The sum of three consecutive odd num
What is the smallest of the three numbers?
Slope intercept form (-6,19) and (3,-2)
Answer:
-7/3 or -2.3
Step-by-step explanation:
1. y2-y1 divided by x2-x1 which would be y2-y1/x2-x1
2. plug in : -2-19/3-(-6)
4. Solution ( -7.3 or -2.3 )
Answer:
[tex]y = -\dfrac{7}{3}x +5[/tex]
Step-by-step explanation:
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
For the line passing through (-6, 19) and (3, -2) , the slope
[tex]m = \dfrac{-2 - 19}{3 - (-6)}\\\\[/tex]
[tex]\\\\m= \dfrac{-21}{9}[/tex]
[tex]m = -\dfrac{7}{3}[/tex]
So slope-intercept form is
[tex]y = -\dfrac{7}{3}x +b\\\\[/tex]
To compute y-intercept, b, plug in any of the two points into the above equation and solve for b
Let's choose point (3, -2)
Plugging x = 3 and y = -2 gives
[tex]-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\[/tex]
So equation of line is
[tex]y = -\dfrac{7}{3}x +5[/tex]
Column 1 Sections of a Lab
Report
19. Problem or Question
20. Hypothesis
21. Materials
22. Procedure
23. Observations
24. Analysis
25. Conclusion
Column 2 Information to Use in a Lab Report
a. If you increase the water temperature, then the yeast will
give off more gas.
b. After five minutes, Balloons A and B expanded.
c. Yeast give off more gas at higher temperatures.
d. What factors help yeast to grow?
e. Balloon B became bigger than Balloon A, so that means
that the yeast in Balloon B gave off more gas.
f. Combine the yeast, sugar and water in a bottle. Put a
balloon on the bottle.
g. Yeast, sugar, warm and cool water, containers
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In 1992, the moose population in a park was measured to be 3590. by 1999, the population was measured again to be 4500. if the population continues to change linearly p(t)= ____ b.) what does your model predict the moose population to be in 2006?
population at 1992 = 3590
Population after Seven years (1999) = 4500
Given two points (t1, P1) and (t2, P2), the slope of the line m can be found.
p1 = (1992, 3590) and p2 = (1999, 4500)
m= ΔP/Δt
m= ((4500-3590))/((1999-1992))
m = 910/7
m=130 is the slope
The linear population function P(t) is
P(t)=130t + P0
Find the Y-Intercept P0
The population function P(t) is measured since the year 1990, year zero. The first moose population was measured in 1992, one year later. This provides an initial condition P (1) = 4500.
P (1) =130 (1) + P0 = 4500
P0 = 4370
P(t)=20t+4630
The moose population P(t) changes linearly year after year. The population function P(t) is measured in terms of t years since 1990.
t= 1990, P (0) =4370
t =1992, P (1) =130 (1) + 4370 = 4500 matches data
t=1999, P (2) = 130(2) + 4370 = 4630
t=2006, P (3) = 130(3) + 4370 = 4760
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In Δ ABC, m ∠ B=26°, a=20 in., and c=10 in. Find b .
Answer:
[tex]b = 10\sqrt{5-4\cos 26^{\circ}}[/tex]
Step-by-step explanation:
Using the Law of Cosines,
[tex]b^2 = a^2 + c^2 - 2ac \cos B \\ \\ b^2 = 20^2 + 10^2 - 2(20)(10)\cos 26^{\circ} \\ \\ b=\sqrt{500-400\cos 26^{\circ}} \\ \\ =10\sqrt{5-4\cos 26^{\circ}}[/tex]
If you rotated the points (0,-1) (-4,-2) (-4,-4) to a 180 degree angle on a graph what would the new points be?
Answer: (-2,3) (1,4) (-1,-4) (2,-3) the answer would be -16,1
Step-by-step explanation: graphing it
The data in this table represents a linear function.
What is the slope of this line?
Y
-16
-24
-44
X -48
6
8
13
14
The slope of the line whose data represents a linear function is m = -1/4.
What is Slope of a line?Slope of an straight line is denoted by m and is the measure of rate of change of 'y' with respect to 'x'. Mathematically -
m = tan(θ) = Δy/Δx
Given is a table representing a linear function. From the question, we can write -
X → 6 8 13 14
Y → -16 -24 -44 -48
We can find the slope of this line using the formula -
m = Δy/Δx
m = (y₂ - y₁) / (x₂ - x₁)
Take any two coordinates from the table -
(x₁, y₁) → (6, -16)
(x₂, y₂) → (8, -24)
Substitute the values in the formula -
m = (8 - 6)/(-24 + 16)
m = - 2/8
m = -1/4
Therefore, the slope of the line whose data represents a linear function is m = -1/4.
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Bertie has 3494 comic books he wants them in groups of 8 how many comics would be left over after putting them in groups of 8
Answer: 6 would be left
Step-by-step explanation: divide 3494 by 8
There will be 6 comics left over after putting them in groups of 8
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Bertie has 3494 comic books he wants them in groups of 8.
∴ The no. of groups can be obtained if we divide the total number of books by no. of books in each group which is,
= (3494/8).
= 438×8 + 6.
So, There will be 6 comics left over after putting them in groups of 8.
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What are five sets of integers that has a mean of -10.
Can you please explain how to get the answer also. :)
The five sets of integers that has a mean of -10 will be 10, -15, -2, -12, and -11.
How to calculate the value?It should be noted that mean simply means average. Therefore, the numbers that will give a mean of -10 will be:
-10, -15, -2, -12, and -11.
Therefore, the mean will be:
= ( - 10 + -15 + -2 + -12 + -11) / 5
= -50 / 5
= -10
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Match the directed line segment with the image of polygon P being transformed polygon Q by translation by the directed line segment
The directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.
How to Interpret Translation of line segments?In this question, the translations are defined by a line segment.
Such that in each translation, we can easily find the segment PQ (the measure and the direction).
And all the points in the Polygon P will be connected by that same segment PQ to the equivalent point in the Polygon Q. (where you only move the segment to the correct location, but the length and direction remains constant)
Thus, to find the line segment for each transformation, you need to correctly measure the length of the segment PQ, and also the direction (that can be defined by an angle).
With the above, we can find the directed line segment for all the given transformations to match the transformed line segment from translation 1 to translation 4.
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Simplify. Rationalize all denominators. 10∛81 - 8∛24
Simplifying the problem by rationalizing all denominators will give result [tex]14\sqrt[3]{3}[/tex]
Lets begin by simplifying the equation;
[tex]10\sqrt[3]{81} - 8\sqrt[3]{24}[/tex]
The result is;
[tex]10 * 3 \sqrt[3]{3} - 8* 2*\sqrt[3]{3}[/tex]
[tex]30\sqrt[3]{3} -16\sqrt[3]{3}[/tex]
Let [tex]\sqrt[3]{3}[/tex] be a
Thus; 30a -16a= 14a
But a is [tex]\sqrt[3]{3}[/tex]
The final solution to this equation is thus;
[tex]14\sqrt[3]{3}[/tex]
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Solve each equation. log 5x+1=-1
Answer:
[tex]5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5[/tex]
. slope
= -3, (0,0)
Write in standard form
Answer:
y= -3x
Step-by-step explanation:
the equation is " y = (slope)x + (y-intercept) " hope this helps !!
What is the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin?
The image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin is (5, 5)
How to determine the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin?The point is given as
Point = (10, 10)
The scale factor is given as
k = 1/2 centered at the origin
The image after a dilation by the scale factor is calculated as
Image = Point * k
This gives
Image = (10, 10) * 1/2
Evaluate
Image = (5, 5)
Hence, the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin is (5, 5)
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Scott is 6 feet tall and casts a shadow that is 8 feet long. a nearby tree cast a show that is x+5 feet long. how tall is the tree? how long is the trees shadow?
The height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
It is given that:
Scott is 6 feet tall and casts a shadow that is 8 feet long. a nearby tree casts a show that is x+5 feet long
By using scale factor:
Let x be the height of the tree
x/6 = = (x + 5)/8
8x = 6(x + 5)
8x = 6x + 30
2x = 30
x = 15 feet
Thus, the height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.
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La suma de dos números es 91 y están en la razón 4 : 3. Calcula el valor de cada número.
The value of each number is 52 and 39.
The ratio given is = 4 :3
Given, the sum of x + y = 91
(4n) + (3n) = 91
7n = 91
n = 13
So,
x = a*n = 4*13 = 52
y = b*n = 3 *13= 39
The ratio of 52:39 is 4:3.
The sum 52+39 = 91
Hence, the numbers are 39 and 52.
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Which coordinates represent P1 and P2 respectively in the coordinate plane below .
Answer:
P1 - (4,2) P2 - (-2,1)
Step-by-step explanation:
You write the point as (x,y) so just put the numbers from the graph into their correct positions
Answer:
[tex]p_{1}(4,2)[/tex] and [tex]p_{2} (-2,1)[/tex]
Step-by-step explanation:
Latitude and longitude are broken into degrees, minutes, seconds and directions, starting with latitude. For instance, an area with coordinates marked 41° 56' 54.3732” N, 87° 39' 19.2024” W would be read as 41 degrees, 56 minutes, 54.3732 seconds north; 87 degrees, 39 minutes, 19.2024 seconds west.
Archie and three friends go on holiday together for a week.
The costs of the holiday will be shared equally between the 4 friends.
These are:
1) £1360 for 4 return plane tickets.
2) £850 for the accommodation.
3) £210 for the care hire for a week.
How much does Archie have to pay for his share of the costs?
The amount that Archie has to pay for his share of the costs is £605
What is the amount of total cost for the holiday?
The total costs of the holiday comprise of plane tickets, accommodation as well as the care hire for a week, in essence, the total costs to be shared equally among the four friends is as shown below:
total costs of holiday=£1360+£850+ £210
total costs of holiday=£2420
Archie's share of costs=£2420/4
Archie's share of costs=£605
In other words, the cost of the holiday, in this case, is not just plane ticket, accommodation cost as well as the cost of care hire, without any of the those , the holiday experience is not complete
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Solve each equation. If necessary, round to the nearest ten-thousandth. log (5 x-4)=3
The solution of the given equation by rounding off it to the nearest ten-thousandth is 4.8170.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: - log (5x - 4)=3
We are given a logarithmic expression: log (5x - 4)=3
We know that e^(log b) = b
Using exponential on both sides, we have
e^(log (5x - 4)) = e^3
5x - 4 = 20.085
5x = 24.085
x = 4.817
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 4.8170.
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Writing Explain how you can find the range of the inverse of f(x)=√x-1 without finding the inverse itself.
Domain of inverse of f(x)=√x -1 is [-1,∞),{x|x≥-1}
Range of inverse of f(x)=√x -1 is [0,∞),{y|y≥0}
Finding the Inverse Function but not the Inverse Function's Domain and Range
First, we must determine the domain and range of the original function f in order to determine the domain and range of an inverse function (x).
1.Find the function's domain and range.
Assume that the domain of the function f(x) is [0,∞),{x|x≥0}
Assume that the range of the function f(x) is [-1,∞),{y|y≥-1}
2. Substitute Domain for Range and Range for Domain
The domain of the calulated function f^-1(x) is [-1,∞),{x|x≥-1}
f^-1(x) calculated function (x) the interval for range is [0,∞),{y|y≥0}
∴Domain of inverse of f(x)=√x -1 is [-1,∞),{x|x≥-1}
Range of inverse of f(x)=√x -1 is [0,∞),{y|y≥0}
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a group of friends are at a baseball game and are purchasing souvenirs. Lacey purchased 4 t-shirts and 2 baseball caps, spending a total of $162. Her Anna purchased 1 t-shirt and 2 baseball caps, which cost her a total of $93. Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?
The price of each souvenirs is 28.33 Dollars.
Let X be the same price of all the t-shirts and all the baseball caps.
Lacey purchased
4 T-shirts and 2 Baseball caps = $162
4X + 2X = $162
6X = $162
Anna purchased
1 T-shirt and 2 Baseball caps = $93
1X + 2X = $93
3X= $93
Now we will add the price of souvenirs purchased by Lacey and Anna to find the price each souvenir.
6X = $162 eq. 1
3X= $93 eq. 2
As we have two equations we will add both equations :
6X + 3X = $162 + $93
Then we will determine the value of X .
9X = $255
X = $255 ÷ 9
X = $28.33
Hence the price of each souvenirs is $28.33 .
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The value of the digit 2 in the number 42,780 is 10 times the value of the digit 2 in which number?
426135 is the number in which the value of 2 is 10 times the value of 2 in 42780.
Given:
The number = 42,780
Here, the place value of 2 is 2000 or 2 thousand.
Let's check all the options for the right answer.
There is only one option with 2 in it.
That is option c 426135
We have given that, the value of 2 should be 10 times the value of 2 in 42780.
That is, 2000 x 10 = 20000.
The value of 2 in 426135 is 20000 or 2 ten thousand.
Thus, 426135 is the number in which the value of 2 is 10 times the value of 2 in 42,780.
Rest of the options are incorrect.
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The question is incorrect and the corrected question is given below.
The value of the digit 2 in the number 42,780 is 10 times the value of the digit 2 in which number?
The options are 34,651 or 146,703 or 426,135 or 510,400
3) The number of sodas you buy VS the total money spent
a) IV:
b) DV:
Answer:
Step-by-step explanation:
the independent variable is money.
sodas are the dependent.
the amount of sodas you buy are dependent on the amount of money you have.
What is the answer to B? I need help with B
Answer:
B) 600000
Step-by-step explanation:
First we need to answer A
13822×623/14 = 615,079
B) 615,079 = 600000
whats the answer ? Its really hard
Putting together the solutions from each of the equations, the 4 letter code is GFBA
Solving Linear EquationsFrom the question, we are to solve each of the linear equations to determine the 4 LETTER CODE
1. -2x + 1 = 3x + 16
Add 2x to both sides
-2x + 2x + 1 = 3x + 2x + 16
1 = 5x + 16
Subtract 16 from both sides
1 - 16 = 5x + 16 - 16
-15 = 5x
x = -15/5
x = -3
The letter that corresponds to this is G
2. 7 - 8x = 4x - 17
Add 8x to both sides
7 - 8x + 8x = 4x + 8x -17
7 = 12x - 17
Add 17 to both sides
7 + 17 = 12x - 17 + 17
24 = 12x
x = 24/12
x = 2
The letter that corresponds to this is F
3. 20 -2(x - 2) = 2x
Clear the parentheses
20 -2x + 4 = 2x
Simplify
24 -2x = 2x
Add 2x to both sides
24 - 2x + 2x = 2x + 2x
24 = 4x
x = 24/4
x = 6
The letter that corresponds to this is B
4. 5(x + 4) = 6x - 5
Clear the parentheses
5x + 20 = 6x - 5
Subtract 5x from both sides
5x - 5x + 20 = 6x - 5x - 5
20 = x - 5
Add 5 to both sides
20 + 5 = x - 5 + 5
25 = x
x = 25
The letter that corresponds to this is A
Hence,
The code is GFBA
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if 2x = 32
find the value of x
Answer:
x = 16
Half of 32 is 16
Therefore, 2 × x(16) = 32
is y = 2x a function? yes or no
Answer:
Yes.
Step-by-step explanation:
A good test to do is the vertical line test. You draw the equation you're trying to determine is or isn't a function, and then draw a vertical line through it, if it goes through once it is a function. If twice then it is not a function. Hope this helps. :)
Evaluate each logarithm.
log₂ 16
The answer to the given logarithm expression is log₂ 16 = 4
A power to which a number must be increased in order to achieve another value is referred to as a logarithm. The easiest way to represent enormous numbers is in this way.
The fact that addition and subtraction logarithms can be used to multiply and divide logarithms is supported by a number of significant features of logarithms. The use of logarithmic operations is subject to a set of rules. These guidelines are known as: Division regulations apply to products. Exponential/Power Law Changes to fundamental laws Rule of Base Change Log elaboration
We need to evaluate log₂ 16
Using the property logₐ (mⁿ) = n logₐ m
16 = 2⁴log₃ 125 can be written as
log₂ 16 = 4 log₂ 2
We know that logₐ a = 14 log₂ 2= 4
Hence , we evaluated the logarithm which is log₂ 16 = 4
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is this correct (just to make sure)
Answer:
yes
Step-by-step explanation:
Three friends eat lunch together. The bill comes to 21 plus 10% tax.if they split the bill and tax evenly, then how much will each person owe?
Each person will owe $7.7
How to calculate the amount each person will pay ?Three friends eat lunch together
The bill accumulates to $10 plus a 10% tax fee
If they split the bill and and tax evenly
The amount each person will pay can be calculated as follows
21 × (1+10/100) /3
= 21 × (1+0.1)/3
= 21 × 1.1/3
= 23.1/3
= 7.7
Hence each person will pay $7.7
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