Answer:
x = 1/8(y^2 + 14y + 73)
Step-by-step explanation:
Take any point on the curve (x, y). This is a parabola that opens to the right and contains terms in x and y^2.
The distance of this point from the focus = its distance from the directrix, so:
sqrt [( x - 5)^2 + (y + 7)^2) = (x - 1)
Squaring both sides:
(x - 5)^2 + (y + 7)^2 = (x - 1)^2
x^2 -10x + 25 + y^2 + 14y + 49 = x^2 - 2x + 1
y^2 + 14y + 73 = 8x
x = 1/8(y^2 + 14y + 73)
Janelle spots some dolphins in the ocean. Her father draws a diagram to show how far down they can go. How far is this relative to sea level? What would an altimeter read at this depth? not college middle school sorry
Answer:
The relative is 1,000 below sea level. The altimeter should read -1,000.
Step-by-step explanation:
I really don't have a explanation, but I did that activity and this was the correct answer.
Lisa spends the same amount of time doing homework each day on Monday she spents of half of her time studying for a history test. on Tuesday, she spent 3/5 of her time studying for the same test in
the two days she spenta bal of 3 hours and 29 minutes studying for the test How much time does
she spend ting homework each day
Flying fish do not actually fly, but glide. Suppose that a fish traveled a distance of 1400 feet at a rate of miles 15 per hour. How many seconds would it take to travel this distance? (Hint: First convert miles per hour to feet per second. Recall that 1 mile = 5280 feet.)
Answer:
63.63 seconds, or round up if you need to?
Step-by-step explanation:
write the polynomial on descending order
[tex]2 {x}^{5 } + 14 - 3 {x}^{4 } \times 7x + 3x ^{3} [/tex]
Answer:
jkjjjjjjujhhhgvvvvvgvhjjhhhgvvg
A race car went 500 miles in 4 hours. What was the average rate of speed? Explain how you got your answer.
Answer:
125 miles per hour.
Step-by-step explanation:
I divided 500 by 4
can someone explain step by step how to do this please. I'm lost :(
(ab)^-6 (b^2 c)^-8 / a^-8 bc^-3
Answer:
a^2/b^23c^5Step-by-step explanation:
(ab)^-6 (b^2 c)^-8 / a^-8 b c^-3 =a^-6 b^-6 b^-16 c^-8 a^8 b^-1 c^3 =a^(-6 + 8) b^(-6 - 16 - 1) c^(-8 + 3) =a^2 b^-23 c^-5 =a^2/b^23 c^5Consider the numbers z = 3√2(cos(135°) + i sin(135o) and w = cos(180o) + i sin(180°).
Which expression is closest to the polar form of z + w?
Answer: A
5(cos(143o) + i sin(143o))
Step-by-step explanation:
The expression that is closest to the polar form of z + w is
[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]
What is complex number?"The number of the form a + ib where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"
What is polar form of the complex number?"The polar form of the complex number z = x + iy is [tex]z=r(cos(\theta)+i~sin(\theta))[/tex] where [tex]r=\sqrt{x^{2} +y^{2} } , ~\theta=tan^{-1}(\frac{y}{x} )[/tex] "
For given question,
We have been given two complex numbers.
[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})[/tex] and [tex]w = cos(180^{\circ}) + i~sin(180^{\circ})[/tex]
We know that,
[tex]cos(135^{\circ})\\=cos(90^{\circ}+45^{\circ})\\=-sin(45^{\circ})\\=-\frac{1}{\sqrt{2} }[/tex]
And
[tex]sin(135^{\circ})\\=sin(90^{\circ}+45^{\circ})\\=cos(45^{\circ})\\=\frac{1}{\sqrt{2} }[/tex]
So, the first complex number would be,
[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})\\\\z = 3\sqrt{2} (-\frac{1}{\sqrt{2} } + i~\frac{1}{\sqrt{2} } )\\\\z=-3+3i[/tex]
We know that [tex]cos(180^{\circ})=-1,~~sin(180^{\circ})=0[/tex]
So the second complex number would be,
[tex]w = cos(180^{\circ}) + i~sin(180^{\circ})\\\\w = -1 + 0i[/tex]
So, the sum of complex numbers z and w would be,
[tex]z+w\\=(-3+3i)+(-1+0i)\\=-4+3i[/tex]
We write the complex number -4 + 3i in the polar form.
Comparing above number with x + iy, we have x = -4 and y = 3
[tex]\Rightarrow r=\sqrt{(-4)^2+3^2}\\ \Rightarrow r=5[/tex]
Also, the value of [tex]\theta[/tex] would be,
[tex]\theta=tan^{-1}(\frac{3}{-4} )\\\\\theta= -36.86^{\circ}\\\\\theta=180^{\circ}-36.86^{\circ}\\\\\theta=143.14^{\circ}[/tex]
So the complex number -4 + 3i in the polar form would be, [tex]5(cos(143.14^{\circ})+i~sin(143.14^{\circ}))[/tex]
Therefore, the expression that is closest to the polar form of z + w is
[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]
Learn more about polar form of complex number here:
https://brainly.com/question/917768
#SPJ3
What is the distance between these set of points?
(1,-2), and (4,2)
sorry i cant add the photo of the graph but whoever the first one is to get it right will get brainliest
Answer:
go to khan academy on you tube he's really good at explaining stuff also sorry that's all i got...
Step-by-step e
PLS ITS LATE WORK NO DUMB ANSWERS
Answer:
day 2
Step-by-step explanation:
day 1 had a 26.19-degree change while day 2 had a 33.47
Answer:
Day 2 is a bigger change.
Step-by-step explanation:
Day 1 change: 26.19
Day 2 change: 33.47
Add the positive version of each number together to find the change, like so:
Day 1: -12.75 to 12.75 and 13.44 to 13.44 12.75+13.44= 26.19
Day 2: -8.83 to 8.83 and 24.64 to 24.64 8.83 + 24.64=33.47
PS: Next time, please be a little nicer with your question.
Which quantity is proportional to 8⁄12?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
GCF of 8 and 12: 48 ÷ 4 = 212 ÷ 4 = 3Put them together: [tex]\frac{2}{3}[/tex]I hope this helps!
Answer:
2/3 , 24/36
Step-by-step explanation:
got it wrong and found out the answers
If m PQS=16, M SQR=(9x+17),and m PQR=(12x-6) find m PQR
Please answer with work
Answer:
[tex]\angle PQR=30^{\circ}[/tex]
Step-by-step explanation:
It is given that,
[tex]\angle PQS=16^{\circ}\\\\\angle SQR=(9x+17)^{\circ}\\\\\angle PQR=(12x-6)^{\circ}[/tex]
We need to find the measure of [tex]\angle PQR[/tex].
From the given figure, [tex]\angle PQR=\angle PQS+\angle SQR[/tex]
Putting all the values, we get :
[tex]12x-6=16+9x+17\\\\12x-9x=16+17+6\\\\3x=39\\\\x=13[/tex]
[tex]\angle PQR=12x-6\\\\=12(3)-6\\\\=30^{\circ}[/tex]
So, the measure of [tex]\angle PQR[/tex] is 30 degrees.
Calculate the unit rate (price per box) $12 for 5 boxes
A children's birthday party at an indoor play center costs $50 to rent the space and $6.25 per child. Gina wants to spend no more than $100 on her son's fourth birthday party. Write an inequality for the number of children who can attend the birthday party, and solve the inequality.
A) 50 + 6.25x 100; x>8
B) 50 + 6.25x 100; x 8
D) 50 + 6.25x 100; x<8
Answer:
D
Step-by-step explanation:
100>50 +6.25x, subtract 50 from both sides
50>6.25x, divide both sides by 6.25
8>x or x<8
Answer:
c
Step-by-step explanation:
What is the slope of the line going through (9,5) and (2,-6).
A local road has a grade of 2%. The grade of a road is its slope expressed as a percent. Find the slope of the road as a fraction and then simplify.
Answer:
[tex]\frac{1}{50}[/tex]
Step-by-step explanation:
2% = [tex]\frac{2}{100}[/tex] = [tex]\frac{1}{50}[/tex]
The slope of the road expressed as fraction is 2/100. When we simplify 2/100, the result obtained is 1/50
How to determine the slope in fractionFrom the question given above, we were told that the grade of the road is 2% which is equal to the slope. Thus, we can express 2% as fraction as illustrated below:
2% = 2/100
How to simplify 2/1002/100 can be simplified to it's lowest term as shown below:
2/100
Divide the numerator and denominator by 2
1/50
Thus,
2/100 = 1/50
Learn more about simplification of fractions:
https://brainly.com/question/16414484
#SPJ9
you guys actually pls help me with this its hard for me
Find the value of x in the triangle shown below.
Answer:
x = 62
Step-by-step explanation:
its an isosceles triangle which means the the two angles on the bottom are equal or something like that. triangles aren't fun
A fencing company charges $22 per foot to install a wood fence.How much will it cost to install a wood fence around a rectangular pool area that is 20 feet wide and 38 feet long?
9514 1404 393
Answer:
$2552
Step-by-step explanation:
The perimeter of the pool area is given by the formula ...
P = 2(L+W)
P = 2(38 +20) = 116 . . . feet
Then the cost of the fence installation is ...
(116 ft)($22/ft) = $2552
Please answer correctly!
Graphing the equation y-3=1/3(x+4)
Thank you.
Answer:
X intercept (-13,0)
y intercept (0,13/3)
Step-by-step explanation:
slope intercept form
y=1/3x+13/3
Sara poured 3/4 of the juice from a 2-liter bottle while serving guests at a party.
How much juice, in liters, is still left in the bottle?
What is the unit rate if the candy is $7.80 for 2 pounds?
Answer:
= 3.9 candy per pound
Step-by-step explanation:
This is a fraction equal to
7.8 candy ÷ 2 pounds
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2
7.8 candy ÷ 2
________
2 pounds ÷ 2
=
3.9 candy
_______
1 pound
=
3.9 candy
_______
pound
= 3.9 candy per pound
need someone’s help with this please!!!
I cant find the answer.
Answer:
The numerator is 3, so the whole thing would say 3/11=12/44
Step-by-step explanation:
divide the second fraction down as much as possible, and you will get 3/11.
12 divided by 4 equals 3
44 divided by 4 equals 11
so 3 is the numerator and 11 is the denominator
Answer:
3
Step-by-step explanation:
lets make teh blank x
x/11 = 12/44
x/11 = 3/11
x = 3
or
x/11 = 12/44
4x/11 = 12/44
4x = 12
x = 3
help lol due tonight
Answer:
Can't see your questions clearly
Step-by-step explanation:
I don't know how to solve this.Please help!
3^x=2
What is the decimal expansion for 14 over 33?
Hi! I believe your answer is 0.42, (simplified form of 0.42424242424) which is 14/33 (or [tex]\frac{14}{33}[/tex] ) as a decimal. I hope this helps you! Good luck and have a great day. ❤️✨
To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds?
help plz
Answer:
480 milligrams.
Step-by-step explanation:
Divide 320 by 92, you get 3.47826087, multiply that by 138 to get your answer (480).
Given m∥n, find the value of x and y.
will give brainiest
Answer:
The value of x and y are x = 15 and y = 63
Step-by-step explanation:
If two adjacent angle formed a straight line, then the two angles formed a pair of linear anglesThe sum of the measures of the linear angles is 180°From the given figure
∵ The angles of measures (9x - 7)° and (4x - 8)° are adjacent angles
∵ The angles of measures (9x - 7)° and (4x - 8)° formed a line
∴ They formed a pair of linear angles
∵ The sum of the measures of the linear angles is 180°
→ That means add them and equate the sum by 180
∴ (9x - 7) + (4x - 8) = 180
→ Add the like terms
∵ (9x + 4x) + (-7 + -8) = 180
∴ 13x + (-15) = 180
→ Remember (+)(-) = (-)
∴ 13x - 15 = 180
→ Add 15 to both sides
∴ 13x - 15 + 15 = 180 + 15
∴ 13x = 195
→ Divide both sides by 13
∵ [tex]\frac{13x}{13}[/tex] = [tex]\frac{195}{13}[/tex]
∴ x = 15
∵ Lines m and n are parallels
∵ A line intersected them
∵ The angles of measures (2y + 2), (9x - 7) are interior alternate angles
∵ The interior alternate angles are equal in measures
∴ 2y + 2 = 9x - 7
∵ x = 15
→ Substitute the value of x
∴ 2y + 2 = 9(15) - 7
∴ 2y + 2 = 135 - 7
∴ 2y + 2 = 128
→ Subtract 2 from both sides
∴ 2y + 2 - 2 = 128 - 2
∴ 2y = 126
→ Divide both sides by 2
∴ [tex]\frac{2y}{2}[/tex] = [tex]\frac{126}{2}[/tex]
∴ y = 63
The values of x and y are 15 and 63, respectively
The angles in the figure are: (9x - 7)° and (4x - 8)°
These angles are adjacent angles.
So, we have:
[tex]\mathbf{9x - 7 + 4x - 8 = 180}[/tex]
Collect like terms
[tex]\mathbf{9x + 4x = 180 + 8 + 7}[/tex]
[tex]\mathbf{13x = 195}[/tex]
Divide both sides by 13
[tex]\mathbf{x = \frac{195}{13}}[/tex]
[tex]\mathbf{x = 15}[/tex]
Also, we have:
[tex]\mathbf{2y + 2 = 9x - 7}[/tex] -- interior angles
Subtract 2 from both sides
[tex]\mathbf{2y = 9x - 9}[/tex]
Substitute 15 for x
[tex]\mathbf{2y = 9\times 15 - 9}[/tex]
[tex]\mathbf{2y = 126}[/tex]
Divide both sides by 2
[tex]\mathbf{y = 63}[/tex]
Hence, the values of x and y are 15 and 63, respectively
Read more about angles in parallel lines at:
https://brainly.com/question/2279752
Fractions-3 3/7- 1 2/7=
Answer:
-4.714
Step-by-step explanation:
Answer:
1 (if the 3 3/7 is positive)
or
-4 5/7 (if the 3 3/7 negative)
PLS HELP, i am literally crying over this, Guaranteed brainliest if you get it right
If 14x + 6 / 3 = -8 + 4x, what is the value of -3x^2 - 7? TYSM
Answer:
2
Step-by-step explanation:
14x+6/3=-8+4x
Using order of operations, this is how I would solve it
14x+6/3=-8+4x
14x+2=-8+4x
add 8 on both sides while subtracting 4x
10x+10=0
10x=-10
x=-1
Now, square -3 which is positive 9. 9-7 is 2. Hope I didn't make any mistakes because I'm a 6th grader btw. Hope it helps.
