Answer:
The standard parabola
y² = -18 x +27
Length of Latus rectum = 4 a = 18
Step-by-step explanation:
Explanation:-
Given focus : (-3 ,0) ,directrix : x=6
Let P(x₁ , y₁) be the point on parabola
PM perpendicular to the the directrix L
SP² = PM²
(x₁ +3)²+(y₁-0)² = [tex](\frac{x_{1}-6 }{\sqrt{1} } )^{2}[/tex]
x₁²+6 x₁ +9 + y₁² = x₁²-12 x₁ +36
y₁² = -18 x₁ +36 -9
y₁² = -18 x₁ +27
The standard parabola
y² = -18 x +27
Length of Latus rectum = 4 a = 4 (18/4) = 18
Solve the inequalities (i) 5 ≤ 2x − 4 ≤ 8 (ii) −10 < 4 −3y/− 5 ≤ 4
Step-by-step explanation:
(i) 5 ≤ 2x − 4 ≤ 8 add 4 to all three expressions
9 ≤ 2x ≤ 12 divide by 2
9/2 ≤ x ≤ 6
(ii) −10 < (4 −3y)/− 5 ≤ 4 multiply all sides by -5
-20 ≤ 4 - 3y < 50 subtract 4
-24 ≤ -3y < 46 divide with -3
-46/3 < y ≤ 8
P = 0.36x – 42
the formula below models the profit p in dollars for a shoe shiner when he shines x pairs of shoes use the formula to find this shoe shiner's profit when he shines 900 pairs of shoes
Answer:
pata nahi
Mark me as a brainliest
3. Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 5
doses, and each measles vaccination consists of 3 doses. Last year, Dr. Potter gave a total of 60
vaccinations that consisted of a total of 225 doses. How many more measles vaccines did Mr.
Potter give than polio?
Please explain the process. THX
Answer:
There are 15 more measles vaccines than polio vaccines
Step-by-step explanation:
Represent Polio with P and Measles with M
Given
5P + 3M = 225
P + M = 60
Required
How much is M greater than P; M - P
Make M the subject of formula in the second equation
[tex]M = 60 - P[/tex]
Substitute this in the first equation
[tex]5P + 3M = 225[/tex] becomes
[tex]5P + 3(60 - P) = 225[/tex]
Open the bracket
[tex]5P + 180 - 3P = 225[/tex]
Collect Like Terms
[tex]5P - 3P = 225 - 180[/tex]
[tex]2P = 45[/tex]
Divide both sides by 2
[tex]P = 22.5[/tex]
Substitute 22.5 for P in [tex]M = 60 - P[/tex]
[tex]M = 60 - 22.5[/tex]
[tex]M = 37.5[/tex]
Calculate the difference; M - P
[tex]M - P = 37.5 - 22.5[/tex]
[tex]M - P = 15[/tex]
Hence, there are 15 more measles vaccines than polio vaccines
A computers is on on sale for $1085. if the original price was reduced by 30%, what was the original price of the Computer ?
Answer:
1.131,5
Step-by-step explanation:
Distribute a negative -(5.5q+7)
Hi there! :)
Answer:
[tex]\huge\boxed{-5.5q - 7}[/tex]
-(5.5q + 7)
Distribute:
-(5.5q) -(7)
-5.5q - 7
Answer:
Z≥0 = {0, 1, 2, .
Step-by-step explanation:
Just took test
can someone please help me???
a is 3/4
b is -8
c is -2
d is 3
Answer:
-b[a + (c-d)^2]
-(-8)[3/4 + (-2 -3)^2]
8 [3/4 + (-5)^2]
8 [3/4 + 25]
8 [25.75]
206
=======================================
Work Shown:
a = 3/4
b = -8
c = -2
d = 3
----------------
c-d = -2-3 = -5
(c-d)^2 = (-5)^2 = 25
a+(c-d)^2 = 3/4 + 25 = 3/4 + 100/4 = 103/4
-b * [ a + (c-d)^2 ] = -(-8)*103/4 = 8*103/4 = (8/4)*103 = 2*103 = 206
----------------
Another way to show the steps could be
[tex]-b[a+(c-d)^2]\\\\-(-8)\left[\frac{3}{4}+(-2-3)^2\right]\\\\8\left[\frac{3}{4}+(-5)^2\right]\\\\8\left(\frac{3}{4}+25\right)\\\\8\left(\frac{3}{4}+\frac{100}{4}\right)\\\\8\left(\frac{3+100}{4}\right)\\\\8\left(\frac{103}{4}\right)\\\\\frac{8}{4}*103\\\\2*103\\\\206\\\\[/tex]
Which is more or less the same thing as the previous section.
----------------
So ultimately,
[tex]-b[a+(c-d)^2] = 206[/tex]
when a = 3/4, b = -8, c = -2, and d = 3.
Use the Method of Lagrange Multipliers to find the Minimum and Maximum of f(x,y) = xy subject to x^2+y^2-xy = 9 g
Answer: The Max fun is 9, and the Min fun is -3
Step-by-step explanation:
Please follow the steps carefully;
Let us consider the function f(x,y) = xy -------------- (1)
We will apply the Lagrange multipliers to maximize the function f(x,y) subject to the constraint g(x,y) = x^2+y^2-xy = 9
By differentiating (1) w.r.t x, we get fx(x,y) = y
By differentiating (1) w.r.t y, we get fy(x,y) = x
By differentiating g(x,y) w.r.t x, we get gx(x,y) = 2x - y
Also By differentiating g(x,y) w.r.t y, we get gy(x,y) = 2y - x
let us take
fx = λgx
where y = λ(2x - y)
y/2x - y = λ ----------- (2)
fy = λgy
where x = λ(2y - x)
λ = x/2y -x ----------- (2)
Let us equate (2) and (3)
y/2x - y = x/2y -x
2y² - xy = 2x² - xy
2y² = 2x² after cancelling like terms
y² = x²
So y = ±x
Now let us substitute y = x into the given constraint
x² + y² - xy = 9
x² + x² - x(x) = 9
x² = 9
therefore x = ± 3
We can conclude that when x = ±3, ⇒ y = ±3
The corresponding points are (3,3), (-3,-3)
Substitue y = -x in the given constraint gives
x² + y² - xy = 9
x² + (-x)² -x(-x) = 9
3x² = 9
x² = 3
x = ±√3
The corresponding points are (√3,-√3), (-√3,√3)
The function value is
f(x,y) = xy
f (√3,-√3) = (√3)(-√3) = -3
f (-√3,√3) = (-√3)(√3) = -3
we get;
f(3,3) = (3)(3) = 9
and
f (-3,-3) = (-3)(-3) = 9
We can conclusively say that ;
The Maximum value of the function is 9
The Minimum value of the function is -3
cheers i hope this helped
One millilitre has about 15 drops. One drop of
water has 1.67 x 1021 H,O (water) molecules.
Estimate the number of molecules in 1 litre of
water. Write down your answer in standard
form.
Answer:
25,576,050 water molecules
Step-by-step explanation:
multiply 1.67 by 1021 = 1705.07
multiply 1705.07 by 15 = 25,576.05
Now multiply 25,576.05 by 1000 (thats how many milliliters are in 1 liter) = 25,576,050
The number of water molecules is 2.505 x 10²⁵.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that one milliliter has about 15 drops. One drop of water has 1.67 x 10²¹ H, O (water) molecules.
Multiply 1.67 by 10²¹ = 1.67 x 10²¹
Multiply 1.67 x 10²¹ by 15 = 2.505 x 10²²
Now multiply 2.505 x 10²² by 1000 (that's how many mill liters are in 1 liter) 2.505 x 10²⁵.
Therefore, the number of water molecules is 2.505 x 10²⁵.
To know more about an expression follow
https://brainly.com/question/14106327
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PLEASE HELP ASAP it is ze homework
Answer:
Figure d)
Monopars are figures that have just one set of parallel lines.
Step-by-step explanation:
It looks like all the figures in group 1 have one set of parallel lines. In group 2, they either have 0 or 2. In group 3, only d has just one set of parallel lines.
So monopars are figures that have just one set of parallel lines.
order the following numbers from least (top) to greatest number( bottom) . 0.40 , 0.489 , 0.430 , 0.480
Answer:
[tex]\Large \boxed{0.40 < 0.430 < 0.480 < 0.489}[/tex]
Step-by-step explanation:
First you have to see the decimal places.
Than the number of digits there is.
So this is how we make it from least to greatest!
Since there is 3 numbers after the decimals in almost all of them...
Than let’s make ‘0.40’ into 3 numbers after the decimal too.
I am sure you have heard that if you add a ‘0’ to a decimal nothing will change right?
So let’s make 0.40 into 3 numbers after the decimal just like the other numbers!
Okay so first let’s add a zero to ‘0.40’... which now this turns into ‘0.400’
Now it will be more easier to compare least to greatest!
0.400 is the least, than comes 0.430, & than would be 0.480, & finally the greatest would be 0.489
Therefore the answer is 0.40 < 0.430 < 0.480 < 0.489.
What are the distances from the point (x,y) to the focus of the parabola and the directrix? Select two answers. A.distance to the directrix: |y+6| B.distance to the focus: (x+4)2+(y−2)2√ C.distance to the directrix: |y−6| D.distance to the focus: (x−2)2+(y+4)2√ E.distance to the directrix: |x+6| F.distance to the focus: (x−2)2+(y+5)2√
Answer:
Option (A) and Option (D)
Step-by-step explanation:
Point on the parabola is (x, y).
Focus given as (2, -4) and directrix of the parabola is y = -6
Therefore, distance of the point from the directrix will be,
d = |(y + 6)|
Similarly, distance of the point (x, y) from the focus will be,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(x-2)^2+(y+4)^2}[/tex]
Therefore, Option (A) and Option (D) will be the correct options.
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 146 . Is the predicted value close to 91.0 , which was the actual diastolicreading? Use a significance level of 0.05.Systolic 117 134 150 113 138 113 144 145Diastolic 85 74 86 55 75 80 106 841. What is the regression equation? (Round to two decimal places as needed.)2. What is the best predicted diastolic pressure for a person with a systolic reading of 146 ?3. Is the predicted value close to 91.0 , which was the actual diastolic reading?A. The predicted value is very close to the actual diastolic reading.B. The predicted value is not close to the actual diastolic reading.C. The predicted value is close to the actual diastolic reading.D. The predicted value is exactly the same as the actual diastolic reading.
Answer:
ŷ = 6.69X - 706.18 ; 270.56; B. The predicted value is not close to the actual diastolic reading.
Step-by-step explanation:
Given the data below :
Systolic reading(x) :
117
134
150
113
138
113
144
145
Diastolic (y) :
85
74
86
55
75
80
106
841
A) Find the regression equation, letting the systolic reading be the independent (x) variable:
Using the online regression calculator :
The regression equation obtained is ;
ŷ = 6.69X - 706.18
Where ;
ŷ = dependent variable
6.69 is the gradient or slope
-706.18 is the intercept, where the line crosses the y - axis.
X - the independent variable (Systolic reading)
B.) Find the best predicted diastolic pressure for a person with a systolic reading of 146 .
ŷ = 6.69X - 706.18
ŷ = 6.69(146) - 706.18
ŷ = 270.56
Is the predicted value close to 91.0
B. The predicted value is not close to the actual diastolic reading.
Determine whether the variable is qualitative or quantitative. Is the variable qualitative or quantitative? favorite rock group
Answer:
qualitative
Step-by-step explanation:
Favorite rock group is the qualitative variable because it shows an attribute. It does not depict a quantity or numbers. The favorite rock group will perform and show their ability to deliver music articles so it is showing quality not quantity. It is an attribute.
Variable is defined as the characteristic being studied so it is a qualitative variable meaning it is showing quality of the characteristic.
which of the following is not a factor in becoming a money smart?
Answer:
Its learning how to read credit card statements
Step-by-step explanation:
Learn how to read your credit card statements and control the way you process them
Damien worked at a grocery store earning $9.00 an hour. He worked 30 hours a week and was paid every two weeks. He paid $62 in taxes and had a $50 savings account deduction. What was Damien's gross income?
Answer:
$540
Step-by-step explanation:
We know Damien earned $9 per hour, worked 30 hours a week and was paid every 2 weeks.
We can write an expression to something like this:
(9 x 30) x 2
Which would give us 540
The question asks for the Gross income (the total income, before any taxes or deductions)
Which means that his gross income was $540
Help me please thank y’all
Answer:
125°
Step-by-step explanation:
Sum of angles of triangle equals 180°:
x + 25° + 30° = 180°x + 55° = 180°x = 180° -55°x = 125°Answer:
x=125
Step-by-step explanation:
because sum of interior angles of a triangle is 180
Find the perimeter of a triangle with sides of 1/12 meter 5/12 meter and 11/12 meter write your answer as a mixed number
Answer:
The answer is 1 5/12.Step-by-step explanation:
Side 1 = 1/12
Side 2 = 5/12
Side 3 = 11/12
Side 1 + Side 2 + Side 3 = P
1/12 + 5/12 + 11/12 = 6/12 + 11/12 = 17/12
The answer is 1 5/12.If f(x) = -1x + 4 then what is f(-2)?
Answer:
[tex]\huge \boxed{f(-2)=6}[/tex]
Step-by-step explanation:
[tex]\sf f(x)=-1x+4[/tex]
Switching x variable with -2.
[tex]\sf f(-2)=-1(-2)+4[/tex]
Evaluating.
[tex]\sf f(-2)=2+4[/tex]
[tex]\sf f(-2)=6[/tex]
Answer:
6Step-by-step explanation:
[tex]f(x) = -1x + 4\\\\f(-2) =?\\\\f(-2) = -1(-2) +4\\f(-2) = 2+4\\f(-2) = 6[/tex]
Which shows a true math fact? A 18.7×3.47=58.157 B 86.128−29.473=56.655 C 37.561+28.94=40.455 D 36.26÷0.50=725.2
Answer:
The correct answer is B.
Explanation:
Putting it into your calculator as you see it gives you the correct answer.
Have a good day! :)
How do I graph this? Also how do identify which values of c for which
lim f(x) exist?
x -> c
Answer:
Step-by-step explanation:
Hello, I attached the graph.
This is a parabola, then a line and finally an horizontal line.
The vertex of the parabola is (0,0) and (2,4) is on the graph.
For the second part, draw a line which is passing by (2,4) and (0,4)
Finally, draw the line y = 4
You can see that f is continuous everywhere except in x = 4.
So, for any c real different from 4 the limit of f(x) exists.
Thank you
Convert 0.00001 to a power of 10
Answer:
1 * 10 ^ -7
Step-by-step explanation:
1 lb = 16 oz. How many lbs (pounds) are in 14 oz (ounces)?
Answer:
0.875
Step-by-step explanation:
14÷16= 0.875
divide the mass value by 16
In 2000, the total number of employees working for
U.S. airlines was 679,967. Round this number to the
nearest thousand. (Source: The Air Transport Asso-
ciation of America, Inc.)
Answer:
680,000
679,967 rounded to the nearest thousand is 680,000.
So, there are around 680,000 employees working for US Airlines. Hope it helps!
Answer:
680,000
Step-by-step explanation:
Look at the hundreds place if it's 5 or higher you round up the thousands place by one. Every place to the right of the hundreds place turns into a zero.
William drove 344 miles in 8 hours. If he continued at the same rate, how far would he travel in 17 hours?
Answer:
731 miles
Step-by-step explanation:
To solve this, we can set up a proportion.
Let's name the number of miles he travels in 17 hours x for now.
8/344=17/x
Simplify 8/344
2/86=17/x
Cross multiply
86*17=2*x
2x=1462
Divide both sides by 2.
x=731
He would travel 731 miles in 17 hours.
Answer:
731 miles
Step-by-step explanation:
Proportions:
344 miles ⇒ 8 hours
W miles ⇒ 17 hours
W = 344*17/8
W = 731
calculate 65 L to quarts. Final answer round two places
Step-by-step explanation:
The approximate equation to convert from liters to quarts is : x • 1.056688.
We enter 65 for x and multiply.
65 • 1.056688 = 68.68472
We round that to the nearest 100th to get our final answer.
Our final answer: 68.68 liters
Simplify. Answer and explanation if you can
Hi there! Hopefully this helps!
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Answer: 6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Calculate 36 to the power of [tex]\frac{1}{2}[/tex].
[tex]\frac{1}{2} = 0.5[/tex]
[tex]36^{0.5} = 6[/tex].
6. Which expressions are equivalent to 9x?
Select all that apply.
A. 8x + x
B. 9x + x
C. 10 - X
D. 5x + x + 3x
E. 7x + x + 2x
Answer:
A. & D.
Step-by-step explanation:
A. 8x + x = 9x
B. 9x + x = 10x
C. 10 - x = 10 - x (not like terms)
D. 5x + x + 3x = 9x
E. 7x + x + 2x = 10x
What is the slope of the line that contains these points? x,12,13,14,,15. y,-4, 2,8,14.
Answer:
[tex]\huge \boxed{{m=6}}[/tex]
Step-by-step explanation:
Let's take two points,
(12, -4) and (13, 2).
slope = (difference of y) / (difference of x)
m = (2 - - 4) / (13 - 12)
m = (2 + 4) / 1
m = 6 / 1 = 6
The slope of the line is 6.
Answer:
6
Step-by-step explanation:
The slope is the change in y over the change in x
m = ( y2-y1)/(x2-x1)
= (14-8)/(15-14)
= 6/1
A local diner has started selling cupcakes and is using the bar chart given below to keep track of how many are sold each day. How many cupcakes will be sold on day n?
Answer:
a + (n-1)*4
Step-by-step explanation:
Day n could be any particular day located on the x-axis of the bar chart. Each bar represents the amount of cupcakes sold on each of the four days numbered from 1 to 4. The height of each bar marks the number of cupcakes sold. According to the chart attached, the number of cupcakes sold on each day is listed below:
Day 1 : 1 cupcake sold
Day 2 : 5 cupckaes sold
Day 3: 9 cupcakes sold
Day 4: 13 cupckaes sold
Studying the graph carefully fully, it will be observed that the number of cupcakes sold increases by a margin of 4 after day one.
As such the number of cupcakes sold in n days can be modeled by:
Using the Arithmetic progression formula:
Tn = a + (n-1)d
d = common difference, = 4
a = first term = 1
n = number of days
Hence, number sold in day n:
a + (n-1)*4
Arithmetic progressio
Answer:
3n−1 cupcakes
Step-by-step explanation:
Help please I would appreciate it !
Answer/Step-by-step explanation:
Given:
Line equation => [tex] 2.1x + 9.9y - 9.2 = 0 [/tex]
Required:
x-intercept and y-intercept of the line.
SOLUTION:
The x-intercept is the point where the line intercepts the x-axis. To find the x-intercept of the line for which the equation is given above, set y = 0 and solve for x.
[tex] 2.1x + 9.9(0) - 9.2 = 0 [/tex]
[tex] 2.1x + 0 - 9.2 = 0 [/tex]
[tex] 2.1x - 9.2 = 0 [/tex]
[tex] 2.1x - 9.2 + 9.2 = 0 + 9.2 [/tex]
[tex] 2.1x = 9.2 [/tex]
[tex] \frac{2.1x}{2.1} = \frac{9.2}{2.1} [/tex]
[tex] x = 4.4 [/tex] (approximated)
The y-intercept is the point where the line intercepts the y-axis. At this point, x = 0. Set x = 0 and solve for y to find the y intercept.
[tex] 2.1(0) + 9.9y - 9.2 = 0 [/tex]
[tex] 9.9y - 9.2 = 0 [/tex]
[tex] 9.9y - 9.2 + 9.2 = 0 + 9.2 [/tex]
[tex] 9.9y = 9.2 [/tex]
[tex] y = \frac{9.2}{9.9} [/tex]
[tex] y = 0.9 [/tex] (approximated)