Answer:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
Step-by-step explanation:
By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.
The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:
[tex]d=\sqrt{(x-(-4))^2+(y-(-2))^2[/tex]
Simplify:
[tex]d=\sqrt{(x+4)^2+(y+2)^2}[/tex]
Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:
[tex]d=|y-3|\text{ or } |3-y|[/tex]
The two equations are equivalent. Therefore:
[tex]\sqrt{(x+4)^2+(y+2)^2}=|y-3|[/tex]
Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:
[tex](x+4)^2+(y+2)^2 = (y-3)^2[/tex]
Expand:
[tex](x^2+8x+16)+(y^2+4y+4)=(y^2-6y+9)[/tex]
Isolate:
[tex]x^2+8x+11=-10y[/tex]
Divide both sides by -10. Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
A cube is intersected by a plane from the top edge of one face to the bottom edge of the opposite face as shown.
What is the shape of the cross-section?
square
rectangle that is not a square
triangle
parallelogram that is not a rectangle
Answer:
B
Step-by-step explanation:
a rectangle that is not a square
The plane will be rectangular which is not a square. Then the correct option is B.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
A cube is intersected by a plane from the top edge of one face to the bottom edge of the opposite face as shown.
Let a be the side length of the cube.
The length of the rectangular plane will be
L² = a² + a²
L = a√2
Then the dimension of the plane is 'a' and 'a√2' units.
The plane will be rectangular which is not a square. Then the correct option is B.
More about the rectangle link is given below.
https://brainly.com/question/10046743
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please help! ten points! thank you
At a pet store, Ms. Pike paid $34.75 for 5 dog bowls and 7 bones. Mr. Moore paid $20.50 for 3 dog bowls and 4 bones. Determine the cost of one dog bowl(x) and one bone(y).
Answer:
Step-by-step explanation:
t a pet store, Ms. Pike paid $34.75 for 5 dog bowls and 7 bones. Mr. Moore paid $20.50 for 3 dog bowls and 4 bones. Determine the cost of one dog bowl(x) and one bone(y).
which function is graphed?
Step-by-step explanation:
hello it's B)
v ::::: ok
.
.
.
.
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2. Which relations are functions? Explain. For each graph, state the domain and range.
Answer:
A. and C. neither of them have a repeating y value if you input a vertical line on the graph
if 1 cm = 10 km then how much is 8 km? And how much is 5 km? i will give brainly
Answer:
0.8 cm = 8km
0.5cm = 5km
hope this helps
Sometimes you can use the distributive property to expand an expression.
You can expand - 3(5 - x) into the equivalent expression -15 + 3x. Show
you can use the distributive property to expand -4(-a+2) to get an
equivalent expression.
how
Given:
After expanding [tex]-3(5-x)[/tex] we get an equivalent expression [tex]-15+3x[/tex].
The given expression is [tex]-4(-a+2)[/tex].
To find:
The equivalent expression by using distributive property.
Solution:
According to the distributive property of multiplication over addition, if a, b, c are real values, then
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]-4(-a+2)[/tex]
Using distributive property of multiplication over addition, we get
[tex]-4(-a+2)=(-4)(-a)+(-4)(2)[/tex]
[tex]-4(-a+2)=4a+(-8)[/tex]
[tex]-4(-a+2)=4a-8[/tex]
Therefore, the expression [tex]4a-8[/tex] is equivalence to [tex]-4(-a+2)[/tex].
No files just type it in please I been stuck in this answer
Answer:
24
Step-by-step explanation:
ate 4 pounds 6 times because monday, tuesday, wednesday, thursday, friday, saturday.
therefore 4x6= 24
How many families in Oats Township have two or more cars?
100
4
1
2
400
200
Answer:
200
Step-by-step explanation:
Good luck <3
Answer:
200
Step-by-step explanation:
hope it helps
The slope of line m is 3/8. Line n is perpendicular to line m. What is the slope of line n?
Answer:
- [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{8} }[/tex] = - [tex]\frac{8}{3}[/tex]
Pls help me with this i don’t really get it pls
Answer:
a y intercept (0,8)
Flat rate 8
b slope is 4
c 3.5 hours
Step-by-step explanation:
The y intercept is where it crosses the y axis, which is (0,8)
The flat rate is the y intercept which is 8
The rate per hour is the slope
m = ( y2-y1)/(x2 -x1)
Using 2 point ( 1,12) and ( 2,16)
= (16 -12)/(2-1)
= 4/1
= 4
The equation is
y = mx+b
y = 4x+8
Let y = 22
22 = 4x+8
Subtract 8 from each side
22-8 = 4x+8-8
14 = 4x
Divide by 4
14/4 = 4x/4
3.5 = x
3.5 hours
(0,8) is the y intercept because it crosses the y axis.
What is the flat rate?We can see that the flat rate is 8, which is the y intercept.
b) Find the slope and write an equation for the line.[tex] \quad\quad\quad\boxed{ \tt{m = \frac{rise}{run} = \frac{ y \tiny{2} \: \small{ - } \: y \tiny{1}}{x \tiny{2} \: \small{ - } \: x \tiny{1}} }}[/tex]
We will use the first 2 points in the graph which is (1,12) and (2,16).[tex]\quad\quad\quad\boxed{ \tt{m = \frac{16 - 12}{2 - 1} }}[/tex]
[tex]\quad\quad\quad\boxed{ \tt{m = \frac{4}{1} }}[/tex]
[tex] \quad\quad\quad\boxed{ \color{green}\tt{m = 4}}[/tex]
The equation is:[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]
c) Jack has $22 for how many hours can he rent an e-bike?Let's use the equation as formula:[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]
Let's y = 22, mx = 4 and b = 8.[tex] \quad \quad \quad \boxed{ \tt{22 =4x + 8}}[/tex]
Let's subtract 8 from each side.[tex] \quad \quad \quad \boxed{ \tt{22 - 8 = 4x + 8 - 8}}[/tex]
[tex] \quad \quad \quad \boxed{ \tt{14 = 4x \: \:\cancel{ \color{red}+ 8 - 8}}}[/tex]
Let's devide it by 4 to cancel out the number 4.[tex]\quad \quad \quad \boxed{ \tt{ \frac{14 = \cancel4x}{ \cancel{4} }}}[/tex]
[tex]\quad \quad \quad \boxed{ \color{green} \tt{3.5 = x}}[/tex]
Hence the answer for this is 3.5 hours or 3h50m. It is approximately 4 hours._________
#LetsStudy
#HikariSquad
What is the height of a rectangular prism with a volume of 60 cubic feet, a length of 3 ft and width 4 ft?
Answer:
5 feet
Step-by-step explanation:
I need to know what this is? Can someone tell me… Honestly. What is the value of x?
Answer:
98º
Step-by-step explanation:
The sum of angles in a triangle is 180
---------------------
The missing angle in the triangle
180 - 45 - 53 = 82º
-------------------------
x is supplementary to 82º
x = 180 - 82
x = 98º
pls help me this is due in 30 minnutes
Answer:
The surface area is 88ft.
Just to let you know just in case if you have the same question is that the formula of finding the surface area of a rectangular prism is A = 2(wl + hl + hw)
It takes Amir 30 minutes to walk to work. If he drives, it takes him 1/3 of that time. What is the latest time that Amir can leave to drive to work and arrive by 9:00 am
Which expression is equivalent to
Hey there!
(a^8)^4
= a^(8)(4)
8(4) = 32
= a^32
Answer: a^32
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The values a,b and c.
Answer:
a = 1, b = - [tex]\frac{1}{8}[/tex], c = 4
Step-by-step explanation:
Given
x - [tex]\frac{1}{8}[/tex] y + 4 ← in the form ax + by + c
with a = 1, b = - [tex]\frac{1}{8}[/tex], c = 4
9. Leonard made a deposit of $4,500 into a
savings account which earns 7% annual
compound interest. Assuming he makes no other
deposits or withdrawals, which of the following
shows the amount of interest his account should
earn after 15 years?
A. $12,415.64
B. $7, 915.64
C. $16,915.64
D. $8,115.64
(please help, it’s urgent) :)
Answer:
id say a
Step-by-step explanation:
The amount of interest his account should earn after 15 years is:
$7, 915.64.
Here, we have,
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here, given that, P =$4,500 , r= 7%, t=15yr , n=365days
Let, A= x
Now, x =$4,500(1+7/100×365)^(365×15)
x=$12415.64
i.e. final amount = $12415.64
so, the amount of interest his account should earn after 15 years is:
$12415.64 - 4500 = $7, 915.64
Hence, the amount of interest his account should earn after 15 years is: $7, 915.64
To learn more on Compound interest click:
brainly.com/question/29335425
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23, 24, 25, 20, 25, 29, 24, 25, 30
Mean?
Median?
Mode?
Range?
Please help?
Answer:
median = 25. that's the answer
Answer:
Mean - 25
median - 25
range - 10
mode - 25
Find the length of AB.
A
O 140°
8 m
B
Round your answer to the nearest hundredth.
ÁB = [ ? ]m
:)
Answer:
19.55m
Step-by-step explanation:
We solve the above question using the formula for Arc Length
The formula of Arc length when central angle is given in degrees = Length of AB
= θ/360 × 2πr
Central angle = θ = 140°
Radius = r = 8m
Hence,
Length AB = 140/360 × 2 × π × 8
= 19.547687622 m
Approximately to the nearest hundredth, the length of AB = 19.55m
Helppp meee please!!
Vertical stretch
Hope this helps! :)
George has a spinner with three equal sections colored orange, blue, and white. He spins the spinner 100 times. What is the experimental probability of landing on the orange section?
Answer:
1/3
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
Experimental probability is based on the result of an experiment that has been carried out multiples times
probability of landing on the orange section = proportion of the orange section / total proportions of all the colours
= 1/3
PLEASE PLEASE HELP ME! thank you so so much
explaining your answer = brainliest/five stars
The radius of a circle is 4 kilometers. What is the area of a sector bounded by a 135° arc?
give the exact answer in simplest form
Answer:
6π
Step-by-step explanation:
(135/360)×π×4²
(135/360)×π×16
=6π
Help me please !!!!!!!!!!!
Answer:
option 1
Step-by-step explanation:
[tex]Area = \frac{3}{4} \times \frac{5}{6} = \frac{15}{24}[/tex]
URGENT PLEASE HELP ME !!!!
Answer:
CO
Step-by-step explanation:
Conditional: If p, then q.
Converse: If q, then p.
Conditional: If the measure of an angle is 90 degrees, then it is a right angle.
If p, then q.
p = the measure of an angle is 90 degrees
q = it is a right angle
Converse:
If q, then p.
If it is a right angle, then the measure of the angle is 90 degrees.
Answer: CO
what is the correct answer
Answer:
D. 2√2
Step-by-step explanation:
In a 45° 45° 90° triangle, the hypotenuse is the leg length multiplied by √2. So divide by √2 to find x.
x = 4/√2 = 2√2
Suzie bought 17.75 lbs of flour. If the price for 1lb is $19.68, calculate the total amount she paid to the shopkeeper
Two containers, A and B begin with equal volumes of liquid.
120 ml is then poured from A to B.
А
B
Container B now contains 4 times as much liquid as A.
Find the volume of liquid left in container A at the end.
A
A
B.
B
Volume left in container A=
20
ml
Answer:
volume left in A is 80ml
Step-by-step explanation:
let original volume in both be x ml
after pouring from A to B
vol in A = x - 120
vol in B = x + 120
now it is given that
vol in B = 4 times vol in A
implies
[tex]x + 120 = 4 \times (x - 120) \\ x + 120 = 4x - 480 \\ 3x = 600 \\ x = 200[/tex]
hence original volume in A is 200ml. after pouring in B it is 200-120 = 80 ml
The bakery manager at the grocery store decides to have a 18% off sale on all bread. You decide to purchase 3 loaves of bread. Let b be the original price of a loaf of bread. Expand the expression 3(b − 0.18b). What do the terms of the expansion represent?
simplify :
26-10/2x5+3
Answer:
16/13 is the answer.
26-10 is 16 and 2x5+3 is 13
Answer:
4
Step-by-step explanation:
26 - 25 + 3
