Using the definition of the derivative,
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{f(x) - f(-2)}{x - (-2)}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac6x + 3}{x + 2}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac{6+3x}x}{x + 2}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{6+3x}{x(x + 2)}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3(x+2)}{x(x + 2)}[/tex]
[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3}{x} = \boxed{-\dfrac32}[/tex]
x + y = −3
y = 2x + 2
Answer:
Step-by-step explanation:
x + y = −3
y = 2x + 2
Substitute the y value of the second equation into the top equation
x + 2x + 2 = - 3
3x + 2 = - 3
3x = -3 -2
3x = - 5
x = -5/3
x + y = - 3
-5/3 + y = - 3
y = -3 + 5/3
y = -1 1/3
find the missing side. Round it to the nearest tenth.
Final Answer: 82.2
formula used: a² + b² = c²
a = 66
b = 49
c = x
Solution:
66² + 49² = x² (note: 66² = 66 × 66 = 4,356 and 49² = 49 × 49 = 2,401)
4,356 + 2,401 = x²
[tex]\sqrt{6,757}[/tex] = [tex]\sqrt{x^2}[/tex]
82.201 = x
rounded to the nearest tenth: 82.2
hope this helps, let me know if its incorrect or not
have a great day ;)
What is the slope of a line parallel to line B?
use the formula v=u+at to find the velocity when the initial velocity is 3m/s2 the time is 7 seconds
Answer:
Step-by-step explanation:
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Ryan loves collecting keychains from his family vacations. He currently has 15 keychains in his collection and wants to add 5 keychains each year. How many keychains will be in his collection in 18 years?
find the 80th term following arithmetic sequence 8,14,20,26
Answer:
The 80th term is 482
Step-by-step explanation:
8,14,20,26
This is an arithmetic sequence
Find the common difference by taking the second term and subtracting the first term
14-8 = 6
We are adding 6 each time
The formula for an arithmetic sequence is
an =a1+d(n-1) where a1 is the first term, d is the common difference and n is the term we are looking for
a80 = 8+6(80-1)
= 8 + 6*79
= 8+474
= 482
The 80th term is 482
Answer: 482
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{Rule:} \\\\\boxed{ \huge \boxed{a_n=a_1+(n-1)d }} } \ \ \\\\\\ 8 \underbrace{}_6 14 \underbrace{}_620\underbrace{}_626 ......a_{80}=? \\\\\\a_1=8 \ \ ; \ \ d=6 \\\\\\ a_{80}=8+(80-1)\cdot 6=480+8-6=482 \\\\\\\\ Answer: \boxed{\boldsymbol{ a_{80}=482}}[/tex]
A function w satisfies w(1) = 5 and w(4) = 1. A
function z satisfies z(3) = 4 and z(4) = 5. What is
the value of w(z(3)) ?
A) 1
B) 2
C) 4.
D) 5
ce A
Answer: A) 1
Since z(3) = 4, w(z(3)) = w(4)Since w(4) = 1, w(z(3)) = w(4) = 1Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your
answers as radicals in simplest form.
Answer:
x =10
y = 10 sqrt(3)/ 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 5 sqrt(3) / x
x sin 60 = 5 sqrt(3)
x = 5 sqrt(3)/sin 60
x = 5 sqrt(3) / sqrt(3)/2
x = 5*2
x =10
tan theta = opp /adj
tan 60 = x/y
ytan 60 = 10
y = x/ tan 60
y = 10/ sqrt(3)
y = 10/ sqrt(3) * sqrt(3)/ sqrt(3)
y = 10 sqrt(3)/ 3
Please help me to solve this question as soon as possible. Thank you
1.6 is a common factor of 36 and y. Find the possible value of y.
A. 25
B. 48
C.57
D. 81
Answer:
the answer is B
Step-by-step explanation:
because only 48 is dividable by 6
Convert this rational number to its decimal form and found to the nearest thousands?
Answer:
7 and 1 respectively
Step-by-step explanation:
1/7= 7 ) 1 (, the basic definition of division
The point (0,0) is a solution to which of these inequalities?
Answer:
c
Step-by-step explanation:
Answer:
C. y - 7 < 2x - 6
Step-by-step explanation:
A. y + 7 < 2x + 6
0 + 7 < 2(0) + 6
7 < 0 + 6
7 < 6 —————- FALSE
B. y + 7 < 2x - 6
0 + 7 < 2(0) - 6
7 < 0 - 6
7 < -6 —————FALSE
C. y - 7 < 2x - 6
0 - 7 < 2(0) - 6
-7 < 0 - 6
-7 < -6 —————TRUE
D. y - 6 < 2x - 7
0 - 6 < 2(0) - 7
-6 < 0 - 7
-6 < -7 ————— FALSE
Find the place value of 8 in 2456.1387.
Tenths
Hundredths
Thousandths
Thousands
Answer: Third Choice. Thousandths
Step-by-step explanation:
Concept:
Here, we need to know the order and name of each place value.
Please refer to the attachment below for the specified names.
Solve:
STEP ONE: Orde and name each place
2 ⇒ One Thousands
4 ⇒ Hundreds
5 ⇒ Tens
6 ⇒ Ones
.
1 ⇒ Tenths
3 ⇒ Hundredths
8 ⇒ One Thousandths
7 ⇒ Ten Thousandths
STEP TWO: Find the number [8] in the number
As we can see from the list above, 8 is at the right of the decimal point, thus, the place value is Thousandths.
Hope this helps!! :)
Please let me know if you have any questions
Find the remainder when the polynomial 9x2 - 4x - 7 is divided by x - 3.
Answer: 62
Step-by-step explanation:
[tex]\displaystyle\bf 9x^2-4x-7 =0 \\\\ Synthetic \ \ division\ \ if \ \ x-3 =0 => x=3 \\\\ then \ \ 3| \underline{ \ 9 \ | \ -4 \ | \ -7 \ | } \\\\ . \!\! \qquad\qquad +|3*9| \ \ 23*3 | \\ .\!\!\!\!\!\1 \qquad \qquad \qquad | \ 23 \ | \ \ \ \boxed{62}[/tex]
What is the value of A when we rewrite (5/2)^x + (5/2)^x+3 as A x (5/2)^x?
A =
Answer:
A = 16.625
Step-by-step explanation:
Given :-
(5/2)^x + (5/2)^( x +3)To rewrite in :-
A. (5/2)^xAnswer :-
(5/2)^x + (5/2)^(x+3) (5/2)^x + (5/2)^x . (5/2)³ (5/2)^x { 1 + (5/2)³ }Hence :-
A = 1 + (5/2)³A = 1+ 125/8 A = 8 + 125/8 A = 133/8A = 16.625PLSS HELPP
I already know the answer just help me by plotting them in the graph.
Answer:
plotting the (x,y) coordinates in graph
Graph the inequality on the axes below.
-5x + 4y > -24
Step-by-step explanation:
-5x + 4y > -24
Plot and draw a graph that's it
Help fast pleaseeeeeeee
Step-by-step explanation:
-2. = [tex] \frac{1}{49} [/tex]-1 = [tex] \frac{1}{7} [/tex]0 = 11. = 72. = 49help me with this two I don't understand
Step-by-step explanation:
5.
[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]
Simplify both radicals.
[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]
Apply Quadratic Formula
First. find the discramnint.
[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]
Now find the divisor 2a.
[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]
Then,take the square root of the discrimant.
[tex] \sqrt{64} = 8[/tex]
Finally, add -b.
[tex] - (4 + 2 \sqrt{7} )[/tex]
So our possible root is
[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]
Which simplified gives us
[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]
Rationalize the denominator.
[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]
Which simplified gives us
[tex] \frac{6 + \sqrt{7} }{29} [/tex].
6. The answer is 2.
9514 1404 393
Answer:
5. x = (6 +√7)/29; a=6, b=1, c=29
6. x = 2
Step-by-step explanation:
5.The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.
[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]
__
6.Use the substitution z=3^x to put the equation in the form ...
z² -3z -54 = 0
(z -9)(z +6) = 0 . . . . . factor
z = 9 or -6 . . . . . . . . value of z that make the factors zero
Only the positive solution is useful, since 3^x cannot be negative.
z = 9 = 3^2 = 3^x . . . . use the value of z to find x
x = 2
For the following equation,find y when x = - 3. Then find x when y = 2. Y = 6x + 8
Answer:
When
when x = - 3 then y=. -10
when y = 2 then x =. -1
Please help me solve this guys pleasee im struggling
Answer:
see below
Step-by-step explanation:
y = x^2 +2x - 8
Factor
y = ( x+4)(x-2)
The zeros are
x+4 = 0 x-2 = 0
x= -4 x= 2
(-4,0) (2,0)
The axis of symmetry is 1/2 way between the zeros
(-4+2)/2 = -2/2 = -1
x = -1
The x coordinate of the vertex is at the axis of symmetry
The y value is found by substituting x=-1
y = (-1+4) (-1-2)= 3*-3 = -9
Vertex ( -1,-9)
The domain is all real numbers
The range is from -9 up
y≥ -9 since it opens upward
A contractor construct to build a house in 30 days. He employed 10 men to build the house. After 20 days. They completed only 1 /3 of the total work. How many more men will be required to finish the remaining work within due time?
Answer:
30
Step-by-step explanation:
First, we can say that because the men do 1/3 of the work in 20 days,
for 10 men:
20 days = 1/3 total work
Because we need the house built in 30 days, and 20 days have already passed, we only have 30-20=10 days left. Furthermore, 20/2=10, so in our equation of 20 days = 1/3 total work, we can divide both sides by 2 to get
10 days = 1/6 total work
The amount of work we need to get done in 10 days is (all of it) - (1/3 of total work) = 1 - 1/3 = 2/3 = 4/6
Since 10 men can do 1/6 of the work in 10 days, 10*4 =40 men can do 1/6 * 4 = 4/6 of the work in 10 days. This is the amount of work that needs to get done. Therefore, the contractor needs 40 (total workers) - 10 (current workers) = 30 new workers to finish the remaining work in due time
A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a red marble, and without replacing it, then drawing a blue marble? P(red, blue)
Answer:
P(red, blue) = 1/12
Step-by-step explanation:
The gift shop at a science museum sells lollipops that are made to look like the planets. Each lollipop is shaped like a sphere and has a radius of 12 mm. whats the volume of each lollipop! ANSWER THIS ASAP
Answer:
7238.23
Step-by-step explanation:
v=4/3πrcubed
solve it and get the answer
pls help quick 10 points
Answer:
6.86 to 2DP.
Step-by-step explanation:
7/12 = 4/DC
Cross multiply:
7DC = 4*12
DC = 48/7
= 6.857.
What type of number is 37 + 1?
Choose all answers that apply:
Whole number
Integer
Rational
Irrational
help
Answer:
Irrational
Step-by-step explanation:
The constant [tex]\pi[/tex], or "pi", is an irrational mathematic constant that corresponds to a non-terminating (never-ending decimal). Because there are an infinite number of digits in pi, pi cannot be expressed as a fraction and therefore is irrational.
Multiplying or adding a rational number does not make pi rational, and therefore the desired answer is (D) Irrational.
please help! will mark brainliest
Answer:
x = 67
Step-by-step explanation:
∠ C = ∠ FGD ( corresponding angles )
Consecutive angles in a parallelogram sum to 180° , then
∠ B + ∠ C = 180 , substitute values
73 + x + 40 = 180
x + 113 = 180 ( subtract 113 from both sides )
x = 67
Answer:
Step-by-step explanation:
<B = <GFE The parallelograms are similar.
<GFD + <GFE = 180 Consecutive angles in a parallogram = 180
<GFD = x + 40 Given
FGE = 73 Step One
x + 40 + 73 = 180 Substitution
x + 113 = 180 Subtract 113 from both sides
x = 67
Find f(-2).....................................
Answer:
1/25
Step-by-step explanation:
f(x) = 5^x
Let x = -2
f(-2) = 5^-2
We know a^-b = 1/a^b
f(-2) = 1/5^2
= 1/25
Answer:
[tex]\frac{1}{25} [/tex]
Step-by-step explanation:
[tex]f(x) = {5}^{x} \\ f( - 2) \\ f( - 2) = {5}^{ - 2} \\ = \frac{1}{ {5}^{2} } \\ = \frac{1}{25} [/tex]
Si Juana tiene dos perros y lo simbolizamos y 2p y le regalan un hato y lo simbolizamos por g como se representa en el leguaje algebraico.
A) 3P
B) 3G
C) 2PTG
D) 2P-G
HELPPPPP ASAP!!!! Thx!! and NOOO FILESSSS!! it's on KHAN ACADEMY!!
Answer:
[tex]32[/tex]
Step-by-step explanation:
[tex]x=\dfrac{180-116}{2}=\dfrac{64}{2}=32[/tex]
when a certain number is added to 11 and the result is multiplied by 3, the final result is 45 . find the number
Answer:
4
Step-by-step explanation:
Let the number = x
Added to 11 = 11+x
Multiply result by 3 = 3(11+x)
Final result = 45
Solving
3(11 + x) =45
33 +3x = 45
3x= 45-33
3x=12
X=4 by dividing both side by 3
