Answer:
(-2, 4)
Step-by-step explanation:
One of the equations is already solved for y, so let's solve the other one for y and by the transitive proprerty of equality, if y = y, then what those y's are equal to are equal to each other. Solving the first equation for y:
x + y = 2 so
y = -x + 2
Let's fill that in for y in the second equation. Where
[tex]y=\frac{1}{2}x+5[/tex], making the substitution,
[tex]-x+2=\frac{1}{2}x+5[/tex]
Combining like terms and getting the x on one side and the constant on the other side of the equals sign:
[tex]-\frac{3}{2}x=3[/tex]
The product of a fraction and its reciprocal is 1 so we will multiply both sides by
[tex]-\frac{2}{3}[/tex] to get:
[tex](-\frac{2}{3})(-\frac{3}{2})x=(3)(-\frac{2}{3})[/tex]
and we end up with x = -2.
Now that we know that, we can sub that in for x in either one of the original equations. I chose the first one:
If x + y = 2, then -2 + y = 2
and y = 4
Therefore, the solution set is (-2, 4)
Solve 25^3k= 625. With the steps please! I'll be give you 90 points (I need help, okay)!
Answer:
k =(2/3)
Step-by-step explanation:
25 ^ (3k) = 625
Replace 25 with 5^2 and 625 with 5^4
5^2^3k = 5^4
We know that a^b^c = a^(b*c)
5^(2*3k) = 5^4
5^ (6k) = 5^4
The bases are the same, so the exponents must be the same
6k = 4
Divide each side by 6
6k/6 = 4/6
k = 2/3
Being timed, help asap!! The figures are similar. Give the ratio of the area/perimeter of the first figure to the second figure
Answer:
Step-by-step explanation:
Ratios of perimeters is a one-to-one measure. From the figure on the left to the one on the right the ratio of the one-to-one measure is 45/25 which reduces to 9/5.
Area is a squared measure. Once we have the perimeter reduced (we do), we square those perimeter measures to find the area ratio.
[tex](\frac{9}{5})^2=\frac{81}{25}[/tex]
Hilary decided to purchase 3 points in order to lower her interest rate on her
$140,000 mortgage. How much additional money does she need to bring to
closing?
A. $4200
B. $4000
c. $6
D. $400
Answer:
A. $4200
Step-by-step explanation:
A "point" is 1% of the loan value, so the cost of 3 points is ...
0.03 × $140,000 = $4,200
Hilary must bring an additional $4200 to closing.
The additional money Hilary needs to bring to closing the mortgage is given by A = $ 4,200
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Typically, one point is equal to 1% of the total loan amount. Therefore, if Hilary is purchasing 3 points to lower her interest rate, she will need to pay an amount equivalent to 3% of her $140,000 mortgage, which is:
On simplifying the equation , we get
3% x $140,000 = $4,200
Hence , the money is $ 4,200
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which of the following congruence postulates can be used to prove that the triangles are
congruent.
SSS
SAS
ASA
HL
Answer:
ASA
Step-by-step explanation:
Angles E/R and O and the sides EO/RO between them are indicated as congruent. Hence the Angle-Side-Angle (ASA) postulate will be the one that is applicable.
[tex]\sqrt{4x+15} -3\sqrt{x} =0[/tex]
[tex]
\sqrt{4x+15}-3\sqrt{x}=0 \\
\sqrt{4x+15}=3\sqrt{x} \\
4x+15=9x \\
-5x=-15 \\
x=\boxed{3}
[/tex]
Hope this helps.
r3t40
A kilowatt-hour is a unit of measure for consumable energy. A kilowatt-hour, written kWh, is equivalent to using 1,000 watts of power in 1 hour. The table above shows the per-kWh rates charged by several electric companies in New England. According to the United States Energy Information Administration, an average household in New England uses between 530 and 730 kWh of energy per month. Which inequality represents how much less in energy costs a household would pay per month if it uses Company D as its energy supplier, than it uses Company B?
Answer:
C. 13.78 ≤ x ≤ 18.98
Step-by-step explanation:
The rate for Company B is show as 17.4 cents per kWh. That for Company D is shown as 14.8 cents per kWh. The savings obtained by using Company D is ...
17.4 - 14.8 = 2.6 . . . . cents per kWh
Then to find the savings a household would experience, we multiply this savings rate by the monthly usage rate of the household.
530 kWh × $0.026/kWh = $13.78
730 kWh × $0.026/kWh = $18.98
So for household usage between these energy values, the savings (x) using Company D will satisfy ...
13.78 ≤ x ≤ 18.98
(08.03 LC) A system of two equations is shown below: Equation C: a = 4b + 5 Equation D: a = 6b − 2 What value of a can be substituted into equation D to solve the system of equations? (5 points)
Answer:
4b + 5
Step-by-step explanation:
Equation C tells us ...
a = 4b + 5
so, the value "4b +5" can be substituted for "a" in Equation D.
_____
In algebra, things that are equal are interchangeable. One can always be substituted for the other.
the value of 'a' that can be substituted into Equation D to solve the system of equations is 19.
To solve the system of equations given by Equation C: a = 4b + 5 and Equation D: a = 6b \\- 2, we are looking for a value of a which satisfies both equations simultaneously. Since equations C and D both define 'a' in terms of 'b', we can set them equal to each other to find the value of 'b', and then use that value to find 'a'.
Step 1: Set Equation C equal to Equation D, since they both equal 'a'.
4b + 5 = 6b - 2.
Step 2: Solve for 'b'.
Subtract '4b' from both sides: 5 = 2b \\- 2.
Add 2 to both sides: 7 = 2b.
Divide both sides by 2: b = 7/2 or 3.5.
Step 3: Substitute the value of 'b' into either Equation C or D to find 'a'.
Using Equation C: a = 4(3.5) + 5 = 14 + 5 = 19.
Therefore, the value of 'a' that can be substituted into Equation D to solve the system of equations is 19.
please help my daughter asap
Answer:
B.
Step-by-step explanation:
The first number minus the 2nd number will close off the distance.
Can someone answer it, and plot it, for 20 points and brainliest answer?
P.S. they're the same question!!! :)
Answer:
x+y=45, (5,40) and ( 25,20)
Step-by-step explanation:
Here we are given the information that Gian was given 45 mins to spend on computer after dinner. Out of those 45 mins , he can either play games of watch videos.
Therefore If the time for which he watches videos is x and that of the time he spend playing game is y , there sum must be equal to 45 mins.
Hence our equation in terms of x andy will be
[tex]x+y=45[/tex]
Now let us see the graph part.
Here we see that the graph is plot on xy plane where x is taken as time taken in watching videos and y as playing games
i) on Monday , he watch 5 minutes in watching videos
Hence x=5 , we put x=5 in x+y=45 and solve it for y
5+y=45
subtracting 5 from both sides
5+y-5=45-5
y=40
Hence he spend 40 mins on playing games.
So we plot Point (5,40) for monday.
i) on Tuesday , he watch 25 minutes in watching videos
Hence x=25 , we put x=25 in x+y=45 and solve it for y
25+y=45
subtracting 25 from both sides
25+y-25=45-25
y=20
Hence he spend 20 mins on playing games.
So we plot Point (25,20) for Tuesday.
Find the product
(2n-2)(2n^2-3n+5)
Answer:
4n^3 -10n^2 +16n -10
Step-by-step explanation:
Use the distributive property to eliminate parentheses, then combine like terms.
= 2n(2n^2 -3n +5) -2(2n^2 -3n +5)
= 4n^3 -6n^2 +10n -4n^2 +6n -10
= 4n^3 +n^2(-6-4) +n(10+6) -10
= 4n^3 -10n^2 +16n -10
PLS HELP SHOW ALL YOUR WORKING OUT :D
BRAINLIEST
Answer:
18.1 cm
Step-by-step explanation:
Work out CD
[tex]\sqrt{16^{2}-7^{2} } = 14.38749457[/tex] ⇒ Pythagoras Theorem
Use CD and AD to work out AC
[tex]\sqrt{14.38749457^{2}+11^{2} } = 18.11077028[/tex] ⇒ Pythagoras Theorem
PLEASE HELP ME WITH #4 !!
Answer:
Step-by-step explanation:
In order to answer all of these questions we need the position function and the acceleration function. We will discuss why when we get there.
The velocity function is given; in order to find the position function we have to take the antiderivative of the velocity function. So in order are the position, velocity, and acceleration functions below:
[tex]s(t)=\frac{1}{3}t^3-\frac{9}{2}t^2+18t+1[/tex]
[tex]v(t)=t^2-9t+18[/tex]
[tex]a(t)=2t-9[/tex]
I know the constant on the position function is 1 because the info given tells me that s(0) = 1.
For the first question, the formula to find the average velocity is as follows:
[tex]v_{avg} =\frac{s(t_{2})-s(t_{1}) }{t_{2}-t_{1} }[/tex]
To find s(t2) and s(t1) we sub in 8 for t2 and 0 for t1 to get the following:
[tex]v_{avg}=\frac{\frac{83}{3}-1 }{8-0}[/tex]
That simplifies to
[tex]v_{avg}=\frac{10}{3}m/sec[/tex]
The second question wants the instantaneous velocity at t = 5. We get this by subbing in a 5 for t in the velocity function:
[tex]v(5)=(5)^2-9(5)+18[/tex] and
v(5) = -2. This means that the velocity of the particle is 2 m/sec, but it is now going in the opposite (or negative) direction.
The third question is asking for the time interval when the particle is moving to the right. On a velocity/time graph, the x's represent the time and the y's represent the velocity. If the "y" values are positive, then the velocity is positive and that means the object is moving to the right. Where the "y" values are negative, that means that the velocity is negative and the object is moving to the left. To find the answer to this problem we think about the positive and negative y values. Because this is a parabola, I know that the places where the graph goes through the x-axis is where the velocity changes from positive to negative and back to positive. In order to find those places where the graph goes through the x-axis I have to factor the velocity function. When I throw that into the quadratic formula on my calculator I get that x = 3 and x = 6. Completing the square on the velocity function gives me a vertex of [tex](\frac{9}{2},-\frac{9}{4})[/tex]
Because the y value of the vertex is negative, that means that the values of x from negative infinity to x = 3 give positive velocity values, between x = 3 and x = 6 the values of the velocity are negative, and from x = 6 to x = positive infinity the velocity is positive again.
So to sum up question 3, the particle is moving to the right on the intervals
(-∞, 3] and [6, ∞)
The fourth question is really tricky. It requires you to remember some of your Physics and how velocity and acceleration vectors are related. If the acceleration and the velocity both have the same sign, whether it be positive or negative, the object is speeding up. If the acceleration and velocity vectors have opposite signs, one positive and one negative, then the object is slowing down. We already know that from negative infinity to 3 the velocity is positive, so let's check the acceleration values in that interval. I only need to test one number, so let's test a(2).
a(2) = 2(2) - 9 and a(2) = -5
-5 means the object is slowing down here since the velocity is positive and the acceleration is negative.
Let's test the interval between 3 and 6. Let's test a(4).
a(4) = -1
Between the interval of 3 and 6 seconds, the velocity is negative. Since the acceleration is also negative, the object is speeding up between the time interval [3, 6].
We already found that from the left of t = 3, the object was slowing down; so it would also be slowing down to the right of t = 6.
Phew! That's it! We're done!
The cities D, E, and F lie, in respective order, approximately in a straight line. The distance from city D to city E is 125 miles. The distance from city D to city F is 160 miles. Find the distance from city E to city F
Answer:
35 miles
Step-by-step explanation:
The segment addition theorem tells you ...
DE + EF = DF
125 + EF = 160
EF = 35 . . . . . . . subtract 125
The distance from E to F is about 35 miles.
PLEASE HELP!!! GIVIN AWAY 20 PTS!!!
Answer:
x-1 = 0 or x-7 =0
x=1 or x=7
Step-by-step explanation:
(x-1) (x-7) =0
Using the zero product property
x-1 = 0 or x-7 =0
x-1+1 =0 +1 or x-7+7 =0+7
x=1 or x=7
WIll mark the brainliest .
N e E d H e L p.
1. A historian is building a model of a famous steamboat using the scale shown in the table. If the length of the model is 32 inches, what was the actual length of the steamboat, in feet? 1 inch = 11 feet.
2. Peanuts cost $0.21 per ounce. How much will a 2.25 pound bag of peanuts cost?
3. Given 1 in = 2.54 cm and 1 cm = 10 mm, how many millimeters are present in 20.0 inches? Use dimensional (unit) analysis to find your answer.
Answer:
352 ft$7.56508 mmStep-by-step explanation:
1. Starting with the equation ...
1 in = 11 ft
You can multiply both sides by 32 to get the answer to your question:
32 in = 352 ft
The actual length of the steamboat was 352 feet.
__
2. There are 16 ounces in a pound, so the cost is ...
$0.21/oz × 16 oz/lb × 2.25 lb = $(0.21×16×2.25) = $7.56
A 2.25 lb bag of peanuts will cost $7.56.
__
3. Using the given conversion factors, we have ...
(20 in) × (2.54 cm/in) × (10 mm/cm) = (20×2.54×10) mm = 508 mm
There are 508 mm present in 20.0 inches.
Answer:
352 ft
$7.56
508 mm
Step-by-step explanation:
1. Starting with the equation ...
1 in = 11 ft
You can multiply both sides by 32 to get the answer to your question:
32 in = 352 ft
The actual length of the steamboat was 352 feet.
__
2. There are 16 ounces in a pound, so the cost is ...
$0.21/oz × 16 oz/lb × 2.25 lb = $(0.21×16×2.25) = $7.56
A 2.25 lb bag of peanuts will cost $7.56.
__
3. Using the given conversion factors, we have ...
(20 in) × (2.54 cm/in) × (10 mm/cm) = (20×2.54×10) mm = 508 mm
There are 508 mm present in 20.0 inches.
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?a. 1/4(x + 30 + 60) = xb. 1/4(x) = x(30 + 60)c. 1/4x(30 + 60) = xd. 1/4(x) = (30 + 60)
Answer:
The equation can be used to find the amount of time Hiroshi spends on his math homework is 1/4 (30 + 60 + x) = x ⇒ answer a
Step-by-step explanation:
* Lets read the problem and take the information to solve the problem
- Hiroshi spends 30 minutes on history homework
- Hiroshi spends 60 minutes on English homework
- Hiroshi spends x minutes on math homework
* From these information
- The total homework time is (30 + 60 + x) minutes
- Hiroshi spends one fourth of his total homework time on math
- The time of math homework is 1/4 the total homework time
∵ The total homework time = (30 + 60 + x)
∵ The time of math homework is 1/4 the total homework time
∴ The time of math homework = 1/4 (30 + 60 + x)
- Then equate the times of math homework
∵ Hiroshi spends x minutes on math homework
∵ The time of math homework = 1/4 (30 + 60 + x)
∴ 1/4 (30 + 60 + x) = x
* The equation can be used to find the amount of time Hiroshi
spends on his math homework is 1/4 (30 + 60 + x) = x
Frankie is practicing for a 5?kilometer race. His normal time is 31 minutes 24 seconds. Yesterday it took him only 29 minutes 47 seconds. How much faster was Frankie yesterday than his normal time?
Answer: 1 minute 37 seconds (97 secs)
Step-by-step explanation:
31 x 60 = 1860
1860 + 24 = 1884
29 x 60 = 1740
1740 + 47 = 1787
1884 - 1787 = 97
Which of the following is a function? A.) {(-2, -4/5), (-1,-1),(0,0),(-1,-1)} B.) {(-2,0),(0,1/2),(0,3/4),(1,1)} C.) {(-2,1),(-1,0),(0,1),(-2,2)} D.) {(-2,4),(-1,1),(0,0),(1,1)}
Answer:
D.
Step-by-step explanation:
A function, by the easy-to-understand definition, is a relation where no x values are shared. The only set where each x value is different is in D. All the other sets share the same x value. Example: Set C has coordinates (-2, 1) and (-2, 2). The x coordinates are the same, so this isn't a function. It is only a relation.
Need help with a math question
Answer:
7.0711
= 7.1 (rounded to nearest tenth)
Step-by-step explanation:
see attached.
For this case we have by definition, that the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
According to the given data, we have the following points:[tex](x_ {1}, y_ {1}) = (6, -5)\\(x_ {2}, y_ {2}) = (- 1, -4)[/tex]
Substituting the points in the formula we have:
[tex]d = \sqrt {(- 1-6) ^ 2 + (- 4 - (- 5)) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (- 4 + 5) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (1) ^ 2}\\d = \sqrt {49 + 1}\\d = \sqrt {50}\\d = 7.0711[/tex]
Rounding off we have to:
[tex]d = 7.1[/tex]
ANswer:
[tex]d = 7.1[/tex]
what is the sum of the rational expressions below?
For this case we have that the fractions have the same denominator, then we can rewrite as:
[tex]\frac {3x + 2 + (2x -5)} {x-1} =[/tex]
We eliminate the parenthesis:
[tex]+*+=+[/tex]
[tex]+*-=-[/tex]
[tex]\frac {3x + 2 + 2x - 5} {x-1} =[/tex]
We add common terms of the numerator:
[tex]\frac {5x-3} {x-1}[/tex]
Thus, the correct expression is option B.
Answer:
Option B
Answer: OPTION B.
Step-by-step explanation:
Given the rational expressions [tex]\frac{3x+2}{x-1}[/tex] and [tex]\frac{2x-5}{x-1}[/tex], we can observe that both have the same denominator, then we can add them.
We must rewrite the denominator [tex]x-1[/tex] and add the numerators. Then:
[tex]=\frac{(3x+2)+(2x-5)}{x-1}[/tex]
Therefore, adding the like terms on the numerator, we get the following sum:
[tex]=\frac{5x-3}{x-1}[/tex]
We can observe that this sum matches with the sum shown in the option B.
Mercury poisoning is dangerous overload of mercury within the body. A major source of mercury within the body, A major source of mercury poisoning is consuming fish that contain mercury. Certain fish are more prone to having higher levels of mercury than others. The pie chart shows the distribution of four breeds of fish at a hatchery. The hatchery has approximately 6,000 fish. A biologist from the Centers for Disease Control and Prevention randomly test 5% of each breed of fish for mercury content. Her findings are shown in the following table. Based on the biologist's findings, if a single salmon is randomly selected from those that were tested, what is the probability that this particular fish would have a dangerous mercury level?
A) 0.001
B) 0.004
C) 0.02
D) 0.08
Answer:
D) 0.08
Step-by-step explanation:
The pie chart shows that of the 6000 fish in the hatchery, 1/4 of them, or 1500 fish are salmon. A 5% sample of that population will be ...
0.05 × 1500 fish = 75 fish
If 6 of these have dangerous levels of mercury, the probability of randomly choosing a contaminated fish from the test group is ...
6/75 = 8/100 = 0.08
The probability of selecting a salmon with dangerous mercury levels can be determined using the given data.
Explanation:To determine the probability of a randomly selected fish having a dangerous mercury level, we need to find the proportion of tested fish that had dangerous mercury levels. From the table, we can see that out of 120 tested salmon, 3 had dangerous mercury levels. So the probability is 3/120, which simplifies to 1/40 or 0.025. Therefore, the correct answer is option C) 0.02.
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PLS HURRY!!!! Ebony waited more than 56 minutes in the doctor’s office. Which set of steps shows how to write an inequality that represents the number of minutes that Ebony waited?
Answer:
x>56
Step-by-step explanation:
Ebony waited more than 56 minutes in the doctor's office. The first step is to recognize the inequality symbols.
"≥" Can be read as more than or equal to
"≤" Can be read as less than or equal to
">" Can be read as more tha
"<" Can be read as less than
In this case, Ebony waited MORE THAN which means that the correct symbol to be used is ">".
The second step is to define a variable. In this case, we're going to say that 'x' represents the time (in minutes) that Ebony waited.
Finally, let's write the inequality.
x > 56 ✔️
Answer:
x>25
Step-by-step explanation:
Thanks guys for all the help :)
Answer:
(2, 6) .
Step-by-step explanation:
The point A has coordinates (5, 9) and B has coordinates (-1, 3).
The midpoint is (5 + -1)/2 , (9 + 3)/2.
= (2, 6) Answer.
What is the solution to the system of equations below?
y= -1/3 and x = –6
Answer: The Answer is (4,-6)
Step-by-step explanation:
Brandon wants to practice his trombone for at least 5.5 hours this week. Write an inequality to represent the number of hours Brandon will spend practicing this week ? I wrote 5.5 h = p. Os this correct?
Answer:
p ≥ 5.5 hrs
Step-by-step explanation:
Let p represent the number of hours Brandon spends practicing per week.
So he practices for atleast 5.5 hrs.
i.e p ≥ 5.5 hrs
The inequality to represent the number of hours Brandon will spend practicing this week is p ≥ 5.5 hrs.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
Brandon wants to practice his trombone for at least 5.5 hours this week.
Let p represent the number of hours Brandon spends practicing per week.
We know the sign for at least is "≥".
So, the inequality is p ≥ 5.5 hrs.
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Which rays form the sides of IHG? PLZ HELP FAST
C and F are the answers, im pretty sure
i got you
The set of rays form the sides of angle IHG include the following;
C. ray IH
F. ray HG.
What is a line segment?In Mathematics and Euclidean Geometry, a line segment is the part of a line in a geometric figure that is bounded by two distinct end points. This ultimately implies that, a line segment typically has a fixed length.
In Mathematics and Euclidean geometry, a ray is composed of two points that are joined by a straight line such as ray IH and ray HG.
By critically observing the figure showing angle IHG, we can reasonably infer and logically deduce that both ray IH and ray HG form it sides.
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Julia opened a new flower shop, and her daily sales are modeled by f(x) = 2(1.25)x. Determine the rate of growth.
A.2%
B.125%
C.75%
D.25%
Answer:
D. 25%
Step-by-step explanation:
Each day, Julia's sales are 1.25 times the previous day's sales. That is, 25% more than the day before. Julia's sales are increasing 25% per day.
ANSWER:
The correct answer is D.25%
STEP-BY-STEP EXPLANATION:
f(x) = 2 * (1.25)^x
This is in the form
y = a b^x
where b is 1 plus the growth rate
b = 1.25 = 1+growth rate
1.25 = 1 + growth rate
.25 = growth rate
25% = growth rate
A rectangular field measures 81
meters by 117
meters. What will it cost to cover the field with pallets of grass each covering 90 square yards and costing $210
per pallet? (Hint: 1 yd almost equals 0.9 m
)
Final answer:
To cover a 81 meter by 117 meter field with pallets of grass, we calculate the area in square yards and then the number of pallets needed. Each pallet covers 90 square yards and costs $210. The total cost is $27,300.
Explanation:
The question involves calculating the cost to cover a rectangular field with pallets of grass. The field measures 81 meters by 117 meters. We will first need to calculate the area of the field in square meters and then convert it to square yards since the pallets cover an area in square yards. Then, we'll find out how many pallets are needed and multiply by the cost per pallet to get the total cost.
First, let's find the area of the field in square meters:
Area = length × width = 81 m × 117 m = 9,477 m²
Now, convert square meters to square yards, using the hint that 1 yard ≈ 0.9 meters. Since the area is given in meters and we have that 1 m² = (1/0.9)² yd², we can use:
Area in yd² = 9,477 m² × (1/0.9)² = 9,477 m² × 1.23456790123 yd²/m² ≈ 11,700 yd²
Each pallet of grass covers 90 square yards, so we divide the total area by the coverage per pallet:
Number of pallets = Area in yd² / Coverage per pallet = 11,700 yd² / 90 yd²/pallet ≈ 130 pallets
Finally, we multiply the number of pallets needed by the cost per pallet to get the total cost:
Total cost = Number of pallets × Cost per pallet = 130 × $210 = $27,300
The total cost to cover the field with pallets of grass will be $27,300.
Final answer:
To cover a 81m by 117m field with pallets of grass, you need approximately 130 pallets, resulting in a total cost of $27,300.
Explanation:
The question asks us to calculate the cost to cover a rectangular field with grass pallets. The field's dimensions are 81 meters by 117 meters. First, we need to calculate the field's area in square meters and then convert that area to square yards as the pallet covers a certain number of square yards. Lastly, we will determine the total cost by multiplying the number of pallets needed by the cost per pallet.
To convert the field area from square meters to square yards, we use the approximation given that 1 yard is almost equal to 0.9 meters. So, we have:
Area in square meters = length × width = 81 m × 117 m = 9477 m²Area in square yards = 9477 m² × (1 yd / 0.9 m)² ≈ 9477 × 1.23456790123 yd² ≈ 11700 yd²To find out how many pallets we need:
Number of pallets = Total area in square yards / Area covered by one pallet = 11700 yd² / 90 yd² per pallet ≈ 130 palletsThe cost to cover the entire field is therefore:
Total cost = Number of pallets × Cost per pallet = 130 × $210 = $27,300What is the solution set of 2x(x - 1) = 3?
First you must distribute the 2x to the numbers inside the parentheses
(2x * x) + (2x * -1) = 3
[tex]2x^{2}[/tex] - 2x = 3
To make this a quadratic equation you can solve bring the 3 over to the left side of the equation by subtracting it to both sides
[tex]2x^{2}[/tex] - 2x - 3 = 0
Use the quadratic equation to solve this (image of the quadratic equation is below)
Remember that quadratic functions are set up like so:
[tex]ax^{2} +bx +c = 0[/tex]
That means that in this equation...
a = 2
b = -2
c = -3
^^^Plug these numbers into the quadratic equation and solve...
[tex]\frac{2+/-\sqrt{(-2)^{2}-4(2)(-3)}}{2(2)}[/tex]
[tex]\frac{2 +/-\sqrt{4+24}}{4}[/tex]
[tex]\frac{2+/-\sqrt{28} }{4}[/tex]
[tex]\frac{2+/-2\sqrt{7} }{4}[/tex]
[tex]\frac{1+/-\sqrt{7} }{2}[/tex]
Keep in mind that +/- is ±
[tex]\frac{1+\sqrt{7} }{2}[/tex]
[tex]\frac{1-\sqrt{7} }{2}[/tex]
^^^Exact answers
Approximations:
1.823
-0.823
Hope this helped!
~Just a girl in love with Shawn Mendes
Find the area of the triangle
Answer:
67.5
Step-by-step explanation:
Used a calculator
Answer:
67.5 sq. ft
Step-by-step explanation:
15 ft is the base, and 9 is the length of one side, if you multiply the two together, you get 135 sq. ft; however, this is just the length of a rectangle twice the size of the triangle, to get the area of the triangle you'll need to divide 135 by 2 which is 67.5 sq. ft.