Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and the range of each function.
y=(x-125)²+125 .
Each function's vertex, axis of symmetry, maximum or lowest value, domain, and range are all described as follows: Vertex: (125,125); range: (125,125); minimum: at y=125; x=125; maximum: no., axis of symmetry is x=125.
Describe Domain and Range.The domain of a function is the set of values that we are allowed to enter into our function.
The set of values that a function can accept as input is known as its range.
According to given data;y=(x-125)²-125
we know that;
y=(x-h)²+k
Vertex: In this form, the vertex (or, in other words, the "pointy bit") is given to us in the (h ,k);here we have (125,125).
Axis of symmetry : Two equal segments of the parabola. It moves straight up and down via the vertex.
Thus, we may formulate an equation for the vertical line that passes through the vertex. It is x=125 in this query..
Maximum and lowest values: Here, we're concerned in examining the vertex to determine whether it is at the maximum or lowest of the parabola's range (i.e., when a negative sign is placed in front of the (x-h) = 0 term, respectively).
Range: The value of range is (125,∞ )
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What is the slope of the line that goes through the points (-4,2) and (8,5)? A. B. C. D.
Answer:
4
Step-by-step explanation:
The slope of the line with points p(x, y) and p′(x′, y′) is given by:
[tex] (\frac{x. \: - \: x}{y. \: \: - y } )[/tex]
[tex] (\frac{8 - ( - 4)}{5 - 2} )[/tex]
12/3
slope = 4
Evaluate -(8/-4) ^2 + 2 - 4^3
Answer:
-(8/-4)² + 2 - 4³ = -66
Step-by-step explanation:
-(8/-4)² + 2 - 4³
Here we need to respect the order of operations.
So ,first we calculate what’s between parentheses :
8/-4 = -2
Then
-(8/-4)² + 2 - 4³ = -(-2)² + 2 - 4³
Then
We calculate the exponent :
(-2)² = (-2) × (-2) = 4
4³ = 4 × 4 × 4 = 64
Then
-(8/-4)² + 2 - 4³ = -4 + 2 - 64
Then
The expression -4 + 2 - 64 contains addition and subtraction.
So ,we start calculating from left to right :
-4 + 2 = -2
Then
-4 + 2 - 64 = -2 - 64 = -66
Conclusion :
-(8/-4)² + 2 - 4³ = -66
ΔE F G is a 30°-60°-90° triangle with m∠ F=90 . Find the coordinates of E in Quadrant III for F(-3,-4) and G(-3,2).FG is the longer leg.
The coordinates of E in Quadrant lll is (3 - [tex]2\sqrt{3}[/tex], -4)
Given,
m < F = 90°
E (x, y) in quadrant lll
F(-3, 4), G(-3, 2)
FG = The longer leg.
FG = [tex]\sqrt{(-3-(-3)^{2} )+(2-(-4)^{2} }[/tex] = [tex]\sqrt{36}[/tex] = 6
FE = [tex]\frac{FG}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }[/tex] = 2[tex]\sqrt{3}[/tex]
GE = 2FE = 2 × 2√3 = 4√3
ΔEFG is a 30° - 60° - 90° triangle with the longest leg FG = 6.
We apply the 30° - 60° - 90° triangle theorem to determine the short side FE and the hypotenuse GE.
l = 4√3
h = 2√3
[tex]\sqrt{(x-(-3))^{2} +(y-(-4))^{2} }[/tex] = (2√3)²
[tex]\sqrt{(x-(-3))^{2} +(y-2)^{2} }[/tex] = (4√3)²
∴ (x + 3)² + ( y + 4)² = 12
(x + 3)² + (y - 2)² = 48
Solving this, we get:
Coordinates of E as (3 - 2√3, -4)
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(15 POINTS PLEASE HURRY!!) Open the parallel lines reflection application. The right set of parallel lines is a reflection across the y-axis of the left set of parallel lines. Click the reflect over y-axis button. Are the two sets of parallel lines the same? What does this mean about how parallel lines change when you reflect them?
Based on the fact that the right line is a reflection across the y-axis, the lines are the same, they are just in a different position.
What is a Reflection?
This refers to the rigid transformation type that is used to represent an image and does not change its size or length of it.
With this understanding, we can see that the pre-image and the image in a rigid transformation are congruent which makes the lines to be the same, even if they are in a different position.
Find the missing term(s) of each arithmetic sequence. -1, □, 11,. . . .
The missing term is 6.
Here the sequence is -1,__, 11...
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Here the sequence is in an arithmetic sequence, as there is a common difference between the two numbers.
To find the nth term of the sequence we have a formula:
[tex]a_{n}[/tex] = a + (n-1)d
From this we can find a common difference, as we know the 3rd term of the sequence.
[tex]a_{3}[/tex] = -1 + (3-1) d
11 = -1 + 2d
2d = 12
d = 6
Now we have to the 2nd term of the series we have
[tex]a_{2}[/tex] = -1 + (2-1) 6
= -1 + 6
= 5
Therefore the 2nd i.e., the missing term of the sequence is 5
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The director of a marching band asks the band members to line up in rows of six, but there are three band members in the last row. Then she tries to line them up in rows of seven, but there are four band members in the last row. Finally, she tries to line them up in rows of eight, but there are five band members in the last row.
The band has fewer than $200$ members.
How many members are there?
Based on the given task content, the number of members in the marching band if the band has fewer than 200 members is 195 members
How to find the number of members in the group?When the band members are told to line up in rows of eight but five is left over. This means the overall number is an odd number.
When they are lined up in rows of six, but three are left over. So, eliminate numbers with 3, 5, 6 ,9, 0.
Finally they are lined up in rows of seven, but four are left over.
So, eliminate numbers with 7 also.
So, all eliminated numbers are : 2,3,4,5,6,7,8,9,10
Left numbers are 1.
Given is that the band has fewer than 100 members. So, it can be 71 ,81 ,91
199, 195, 193, 191
We can check with 81.
81/4 = 20 remainder 1
81/6 = 13 remainder 3
81/7 = 11 remainder 4
So, the answer is 81.
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Ali hypothesized that increasing fertilizer would increase plant growth. Four groups of thirty similar plants were given 0 to 15 ml of fertilizer, as shown in the graph. The change in plant height for each group over a two-week period was averaged and recorded.
Plant Group
Fertilizer Added (mL)
Avg. Growth (cm)
A
0
4
B
5
6
C
10
8
D
15
3
What is the best conclusion based on this data?
The hypothesis was not supported because the data indicated that fertilizing plants does not improve plant growth.
The hypothesis was supported; to get the best growth, use 5 milliliters of fertilizer per plant.
The hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.
The hypothesis was supported; to get the best growth, use 15 milliliters of fertilizer per plant
The conclusion based on this data is that C. The hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.
How to illustrate the information?It should be noted that from the information, the change in plant height for each group over a two-week period was averaged and recorded.
It should be noted that as more fertilizer was added, the height of the plant reduced. This shouldn't be so.
Therefore, the conclusion based on this data is that the hypothesis was not supported; the data indicated that too much fertilizer can inhibit plant growth.
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Answer: C
Step-by-step explanation: Edge 2022
Please help of 3 through 6
Answer:
3, 9% more people have green as their favorite color over yellow. 4. Picture is cut off so I can't see sorry 5. science and social studies 6. Mike spends 40% more time studying math then he does science
Step-by-step explanation:
PLEASE HELP?
Pedro went to the store and spent $36.85. He paid with a $50 bill. How much money will he get back as
change? Show All Your Work for full credit.
Answer:
Step-by-step explanation:
change = dollar_amount - spent_amount
change = 50 - 36.85
change = 13.15
The diagram below shows a large cone divided horizontally into two parts A and B. Given that the vertical height of A and B are equal, and that the volume of A is x cm³. Express the volume of the entire large cone in terms of x. [2] If the volume of part B is 3500 cm³, calculate the volume of cone A. [2]
Answer:
3500cm3
Step-by-step explanation: since A and B are equal, and B has a volume of 3500 cm3 then A will have the same.
Extra: The horizontal measure of A is 1500 and the verticle is 1500
x over 8 = 3 solve for x
Answer:
x = 24
Step-by-step explanation:
[tex]\frac{x}{8}[/tex] = 3 ( multiply both sides by 8 to clear the fraction )
x = 8 × 3 = 24
Answer: 24
Step-by-step explanation:
x/8 = 3
x = 3x8
x = 24
Position and label each triangle on the coordinate plane.
right ΔM N O with right angle at point M and legs of lengths a and 2 a .
We need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).
It is given that Δ MNO with right angle at point M has legs of lengths a and 2a .
We have to position the triangle on coordinate plane.
What is a right angled triangle ?
A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.
As per the question ;
The triangle is a right angle triangle, so it's two sides can be located
on axis.
Place the right angle of the triangle Δ MNO at M.
i.e., M will have coordinates (0,0)
The origin will allow the two legs to be along the x and y-axes , so position the triangle in the first quadrant.
As N is on the y-axis ;
Its x-coordinate will be 0 and the y-coordinate will be a , because the leg is a units long.
i.e., N will have coordinates (0,a)
As O is on the x-axis,
its y-coordinate will be 0 and the x-coordinate will be 2a , because the leg is 2a units long.
i.e.,
O will have coordinate (2a,0)
We can put these coordinates after placing the triangle in the first quadrant i.e., M (0,0) , N (0,a) & O (2a,0).
Thus , we need to position the right triangle Δ MNO in the first quadrant with coordinates , M(0,0) , N (0,a) & O (2a,0).
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After robbing a bank in Dodge City, a robber gallops off at 14 mi/h. 30 minutes later, the marshall leaves to pursue the robber at 16 mi/h. How long (in minutes) after the marshall takes off does it take the marshall to catch up to the robber?
Answer:
Step-by-step explanation:
The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.
How long will it take to catch up with the robber?Let 30minutes = 0.5 hours.
Let x represent the time for which the marshal has ran.
On this note, the robber must have galloped at; (x +0.5) hours.
Hence, it follows from the task content that if they are at the same distance from the bank; we have;
14(x+0.5) = 16(x)
14x + 7 = 16x
7 = 2x
x = 7/2 = 3.5 hours.
= 3.5 × 60minutes = 210minutes.
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Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary.rolling a pair of dice and getting a sum of either 6 or 10
According to the question, to check whether the events are mutually exclusive or not mutually exclusive for the rolling pair of dice to get the total either as six or ten.
What are mutually exclusive events?
Mutually exclusive events are those events which cannot happen at the same time .For instance, in any event nobody can run forward or backward together at the same time.
Rolling a pair of dice to get the sum as 6, then is not mutually exclusive.
The calculation is as shown below:
P(E) = 6+5-1/36
= 10/36
= 5/18
= 27.8 %
Now, rolling a pair of dice to get either the sum as 6 or 10.
P(6 or 10)
= P(6)+P(10)
= 5/36+ 3/36
= 8/36
= 2/9
= 22%
Hence, it is not mutually exclusive event because the calculated percentage is 22%.
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200 learner's in grade 10 class.107 learner's takes history.63 learners take science and 147 learner's take both history and science and how many learner's take neither of the subjects
Answer:
I believe the answer is 30.
Step-by-step explanation:
-
Earth's radius is approximately 6400 kilometers. What are the surface area and volume of the Earth? Round to the nearest tenth if necessary.
The surface area of earth is 514.4million [tex]Km^{2}[/tex] and the volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].
Radius of Earth = 6400 (approximately).
Earth is a sphere. So by using the formula of Surface Area of sphere we can calculate the Surface area of earth as follows,
Surface Area of Earth = 4[tex]\pi r^{2}[/tex] = 4 × (3.14) × [tex](6400)^{2}[/tex]
= 4 × 3.14 × 40960000
= 514457600 [tex]Km^{2}[/tex]
= 514.4million [tex]Km^{2}[/tex]
The surface area of earth is 514.4million [tex]Km^{2}[/tex] .
Similarly, by using the formula of volume of sphere we can calculate the volume area of earth as follows,
Volume of Earth = (4/3)[tex]\pi r^{3}[/tex]
= (4/3)×(3.14)×[tex](6400)^{3}[/tex]
=(1.3333)(3.14)(2.6214 × [tex]10^{11}[/tex])
= 1.0975 × [tex]10^{12}[/tex] [tex]Km^{3}[/tex]
= 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex]
The volume of the Earth is 1.1 ×[tex]10^{12}[/tex] [tex]Km^{3}[/tex].
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COORDINATE GEOMETRY Find the measures of the sides of Δ J K L and classify each triangle by the measures of its sides. (Lesson 4-1)
J(16,14), K(7,6), L(-5,-14)
ΔJKL has sides that are of 70.37 units.
What exactly is a triangle?A triangle is a polygon with three vertices and three edges. It is a fundamental geometric shape.Triangle ABC represents a triangle with three vertices: A, B, and C.Any three non-collinear points define a unique triangle and, by extension, a unique plane in Euclidean geometry.So,
The formula of perimeter: √(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(7−16)²+(6−14)²= 70.37 unitsThen, each side of the triangle will be: 70.37 units
Therefore, ΔJKL has sides that are 70.37 units.
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The distance from Charlotte, North Carolina, to Knoxville, Tennessee, is
2.31 × 10 miles. The distance from Charlotte, North Carolina, to El Paso,
Texas, is about 7 times that distance. What is the approximate distance
from Charlotte to El Paso?
A. 1.62 × 10 miles
B. 9.31 × 10 miles
C. 1.62 × 10 miles
D. 9.31 × 10 miles
The approximate distance from Charlotte to El Paso is 1. 62 × 10 miles . Options A and C
How to determine the distanceFrom the information given, we have that;
Distance from Charlotte, North Carolina, to Knoxville, Tennessee, is 2.31 × 10 milesDistance from Charlotte, North Carolina, to El Paso, Texas, is about 7 times that distanceTo determine the distance from Charlotte to El Pasco, we have the expression
= 7 × distance from Charlotte to Knoxville
Substitute the value
= 7 × 2.31 × 10 miles
= 1. 62 × 10 miles
Thus, the approximate distance from Charlotte to El Paso is 1. 62 × 10 miles . Options A and C
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Owen drove 9 miles total five days this week on Saturday he drove 17 miles to his grandmas house how many total miles did he drive this week
Answer:
26 miles
Step-by-step explanation:
add 9 miles to 17 miles= 26 miles
State the domain and the range.
1. f(x) = x² -1
2. f(x) = 1/ (3x+5)
3. f(x) = x4
4. f(x) = 1/2x
5. f(x) = (9x-7)/3
Step-by-step explanation:
remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).
1.
domain : -infinity < x < +infinity
range : -1 <= y < +infinity
due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...
2.
domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.
the only forbidden value of x is therefore
3x + 5 = 0
3x = -5
x = -5/3
so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)
range : -infinity < y < +infinity
3.
domain : -infinity < x < +infinity
range : 0 <= y < +infinity
due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.
4.
this is 1/(2x) as I understand it.
similar to 2. we must avoid at 1/0 situation.
so, x must not be 0. everything else is possible
domain : (-infinity < x < 0) OR (0 < x < +infinity)
range : -infinity < y < +infinity
5.
everything is allowed and possible.
domain : -infinity < x < +infinity
range : -infinity < y < +infinity
Suppose the production function is given by q = 3k 4l. what is the average product of capital when 10 units of capital and 10 units of labor are employed?
a) 45
b) 3
c) 4
d) 7
The correct option is d) 7.
A production function indicates the proportion of a combination of inputs (labor and capital) that produces a given amount of output. Firms determine the quantity produced given the output price level and the quantity of a combination of input factors provided by the prices of capital and labor. Dividing the output by the number of capital and labor units employed gives the average capital and labor production, respectively.
The production functions,
Q = 3 K + 4 L
k = 10
L = 10
Q = 3 ( 10 ) + 4 ( 10 )
Q = 30 + 40
Q = 70
Average capital production is calculated by dividing output (Q) by the amount of capital used to produce that output (K).
Average capital production = output / capital
= 70 / 10
= 7
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I need help with this question that’s for my geometry class.
By Euclid's axioms we proved that AC=BD
Things which are equal to the same thing are also equal to one another.
If equals be added to equals, the wholes are equal.
If equals be subtracted from equals, the remainders are equal.
Things which coincide with one another are equal to one another.
The whole is greater than the part.
given that , B is in between A and C
and C is between B and D
and also given that AB=CD
let AC=AB+BC .......(1)
BD=BC+CD ........(2)
subtract 1-2
we get, AC-BD=AB+BC-BC-CD
AC-BD=AB-CD
we know AB=CD so we get
AC-BD=0
AC=BD
Hence, Proved
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Answer:
We established that AC=BD using Euclid's axioms.
Step-by-step explanation:
Things that are equivalent to one another are also equivalent to the same object.
The wholes are equal if equals are added to equals.
The remainders are equal when equals are subtracted from equals.
Things are equivalent to one another if they occur simultaneously.
A component cannot possibly equal the whole.
given that , B is in between A and C
and C is between B and D
and also given that AB=CD
let AC=AB+BC .......(1)
BD=BC+CD ........(2)
subtract 1-2
we get, AC-BD=AB+BC-BC-CD
AC-BD=AB-CD
we know AB=CD so we get
AC-BD=0
AC=BD
Hence, Proved
Which value of p is a solution to this equation?
p–6=2
Answer:
[tex] \sf \large \: p = 8[/tex]
Step-by-step explanation:
Let's solve the equation step by step,
p – 6 = 2
Add +6 to both sides
p - 6 + 6 = + 6
p = 8
Answer:
8
Step-by-step explanation:
Find the coordinates of point I so ΔI K L is the indicated type of triangle. Point J has coordinates (0,0) and point K has coordinates (2 a, 2 b) .
scalene triangle
The coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).
It is given that in ΔL K L , J has coordinates (0,0) and K has coordinates (2 a, 2 b) .
We have to find the coordinates of point L so that , ΔL K L is a scalene triangle.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
The ΔL K L is a scalene triangle.
J has coordinates (0,0)
K has coordinates (2 a, 2 b) .
The possible coordinate of the point L will be (0,y) or (2a,y).
Let's check it.
Using the distance formula ;
JK = [tex]\sqrt{(2a-0)^2 + (2b -0)^2}[/tex]
JK = [tex]\sqrt{(4a^2 + 4b^2)}[/tex]
JK = [tex]2\sqrt{a^2 + b^2}[/tex]
Similarly ;
JL = [tex]\sqrt{0^2 + y^2}[/tex]
JL = y
And
KL = [tex]\sqrt{4a^2 + (2b - y)^2}[/tex]
The sides are all of different lengths, so , we can conclude that this is a scalene triangle.
Thus , the coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).
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how to solve this question??
limx→0sinaxcosbxsincx=limx→0(cosbx⋅sinaxax⋅cxsincx⋅ac)=ac
. If there are 4.90 Cal in 10.0 g of parsley, how many joules are in 12.1 g of parsley?
The joules are in 12.1 g of parsley is 24.806936 Joules of energy
10g has 4.9 cal
1g has 4.9/10 cal
Energy in 12.1 g = 4.9 x 12.1 / 10 = 5.929 Cal = 5.929 x 4.18400 = 24.806936 Joules of energy [1 calorie = 4.18400]
In the International System of Units (SI), a joule is a unit of work or energy equal to the work done by a force of one newton acting through one meter. It is named after the English scientist James Prescott Joule and equals 107 ergs, or about 0.7377 foot-pounds. The joule is equivalent to one watt-second in electrical terms, which is the amount of energy released in one second by a current of one ampere through a resistance of one ohm.
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I WILL AWARD BRANLIST!!! Math Question ... Find the measure of
Thank you !!! for the help :)
The measure of ∠B rounded to the nearest whole number is 71°
TrigonometryFrom the question, we are to calculate the measure of ∠B.
In the given diagram, we have a right triangle.
In the right triangle,
The hypotenuse is 21
Adjacent is 7
From SOH CAH TOA,
We have that
sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent
Thus,
we can write that
cos B = 7/21
cos B = 1/3
B = cos⁻¹(1/3)
B = 70.528
B ≈ 71°
Hence, the measure of ∠B rounded to the nearest whole number is 71°
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Pls help with these 2 problems for 15 points
Answer:
1) 15
Step-by-step explanation:
The smallest integer is 15 because,
There are 7 consecutive integers with n + 6 being the largest, therefore:
7n + 21 = 6(6 + n)
7n + 21 = 36 + 6n
7n - 6n + 21 = 36
n + 21 = 36 ⇒ n = 36 - 21 = 15
Hope this helps!
2) -3
2/5 = .4
12. Solve for y in -2y+4x=12
Answer: The answer would be x = -3 + 0.5y.
Step-by-step explanation: pls give me brainliest. may help w/ my depression.
