Answer:
20
Step-by-step explanation:
The GCF of 4 and 16 is 4.
[tex] \frac{4}{4} = 1 [/tex]
[tex] \frac{16}{4} = 4 [/tex]
We can rewrite this using the distribute property like so:
[tex] 4(1 + 4)[/tex]
Using the distribute property:
[tex] = 4 + 16[/tex]
[tex] = 20[/tex]
We can also add inside the parentheses and multiply we'll get the same answer.
[tex] = 4(5) \\= 20[/tex]
Please answer all question
(1)
(a) Use the fact that [tex]\sqrt{x^2} = |x|[/tex] for all [tex]x[/tex]. Since [tex]x\to+\infty[/tex], we have [tex]x>0[/tex] and [tex]|x| = x[/tex].
[tex]\displaystyle \lim_{x\to\infty} \frac{\sqrt{9x^2 - 2}}{x + 4} = \lim_{x\to\infty} \frac{\sqrt{x^2} \sqrt{9 - \frac2{x^2}}}{x + 4} \\\\= \lim_{x\to\infty} \frac{ x \sqrt{9 - \frac2{x^2}}}{x+4} \\\\= \lim_{x\to\infty} \frac{\sqrt{9 - \frac2{x^2}}}{1 + \frac4x} \\\\= \frac{\sqrt9}1 = \boxed{3}[/tex]
(b) This time [tex]x\to-\infty[/tex], so [tex]x < 0[/tex] and [tex]|x| = -x[/tex].
[tex]\displaystyle \lim_{x\to\infty} \frac{\sqrt{9x^2 - 2}}{x + 4} = \lim_{x\to\infty} \frac{\sqrt{x^2} \sqrt{9 - \frac2{x^2}}}{x + 4} \\\\= \lim_{x\to\infty} \frac{ \boxed{-x} \sqrt{9 - \frac2{x^2}}}{x+4} \\\\= (-1) \times \lim_{x\to\infty} \frac{\sqrt{9 - \frac2{x^2}}}{1 + \frac4x} \\\\= -\frac{\sqrt9}1 = \boxed{-3}[/tex]
(c) We immediately have
[tex]\displaystyle \lim_{x\to\infty} (x - \sqrt x) = \boxed{\infty}[/tex]
since [tex]x > \sqrt x[/tex] for all [tex]x > 1[/tex].
(d) Introduce a difference of squares by factoring in the limand's conjugate. The rest mirrors what we did in (a)/(b).
[tex]\displaystyle \lim_{x\to\infty} \left(\sqrt{x^2 + 12x} - x\right) = \lim_{x\to\infty} \frac{\left(\sqrt{x^2+12x} - x\right) \left(\sqrt{x^2+12x} + x\right)}{\sqrt{x^2 + 12x} + x} \\\\ = \lim_{x\to\infty} \frac{\left(\sqrt{x^2+12x}\right)^2 - x^2}{\sqrt{x^2+12x}+x} \\\\ = \lim_{x\to\infty} \frac{12x}{\sqrt{x^2+12x}+x} \\\\ = \lim_{x\to\infty} \frac{12}{\sqrt{1 + \frac{12}x} + 1} = \frac{12}{\sqrt1 + 1} = \boxed{6}[/tex]
(e) Divide through by the highest-degree exponential term.
[tex]\displaystyle \lim_{x\to\infty} \frac{12e^{2x} - 3e^{3x}}{2e^{2x} + 4e^{3x}} = \lim_{x\to\infty} \frac{12e^{-x} - 3}{2e^{-x} + 4} = \frac{0 - 3}{0 + 4} = \boxed{-\frac34}[/tex]
(2) By definition of the derivative, we have
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]
For [tex]f(x) = \sqrt{x^2+1}[/tex], the limit becomes
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\sqrt{(x+h)^2+1} - \sqrt{x^2+1}}h[/tex]
Factor in the conjugate.
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\left(\sqrt{(x+h)^2+1} - \sqrt{x^2+1}\right) \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\left(\sqrt{(x+h)^2+1}\right)^2 - \left(\sqrt{x^2+1}\right)^2}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\bigg((x+h)^2+1\bigg) - (x^2+1)}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{2xh + h^2}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{2x + h}{\sqrt{(x+h)^2+1} + \sqrt{x^2+1}}[/tex]
[tex]\implies \boxed{f'(x) = \displaystyle \lim_{h\to0} \frac{x}{\sqrt{x^2+1}}}[/tex]
(3) The tangent line to
[tex]y = \frac1{x^2+1}[/tex]
at the point (2, 1/5) has slope equal to the derivative [tex]\frac{dy}{dx}[/tex] when [tex]x = 2[/tex]. Compute the derivative; since [tex]y = \frac1{f(x)^2}[/tex] where [tex]f(x)[/tex] is the function from the previous problem, using the chain rule gives
[tex]y = \dfrac1{f(x)^2} \implies \dfrac{dy}{dx} = -\dfrac{2f'(x)}{f(x)^3} = -\dfrac{2 \times \frac{x}{\sqrt{x^2+1}}}{\left(\sqrt{x^2+1}\right)^3} \\\\ \implies \dfrac{dy}{dx} = -\dfrac{2x}{(x^2+1)^2}[/tex]
The tangent line at (2, 1/5) then has slope
[tex]\dfrac{dy}{dx}\bigg|_{x=2} = -\dfrac{2\times2}{(2^2+1)^2} = -\dfrac4{25}[/tex]
Using the point-slope formula, the equation of the tangent line is
[tex]y - \dfrac15 = -\dfrac4{25} (x - 2) \implies \boxed{y = -\dfrac{4x - 13}{25}}[/tex]
Jose pays $25 an hour for a tutor. Which expression represents the total cost of a tutor for the afternoon?
Question 6 options:
25h
25 ÷ h
h25
h + 25
Answer:
25h
I hope this helps :)
Use the grouping method to factor this polynomial completely.
3x3 + 12x2 + 2x + 8
A. (3x2 + 4)(x+4)
B. (3x2 + 4)(x+2)
C. (3x2 + 2)(x + 2)
O D. (3x2 + 2)(x+4)
Answer:
[tex]D)\:(3x^{2} +2)(x+4)[/tex]
Step-by-step explanation:
[tex]3x^{3} + 12x^{2} + 2x + 8[/tex]
Group, [tex]3x^3+12x^2+2x+8[/tex] [tex]=(3x^{3} +12x^{2} )+(2x+8)[/tex]factor out [tex]3x^{2}[/tex]in the first and 2 in the second group.
[tex]3x^{2} (x+4)+2(x+4)[/tex]
Factor out common term [tex]x+4[/tex] by using distributive property.
polynomial [tex]3x^{2} +2[/tex] is not factored since it does not have any rational roots.
[tex](3x^{2} +2)(x+4)[/tex]
_____________________________
Answer:d
Step-by-step explanation:
Twelve dogs and cats receive 77 biscuits.
A dog receives 7 biscuits,one biscuit more than a cat.
How many dogs were there?
Answer:
6 dogs are there who ate the biscuits
I have an 20 pound bag of food. If it is 2/3 full right now, how much dog food is in the bag?
Answer:
2/3multiply by20 u get 13.3 pounds
22/7 - 4/7
A)2
B)2 4/7
C)2 5/7
D)3
Answer:
None of the option is correct.
The right answer is 18/7 or 2.57
Step-by-step explanation:
find the value of a cube + b cube when a+b = 5 and ab = 3
As we know :
[tex] \boxed{ \boxed{ {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) }}[/tex]now let's plug the value of given terms :
(5)³ = a³ + b³ + (3×3)(5)125 = a³ + b³ + 45a³ + b³ = 125 - 45 a³ + b³ = 80Answer:
babawi lang sana
Step-by-step explanation:
naul pi
Find the midpoint of the line segment joining the points P, and P2
P1 = (2, -5); P2 = (4.9)
a bakery worker ordered 3,000 eggs when only 300 eggs were needed. Which explains how many more eggs were ordered than were needed?
Answer:
2700 more eggs were ordered
What would the answer be image below
Answer:
The points would be: (-3, 3) (-4, -1) (2, -1) (1, 3)
Step-by-step explanation:
Because when you move 4 units left, all of the x values in the points will go down by 4, and when you move 2 units down, the y values will go down by 2 units. So when applied to the points shown, you get the answer I put.
I believe this is correct? Hope it helps!
What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps. units² Trapezoid A B C D on a coordinate plane with vertex A at negative 1 comma 5, vertex B at 3 comma 2, vertex C at 0 comma negative 2, and vertex D at negative 13 comma negative 11. Angle A is shown to be a right angle.
Answer:
62.5 units squared.
Step-by-step explanation:
Find the values of x, y, and z in the triangle to the right
Answer:
x = 36 , y = 64 , z = 80
Step-by-step explanation:
Exterior angle equals the sum of opposite interior angle.
3x + 8 = x + z
3x - x - z = -8
2x - z = -8 ------------ (I)
z + 3x - 8 = 180 {linear pair}
3x + z = 180 + 8
3x + z = 188 --------------(II)
Add (I) and (II) and z will be eliminated and we can find the value of 'x'
(I) 2x - z = -8
(II) 3x + z = 188 {Now add}
5x = 180
x = 180/5
x = 36
Plugin x = 36 in equation (II)
3*36 +z = 188
108 + z = 188
z = 188- 108
z = 80
x + y + z = 180 ----------------(III) {angle sum property of triangle}
36 + 80 +y = 180
116 + y = 180
y = 180 - 116
y = 64
a) 16 / (-4)
b) (-56) / 8
c) (-28) / (-2)
First correct answer gets Brainliest
Answer:
2nd option is the correct answer
If two complementary angles are in a 2:3 ratio, what is the degree measure of each angle?
Answer:
The other angle's measure is 2/3 (54) = 108/3 = 36 degrees.
A correlation of r = 0.35 is?
moderate and positive
strong and positive
weak and positive
Answer:
r = 0.35 is Moderate and positive
Step-by-step explanation:
A correlation of r = 0.35 represents a moderate and positive relationship between two variables.
You are really excited to have found a Puch Maxi Moped from the mid Eighties, and the spring weather is making you want to get out and ride it around. It doesn't run on straight gasoline, you have to mix the oil and gas together in a specific ratio of 2.4 fl. oz. of oil for every gallon of gasoline.
You have 3.75 gallon of gas. How much oil should you add?
Answer:
Step-by-step explanation:
You should add 9 fl. oz. of oil to your 3.75 gallons of gas.
Puch Maxi Moped from the mid-Eighties now since this moped doesn't run on straight gasoline, you need to create a special fuel mixture. This involves combining oil and gas in a specific ratio. The magic ratio here is 2.4 fl. oz. (fluid ounces) of oil for every gallon of gasoline.
You mentioned you've got 3.75 gallons of gas. To figure out how much oil you need, we can use some math. First, let's find out how much oil is required for one gallon of gas:
2.4 fl. oz. of oil/gallon x 1 gallon = 2.4 fl. oz. of oil.
So, for 3.75 gallons of gas, you'll need:
2.4 fl. oz. of oil/gallon x 3.75 gallons = 9 fl. oz. of oil.
You should add 9 fluid ounces of oil to your 3.75 gallons of gas to create the proper fuel mixture for your Puch Maxi Moped.
To know more about Ratio here
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(7x³-11x-1)-(12x³+x²-8)
Answer:
[tex]- 5 {x}^{3} - {x}^{2} - 11x + 7 \\ [/tex]
Step-by-step explanation:
Before solving that we have to know that,
[tex]( + ) \times ( + ) = ( + ) \\ ( - ) \times (- ) = ( + ) \\ ( + ) \times ( - ) = (- )[/tex]
Let's solve now.
[tex]7 {x}^{3} - 11x - 1 - (12 {x}^{3} + {x}^{2} - 8) \\ 7 {x}^{3} - 11x - 1 - 12 {x}^{3} - {x}^{2} + 8 \\ 7 {x}^{3} - 12 {x}^{3} - {x}^{2} - 11x - 1 + 8 \\ = - 5 {x}^{3} - {x}^{2} - 11x + 7[/tex]
Hope this helps you.
Let me know if you have any other questions :-):-)
10
h
+
6
−
5
h
+
3
sorry its weird, you can type it out it wont let me put it normally.
Answer: 5h+9
Step-by-step explanation:
10h + (-5h)
5h+(6(+3))
A bridge connecting two cities separated by a lake has a length of 3.961 mi.
Use the table of facts to find the length of the bridge in yards.
Round your answer to the nearest tenth.
Conversion facts for length
12 inches (in) = 1 foot (ft)
3 feet (ft) = 1 yard (yd)
36 inches (in) = 1 yard (yd)
5280 feet (ft) = 1 mile (mi)
1760 yards (yd) = 1 mile (mi)
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#11 help please !!!!!!!
Answer:
Step-by-step explanation:
300/100 = 3 = 1%
if 3 = 1% then 3/2 or 1.5 = 0.5%
5 x 3 = 15 = 5%
15 + 1.5 = 16.5 = 5.5%
5. What is the value of y in the solution to the systems of linear equations shown below?
12x + 6y + 7z= -35
7x- 5y - 6z= 200
x+y= -10
Answer:
x=[tex]\frac{60}{121}[/tex],z=[tex]\frac{535}{121}[/tex],y=-10
Step-by-step explanation:
Answer:
[tex]1) \: \: 12x + 6y + 7z = - 35 \\ 6y = - 35 - 12x + 7z \\ y = \frac{ - 35 - 12x + 7z}{6} \\ \\ 2) \: \: 7x - 5y - 6z = 200 \\ - 5y = 200 - 7x + 6z \\ y = \frac{200 - 7x + 6z}{ - 5} \\ \\ 3) \: \: x + y = - 10 \\ y = - 10 - x \\ [/tex]
(Write your answers on the space provided) The World Health Organization (WHO) reported that about 16 million adolescent girls between 15 and 19 years of age give birth each year. Knowing the adverse effects of adolescent childbearing on the health of the mothers as well as their infants, a group of students from Magiting High School volunteered to help the government in its campaign for the prevention of early pregnancy by giving lectures to 7 Barangays about the WHO guidelines on teenage pregnancy. The group started in Barangay 1 and 4 girls attended the lecture. Girls from other barangays heard about it, so 8 girls attended from Barangay 2, 16 from Barangay 3, and so on. a. Make a table representing the number of adolescent girls who attended the lecture from Barangay 1 to Barangay 7 assuming that the number of attendees doubles each Barangay 4 3 5 6 2 7 1 Barangay Number of Attendees b. Form a sequence representing the number of adolescent girls who attended the lecture from Barangay 1 to Barangay 7. C. Because people who heard about the lecture given by the group thought that it would be beneficial to them, five more different barangays requested the group to do the lectures for them. If the number of young girls who will listen to the lecture from these five Barangays will increase in the same manner as that of the first 7 Barangays, determine the total number of girls who will benefit from the lecture.
The sequence of the number of girl attendees at each Barangay is nonzero, given by multiplying the number of attendees in the previous Barangay by 2
The required values are;
a. The completed table is presented as follows;
[tex]\underline{\begin{array}{|l|c|c|c|c|c|c|c|}\mathbf{Barangay}&1&2&3&4&5&6&7\\\mathbf{Number \ of \ attandees}&4&8&16&32&64&128&256\end{array}}[/tex]
b. The sequence of the number of girls attendees aₙ = 4×2⁽ⁿ⁻¹⁾
c. The sum of beneficiaries of the lecture from the twelve Barangay is 16,384 girls
Reason:
Known parameters are;
Number of girls that attended the lecture at Barangay 1 = 4 girls
Number of girls that attended from Barangay 2 = 8 girls
Number that attended from Barangay 3 = 16 girls
a. The required table with the assumption that the number of girls that attended at each Barangay from Barangay 1 to Barangay 7 doubles, is presented as follows;
[tex]\begin{array}{|l|c|c|c|c|c|c|c|}Barangay&1&2&3&4&5&6&7\\Number \ of \ attandees&4&8&16&32&64&128&256\end{array}[/tex]b. The sequence of the number of girls who attended the lecture from Barangay 1 to Barangay 7 is presented as follows;
The sequence is a geometric progression having the form, aₙ = a·r⁽ⁿ⁻¹⁾
The first term of the sequence, a = 4
The common ratio, r = 2 (each term is twice the previous term)
n = The number of terms
The sequence is therefore;
aₙ = 4·2⁽ⁿ ⁻ ¹⁾c. The total number of girls in the geometric progression, (G. P.) is given by the sum of a G. P. as follows
[tex]S_n = \dfrac{a \cdot (r^n - 1 )}{r - 1}[/tex]
Where;
n = The number of terms = 7 + 5 = 12
Which gives;
[tex]S_{12} = \dfrac{4 \times (2^{12} - 1 )}{2 - 1} = \dfrac{4 \times 4,096 }{1} = 16,384[/tex]The total number of girls who will benefit from the lectures, S₁₂ = 16,384 girls
Learn more about geometric progression here:
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Can someone give me advice please..I'm having a panic attack because a car hit my car when i was turning on a yellow arrow and it was clear but this brown jeep speeded to hit my car. how do i fix it without my dad knowing. i am willing to pay a lot to fix it but i just don't want to get in trouble and I don't want him finding out :(
Answer:
keep the car at a friends house untill you find a place to get it fixed at... or keep it at a trustworthy family members house.
If these don't help then im sorry.
Help plz very urgent
Answer:
N+5
Step-by-step explanation:
4,9,14,19
4+5=9+5=14+5=19….
Find the Measure of The missing angles
Answer:
∆K = 98°
∆M = 82°
∆G = 118°
∆H = 62°
Step-by-step explanation:
∆K & ∆G is by corresponding angle
and
∆M & ∆H is by linear pairs
If y varies directly as x and as the square of z, and y =25/9 when x=5 and z=1, find y when x =1 and z=4
Answer:
y= 80/9
Step-by-step explanation:
Given
" y varies directly as x" and "as the square of z" so y = x* z²* some number
if y =25/9 when x= 5, z= 1 and y = x*z²* some number
then 25/9 = 5 * 1² * some number
5*(5/9) = 5 * some number
therefore y = x* z²* (5/9)
y= ? when x=1 , z= 4
y = x * z² * (5/9)
y = 1 * 4² * (5/9)
y = 16*5 / 9
y = 80/9
How do you plot a fraction on a graph that only allows whole numbers?
Answer:
Depends, rise over run could be considered a fraction, or if it's a number that has a whole number like one and 3/4 then you just plot the point to the best of your ability. In other words guess.
36 workers can complete a piece of work in 12 days how many workers should be removed to complete the same work in 24 days
please explain step by step
Jake made punch by combining 2.75 liters of orange juice, 1.25 liters of pineapple juice, and 3.5 liters of soda. He then poured equal amounts of all the punch into 3 different containers. How much punch did Jake pour into each container?
Answer:
He poured 2.5 liters into each container
Step-by-step explanation:
Add 2.75, 1.25, and 3.5 together to get 7.5. Divide 7.5 by 3 and you get 2.5 liters per container.