(a) Find the slope of the curve y= x^2 - 2x - 3 at the point P(2, -3) by finding the limit of the secant slopes through point P.
(b) Find an equation of the tangent line to the curve at P(2, -3)
Answer:
Step-by-step explanation:
P=(2,-3)
Q=(a,a²-2a-3)
[tex]\Delta y=a^2-2a-3-(-3)=a^2-2a\\\Delta x=a-2\\\\\displaystyle \lim_{a \to 2} \dfrac{a^2-2a-3-(-3)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a^2-2a}{a-2} \\\\=\lim_{a \to 2} \dfrac{a(a-2)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a}{1} \\\\=\lim_{a \to 2} a \\\\=2\\[/tex]
Proof:
y'=(x²-2x-3)'=2x-2
y'(2)=2*2-2=2
hiiiii please help me!!!!
Answer:
-i
Step-by-step explanation:
'i' is the square root of -1, so i^2 would be -1. so now:
[tex]i^3 = (i^2)i = (-1)i = -i[/tex]
Slope-Intercept
Functions
Acellus
Find the equation to the line below.
1
Answer:
y=4x+1
Step-by-step explanation:
First the slope of the line is 4. The equation of the line is y-1=4x, y=4x+1
Which value of q is a solution to this equation?
q
-- = 2
9
answers:
A: q=4
B: q=0
C: q=2
D: q=6
Can somebody please help? I been struggling to answer this!
Answer:
the first option is the answer. I am sure of this
Answer:
the first option is the answer
If JL = 8x-3 and LK = 4x + 57, Find JK
Answer: JK = 234
Concept:
Here, we need to know the idea of the segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
PART I: Find the value of xGiven information
JL = 8x - 3
LK = 4x + 57
Given expression deducted from the given figure
JL = LK
Substitute values into the expression
8x - 3 = 4x + 57
Add 3 on both sides
8x - 3 + 3 = 4x + 57 + 3
8x = 4x + 60
Subtract 4x on both sides
8x - 4x = 4x + 60 - 4x
4x = 60
Divide 4 on both sides
4x / 4 = 60 / 4
x = 15
-------------------------------------------------------------------------------
PART II: Find the value of JKGiven information
JL = 8x - 3
LK = 4x + 57
x = 15
Given expression deducted from the segment addition postulate
JK = JL + LK
Substitute values into the expression
JK = 8x - 3 + 4x + 57
JK = 8(15) - 3 + 4(15) + 57
Simplify by multiplication
JK = 120 - 3 + 60 + 57
Simplify by simple operation (addition/subtraction)
JK = 117 + 60 + 57
JK = 177 + 57
[tex]\boxed{JK=234}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Lynn regularly works a 40-hour week and earns $14 per hour. She receives time-and-a-half pay for each hour of overtime she works. Last week she worked 43 hours.
a) What was her regular pay for the week?
b) | What is her hourly overtime rate?
c) What was her overtime pay for the week?
d) What was her total gross pay for the week?
e) What was her approximate NET pay for the week?
Answer:560
Step-by-step explanation:
Find the distance between X(-3, 8) and Z(-1,5) *
what is it :’)
1.) √12 is a natural, whole, integer, rational or irrational number
What angles would have to be congruent to prove the triangles are congruent by SAS?
A. AEB = CED
B. AEB = DEC
C. ECD = EAB
D. CDE = ABE
If m ZABD = 83º, what are mZABC and m ZDBC?
3x+33° D
(Ex-6)°
B
mZABC = °
Answer:
∠ ABC = 48°
Step-by-step explanation:
∠ ABC + ∠ DBC = ∠ ABD , that is
6x - 6 + 3x + 8 = 83
9x + 2 = 83 ( subtract 2 from both sides )
9x = 81 ( divide both sides by 9 )
x = 9
Then
∠ ABC = 6x - 6 = 6(9) - 6 = 54 - 6 = 48°
Calculate the volume of the cylinder & Pie = 3.14 Zom 10cm and radius 7cm
Answer:
1538.6cm^3
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
Find the solution to the system of equations below
y=-5x+3
2x-3y=8
Answer: (1, -2)
Concept:
There are three general ways to solve the system of equations:
Elimination SubstitutionGraphingHere, we are going to use the elimination method to solve.
Solve:
Given
[tex]\left \{ {{y=-5x+3} \atop {2x-3y=8}} \right.[/tex]
Convert the first equation's arrangement to correlate with the second equation
[tex]\left \{ {{5x + y=3} \atop {2x-3y=8}} \right.[/tex]
Multiply 3 on both sides in the first equation
[tex]\left \{ {{15x + 3y=9} \atop {2x-3y=8}} \right.[/tex]
Eliminate [y] by adding the two equations
[tex]17x = 17[/tex]
Divide both sides by 17
[tex]17x / 17=17/17[/tex]
[tex]x=1[/tex]
[tex]y=-5x+3=-5(1)+3=-5+3=-2[/tex]
[tex](1, -2)[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Simplify the radical expression.
[tex] \sqrt{40} [/tex]
Answer:
√40 = √ ( 2× 2 ×2 ×5) = 2√10
.........
Which one does not belong? Explain your reasoning.
Answer:
17
Step-by-step explanation:
17 is the only prime number present.
Answer:
17 does not belong
Step-by-step explanation:
In this image (and problem), 17 is the only prime number there.
Hopefully this helped you out!
1.) 10 is a natural, whole, integer, rational or irrational number
Answer:
10 is whole number .......
yes ten is natural,whole, integers,rational
Step-by-step explanation:
because natural contains all numbers wiThout 0 and whole contains all numbers with 0 so 10 is both of them.Integers are the number which is not a fraction,it is a whole number.And 10 is a rational number because all integers are rational.But it is not irrational.
An angle measures 46° more than the measure of its complementary angle. What is the
measure of each angle?
Answer:
Angle + the Complementary angle = 90 degrees. Let x be the measure of the angle under the question. Then the measure of the Complementary angle is (x+46) degrees, and you have this equation x + (x+46) = 90, or 2x+ 46 = 90, or 2x = 90 - 46 = 44. Then x =  = 22. The given angle has the measure of 22 degrees. The complementary angle is 90-22 = 68 degrees. Check. 68 - 22 = 44 degrees. Correct !!
write each fraction number as a decimal 2 1/8
Answer:
2 1/8 as a decimal is 2.125
Step-by-step explanation:
Answer:
2.125
Step-by-step explanation:
To find the decimal version of the fraction number, you need to divide 1/8, which is .125; combining that with the original whole number, you get 2.125.
polygons are similar find the scale factor of the smaller figure to the larger figure
Answer:
Step-by-step explanation:
(70 POINTS + BRAINLYIEST)
Solve Geometric Sequence:
243, ___, ___, ___, ___, ___, 1/3
Solve for middle terms + r (common ratio)
Hi! I'm happy to help!
To solve this, we first need to find our what could give us 1/3. WE realize that the sequence is descending, so we must be dividing. We can then, from here, multiply our top number by 1/3, because that is our end number, and could possibly work for our common ratio. From this, we can check if this fits in our equation. (dividing by 3)
243×1/3=81
81×1/3=27
27×1/3=9
9×1/3=3
3×1/3=1
1×1/3=1/3
We can check if this is the correct amount of numbers that would fit into the geometric sequence. Let's see if this fits in:
243, 81, 27, 9, 3, 1, 1/3
This does fit into our geometric sequence. Our middle terms are underlined. (missing numbers)
Our common ratio is the number we multiply the previous number by to get our next, so our common ratio is 1/3.
So, our geometric sequence is 243, 81, 27, 9, 3, 1, 1/3, our middle terms are 81, 27, 9, 3, and 1. Our common ratio is 1/3.
I hope this was helpful, keep learning!
Answer:
Middle terms 81, 27, 9, 3, 1 or -81, 27, -9, 3, -1Common ratio 1/3 or -1/3Step-by-step explanation:
Given:
t₁ = 243, t₇ = 1/3To find the terms in between.
Find the common ratio first:
tₙ = t₁rⁿ⁻¹1/3 = 243*r⁶r⁶ = 1/729r = [tex]\sqrt[6]{1/729}[/tex]r = ± 1/3The terms in between are:
t₂ = 243*1/3 = 81 or -81t₃ = 81*1/3 = 27 t₄ = 27*1/3 = 9 or -9t₅ = 9*1/3 = 3t₆ = 3*1/3 = 1 or -15.04 x 104 =
200.8
504
5,044
50,400
none of these
Answer:
none of these
Step-by-step explanation:
5.04*100=524.16
Answer:
none of these
Step-by-step explanation:
5.04 x 104 = 524.16
there is no option with 524.16
so none of these
A Cheetah running at 61 miles per hour is chasing an American Antelope that is running
at a rate of 1583 meters per minute.
Which animal is running at a faster rate?
Answer:
Cheetah
Step-by-step explanation:
American Antelope's speed = 94980 meters per hour
= 59 miles per hour
The Cheetah is faster than the American Antelope
Answer:
Step-by-step explanation:
The American Antelope is going at a rate of 1583 meters / minute
1583 m [ 1 km / 1000 m ] = 1.583 km / minutes
In an hour, the Antelope will go 1.583 km / minute * 60 min / hour
1.583 * 60 = 94.98 km / hour
The cheetah is going 61 miles / hour * 1.6 km / mile = 97.6 km/hour
The Cheetah is not going to go hungry tonight.
Are Quadrilaterals A and C congruent??
Answer:
It turns out that knowing all four sides of two quadrilaterals are congruent is not enough to conclude that the quadrilaterals are congruent. Unlike with triangles, some information about angles is needed in order to conclude that two quadrilaterals are congruent. I will give you the video that might be helpful. I dont own the video but i hope it helps you . <3
Step-by-step explanation:
https://www.khanacademy.org/math/cc-fifth-grade-math/properties-of-shapes/imp-quadrilaterals-2/v/quadrilateral-types-exercise
For the function f(x) = −2x − 9, identify the values of f(0), f(1/2), and f(−2)
Step-by-step explanation:
f(0)=-2(0)-9=0-9=-9
f(1/2)=-(1/2)-9=-1/2 -9=-19/2
f(-2)=-2(-2)-9=4-9=-5
Answer:
f(0) = -9f(1/2) = -10f(-2) = -5Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Question One. Identify the value of f(0)
f(x) = -2x - 9
f(0) = -2(0) - 9
f(0) = 0 - 9
f(0) = -9
Question Two. Identify the value of f(1/2)
f(x) = -2x - 9
f(1/2) = -2(1/2) - 9
f(1/2) = -1 - 9
f(1/2) = -10
Question Three. Identify the value of f(-2)
f(x) = -2x - 9
f(-2) = -2(-2) - 9
f(-2) = 4 - 9
f(-2) = -5
Hope this helps!! :)
Please let me know if you have any questions
62.9042 to the nearest hundredth
Answer:
62.9
Step-by-step explanation:
In a hotel, 40 people occupy excatly 26 rooms. Each room is occupied by either one or two people. How many rooms are occupied by exactly one person?
Explanation:
Let's say that the first 26 people will occupy each of the 26 rooms. This means that, so far, there's one person per room.
There are 40-26 = 14 people left. Let's say those 14 people occupy the first 14 rooms. This means that the first 14 rooms now have 2 people in them per room. The remaining 26-14 = 12 rooms still have one person per room.
Find the difference. 87,000,000,976 – 6,998,765,824
Answer:
80001235152
Step-by-step explanation:
hope this helped!
CAN SOMEONE TAKE A QUICK LOOK AT THIS AND HELP ME OUT
Answer:
9/79/169%, 523.2, 458 (to 3sf)
Step-by-step explanation:
Example 1:
16/169×100%=9/79/169% of the students
Example 2:
87.2%×600=523.2 students
Example 3:
27.3%=125 students
100%=458 students (to 3sf)
Find the height of the triangle by applying formulas for the area of a triangle and
your knowledge about triangles.
A. 5.8 mm
B. 2.0 mm
OC. 4.4 mm
D. 6.2 mm
Answer:
Step-by-step explanation:
a= 12 mm ; b = 16 mm ; c = 18 mm
s = (a + b+c)/2
[tex]=\dfrac{12 + 16 + 8}{2}\\\\= \dfrac{36}{2}\\\\= 18\\\\[/tex]
s -a = 18 - 12 = 6 mm
s -b = 18 - 16 = 2 mm
s -c = 18 - 8 = 10 mm
[tex]area = \sqrt{s(s -a)(s-b)(s-c)}[/tex]
[tex]= \sqrt{18*6*2*10}\\\\= \sqrt{2160 }\\\\=46.47\\\\=46 \ mm^{2}\\[/tex]
[tex]\dfrac{1}{2}* \ base * \ height = 46\\\\\dfrac{1}{2}*16* \ height = 46\\\\height = \dfrac{46*2}{16}\\\\[/tex]
= 5.75
Height = 5.8 mm
Answer:
A. 5.8mm
Step-by-step explanation:
[tex]area \: of \: triangle = \sqrt{s(s - a) \times (s - b) \times (s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{12 + 8 + 16}{2} \\ s = 18 \\ area \: of \: triangle \: = \sqrt{18(18 - 12) \times (18 - 8) \times (18 - 16)} \\ = \sqrt{2160} \\ = 46.47 {m}^{2} \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \\ 46.47 = \frac{1}{2} \times 16 \times h \\ h = \frac{46.47}{8} \\ h = 5.8mm[/tex]
32600÷9330?
Please answer:(
Answer:
3.49410504
It is the answer hope it helps.
Mark me as Brainliest plz
Answer:
3.49410503751
Step-by-step explanation:
But as a smaller version it is
3.494