From the two plans for a set price the second graph in this issue is the right one.
A linear function is what?The following is the definition of a linear function's slope and intercept:
y = mx + b.
where:
The rate of change is represented by the slope m.
The starting quantity is represented by the intercept b.
We have it for the plan with the fixed price:
Compared to the other plan, the slope is higher.
There is no intercept.
As a result, it is less expensive for fewer trips.
We have the following for the plan with the set price plus the fee:
Compared to the other plan, the slope is smaller.
There is an intercept that exceeds zero.
As a result, paying for more visits results in lower expenditures.
Hence, the second graph in this issue is the right one.
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Assumptions: Tax depreciation is straight-line over three years. Pre-tax salvage value is 25 in Year 3 and 50 if the asset is scrapped in Year 2. Tax on salvage value is 40% of the difference between salvage value and book value of the investment. The cost of capital is 20%.
Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.
To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:
Assumptions:
Tax depreciation is straight-line over five years.
Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.
Tax on salvage value is 30% of the difference between salvage value and book value of the investment.
The cost of capital is 12%.
Given:
Initial investment cost = $50,000
Useful life of the equipment = 5 years
To calculate the depreciation expense each year, we divide the initial investment by the useful life:
Depreciation expense per year = Initial investment / Useful life
Depreciation expense per year = $50,000 / 5 = $10,000
Now, let's calculate the book value at the end of each year:
Year 1:
Book value = Initial investment - Depreciation expense per year
Book value \(= $50,000 - $10,000 = $40,000\)
Year 2:
Book value = Initial investment - (2 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (2 \times$10,000) = $30,000\)
Year 3:
Book value = Initial investment - (3 \(\times\) Depreciation expense per year)
Book value = $50,000 - (3 \(\times\) $10,000) = $20,000
Year 4:
Book value = Initial investment - (4 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (4 \times $10,000) = $10,000\)
Year 5:
Book value = Initial investment - (5 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (5 \times $10,000) = $0\)
Based on the assumptions, the salvage value is $10,000 in Year 5.
If the asset is scrapped in Year 4, the salvage value is $15,000.
To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:
Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)
For Year 5:
Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)
For Year 4 (if scrapped):
Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)
Now, let's calculate the after-tax cash flows for each year:
Year 1:
After-tax cash flow = Depreciation expense per year - Tax on salvage value
After-tax cash flow = $10,000 - $0 = $10,000
Year 2:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 3:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 4 (if scrapped):
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $15,000 - $1,500 = $13,500
Year 5:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $10,000 - $3,000 = $7,000
Now, let's calculate the net present value (NPV) using the cost of capital of 12%.
We will discount each year's after-tax cash flow to its present value using the formula:
\(PV = CF / (1 + r)^t\)
Where:
PV = Present value
CF = Cash flow
r = Discount rate (cost of capital)
t = Time period (year)
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment
Let's calculate the NPV:
PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)
PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)
PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)
PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)
PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)
NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000
NPV = $22,954.24 - $50,000
NPV = -$27,045.76
The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.
Therefore, the investment may not be favorable.
Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.
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The complete question may be like :
Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.
You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.
Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.
Points A and B have coordinates A(–4,2) and B(3,–6) . Find the coordinates of point P, the weighted average of points A and B, in which point A has a weight of 2 and point B has a weight of 5.
HELP ME GEOMETRY THX
The coordinates of the point P is P(x, y) = (1, - 26 / 7). (Correct choice: C)
How to calculate a resultant point's coordinates using the weighted averages method?
We must locate the third point by applying a method based on a weight average-like formula after finding the coordinates of two points on the Cartesian plane:
P(x, y) = (2 / 7) * A(x, y) + (5 / 7) * B(x, y)
P(x, y) = (2 / 7) * (- 4, 2) + (5 / 7) * (3, - 6)
P(x, y) = (- 8 / 7, 4 / 7) + (15 / 7, - 30 / 7)
P(x, y) = ( 7 / 7, - 26 / 7)
P(x, y) = ( 1, - 26 / 7)
Therefore, the coordinates of the point P is P(x, y) = ( 1, - 26 / 7).
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The coordinates of the point P is P(x, y) = (1, - 26 / 7). (Correct choice: C)
How to calculate a resultant point's coordinates using the weighted averages method?
We must locate the third point by applying a method based on a weight average-like formula after finding the coordinates of two points on the Cartesian plane:
P(x, y) = (2 / 7) * A(x, y) + (5 / 7) * B(x, y)
P(x, y) = (2 / 7) * (- 4, 2) + (5 / 7) * (3, - 6)
P(x, y) = (- 8 / 7, 4 / 7) + (15 / 7, - 30 / 7)
P(x, y) = ( 7 / 7, - 26 / 7)
P(x, y) = ( 1, - 26 / 7)
Therefore, the coordinates of the point P is P(x, y) = ( 1, - 26 / 7).
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What parallelogram has a base of 2 units and a height of 4 units
Answer:
C
Step-by-step explanation:
The parallelogram in C has a base of 2 units and a height o 4 units.
A rocket is launched from the ground at an initial velocity of 39.2 meters per second. Which equation can be used to model the height of the rocket after t seconds?
s(t) = –4.9t2 + 39.2
s(t) = –4.9t2 + 39.2t
s(t) = –4.9t2 + 39.2t + 39.2
s(t) = –4.9t2 + 39.2t – 39.2
The quadratic equation that models the height of the rocket after t seconds is:
s(t) = -4.9t² + 39.2t.
What is the quadratic function for a projectile's height?Considering the height in meters, the equation is given by:
s(t) = -4.9t² + v(0)t + h(0)
In which:
v(0) is the initial velocity, in m/s.h(0) is the initial height, in m.In this problem, we have that v(0) = 39.2, h(0) = 0, hence the equation is:
s(t) = -4.9t² + 39.2t.
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Answer: B
Step-by-step explanation: on Edge (*^*)
Brett can swim 5 laps in 16 minutes. How many laps can he swim in 48 minutes?
a company manufactures commercial and domestic heating systems at two plant sites, it can produce no more than 1300 units per month, and it needs to fill orders at least 500 commercial units and 650 domestic units.
a)write the system of inequalities that describes the constraint on the production for these orders.
b) graph the solution sets of this system of inequalities.
The system of inequalities are : C + D ≤ 1300 ; C≥500 and D≥650
The graph can be made using these three inequalities.
How do you describe linear inequality with two variables?
The solution(s) of a linear inequality in two variables like mx + ny > p is value in pair (x, y) that satisfies the inequality when the values of x and y are substituted into that inequality. The graph of that inequality in two variables is the set of points that represents all roots to the inequality.
Let the commercial units be represented by C and Domestic units by D,
Given that both units are not more than 1300.
Means, C + D ≤ 1300
Also Given that, Commercial units are atleast 500 i.e, C≥500
Similarly, for domestic D≥650
a)The system of inequalities are:
C+D ≤1300
C≥500
D≥650
b)Graph for the above inequalities
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Refer to the graph attached with solution.
Mai's class volunteered to clean a park with an area of square mile. Before they took a lunch break, the class had cleaned of the park. How many square miles had they cleaned before lunch?
The class had cleaned x × A square miles before lunch.
Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).
If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:
Area cleaned before lunch = x × A
Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.
Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).
If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:
Before lunch, the area was cleaned = x A
We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.
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I learned that (1) _____ is a number written at the upper right of a certain number called (2) ______ . it indicates how many times the base is taken as a factor. I also learned the different laws of the exponent. I have known now that the product of x² * x⁴ is equal to x⁶
Answer:
(1) exponent, (2) base
Step-by-step explanation:
An exponent is a quantity that represents the power to which a given number is to be raised.
A base can be any whole number greater than 0.
6. Mrs. Ramirez' groceries cost $50 before tax, and the total including sales tax was $55. What is
the sales tax rate that Mrs. Ramirez paid?
Answer:sales tax rate would be 0.1
using the formula
Sales tax rate = Sales tax percent / 100
the number 5 and 20 have a special relationship: 1/5 is equivalent to 20% and 1/20 is equivalent to 5% are there any other numbers that have a relationship like this? why does this relationship happen?
Please help
The other numbers are 2 and 50. These relationships are like this because the product of both numbers gives a 100
FractionsFraction is the ratio of two integers. It is written in the form a/bFrom the information given, we are to determine the other numbers like 5 and 20 that form the given relationship.
The other numbers that form this relationship are 2 and 50
Get their percentages1/2 * 100 = 50%
1/50 * 100 = 2%
Thesee relationships are like this because the product of both numbers gives a 100
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Help me please!!!
Whoever answers right gets brainliest!
The equation that best describes the relation is y = -x+1 ( optionD)
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Taking x(0,1) and y ( 1,0)
therefore the slope of the line
= 0-1/1-0
= -1/1 = -1
the equation a line is given as
y-y1 = m(x-x1)
= y-1 = -1( x - 0)
= y-1 = -x
y = -x +1
therefore the equation that describe relation is y = 1-x or y = -x+1
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>) Which unit is best to use to measure the length of a soccer field? D)) miles inches )) yards centimeters
Find the third iterate x3 of f(x) = 2x + 3
for an initial value of x0 = 2
a. 7
b. 15
c. 17
d. 37
For the function f(x) = 2x + 3 the third iterate x₃ is 37
To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,
we can apply the function repeatedly.
Starting with x₀ = 2:
x₁ = f(x₀)
= 2(2) + 3
= 7
x₂ = f(x₁)
= 2(7) + 3 = 17
x₃ = f(x₂)
= 2(17) + 3
= 37
Therefore, the third iterate x₃ is 37.
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Which is a trinomial in one variable of degree 5 in standard form?
o 5x4 + 3x – 7
o 2 + 4x2 + 5x3
o 3x5 + 3x2 + 6
• 3x + 2x2 – 6x5
Answer:
C) 3x⁵ + 3x² + 6Step-by-step explanation:
A) 5x⁴ + 3x – 7 ⇒ degree 4 in standard formB) 2 + 4x² + 5x³ ⇒ degree 3 not in standard formC) 3x⁵ + 3x² + 6 ⇒ degree 5 in standard formD) 3x + 2x² – 6x⁵ ⇒ degree 5 not in standard formAnswer:
Option C
Step-by-step explanation:
Here degrees are
5,2,1Highest degree=5✓
In standard form?
5>2>1 YesA rectangle has a perimeter of 18 cm. The long side is 1 cm more than three times the small side. How big is the small side?
Two draws are made at random with replacement from a box containing five tickets. The tickets are labeled: Z, E, B, R, A. a) What is the chance of getting a vowel (A, E, I, O, or U) at least once in the two draws? b) What is the chance that the two letters are different?
a. the probability of getting no vowels in two draws is (3/5) x (3/5) = 9/25. b. the chance that the two letters drawn are different is 12/25.
a) To find the probability of getting at least one vowel in two draws with replacement, we can use the complement rule. The complement of getting at least one vowel is getting no vowels at all.
The probability of getting no vowels in one draw is 3/5 (since there are 3 consonants in the box of 5 tickets).
Therefore, the probability of getting no vowels in two draws is (3/5) x (3/5) = 9/25.
The probability of getting at least one vowel in two draws is one minus the probability of getting no vowels, so:
P(at least one vowel) = 1 - P(no vowels) = 1 - 9/25 = 16/25.
Therefore, the chance of getting a vowel at least once in the two draws is 16/25.
b) To find the probability that the two letters drawn are different, we need to consider two cases: (1) the first letter is a vowel and the second is a consonant, and (2) the first letter is a consonant and the second is a vowel.
Case 1: The first letter is a vowel and the second is a consonant. The probability of the first letter being a vowel is 2/5 (since there are 2 vowels in the box of 5 tickets), and the probability of the second letter being a consonant is 3/5. Therefore, the probability of this case is (2/5) x (3/5) = 6/25.
Case 2: The first letter is a consonant and the second is a vowel. The probability of the first letter being a consonant is 3/5, and the probability of the second letter being a vowel is 2/5. Therefore, the probability of this case is (3/5) x (2/5) = 6/25.
Since the two cases are mutually exclusive (the two letters cannot be both a vowel and a consonant at the same time), we can add their probabilities to find the total probability that the two letters are different:
P(two letters are different) = P(case 1) + P(case 2) = 6/25 + 6/25 = 12/25.
Therefore, the chance that the two letters drawn are different is 12/25.
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6 friends all use $2 off coupons to buy themselves movie tickets. They spend a total of $42 Write the equation
Answer:
(C / n) + 2
Step-by-step explanation:
Amount spent (C) = 42
Number of friends (n) = 6
Coupon on ticket = $2
Original price of ticket will be :
Cost per coupon ticket = (Total amount spent / number of friends)
(Total amount spent / number of friends) + coupon on ticket
= (C / n) + 2
= (42 /6) + 2
= 7 + 2
= 9
11. Classify △ABC by its sides AND angles. Place only ONE option in EACH box.
acute
obtuse
equilateral
isosceles
scalene
right
Classification by angles:
Classification by sides:
Step-by-step explanation:
this is simply per definition.
it is an obtuse triangle, because one angle (B) is larger than 90°.
it is a scalene triangle, because all 3 sides have different lengths.
"acute" would mean that all 3 angles are smaller than 90°.
"right" or "right-angled" would mean that one angle is exactly 90°.
"equilateral" would mean that all 3 sides are equally long.
"isoceles" would mean that 2 sides are equally long.
Given the following table of values for the function f(x), determine f^-1(4)
Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3
What is the inverse of a function?The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.
In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;
Taking two points from the table;
m = y₂ - y₁ / x₂ - x₁
m = 0 - (-3) / -9 - (-11)
m = 3 / 20
Using the slope and one point on the table;
y = mx + x
-3 = 3/20(-11) + c
-3 = -1.65 + c
c = -3 + 1.65
c = -1.35
Putting the slope and y - intercept together;
y = 3/20x - 1.35
y = 3/20x - 27/20
f(x) = 3/20x - 27/20
Taking the inverse of the function;
f⁻¹(x) = (20x + 27)/3
To find the value of f⁻¹(4), we just need to substituting the value of x in the function;
f⁻¹(4) = (20(4) + 27)/3
f⁻¹(4) = 107/3
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use logical equivalence theorem to verify the logical equivalence below
p ∨ q → r ≡ (p → r) ∧ (q → r)
By logical equivalence theorem, we find that composite proposition p ∨ q → r is equivalent to composite proposition (p → r) → (q → r).
How to demonstrate a logical equivalence by means of theorems
Propositions are structures that contains a truth value, and can be, but not exclusively, a sentence. Propositions can be simple or composite, that is, a combination of simple propostions and operators.
In this problem we must determine that a given composite proposition is equivalent to another composite proposition by means of logical equivalence theorem. First, write the complete proposition:
p ∨ q → r
Second, use a conditional formula:
¬ (p ∨ q) ∨ r
Third, apply the DeMorgan's theorem:
(¬ p ∧ ¬ q) ∨ r
Fourth, use distributive property:
(¬ p ∨ r) ∧ (¬ q ∨ r)
Fifth, use conditional formula once again:
(p → r) → (q → r)
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4tan(x)-7=0 for 0<=x<360
Answer:
x = 65.26 degrees or x = 245.26 degrees.
Step-by-step explanation:
To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:
4tan(x) = 7
Then, we can divide both sides by 4 to get:
tan(x) = 7/4
Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:
x = tan^-1(7/4)
Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).
However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).
To find the solution in the first quadrant, we can simply use the value we just calculated:
x = 65.26 degrees (rounded to two decimal places)
To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:
x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)
So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:
x = 65.26 degrees or x = 245.26 degrees.
Pina filled out the following information on the back of her monthly statement:
Ending balance from statement $1,139.78
Deposits outstanding
+ $280.67
Total of checks outstanding
- $656.91
Revised statement balance
Balance from checkbook
$763.54
Find Pina's revised statement balance. Does her account reconcile?
Answer:
yes
Step-by-step explanation:
It is true that Pina's account reconciles.
The monthly statement is given as:
Ending balance from statement $1,139.78 Deposits outstanding + $280.67 Total of checks outstanding - $656.91 Revised statement balance $ Balance from checkbook $763.54Start by calculating the revised statement at the end of the month.
This is calculated using:
\(Revised = Ending\ Balance + Deposit\ Outstanding - Checks\ Outstanding\)
So, we have:
\(Revised = \$1139.78 + \$280.67 - \$656.91\)
Evaluate the expression
\(Revised = \$763.54\)
By comparison, the revised statement equals the balance from the checkbook.
Hence, we can conclude that her account reconciles.
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i need help can someone help me
The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the sine of angle 41°
sin 41° = 2.5/x {opposite/hypotenuse}
x = 2.5/sin 41° {cross multiplication}
x = 3.8106
Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
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2x² + 5x, what will it a Perfect Square? make
Answer:
2x² + 5x + c = 0
For this quadratic equation to have one double root, the discriminant must equal 0.
5² - 4(2)(c) = 0
25 - 8c = 0
c = 25/8
2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.
Explanation:2x² + 5x is not a perfect square.
A perfect square is an expression that can be factored into the square of a binomial. To determine if an expression is a perfect square, we can look at the coefficient of x². In this case, the coefficient is 2, which is not a perfect square.Learn more about Perfect Square here:https://brainly.com/question/34063927
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Is 2x - 3 = -7 x + 2 > y a true or false statement?
!!!!!!!!! Helppppppp plsssss
Answer:
(6 / 4) * (7 + 9)
Step-by-step explanation:
sry that took me so long lol
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
help asap plsplspls!! :)
Select ALL of the solutions of the following system of linear inequalities below.
The solutions of the system of inequalities are:
(0, 3)
(6, 2)
How to find the solutions of the system?Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).
And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.
Then the points that are solutions are:
(0, 3)
(6, 2)
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The base length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle? (5 points) a 2 square feet b 4 square feet c 6 square feet d 8 square feet
Answer:
B. 4 square feet
Step-by-step explanation:
The formula for area of a triangle is length x height / 2 so 4 x 2 is 8 then divided by 2 is 4.
Answer: 4
Base 4
hight 2
4x2=8 ÷ 2 or 1/2 Equals 4
Formula L x W ÷ 2 or 1/2