{3}{\sqrt[]{6}}\times\frac{\sqrt[]{6}}{\sqrt[]{6}} \\ =\frac{3\times\sqrt[]{6}}{\sqrt[]{6}\times\sqrt[]{6}}=\frac{3\sqrt[]{6}}{6} \\ =\frac{\sqrt[]{6}}{2} \\ \text{Thus,} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{6}}{2} \end{gathered}[/tex]Hence, cos θ is evaluated to be
[tex]\frac{\sqrt[]{6}}{2}[/tex]The second option is the correct answer.
15Find the volume of the following triangular prism. *5 in6.1in13 in7 in215.5 cubic inches220.5 cubic inches225.5 cubic inches227.5 cubic inches
Volume V = Area of triangle x Height
. = (7x5/2) • 13
. = (17.5) • 13
. = 227.5
Then ANSWER IS
Prism volume V= 227.5 cubic inches
Vertices A(a, -6, 2), B(4,b,-9), C(3,5,c) and D(-2,-5,11) form a parallelogram. Determine the values of a,b,c.
Let's do a quick draw to help us visualize the problem:
That's a generic parallelogram, to verify that it's a parallelogram we can see that
[tex]\begin{gathered} AB=CD \\ \\ BC=AD \end{gathered}[/tex]The opposite lengths are equal, then, let's do something similar here, let's say that
[tex]\vec{AB}=\vec{CD}[/tex]then
[tex]\begin{gathered} \vec{AB}=B-A=(4,b,-9)-(a,-6,2)=(4-a,b+6,-9-2) \\ \\ \vec{AB}=(4-a,b+6,-11) \end{gathered}[/tex]And the vector CD
[tex]\begin{gathered} \vec{CD}=D-C=(-2,-5,11)-(3,5,c)=(-2-3,-5-5,11-c) \\ \\ \vec{CD}=(-5,-10,11-c) \end{gathered}[/tex]Let's impose our condition
[tex]\begin{gathered} \begin{equation*} \vec{AB}=\vec{CD} \end{equation*} \\ \\ (4-a,b+6,-11)=(-5,-10,11-c) \\ \\ \end{gathered}[/tex]Then
[tex]\begin{gathered} 4-a=-5 \\ \\ b+6=-10 \\ \\ 11-c=-11 \end{gathered}[/tex]By solving that equations we get
[tex]\begin{gathered} a=9 \\ \\ b=-16 \\ \\ c=22 \end{gathered}[/tex]Which of the statements is true about the data displayed in the scatter plot? Computer Cost vs. Speed 2.6 2.2 1.8 Cost (s in thousands) 1.4 1.0 2.2 Speed (GHz) А It shows a positive correlation. B It shows a negative correlation. С It shows no correlation. D As speed increases, cost decreases.
From the graph, we can see that the data displayed correspond to a positive correlation.
Positive correlation is a relationship between two variables in which both variables move in the same direction. In this case when the speed increases the cost also increases.
Therefore, the answer is A: its shows a positive correlation
Suppose you won a free ticket to a three-hour Katy Perry concert. At the box office, the ticket would cost $140.00. If you do not go tothe concert, you could instead work on a project for which you are being paid $31.00 per hour.The opportunity cost of going to the Katy Perry concert is $______
Simply put, opportunity cost is the loss you incur for choosing something because of other alternatives.
Now, if you choose to go to the Katy Perry concert, the ticket costs $140. But you aren't paying because you got it for free!
On the other hand, if you don't go, you can word on a project at $31 per hour for 3 hours, that would give you:
31 * 3 = $93
Thus, you can earn a potential $93 by not going to the concert. If you choose to go to the concert, you are forgoing the potential of earning $93!
Thus, we can say:
The opportunity cost of going to the Katy Perry concert is $93
Which is a counterexample to the statement?If a number is even, then the number is greater than 10.O 7O 8O 13O 16Is the answer 16?
Answer:
The counterexample to the statement is 8
Explanation:
A counterexample is an example that opposes or contradicts a given theory.
For the given theory;
"If a number is even, then the number is greater than 10."
We all know that not all even numbers are greater than 10.
So, a counterexample is an example from the options that will disprove the theory. That is an option that is an even number but is not greater than 10.
From the options, Only 8 is an even number that is not greater than 10.
Therefore;
The counterexample to the statement is 8
Find the unknown number in the proportion. Reduce your answer to lowest terms. 3/n = 9/11/8
we can re-write the right-hand side
That is;
[tex]\frac{3}{n}=9\times\frac{8}{11}[/tex][tex]\frac{3}{n}=\frac{72}{11}[/tex]cross-multiply
[tex]72\times n=3\times11[/tex]72 n = 33
Divide both-side of the equation by 72
[tex]\frac{72n}{72}=\frac{33}{72}[/tex][tex]n=\frac{33}{72}[/tex][tex]n=\frac{11}{24}[/tex]If the base of the triangle is 1, how is the height of thetriangle associated with the common difference of thesequence and the slope of the line?
1) Gathering the data
Triangle base = 1
Triangle height = 2
Common difference: 2
Slope: m
Considering the points (0,2) and (1,4)
m =4-2/1-0 m=2
2) Working with the picture:
Looking at those triangles, whose base is 1 and height is 2 we can say that the common difference (2) is the same as the slope (2) In other words,
The height of the triangle is equal to the slope. The sequence goes on and on but the height remains the same as the slope of the line. In this case, the slope is m=2
Does a maximum value exist for y = 8x^2 + 80x + 72? Explain your answer.
Solution
Reason 1:
[tex]\begin{gathered} y=8x^2+80x+72 \\ \\ \Rightarrow\frac{dy}{dx}=16x+80 \\ \\ \frac{d^2y}{dx^2}=16>0(\text{ Minimum\rparen} \end{gathered}[/tex]Reason 2:
Since the coefficient of x is positive, the graph is going to be minimum.
Maximum value does not exist.
What is the least common multiple of 9 and 2?
The muliples of 9 are: 9, 18, 27, 36, 45, ...
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26,...
So, the common multiples are 18, 36, 54,...
Therefore, the least common multiple is 18
Answer: 18
why might interpreting multiplication by a negative number as a 180 degrees rotation make sense?
If we think of all the numbers as being on a line and from the left come the negative numbers, there is the zero [Neutral element] and to the rigth we have the positive numbers, then understanding the product as a rotation of 180° makes complete sence, since the magnitude is going to change but will be "written" on the opposite side.
I need help with the mathematical expressionsI need the specific answers to mark brainliest
We are given the following expression
[tex]20+4(x+3y)-4x-8y-12+x_{}[/tex]We are asked to identify the properties that were used to simplify the expression.
First of all, the distributive property of multiplication has been used
[tex]4(x+3y)=4x+12y\text{ }\mleft\lbrace a(b+c)=ab+ac\}\mright?[/tex]Next, combine the like terms property has been used
[tex]\begin{gathered} 20-12+4x-4x+x+12y-8y_{} \\ (20-12)+(4x-4x+x)+(12y-8y) \end{gathered}[/tex]Next, we have performed simple addition and subtraction so that the expression is reduced to
[tex]8+x+(12y-8y)_{}[/tex]Then, we again used the distributive property of multiplication
[tex]12y-8y=y(12-8)\text{ }\mleft\lbrace ab-ac=a(b-c)\}\mright?[/tex]Finally, the simplified expression is
[tex]8+x+4y[/tex]Question 2:
The following statements are equivalent because of Associative Property of Addition
[tex]\begin{gathered} x+(y+9)=(x+y)+9_{}_{} \\ a+(b+c)=(a+b)+c_{} \end{gathered}[/tex]Question 3:
Using the Commutative property we can write
[tex]\begin{gathered} 4\cdot a\cdot b \\ 4\cdot b\cdot a \\ a\cdot4\cdot b \end{gathered}[/tex]As per the commutative property, the order doesn't matter.
The result of multiplication will be the same
3 Which of the following is a factual statement about the coordinate plane? А The coordinates of the origin are (1, 1). B It was first conceled by Sir Isaac Newton. C It can only be expressed on graph paper. D It has no edges.
D
In the graph we just showed the origin, but the plane goes from negative infinite to positive infinite for x and y axis
Explanation
A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called y-axis and a horizontal line called x-axis. These are perpendicular lines that intersect each other at zero, and this point is called the origin
Step 1
A)The coordinates of the origin are (1, 1).
False, the coordinates of the origin are (0,0)
Step 2
B) It was first conceled by Sir Isaac Newton
False, The invention of Cartesian coordinates in the 17th century is given to René Descartes
Step 3
C It can only be expressed on graph paper
False, you can use other drawing tools, a pc for example
Step 4
D It has no edges.
True, in the graph we just showed the origin, but the plane goes from negative infinite to positive infinite for x and y axis
I hope this helps you
Find the zero of h(x) = 3/4x - 72
To find the zero of a function, you equal that function to 0
[tex]\frac{3}{4}x-72=0[/tex]Then, you solve the variable x:
1. Add 72 in both sides of the equation
[tex]\begin{gathered} \frac{3}{4}x-72+72=0+72 \\ \\ \frac{3}{4}x=72 \end{gathered}[/tex]2. Multiply both sides of the equation by 4
[tex]\begin{gathered} 4(\frac{3}{4}x)=72\cdot4 \\ \\ 3x=288 \end{gathered}[/tex]3. Divide both sides of the equation into 3
[tex]\begin{gathered} \frac{3}{3}x=\frac{288}{3} \\ \\ x=96 \end{gathered}[/tex]Then, the zero of the given function is in x=96. Coordinates (96,0)Find the qualities indicated without using the Pythagorean theorem.(Round to the nearest degree is needed)
ANSWER
[tex]\begin{gathered} (a)A=45\degree \\ (b)c=14.1^{\prime} \end{gathered}[/tex]EXPLANATION
First, let us find the value of c using the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]where a and b are the other two legs of the triangle, and c is the hypotenuse
Therefore, we have that:
[tex]\begin{gathered} 10^2+10^2=c^2 \\ \Rightarrow100+100=c^2 \\ 200=c^2 \\ \Rightarrow c=\sqrt[]{200} \\ c=14.1^{\prime} \end{gathered}[/tex]Next, we find the measure of A by using the trigonometric ratios, SOHCAHTOA, of right angles:
[tex]\tan A=\frac{opposite}{adjacent}[/tex]Therefore, we have:
[tex]\begin{gathered} \tan A=\frac{10}{10} \\ A=\tan ^{-1}(1) \\ A=45\degree \end{gathered}[/tex]That is the answer.
Solve the equation (the answer might be no solution or “all real numbers “)8c+7c+6=66
We have the equation:
8c + 7c + 6 = 66
We add the c terms, and add -6 to each side of the equation (to cancel the 6 on the left-hand side):
15c + 6 - 6 = 66 - 6
15c = 60
Now, we divide each side of the equation by 15:
15c/15 = 60/15
c = 4
So the value of the variable c is 4.
#61 explain WHY the answer is correct, it confuses me
To answer this question we need to remember what the derivative and the second derivative tells us geometrically:
The derivative of a function tells us the slope of the tangent line to the function; which means that we can determine if a function is increasing or decreasing if we look at the sign of its derivative:
• If the derivative is positive then the function is increasing.
,• If the derivative is negative then the function is decreasing.
The second derivative of a function tells us the concativity of a function:
• If the second derivative is positive then the function is concave up.
,• If the second derivative is negative then the function is concave dowm.
Now that we know this we can sketch a function:
For the first interval we know that the derivative is negative and the second derivative is also negative which means that the function has to be decreasing and concave down.
For the second interval we know that the derivative is negative and the second derivative is positve which means that the function has to be decreasing and concave up.
what is the correct classification for the following two linear equations?-2x + y =3y = -1/2 x-2A. Parallel Lines B. Perpendicular Lines
Solution
we are given the two linear equations
First Equation
[tex]\begin{gathered} -2x+y=3 \\ \\ y=2x+3 \end{gathered}[/tex]Second Equation
[tex]y=-\frac{1}{2}x-2[/tex]Let mA and mB denotes the gradient of the first and second equation respectively written as
[tex]m_A\text{ and }m_B[/tex]Using the slope - intercepty form, one can see that
[tex]\begin{gathered} m_A=2 \\ \\ m_B=-\frac{1}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} m_A\times m_B=2\times-\frac{1}{2} \\ \\ m_A\times m_B=-1 \end{gathered}[/tex]Therefore, the lines are Perpendicular
Option B