The solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.
Define logarithmIn mathematics, a logarithm is the inverse operation to exponentiation. Given a base b and a positive number y, the logarithm of y with respect to the base b is the exponent to which b must be raised to yield y. In other words, if x is the logarithm of y with respect to base b, then bˣ = y.
We can begin solving this equation by isolating the exponential term on one side of the equation and taking the logarithm of both sides.
2,401 = 7⁶⁻²ˣ
Taking the logarithm base 7 of both sides:
log₇(2,401) = log₇(7⁶⁻²ˣ )
Using the property of logarithms that states that log base a (aᵇ) = b, we can simplify the right-hand side of the equation:
log₇(2,401) = (6-2x)log₇(7)
Since log₇(7) = 1, we can further simplify:
log₇(2,401) = 6-2x
-2x = log₇(2,401) - 6
x = (6 - log₇(2,401))/2
Using a calculator, we find:
x ≈ 1.4076
Therefore, the solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.
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Use the FOIL method to find the product. Express the product in descending powers of the variable.
(7+6x)(1-5x)
What is ? Complete the statement.
is the ratio of the circumference to the ?
rence of a Circle-Instruction-Level G
area
circumference
radius
diameter
of a circle.
The ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.
Define circleA circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference, and the distance across the circle passing through the center is called the diameter.
The circumference of a circle with radius r is given by the formula:
C = 2πr
The area of a circle with radius r is given by the formula:
A = π×r²
Therefore, the ratio of the circumference of a circle with radius r to its area is:
C/A = (2πr) / (πr²)
Simplifying the expression by canceling out π and r from the numerator and denominator, we get:
C/A = 2/r
Therefore, the ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.
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The complete question is:
Find the following ratio.
The ratio of circumference of circle with radius r to its area.
Find the y value if the line through (-4, -10) and (2, y) has a slope of 4.
Answer:
y=14
Concept Used:
Slope of a line: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where (x1,y1) and (x2,y2) are passing points
Step-by-step explanation:
On substitution:
[tex]4 = \frac{y-(-10)}{2-(-4)}[/tex]
Solving for y:
y = 14
which of the following sample spaces would satisfy the definition of a continuous random variable?
x={odd integers between 5 and 15}
×=[0,500]
x=[0,1,2,3]
x=[the number of days in the week that have the letter "r"]
Answer:The sample space that satisfies the definition of a continuous random variable is: ×=[0,500]
Step-by-step explanation:
The sample space that satisfies the definition of a continuous random variable is: ×=[0,500]
A continuous random variable is a variable that can take on any value within a certain range of values, typically a continuous interval. This means that there are an infinite number of possible values that the variable can take on, and the probability of any particular value is zero.
In contrast, the other sample spaces listed are all discrete random variables, meaning that they can only take on a finite or countable number of values. For example, the first sample space x={odd integers between 5 and 15} can only take on 6 possible values (5, 7, 9, 11, 13, or 15), and the third sample space x=[0,1,2,3] can only take on 4 possible values.
The fourth sample space x=[the number of days in the week that have the letter "r"] is also a discrete random variable, as it can only take on values of 0, 1, 2, or 3 (depending on how many days of the week have the letter "r").
Therefore, the only sample space that satisfies the definition of a continuous random variable is ×=[0,500].
PLEASE HELP ASAP TY IN ADVANCE!!
1. The Lifetime of the Sun. When the Sun formed 70% of its mass was hydrogen. 13% of that mass is at the Sun’s core where it is available for the nuclear fusion reaction that powers the Sun.
a. Given the mass of the Sun ms = 1.99 × 1030 kg, calculate the total mass of hydrogen at the Sun’s core available for nuclear fusion over its lifetime.
b. Given that the Sun fuses about 600 billion kg of hydrogen every second, calculate how long the Sun’s original supply of hydrogen can last. Express your answer in billions of years.
c. Given that the Sun is now 4.6 billion years old, how much longer will it take before it runs out of fuel?
Step-by-step explanation:
I think you mean the sun's mass is 1.99 × 10³⁰ kg.
70% of that is hydrogen :
1.99 × 10³⁰ × 0.7 = 1.393 × 10³⁰ kg
a.
13% of that is in the core :
1.393 × 10³⁰ × 0.13 = 0.18109 × 10³⁰ = 1.8109 × 10²⁹ kg
b.
600 000 000 000 kg = 6.0 × 10¹¹ kg/s
so, 1.8109 × 10²⁹ kg will last
1.8109 × 10²⁹ / (6.0 × 10¹¹) = 0.301816666... × 10¹⁸ =
= 3.01816666... × 10¹⁷ seconds
60 seconds per minute.
60 minutes per hour.
24 hours per day.
365 days per year.
1 000 000 000 years.
that is
31,536,000,000,000,000 seconds in 1 billion years =
= 3.1536 × 10¹⁶ seconds in 1 billion years
so, this will go on for
3.018166666... × 10¹⁷ / 3.1536 × 10¹⁶ billion years =
= 0.957054372... × 10¹ = 9.57054372... billion years.
c.
the sun has already "spent" 4.6 billion years, so, that leaves about
9.6 - 4.6 = 5 billion years
According to the information, the total mass of hydrogen available for nuclear fusion in the Sun's core is 10^29 kg, the duration of the oroginal supply of hydrogen of the sun is 3.02 × 10^17 seconds, and the left time of the sun is 4.98 billion years.
How to calculate the total avaliable mass of hydrogen at the Sun's core?a. The total mass of hydrogen available for nuclear fusion in the Sun's core is:
0.7 × 1.99 × 10^30 kg × 0.13 = 1.81 × 10^29 kg
How long the sun's original suply of hydrogen can last?
b. To find how long the Sun's original supply of hydrogen can last, we need to divide the total mass of hydrogen available for nuclear fusion by the rate at which the Sun fuses hydrogen:t = (1.81 × 10^29 kg) / (6 × 10^11 kg/s) = 3.02 × 10^17 seconds
Converting to billions of years:
t = (3.02 × 10^17 s) / (3.15 × 10^16 s/billion years) = 9.58 billion years
How to calculate how much longer will it take before it runs ouut out fuel?c. The Sun has already burned for 4.6 billion years, so the amount of time it has left before it runs out of fuel is:
9.58 billion years - 4.6 billion years = 4.98 billion years
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Can you please help me with this?
Answer:
a= Acute
b=Obtuse
c= Acute
d= Right
50 Points! Multiple choice Algebra question. State the number of real zeros for the function whose graph is shown. Photo attached. Thank you!
The number of real zeros for the function whose graph is shown include the following: D. 0.
What is a polynomial function?In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.
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What is this from vertex to standard form ?
Answer:
y = -x^2-2x-2Step-by-step explanation:
vertex form = y=a(x-h)^2+k
standard form = y=ax^2+bx+c
the most straightforward way to solve it is to expand the vertex form
we get :
-(x+1)(x+1)-1
= -(x^2+x+x+1) - 1
note: remember to leave the negative sign out of the parentheses and distribute it after - otherwise you may mix up signs
= (-x^2-x-x-1) - 1
= -x^2-2x-1-1
= -x^2 - 2x - 2
So, in standard form, it is y=-x^2-2x-2
Hope this helps!
The simplest form of log5+log6-log2
The simplest form of log5+log6-log2 is: log15.
What is the simplest form?Let us simplify log5 + log6 - log2 by making use logarithmic rules:
log a + log b = log (ab)
log a - log b = log (a/b)
So,
log5 + log6 - log2
= log (5 x 6) - log2
= log30 - log2
Now let make use of the logarithmic rule:
log a - log b = log (a/b) = log a - log b
log30 - log2
= log (30/2)
= log15
Therefore the simplest form is log15.
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Write the linear equation that gives the rule for this table.
X
4
5
6
7
Y
24
30
36
42
Write your answer as an equation with y first, followed by an equals sign.
The equation of the line passing through the given points is y = 6x
Given that are the values of x and y coordinates we need to find the equation of the line using them,
So, considering the points (4, 24) and (5, 30),
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),
Therefore, the required equation is =
y-24 = 30-24/5-4 (x-4)
y-24 = 6(x-4)
y-24 = 6x-24
y = 6x
Hence, the equation of the line passing through the given points is y = 6x
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The members of the Junior National Honors Society at Franklin Middle School are required to complete community service hours. The box plots show the volunteer service hours performed by the 7th and 8th graders. 7th Graders 8th Graders 3.5 4 4.5 Community Service 5 5.5 6 6.5 7 7.5 Number of Hours Which statement is best supported by the information in the box plots?
Answer:
The statement that is best supported by the information in the box plots is:
* The 8th graders completed more community service hours than the 7th graders.
The 8th grade box plot is shifted to the right of the 7th grade box plot, which indicates that the 8th graders had a higher median number of community service hours. The 8th grade box plot also has a wider spread, which indicates that there was more variation in the number of community service hours completed by the 8th graders.
However, it is important to note that the box plots do not provide information about the total number of community service hours completed by each group of students. It is possible that some 7th graders completed more community service hours than some 8th graders.
Step-by-step explanation:
Answer:The 8th graders completed more community service hours than the 7th graders
Step-by-step explanation:
I would be thankful if you help
To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:
[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]
Understanding MatrixThe solution provided above uses a method of matrix called Echelon.
Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.
By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.
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Justin mowed 45% of her garden in 18 minutes.how many minutes will it take him to mow all of his garden at this rate? Explain
If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:
45/100 = 18/x
where "x" is the unknown number of minutes it would take to mow 100% of the garden.
To solve for "x," we can use cross-multiplication:
45x = 100 * 18
Simplifying the right-hand side:
45x = 1800
Dividing both sides by 45:
x = 40
Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.
To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.
From the following, calculate the cost of ending inventory and cost of goods sold for the weighted-average method, ending inventory is 59 units. (Round your intermediate calculations and final answers to the nearest cent.) Beginning inventory and purchases Units Unit cost January 1 4 $ 1.50 April 10 11 2.00 May 15 11 2.50 July 22 16 2.75 August 19 17 3.50 September 30 21 3.70 November 10 31 3.90 December 15 17 4.30
The cost of ending inventory using the weighted-average method is $198.24.
What is the cost of ending inventory?An ending inventory is often derived by adding new purchases to beginning inventory and then subtracting the cost of goods sold.
To calculate it using the weighted-average, we must compute the weighted average cost per unit and then multiply the weighted average cost per unit by the number of units in ending inventory to get the cost of ending inventory.
The total cost of goods available for sale is:
= (4 x 1.50) + (11 x 2.00) + (11 x 2.50) + (16 x 2.75) + (17 x 3.50) + (21 x 3.70) + (31 x 3.90) + (17 x 4.30)
= $430.7
The total units available for sale is:
= 4 + 11 + 11 + 16 + 17 + 21 + 31 + 17
= 128
The weighted average cost per unit is:
= $430.70 / 128 units
= $3.36484375
= $3.36
The cost of ending inventory will be:
= 59 units x $3.36
= $198.24
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A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder with a height of 5 in and a diameter of 6in . The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company has a total of 4521.6in^2 of paper available, how many labels can be made? Use 3.14 for n , and do not round your answer.
48 labels can be made if the company has a total of 4521.6in² of paper available.
We can calculate the number of labels by finding the surface area of the side of the can.
What is the surface area of the side of the can?The surface area of the side of the can is the circumference of the base times the height:
C = πd
C = 3.14 x 6
C = 18.84 in
Area = C x h
Area = 18.84 x 5
Area = 94.2 in²
Therefore, each label requires 94.2 in² of paper.
To find the number of labels that can be made, we divide the total amount of paper by the amount needed per label:
Number of labels = Total area of paper / Area per label
Number of labels = 4521.6 / 94.2
Number of labels = 48
Therefore, 48 labels can be made using a total of 4521.6in² of paper.
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3 + 1 + 2 − 7 = + 22
Answer: The answer is false
Answer:
False
Step-by-step explanation:
If you were asking true or false it is false
what principal will have majority value of $10,000 at 8.25% p.a in three months?
__________________________________
Simple Interest: A = P × i ÷ 100 × n = 10,000 × 8.25 ÷ 100 × 3= 247.5= 10,000 + 247.5= $10,247.5 Compound Interest: A = P (1 + i ÷ 100) n = 10,000 (1 + 8.25 ÷ 100) ³= $12,684.80The Compound Interest Principal Will Have Majority Value In 3 Months__________________________________
Please help solve graphs
The graphs are:
1) not one-to-one
2) one-to-one
3) not one-to-one
Are the graphs one-to-one?A graph represents an one-to-one function only if.
We can't draw a vertical line that touches the graph twice or more.
We can't draw an horizontal line that touches the graph twice or more.
For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.
Similarly forthe third graph, the line y = 0 touches two points-
So these two are not one-to-one.,
For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.
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If cosθ=-1/3 and θ is in quadrant III, find the exact values of sinθ,tanθ,secθ,cscθ,and cotθ. You can use the identities or x, y, r.
The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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what is the mean absolute deviation of 8,2,7,8,6,10,2,1,10,6
Answer:
The mean absolute deviation of 8,2,7,8,6,10,2,1,10,6 is 2.24.
To calculate the mean absolute deviation, we first need to find the mean of the data set. The mean is the sum of all the values in the data set divided by the number of values. In this case, the mean is 7.
Once we have the mean, we can find the mean absolute deviation by finding the absolute value of the difference between each value in the data set and the mean. For example, the absolute value of the difference between 8 and 7 is 1. We then add up all of the absolute values and divide by the number of values in the data set. In this case, the mean absolute deviation is 2.24.
Here is the formula for the mean absolute deviation:
```
MAD = (|x1 - μ| + |x2 - μ| + ... + |xn - μ|) / n
```
Where:
* MAD is the mean absolute deviation
* x1, x2, ..., xn are the values in the data set
* μ is the mean of the data set
* n is the number of values in the data set
Step-by-step explanation:
Using Trig to Find a Side
Using trigonometric ratio, the value of x in the figure is 2.61 units
What is the trigonometric ratiosThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In this problem, we have the adjacent side and we need to find the opposite side.
The ratio that gives us room to find this is the tangent to the angle
tanθ = opposite / adjacent
tan 43 = x / 2.8
x = 2.8 * tan 43
x = 2.61
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You buy tomatoes in 25 pounds cases. One portion of salad requires.75 ounces of tomatoes. How many portions can be made with one case
Answer: 5.3 repeated portions or about 5 portions
Step-by-step explanation: 25 pounds = 400 ounces
400/75 = 5.3 repeated
Answer:33
Step-by-step explanation:
Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints.
The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100
What is an inequality?The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.
The specified equations obtained from the constraints in slope intercept form are;
y = -0.5·x + 7; The region below the graph is shaded
y = -0.75·x + 9; The region below the graph is shaded
x = 0; The region to the right of the line x = 0 is shaded
y = 0; The region above the line y = 0 is shaded
The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9
Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3
The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)
The value of the function g for each of the feasible region are therefore;
g(0, 0) = 8 × 0 + 12 × 0 = 0
g(0, 7) = 8 × 0 + 12 × 7 = 84
g(8, 3) = 8 × 8 + 12 × 3 = 100
g(12, 0) = 8 × 12 + 12 × 0 = 96
The maximum possible value of g therefore is 100, which is the value at the point (8, 3)Please find attached the graph of the inequalities showing the feasible region created with MS Excel
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Use the substitution u = 1/y and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. -3/x + 4/y = 5 and 1/x - 2/y = -3
In the figure , < ___ and < ___ have measures equal to 35 degrees
For circle O, For circle O, m CD=125° and m∠ABC = 55°. In the figure, ∠ ABO and ∠ BCO have measures equal to 35°.
How can you be sure that ∠ ABO and ∠ BCO have measures equal to 35° in the circles?For circle O, m(arc CD) = 125° and m∠ABC = 55°.
First, we use central angle to find that ∠COB is 125°,
give that ∠COB = arc CD
Next, we use complementary angles to find that ∠BCA is 35°,
given that ∠ABC + ∠BCA = 90°.
Then, we use the sum of interior angles in a triangle to find that ∠CBO is 20°; given that:
∠CBO + ∠COB + ∠BCO = 180°.
∠BCO = ∠BCA = 35°
∠COB = 125°
125° + 35° = 160°
180° + 160° = 20°
Finally, we use angle addition postulate to find that ∠ABO is also 35°.
Therefore, <ABO and <BCO both have measures of 35° in the figure.
The above answer is in response to the question below;
For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.
a. the first could be AOB, ABO, or BOA
b. the second could be BCO, OBC, or BOC
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17. The Amethyst Woodstar species of
hummingbird beats its wings about
80 times per second. If there are
60 seconds in a minute, about how
many times does the Amethyst
Woodstar beat its wings in
9 minutes?
A 12,600
B 37,800
C50,400
D 43,200
If the Amethyst Woodstar species of hummingbird beats its wings about 80 times per second and there are 60 seconds in a minute, it beats its wings D. 43,200 times in 9 minutes.
How is the number of times determined?The number of times that the Amethyst Woodstar species of hummingbird beats its wings in 9 minutes can be determined using the mathematical operation of multiplication.
The number of times it beats its wings = 80 seconds per second
The total number of minutes involved = 9 minutes
1 minute = 60 seconds
The total number of times it beats in 9 minutes = 43,200 (80 x 60 x 9)
Thus, using multiplication operation, the number of times the bird beats its wings is Option D.
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A manufacturer earned $55 per hour of labor when it opened. Each year the
manufacturer earns an additional 7% per hour. Write a function that gives the
amount A(t) that the plant earns per hour t years after it opens.
Write a exponential function
The exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]
A manufacturer earned $55 per hour of labor when it opened.
Each year the manufacturer earns an additional 7% per hour.
Since the manufacturer earns an additional 7% per hour each year, the amount earned per hour can be represented as follows:
[tex]A(t) = 55(1 + 0.07)^t[/tex]
where t is the number of years after the plant opened. T
This can be simplified as function:
[tex]A(t) = 55(1.07)^t[/tex]
Therefore, the exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]
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For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose the best description of its solution. If the system has exactly one solution, give its solution. (see attached)
The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:
A. System A = Inconsistent (No solution)
B. System B = Consistent dependent (Indefinitely many solutions)
C. System C = Consistent independent (A unique solution)
How to identify the systems of linear equationsTo identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.
Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.
Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.
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what is the quotient?
Answer:
a quotient is the result obtained by dividing one quantity by another.
What is the average of the two bases in the following trapezoid in feet? 22 ft 14.75 ft 11 ft 18 ft
Answer: 18 feet.
Step-by-step explanation:
Average of bases = (22 + 14.75) / 2
Average of bases = 18.375
18.375 to the nearest tenth is = 18ft
Therefore, the average of the two bases of the trapezoid is 18 feet.
