Answer:
The first mechanic worked 5 hours
The second mechanic worked 15 hours
======================================================
Work Shown:
x = number of hours the 1st mechanic worked
y = number of hours the 2nd mechanic worked
75x = total amount charged by the 1st mechanic
95y = total amount charged by the 2nd mechanic
75x+95y = total charged both mechanics combined
75x+95y = 1800 is the first equation to set up
The other equation is x+y = 20 since the total combined time spent was 20 hours.
Solve for y to get y = 20-x
Then plug it into the first equation to solve for x.
75x+95y = 1800
75x+95( y ) = 1800
75x+95(20-x) = 1800 ....... replace y with 20-x
75x+1900-95x = 1800
-20x+1900 = 1800
-20x = 1800-1900
-20x = -100
x = -100/(-20)
x = 5
Now we can determine the value of y
y = 20-x
y = 20-5
y = 15
The first mechanic worked 5 hours.
The second mechanic worked 15 hours.
Calculate the average inflation rate between 2006 and 2009 and between 2009 and 2012.
In 2006, the quantity of money (in billions of dollars) was 1,366, the velocity was 10.253, the real GDP (in billions of 2012 dollars) was 15,338, and the GDP deflator was 0.913.
In 2009, the quantity of money (in billions of dollars) was 1,692, the velocity was 8.687, the real GDP (in billions of 2012 dollars) was 15,423, and the GDP deflator was 0.953.
In 2012, the quantity of money (in billions of dollars) was 2,461, the velocity was 6.719, the real GDP (in billions of 2012 dollars) was 16,197, and the GDP deflator was 1.021.
Answer:
To calculate the average inflation rate between 2006 and 2009, we need to determine the percentage change in the GDP deflator over that period.
The GDP deflator is given by the equation:
GDP deflator = (Nominal GDP) / (Real GDP)
Let's calculate the GDP deflator for both 2006 and 2009:
GDP deflator in 2006 = (1366 billion dollars) / (15338 billion 2012 dollars) = 0.0889
GDP deflator in 2009 = (1692 billion dollars) / (15423 billion 2012 dollars) = 0.1097
Now, we can calculate the percentage change in the GDP deflator:
Percentage change = ((GDP deflator in 2009 - GDP deflator in 2006) / GDP deflator in 2006) * 100
= ((0.1097 - 0.0889) / 0.0889) * 100
= (0.0208 / 0.0889) * 100
= 23.39%
Therefore, the average inflation rate between 2006 and 2009 is approximately 23.39%.
To calculate the average inflation rate between 2009 and 2012, we need to determine the percentage change in the GDP deflator over that period.
Let's calculate the GDP deflator for both 2009 and 2012:
GDP deflator in 2009 = 0.1097
GDP deflator in 2012 = 1.021
Now, we can calculate the percentage change in the GDP deflator:
Percentage change = ((GDP deflator in 2012 - GDP deflator in 2009) / GDP deflator in 2009) * 100
= ((1.021 - 0.1097) / 0.1097) * 100
= (0.9113 / 0.1097) * 100
= 830.94%
Therefore, the average inflation rate between 2009 and 2012 is approximately 830.94%.
4) 1,1,4,8,9,27, 16, 64, m, n,.
n-m es:
Suceciones
Answer:
m = 25
n = 100
Step-by-step explanation:
1, 1, 4, 8, 9, 27, 16, 64, m, n, ....
In this series,
Each term on the odd place is obtained by adding first 'n' odd numbers to the previous term.First term = 1
Third term = 1 + 3 = 4
Fifth term = 4 + 5 = 9
Seventh term = 9 + 7 = 16
So, ninth term = 16 + 9 = 25
[tex]\boxed{\bf m = 25}[/tex]
Each term on the even place is the cube of natural numbers.Second term = 1³ = 1
Fourth term = 2³ = 8
Sixth term = 3³ = 27
Eighth term = 4³ = 64
Tenth term = 10³ = 100
[tex]\boxed{\bf n = 100}[/tex]
how much money must be deposited now in an account paying 3.5% annual interest, compounded monthly, to have a balance of 20,000 after 15 years?(show work please)
Approximately $10,758.90 must be deposited now in the account to have a balance of $20,000 after 15 years, assuming a 3.5% annual interest rate compounded monthly.
To calculate the amount of money that must be deposited now to have a balance of $20,000 after 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final balance ($20,000)
P = principal amount (initial deposit we want to find)
r = annual interest rate (3.5% or 0.035 as a decimal)
n = number of times interest is compounded per year (monthly, so n = 12)
t = number of years (15)
Substituting the given values into the formula:
$20,000 = P(1 + 0.035/12)^(12*15)
Next, we can simplify the equation and solve for P:
$20,000 = P(1 + 0.0029166666666667)^(180)
$20,000 = P(1.0029166666666667)^(180)
To isolate P, we divide both sides of the equation by (1.0029166666666667)^(180):
P = $20,000 / (1.0029166666666667)^(180)
P ≈ $10,758.90
Therefore, approximately $10,758.90 must be deposited now in the account to have a balance of $20,000 after 15 years, assuming a 3.5% annual interest rate compounded monthly.
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If 20700 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
Rounding to the nearest cent, the value of the investment at the end of 5 years for the different compounding methods are:
Annually compounded: $31,730.82
Semi-annually compounded: $31,992.85
Quarterly compounded: $32,136.11
Monthly compounded: $32,232.45
Daily compounded: $32,265.83
To calculate the value of the investment at the end of 5 years, we can use the compound interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A is the final amount (value of the investment)
P is the principal amount (initial investment)
r is the interest rate (in decimal form)
n is the number of compounding periods per year
t is the number of years
Given:
Principal amount (P): $20,700
Interest rate (r): 9% per year (0.09 in decimal form)
Number of compounding periods per year (n): It is not specified in the question. We will assume it to be annually.
Using the formula, we can calculate the value of the investment for different compounding methods:
Annually compounded:
A = 20700 * (1 + 0.09/1)^(1*5) = 20700 * (1.09)^5 ≈ $31,730.82
Semi-annually compounded:
A = 20700 * (1 + 0.09/2)^(2*5) = 20700 * (1.045)^10 ≈ $31,992.85
Quarterly compounded:
A = 20700 * (1 + 0.09/4)^(4*5) = 20700 * (1.0225)^20 ≈ $32,136.11
Monthly compounded:
A = 20700 * (1 + 0.09/12)^(12*5) = 20700 * (1.0075)^60 ≈ $32,232.45
Daily compounded:
A = 20700 * (1 + 0.09/365)^(365*5) ≈ $32,265.83
Rounding to the nearest cent, the value of the investment at the end of 5 years for the different compounding methods are:
Annually compounded: $31,730.82
Semi-annually compounded: $31,992.85
Quarterly compounded: $32,136.11
Monthly compounded: $32,232.45
Daily compounded: $32,265.83
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7.) According to the quantity equation, changes in the money supply will lead directly to
changes in the price level if velocity and real GDP are unaffected by the change in the
money supply. Will velocity change over time? What factors might lead to changes in
velocity? Are those changes related to changes in the money supply?
According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.
For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.
For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.
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X+5<5x-3 solve the equation.
3.1 Which basic property of operations was used in each of the following
calculations?
3.1.1 25 x 4 = 4 x 25 = 100
3.1.2 412 412 412 + (-412) = 0
3.1.3 25 +37
-
=
= 20 + 5+ 30+7
= 20 +30 +5+7
= 50+ 12 = 62
3.1.1 The basic property of operations used is the commutative property of multiplication.
3.1.2 The basic property of operations used is the additive inverse property.
3.1.3 The basic property of operations used is the associative property of addition.
3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.
3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.
3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.
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Provide reasons for the proof of the triangle proportionality theorem. 25 points
The two column proof is completed below
Statement Reason
1. line KI parallel to line MN Given
2. ∠ JKL ≅ ∠ JMN and ∠ JLK ≅ ∠ JNM Corresponding angles are equal
3. Δ JKL ~ Δ JMN Similar triangles
4. (JM)/(JK) = (JN)/(JL) Ratios of corresponding sides are
equal
5. JM = JK + KM and JN = JL + LN Segment Addition Postulate
6. (JK + KM)/(JK) = (JL + LN)/(JL) Substitution property
7. (JK)/(JK) + (KM)/(JK) = (JL)/(JL) + (LN)/(JL) Addition of fractions
8. 1 + (KM)/(JK) = 1 + (LN)/(JL) Simplify
9. (KM)/(JK) = (LN)/(JL) Simplify (the required proof)
What are similar triangles?Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.
The equality of corresponding sides of similar triangles is used in the proof and it helped to state that: (JM)/(JK) = (JN)/(JL).
Further calculations were substitution and simplifying
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In a bank, 20 customers on the average, are served by a cashier in an hour. If
the service time has exponential distribution, what is the probability that;
(i) It will take more than 10 minutes to serve a customer?
(ii) A customer shall be free within 4 minutes
(i) The probability that it will take more than 10 minutes to serve a customer is approximately 0.1353.
(ii) The probability that a customer shall be free within 4 minutes is approximately 0.4866.
To solve this problem, we can use the exponential distribution formula. The exponential distribution is often used to model the time between events occurring at a constant average rate. In this case, we want to find the probability of specific service times.
Let's denote λ as the average number of customers served per hour. Given that 20 customers are served on average, we can determine λ by dividing the average number of customers by the time taken to serve them, which is 1 hour. Therefore, λ = 20 customers/hour.
Now, we can calculate the probability using the exponential distribution formula:
(i) To find the probability that it will take more than 10 minutes to serve a customer, we need to convert 10 minutes to hours, which is 10/60 = 1/6 hour. Let's call this value x.
The probability can be calculated as P(X > x) = 1 - P(X ≤ x), where X follows an exponential distribution with rate parameter λ.
P(X > 1/6) = 1 - P(X ≤ 1/6)
= 1 - (1 - [tex]e^{(-\lambda x))[/tex] [Using the cumulative distribution function (CDF) of the exponential distribution]
= [tex]e^(- \lambda x)[/tex]
= [tex]e^{(-20/6)[/tex]
≈ 0.1353
(ii) To find the probability that a customer shall be free within 4 minutes, we convert 4 minutes to hours, which is 4/60 = 1/15 hour. Let's call this value y.
The probability can be calculated as P(X ≤ y), where X follows an exponential distribution with rate parameter λ.
P(X ≤ 1/15) = 1 - [tex]e^{(-\lambda y)[/tex]
= 1 - [tex]e^{(-20/15)[/tex]
≈ 0.4866
Therefore, the probability that a customer shall be free within 4 minutes is approximately 0.4866.
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A kids pool had a small opening through which water sometimes leaked out. Water was poured into the pool from time to time. The graph shows the amount of water in the pool (y), in gallons, at certain times (x), in hours.
Which of the following statements best describes the amount of water in the pool ?
1) it is increasing during the time interval 4
2) it is increasing during the time interval 10
3) it is decreasing during the time interval 4
4) it is decreasing during the time interval 10
The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.
How to determine the the interval of the water in the pool?To determine the time interval of the water in the pool the following is carried out.
At 0 hour, the water is at the level of = 40 gallons
At 1 hour, the water decreased to = 25 gallons.
At 2 hours, the water decreased to = 10 gallons.
The water remained at a constant level till 4 hours.
Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.
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6) 1,1,3,8,19, 41
a) 60
b) 81
c) 90
d) 101
Analogias
The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.
To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:
1 1 3 8 19 41
0 2 5 11 22
Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.
Let's check if the differences between consecutive terms are square numbers:
2 = 1²
5 = 2² + 1²
11 = 3² + 2²
22 = 4² + 3²
Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:
41 + 57 = 98
Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.
Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
b) [tex]MN = 6\frac{3}{4}[/tex]
Step-by-step explanation:
In ΔPQN and ΔLMN,
∠PQN = ∠LMN (given)
∠PNQ = ∠LNM (vertically opposite angles)
Since two angles in the triangles are same, the third angle must alos be same
Therefore,
∠QPN = ∠MLN
By AAA property, the two triangles are similar
Therefore,
[tex]\frac{PQ}{LM} =\frac{QN}{MN} =\frac{PN}{LN} \\\\\implies \frac{8}{6} =\frac{9}{MN} =\frac{PN}{LN} \\\\\implies \frac{8}{6} =\frac{9}{MN}\\\\\implies MN =\frac{9*6}{8}\\\\\implies MN =\frac{54}{8}\\\\\implies MN =\frac{27}{4}\\\\\implies MN =6\frac{3}{4}[/tex]
According to the quantity equation, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply. Will velocity change over time? What factors might lead to changes in velocity? Are those changes related to changes in the money supply?
Furthermore, changes in velocity do not always lead to shifts in the price level or nominal GDP.
The quantity theory of money suggests that changes in the money supply may result in changes in the price level if there is no change in velocity and real GDP. Changes in velocity are related to changes in the amount of money required to finance transactions. A shift in velocity can occur due to several factors, including financial innovation and changes in regulations, technology, and consumer preferences.
However, such changes may not necessarily be related to shifts in the money supply.According to the quantity theory of money, MV = PY, where M refers to the money supply, V refers to the velocity of money, P refers to the price level, and Y refers to real GDP. Thus, a change in the money supply is anticipated to result in an equal change in the nominal GDP, given that velocity and real GDP remain unchanged.
A shift in velocity can be brought about by a number of factors, including financial innovation and changes in regulations, technology, and consumer preferences. Velocity is defined as the number of times per unit of time that the monetary unit is used for transactions in the economy.
When velocity changes, the amount of money required to finance transactions also changes.The quantity theory of money asserts that an increase in the money supply will raise the price level and nominal GDP, holding constant the velocity and real GDP. Nonetheless, changes in velocity are often associated with changes in financial innovation and regulations, consumer behavior and technology, rather than changes in the money supply.
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PLEASE HELP AS SOON AS POSSIBLE
A. The slope intercept form of the graph is y = -10x + 100.
B. The slope intercept form equation can be gotten using two points to find the slope and the y-intercept.
C. The slope represents the change in the percentage of battery remaining with respect to the change in number of hours.
How to represent equation in slope intercept form?
The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using the (0, 100) and (1, 90). Hence,
m = 90 - 100 / 1 - 0
m = -10 / 1
m = -10
Therefore,
y = -10x + b
y = -10x + 100
B. The slope intercept form equation can be found using two points in the graph.
C. The slope in this situation represent the change in the percentage of battery remaining with respect to the change in number of hours.
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GEOMETRY 100 POINTS CHALLENGE
Answer:
∠D = 44
Step-by-step explanation:
Since EF║DG, ED is a transversal
⇒ ∠E + ∠D = 180
⇒ ∠D = 180 - ∠E
= 180 - 136
= 44
⇒ ∠D = 44
How many roots do the functions have in common?
�
(
�
)
=
�
2
−
9
f(x)=x
2
−9f, left parenthesis, x, right parenthesis, equals, x, squared, minus, 9
A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens up. The function has a y-intercept at zero, eight, an x-intercept at two, zero, a minimum around six, negative six point five, and another x-intercept at ten, zero.
There are no roots of the given functions in common.
To find the roots of the functions in common, the two given functions will have to be equated to each other. So the answer to the given question will be determined by finding the roots of the given equations. The given equations are: (�)=�2−9f(x)=x2−9
Here, the first equation is a linear equation and the second one is a quadratic equation. The number of roots of these two functions in common will be the number of solutions to the equation obtained by equating these two given equations.
Now, equating the given equations, we have (�) = f(x)2 - 9 ⇔ � - f(x)2 = 9.The equation obtained by equating the two given equations is a quadratic equation. Let p(x) = � - f(x)2, then the above equation can be written as p(x) = 9.
Since the discriminant, D = b^2 - 4ac = 0 - 4(1)(9) = - 36 < 0, this means the quadratic equation doesn't have any real solutions. Hence, there are no roots of the given functions in common.
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If 400 x 300 = 120,000
And 40 x 30 is 1,200
Fill in the blanks and show your work
*_____ x ______ = 12,000?
Answer:
this list
Step-by-step explanation:
1×12000=12000
2×6000=12000
3×4000=12000
4×3000=12000
5×2400=12000
6×2000=12000
8×1500=12000
10 ×1200=12000
12 ×1000=12000
Solve for m∠PNM.
58
186
97
87
The calculated measure of m∠PNM is 87 degrees
How to calculate the meausre of m∠PNM.from the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
PM = 360 - 64 - 122
Evaluate
PM = 174
Next, we have
m∠PNM = 1/2 * 174
So, we have
m∠PNM = 87
Hence, the measure of m∠PNM is 87 degrees
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Marvin ran 7 1/4 miles on Saturday and 6 1/4 miles on Sunday. How many miles did Marvin run in all?
Write your answer as a fraction or as a whole or mixed number.
Answer: 13 1/2
Step-by-step explanation:
There are a few methods to complete this problem, but here is one of the simplest methods by separating the parts:
First, we rewrite our equation with parts separated
7 + 1/4 + 6 + 1/4
Next, we solve the whole number parts
7 + 6 = 13
Solving the fraction parts and reducing the result to the lowest terms
1/4 + 1/4 = 2/4
2/4 = 1/2
Combining the whole and fraction parts
13 + 1/2 = 13 1/2
Hope this helps! Please feel free to ask any questions if needed :)
100 Points! Geometry question. Find x and y. Photo attached. Please show as much work as possible. Thank you!
Answer: 35x/2 + 9y −5
Step-by-step explanation:
QUESTION 4
What is the formal null hypothesis?
Ομ
μ
= P
English Spanish
Ομ
Language
= μ
Korean
#μ
Teacher Support
Ομ
English
Spanish
O The means are not all equal.
#μ
Korean
The formal null hypothesis, denoted as H₀, for the comparison of means in this context would be: H₀: μ₁ = μ₂ = μ₃
In words, the null hypothesis states that the population means of English, Spanish, and Korean language proficiency levels (represented by μ₁, μ₂, and μ₃, respectively) are all equal.
The null hypothesis assumes that there is no significant difference between the means of the three language proficiency levels. It suggests that any observed differences in the sample means are due to random sampling variability and not representative of true differences in the population means.
When conducting hypothesis testing, the null hypothesis is initially assumed to be true, and the alternative hypothesis (H₁) is formulated as the opposite or complementary statement. In this case, the alternative hypothesis would be:
H₁: At least one of the population means of English, Spanish, and Korean language proficiency levels is different.
To determine whether to reject the null hypothesis, statistical tests such as analysis of variance (ANOVA) or t-tests can be used to compare the means of the language proficiency levels. If the test results provide sufficient evidence to reject the null hypothesis, it suggests that there are significant differences between the means of the language proficiency levels.
It's important to note that this is a generic explanation of the formal null hypothesis in the context of comparing means. The specific null hypothesis may vary depending on the research question and the variables being compared.
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Simplify 2 √ 2u − 7 √ 3v
Answer:
To simplify the expression 2√(2u) - 7√(3v), we can combine like terms.
Since both terms have square roots, we can look for any common factors within the square roots. In this case, we can factor out the square root of 2 from the first term and the square root of 3 from the second term:
2√(2u) - 7√(3v) = 2√2 √u - 7√3 √v
Now, we can simplify further by combining the coefficients outside the square roots:
2√2 √u - 7√3 √v = 2√2u - 7√3v
Therefore, the simplified form of 2√(2u) - 7√(3v) is 2√2u - 7√3v.
GEOMETRY 100 POINTS CHALLENGE
Answer:
x = 9
Q = 64
Step-by-step explanation:
Since QRST is a trapezoid
∠Q = ∠R
9x - 17 = 4x + 28
9x - 4x = 28 + 17
5x = 45
x = 45/5
x = 9
∠Q = 9x - 17
= 9*9- 17
= 81 - 17
= 64
Choose the correct answer below
The correct statement is;
False, because x = [tex]cos^-^1({\frac{-1}{2} )[/tex] is in the interval [tex]( -\frac{\pi }{2} , \frac{\pi }{2} )[/tex] that is, [tex]cos^-^1({\frac{-1}{2} )[/tex] = [tex]\frac{2\pi }{3}[/tex]. So all solutions of cos x = -1/2 will be x = 2π/3 + 2nx and x = 4π/3 + 2nx.
Option D
How to determine the statementFrom the information given, we have that;
All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx
There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx
Such that n is an integer.
This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.
The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.
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In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= [tex]\frac{18}{36}[/tex]
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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when you answer the question in the picture, make sure to explain your answer in steps. Thank you.
Answer:
Step-by-step explanation:
help me asap. my exam is tomorrow.
The total surface area of the doghouse is 1452 ft²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.
area of the roof part = 2( 13×11) + 2( 12× 10)×1/2
= 286 + 720
= 1006 ft²
surface area of the building
= 2( lb + lh + bh) -bh
= 2( 10× 11 + 10×8 + 11×8) - 10×11
= 2( 110+80+88)-110
= 2( 278) -110
= 556 -110
= 446ft²
The total surface area = 1006 + 446
= 1452 ft²
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Fill in the table 'using this function rule.
y = -5x+2
x
-1
0
1
2
y
0
0
0
X
4
S
Answer:
7, 2, -3, -8
Step-by-step explanation:
y = -5x + 2 Substitute in -1 for x
y = -5(-1) + 2
y = 5 + 2
y = 7
y = -5x + 2 Substitute in 0 for x
y = -5(0) + 2
y = 0 + 2
y = 2
y = -5 + 2 substitutes in 1 for x
y = -5(1) + 2
y = -5 + 2
y = -3
y = -5x + 2 Substitute in 2 for x
y = -5(2) + 2
y = -10 + 2
y = -8
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Find all points on the x-axis that are 16 units from the point (5,-8)
To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.
d = √((x - 5)² + (0 - (-8))²)
Simplifying:
d = √((x - 5)² + 64)
Now, we want the distance d to be equal to 16 units. So, we set up the equation:
16 = √((x - 5)² + 64)
Squaring both sides of the equation to eliminate the square root:
16² = (x - 5)² + 64
256 = (x - 5)² + 64
Subtracting 64 from both sides:
192 = (x - 5)²
Taking the square root of both sides
√192 = x - 5
±√192 = x - 5
x = 5 ± √192
Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:
Point 1: (5 + √192, 0)
Point 2: (5 - √192, 0)
In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).
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