The average rates of change of f(x) and their corresponding intervals are given as:
Interval Rate of Change
[-5, -1] -8
[-4, -1] -7
[-3, 1] -4
[-2, 1] -3.
What is the explanation for the above?Step 1 - See Table Attached
Step 2 - State the formula for rate of change
The formula for rate of change is given as:
= [change in f(x)] / [change in x]
a) For interval [5, -1] ⇒
Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]
= [-1 - 35] / [-1+5]
= -36 / 4
= - 8
b) For interval [-4, -1] ⇒
rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]
= [3 - 24] / [-1 + 4]
= -21/3
= - 7
c) interval [-3,1] ⇒
rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]
= [-1 - 15] / [1 + 3]
= -16/4
= - 4
d) interval [-2,1] ⇒
rate of change = [f (1) - f(-2)] / [1 - (-2)]
= [ -1 - 8] / [1 + 2]
= -9/3
= -3
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x/7 ≥ -6 solve for x please
x/7 >= -6
x×1/7 >= -6
x>= -6 ÷ 1/7
x>= -6× 7/1
x>= -6×7/1
x>= -42
A researcher asks the first 10 people he meets at a shopping mall about their opinions on a certain brand of shampoo. This is an example of a ________________.
A. self-selecting sample
B. convenience sample
C. random sample
D. systematic sample
Answer:
i believe the answer is A
Step-by-step explanation:
Please Urgent help,,,,
Answer:
This is the i-ready test, you have to try your best because if someone were to give you the answer, that will be cheating. The test provides teachers with a complete picture of student performance relating to their grade level and national norms. So, just try your best so you can get the lessons that are right for you.
(Im just saying but you don't have to listen to me ^^)
The equation x2 - 10x + 17 = - y2 - 2y describes a circle in the coordinate plane. Find the radius of the circle and the coordinates of its center.
Answer:
the center is (5,-1) and the radius is 3
Step-by-step explanation:
An arithmetic sequence has a first term of 4 and a common difference of 3. What is the 20th term
of the sequence?
Answer:
61
Step-by-step explanation:
aₙ = a₁ + (n - 1)d
aₙ = 4 + (20 - 1)3
aₙ = 4 + (19)3
aₙ = 4 + 57
aₙ = 61
The function h(x) = 1/4 |x| is a transformation of the absolute value parent
function, f(x) = |x|. Which graph shows h(x)?
The graph which shows the function h(x) according to the task content is; Choice B.
Which graph shows the function h(x)?It follows from the task content that the function h(x) = f(x)/4.
On this note, it follows that the values of h(x) in each case is one-fourth of the value of f(x).
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( Brain + 100 points ) A triangle has an area of 30 cm squared. What might the base and height be? Give 3 examples.
[tex]\text{The base and height have to be factors of 60, since}\\\\~~~~~~~~\text{Area}= \dfrac{1}{2} \times \text{Base} \times \text{Height}\\\\\implies 30 = \dfrac 12 \times \text{Base} \times \text{Height}\\\\\implies \text{Base} \times \text{Height}= 60[/tex]
[tex]\textbf{Example 1:}\\\\\text{Height} = 6~ cm \\\\\text{Base} = 10~ cm\\\\\text{Area} = \dfrac 12 \times 6 \times 10 = 30~ cm^2\\\\\textbf{Example 2:}\\\\\text{Height} = 5~ cm\\\\\text{Base} = 12~ cm\\\\\text{Area} = \dfrac 12 \times 12 \times 5 = 30~ cm^2\\\\\textbf{Example 3:}\\\\\text{Height} =4~ cm\\\\\text{Base} = ~15 ~cm\\\\\text{Area} = \dfrac 12 \times 15 \times 4 = 30~ cm^2[/tex]
Let's see
Base be B
Height be H
So
1/2BH=30BH=2(30)BH=60The ppossible values are
B=6,H=10H=6,B=10H=3,B=20B=3,H=20B=2,H=30H=2,B=30H=1,B=60B=1,H=60P = 3t² + 7t
Work out the value of P when t = -4
Answer:
P = 20
Step-by-step explanation:
Hello!
We can solve this by substituting -4 for t.
EvaluateP = 3t² + 7tP = 3(-4²) + 7(-4)Remember that any negative number squared is the absolute value of that number squared.
P = 3(|-16|) - 28P = 3(16) - 28P = 48 - 28P = 20The final evaluation is 20.
) A philanthropist pledges to donate 12% of
a fund each year. If the fund initially has
$681,000.00, how much will the fund
have after 9 years?
answer 7344012
percent *612000 =
(12:100)*612000 =
(12*612000):100 =
7344000:100 = 73440
Now we have: 12 percent of 612000 = 73440
Question: What is 12 percent of 612000?
Percentage solution with steps:
Step 1: Our output value is 612000.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$612000=100\%$.
Step 4: Similarly, $x=12\%$.
Step 5: This results in a pair of simple equations:
$612000=100\%(1)$.
$x=12\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{612000}{x}=\frac{100\%}{12\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{612000}=\frac{12}{100}$
$\Rightarrow x=73440$
Therefore, $12\%$ of $612000$ is $73440$
6 Silas lost 11 pounds in a year after joining the basketball team and now
weighs 88 pounds. Find the ratio of his current weight to his weight before
he joined the basketball team. Express the ratio in simplest form.
Answer:
8:9
Step-by-step explanation: Add 88+11 to get his weight before=99 Pounds. Then you put together the ratio. 88:99.
The GCF for those numbers would be 11, so divide them both by 11, to get a final answer of 8:9
translate the equation 49 is what percent of 66?
Answer:
49 ÷ 66 × 100= x
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Match the polar equations to their rectangular forms.
Answer:
C, A, E, B, D
Step-by-step explanation:
The conversion relations between rectangular and polar coordinates can be used to find the polar coordinate equivalents. Those relations are ...
x = r·cos(θ)y = r·sin(θ)x² +y² = r²__
x = 2Using the expression for x, this is ...
r·cos(θ) = 2
r = 2/cos(θ) . . . . divide by cos(θ)
r = 2·sec(θ) . . . . use the trig identity
__
x²+y²=36From above, this becomes ...
r² = 36
r = 6 . . . . . . take the square root
__
x²+y²=2yFrom above, this becomes ...
r² = 2·r·sin(θ)
r = 2·sin(θ) . . . . . . divide by r
__
x=√3yUsing the above relations, this is ...
r·cos(θ) = √3·r·sin(θ)
1/√3 = sin(θ)/cos(θ) . . . . . . divide by √3·r·cos(θ)
tan(θ) = 1/√3 ⇒ θ = arctan(1/√3)
θ = π/6
__
x=yFrom above, this is ...
r·cos(θ) = r·sin(θ)
1 = sin(θ)/cos(θ) = tan(θ) . . . . divide by r·cos(θ)
θ = arctan(1)
θ = π/4
_____
Additional comment
An equation of the form y = kx defines a line through the origin and through opposite quadrants of the Cartesian plane. Above, we found the equivalent polar equation to be θ = arctan(k). Using the principal branch of the arctangent function, this is the equation of a ray.
However, the tangent function is periodic with period π, so θ = arctan(k)+π is also an equivalent to the rectangular equation. It is the opposite ray, so forms the complete line when joined with the first ray.
The correct answer for the polar coordinates will be C, A, E, B, D
What is a polar coordinate system?
The polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane. The pole is the reference point, and the polar axis is the ray from the pole in the reference direction.
The conversion relations between rectangular and polar coordinates can be used to find the polar coordinate equivalents. Those relations are ...
x = r·cos(θ)
y = r·sin(θ)
x² +y² = r²
x = 2
Using the expression for x, this is ...
r·cos(θ) = 2
r = 2/cos(θ) . . . . divide by cos(θ)
r = 2·sec(θ) . . . . use the trig identity
x²+y²=36
From above, this becomes ...
r² = 36
r = 6 . . . . . . take the square root
x²+y²=2y
From above, this becomes ...
r² = 2·r·sin(θ)
r = 2·sin(θ) . . . . . . divide by r
x=√3y
Using the above relations, this is ...
r·cos(θ) = √3·r·sin(θ)
1/√3 = sin(θ)/cos(θ) . . . . . . divide by √3·r·cos(θ)
tan(θ) = 1/√3 ⇒ θ = arctan(1/√3)
θ = π/6
x=y
From above, this is ...
r·cos(θ) = r·sin(θ)
1 = sin(θ)/cos(θ) = tan(θ) . . . . divide by r·cos(θ)
θ = arctan(1)
θ = π/4
However, the tangent function is periodic with period π, so θ = arctan(k)+π is also equivalent to the rectangular equation. It is the opposite ray, so forms the complete line when joined with the first ray.
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EASY POINTS EVALUATION
Answer:
[tex] \frac{4}{9} [/tex]
Step-by-step explanation:
[tex]( \frac{16 {}^{ \frac{1}{2} } }{81 { }^{ \frac{1}{2} } }) \\ ( \frac{ {4}^{2 \times \frac{1}{2} } }{9^{2 \times \frac{1}{2} } }) \\ ( \frac{4^{1} }{9 ^{1} } ) \\ \frac{4}{9} [/tex]
[tex]: \: \implies \: \sf{ \bigg( \dfrac{4 {}^{2} }{9 {}^{2} } \bigg) } {}^{ \frac{1}{2} } \\ \\ : \: \implies \: \sf{ \bigg( \dfrac{4 {}^{ \: 2 \times \frac{1}{2} } }{9 {}^{ \: 2 \times \frac{1}{2} } } \bigg) } \\ \\ : \: \implies \: \sf{ \bigg( \dfrac{4 {}^{ \: \cancel2 \times \frac{1}{ \cancel2} } }{9 {}^{ \: \cancel2 \times \frac{1}{ \cancel2} } } \bigg) } \\ \\ : \: \implies \: \sf{ \bigg( \dfrac{4 {}^{ \: 1 }}{9 {}^{ \: 1 } } \bigg) } \\ \\ : \: \implies \: \red{\bf{ \bigg( \dfrac{4 }{9 } \bigg) } }[/tex]
Read the excerpt from "On Beholding the Mountain."
Yes! The poor heart I used to think so brave
Is all afire, though none the flame may see.
Like to the salt-kilns there by Tsunu's wave,
Where toil the fisher-maidens wearily.
Identify the metaphor and its purpose.
The heart is a salt-kiln and reflects the intesity of pain.
The flames allow the heart to see.
The heart's flame serves as a symbol of hope for the fisherman.
The heart's flame illustrates the intensity of the writer's emotion.
The metaphor and its purpose from the excerpt from "On Beholding the Mountain" is "The heart's flame illustrates the intensity of the writer's emotion".
What is metaphor?A metaphor is a figure of speech which is used to compare two things without using "like" or "as", by making the object of the metaphor take on the characteristic of the other thing.
It is also the use of a word or phrase to refer to something that it is not, invoking a direct similarity between the word or phrase used and the thing described but without the words like or as, which would imply a simile.
Therefore, the correct answer is option D; The heart's flame illustrates the intensity of the writer's emotion.
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Simplify this algebraic expression completely.
7x-5(x+6)
A. 2x-1
B. 2x+1
C. 2x+11
D. 2x-30
Answer:
D. 2x-30
Step-by-step explanation:
7x-5(x+6)
7x-5x-30
2x-30
CAN SOMEONE PLEASE PLEASE PLEASE HELP ME, YOU’LL GET FREE EASY POINTS IF YOU GIVE ME THE RIGHT ANSWER !!
Answer:
1. Reflection
2. G` will coincide with A, because having a reflection along with BC would mean G` directly goes on A.
3. GBC is congruent to triangle ABC because triangle GBC and triangle ABC have the same exact line measurements, and angles, and share a line.
Step-by-step explanation:
I don't know your notes on 6/3 so number 3 might not be 100% correct.
Answer:
reflection across BCthe image of a vertex will coincide with its corresponding vertexSSS: AB≅GB, AC≅GC, BC≅BC.Step-by-step explanation:
We want to identify a rigid transformation that maps congruent triangles to one-another, to explain the coincidence of corresponding parts, and to identify the theorems that show congruence.
__
1.Triangles GBC and ABC share side BC. Whatever rigid transformation we use will leave segment BC invariant. Translation and rotation do not do that. The only possible transformation that will leave BC invariant is reflection across line BC.
__
2.In part 3, we show ∆GBC ≅ ∆ABC. That means vertices A and G are corresponding vertices. When we map the congruent figures onto each other, corresponding parts are coincident. That is, vertex G' (the image of vertex G) will coincide with vertex A.
__
3.The markings on the figure show the corresponding parts to be ...
side AB and side GBside AC and side GCangle ABC and angle GBCangle BAC and angle BGCAnd the reflexive property of congruence tells us BC corresponds to itself:
side BC and side BCThere are four available congruence theorems applicable to triangles that are not right triangles
SSS -- three pairs of corresponding sidesSAS -- two corresponding sides and the angle betweenASA -- two corresponding angles and the side betweenAAS -- two corresponding angles and the side not betweenWe don't know which of these are in your notes, but we do know that all of them can be used. AAS can be used with two different sides. SAS can be used with two different angles.
SSS
Corresponding sides are listed above. Here, we list them again:
AB and GB; AC and GC; BC and BC
SAS
One use is with AB, BC, and angle ABC corresponding to GB, BC, and angle GBC.
Another use is with BA, AC, and angle BAC corresponding to BG, GC, and angle BGC.
ASA
Angles CAB and CBA, side AB corresponding to angles CGB and CBG, side GB.
AAS
One use is with angles CBA and CAB, side CB corresponding to angles CBG and CGB, side CB.
Another use is with angles CBA and CAB, side CA corresponding to angles CBG and CGB, side CG.
Nasir is laying out a garden in the shape of a right triangle. he draws it on the coordinate grid below. The three vertices of his garden are at the points A (-3,-4), B(6, -4), and C (6,8). he wants to enclose the garden with a fence that runs along its perimeter. how many feet of fencing will Nasir needs?
Step-by-step explanation:
it is not important that the triangle is right-angled.
but the distance between each pair of points is calculated via Pythagoras
c² = a² + b²
with c being the Hypotenuse (baseline opposite of the 90° angle) = distance between the end points, and a and b are the legs (= the x and y coordinate differences of the 2 end points) of the virtual right-angled triangles between each pair of points.
so,
AB² = (6 - -3)² + (-4 - -4)² = 9² + 0² = 81
AB = 9 ft
BC² = (6 - 6)² + (8 - -4)² = 0² + 12² = 144
BC = 12 ft
and now for AC, which is because of the special case of how the main triangle is placed and oriented, the same calculation as with Pythagoras for the main right-angled triangle. but I keep showing you the point distance calculation, because this is what you will need in the future for more general triangle or other shapes calculations :
AC² = (6 - -3)² + (8 - - 4)² = 9² + 12² = 81 + 144 = 225
AC = 15 ft
so, Nasir will need
9 + 12 + 15 = 36 ft
of fencing.
A 20-foot guy (support) wire is being used to support a flag pole. The distance from the flagpole to where the guy wire is bolted to the
ground is 9 feet. What is the measure of the angle formed by the guy wire and the ground where the wire is bolted? Round your
answer to two decimal places.
Answer:
ok so i think its a becuase thats wgat i got
Step-by-step explanation:
For a monthly family cookout, David
buys 3 packages of hot dogs and 4
packages of hamburger patties.
Hot dog packages each contain a hot
dogs. Hamburger packages each
contain y hamburger patties.
Complete the expressions for the total number of hot dogs and hamburger
patties David buys for 6 cookouts.
Use the number pad to enter your answers in the boxes.
6(
x+
Answer:
help me to find Xian pleaseee:( i miss him so much:(
sorry for answering Non sense po i hope u understand me ty po!
Solve, using the substitution method.
x = 10
y = 2x – 6
(10, 14)
(10, 4)
(10, –4)
(10, –1)
Answer:
(10, 14)
Step-by-step explanation:
Hello there!
Given such a problem, we have been told to use substitution method to solve it.
To cut it short, substitution refers to replacing a variable with a value.
Here is a way to solve this problem even in future:
simplify the equation givensolve the equation for the variable x or ysubstitute as step 2 above for the other variablesolve the newly obtained equationand finally solve the equation to find the value of variable not yet obtained.Back to our problem,
y = 2x - 6, x = 10
Substitute x into equation y = 2x - 6
y = 2(10) - 6
= 20 - 6
= 14
. ° . x = 10, y = 14
Variables in terms of x and y
(x, y) = (10,14) ✓
This is our answer.
I hope this helps.
Have a nice studies.
A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets. There were more student tickets sold than adult tickets. How many adult tickets were sold?
A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets is mathematically given as
How many adult tickets were sold?Generally, the equation for a sold tickets is mathematically given as
S=x+72
Therefore
x+x+72=772
2x+72=772
2x=772-72
x=350
In conclusion, tickets sold was
x=350
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Bring to Standard form -2k^3-k^3+8k
Answer:
-3k^3+8k
Step-by-step explanation:
-2k^3-k^3+8k
Combine like terms
-3k^3+8k
Answer: Standard Form: [tex]-3k^3+8k[/tex]
Step-by-step explanation:
[tex]-k*(3k^2-8)=-3k^3+8k[/tex]
Step 1:
[tex]((0 - 2k^3) - k^3) + 8k[/tex]
Pull out like factors, Pulling out like terms: [tex]8k - 3k^3 = -k[/tex] • [tex](3k^2 - 8)[/tex]
Factoring: [tex]3k^2 - 8[/tex]
Final result:
[tex]-3k^3+8k[/tex]
the diagram shows a right angled triangle. 9cm 15cm x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
Answer:
31°
Step-by-step explanation:
As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.
=============================================================
Solving :
⇒ tan x° = 9/15
⇒ tan x° = 3/5
⇒ x = tan⁻¹ (0.6)
⇒ x = 31°
The size of the unknown angle "x"
Solution:We'll have to check which is the appropriate one from SOHCAHTOA.
In this question we'll have to use tan because opposite and adjacent is given.
[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]
Substitute according to the formula.
[tex]tan \: x= \frac{9}{15}[/tex]
We'll have to use tan inverse.
[tex]x={tan}^{-1}(\frac{9}{15})[/tex]
[tex]x=30.96375653[/tex]
[tex]\large\boxed{x=31° }[/tex]
Hence, the size of the unknown angle "x" is 31°
One number is 2 more than 2 times another their product is 40 find the numbers
Answer:
10 and 4; and -8 and -5.
major each of the following angles write it measures right weather it is acute ,obtuse, right angle A straight angle or a reflex angle
Answer:
i = right angle
ii = obtuse angle
iii = straight angle
iv = obtuse angle
v = acute angle
Step-by-step explanation:
an acute angle is an angle less than 90 degrees
an obtuse angle is an angle more than 90 degrees
a right angle is an angle equivalent to 90 degrees (looks like two straight lines perpendicular)
a straight angle is an angle equivalent to 180 degrees (looks like a straight line)
a reflex angle is an angle greater than 180 degrees
so, ...
i = right angle
ii = obtuse angle
iii = straight angle
iv = obtuse angle
v = acute angle
How to solve this problem for my algebra class
Answer: it suggests that this equation has no remainder and that the value of x is the factor.
The ratio of the one leg of
the right triangle to the other
leg of the right triangle must
be 8:7. Determine the
greatest length of one leg of
the right triangle given the
other leg of the right triangle
is 10.5 feet.
The legs of the triangle are 6.91 feet, 7.9 feet, and 10.5 feet.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The ratio of the one leg of the right triangle to the other leg of the right triangle must be 8:7.
Let x be one leg and y be another leg. Then we have
x/y = 8/7
y = 7x/8
Then the greatest length of one leg of the right triangle given the other leg of the right triangle is 10.5 feet will be
10.5² = x² + (7x/8)²
110.25 = x² + 49x²/64
110.25 = 113x²/64
x² = 62.44
x = 7.902
x ≅ 7.9 feet
Then the other leg will be
y = 7.9 x 7 / 8
y = 6.91
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Find it and give me a step by step explanation thank you
Answer:
50.13
Step-by-step explanation:
We can easily find the area of our square, so to get that over with, 6*6=36. Now, for our circle, a full circle would be A=pi*r^2, but we only have half a circle. That means our equation will be A= 1/2(pi*r^2). We have our diameter, but we need our radius. Radius is just half the diameter, so 6/2=3. Now, we multiply. 3^3 is 9, and 9*3.14 is 28.26. All we have to do now is divide that by 2. If we do that, we get 14.13. The area of the semi-circle is 14.13. But we still have to add it to the area of the square, which will be our final step. 36+14.13=50.13, which is your area.
Hope this helps!
There are 97 students in South High School. South High School offers only Chinese and Spanish. There are 5 more students in Chinese than in Spanish, and every student takes at least one language. If 41 students take only Spanish, then how many take both languages?
Answer:
5
Step-by-step explanation:
Spanish: 46
Chinese: 51
Both languages: 46 - 41 = 5
Hope this helps
Using the figure below, if the m21= 55°, what is the m2?
Answer: [tex]125^{\circ}[/tex]
Step-by-step explanation:
Angles that form a straight angle are supplementary, so:
[tex]m\angle 1+m\angle 2=180^{\circ}\\ \\ 55^{\circ}+m\angle 2=180^{\circ}\\ \\ m\angle 2=\boxed{125^{\circ}}[/tex]