The slope of the line that contains the given points G(8,1), H(8,-6) is -1.
It is given in the question that the line contains the points G(8,1) and H(8,-6).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (8,1)
(c,d) = (8,-6)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points A(8,1), F(8,-6) is given by:-
(-6-1)/(8-1) = -7/7 = -1
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For j(x) = 3x-1, find j(x+h)-j(x)
h
O 3x-1(3¹ +1)
h
○ 3²-1(30)
h
3x-1(3-1)
h
O (x-1)(3+1)
h
-3h is value of function j(x +h)-j(x) .
What is functions ?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.j(x) = 3x-1
J(x + h ) = 3 ( x + h ) + 1
put the value
j(x +h)-j(x) = 3x-1 - 3 ( x + h ) + 1
= 3x - 1 - 3x -3h + 1
= -3h
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Three more than a number j is at most 12
Answer:
j + 3 ≤ 12
Hope this helps :)
Solution, Explanation, & Check part below
Step-by-step explanation:
1. Isolate variable by doing the inverse operation which is subtracting 3 on both sides of the equation.
j + 3 ≤ 12
- 3 - 3
j ≤ 9
j can be any number that is less than 9 or equal to 9.
Check:
9 + 3 ≤ 12
12 ≤ 12
12 is equal to 12 ✓
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
Jupiter takes 9.9259 hours to rotate on its axis and has a tangential speed of 12,293 m/s. what is the radius of jupiter? 7,781.6 km 19,420 km 48,893 km 69,912 km
Given that Jupiter takes 9.9259 hours to rotate on its axis and has a tangential speed of 12,293 m/s, then its radius is 69,912 km.
Tangential speed is defined as the measure of the circumference of the circular path the object is moving along divided by the value of the amount of time it took to complete one rotation.
tangential speed = C/t
where C = circumference
t = time it took to complete one rotation
Given that Jupiter takes 9.9259 hours to rotate on its axis and has a tangential speed of 12,293 m/s, solve for the circumference of Jupiter.
C = tangential speed x time
C = 12,293 m/s (9.9259 hours)(3600s/hr)
C = 439,268,719.3 m
Using the formula for circumference, solve for the radius of Jupiter.
C = 2πr
r = C / 2π
r = 439,268,719.3 m/2π
r = 69,911,788.03 m
r = 69,912 km
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Answer:
D. 69,912 km
Step-by-step explanation:
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
In 2004,8 million Americans over the age of 7 participated in mountain biking, and in 2006,8.5 million participated.
b. Based on the data, what is the growth per year of the sport?
The growth per year in Mountain Biking is 0.25 Million
In the year 2004 - 8 Million people participated
So, the slope point becomes (2004,8)
In the year 2006 - 8.5 Million people participated
So, the slope point becomes (2006,8.5)
Now we have points as :
[tex]X_1[/tex] = 2004
[tex]Y_1[/tex] = 8
[tex]X_2[/tex] = 2006
[tex]Y_2[/tex] = 8.5
Growth per year in the sport :
= [tex]Y_2[/tex] - [tex]Y_1[/tex] / [tex]X_2[/tex] - [tex]X_1[/tex]
= 8.5 - 8 / 2006 - 2004
= 0.5 / 2 = 0.25
Therefore, Growth per year in the sport is 0.25 Million per year
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Any help please? Question down below
My little sister, Savannah, is three years old and has a piggy bank that she wants to fill. She
started with five pennies and each day when I come home from school, she is excited when I give her three pennies that are left over from my lunch money. How much money will Savannah have after 10 days? How many days will it take for her to have at least $1.50? Justify your answer with a mathematical model of the problem situation.
The amount of money Savannah will have after 10 days is $0.35
Convert penny to dollar1 penny = $0.01Amount Savannah started with = 5 pennies
= $0.01 × 5
= $0.05
Additional amount per day = 3 pennies
= $0.01 × 3
= $0.03
Number of days = 10Total savings in 10 days = 0.05 + 0.03(10)
= 0.05 + 0.3
= $0.35
Number of days it will take for her to have at least $1.50 = 0.05 + 0.03d
1.50 - 0.05 = 0.03d
1.45 = 0.03d
d = 1.45 / 0.03
d = 48.33333333333333
Approximately,
d = 48.33 days
Therefore, the number of days it will take for her to have at least $1.50 us 48.33 days
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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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Write an equation in standard form of the circle with the given center and radius.
center (-6,3) , radius 8 .
The equation in standard form of the circle with radius 8 and center located at (-6 , 3) is (x + 6)^2 + (y - 3)^2 = 64.
The standard form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-6 , 3)
r = 8
(x - -6)^2 + (y - 3)^2 = 8^2
(x + 6)^2 + (y - 3)^2 = 64
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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
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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Find the ellipse centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1). write your equation in the form ax2 bxy cy2 = 1.
The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as
-0.3523x^2 0.5284xy 15.9268y^2 = 1.
Find the ellipse centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1).?Generally, the equation for three points is mathematically given as
a+2b+4c=1.....1 for the variable (1, 2)
4a+4b+4c=1.....2 for the variable (2, 2)
9a+3b+c=1.....3 for the variable (3, 1)
Step 1
Here we solve equations 1 and 2 simultaneously to find the value of b
Therefore
equ 2-equ1
3a+2b=0
b=-1.5a....4
Step 2
We solve equations 1 and 3 simultaneously to find the value of c
Where
9*equ1-equ3 gives
-15b-35c=-8
c=8-15b
subbing equ 4 we have
c=8+22.5a ....5
Step 3
Put values of b and c in equation 2, and we have
4a-6a+32+90a=1
a=-31/88
a=-0.3523
The value of b will be
b=-1.5*a
b=0.5284
The value of b will be
c=8-22.5*a
c=15.9268
Step 4
In conclusion, the equation is given as
By substituting the values of a b and c into the general formula we have
-0.3523x^2 0.5284xy 15.9268y^2 = 1.
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Two things are consistent if they are in agreement with each other. What does it mean for your actions to be consistent with your words?
It implies that you follow through on your commitments and don't just claim you'll do something before breaking your word.
For eg: - If one says that I will complete the quiz by tomorrow, then being consistent implies I must complete the quiz by tomorrow. On the other hand, if I fail to meet the test by tomorrow then I am being inconsistent with my words. Therefore, both the task at hand and my words are consistent with each other
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4. What is the rate of change of the linear function that has a graph that passes
through the points (-1, 3) and (-2,-4)?
The rate of change of the function that has a graph that passes
through the points (-1, 3) and (-2,-4) is slope and is equal to 7.
The slope of a line is outlined because the amendment in y coordinate with relevancy the amendment in x coordinate of that line. cyber web amendment in y coordinate is Δy, whereas cyber web amendment within the x coordinate is Δx. The slope of a line is calculated victimisation 2 points lying on the line. Given the coordinates of the 2 points, we are able to apply the slope of line formula m = y₂ - y₁ / x₂ - x₁ where (x₁ ,y₁) are the coordinate of first point and (x₂ ,y₂) are the coordinate of second point.We have given two points (-1, 3) and (-2,-4) .
Rate of change of graph is given by slope
Using slope formula , we get
m = -4 - 3 / -2 - (-1)
m = -7 / -2 + 1
m = -7 / -1
m = 7
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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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Hourly Pay Rate: $13.17
Mon
in 7:15
out 10:15
Lunch
In 1:30
Out 7:45
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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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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Substitute -3for{x} in each of the following equations. What is the value of y ?
a. y = 2x+3
In the equation y = 2x + 3, the value of y when we substitute -3 for x is -3.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the equation y = 2x + 3, if we substitute -3 for x, the equation becomes
y = 2(-3) + 3
Performing the arithmetic operations, we can have the value of y.
y = 2(-3) + 3
y = -6 + 3
y = -3
Hence, for the equation y = 2x + 3, y is -3 when x is -3.
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Mary has two bags of nuts, one with 60% peanuts and the other with 12% peanuts. To make a 5 lb bag of 44%, how much of each should Mary use?
peanuts + peanuts = peanuts
-----------------------
0.60x + 0.35(8-x) = 0.50*8
------
60x + 35*8 - 35x = 50*8
what property is -28 = -28
The numbers -28 = -28 are representing the reflexive property.
What is reflexive property?According to the Reflexive Property, x=x for every real number x. The meaning of the reflexive property is that the two expressions will have identical answers.
Suppose for square the two expressions for the length are 2x - 2 and ( 4x / 2 - 2 ). The two lengths of the square will have the same value.
2x - 2 = ( 4x / 2 - 2 ).
2x - 2 = 2x - 2
This is called reflexive property. Therefore, the numbers -28 = -28 are representing the reflexive property.
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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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What is true about the sum of the two polynomials?
6s2t – 2st2
4s2t – 3st2
The sum is a binomial with a degree of 2.
The sum is a binomial with a degree of 3.
The sum is a trinomial with a degree of 2.
The sum is a trinomial with a degree of 3.
The true about the sum of the two polynomials- 6s^2t – 2st^2 and 4s^2t – 3st^2 is The sum is a binomial with a degree of 3.
What are polynomials?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
Now the given polynomials are,
6s^2t – 2st^2 and 4s^2t – 3st^2
Now adding these two polynomials we get,
Sum of polynomials = 6s^2t – 2st^2 + 4s^2t – 3st^2
Taking alike terms together,
= 6s^2t + 4s^2t – 2st^2 – 3st^2
Now simplifying we get,
= 10s^2t – 5st^2
Here we see that the highest power of a variable is 2.
Thus this sum of polynomials is a binomial.
Now sum of the powers of variable s and t = 2 + 1 = 3
Thus, Degree of the sum of polynomials is 3.
Thus, the true about the sum of the two polynomials- 6s^2t – 2st^2 and 4s^2t – 3st^2 is The sum is a binomial with a degree of 3.
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Find the percent of the given number. 26 % of 500
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 26 % of 500 is 130.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 26 % of 500
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
26 % of 500 = 26/100 of 500
26/100 × 500 = 130
Therefore, the percent of the given number 26 % of 500 is 130.
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what is the GCF in 67 and 146
Answer:
1.
Step-by-step explanation:
67 is a prime number so we write
67 = 1 * 67
The GCF of 67 and 146 is 1.
Write – 90 7 50 as a decimal number.
The value of – 90 7 50 written as a decimal number is -90. 14
What are decimals?Decimals are the types of numbers, having a whole number and the fractional part that is separated by a decimal point.
The dot present that is found between the whole number and fractions part is known as the decimal point.
Given the mixed fraction;
– 90 7 50
Let's convert to improper fractions;
-4507 /50
Find the ratio
-90. 14
Thus, the value of – 90 7 50 written as a decimal number is -90. 14
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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
what number decreased by 66 2/3 is 18? please help!!
Answer: 84 2/3
Step-by-step explanation:
x-66 2/3=18
x=18 + 66 2/3
x=18 + 66 + 2/3
x=84 + 2/3
x=84 2/3
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.
