Answer:
$148.4
Step-by-step explanation:
140 times 0.03=4.2
4.2=8.4
140+8.4=148.4
Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y= -1
Stumped :/
Given statement solution is :- The equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.
To derive the equation of a parabola with a focus and directrix, we can use the definition of a parabola.
Let's assume the vertex of the parabola is (h, k), and the distance between the focus and the vertex is denoted as "p." The directrix of the parabola is a horizontal line given by the equation y = k - p.
In this case, the focus is at (-5, 5), so the vertex is at (h, k) = (-5, 5). The directrix is given by y = -1.
Using the definition of a parabola, we can find the distance between the focus and vertex as the same distance between the vertex and the directrix. So, we have:
k - p = -1 (Equation 1)
Since the vertex is (-5, 5), we substitute these values into Equation 1:
5 - p = -1
Solving for p:
p = 5 - (-1)
p = 6
Now we have the value of p, which is the distance between the focus and the vertex.
The equation of a parabola with a vertical axis of symmetry is given by (x - h)^2 = 4p(y - k).
Substituting the values of h, k, and p, we get:
(x + 5)^2 = 4(6)(y - 5)
Simplifying further:
(x + 5)^2 = 24(y - 5)
This is the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.
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Help me solve for the maximum occurring point
Answer:
xy+y7
Step-by-step explanation:
A statistician is looking at 2 data sets. Data Set A has a mean of 7 5 points
and a standard deviation of 2.3. Data Set B has a mean of 7 and a
standard deviation of 5.1. Which of the following statements is
true?
A. Since two means are equal, the two data sets are identical.
B. The data values in Data Set A are more spread out than the data values in Data Set B.
C. The data values in Data Ser B are more spread out than the data values in Data Set A.
D. Statements a and ax are both correct.
A factory ships 225 boxes to fill an order. The total price of the parts un each box is $3990. What is the total value of the shipment?
Answer:
$897750
Step-by-step explanation:
3990 x 225 = 897750, so the total price of the shipment is: 897750
primitive of (x+1)e^x
[tex]\int{(x+1)e^x} dx[/tex]
Integrate by parts: [tex]\int{fg'} = fg - \int{f'g}[/tex], where [tex]f = x+1[/tex], [tex]g' = e^x[/tex], [tex]f' = 1[/tex] and [tex]g = e^x[/tex]
[tex]\int{(x + 1)e^x} dx = (x+1)e^x - \int{e^x} dx\\= (x + 1)e^x - e^x + C = xe^x + C[/tex]
marta has a lower probability of winning than Elena has. Which could be the outcome that marta needs to win the game? select three options.
Answer:pic
Step-by-step explanation:
Un agricultor a adus la piață 18 saci cu câte 42 de kg de cartofi și 28 de saci cu câte 36 kg de vinete Ce cantitate de legume a adus țăranul la piata
Answer:
the number of vegetables did farmer bring to the market is 1764 vegetables
Step-by-step explanation:
The calculation of the number of vegetables did farmer bring to the market is given below:
= 18 bags × 42 kgs + 28 bags × 36 kgs
= 756 + 1008
= 1764 vegetables
Thus, the number of vegetables did farmer bring to the market is 1764 vegetables
Annie and Maria traveled overseas for days and stayed in three different hotels in three different cities: Stockholm, Sweden; Oslo, Norway; and Paris, France. The total bill for all nights (not including tax) was . The total tax was . The nightly cost (excluding tax) to stay at the hotel in Paris was more than the nightly cost (excluding tax) to stay in Oslo. Find the cost per night for each hotel excluding tax.
Answer:
The answer is below
Step-by-step explanation:
Annie and Maria traveled overseas for 7 days and stayed in three different hotels in three different cities: Stockholm, Sweden; Oslo, Norway; and Paris, France.
The total bill for all seven nights (not including tax) was $1040. The total tax was $106. The nightly cost (excluding tax) to stay at the hotel in Paris was $80 more than the nightly cost (excluding tax) to stay in Oslo. Find the cost per night for each hotel excluding tax.
Solution:
Let x represent the cost per night to stay in Paris (France), let y represent the cost per night to stay in Stockholm (Sweden) and let z represent the cost per night to stay in Oslo (Norway).
They spent 1 night in Paris, 4 nights on Stockholm and 2 nights in Oslo, hence:
x + 4y + 2z = $1040 (1)
They were taxed 8% in Paris, 11% in Stockholm and 10% in Oslo, hence:
(8% of x) + (11% of 4y) + (10% of 2z) = $106
0.08x + 0.44y + 0.2z = 106 (2)
Also, The nightly cost (excluding tax) to stay at the hotel in Paris was $80 more than the nightly cost (excluding tax) to stay in Oslo. Hence:
x = z + 80
x - z = 80 (3)
Solving equations 1, 2 and 3 simultaneously gives:
x = $200, y = $150 and z = $120
Therefore they spent $200 per night in Paris, $150 per night in Stockholm and $120 per night in Oslo.
Let u = ⟨–2, –3⟩ and v = ⟨3, –1⟩. Which graph shows u – v?
A) The first graph
It is indeed correct on Edge
The graph shows (u - v) for the given vectors u and v will be the one with vectors at (-5, -2).
What is vector ?A vector is an object that has both a magnitude and a direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
We have,
u = (-2, -3) and v = (3, -1)
So,
To subtract two vectors, subtract the corresponding components.
i.e. The difference of u and v vector = ( u₁ - v₁, u₂ - v₂)
i.e.
u = (-2, -3) and v = (3, -1)
i.e.
u₁ = -2,
u₂ = -3,
v₁ = 3,
v₂ = -1
Now,
(u - v) = ( u₁ - v₁, u₂ - v₂)
i.e.
(u - v) = [( -2 - 3 ), ( -3 - (-1) )]
On solving,
We get,
(u - v) = (-5, -2)
Hence, we can say that the graph shows (u - v) for the given vectors u and v will be the one with vectors at (-5, -2).
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In the diagram below, the red angle $(\angle YAK)$ and the blue angle $(\angle OAT)$ are both right angles. If $\angle YAO=23^\circ,$ then what is the measure of $\angle KAT$?
Answer:a
Step-by-step explanation:
Answer:
Hey kroy21; the answer is 23°.
Step-by-step explanation:
Angle YAO and angle KAT are both complementary to angle OAK.
Angle OAK= 90°- Angle YAO
= 90° - 23°
= 67°
Then:
Angle KAT= 90° - Angle OAK
=90° - 67°
=23°
Hope this helps!!!
:o)
plz help asap!!!
Imagine you are hanging two identical picture frames. Each frame is 28 inches wide and the wall you are hanging them on is 10 feet wide. There needs to be 8 inches of space in between the two frames. How far do the frames need to be from the left and right side of the walls in order to be centered?
Answer:
27 inches from each side to be centered
Step-by-step explanation:
PLEASE ANSWER THIS ALSO!!!
Answer:
Options (A), (C) and (E)
Step-by-step explanation:
Given equation is,
-3x + 7 = -5 + x
-3x + 7 - 7 = -5 + x - 7
-3x = -5 + x - 7 Option (C)
-3x = x - 12
-3x - x = -12
-4x = -12 Option (A)
4x = 12 Option (E)
[tex]\frac{4x}{4}=\frac{12}{4}[/tex]
x = 3
Therefore, Options (A), (C) and (E) are the correct options.
how do the graphs of f(x)= x and g(x)= 3|x| relate
a.
The graph of g(x) is the graph of f(x) stretched vertically.
c.
The graph of g(x) is the graph of f(x) shrunk vertically.
b.
The graph of g(x) is the graph of f(x) shifted down 3.
d.
The graph of g(x) is the graph of f(x) shifted up 3.
Please select the best answer from the choices provided
A
B
C
D
Answer: a.) The graph of g(x) is the graph of f(x) stretched vertically.
Step-by-step explanation: hope that helps! < 3
Find the length of side x in simplest radical form with a rational a
denominator.
Step-by-step explanation:
[tex] \cos(30) = \frac{x}{4} \\ x = 2 \sqrt{3} [/tex]
3x(x + 6) = -10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using the ± symbol. DESCRIBE AND JUSTIFY THE METHODS YOU USED TO SOLVE THE QUADRATIC EQUATION!
Answer:
Step-by-step explanation:
Expand it: [tex]3x^2 + 18x = -10[/tex]
Add 10 to both sides: [tex]3x^2 + 18x + 10 = 0[/tex]
Divide both sides by 3: [tex]x^2 + 6x + \frac{10}{3} = 0[/tex]
Find a, b for [tex](x + a)^2 + b = x^2 + 2x + a^2 + b \overset{!}{=} x^2 + 6x + \frac{10}{3}[/tex]
It’s [tex]a = \frac{6}{2} = 3 \land b = \frac{10}{3} - a^2 = 3 + \frac{1}{3} - 9 = -6 + \frac{1}{3}[/tex]
So, inserting it leads to: [tex](x+3)^2 -6 + \frac{1}{3} = 0[/tex]
Subtract b from both sides: [tex](x+3)^2 = 6-\frac{1}{3}[/tex]
Apply square root to both sides and consider the two solutions: [tex]x + 3 = \pm\sqrt{6-\frac{1}{3}}[/tex]
Subtract 3 from both sides and you get [tex]x = -3 \pm \sqrt{6 - \frac{1}{3}}[/tex]
Answer:
I think it's x = - 9 - √51/3 , -9 + √51/3
Which graph is a function of x?
Answer:
Step-by-step explanation:
No picture. But a function must satisfy the vertical line test. Which means that each value of x has only one value for y. If a graph shows two values for y for a single value of x it is not a function.
A friend who works in a big city owns two cars, one small and one large. Three-quarters of the time he drives the small car to work, and one-quarter of the time he takes the large car. If he takes the small car, he usually has little trouble parking and so is at work on time with probability 0.8. If he takes the large car, he is on time to work with probability 0.6. Given that he was at work on time on a particular morning, what is the probability that he drove the small car
Answer:
0.8 = 80% probability that he drove the small car
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Being at work on time.
Event B: Driving the small car.
Probability of being at work on time:
0.8 of 0.75(small car).
0.6 of 0.25(large car). So
[tex]P(A) = 0.8*0.75 + 0.6*0.25 = 0.75[/tex]
At work on time, using the small car:
0.8 of 0.75
So
[tex]P(A \cap B) = 0.8*0.75 = 0.6[/tex]
What is the probability that he drove the small car
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.6}{0.75} = 0.8[/tex]
0.8 = 80% probability that he drove the small car
Express the radical using the imaginary unit I. Express your answer in simplified form
-22
Given:
The radical expression is
[tex]\pm \sqrt{-22}[/tex]
To find:
The simplified form of the given expression by using the imaginary unit i.
Solution:
We have,
[tex]\pm \sqrt{-22}[/tex]
It can be written as
[tex]\pm \sqrt{-22}=\pm \sqrt{22}\sqrt{-1}[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]
[tex]\pm \sqrt{-22}=\pm \sqrt{22}i[/tex] [tex][\because \sqrt{-1}=i][/tex]
Therefore, [tex]\pm \sqrt{-22}=\pm \sqrt{22}i[/tex].
PLEASE HELP ON TIMMER!!!
Example 4
You want to reduce the size of a picture to place in a
small frame. You aren't sure what size to choose on
the photocopier, so you decide to reduce the picture
by 15% each time you scan it until you get it to the
size you want. If the picture was 10 inches long at the
start, how long is it after 3 scans?
; A=
;=
Equation Used:
y=
Answer: ooop
Step-by-step explanation:
sorry I cat help you I don't know this
Answer the question below.
Answer: H
Step-by-step explanation:
Point C line CB line segment CA and ray CD
Classify the equation as having one solution, infinitely many solutions or no
solution. *
9r + 5 – 4 = 4r + 5r – 12
Choose
Answer:
No solutions
Step-by-step explanation:
Simplify both sides of the equation as much as possible:
9r + 5 - 4 = 4r + 5r - 12
9r + 1 = 9r - 12
Both sides have "9r" which when cancel out, leave the equation as:
+1 = -12
This means there are no solutions.
What is the volume of the following rectangular prism?
3/20 units^2
2/3 units
Answer:1/10^3
Step-by-step explanation:
3/20×2/3=1/10^3
Area of the base×height
Hope it helps❤
Step-by-step explanation:
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
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\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7
\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1).
User avatar
MM
Posts: 82
Joined: Tue Jul 22, 2008 7:36 am
Location: Bulgaria
Reputation: 7
\-x+sqrt1−x
2
\-=sqrt2(2
Donovan is training for a marathon. He currently can run 1 lap around the track in 0.85 minutes. How long will it take him to run 12.5 laps?
ASAP
Answer:
10.625
Step-by-step explanation:
Answer:
10 minutes and 37.5 seconds
Step-by-step explanation:
0.85 is 51 seconds. I will be using this because it is easier for me.
Multiply 51 • 12 = 612 seconds for 12 laps. Divide 612 ÷ 60 = 10.2. You get 10.2 minutes. This is 10 minutes and 12 seconds for 12 laps.
Divide 51 by 2 to find how long it takes for 1/2 a lap. You will get 25.5 seconds for half a lap.
Add them together: 10 min 12 sec + 25.5 sec = 10 minutes and 37.5 seconds
For a baseball game, organizers estimate that 15,000 people will attend if it is not raining. If it is raining, organizers estimate that 9,000 people will attend. On the day of the game, meteorologists predict a 60% chance of rain. Determine the expected number of people who will attend this game.
Answer:
9,000
Step-by-step explanation:
This question seems to be somewhat incomplete, but 60% is above 50 and we round if its above 5, which essentially gives the answer.
identify ROTATIONS
WHICH COLOR
SHOWS THE
ORANGE SHAPE
ROTATED 270°
COUNTER-
CLOCKWISE?
?
Answer:
blue
Step-by-step explanation:
270° moves by 3 quadrants
Answer:
Blue
Step-by-step explanation:
Rotate 1/2 circle (180°) counterclockwise and you go through the yellow to the green.
Go another 1/4 circle (90°) and you get to the blue.
180° + 90° = 270°
1. List all the possible rational solutions for each equation.
a. 4x4 + 13x3 - 124 x2 + 212x - 8 = 0
Answer:
x=−7.974656,0.038604
Step-by-step explanation:
4x4+13x3−124x2+212x−8=0
Brainleist please
The possible rational solutions for the given equation are x= −7.974656 and 0.038604.
What is an equation?
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is [tex]4x^4+13x^3-124x^2+212x-8=0[/tex].
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Substitute x= ±1, ±1/2, ±1/4, ±2, ±4, ±8 in the given equation and verify
When x=1,
[tex]4(1)^4+13(1)^3-124(1)^2+212(1)-8=0[/tex]
⇒ 4+13-124+212-8=0
⇒ LHS ≠RHS
When x= -1
[tex]4(-1)^4+13(-1)^3-124(-1)^2+212(-1)-8=0[/tex]
⇒ 4-13-124-212-8=0
⇒ LHS ≠RHS
When x=1/2
[tex]4(\frac{1}{2} )^4+13(\frac{1}{2} )^3-124(\frac{1}{2} )^2+212(\frac{1}{2} )-8=0[/tex]
⇒ 1/4 +13/8 -31+106-8=0
⇒ LHS ≠RHS
When x=-1/2
[tex]4(-\frac{1}{2} )^4+13(-\frac{1}{2} )^3-124(-\frac{1}{2} )^2+212(-\frac{1}{2} )-8=0[/tex]
⇒ 1/4 -13/8 -31-106-8=0
⇒ LHS ≠RHS
Similarly Find every combination of ±p/q, where p is a factor of the constant and q is a factor of the leading coefficient.
Here, x= −7.974656 and 0.038604
Therefore, the possible rational solutions for the given equation are x= −7.974656 and 0.038604.
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the product of Diego's height and 3is 57
use the variable d to represent Diego's height
Answer:
Step-by-step explanation:
Let diago's height be d
d into 3=57
3d=57
d=57/3
d=19
diago's height=19 units
14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34) What is the summation notation for the arithmetic series? Enter the correct values for x, y, and z.
x =
y =
z =
Answer:
total -70
Step-by-step explanation:
x =18
y=-28
Z = -60
An Arithmetic series: 14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)
The Total value is = -70
x = 18
y = -28
Z = -60
Calculation of Arithmetic SeriesAn Arithmetic series: 14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)
1st an 2nd element difference is = 14 - 6 = 8
2nd and 3rd element difference is = - 6 - 2 = -8
3rd and 4th element difference is = - 2 + 10 = 8
4th and 5th element difference is = -10 + 18 = 8
The difference (x,y and z) is 8 and also it's negative because the series is lowering the previous value.
Now, Proof of x,y and z = - 8
14 - 8 = 6
6 - 8 = - 2
- 2 - 8 = - 10
- 10 - 8 = - 18
- 18 - 8 = - 26
-26 - 8 = -34
Therefore, The value is = total -70
x = 18
y = -28
Z = -60
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Nadya has 36 blueberries and 45 raspberries that she will be putting into cups of yogurt to make after-school snacks. She wants to put an equal number of blueberries and an equal number of raspberries into each cup. She uses all the berries. How many cups does she make {Use G.C.F.}
Answer:
Number of blueberries = 36
Number of raspberries = 45
You need to find the Number in Each.
HCF Of 36 and 45 =is 9
This answer is
36/9
please help me ASAP!!!
Answer:
18
Step-by-step explanation:
parallel lines cut by a transversal are proportional, thus we can set up a ratio to solve for the missing value
7/14 = 9/x
7x = 126
x = 18