The correct option is that B. Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
How to explain the informationSelena is correct. She simplified correctly and then evaluated correctly after substituting the values for the variables. Drake is incorrect because he should have simplified first, before substituting the values for the variables.
When Drake substituted the values for the variables first, he ended up with the expression (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1. This is incorrect because he did not simplify the expression first. If he had simplified first, he would have gotten the expression (StartFraction negative 2 Over 1 Endfraction) Superscript negative 1, which is equal to one-half.
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Instructions: Draw a segment AB
on your paper. Then construct a segment A′B′
that is congruent to your segment AB
using only a compass and straightedge. Upload a photo of AB
and A′B′
together on the same image.
The segment AB and A'B' are attached accordingly.To construct a segment A'B' that is congruent to segment AB using only a compass and straightedge, follow these steps.
The steps to be taken1. Draw a line segment AB on your paper.
2. Place the compass at point A and adjust its width to any convenient length.
3. Without changing the width of the compass, draw an arc intersecting the line segment AB at point C.
4. Keeping the same width of the compass, place it at point C and draw another arc that intersects the previous arc.
5. Label the point of intersection of the arcs as D.
6. Draw a straight line connecting point D and point B.
7. The line segment A'B' is now congruent to segment AB.
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A movie rental store gives a free popcorn to every 15th customer and a free movie rental to every 40th customer. Which customer was the first to win both prizes?
PLEASE HELP ME ANSWER THIS QUESTION, THANKS!
Answer:
(a) therefore the equation is
a(t) = -1000t + 32800
Step-by-step explanation:
(a) a(t) = mt + b
(8, 24800). ( 20, 12800)
(t, a). ( t¹ , a¹)
slope or gradient, m = a¹ - t¹
a - t
m = 12800 - 24800
20 - 8
m = -12000
12
m = -1000
The slope is -1000
let's use (8, 24800) to find b.
24800 = -1000 (8) + b
24800 = -8000 + b
b= 24800 + 8000
b = 32800
therefore the equation is
a(t) = -1000t + 32800
(b) Since the slope is negative (-1000), it means that the altitude is decreasing at a constant rate of 1000 feet per minute. The negative sign indicates the descent, as the altitude is decreasing over time.
Therefore, the slope tells us that the plane is descending at a constant rate of 1000 feet per minute.
(c) The value 32800 tells us the initial altitude of the plane before descending. It indicates the starting point or the initial position of the aircraft above the ground level.
Therefore, the value 32800 represents the initial altitude of the plane before it began descending.
Using what you know about arclength, volume and surface to sketch and
calculate the following:
1. The area under the curve of f(x) = 2[tex]\sqrt{x}[/tex] from x = 1 to x = 9 is 16 square units.
2. Volume: 1936π/5 cubic units by sliding semi-circle and triangle.
3. Volume: -102π cubic units, Surface Area: (400π + 206)/3 square units.
1. To calculate the area of the region formed in the first quadrant under the function f(x) = 2 between x = 1 and x = 9, we can use integration. The integral of f(x) = 2 with respect to x from 1 to 9 is:
∫[1, 9] 2 dx = 2 * [x] evaluated from 1 to 9 = 2 * [(9) - (1)] = 2 * [8] = 16.
Therefore, the area of the region is 16 square units.
2. To calculate the volume created by sliding a semi-circle and an equilateral triangle along the x-axis, we can use the method of cylindrical shells. The volume of each shell is given by the formula:
V = 2πxf(x)dx.
We integrate the volume of each shell over the interval [1, 4] for the semi-circle and [4, 9] for the triangle:
V = ∫[1, 4] 2πx(2) dx + ∫[4, 9] 2πx(2) dx
= 4π∫[1, 4[tex]] x^(^3^/^2^)[/tex]dx + 4π∫[4, 9] [tex]x^(^3^/^2^)[/tex]dx.
Using the power rule of integration, we have:
V = 4π * [(2/5)[tex](4^(^5^/^2^) - 1^(^5^/^2^))] + 4π * [(2/5)(9^(^5^/^2^) - 4^(^5^/^2^))][/tex]
= 4π * [(2/5)(31)] + 4π * [(2/5)(211)]
= 248π/5 + 1688π/5
= 1936π/5.
Therefore, the volume created by sliding the semi-circle and equilateral triangle along the x-axis is 1936π/5 cubic units.
3. To calculate the resulting volume using two integrals, we can subtract the volume of the equilateral triangle from the volume of the semi-circle. The volume of the semi-circle is given by:
V(semi-circle) = ∫[1, 4] π[tex](2)^(2)[/tex]dx
= π∫[1, 4] 4x dx
= 4π∫[1, 4] x dx
= 4π * [(1/2)x^2][tex][(1/2)x^2][/tex] evaluated from 1 to 4
= 4π * [(1/2)(16) - (1/2)(1)]
= 4π * [8 - 1]
= 28π.
The volume of the equilateral triangle is given by:
V(triangle) = ∫[4, 9][tex](2)^(2)[/tex] dx
= ∫[4, 9] 4x dx
= 4∫[4, 9] x dx
= 4 *[tex][(1/2)x^2][/tex]evaluated from 4 to 9
= 4 * [(1/2)(81) - (1/2)(16)]
= 4 * [(1/2)(65)]
= 130.
The resulting volume is:
Volume = V(semi-circle) - V(triangle)
= 28π - 130
= -102π cubic units.
To calculate the surface area of the solid, we need to consider the surfaces of the semi-circle, triangle, and two quadrilaterals. The surface area of the semi-circle is given by:
Surface area(semi-circle) = ∫[1, 4] 2π(2) ds.
The differential arc length ds can be expressed as ds = [tex]\sqrt{(1 + (f'(x))^2)}[/tex] dx, where f(x) = 2. Since f(x) = 2, we have f'(x) = 0. Therefore, ds = [tex]\sqrt{(1 + 0^2) }[/tex]dx = dx.
Substituting this in the integral, we have:
Surface area(semi-circle) = ∫[1, 4] 2π(2) dx
= 4π∫[1, 4] 2 dx
= 8π * [tex][(2/3)x^3][/tex] evaluated from 1 to 4
= 8π * [(2/3)(64) - (2/3)(1)]
= 8π * [128/3 - 2/3]
= 8π * (126/3)
= 336π.
The surface area of the triangle is given by:
Surface area(triangle) = ∫[4, 9] (2) dx
= 2∫[4, 9] dx
= 2 * [x] evaluated from 4 to 9
= 2 * [(9) - (4)]
= 2 * [5]
= 10.
The surface area of the two quadrilaterals is equal to the sum of the areas of the semi-circle and triangle, which is:
Surface area(quadrilaterals) = 2 * (28π + 130)
= 2 * (28π + 130π/1)
= 316π.
Therefore, the total surface area of the solid is:
Surface area = Surface area(semi-circle) + Surface area(triangle) + Surface area(quadrilaterals) - Difference between the semi-circle and the triangle at x = 4
= 336π + 10 + 316π - (28π - 130)
= 400π + 206.
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The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1,400. If the annual percentage rate is 15.6% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent.
Answer:
Step-by-step explanation:
To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.
Given:
Average daily balance for November = $700
Unpaid balance at the end of November = $1,400
Annual percentage rate (APR) = 15.6%
Step 1: Calculate the interest charged for the month of November.
Interest = (Average daily balance * APR * Number of days in the month) / 365
Number of days in November = 30
Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)
Step 2: Add the interest to the unpaid balance to get the total balance on December 1.
Total balance = Unpaid balance + Interest
Total balance = $1,400 + $36.44 = $1,436.44
Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).
The total balance on the next billing date December 1 is $1,509.20.
What is an annual percentage rate?The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).
Given,
The average daily balance of a credit card for November = is $700Unpaid balance at the end of the month = $1,400The annual percentage rate = 15.6%Then, the percentage rate for November = [tex]\sf\frac{15.6}{100}[/tex] × 700
[tex]\sf = \$109.20[/tex]
Balance on 1st December = unpaid balance at the end of November + percentage rate
[tex]\sf = $1400 +$109.20[/tex]
[tex]\sf =\$1509.20[/tex]
Therefore, the total balance on the next billing date December 1 is $1,509.20.
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How much more (or less) output will the average American have next year if the $22 trillion U.S. economy (GDP) grows (or contracts) by 1% assuming a population of 340 million.
Answer:
The **Gross Domestic Product (GDP)** is the total value of goods and services produced in a country in a year. According to the World Bank, the GDP of the United States was **$22.67 trillion** in 2020.
If the U.S. economy grows by 1%, the GDP would increase by **$226.7 billion** (1% of $22.67 trillion). If the U.S. economy contracts by 1%, the GDP would decrease by **$226.7 billion**.
The average American output is measured by Gross Domestic Product per capita (GDP per capita). According to the World Bank, the GDP per capita of the United States was **$68,309** in 2020.
If we assume that the population of the United States is 340 million people, then each person's share of GDP would be approximately **$201** ($68,309 divided by 340 million).
Therefore, if the U.S. economy grows by 1%, each person's share of GDP would increase by approximately **$0.67** ($201 times 1% growth rate). If the U.S. economy contracts by 1%, each person's share of GDP would decrease by approximately **$0.67** ($201 times 1% contraction rate).
Find (a) the range and (b) the standard deviation for the sample.
(a) The range is.
(Round to one decimal place as needed.)
(b) The standard deviation is.
(Round to one decimal place as needed.)
Value Frequency
23456
33421
(a) The range is 1.38.
(b) The standard deviation is 0.46.
How to calculate the range of a data set?In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;
Range of data set = Highest number - Lowest number
Range of data set = 85.63 - 84.25
Range of data set = 1.38.
In Mathematics and Statistics, the standard deviation of any data set can be calculated by using this formula:
Standard deviation, δx = √(1/n × ∑(x - [tex]\bar{x}[/tex])²)
Mean = (85.54+84.33+85.15+85.63+84.25+85.18+84.78+85.36+85.04)/9
Mean = 85.03
Standard deviation, δx = √[(85.54-85.03)² + (84.33-85.03)² + (85.15-85.03) + (85.63-85.03)² + (84.25-85.03)² + (85.18-85.03)² + (84.78-85.03)² + (85.36-85.03)² + (85.04-85.03)²
Standard deviation, δx = √0.21
Standard deviation, δx = 0.46.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
50 Pts!!!!!
What is the value today of a car purchased 5 years ago for $7,950.00?
Value of car = $
The estimated value of the car today would be around $1,987.50.
The value of a car purchased 5 years ago for $7,950.00 would depend on various factors, including the make, model, condition, mileage, market demand, and depreciation rates.
However, without specific details about the car, it is difficult to provide an accurate value. Generally, vehicles depreciate over time due to wear and tear, technological advancements, and changing market conditions.
On average, cars can depreciate between 15% and 25% annually. Considering this range, the car's value today could be estimated by applying an average annual depreciation rate.
Assuming a conservative depreciation rate of 15% per year, the value of the car after 5 years would be approximately:
[tex]\$7,950.00 - (5 years \times 15\% \$7,950.00) = \$7,950.00 - \$5,962.50 = \$1,987.50[/tex]
However, it's important to note that this is a rough estimate, and the actual value could vary based on the factors mentioned earlier. To get a more accurate value, it's recommended to consult sources like used car price guides, local market listings, or professional appraisers.
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A televison and dvd player cost a total of $1164. The cost of the television is two times the cost of the dvd player. Find the cost of each item
Answer:
388 for the DVD
776 for the TV
Step-by-step explanation:
$1164= 2x + x
1164÷3
2[388] + 388 = 1164
mr lim was asked to paint 8 rings on a floor. the dimension of each ring is as shown on the right. Calculate the cost of painting the rings at $3 per m2. Take pie 3.14
Answer ASAP
Answer:
Area of a ring = π (R² – r²)
where R is the outer radius and r is the inner radius of the ring.
Since there are 8 rings, we need to multiply this area by 8 to get the total area:
Total area = 8 × 2.355 m²
Total area = 18.84 m²
Now, to find the cost of painting, we need to multiply the total area by the rate per m², which is $3:
Cost of painting = 18.84 m² × $3/m²
Cost of painting = $56.52
Therefore the cost of painting the rings at $3 per m² is $56.52.
The coefficient of 8. 2Nis
08
16
02
The coefficient of 8.2N1602 is 8.2N.
The given number is 8.2N1602, and you're required to find the coefficient of the number. The coefficient is the numerical factor that a term is multiplied by in an algebraic expression.
It is usually a number, but it may also be a letter that represents a number. The coefficient is the number that appears before the variable or term. For instance, in 3xy, 3 is the coefficient.In the given number, the coefficient is 8.2N, which is a decimal number.
A decimal is a number that uses place value and a decimal point to show the value of digits to the right of the decimal point.In general, decimals are a method of writing fractions that have a denominator of 10 or a power of 10.
The decimal 8.2 is 8 and 2 tenths, or 8.2/10. To convert a decimal number to a fraction, multiply the decimal by the appropriate power of 10 to make the decimal whole. In this case, we have 8.2N, which is already in decimal form.
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Parallelogram Properties - Diagonals
Jun 06, 4:06:26 PM
In parallelogram JKLM if LJ-46 find LN.
J
K
N
M
If LJ is given as 46 units in parallelogram JKLM, we can conclude that LN is equal in length to JK
To find the length of LN in parallelogram JKLM, we can utilize the properties of parallelograms, particularly the diagonals.
In a parallelogram, the diagonals bisect each other. This means that the diagonal LN divides the parallelogram into two congruent triangles, JLN and KLN.
Given that LJ is 46 units, we know that LK, the other half of the diagonal, is also 46 units.
Now, we have a triangle JLN, in which we know LJ (46 units) and LK (46 units). Since JL and LK are congruent sides of a triangle, we can conclude that JLKN is an isosceles trapezoid.
In an isosceles trapezoid, the diagonals are also congruent. Therefore, LN is equal in length to JK.
Hence, LN = JK.
Since we don't have any specific information about the length of JK provided in the question, we cannot determine the exact length of LN without additional information. However, we can say that LN is equal in length to JK based on the properties of parallelograms and isosceles trapezoids.
In summary, if LJ is given as 46 units in parallelogram JKLM, we can conclude that LN is equal in length to JK. However, without knowing the length of JK specifically, we cannot determine the exact length of LN.
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A fish tank with a rectangular base 80 cm by 40 cm contained 33.6 liters of water. water was poured into the tank until it was 60% full. Mr Hoi found that it had contained 62.4 litres of water more than before. what is the height of the fish tank?
Answer ASAP
The height of the fish tank is 75 cm. The tank is filled to 60% of its capacity, so the total volume of water is 60% of the tank's.
To find the height of the fish tank, we can follow these steps:
Step 1: Calculate the volume of the tank before the water was poured.
The base of the tank has dimensions 80 cm by 40 cm, so the initial volume of the tank is given by:
Volume_before = length * width * height
= 80 cm * 40 cm * h
= 3200h cm³
Step 2: Calculate the volume of water that was poured into the tank.
The tank was initially filled with 33.6 liters of water, which is equivalent to 33,600 cm³.
Step 3: Calculate the additional volume of water poured into the tank.
The additional volume of water is 62.4 liters, which is equivalent to 62,400 cm³.
Step 4: Calculate the total volume of water after pouring.
The total volume of water in the tank after pouring is:
Total_volume = Volume_before + Volume_poured
= 3200h cm³ + 33,600 cm³ + 62,400 cm³
= 3200h cm³ + 96,000 cm³
Step 5: Calculate the height of the tank.
The tank is filled to 60% of its capacity, so the total volume of water is 60% of the tank's volume. We can set up the following equation:
Total_volume = 0.6 * Volume_before
3200h cm³ + 96,000 cm³ = 0.6 * 3200h cm³
Simplifying the equation:
3200h cm³ + 96,000 cm³ = 1920h cm³
1280h cm³ = 96,000 cm³
h = 96,000 cm³ / 1280 cm³
h = 75 cm
Therefore, the height of the fish tank is 75 cm.
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Need help with this answer
Answer:
2 groups of 7 children and
1 group of 2
Step-by-step explanation:
if you want to find out how many times it would take? divide 16 by 7
= 2
and 2 left
because 7 * 2 = 14
16-14 = 2
Hope you understand
I just need help with the first step for verifying this trigonometric identity, which is to get the common denominator.
[tex]\textit{Pythagorean Identities} \\\\ 1+\cot^2(\theta)=\csc^2(\theta)\implies \cot^2(\theta)=\csc^2(\theta)-1 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cfrac{1}{\csc(x)+1}+\cfrac{1}{\csc(x)-1}~~ = ~~2\sec(x)\tan(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{\csc(x)+1}+\cfrac{1}{\csc(x)-1}\implies \cfrac{[\csc(x)-1]~~ + ~~[\csc(x)+1]}{\underset{ \textit{difference of squares} }{[\csc(x)+1][\csc(x)-1]}} \\\\\\ \cfrac{[\csc(x)-1]~~ + ~~[\csc(x)+1]}{\csc^2(x)-1^2}\implies \cfrac{2\csc(x)}{\csc^2(x)-1}\implies \cfrac{2\csc(x)}{\cot^2(x)}[/tex]
[tex]2\cdot \cfrac{\csc(x)}{\cot(x)\cot(x)}\implies 2\cdot \cfrac{\csc(x)}{\cot(x)}\cdot \cfrac{1}{\cot(x)}\implies 2\cdot \cfrac{\csc(x)}{\cot(x)}\cdot \tan(x) \\\\\\ 2\cdot \cfrac{~~ \frac{ 1 }{ \sin(x) } ~~}{\frac{\cos(x)}{\sin(x)}}\cdot \tan(x)\implies 2\cdot \cfrac{ 1 }{ \sin(x) }\cdot \cfrac{\sin(x)}{\cos(x)}\cdot \tan(x) \\\\\\ 2\cdot \cfrac{1}{\cos(x)}\cdot \tan(x)\implies 2\sec(x)\tan(x)[/tex]
Write the domain and range of the function using interval notation
The domain and the range of the function are (-∝, ∝) and (-1, ∝), respectively
Calculating the domain and range of the graph?From the question, we have the following parameters that can be used in our computation:
The graph
The above graph is a polynomial function
The rule of this function is that
The domain is the set of all real values
In this case, the domain is (-∝, ∝)
For the range, we have
Range = (-1, ∝)
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HELP PLEASE!!!!! Graph the linear inequality>>>.
The exponential equation to model this scenario is given by y = 200(0.85)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A linear inequality has the form of a linear equation, showing the non equal comparison between numbers and variables.
The linear inequality y ≤ (1/3)x - 5 passes through the point (0, -5) and (15, 0)
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The table below shows an inequality and a number by which to multiply both sides.
Inequality
-2<3
Multiply each
side by
-5
What is the resulting true inequality?
O-10 <-15
O-10>-15
O 10 <-15
O 10 >-15
The resulting true inequality from -2 < 3 is 10 > -15
How to determine what the resulting true inequality is?From the question, we have the following parameters that can be used in our computation:
Inequality
-2 < 3
Also, we have
Multiply each side by -5
Using the above as a guide, we have the following:
-5 * -2 < 3 * -5
Evaluate
10 > -15
Hence, the inequality is 10 > -15
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Josiah’s parents pay him for each chore he completes. He created a table to show his earnings each week for the past month.
Josiah’s Earnings
Week 1
Week 2
Week 3
Week 4
Chores Completed
4
6
4
5
Money Earned
$12
$18
$12
Which graph correctly depicts his earnings including the last week?
On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (4, 12), (5, 15), and (6, 18) are plotted.
On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (12, 4), (15, 5), and (18, 6) are plotted.
On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (4, 12), (6, 2), (6, 18), and (8, 8) are plotted.
On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (4, 12), (5, 18), and (6, 18) are plotted.
The graph that correctly depicts Josiah's earnings, where the amount he earns and the number of chores completed is a proportional relationship, is the option;
On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (4, 12), (5, 15), and (6, 18) are plotted.
What is a proportional relationship?A proportional relationship is one in which the ratio of the terms in the ordered pairs in the relation are the same.
The table in the question can be presented as follows;
[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-5} & Week 1& Week 2 & Week 3 & Week 4 \\ \cline{1-5}Chores Completed & 4 & 6 & 4 & 5 \\\cline{1-5}Money Earned & \$12 & \$18 & \$12 & \multicolumn{1}{|c|}{} \\\cline{1-5}\cline{1-5}\end{tabular}[/tex]
The data in the above table indicates that when Josiah completes 4 chores, he earns $12, and when he completes 6 chres he earns $18
The amount Josiah earns and the number of chores Josiah completes is a proportional relationship, which indicates;
The amount Josiah earns per chore is therefore; $12/4 = $18/6 = $3 per chore
The amount Josiah earns per chore, indicates that in week 5, the amount Josiah earns, when he completes 5 chores is; Amount earned = 5 × $3 = $15
The points on the graph are therefore; (4, 12), (6, 18), (5, 15)
The correct option is therefore; (4, 12), (5, 15), (6, 18)
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Answer:
a
Step-by-step explanation:
...
Y is directly proportional to x when y = 30 x=6 work out the value of y when x= 12
Answer:
y = 60
Step-by-step explanation:
given y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
to find k use the condition when y = 30 , x = 6
30 = 6k ( divide both sides by 6 )
5 = k
y = 5x ← equation of proportion
when x = 12 , then
y = 5 × 12 = 60
Equation of a line
(Answer and explanation please and thanks)
Answer:
a) m = 4/5, b = -3
y = (4/5)x - 3---slope-intercept form
b) The original line has slope 4/5, so a perpendicular line will have slope -5/4.
An equation for this line is y = (-5/4)x + c, where c is any constant. For example, if
c = 0, then y = (-5/4)x.
To graph y = (-5/4)x:
Start at the origin. Go up 5 units, then left 4 units. Plot the point (-4, 5). Draw a straight line that goes through these two points.
Given sec 0= radical 10/2, what is cos?
Given sec 0= radical 10/2, cos(0) is equal to √10/5.
How to find the value of cosTo find the value of cosine (cos) given the value of secant (sec), we can use the reciprocal identity between these two trigonometric functions.
The reciprocal identity states that:
sec(x) = 1/cos(x)
In this case, we are given sec(0) = √10/2.
We can rewrite this as:
1/cos(0) = √10/2
Multiplying both sides by cos(0), we get:
cos(0) * (1/cos(0)) = cos(0) * (√10/2)
The cos(0) terms cancel out on the left side, giving us:
1 = (√10/2) * cos(0)
Now, to isolate cos(0), we divide both sides by (√10/2):
1 / (√10/2) = cos(0)
To simplify the expression on the left side, we rationalize the denominator:
(1 * 2) / √10 = cos(0)
2/√10 = cos(0)
To express cos(0) in simplified radical form, we multiply the numerator and denominator by √10:
(2 * √10) / (√10 * √10) = cos(0)
(2√10) / 10 = cos(0)
Simplifying further, we get:
√10 / 5 = cos(0)
Therefore, cos(0) is equal to √10/5.
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2 x + y = 8 x + y = 4 The lines whose equations are given intersect at
Answer:
(4, 0 )
Step-by-step explanation:
2x + y = 8 → (1)
x + y = 4 ( subtract x from both sides )
y = 4 - x → (2)
substitute y = 4 - x into (1)
2x + 4 - x = 8
x + 4 = 8 ( subtract 4 from both sides )
x = 4
substitute x = 4 into (2)
y = x - 4 = 4 - 4 = 0
solution is (4, 0 )
cuanto es 1 mas 1? dende ecuaciones y detalles es para mi examen virtual please
Answer:
2
Step-by-step explanation:
1+1=2
A binomial experiment for the random variable X was performed with 10 trials. The probability of success was found
to be 0.43. Determine the following probabilities: [Round to four decimal places.]
a.) P(X= 7) =
b.) P(X < 4) =
c.) P(X> 6) =
Check
Answer:
a. 0.0369
b. 0.3822
c. 0.0468
Step-by-step explanation:
The function c = 1.50(n – 2) + 5.50 represents the cost c in dollars of printing n invitations. Which of the following is not true?
The statement "Each invitation costs $1.50 to print" is not true based on the given function. The cost depends on the number of invitations printed, as represented by c = 2.50(n – 2) + 1.50.
Among the given statements, the one that is not true is: "One can not print just one invitation."
The given function states that the cost of printing n invitations is represented by c = 2.50(n - 2) + 1.50. This function suggests that for each additional invitation beyond two, it costs an extra $2.50 to print. However, the function does not impose any restriction on the minimum number of invitations that can be printed.
Therefore, it is indeed possible to print just one invitation. The cost for one invitation would be c = 2.50(1 - 2) + 1.50 = 2.50(-1) + 1.50 = -2.50 + 1.50 = -1.00 dollars. Although printing a negative cost may not make practical sense, the statement that one cannot print just one invitation is not true based on the given function.
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Question
The function c = 2.50(n – 2) + 1.50 represents the cost c in dollars of printing n invitations. Which of the following is not true? One can not print just one invitation. Each invitation costs $1.50 to print For each additional invitation, it costs an extra $2.50 to print. The cost depends on the number of invitations printed.
Type the correct answer in each box. Spell all the words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).
Two shaded triangles are graphed in an x y plane. The vertices are as follows: first: A (8, 8), B (10, 4), and C (2, 6); second: A prime (6, negative 8), B (8, negative 4), and C (0, negative 6).
We can show that ∆ABC is congruent to ∆A′B′C′ by a translation of
2
unit(s)
and a
across the
x
-axis.
We can show that ∆ABC is congruent to ∆A′B′C′ by a translation of 2 units left and a reflection across the x-axis.
How to perform the sequence of transformations on triangle ABC?In Mathematics and Geometry, the translation of a graph to the left means a digit would be subtracted from the numerical value on the x-coordinate of the pre-image:
g(x) = f(x + N)
In order to apply a translation of two (2) units to the left to triangle ABC, we would use this transformation rule;
(x, y) → (x - 2, y)
A (8, 8) → A (6, 8).
B (10, 4) → B (8, 4).
C (2, 6) → C (0, 6).
In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
Next, we would reflect triangle ABC across the x-axis as follows;
(x, y) → (x, -y)
A (6, 8) → A' (6, -8).
B (8, 4) → B' (8, -4).
C (0, 6) → C' (0, -6).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
In the space provided below, write the converse of each of the following statements and tell whether the converse is true or false.
a) If A, then B.
b) Rain implies wet
c) If an angle is 45 degrees angle, then it is acute.
d) If a quadrilateral is a square, then all sides of this quadrilateral are congruent.
The converse of statement a) is undetermined, the converse of statement b) is generally false, the converse of statement c) is false, and the converse of statement d) is false.
To write the converses of the given statements and determine their truth value, let's examine each statement individually:
a) Original Statement: If A, then B.
Converse: If B, then A.
The converse of the original statement is true if and only if the original statement is true. The truth value of the converse cannot be determined without additional information about the relationship between A and B.
b) Original Statement: Rain implies wet.
Converse: Wet implies rain.
The converse of the original statement is generally false. The fact that something is wet does not necessarily mean that it rained. Wetness can be caused by various factors other than rain, such as water spills, humidity, or other sources of moisture.
c) Original Statement: If an angle is a 45-degree angle, then it is acute.
Converse: If an angle is acute, then it is a 45-degree angle.
The converse of the original statement is false. Not all acute angles are 45 degrees. Acute angles can have a range of measures less than 90 degrees, but they are not limited to being 45 degrees specifically.
d) Original Statement: If a quadrilateral is a square, then all sides of this quadrilateral are congruent.
Converse: If all sides of a quadrilateral are congruent, then it is a square.
The converse of the original statement is false. Not all quadrilaterals with congruent sides are squares. A rhombus, for example, is a quadrilateral with all sides congruent but is not necessarily a square.
In conclusion, the converse of statement a) is undetermined, the converse of statement b) is generally false, the converse of statement c) is false, and the converse of statement d) is false.
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Answer 32. Down below
The expression for the variable b in terms of a, S, and n in the formula for the sum of an arithmetic sequence is; b = (2·S/n) - a
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each subsequent term in the sequence increases from the value of the previous term by the same amount.
The formula for finding the finite sum of an arithmetic sequence can be presented as follows; S = (n/2)·(a + b), where;
n = The number of terms in the sequence
a = The first term in td sequence
b = The last term in the sequence
The steps that can be used to make the variable b the subject of the equation, are;
S = (n/2)·(a + b)
a + b = 2·S/n
b = 2·S/n - a
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What is the end behavior of the graph?
Answer: the second option.
