ANSWER
[tex]\text{ The equation of the parabola is; \lparen y - 7\rparen}^2\text{ = 10\lparen x - 3.5\rparen}[/tex]EXPLANATION
Given that;
The focus of the parabola is (6, 7)
The directrix is 1
Follow the steps below to find the equation of the parabola
Step 1; Write the general formula of the parabola equation
[tex]\text{ \lparen y - k\rparen}^2\text{ = 4p\lparen x - h\rparen}^[/tex]Recall, that the vertex of the parabola midway between the focus and directrix
Hence, h can be calculated below has
[tex]\begin{gathered} \text{ h = }\frac{\text{ k}}{\text{ 2}} \\ \\ \text{ h = }\frac{7}{2} \\ \text{ h = 3.5} \end{gathered}[/tex]Also, p is the distance of vertex to directrix
p = 6 - 3.5
p = 2.5
Step 2; Substitute the calculated data into the formula in step 1
[tex]\begin{gathered} \text{ \lparen y - 7\rparen}^2\text{ = 4}\times2.5\text{ \lparen x - 3.5\rparen} \\ \text{ \lparen y - 7\rparen}^2\text{ = 10\lparen x - 3.5\rparen} \end{gathered}[/tex]Answer:
x=(y-7)^2/10 +7/2
Step-by-step explanation:
khan
Solve for z-4z-5=30-9z
-4z-5=30-9z
Move the letters to the right:
-4z+9z= 30+5
Combine like terms
5z=35
Divide both sides by 5
5z/5 = 35/5
z = 7
5x + 7y + 2z = -79x + 7y + 2z = 52x - 7y - 5z = -2x = ?y = ?z = ?
x = 3, y = -6, z = 10
Explanations:The given equations are:
5x + 7y + 2z = -7..............(1)
9x + 7y + 2z = 5.................(2)
2x - 7y - 5z = -2......................(3)
Make x the subject of the formula in equation (1)
5x = -7 - 7y - 2z
x = ( -7 - 7y - 2z) / 5 ...........(4)
Substitute equation (4) into equations (2) and (3)
[tex]\begin{gathered} 9(\frac{-7-7y-2z}{5})+\text{ 7y + 2z = 5} \\ \text{Multiply through by 5} \\ 9(-7-7y-2z)\text{ + 35y + 10z = 25} \\ -63-63y-18z+\text{ 35y + 10z = 25} \\ 28y+8z\text{ = -}88 \\ 7y\text{ + 2z = -22}\ldots\ldots\ldots.(5) \end{gathered}[/tex][tex]\begin{gathered} 2(\frac{-7-7y-2z}{5})-7y-5z=-2 \\ \text{Multiply through by 5} \\ 2(-7-7y-2z)-35y-25z=-10 \\ -14-14y-4z-35y-25z\text{ = -}10 \\ 49y+29z\text{ = -4}\ldots\ldots\ldots(6) \end{gathered}[/tex]Solve equations (5) and (6) simulataneously:
Make z the subject of the formula from equation (5), the equation becomes:
[tex]\text{z = }\frac{-22-7y}{2}\ldots\ldots\ldots(7)[/tex]Substitute equation (7) into equation (6)
[tex]\begin{gathered} 49y\text{ + 29(}\frac{-22-7y}{2})=-4 \\ \text{Multiply through by 2} \\ 98y\text{ -}638-203y\text{ = -}8 \\ 105y\text{ = }8-638 \\ 105y\text{ = }-630 \\ y\text{ = }\frac{-630}{105} \\ y\text{ = -6} \end{gathered}[/tex]Put the value of y into equation (7)
[tex]\begin{gathered} z\text{ = }\frac{-22-7(-6)}{2} \\ z\text{ = }\frac{-22+42}{2} \\ \text{z = }\frac{20}{2} \\ z\text{ = 10} \end{gathered}[/tex]Put the value of z into equation (4)
[tex]\begin{gathered} \text{x = }\frac{-7-7y-2z}{5} \\ x\text{ = }\frac{-7-7(-6)-2(10)}{5} \\ x\text{ = }\frac{-7+42-20}{5} \\ x\text{ = }\frac{15}{5} \\ x\text{ = 3} \end{gathered}[/tex]HS: Statistics [M] (Sequential) Estimates and Sample Sizes5. Find the critical values and that correspond to a 95% confidence level and a sample size of 9.1.344, 21.9552.733, 15.5072.180, 17.5352.700, 19.023
We are asked to find the left and right critical values.
The confidence level is 95%
Significance level = 1 - 0.95 = 0.05
Sample size: n = 9
Degree of freedom = n - 1 = 9 - 1 = 8
So, the significance level is 0.05 and the degree of freedom is 8.
Using any chi-square critical value table or calculator,
Left critical value: χ²L = 2.733
Right critical value: χ²R = 15.507
Therefore, the chi-square left and right critical values are
2.733, 15.507
When finding slant asymtoptes, do you prefer long divison or synthetic division to find the equation of the line? Why? 3-5 scentences
Define Synthetic Division: In algebra, the synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division
When finding slant asymtoptes, I prefer synthetic division to find the equation of the line. This is because:
(i) it allows one to calculate without writing variables
(ii) it also uses calculations and takes significantly less space on paper than long division.
(iii) the subtarction in long division are converted to additions by switching the signs at the very begining, preventing sign errors
Answer each part. If necessary, round your answers to the nearest hundredth.(a) At Garcia's Bike Rentals, it costs $33 to rent a bike for 8 hours.How many dollars does it cost per hour of bike use?dollars per hour(b) Keiko bought 12 pounds of flour for $6.How many dollars did she pay per pound of flour?dollars per pound i need help with this problem.
(a) At Garcia's Bike rentals, it cost $33 to rent a bike for 8 hours.
We are asked to find how many dollars will an hour of bike use cost.
Let x be the cost in dollars of an hour of bike us.
If 8hours = $33
1 hour = $x
Lets cross multiply:
8 * x = 33 * 1
8x = 33
Let's divide both sides by 8
x = 33/8
x = $4.125
Therefore, per hour of bike use is $4.125
(b) Keiko bought 12 pounds of flour for $6.
We are to find how many dollers she paid per pound of flour.
Let y be the amount in dollar he paid per pound of flour.
If 12 pound = $6
1 pound = $y
Let's cross multiply:
12 * y = 6 * 1
12y = 6
Divide both sides by 12:
y = 6/12
y = $0.5
Therefore, she pays $0.5 per pound of flour.
hello, can you help me with this plane trigonometry question please thank you for your time.
Let
x -----> the measure of the missing angle
we know that
In the right triangle show
sin(x)=6/9 ------> by opposite side divided by the hypotenuse
so
using a calculator
x=arc sin(6/9)=41.81 degrees
therefore
the measure of the angle is
41.81 degreessolve for x below, given that s || r respectively:
First we will draw a parallel to s and r that pass on B
with this image we can find the next equation
[tex]x=(180-133)+(180-120)[/tex][tex]x=47+60=107[/tex]the answer is x=107
Translate to a proportion and solve. $72 is what percent of $96?$72 is ...% of $96
Need to find $72 is what percent of $96.
Let x be required percentage.
Then translate the given expression in mathematical form as follows:
[tex]\begin{gathered} 72=\frac{x}{100}\cdot96 \\ 72\cdot100=x\cdot96 \\ \frac{7200}{96}=x \\ 75=x \end{gathered}[/tex]So, the required percent is 75%.
Rewrite the following statement using a natural logarithm. Fill in each blank with the appropriate letter or number. e^a=b is equivalent to ln (_____)=______
Given the exponential expression:
[tex]e^a=b[/tex]We will rewrite the expression using a natural logarithm
so,
[tex]\begin{gathered} \ln e^a=\ln b \\ a\cdot\ln e=\ln b \\ a\cdot1=\ln b \\ a=\ln b \end{gathered}[/tex]so, the answer will be:
[tex]a=\ln b[/tex]Given that sin(0)2/13and 0 is in Quadrant IV, what is cos(20)?13,
1) Let's use a trigonometric identity for this question:
[tex]\begin{gathered} \cos (2\theta)=1-2\sin ^2(\theta) \\ \cos (2\theta)=1-2\cdot(\frac{-2\sqrt[]{13}}{13})^2 \end{gathered}[/tex]Notice that for that double angle identity, we need to pick the one that relates the value of the sin(theta):
[tex]\begin{gathered} \cos (2\theta)=1-2\cdot(\frac{-2\sqrt[]{13}}{13})^2 \\ \cos (2\theta)=1-2(\frac{52}{169}) \\ \cos (2\theta)=1-2(\frac{4}{13}) \\ \cos (2\theta)=1-\frac{8}{13}=\frac{5}{13} \end{gathered}[/tex]2) In Quadrant IV the sign of the cosine function is :
Which binomial is a factor of the polynomial? x^2 + x - 6
A)(x + 6)
B)(x - 2)
C)(x + 2)
D)(x - 6)
To find the binomial factors, we just need to factorize the expression
To factorise the expression, you look for two factors of 6 that there sum or difference will give the cosfficient of the middle term.
[tex]\begin{gathered} \text{factors of 6=3 and 2} \\ 1=\text{ 3-2} \\ \text{Hence replace the middle term with the factors we have obtain} \end{gathered}[/tex]We have
[tex]x^2+3x-2x-6[/tex]We now take the common factor by splitting the expression into two
[tex]\begin{gathered} x(x+3)-2(x+3)_{} \\ (x-2)(x+3) \end{gathered}[/tex](x-2) is the factor of the polynomial
The r option is B
What is the solution to this equation?X+ 17 = 25A. x = 9B. x = 42C. x = 12D. X = 8
answer: D
7 multiplied by the difference of 6 and 5"
7 multiplied by the difference of 6 and 5, can be translated to
[tex]\begin{gathered} 7(6-5) \\ \\ \text{and when simplified is} \\ 7(1) \\ =7 \end{gathered}[/tex]Compute the value of the discriminant and give the number of real solutions of the quadratic equation.-2x² + 6x - 3=0Discriminant:12Number of real solutions:
Given:
[tex]-2x^2+6x-3=0[/tex][tex]a=-2\text{ ; b=6 ; c=-3}[/tex][tex]D=b^2-4ac[/tex][tex]D=6^2-4(-2)(-3)[/tex][tex]D=36-24[/tex][tex]D=12[/tex]Discriminant = 12
12>0
Therefore, the quadratic equation has two real roots.
find how much money will be in the account given each principal, compound interest rate, and amount of time. also, determined the amount of Interest assume interest is compounded yearly. p=$7000, r=6%, t=3 years
Apply the compound interest formula:
A = P (1+r)^t
Replacing:
A = 7,000 (1+ 6/100) ^3
A = 7,000 ( 1.06)^3
A = $8,337.11
Amount of interest:
8,337.11-7000 = $1,337.11
If you pick a card from a well shuffled deck, what is the probability that you get a face card or a spade?1/215/2611/261/13
Hello!
To solve this exercise, we must divide it into three possible cases:
• obtain a face card
,• obtain a spade card
,• obtain a face card from spades
First, let's remember that one deck hks 52 different cards, divided into 4 suits. Each suit has these cards:
• A, 2, 3, 4, 5, 6, 7, 8, 9, 10, ,J, Q, K,.
Knowing it, let's calculate some probabilities:obtain a face card:3 cards x 4 suits = 12 cards in a total of 52, so:
[tex]\frac{12}{52}[/tex]obtain a spade card13 possible cards in a total of 52, so:
[tex]\frac{13}{52}[/tex]obtain a face card from spades3 possible cards, in a total of 52.
Calculating the probability:We must use the "or rule", which means to sum the result of the first condition with the result of the second condition. As these first two conditions cannot ocurr together, we have to subtract the third condition. Look:
[tex]\begin{gathered} \frac{12}{52}+\frac{13}{52}=\frac{25}{52} \\ \\ \frac{25}{52}-\frac{3}{52}=\frac{22}{52}=\frac{11}{26} \\ \end{gathered}[/tex]Answer:Third alternative.
ha's reme
Mark earned $98.50 for working ten hours. Cindy earned 145.50 for working ten hours. What does each person make per hour of work? Tell answer and do a step by step model please.
Given that
1) Mark earns $98.50 for ten hours
2) Cindy earns $145.50 for ten hours
We are required to find how much each person makes per hour
Step 1
We can find how much each person earns per hour by using the formula below
[tex]undefined[/tex]Find how much Mark earns per hour
which numbers would be located in the shaded part of the diagrama? -1.7. -8. 2/3 10
The answer is 8
integers comprises of negative and positive whole numbers.
Only positive integers are regarded as whole numbers.
so, if you take away whole numbers (that is, positive integers), you are left with only the negative integers. And the only negative integer in the option given is -
Let f(x) = x2-3x and g(x) = x-3. Find and simplify a rule (expression) for (fog)(x). (DO NOT FACTOR YOUR ANSWER.)
Explanation
[tex]\begin{gathered} f(x)=x^2-3x \\ g(x)=x-3 \end{gathered}[/tex]
Step 1
replace g(x) in f(x),where x
[tex]\begin{gathered} f(x)=x^2-3x \\ (f\circ g)(x)=(x-3)^2-3(x-3) \end{gathered}[/tex]Step 2
operate
remember:
[tex](a-b)^2=a^2-2ab+b^2[/tex]Hence,
[tex]\begin{gathered} (f\circ g)(x)=(x-3)^2-3(x-3) \\ (f\circ g)(x)=(x^2-2\cdot x\cdot3+3^2)-3(x-3) \\ (f\circ g)(x)=(x^2-6x+9)-3x+9 \\ (f\circ g)(x)=x^2-6x+9-3x+9 \\ (f\circ g)(x)=x^2-9x+18 \end{gathered}[/tex]I hope this helps you
AcellusConvert this decimal into its fractionalform, simplified completely.0.650
Explanation
Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.9, the nine is in the tenths place, so we place 9 over 10 to create the equivalent fraction, 9/10. If needed, simplify the fraction.
Step 1
move the decimal point 2 space to the right
[tex]0.650\rightarrow65[/tex]now,
[tex]\frac{65}{10^2}=\frac{65}{100}[/tex]hence, the answer is
[tex]\frac{65}{100}[/tex]the answe is 65/100
1. Identify the solution set of y = -x + 3 on the coordinate grid below. YA 6 5 4 3 2- 1 1 2 3 4 5 6 X -6 -5 -4 -3 -2 -1 0 1 2 -3 -4 -5 -6 IPDF
we have the inequality
[tex]y\text{ }\ge-x+3[/tex]the solution set of this inequalitty is the shaded area above the solid line y=-x+3
using a graphing tool
see the attached figure to better understand the problem
please wait a minute ( i will draw the solution)
On this problem, the answer has been worked out, but you must fill in the blanks in the solution.It is believed that 25% of U.S. homes have a direct satellite television receiver. How large a sample is necessary to estimate the true proportion of homes that do with 95% confidence and within 3 percentage points? How large a sample is necessary if nothing is known about the proportion?Solution: Notice that there are two questions, both about sample size for a proportion, so we use the formula
SOLUTION
Step 1 :
We need to know how large a sample is necessary.
Let p denotes the United States Homes have a direct satellite TV Receiver is 25 % or 0. 25.
From the information, we know that E is 3 % or 0.03 and the confidence interval of 95%.
When p is known, then the sample size formula is :
[tex]\begin{gathered} n\text{ = }^{}\frac{\lbrack Z_{\frac{\alpha}{2}}\rbrack^2}{E^2}\text{ X p x q} \\ \text{where p + q = 1} \end{gathered}[/tex]When p is unknown, then the sample size formula is:
[tex]n\text{ = }\frac{\lbrack Z_{\frac{\propto}{2}}\rbrack^2}{E}\text{ X 0.25}[/tex]Now, we have to determine:
[tex]Z_{\frac{\alpha}{2}}[/tex]The confidence level is :
[tex]1\text{ - }\alpha[/tex]We know that:
[tex]\begin{gathered} \alpha\text{ = 95\% = 0.95} \\ 1\text{ - }\alpha\text{ = 1 - 0.95} \\ \text{1 - }\alpha\text{ = 0.05} \\ Z_{\frac{\alpha}{2}\text{ }}=\text{ 0.05/ 2} \end{gathered}[/tex][tex]Z_{\frac{0.05}{2}\text{ }}=\text{ 1.96 ( using table value )}[/tex]If we use the known p, then the sample size is :
[tex]\begin{gathered} n\text{ = }\frac{(1.96)^2}{(0.03)^2}\text{ X ( 0.25 ) ( 0.75 )} \\ n\text{ = }\frac{3.8416}{0.0009}\text{ x 0.1875} \\ \text{n = 4268.44444 x 0.1875} \\ n\text{ = 800.333} \\ n\text{ }\approx\text{ 801} \end{gathered}[/tex]If we use the known p, then the sample size is 801.
Therefore, a sample n is 801.
Step 2 :
If we use the un-known p , then the sample size is :
[tex]\begin{gathered} n\text{ = }\frac{(1.96)^2}{(0.03)^2}\text{ x 0. 25} \\ \text{n = }\frac{3.8416}{0.0009}\text{ x 0.25} \\ n\text{ = 4268.44444 x 0.25} \\ \text{n = 1067. 11111} \\ n\approx\text{ 1068} \end{gathered}[/tex]If we use the unknown p, then the sample size is approximately 1068.
Therefore, a sample n is 1068.
find the mean of the data sets round to the nearest integer. 3. {12,17,16,18,15,16,15,16}
Assume that adults have IQ scores that are normally distribüted with a mean of 104.6 and a standard deviation 15.8.Find the first quartile Q.which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.)The first quartile ls:
The z-score in which the bottom 25% lies is equal to -0.67.
Given a mean score of 104.6 and a standard deviation of 15.6
[tex]\begin{gathered} X=\mu+(-0.67)\sigma \\ \text{Substitute} \\ \mu=104.6,\sigma=15.6 \\ \\ X=104.6+(-0.67)(15.6) \\ X=104.6-10.452 \\ X=94.148 \end{gathered}[/tex]Rounding to one decimal place, the score separating the bottom 25% or the first quartile is 94.1.
ExerciseComplete the sentence.Two lines that do not intersect and are also not parallel arelineshorizontalperpendicualskew1vertical
Lines that do not intersect and also are not parallel are said to be skew lines.
Skew lines are lines that do not intersect, are not parallel, also they are not perpendicular to each other.
ANSWER:
Skew
if using the method of completing the square to solve the quadratic equation x squared + 16x - 5 equals 0 which number would have to be added to complete the square
Given the quadratic equation :
[tex]x^2+16x-5[/tex]It is required to make a complete square
The coefficient of x = 16
so, we will add : the square of ( half of the coefficient x )
so, half of 16 = 0.5 * 16 = 8
Square of 8 = 64
So, the complete square will be as following ;
[tex]\begin{gathered} x^2+16x-5+64-64 \\ =x^2+16x+64-5-64 \\ =(x^2+16x+64)+(-5-64) \\ =(x+8)^2+(-69) \\ \\ =(x+8)^2-69 \end{gathered}[/tex]
the transformation form (vertex form) of the absolute value function is y=a×[x-h] +k. what is the value of a, h and k in the parent function y=[x]
We have the parent function y=x^2 and we have to express it in vertex form.
We can rearrange it like:
[tex]\begin{gathered} y=x^2 \\ y=x^2+0 \\ y=(x-0)^2+0 \end{gathered}[/tex]This is the result as the vertex of the parent function is at (h,k)=(0,0).
The quadratic coefficient is 1.
Answer: a=1, h=0, k=0
There were 23.7 million licensed drivers in California in 2009 and 22.76 in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the numbers of years since 2004, assuming growth isa) Linear N(t) = 0.188t + 22.76 million drivers b) Exponential N(t) =
Answer:
[tex]N(t)=22.76(1.0081)^t[/tex]Explanation:
The exponential function is of the form:
[tex]N(t)=a(b)^t[/tex]In 2004, (i.e. t=0), the number of licensed drivers = 22.76 million
[tex]\begin{gathered} N(t)=22.76,t=0 \\ 22.76=a(b)^0 \\ \implies a=22.76 \end{gathered}[/tex]In 2009, the number of licensed drivers = 23.7 million
[tex]\begin{gathered} a=22.76,N(t)=23.7,t=2009-2004=5 \\ N(t)=a(b^t)\implies23.7=22.76(b)^5 \end{gathered}[/tex]We solve for the value of b:
[tex]\begin{gathered} 23.7=22.76(b)^5 \\ b^5=\frac{23.7}{22.76} \\ b=\sqrt[5]{\frac{23.7}{22.76}} \\ b=1.0081 \end{gathered}[/tex]Therefore, an exponential formula for the number, N, of licensed drivers in the US as a function of t, the numbers of years since 2004 is:
[tex]N(t)=22.76(1.0081)^t[/tex]Note: N(t) is in millions
A worker pushes a wheelbarrow with a force F of 60 N downward and to the left, as shown in the figure below. The anglethe handle makes with the horizontal is 42°, and the wheelbarrow Is moved 19 m. Find the work W done, In joules (1).Do not round any intermediate computations, and round your answer to the nearest hundredth.42°FW =?
Concept
[tex]undefined[/tex]The graph of 2x - 5y = 10 is shown on the grid. He у 10 Which ordered pair is in the solution set of 2x - 5y > 10? in E
Write the inequality
[tex]2x-5y\ge10[/tex]now we can repalce each ordered pair to check the inequality
if the inequality is right the pair is a solution
A. (0,5)
[tex]\begin{gathered} 2(0)-5(5)\ge10 \\ 0-25\ge10 \\ -25\ge10 \end{gathered}[/tex]
on this case -25 isnt greater than or equal to 10 then is wrong
B. (5,0)
[tex]\begin{gathered} 2(5)-5(0)\ge10 \\ 10-0\ge10 \\ 10\ge10 \end{gathered}[/tex]10 is equal to 10 then this option is RIGHT
C. (-2,5)
[tex]\begin{gathered} 2(-2)-5(5)\ge10 \\ -4-25\ge10 \\ -29\ge10 \end{gathered}[/tex]
-29 isnt greater than or equal to 10 then is wrong
D. (-5,2)
[tex]\begin{gathered} 2(-5)-5(2)\ge10 \\ -10-10\ge10 \\ -20\ge10 \end{gathered}[/tex]-29 isnt greater than or equal to 10 then is wrong
finally the only solution is B (5,0)