Answer:
Step-by-step explanation:
If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:
[tex](x-h)^2=4p(y-k)[/tex]
p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:
[tex](x-4)^2=4(6)(y-0)[/tex] and simplify to
[tex](x-4)^2=24y[/tex] which is the first choice you're given.
The equation that shows the parabola when parabola has the focus at (4, 6) and the directrix y = –6 should be considered as the (x – 4)2 = 24y.
What is a parabola?In terms of mathematics, a parabola represent the plane curve in which there is the mirror-symmetrical and should be made of U-shaped.
Since there has the focus at (4, 6) and the directrix y = –6
So the first equation should be considered.
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what is the solution to 2/3(9x-6)=4(x+2)+2
Answer:
7
Step-by-step explanation:
please help me i will give brianliest
Answer:
8 is the right answer
Step-by-step explanation:
in triangle swu,, wT bisect and perpendicular on su
so the triangle is isosceles triangle
therfore,Sw =, 8
Solve the system of equations by substitution.
x+y=32
y=7x
Answer:
x=4
Step-by-step explanation:
since y=7x
x+7x=32
8x=32
x=4
Answer:
x=4
Step-by-step explanation:
x+y=32
y=7x
Since Y can be replaced by 7x, substitute into eq1.
x+y( notice y can be replaced by 7x) =32
x+7x=32 ( Y got replaced
8x=32
Divide 8 on both sides.
x=4
Hope this helps plz hit the crown :D
-5 1/4 - (-7 1/2) Simplify, help asap
Answer:
2 1/4
Step-by-step explanation:
Answer:
2.25
Step-by-step explanation:
Which expression is equivalent to 1/8 - 3/8?
Answer:
2/16-6/16
Step-by-step explanation:
Help pls .. Determine if the two triangles are congruent. If they are , state how you know.
A. SAS
B. AAS
C. Not enough information
D.SSS
Answer:
C. not enough info
Step-by-step explanation:
Since the indicated angle in the triangle on the left is between the two sides that are marked congruent, and the marked angle on the triangle on the right is not between the two marked sides, there is not enough information to say whether the two triangles are congruent or not.
please help me and my mom can't figure it out at all
Answer:
simple
Step-by-step explanation:
p= 30
hahahaha asking how
ok let's go
that 90°is also 90°in those angles around it
for the 140
sum of angles in a straight line =180
180-140
that's 40
90+40 =130
then sum of angles in a triangle=180
therefore 180-130=50
MAGIC/WISDOM
hope it's helpful thank me later
Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upper F left-parenthesis 0 right-parenthesis equals 5. Find the value of Upper F left-parenthesis b right-parenthesis for b equals 0 comma 0.1 comma 0.2 comma 0.5 comma and 2.0.
It looks like you're given
F'(x) = 3x² + 7
and
F (0) = 5
and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.
The first is done for you, F (0) = 5.
For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:
[tex]F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt[/tex]
[tex]F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt[/tex]
[tex]F(x)=5+(t^3+7t)\bigg|_0^x[/tex]
[tex]F(x)=5+x^3+7x[/tex]
Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.
On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is
F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x
Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.
A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).
Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have
x₁ = x₀ + 0.1 = 0.1
y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7
x₂ = x₁ + 0.1 = 0.2
y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403
x₃ = x₂ + 0.3 = 0.5
y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539
x₄ = x₃ + 1.5 = 2.0
y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164
You use a battery to power a small hand-held fan to keep cool in the summer. What way is energy transformed?
A:Mechanical to Potential to Kinetic
B: electrical to chemical to potential
C: electrical to kinetic to potential
D: Chemical to electrical to kinetic
Answer:
c electrical to kinetic
Answer:
D
Step-by-step explanation:
Chemical to electric to kinetic
Pleas help me find the answer and show the work to this question
Answer:
[tex]Leg\ 1 = 8[/tex]
[tex]Leg\ 2 = 15[/tex]
Step-by-step explanation:
Given: See Attachment
Required
Determine the length of the legs
To do this, we apply Pythagoras theorem.
[tex]Hyp^2 = Adj^2 + Opp^2[/tex]
In this case:
[tex]17^2 = x^2 + (2x- 1)^2[/tex]
Open Bracket
[tex]17^2 = x^2 + 4x^2- 2x-2x + 1[/tex]
[tex]17^2 = 5x^2 - 4x + 1[/tex]
[tex]289= 5x^2 - 4x + 1[/tex]
Collect Like Terms
[tex]5x^2 - 4x + 1 - 289 = 0[/tex]
[tex]5x^2 - 4x - 288 = 0[/tex]
Solving using quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
So:
[tex]x = 8[/tex] or [tex]x = -7.2[/tex]
Since, x can't be negative, then:
[tex]x = 8[/tex]
One of the leg is:
[tex]Leg\ 1 = x[/tex]
[tex]Leg\ 1 = 8[/tex]
[tex]Leg\ 2 = 2x - 1[/tex]
[tex]Leg\ 2 = 2*8 - 1[/tex]
[tex]Leg\ 2 = 16 - 1[/tex]
[tex]Leg\ 2 = 15[/tex]
how many ways can 3 yearbooo posters out of a total of 6 posters be displayed across a wall?
Answer:
69
Step-by-step explanation:
Given that a baby is 8month and her elder sister is 4 years old, express their ages as a ratio
Answer:
11.10
Step-by-step explanation:
may be not sure about it
Answer:
1:6
Step-by-step explanation:
1 year = 12 months
4 year = 4 × 12 months
= 48 months
Baby = 8 months
Elder sister = 48 months
B : ES
8 : 48
÷8:÷8
1 : 6
please help me graph it!
Antonio completed the right column of the table to help him find the sum of twonights and 1/5. In which step did his first ever occur?
Help plsssssss.................
Answer:
B
Step-by-step explanation:
you do 0.74 + 0.18 and then subtract 0.8
You can spend up to $35 on a shopping trip. You want to buy a shirt that cost $14. Write and solve an inequality that represents the amount of money you will have left if you buy the shirt
Answer:
Step-by-step explanation:
a. 35 greater than or equal to 14 + x
35 - 14 = 21
x = $21
b. If the shirt is 30% off it would cost $9.80
14 x 0.3 = 4.2
14 - 4.2 = 9.8
35 is greater than or equal to 9.80 + x
35 - 9.8 = 25.2
x = $25.20
This changes the inequality by making x greater than it was in part a
c. Yes, you do have enough money to buy the shirt that is on sale and a pair of pants. x is the amount that you have left to spend after you buy the shirt that is on sale. 25.20 is greater than the cost of the pants.
Using the formula for Fahrenheit and Celsius temperatures, F = 9/5 C + 32.
If the temperature is currently 25 degrees F. what is the temperature in C
degrees? Round to the nearest WHOLE number. LABEL
Answer:
-4 degrees Celsius
Step-by-step explanation:
F = 25
Substitute into formula: 25 = 9/5C + 32
subtract 32 from each side: -7 = 9/5C
multiply each side by the reciprocal of 9/5, which is 5/9
-7(5/9) = C
C = -35/9 which is close to -36/9 which is -4 degrees Celsius
a line contains the points P(1,1) and Q(7, 10). What is the slope of the line
Answer:
1.5
Step-by-step explanation:
Well, if we calculate the divisionary constant between the two values we can establish a quantum link on the 4th dimension and then add 12 to both sides of the equation, then calculate the square of the 7th digit in the alphabet, giving the answer 1.5.
or like,
change in y value divided by change in x value, giving;
(10-1) / (7-1)
PLEASE HELP FASTT!!!!!!!!!!!!!!!!!!!!!!Determine whether each ratio is equivalent to 1/2,3/9, or 5/7.
Write the ratio in the correct box.
A large tank holds 1.9 x 10^7 gallons of oil. How much oil can be stored in 9 tanks. Write your answer in scientific notation.
Answer:
1.71 × 10^8 gallons
Step-by-step explanation:
1.9 × 10^7 = 19,000,000
19,000,000 × 9 = 171,000,000
171,000,000 in scientific notation is 1.71 × 10^8
Subtract. Write your answer as a fraction in simplest form.
5/8 - (-7/8)= ???
Factored quadratic equation for (x + 10)(x -2)=0
Ruby has $2.10 in nickels and dimes.
She has three as many dimes as nickels. How many nickels and dimes does she have?
Answer:
$
Step-by-step explanation:
Unit conversion is the conversion of one unit to another unit with its standard conversion.
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
The number of nickels is 5.
The number of dimes is 15.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
Now,
Let,
Dimes = 3x
Nickels = x
Now,
The total number of cents.
10(3x) + 5x = 180
30x + 5x = 180
35x = 180
x = 5.14
x = 5
Now,
3x = 3 x 5 = 15
Thus,
The number of nickels is 5.
The number of dimes is 15.
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22 POINTS ( LOTS OF POINTS) A student answered 81 problems on a test correctly and received a grade 90%.
How many problems were on the test, if all the problems were worth the same
number of points?
I think 88 problems were on the test.
HELP ME PLZ
A figure is shown in the image. What is the measure, in
degrees of
А. 95.4
B. 52.1
C. 74.2
D. 64.7
Answer:
Step-by-step explanation:
angles x, 2x, and 23.7 add up to 180 degrees
x + 2x + 23.7 = 180
3x + 23.7 = 180
subtract 23.7 on both sides
3x + 23.7 - 23.7 = 180 - 23.7
3x = 156.3
divide both sides by 3
x = 52.1
Angle C is a straight line = 180 degrees
Angle B is found by adding 32.5 and x, and subtracting it from 180 degrees (since three angles in a triangle must add up to 180)
we found x = 52.1 degrees
so angle B = 180 - 32.5 - 52.1 = 95.4 degrees
please give heart and brainliest :)
Please help me thank you so much I appreciate it
Answer:
right =86
left=94
Step-by-step explanation:
they should add up to 180 so,
6x+52+9x+23 =180
then solve for x
15x+75=180
subtract 75
15x=105
divide by 15
x=7 ,
the left side is
6(7)+52=
42+52=94
the right side
9(7)+23=
63+23=86
(please mark brainliest if correct)
helppppp nowwwwwww plsss
Answer:
c!
Step-by-step explanation:
good luck! :)
help pls. it would be much appreciated
Step-by-step explanation:
By Sine rule, BC/sin93° = 11/sin42°.
Therefore BC = 16.4.
negative 12 minus negative 13
Answer:
jflsnfjclewndlsfjnenqwpcpoop
Step-by-step explanation:
Hehe
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Write the equation of the line with a slope of -1.6 and a y-intercept of 4 in slope-
intercept form.
Answer:
y = -1.6x + 4
Step-by-step explanation:
y = mx + b
y = (-1.6)x + (4)
y = -1.6x + 4
The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = - 1.6x + 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Slope of the line (m) = - 1.6
And, The y - intercept = 4
We know that;
The slope intercept form of an equation of line is,
⇒ y = mx + b
Where, 'm' is slope of the line and 'b' is y - intercept of the line.
Hence, The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = mx + b
⇒ y = - 1.6x + 4
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