The equation of the perpendicular line is y = -3x - 60
How to determine the line equation?The equation is given as
12y - 4x = 8
Make y the subject
12y= 4x + 8
y = 1/3x + 2/3
The point is also given as
Point = (-10, -30)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/3
This means that the slope of 12y - 4x = 8 is 1/3
So, we have
m = 1/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -3
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -3
(x₁, y₁) = (-10, -30)
So, we have
y = -3(x + 10) - 30
Evaluate
y = -3x - 30 - 30
y = -3x - 60
Hence, the perpendicular line has an equation of y = -3x - 60
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Use the information and diagram to complete the proof. Given: C is the midpoint of AD¯¯¯¯¯¯¯¯.∠BAC≅∠EDC Prove: △BAC≅△EDC Triangles A B C and D E C share vertex C, where C is between A & D and C is between B & E. Angles A & D are right angles.© 2016 StrongMind. Created using GeoGebra. Statements Reasons 1. ∠BAC≅∠EDC 1. Given 2. C is the midpoint of AD¯¯¯¯¯¯¯¯. 2. Given 3. C bisects AD¯¯¯¯¯¯¯¯. 3. Definition of midpoint 4. AC¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ 4. Definition of bisect 5. ∠ACB and ∠DCE are vertical angles. 5. Definition of vertical angles 6. ∠ACB≅∠DCE 6. Vertical Angle Theorem 7. △BAC≅△EDC 7. _[blank]_ Stephanie and Miranda disagree about which reason goes in the blank for Statement 7.Stephanie states that the missing reason is the ASA Congruence Theorem, but Miranda says the missing reason is the SAS Congruence Postulate.Answer the following two questions.Which student, if either, is correct? Why? Select two answers: one for Question 1 and one for Question 2.
Solution:
Given:
Stephanie is correct. Because:
[tex]\begin{gathered} \angle A\cong\angle D \\ \\ AC\cong DC \\ \\ \angle C\cong\angle C \end{gathered}[/tex]Thus, the proof shows that two pairs of corresponding angles and the included sides are congruent.
Solve the inequality: 3x + 4 < 5
Answer in interval notation.
Answer:
0.3 recurring
Step-by-step explanation:
3x+4<5. -4
3x<1. ÷3
×<0.333
Given the following table of values determine the value of X where f(x) has a local minimum. Assume that f is continuous and differentiable for all reals
We have to find the value of x for which f(x) has a minimum.
Extreme values of f(x), like minimum or maximum values, correspond to values of its derivative equal to 0.
In this case f'(x) = 0 for x = -2 and x = 0.
We can find if this extreme value is a minimum if the second derivative f''(x) is greater than 0.
In this case, f'(x) = 0 and f''(x) > 1 for x = 0.
Then, x = 0 is a local minimum.
Answer: x = 0
this is a Statistics question. Please help
Using the normal distribution, it is found that the measures are given as follows:
a) Proportion with less than 125 mg/dl: 0.16.
b) Percentage between 200 and 225 mg/dl: 2.35%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the cholesterol levels are given as follows:
[tex]\mu = 150, \sigma = 25[/tex]
The proportion below 125 mg/dl is the p-value of Z when X = 125, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (125 - 150)/25
Z = -1
Z = -1 has a p-value of 0.16, rounded with the Empirical Rule, which is the proportion.
The proportion with cholesterol levels between 200 and 225 mg/dl is the p-value of Z when X = 225 subtracted by the p-value of Z when X = 200, hence:
X = 225
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (225 - 150)/25
Z = 3
Z = 3 has a p-value of 0.9985.
X = 200
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (200 - 150)/25
Z = 2
Z = 2 has a p-value of 0.975.
0.9985 - 0.975 = 0.0235 = 2.35%, which is the percentage.
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Which of the following is a solution to the inequality below?
Answer:
4u + 6 > 30
4u > 24
u > 6
Solution is u = 6
Answer:
4u+6>30
4u>30-6
4u>24
u>6
Answer:
u>6
I wills send you a picture
Draw the tank
we can use the formula of the volume of a cylinder
[tex]V=\pi\times r^2\times h[/tex]we can repalce the value of the volume (320pi) and the height
[tex]\begin{gathered} 320\pi=\pi\times r^2\times20 \\ 320\pi=20r^2\pi \end{gathered}[/tex]now solve for r^2 dividing 20pi on both sides
[tex]\begin{gathered} \frac{320\pi}{20\pi}=r^2 \\ \\ r^2=16 \\ \end{gathered}[/tex]and solve for r using roots
[tex]\begin{gathered} r=\sqrt[]{16} \\ \\ r=4 \end{gathered}[/tex]the value of the radious is 4ft and the diameter double, then
[tex]\begin{gathered} d=2\times4 \\ d=8 \end{gathered}[/tex]diameter of the cylinder is 8 ft then rigth option is C
A small regional carrier accepted 23 reservations for a particular flight with 2o seats. 14 reservations went to regular customers who will arrive for the flight. each of the remaining passengers will arrive for the flight with a 50 % chance ,independently of each other. (answers accurate to 4 decimal places.) Find the probability that overbooking occurs find the probability that the flight has empty seats
Let's begin by identifying key information given to us:
Number of seats = 20
Number of reservation = 23
14 regular customers show up. So, we have:
[tex]23-14=9RemainingCustomers[/tex]The number of seats left is:
[tex]20-14=6seats[/tex]Overbooking means that more than 6 remaining customers show up (that could mean 7 or 8 or 9 of the remaining customers show up)
The probability of more than 6 customers arriving is given by:
We are reviewing a module and I don't remember how to do it.
The coordinate of point X which is 5/6 of the distance between P and Q is 5/11
Here, we want to calculate the coordinates of point X which is 5/6 of the distance between P and Q
Mathematically, we can use the internal division formula.
In this case, the coordinates of y is 0 in all cases
So the coordinates of P is (-5,0) while the coordinates of Q is (7,0)
Now, the coordinates of X divides the line PQ in the ratio 5 to 6
Using the internal divison formula, we have;
[tex](x,y)\text{ = }\frac{mx_2+nx_1}{m+\text{ n}},\text{ }\frac{my_2+ny_1}{m+\text{ n}}[/tex]In this case however, we are going to focus on the x-axis part of the question since the values of y at all points is 0
m , n are the division values which are 5 and 6 respectively in this case
x2 is 7 while x1 is -5
Substituting all of these, we have;
[tex]\begin{gathered} (x,y)\text{ = }\frac{5(7)\text{ + 6(-5)}}{11},\text{ 0} \\ \\ (x,y)\text{ = }\frac{35-30}{11},\text{ 0} \\ (x,y)\text{ = }\frac{5}{11},\text{ 0} \end{gathered}[/tex]So the coordinate of point X which is 5/6 of the distance between P and Q is 5/11
I need help with this practice problem I’m having trouble solving it
A generic cosecant function is
[tex]f(x)=A\csc (kx+\theta)+C[/tex]We must find A, k, θ, and C using the information that we have.
Finding A:
To find A we can use the range of the function, we know there is a gap between -9 and 5, that's the crucial information, the value of A will be the mean of |-9| and |5| (in modulus!), therefore
[tex]A=\frac{|-9|+|5|}{2}=\frac{9+5}{2}=\frac{14}{2}=7[/tex]Therefore
[tex]f(x)=7\csc (kx+\theta)+C[/tex]Finding C:
We can use the fact that we know A and find C, let's suppose that
[tex]\csc (kx+\theta)=1[/tex]For an unknown value of x, it doesn't matter, using the range again we can use the fact that 5 is a local minimum of the function, therefore, when the csc(kx + θ) is equal to 1 we have that the function is equal to 5
[tex]\begin{gathered} 5=7\cdot1+C \\ \\ C=-2 \end{gathered}[/tex]And we find that C = -2. Tip: You can also suppose that it's -1 and use -9 = 7 + C, the result will be the same.
Finding k:
Now we will use the asymptotes, we have two consecutive asymptotes at x = 0 and x = 2π, it means that the sin(kx) is zero at x = 0 and the next zero is at x = 2π, we know that sin(x) is zero every time it's a multiple of π, which gives us
[tex]\begin{gathered} \sin (0)=0\Rightarrow\sin (k\cdot0)=0\text{ (first zero | first asymptote)} \\ \sin (\pi)=0\Rightarrow\sin (2k\pi)=0\Rightarrow k=\frac{1}{2}\text{ (second zero | second asymptote)} \end{gathered}[/tex]Therefore, k = 1/2
[tex]f(x)=7\csc (\frac{x}{2}+\theta)-2[/tex]Finding θ:
It's the easiest one, since we have a zero at x = 0 it implies that θ = 0
Therefore our function is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]Final answer:
[tex]f(x)=7\csc \mleft(\frac{x}{2}\mright)-2[/tex]
3. At which of the following angles is the tangent function undefined?(1) 0 =180°(3) 0 = 45°(4) 0 =-360°(2) 0=-90°
The correct answer is angle 90 degrees.
Explanation:
The tangent of angle 90 degrees is undefined.
[tex]undefined[/tex]five pounds of sugar cost $4.05 how much sugar do you get per dollar? round your answer to the nearest hundredth, if necessary.
Given:
The cost of five pounds of sugar is $4.05.
Explanation:
To determine the amount of sugar that individual get for 1 dollar, divide 4.05 by 5.
Divide 4.05 by 5 to determine the amount of sugar individual get per dollar.
[tex]\frac{4.05}{5}=0.81[/tex]
Which of the following sampling methods would most likely have the smallest margin of erro?A. Roll a die 1000 times and estimate the proportion of 5's that result.OB. Sample 250 registered voters in a large city and ask them their political preference and use the results to estOC. Flip a coin 100 times and estimate the proportion of "heads" that resul.OD. Sample 10 adults and ask them if they support the current President's foreign policy and use this data to reReset SelectionMext
The sample methodology whose accuracy is better than another is the one with more approximation, this comes from the number of repetitions.
Therefore, option A is the one with more approximation, which mean the least error margin.
What do you notice about the measures of the sides or the measures of angles that form triangles?
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
Find the vertex of the following equation: y = -5x² - 270x - 520
In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:
[tex]y=ax^2+bx+c[/tex]Comparing with the given equation, we have a = -5, b = -270 and c = -520.
Now, let's calculate the x-coordinate of the vertex using the formula below:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ x_v=\frac{-(-270)}{2\cdot(-5)} \\ x_v=\frac{270}{-10} \\ x_v=-27 \end{gathered}[/tex]Using this value of x in the equation, we can find the y-coordinate of the vertex:
[tex]\begin{gathered} y_v=-5x^2_v-270x_v-520 \\ y_v=-5\cdot(-27)^2-270\cdot(-27)-520 \\ y_v=-5\cdot729+7290-520 \\ y_v=-3645+7290-520 \\ y_v=3125 \end{gathered}[/tex]Therefore the vertex is located at (-27, 3125).
57. do not use the answer under the line in the explanation itself, only refer to it to make sure of your work. USE DERIVITIVES NOT GRAPHING
Explanation
Question 57
[tex]\:f\left(x\right)=2x^3-15x^2+24x[/tex]To find the extreme values
[tex]\begin{gathered} \mathrm{Suppose\:that\:}x=c\mathrm{\:is\:a\:critical\:point\:of\:}f\left(x\right)\mathrm{\:then,\:} \\ \mathrm{If\:}f\:'\left(x\right)>0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:maximum.} \\ \mathrm{If\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)>\:0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:minimum.} \\ \mathrm{If\:}f\:'\left(x\right)\mathrm{\:is\:the\:same\:sign\:on\:both\:sides\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:neither\:a\:local\:maximum\:nor\:a\:local\:minimum.} \end{gathered}[/tex]So, we will have the steps below
Step 1:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=0\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=0 \\ \mathrm{Minimum}\left(0,\:0\right) \end{gathered}[/tex]Step2:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=1\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=11 \\ \mathrm{Maximum}\left(1,\:11\right) \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=4\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-16 \\ \mathrm{Minimum}\left(4,\:-16\right) \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=5\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-5 \\ \mathrm{Maximum}\left(5,\:-5\right) \\ \end{gathered}[/tex]Thus, we will have
[tex]\mathrm{Minimum}\left(0,\:0\right),\:\mathrm{Maximum}\left(1,\:11\right),\:\mathrm{Minimum}\left(4,\:-16\right),\:\mathrm{Maximum}\left(5,\:-5\right)[/tex]Hence, our answer is
[tex]\begin{gathered} \begin{equation*} \mathrm{Minimum}\left(4,\:-16\right) \end{equation*} \\ \begin{equation*} \mathrm{Maximum}\left(1,\:11\right) \end{equation*} \end{gathered}[/tex]Remi and Pam start at the same point and begin jogging in different directions. Remi is jogging east at a speed of 3 miles per hour. Pam is jogging south at a speed of 4 miles per hour. After how many hours will they be exactly 15 miles apart?
The number of hours (time) after which both Remi and Pam would be exactly 15 miles apart is 3 hours.
How to determine the number of hours (time)?First of all, we would have to determine the amount of distance (d) covered by both Remi and Pam.
Let t represent the number of hours (time) to cover these distances. Let r represent the distance covered (traveled) by Remi.Let p represent the distance covered (traveled) by Pam.Mathematically, the distance covered (traveled) by a physical body (object) can be calculated by using this formula:
Distance = speed × time
For the distance covered (traveled) by Remi, we have:
r = 3 × t
r = 3t.
For the distance covered (traveled) by Pam, we have:
p = 4 × t
p = 4t.
Also, the amount of distance (d) covered by both Remi and Pam forms a right-angled triangle as they both jogged East and South respectively. Therefore, there distances can be modeled by Pythagorean theorem:
d = r² + p²
Substituting the parameters into the formula, we have;
15² = 3t² + 4t²
225 = 9t² + 16t²
225 = 25t²
Dividing both sides by 25, we have:
t² = 225/25
t² = 9
t = √9
Time, t = 3 hours.
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Find the equation of the linear function x 1 2 3 4 y 1 6 11 16
We solve as follows:
*We determine first the slope (m), that is:
[tex]m=\frac{6-1}{2-1}\Rightarrow m=5[/tex]Now, using the slope and one point of the line, we replace in the following expression:
[tex]y-y_1=m(x-x_1)[/tex]We can use any point of the line, but I will be using the point (1, 1), that is:
[tex]y-1=5(x-1)[/tex]Now, we solve for y:
[tex]\Rightarrow y-1=5x-5\Rightarrow y=5x-4[/tex]. Calculate: (81)3/2
Calculate:
[tex]81^{\frac{3}{2}}[/tex]The fractional exponent can be written as:
[tex]\sqrt[2]{81^3}=(\sqrt[]{81})^3[/tex]The square root of 81 is 9, thus:
[tex](\sqrt[]{81})^3=9^3=729[/tex]Jane, Chau, and Deshaun have a total of $82 in their wallets. Deshaun has 2 times what Jane has. Chau has $6 less than Jane. How much does each have?
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
let x represent represent the amount of Jane.
let Y represent represent the amount of chau.
let z represent represent the amount of Deshaun.
Jane, Chau, and Deshaun have a total of $82" can be represented as
x + y + z = $82 .......(1)
Deshaun has 4 times what Jane has. It can be represented mathematically as
y = 2x .......(2)
Chau has $6 less than Jane. It can be represented mathematically as
z= x- 6 .......(3)
we can now solve the equations using the substitution method
substitute equation (2) and (3) into equation (1)
x + y + z = $82
x + 2x + x-6 = $82
4x -6 = $82
4x - 6 = $82
4x = $82 + 6
4x = 88
x = $22
from equation 2
y = 2x
y = 2 x 22 = $44
z = x- 6
z = 22 - 6
z=$16
Jane, Chau, and Deshaun have $22, $16 and $44 respectively in their wallets.
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Mario bought a $2,300 refrigerator on an installment plan. The installment agreement
included a $230 down payment and 18 monthly payments of $125 each. What is the
total finance charge?
O $180
O $225
O $145
O $195
$225,The term "instalment payments" describes a client paying a bill over a set period of time in incremental amounts. Start billing for nothing. A payment schedule agreed upon by the buyer and seller is known as installment payments.
What is installment payment?
The term "instalment payments" describes a client paying a bill over a set period of time in incremental amounts. Start billing for nothing. A payment schedule agreed upon by the buyer and seller is known as installment payments. Typically, it is mentioned unequivocally in a contract's or invoice's payment terms.
one of a series of regular loan, debt, or other payment installments; also, the system of monthly payments: This kind of installment payment is not subject to an additional cost.
An installment is a portion or segment of something, such as the most recent episode of your favorite TV show or the installment you pay each month toward your credit card debt.
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What is this sign of 30ﾟ angle and the sign of the 60ﾟ angle
We are asked to find out the values of sine 60° and sine 30°
Recall from the trigonometric ratios,
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the given triangle,
With respect to angle 60°, the opposite side is 25√3 ft and the hypotenuse is 50 ft.
Let us substitute these values into the above sine ratio
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 60\degree=\frac{25\sqrt[]{3}}{50} \\ \sin 60\degree=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]So, the value of sine 60° is √3/2
From the given triangle,
With respect to angle 30°, the opposite side is 25 ft and the hypotenuse is 50 ft.
Let us substitute these values into the above sine ratio
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 30\degree=\frac{25}{50} \\ \sin 30\degree=\frac{1}{2} \end{gathered}[/tex]So, the value of sine 30° is 1/2
Therefore, the sine of 60ﾟ angle is √3/2 and the sine of 30ﾟ angle is 1/2
the product of 12 and 3 decreased by 6
the product of 12 and 3 decreased by 6
we have that
the product of 12 and 3 ------> is number 12 multiplied by 3
12*3
decreased by 6
12*3-6=36-6=30
the answer is 303(-4+x)<-33 I need to solve for x
Simplify the inequality.
[tex]\begin{gathered} \frac{3(-4+x)}{3}<-\frac{33}{3} \\ -4+x+4<-11+4 \\ x<-7 \end{gathered}[/tex]So answer is x<-7.
B and Care sets of real numbers defined as follows.
Answer:
[tex]\begin{gathered} B\cap C=\phi \\ (-\infty,\text{ 1)}\cup\lbrack9,\infty) \end{gathered}[/tex]Step-by-step explanation:
Solve this situation with the help of the number line, if B and C are sets of real numbers defined as follow:
The intersection is an interval that lies within all of the given intervals. If no such intersection exists then the set is empty.
In this case, for the intersection between B and C:
[tex]\begin{gathered} B\cap C=\phi \\ \end{gathered}[/tex]For the union between B and C:
[tex](-\infty,\text{ 1)}\cup\lbrack9,\infty)[/tex]A volleyball drops 8 meters and bounces up 2 meters.
Use the expression |-8 + 2 to find the total distance
the volleyball travels. The total distance the volleyball travels is
✓meters.
The volleyball travelled a total distance of 10 meters
How to determine the total distance travelled by the volleyball?From the question, the given parameters are
Initial height = 8 meters
Height of bounce = 2 meters
The expression of the total distance is represented as
Total distance = |-8| + 2
Remove the absolute symbol
Total distance = 8 + 2
Evaluate the sum
Total distance = 10
Hence, the total distance travelled by the volleyball is 10 meters
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every week, Hector works 20 hours and earns $210.00. he eans a constant amount per hour. write an equation that can be used to determine the number of hours, h, Hector works given the number of weeks, w.
From the question, we're told that Hector earns $210.00 for working 2hours every week. Let's go ahead and determine
Sports Authority marks up New Balance sneakers $30 and sells them for $109. Markup is on cost. What are the cost and percent markup?
Answer: $79 and percentage is 36%
This is from my prep guideI will provide the answer options in another picture
In order to determine the corresponding graph to the given function f(x), consider the y-intercept of the function (the value of the y-coordinate of the curve when x = 0).
The y-intercept is the value of f(x) for x= 0. Replace x = 0 into the given function:
[tex]f(0)=(\frac{1}{2})^{0+1}+3=\frac{1}{2}+3=\frac{7}{2}[/tex]Then, the point of intersection of the curve with the y-axis is (0 , 7/2) or (0 , 3.5).
You can notice that from the given answer choices, that option two (up right side) has the required y-intercept. Then, that graph matches with the given function.
h(x) =-4x+ 3; Find h(x-1)
Answer:
h(x-1) = - 4x + 7
Explanation:
To find h(x - 1), we need to replace x by (x-1) on h(x). Then:
[tex]\begin{gathered} h(x)=-4x+3 \\ h(x-1)=-4(x-1)+3 \\ h(x-1)=-4x-4(1)+3 \\ h(x-1)=-4x+4+3 \\ h(x-1)=-4x+7 \end{gathered}[/tex]Therefore, h(x-1) = - 4x + 7
Classifying systems of linear equations from graphsFor each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solution.System ASystem B System C
Consistent dependant system- System B: It has infinite number of solutions, in this case, the graphs of the lines are the same.
Consistent independent system- System C: It has exactly one solution. In this case, both lines cross each other at exactly one point.
Solution : (-2,-2)
Inconsistent: System A.
When a system has no solution, lines never cross each other.