The equation of the scatter plot is (a) y = 100x + 2
How to determine the equation of the scatterplot?The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{102 - 2}{1 - 0}[/tex]
m = 100
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 100(x -0) + 2
Evaluate
y = 100x + 2
Hence, the equation of the scatter plot is (a) y = 100x + 2
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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:
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
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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In the image, two circles are centered at A. The circle containing Bwas dilated to produce the circle containing B: What is the scale factor of
the dilation?
OA 1.
OB. 2
OC. 0.5
OD. -0.5
The scale factor of the dilation is 0.5
How to determine the scale of dilation?From the figure, we have the following lengths:
AB = 2
AB' = 1
The scale factor of dilation is then calculated as:
Scale factor = AB'/AB
This gives
Scale factor = 1/2
Evaluate
Scale factor = 0.5
Hence, the scale factor of the dilation is 0.5
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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=60BRANILY FOR CORRECT ANWSER
What is the solution for x2 + 4x < 77? –11 < x < 7 –7 < x < 11 x < –7 or x > 11 x < –11 or x > 7
Answer:
-11 < x < 7
Step-by-step explanation:
Inequalities:x² + 4x < 77
Subtract 77 from both sides
x² + 4x - 77 < 0
To find the zero points (Roots),
Make x² + 4x - 77 = 0
Now find the factors
x² + 11x - 7x - 77 = 0
x(x + 11) - 7(x + 11) = 0
(x +11) (x - 7) = 0
x + 11 = 0 or (x -7) = 0
x = -11 or x = 7
So, the solutions of the inequality is between (-11) and 7
-11 < x < 7
Answer:
x < –11 or x > 7 is the correct answer!!
Step-by-step explanation:
The answer above this was just slightly wrong. I took the exam and put my answer as option b and got it correct. Here is how I solved it correctly!
To solve the inequality x^2 + 4x > 77, we can factor the quadratic expression as (x - 7)(x + 11) > 0
To determine the solution, we consider the signs of each factor:
(x - 7) > 0 and (x + 11) > 0
This means x is greater than 7 or x is less than -11.
So, the simplified solution to the inequality x^2 + 4x > 77 is:
x < -11 or x > 7
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]
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
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
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]
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°
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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There are 1,570 souvenir paperweights that need to be packed in boxes. Each box will hold 17 paperweights. How many boxes will be needed? boxes will be needed to hold all the souvenir paperweights.
Answer:
93 boxes will be needed.
Step-by-step explanation:
Divide 1570 ÷ 17
This gives the answer 92.35
So 92 boxes won't be enough. 0.35 of a box itsn't helpful in the real world. So you need 93 boxes.
i need help i also need answers
Answer:
23
Step-by-step explanation:
Given Shane hits 5 HRs out of 100 At-bats,
[tex]\frac{x}{460} = \frac{5}{100} \\\frac{x}{460} (460) = \frac{5}{100} (460)\\x = 23[/tex]
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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The diameter of a circle is 50 m. Find its area to the nearest whole number.
How do I Solve this equation
Hey there!
Solve for f :
Answer :f = 27.9 ✅
Explanation:> Given expression :
[tex] \displaystyle \frac{f}{9} = 3.1 \\ \\ [/tex]
> Multiply both sides by 9 :
[tex] \displaystyle \frac{f}{9} \times \red{9} = 3.1 \times \red{9} \\ \\ \Longrightarrow \boxed{ \green{f = 27.9}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore, our answer is f = 27.9
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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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P = 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 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:
One number is 2 more than 2 times another their product is 40 find the numbers
Answer:
10 and 4; and -8 and -5.
A breakfast bar comes in two sizes. The 5-ounce bars come in a box of 10. A box of the 7-ounce has 6 bars. The 5-ounce bar contains 15 grams of dietary fiber. How many grams of dietary fiber are in one box of the 7-ounce bars?
126 Grams Per Box
Step-by-step explanation:
15 grams of fiber / 5 ounces = 3 grams
3g X 7oz = 21g
21g X 6b = 126g
G - Grams
Oz - Ounces
B - Bars
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!
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
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:
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
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 ^^)
8. Write the equation of the line in slope-intercept form that has the following points: (4, 5) (-1,2)
Answer: y = 3/5x + 13/5
Step-by-step explanation:
To solve this you would have to use slope-point form Y − y1 = m(x − x1)
In this case, you would plugin your x and y values from your 1 point. It would look something like this. y - 2 = m(x + 1). But now the issue is we don't know our slope, To find out a slope you would use 2 - y1/x2 -x1 which would be 3/5 so, in the end, the equation would look like y - 2 = 3/5 (x + 1). Now solve for Y and your answer would be y = 3/5x + 13/5
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.
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]