Answer:
3/2
Step-by-step explanation:
w/3=3(w-1)-1
w=9w-9-3
-8w=-12
w=3/2
Trish had a square garden with side lengths of 8 feet. She expanded her garden to 10 feet by 8 feet. By how many square feet did she expand the area of her garden?
Answer:
[tex]16\:\mathrm{ft^2}[/tex]
Step-by-step explanation:
Trish's initial garden had an area of [tex]8\cdot8=64\:\mathrm{ft^2}[/tex]. After expanding her garden to be 10 feet by 8 feet, the garden has an area of [tex]8\cdot 10=80 \:\mathrm{ft^2}[/tex]. Therefore, the garden was expanded by [tex]80-64=\boxed{16\:\mathrm{ft^2}}[/tex]
Find
[tex] \frac{dy}{dx} [/tex]
if
[tex]y = (x + \sqrt{x} )^{2} [/tex]
Answer:
[tex]\displaystyle y' = 2x + 3\sqrt{x} + 1[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsAnything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (x + \sqrt{x})^2[/tex]
Step 2: Differentiate
Chain Rule: [tex]\displaystyle y' = 2(x + \sqrt{x})^{2 - 1} \cdot \frac{d}{dx}[x + \sqrt{x}][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}})^{2 - 1} \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}][/tex]Simplify: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}][/tex]Basic Power Rule: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 \cdot x^{1 - 1} + \frac{1}{2}x^{\frac{1}{2} - 1})[/tex]Simplify: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2}x^{-\frac{1}{2}})[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2x^{\frac{1}{2}}})[/tex]Multiply: [tex]\displaystyle y' = 2[(x + x^{\frac{1}{2}}) + \frac{x + x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}][/tex][Brackets] Add: [tex]\displaystyle y' = 2(\frac{2x + 3x^{\frac{1}{2}} + 1}{2})[/tex]Multiply: [tex]\displaystyle y' = 2x + 3x^{\frac{1}{2}} + 1[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = 2x + 3\sqrt{x} + 1[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Sophia is organizing textbooks on her bookshelf. She has an English textbook, a biology textbook, a history textbook, and a writing textbook. How many different ways can she line the textbooks up on her bookshelf?
Answer:
I believe it's 24 combinations.
Step-by-step explanation:
I found how many there were when starting with English, and there were six. I multiplied this by four (for the four books) and found 24.
Hope this helps! Have a nice day :)
Answer:
24 ways
Step-by-step explanation:
English, biology, history, writing
English, history, writing, biology
English, writing, biology, history
English, biology, writing, history
English, history, biology, writing
English, writing, history, biology
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
So there is going to be 6 different ways in every textbook you put in front, [amount of textbook (4)] x [different ways (6)] = 24 ways
btw there is a easier way of doing this but i forgot ;-;
Meliah wants to make a gallon of punch. She uses 2 quarts of orange juice, 1 cup of lemon juice, and 2 1/2 pints of pineapple juice. How many cups of water should she add to make 1 gallon?
Answer:
2 cups of water
Step-by-step explanation:
Meliah wants to make a gallon of punch.
Note that
1 gallons = 16 cups
For Orange juice
She uses 2 quarts of orange juice,
1 quart = 4 cups
2 quarts = x
Cross Mulitiply
2 × 4 cups = 8 cups
For lemon juice
1 cup of lemon juice
For pineapple juice
2 1/2 pints of pineapple juice.
1 pint = 2 cups
2 1/2 pints = x
Cross Mulitiply
2 1/2 × 2 cups = 5 cups
Total number of cups
= 8 cups orange juice + 1 cup lemon juice + 5 cups of pineapple juice
= 14 cups
Hence, the number of cups of water she should add to make 1 gallon is calculated as:
16 cups - 14 cups
= 2 cups of water
heelppppppppppp URGENTTTTT
Marking brainliest pls help!!!!
Answer:
He would recognize Lincoln's accomplishments which a good amount was about his documents like the Emancipation document.
Step-by-step explanation:
Also, he did his "I have a dream" speech on the Lincoln Memorial.
Rocco has a weekly reading schedule, reading for 4 hours per day on some days and 2 hours per day on the other days. He reads a total of 24 hours in a seven-day week. On how many days does he read for 4 hours?
Answer:
hm
Step-by-step explanation:
and then I say no one knows where I I am to find it and then he
1.write an inequality for the following situation no more than 10 people are allowed in the elevator.
2. Write an inequality for the following situation for the tour bus to run at least eight people must sign up
3. Write an inequality
for the following
situation:
The most you will pay for
a pair of jeans is $60.
4. Write in any quality for the following situation and 20 people showed up to the party
Answer:
1. [tex]p \leq 10[/tex] where [tex]p[/tex] represents the total number of people.
2. [tex]p \geq 8[/tex] where [tex]p[/tex] represents the total number of people.
3. [tex]c \leq 60[/tex] where [tex]c[/tex] represents the cost of a pair of jeans.
4. [tex]p > 20[/tex] where [tex]p[/tex] represents the total number of people.
Step-by-step explanation:
Question 1 explanation: Since no more than 10 people are allowed in the elevator, that means 10 and under are allowed, so the inequality would be [tex]p \leq 10[/tex].
Question 2 explanation: Since the tour bus needs at least 8 people to sign up to run, that means 8 and more people will allow the tour bus to run, so the inequality would be [tex]p \geq 8[/tex]
Question 3 explanation: Since the most you will pay for a pair of jeans is $60, that means jeans costing $60 and under are fine, so the inequality would be [tex]c \leq 60[/tex].
Question 4 explanation: Since over 20 people showed up to the party, that means there were more than 20 people at the party, so the inequality would be [tex]p > 20[/tex].
What is the equation of the circle with: center (5, 7) and point on the circle: (-2, 8)
Answer:
[tex](x-5)^2+(y-7)^2=50[/tex]
Step-by-step explanation:
Hi there!
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at [tex](h,k)[/tex] and r is the radius
Plug in the center (5,7)
[tex](x-5)^2+(y-7)^2=r^2[/tex]
Plug in the given point (-2,8) to solve for r²
[tex](-2-5)^2+(8-7)^2=r^2\\(-7)^2+(1)^2=r^2\\49+1=r^2\\50=r^2[/tex]
Therefore, r² is equal to 50. Plug this back into [tex](x-5)^2+(y-7)^2=r^2[/tex]
[tex](x-5)^2+(y-7)^2=50[/tex]
I hope this helps!
Which of the following tables of values represent a function ? Circle all that apply
Answer:
The last one
Step-by-step explanation:
Which statement describes graph
Answer:
Step-by-step explanation:
There are no statements here
What is 5x-3 equal to
Answer:
-15
Step-by-step explanation:
Answer:
-15 hdbdudbdjsbakznzbzjzbzbz
Jerome photographed an aquarium that measured 12 inches by 18 inches by 24 inches. Lim photographed an aquarium that was 12 inches by 30 inches by 12 inches. Both aquariums are rectangular prisms. How much more volume does Jerome’s aquarium have than Lim’s?
Answer:
the answer is 864 in3
Step-by-step explanation:
Jerome photographed an aquarium that measured 12 inches by 18 inches by 24 inches.
So V=LxWxH....
12 x 18 x 24= 5,184
Then...
Lim photographed an aquarium that was 12 inches by 30 inches by 12 inches.
So= V=LxWxH
12 x 30 x 12=4,320
And they need to see who has more so 5,184-4,320=864in3
I hope this helps also Into Math said it was correct :)
Find an equation of the circle that has center (-2, 6) and passes through (-6, 1).
Answer:
(x+2)^2 + (y-6)^2 = 41
Step-by-step explanation:
The equation for a circle is (x-h)^2+(y-k)^2=r^2
So first, it is known that the circle's center is at (-2,6), Therefore, this can be filled in:
(x+2)^2+(y-6)^2=r^2
Next, we need to find the radius, and one of the points is already known, being (-6, 1)
With this, find the distance between these two points by doing the Pythagorean Theorem, a^2+b^2=c^2. The a^2 would be the x value changed and the b^2 would be the y value changed between the two numbers. Note that this is interchangeable.
To find a:
-2 to -6 = change of 4
To find b:
6 to 1 = change of 5
Next, write out the equation for this:
4^2+5^2=c^2
16+25=c^2
41=c^2
c = √41
The radius would be √41, so the equation can now be completed. Since c will be brought to the second power, this will cancel out the square root.
(x+2)^2 + (y-6)^2 = 41
Hope that helps.
Norma makes bags.
She makes 17 bags an hour.
Norma works for 6 hours each day, 5 days a week.
Each bag is checked.
If the bag is perfect, it is put in a box.
When there are 12 bags in a box it is full.
One week 90% of the bags Norma made were perfect.
Work out the number of boxes completely filled with bags made by Norma.
Answer:
38
Step-by-step explanation:
She makes 17 bags an hour. Multiply 17 bags by each hour. Additionally, multiply that by 5 for each day worked. The total number is 510.
Out of 510 bags made in that week, only 90% are perfect. 90% of 510 is 459.
If there are 459 bags, and each box can hold 12, how many boxes will be full? Keep adding bags into boxes until you reach 0 bags. The equation you'll want is 459/12.
38 boxes will be full, with 3 remainder bags.
Rewrite in simplest terms:
10 (7g - 9h) -4h - 8 (-8 +8g)
Answer:
=6g + −94h + 64
Step-by-step explanation:
Let's simplify step-by-step.
10(7g−9h)−4h−8(−8+8g)
Distribute:
=(10)(7g)+(10)(−9h)+−4h+(−8)(−8)+(−8)(8g)
=70g+−90h+−4h+64+−64g
Combine Like Terms:
=70g+−90h+−4h+64+−64g
=(70g+−64g)+(−90h+−4h)+(64)
=6g + −94h + 64
Answer:
your answer is 6g-94h+64
Step-by-step explanation:
1. 10 (7g - 9h) -4h - 8 (-8 +8g)
2. 70g-90h-4h+64-64g
3. 6g-94h+64
Look at the parallelogram pictured in Figure 1. What is the area of the
parallelogram?
Answer:
45m²
Step-by-step explanation:
=> Area = base × height
=> A = 5m × 9m
=> A = 45m²
When using the quadratic formula to solve 7x2 – 3x + 2 = 0, which number will be squared as part of the formula?
Answer:
The value of b will be squared
Step-by-step explanation:
Recall that the quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
You will see that the only squared coefficient is b.
need help on question 26
Answer:
y = 2x - 3.
Step-by-step explanation:
26, The slope is 2 and y-intercept is -3
simplify 4 -2y + (-8y) + 6.2
Answer:
-10y+10.2
hope this helps
have a good day :)
Step-by-step explanation:
PLS HELP!!!!!!
What is the solution of the system shown?
0 (2, 2)
O (2,3)
O (3,2)
Answer:
(3,2)
Step-by-step explanation:
Answer:
3.2
Step-by-step explanation:
the question is in the image.(no links)
Answer:
I don't know but I think the answer is 3
Which expression is equivalent to a2 + 2a – 8?
A. (a + 2)(a – 4)
O B. (a + 1)(a – 8)
o C. (a - 1)(a + 8)
D. (a + 4)(a - 2)
Answer:
D
Step-by-step explanation:
(a+4)(a-2)=a^2+2a-8
a*a=a^2
a*(-2)=-2a
a*4=4a
4*(-2)=-8
a^2-2a+4a-8=a^2+2a-8
hey! please help i’ll give brainliest
Answer:
True
Step-by-step explanation:
Adding -ed to a verb will make it a simple past tense verb
Hope this helps :)
Answer:
True
Step-by-step explanation:
it is past tense
Find the missing exponent: p^2 ∙ p^3 ∙p^? = p^9
Answer:
34
Step-by-step explanation:
What is the area of triangle ABC?
9514 1404 393
Answer:
C. 36√3 square units
Step-by-step explanation:
Your knowledge of special triangles tells you that height CD is ...
CD = 6√3
so the area is ...
A = 1/2bh
A = 1/2(12)(6√3) = 36√3 . . . . square units
_____
Additional comment
The 30°-60°-90° right triangle that is half an equilateral triangle has a short side equal to half the length of the long side. The Pythagorean theorem tells you that the middle-length side is √(2²-1²) = √3 times the shortest side. That is, the side length ratios in this "special" triangle are ...
1 : √3 : 2
This means the length DB is 12/2 = 6, and the length CD is 6√3.
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
Side lengths- LK = 1.56 JK = 2.88
Step-by-step explanation:
Use tan for LK. Tan 26 = x/3.2, x = 1.56 to the nearest hundredth. Use cosine for JK. Cos 26 = x/3.2, x = 2.88 to the nearest hundredth.
y = kx
In the equation, what does "k" represent?
Answer: it’s the number that stays the same
Step-by-step explanation: ex. y = 24(6x)
The three numbers are in the ratio 4:5:6 . If the sum of the largest and
the smallest number is equal to the sum of second largest number
and 55. Find the numbers. pls answer the question fast I don't have time
Answer:
Step-by-step explanation:
Let the 3 numbers be 4x , 5x and 6x
4x + 6x = 5x + 55
10x = 5x + 55 Subtract 5x from both sides.
5x 5x
5x = 55 Divide by 5
x = 55/5
x = 11
Therefore the numbers are
3*11 = 33
4*11 = 44
5*11 = 55
12. The following list shows the number of new memberships that a gym
has sold each day over the past week: 4, 2, 9, 2,0,3, 8. Which of the
following is not a true statement? *