[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{vertex}{\stackrel{h}{-6}~~,~~\stackrel{k}{4}}\qquad \implies f(x)=a[x-(-6)]^2+4\implies \underline{f(x)=a(x+6)^2+4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]f(x-2)=a[(x-2)+6]^2+4\implies \underline{f(x-2)=a(x+4)^2+4} \\\\\\ f(x-2)-2\implies [a(x+4)^2+4]-2\implies \underline{a(x+4)^2+2=g(x)} \\\\\\ a[x-(\stackrel{h}{-4})]^2\stackrel{k}{+2}=g(x)\qquad \stackrel{vertex}{-4~~,~~2}[/tex]
PLEASE HELP!! IT'S DUE TONIGHT!
Answer:
Step-by-step explanation:
All triangles without exception, have 3 angles that add to 180o.
You know two of them. The statement above will help you get the third.
35 + 33 + x = 180 Combine the left
68 + x = 180 Subtract 68 from both sides.
x = 180 - 68
x = 112
Answer: The value of x is 112
Step-by-step explanation:
add the two values given: 35+33= 68
then subtract 68 from 180 (sum of angles is 180°) = 112
112+35+33= 180
Solve 37+z≤54. Graph the solution.
Answer:
z ≤ 17
Step-by-step explanation:
Step 1: Subtract 37 from both sides.
[tex]37 + z - 37\leq 54-37[/tex] [tex]z\leq 17[/tex]how do you work this out
Answer:
gradient = 2
Step-by-step explanation:
calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (5, 8) ← 2 points on the line
m = [tex]\frac{8-0}{5-1}[/tex] = [tex]\frac{8}{4}[/tex] = 2
Please answer as soon as possible, and show all work. Thank you.
Answer:
[tex]\displaystyle f'(x) = -12x^2 + 4x[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Expanding/FactoringCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationThe definition of a derivative is the slope of the tangent line: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = -4x^3 + 2x^2[/tex]
Step 2: Differentiate
[Function] Substitute in x: [tex]\displaystyle f(x + h) = -4(x + h)^3 + 2(x + h)^2[/tex]Substitute in functions [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-4(x + h)^3 + 2(x + h)^2 - \big( -4x^3 + 2x^2 \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-12hx^2 - 12h^2x + 4hx - 4h^3 + 2h^2}{h}[/tex]Factor: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h \big( -12x^2 - 12hx + 4x - 4h^2 + 2h \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} -12x^2 - 12hx + 4x - 4h^2 + 2h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = -12x^2 - 12(0)x + 4x - 4(0)^2 + 2(0)[/tex]Simplify: [tex]\displaystyle f'(x) = -12x^2 + 4x[/tex]∴ the derivative of the given function will be equal to -12x² + 4x.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the distance between (−9, 6) and (10, 6) ?
Enter your answer in the box.
Solution:
Step-1: Plot the points on the graph.
~Graph attached
Step-2: Find the distance by counting
We can see that (-9,6) is 9 units to the left of the origin and 10 units further to reach (10, 6).
Distance between two points: 9 + 10 Distance between two points: 19 unitswhat is 4 2/3 × 6 7/10
Answer:
[tex]31 \frac{4}{15}[/tex]
Step-by-step explanation:
(convert the mixed numbers into improper fractions = [tex]a\frac{b}{c} = \frac{a*c+b}{c}[/tex] )
[tex]\frac{4*3+2}{3}*\frac{6*10+7}{10}[/tex]
Steps if needed:
4*3 = 12+2 =14
6*10=60+7=67
[tex]\frac{14}{3} *\frac{67}{10}=\frac{14*67}{3*10}[/tex]
= [tex]\frac{938}{30}[/tex]
Simplify: Divide by 2
[tex]\frac{469}{15}[/tex] || 938/2 = 469 30/2 = 15
Convert your answer to a mixed fraction
[tex]31\frac{4}{15}[/tex]
469/15 = 31.26....
15*31 = 465
465+4 = 469
So your answer is 31 4/15
A pencil is 712 inches long.
How long is the pencil in centimeters?
Answer:
1808.48 centimeters long
Answer:
1808.48 cm
Step-by-step explanation:
the conversion from inches to cm is 2.54cm per inch
with that in mind,
take the 712 inch pencil and multiply it by 2.54 cm to convert it
leading to
712 * 2.54 = 1808.48 cm long.
What is half of a hundred?
Answer:
50
Step-by-step explanation:
3. Megan is having a meal with her friends.
She is going to choose one starter, one main and one dessert.
This is the menu.
Starter Main Dessert
Soup
£2.50 Chicken
£6,25 Trifle
£3.50
Prawns
£4.25 Beef
£8.00 Brownie
£4.00
Melon
£3.50 Pork
£7.50 Eton Mess £4.50
Megan has £15
List all the possible combinations that Megan can afford.
SCT,SCB,SCE,SBT, SBBR, SBE,SPT,SPB,SPE
PCT,PCB,PCE,PBT,PBBR, PBE, PPO,T,PPOB,PPOE
MCT,MCB,MCE,MBT,MBBR,MBE,MPT,MPB,MPE
THIS is in abrieviations.
5 3/7 x 3 1/2 pls help me bc iwill get trouble
Answer:
19
Step-by-step explanation:
Here is a square of side 2a and an equilateral triangle of side a + 1
The perimeter of the square is greater than the perimeter of the triangle.
Work out the range of possible values of a.
Answer: a>0.6
Step-by-step explanation:
Find the slope of the line in the image below.
Solution:
It should be noted:
Slope = Rise/RunUsing the formula:
Slope = Rise/Run=> Rise = 1; Run = 2=> Slope = 1/2Correct option is A.
1 / sec^2x + 1 / csc^2x = 1
I need help verifying the trig function with steps.
Step-by-step explanation:
answer is provided in picture
Giving right answer branleist
Answer:
Slope is -0.6, hope this helps
What is the value of x in this triangle ?
Solve 5^3x = 1400. Round to the nearest hundredth.
(PLEASE don't delete this. I really need help with this.)
Answer:
11.20
Step-by-step explanation:
I did this by first doing 5 x 5 x 5 which got me 125. Then I took 1400/125 to get 11.2. However you said round to the nearest hundredth which would be 11.20
When you measure an angle you usually have to choose between two numbers because
protractors are designed to measure angles that start on either the right or left side.
There are two angles to measure in each of the problems on this sheet and the next. The
angle on the left side is angle A. The angle on the right side is angle B. Find and record
the measure of both angles in each problem.
1 The measure of angle A is ___
degrees.
2 The measure of angle B is ___ degrees.
Answer:
B= 25°
A=138° /139°
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What can you take away from 800 to make 500?
Answer:
it would be 800-300 =500.
the 8th term of an arithmetic sequence is -42 and the 16th term is -74. Find and simplify an expression for the nth term
Answer:
[tex]a_{n}[/tex] = - 4n - 10
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₈ = - 42 and a₁₆ = - 74 , then
a₁ + 7d = - 42 → (1)
a₁ + 15d = - 74 → (2)
subtract (1) from (2) term by term to eliminate a₁
8d = - 74 - (- 42) = - 74 + 42 = - 32 ( divide both sides by 8 )
d = - 4
substitute d = - 4 into (1) and solve for a₁
a₁ + 7(- 4) = - 42
a₁ - 28 = - 42 ( add 28 to both sides )
a₁ = - 14
Then
[tex]a_{n}[/tex] = - 14 - 4(n - 1) = - 14 - 4n + 4 = - 4n - 10
Answer:
[tex]a_{n}=-10-4n[/tex]
Step-by-step explanation
[tex]a_{n}=a_{1}+(n-1)d\\Given:a_{8}=-42\\&a_{16}=-74\\Hence: \\a_{8}=a_{1}+7d=-42 (1)a_{16}=a_{1}+15d=-74 (2)\\ \left \{ {{a_{1}+7d=-42} \atop a_{1}+15=-74}} \right. \\(2)-(1):8d=-32\\ d=-32/8 =-4\\Substitute :d=-4 in equation (1)"\\-42=a_{1}+7(-4)\\-42=a_{1}-28\\a_{1}=-14\\Hence:\\a_{n}=-14-(n-1)4\\a_{n}=-14-4n+4\\a_{n}=-10-4n[/tex]
It’s graphs just help
Answer:
The answer is D
Step-by-step explanation:
There you go!!
Peter can mow his lawn in 6 minutes. Peter's son can mow it in 8 minutes. How long will it take them to do it together?
Answer:
3 minutes 26 seconds
Step-by-step explanation:
rate x time in Distance problems, and W = rate x time in work problems. The Work is generally 1, the whole job.
For Peter the formula is 1 (lawn mowed) = 1/6 lawn per minute x 6 minutes.
For the son the formula is 1 = 1/8 * 8.
Add their rates together, 1/8 + 1/6 = 3/24 + 4/24 = 7/24.
The equation for their rate working together is 1 = 7/24 * t
Divide both sides by 7/24 to find t. t = 1 / 7/24 = 1 * 24/7 = 24/7 = 3 and 3/7 minutes = approx. 3 minutes 26 seconds.
For a standard normal distribution, find the approximate value of p (z greater-than-or-equal-to negative 1.25). use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 11% 39% 61% 89%
For a standard normal distribution, the approximate value of p
( z≥-1.25 ) is 0.8945.
What is a standard normal distribution?The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation.
As we know that Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
It is given that z-score≥-1.25
From the standard normal table, the p-value corresponding to z≥-1.25 is
0.8945.
Therefore, For a standard normal distribution, the approximate value of p ( z≥-1.25 ) is 0.8945.
To get more about standard normal distribution visit:
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Answer:
89%
Step-by-step explanation:
To make it easy. Hope this helps
help me figure it out
help!!! meee ASAPPP 18 + brainlest
Answer:
Angle CFD = 30°
Step-by-step explanation:
HOPE THIS HELP YOU,FOR ANY QUESTION PLEASE ASK ME
The magnitude, M, of an earthquake is defined to be M = log StartFraction I Over S EndFraction, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a "standard" earthquake, which is barely detectable. What is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth. 2 3 2004. 5 6. 9.
Answer:
9
Step-by-step explanation:
7. Find the area of the figure.
Is it right??
Answer:
28.5 units²
Step-by-step explanation:
You are correct.
You divided the figure into a square, a rectangle and a triangle.
You can also just divide into a rectangle and a triangle as I did below, and there are other ways of dividing the figure to find the area.
Bottom rectangle: 8 units by 3 units
Top triangle: base = height = 3 units
total area = area of rectangle + area of triangle
total area = length × width + base × height / 2
total area = 8 units × 3 units + 3 units × 3 units / 2
total area = 24 units² + 4.5 units²
total area = 28.5 units²
which is equivalent to 1/2 sin 30
Answer:
1/2
Step-by-step explanation:
Sin 30 degree equals to the fractional value of 1/ 2. In the same way, we can derive other values of sin degrees like 0°, 30°, 45°, 60°, 90°,180°, 270° and 360°.
Answer:Sin 30=1/2
Step-by-step explanation:
A vendor buys x kg of peanuts and kg of cashew nuts.
(a) To get a good bargain, she must buy a minimum of 10 kg of peanuts and a minimum of 5 kg of cashew nuts.
(i)Write TWO inequalities which satisfy these conditions.
(ii) She buys no more than 60 kg of nuts. Peanuts cost $4.00 per kg and cashew nuts cost $8.00 per kg and she spends at least $200.
Write Two inequalities which satisfy these conditions.
The inequalities that satisfy this condition is 4x + 8y ≥ 200 and x + y ≤ 60
What is an inequality?
An inequality is an expression that shows the non equal comparison between two or more numbers and variables.
Let x represent the number of peanuts and y represent the number of cashew nuts.
She must buy a minimum of 10 kg of peanuts and a minimum of 5 kg of cashew nuts. Hence:
x ≥ 10, y ≥5
Also:
x + y ≤ 60
And:
4x + 8y ≥ 200
The inequalities that satisfy this condition is 4x + 8y ≥ 200 and x + y ≤ 60
Find out more on inequality at: https://brainly.com/question/24372553
Song randomly pulled a marble from a bag, recorded its color, put it back, and repeated. The results are shown in the following table.
Color Frequency
Blue 22
Green 19
Purple 20
Red 18
Yellow 21
If Song were to repeat the experiment 25 more times, how many of those times should he expect to pull a purple marble?
Enter your answer as a number, like this: 42
Step-by-step explanation:
when counting the events we see, he did
22+19+20+18+21 = 100 experiments.
and he got in 20 cases out of the possible 100 a purple marble.
that means the observed probability to pull a purple marble is 20/100 = 1/5.
now he does 25 more pulls.
each with the probity of 1/5 to pull a purple marble.
so, he should expect to pull a purple marble 25×1/5 = 5 times.
What is the distance between (4, −3) and (9, −3) ? Enter your answer in the box.
Answer:
5 units
Step-by-step explanation:
Luckily, we don't need to use the distance formula as we just need to find the distance between the x-coordinates. Thus, |4-9| = |-5| = 5, which means that the distance between (4,-3) and (9,-3) is 5 units
Answer:
5
Step-by-step explanation:
Point (4, -3) and point (9, -3) have the same y-coordinate of -3. Therefore, both points are on the line y = -3.
Any line that is y = {number} is a horizontal line.
Therefore, to find the distance between the points, find the difference between the x-values:
9 - 4 = 5
Therefore, the distance between (4, −3) and (9, −3) is 5