Write an equation that passes through (-3,2) and (-2,5) in slope intercept form
Answer:
y = 3x + 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (- 2, 5 )
m = [tex]\frac{5-2}{-2-(-3)}[/tex] = [tex]\frac{3}{-2+3}[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 2, 5 )
5 = 3(- 2) + c = - 6 + c ( add 6 to both sides )
11 = c
y = 3x + 11 ← equation of line
Naomi invested $920 in a account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2310
Answer:
We can use the continuous compound interest formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate (as a decimal), and t is the time (in years). We can rearrange this formula to solve for t:
t = ln(A/P) / r
where ln is the natural logarithm function.
Using the given values, we have:
P = 920
A = 2310
r = 0.047
So,
t = ln(2310/920) / 0.047
t ≈ 18.8 years
Rounding to the nearest year, it would take about 19 years for the value of the account to reach $2310.
Answer:
19 years
Step-by-step explanation:
please help with this question! thank you :))
Answer:
2x
Step-by-step explanation:
it is x+x or 2x, since if x>=0, the absolute value of x is just x, then we can say that it is x+x without the absolute value symbols. :)
For the following figure, match the correct corresponding statement:
Column A
1.
:
2.
:
3.
:
4.
AB ≅:
AB ≅
5.
GF ≅:
GF ≅
6.
EG ≅:
EG ≅
7.
▼BCA ≅:
▼BCA ≅
8.
▼GEF ≅:
▼GEF ≅
Column B
a. EF
b.
c. AC
d.
e. CB
f. ▼CAB
g.
h. ▼FGE
Although the statements are not clearly written, the proof that ΔABC ≅EFG is:
AC = EG - Given
BA = FE - Given
BC = FG - Given
∠ABC = ∠EFG - Given
∠BAC = ∠FEG - Given
∠BCA = ∠FGE - Given
Thus, ΔABC ≅EFG on the bases of the S-S-S Angle postulate or the A-A-A congruence postulate.
What is the definition of the above postulates?The S-S-S Angle Postulate and the A-A-A Congruence Postulate are both mathematical principles used to prove that two triangles are congruent (having the same size and shape).
The S-S-S Angle Postulate states that if two triangles have three sides that are congruent to the corresponding sides of another triangle, then the triangles are congruent.
The A-A-A Congruence Postulate, on the other hand, states that if two triangles have three angles that are congruent to the corresponding angles of another triangle, then the triangles are congruent.
Both of these postulates are fundamental to the study of geometry and are used to prove a wide range of geometric theorems and relationships.
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Solve the system.
x - 3y - 5z = 7
6y + z = 27
6x + 5y - 6z = 85
Enter your answer as an ordered triple.
([?], [ ], [])
Enter
Answer:
(-6, 4/3, 7)
Step-by-step explanation:
To solve the system of equations, we can use elimination or substitution. Here, we will use elimination:
First, we can eliminate z by adding the first and third equations:
x - 3y - 5z = 7
6x + 5y - 6z = 85
7x + 2y = 92
Next, we can use the second equation to eliminate z from the second equation:
6y + z = 27
-6z from both sides:
6y = -6z + 27
Divide both sides by 6:
y = -z/6 + 9/2
Now, we can substitute y = -z/6 + 9/2 into the equation 7x + 2y = 92:
7x + 2(-z/6 + 9/2) = 92
7x - z/3 + 9 = 92
7x - z/3 = 83
Multiplying both sides by 3 to eliminate the fraction:
21x - z = 249
We now have two equations:
7x + 2y = 92
21x - z = 249
To eliminate x, we can multiply the first equation by 3 and subtract it from the second equation:
21x - z = 249
- (3 * (7x + 2y = 92))
-----------------------------------------------------------------
-13x - 6z = -215
Solving this equation for z, we get:
-13x - 6z = -215
6z = 13x + 215
z = (13/6)x + 35 + 1/3
Now we can substitute this value of z into one of the equations to solve for y. Let's use the second equation:
6y + z = 27
6y + [(13/6)x + 35 + 1/3] = 27
6y + (13/6)x + 35 + 1/3 - 27 = 0
6y + (13/6)x + 8 + 1/3 = 0
6y + (13/6)x = -25/3
y = (-13/36)x - (25/18)
Finally, we can substitute these values for x, y, and z into one of the original equations to check our work. Let's use the first equation:
x - 3y - 5z = 7
x - 3[(-13/36)x - (25/18)] - 5[(13/6)x + 35 + 1/3] = 7
x + (13/12)x + (25/6) - (65/6)x - 175 - (5/3) = 7
-51x/12 - 215/6 = 7
-17x/4 - 35/2 = 7
-17x/4 = 21/2
x = -6
Substituting this value of x into the expressions we found for y and z, we get:
y = (-13/36)x - (25/18) = (13/6) - (25/18) = 4/3
z = (13/6)x + 35 + 1/3 = -(13/6)*6 + 35 + 1/3 = 7
If the vertex of the function is at the. 0, 0. 5 what is the recommended amount of mulch for a flower bed with a radius of 20 feet round to the nearest 10th if necessary
the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.
The given information about the vertex of the function does not appear to be relevant to the question about mulch for a flower bed. However, we can still solve the problem using the given radius of the flower bed.
The formula to find the recommended amount of mulch for a circular flower bed is:
Mulch = π * r^2 * d
Where r is the radius of the flower bed and d is the desired depth of the mulch.
Assuming a desired depth of 0.5 feet, we can plug in the given radius of 20 feet to the formula:
Mulch = π * (20 feet)^2 * 0.5 feet
Mulch = π * 400 square feet * 0.5 feet
Mulch = 200π cubic feet
To find the approximate value in decimal form, we can use the approximation π ≈ 3.14:
Mulch ≈ 200 * 3.14
Mulch ≈ 628 cubic feet
Rounding to the nearest tenth, we get:
Mulch ≈ 628.3 cubic feet
Therefore, the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.
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How do you find the surface area for this? Anything helps! (will give brainliest)
Answer:
95.2 square yards
Step-by-step explanation:
8(3) + 2(1/2)(3)(7.2) + 2(1/2)(8)(6.2)
= 24 + 21.6 + 49.6 = 95.2 square yards
What is the hundredth digit of pi? This would include the 3 in the beginning.
There are 60,094 people under the age of 14 years old
There are 212,468 people age between 15 and 64 years old
There are 42,362 people over the age of 65 years old
What is the Age Dependency Ratio as a decimal rounded to the Thousandths place?
Answer:
67.466%
Step-by-step explanation:
No. of people aged below 14 years old= 60,094
No. of people aged between 15 and 64 years old= 212,468
No. of people aged above 65 years old= 42,362
Age Dependency Ratio= No. of people aged between 15 and 64 years old
/Total People
= [tex]\frac{212,468}{60,094+212,468+42,362}[/tex] × 100
= [tex]\frac{212,468}{314,924}[/tex] × 100
= 67.466%
∴ the Age Dependency Ratio is 67.466%.
The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
2x3 + 6x2 + 4x + 12
2x3 + 6x2 + 6x + 18
2x2 + 6x + 5
2x2 + 5
The width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.
Given that:
Area, A(x) = 2x³ + 6x² + 5x + 15
Length, L = x + 3
The formula for the area of a rectangle is:
A = length x width
A(x) = (x + 3) · W
A(x) / (x + 3) = W
W = (2x³ + 6x² + 5x + 15) / (x + 3)
W = [2x²(x + 3) + 5x(x + 3)] / (x + 3)
W = [(2x² + 5)(x + 3)] / (x + 3)
W = 2x² + 5
Therefore, the width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.
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Write the equation of a line perpendicular to y = x - 5 and passing through the point (-3,9).
1. y = -x + 6
2. y = -x + 9
3. y = -x + 12
4. y = x + 12
The equation of line perpendicular to y=x-5 passing through (-3,9) is y=-x+6.
What is a perpendicular line?Two distinct lines intersecting each other at 90 degrees or at a right angle are called perpendicular lines
Equation:To find the equation of a line perpendicular to y = x - 5, we need to first determine the slope of the original line. The slope of a line in slope-intercept form (y = mx + b) is the coefficient of x, so in this case, the slope of the original line is 1.
Since we want to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1.
So, the slope of the perpendicular line is -1, and we also know that it passes through the point (-3,9).
We can use the point-slope form of a line to write the equation of the perpendicular line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope of the line.
Substituting the values we know, we get:
y - 9 = -1(x - (-3))
Simplifying this expression, we get:
y - 9 = -x - 3
Adding 9 to both sides, we get:
y = -x + 6
Therefore, the equation of the line perpendicular to y = x - 5 and passing through the point (-3,9) is:
y = -x + 6
So the answer is option 1: y = -x + 6.
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Solve the following linear equation for
x
x.
5
x
−
2
+
x
=
9
+
3
x
+
10
5x−2+x=9+3x+10
Alex's porch has a length and width of 12 feet each. He wants to paint the porch with a
water sealant that costs $35 per square foot. However, his wife wants him to change
the length of the porch to 14 feet. What would the difference in cost of applying sealant
be if Alex does extend his porch length?
Answer: $1820
Step-by-step explanation:
Area = Length*Width
Forst we have to solve for the area.
A = 12 * 12
A = 144 ft^2
Next we have to multiply be the cost per square foot.
144 * 35
= $5040
Solve for the area.
A = 14 * 14
A = 196 ft^2
Multiply by the cost per square foot.
196 * 35
= $6860
Lastly subtract both costs:
6860 - 5040 = 1820
Therefore the difference in cost would be $1820.
Hope this helps :)
Adrienne earns $98 for working 8 hours. If she earned $453.25, How many hours did she work?
Answer:
37 hours
Step-by-step explanation:
First, we will find the amount of money that Adrienne makes per hour: 98/8, which equals $12.25.
Now, we can find the number of hours it takes to earn $453.25 by dividing it by $12.25:
$453.25 / $12.25 = 37 hours
During a thunderstorm at a sports event, a detector goes off to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table.
Lightning detector activates Lightning detector does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
What is the ratio of false positives to false negatives in this scenario? Round your answer to one decimal place.
0.1
1.5
2.3
3.5
The ratio of false positives to false negatives in this scenario is 3.5.
3.5 is the correct answer. False positives are lightning detector activations when there is no lightning in the area. False negatives are lightning detector not activations when there is lightning in the area. To calculate the ratio of false positives to false negatives, divide the false positives (7%) by the false negatives (2%). 7/2 = 3.5. Therefore, the ratio of false positives to false negatives in this scenario is 3.5.
The ratio of false positives to false negatives in this scenario is 3.5.
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Answer:
i took the test :)
Step-by-step explanation:
3.5
Find the square of: 5i√3
Answer: We have:
(5i√3)² = (5i)²(√3)² = -25(3) = -75
Therefore, the square of 5i√3 is -75.
Step-by-step explanation:
The square of the complex number of 5i√3 is 75.
What is a complex number?A complex number is the sum of a real number and an imaginary number.
To find the square of the complex number, 5i√3, we use the following Steps below
Step1: Square the expression
(5i√3)²Step 2: use the law of surd to seperate each of the terms in the expression
[(5i)²(√3)²]Note: In complex number notation,
i×i = 1Therefore,
25(3)75Hence, square of 5i√3 is 75
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the two plates of a capacitor hold 2500 μc and –2500 μc of charge, respectively, when the potential difference is 960 v. what is the capacitance?
2.6 * 10⁻⁶ F is the capacitance.
What is a capacitor short answer?
A capacitor is a component used in electrical circuits to hold charges. The idea behind how a capacitor functions is that when an earthed conductor is moved close to a conductor, its capacitance increases noticeably.
As a result, a capacitor contains two plates with equal and opposing charges that are spaced apart. Two conductors that are near to one another and are isolated from one another make up a capacitor, a device for storing electrical energy. The parallel-plate capacitor is a straightforward illustration of such a storage device.
We have realtion Q=CV
where Q is charge , C is capacitance and V is voltage.
C=Q/V
C=(2500 * 10⁻⁶)/960
C= 2.6 * 10⁻⁶ F
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How many flowers, spaced every 4 in. , are needed to surround a circular garden with a 100-ft radius? use 3. 14
Answer:the answer would be around 300 or 314
if you have 100ft in a circle and divided the space using the equation it what you get .
Step-by-step explanation:
Please help to complete this chart pleaseeeeeee
The completed chart for a one-time investment made in the amount of $9,200 is attached below.
How to calculate interest rate and compounding periods?For Annually compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.06)¹⁵
A = $9,200 (1.06)¹⁵
A = $22,048.34
For Semi-Annually compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.03)³⁰
A = $9,200 (1.03)³⁰
A = $21,214.29
For Quarterly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.015)⁶⁰
A = $9,200 (1.015)⁶⁰
A = $20,947.34
For Monthly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.005)¹⁸⁰
A = $9,200 (1.005)¹⁸⁰
A = $20,812.09
For Weekly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.0012)⁷⁸⁰
A = $9,200 (1.0012)⁷⁸⁰
A = $20,756.54
For Daily compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.0002)⁵⁴⁷⁵
A = $9,200 (1.0002)⁵⁴⁷⁵
A = $20,726.55
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Image transcribed:
1. Fill in the chart for the following investment.
A one-time investment is made in the amount of $9,200 for 15 years at an APR of 6%.
Compound Interest: A = P (1 + i)", where A is the final amount, P is the principal invested, i is the interest rate per compounding period, and n is the number of compounding periods.
someone please help I'll give brain list (I'm failing)
Answer:
1) 3rd one down 1 7/12 ( the one you've selected well doneee)
2)pretty sure its also the 3rd one down ( don't come for me if its wrong)
Step-by-step explanation:
4 1/6 = 25/6
5 3/4= 23/4
25/6 x4= 100/24
23/4 x 6 = 138/24
138/24 - 100/24 = 38/24
divide by 2:
19/12= 1 7/12
Obtain the volume of rectangular boxes with a, 2b and 3c as length, breadth and height respectively
Step-by-step explanation:
The volume of a rectangular box is given by the formula:
Volume = length x breadth x height
In this case, the length is a, the breadth is 2b, and the height is 3c. So, the volume can be calculated as:
Volume = a x 2b x 3c
= 6abc
Therefore, the volume of the rectangular box with a, 2b and 3c as length, breadth and height respectively is 6abc.
5 less than a qoutient of a number and 3
Answer:
The solution to the equation is -7
Step-by-step explanation:
I hate these kinds of Questions but it all comes down to how you mathematically interpret it.
The sales tax in California is 7.25%. If you go to a store to buy a pair of jeans that has a price of $40, how much will you pay in sales tax
You will pay $2.90 in sales tax in California for a pair of jeans that costs $40.
What is sales tax?At the time of sale, a tax known as sales tax is applied to the cost of products or services. The state, county, or city where the transaction occurs determines the tax rate, which is often expressed as a percentage of the purchase price. The vendor is responsible for collecting sales tax and remitting it to the relevant government body. Sales taxes are levied in order to raise money for the government and pay for essential services like infrastructure, healthcare, and education. Because it is based on the quantity of goods or services consumed rather than income or wealth, sales tax is a sort of consumption tax.
Given that, sales tax in California is 7.25%.
Thus,
Sales tax = price of jeans x sales tax rate
Sales tax = $40 x 0.0725
Sales tax = $2.90
Therefore, you will pay $2.90 in sales tax in California for a pair of jeans that costs $40.
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the coc admissions department wants to see how many students would be in favor of using a new program to register for classes. they put a link on their website so that any students that want to try out the program can. the students can then take a survey and say how well they like the new system. this is what method of collecting data was used: group of answer choices convenience census cluster systematic voluntary response simple random sample (srs) stratified
The method of collecting data that was used in the given scenario is voluntary response.
A voluntary response method of data collection is a research technique that allows participants to decide whether or not they want to be included in the sample.
When participants are allowed to choose whether or not to participate, this is known as self-selection.
This method has a disadvantage in that it could lead to bias in the data because those who respond to the survey may not represent the entire population of interest.
In the given scenario, the COC admissions department put a link on their website so that any students that want to try out the program can. The students can then take a survey and say how well they like the new system. This means that the method of collecting data that was used is voluntary response.
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Riley has 200 stamps.
35% are from Russia.
20% are from Australia.
10% are from Asia.
The rest are from North America. How many stamps are from North America?_
Riley has 200 stamps.
35% are from Russia.
20% are from Australia.
10% are from Asia.
The rest are from North America. How many stamps are from North America?
Answer:
70 stamps are from North America
Step-by-step explanation:
All I did was add the percentages together
35+20+10= 65
I then took 65% of 200 to get 70.
alice refuses to sit next to either bob or carla. derek refuses to sit next to eric. how many ways are there for the five of them to sit in a row of chairs under these conditions?
The total number of ways five of them to sit in a row of chairs under the given condition is equal to 152 ways.
Use the principle of inclusion-exclusion to solve this problem.
Let us first consider the case where Alice sits next to Bob or Carla.
Now, treat Alice, Bob, and Carla as a block, which can be arranged in 3! = 6 ways.
Within this block, Alice can sit in two different positions,
And Bob and Carla can sit in the remaining two positions.
There are 6 x 2 = 12 ways for Alice to sit next to Bob or Carla.
Now,
Let us consider the case where Derek sits next to Eric.
Treat Derek and Eric as a block,
which can be arranged in 2! = 2 ways.
Within this block,
Derek can sit in two different positions,
And Eric can sit in the remaining position.
There are 2 x 2 = 4 ways for Derek to sit next to Eric.
However,
Double-counted the case where Alice sits next to Bob or Carla AND Derek sits next to Eric.
Treat Alice, Bob, Carla, Derek, and Eric as two blocks,
which can be arranged in 2! x 3! = 12 ways.
Within each block,
There are 2 ways to arrange the people.
There are 12 x 2 x 2 = 48 ways for both conditions to be satisfied.
Using the principle of inclusion-exclusion,
The total number of ways for the five of them to sit in a row of chairs under these conditions.
Total
= total number of ways - number of ways Alice sits next to Bob or Carla - number of ways Derek sits next to Eric + number of ways both conditions are satisfied
= 5! - 12 - 4 + 48
= 152
Therefore, there are 152 ways for the five of them to sit in a row of chairs under these conditions.
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Identify the area of a regular pentagon with side length 21
in.
rounded to the nearest tenth.
The area of regular pentagon is 758.7 square in.(rounded to the nearest tenth.)
What is pentagon?A pentagon is a specific type of polygon with 5 sides and 5 angles. The word “pentagon” is constructed of two words, namely Penta and Gonia, which defines five angles. So in a simplified way it can be said that pentagon is a polygon having 5 sides.
Here is a regular pentagon with side length 21 in.
Area of regular pentagon (A)= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} a^{2}[/tex]
Here a= 21 in
So Area = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} (21)^{2}[/tex] square in.
= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} 441[/tex] "
≈758.73053 square in
= 758.7 square in. ( rounded to the nearest tenth).
Hence the area of regular pentagon is 758.7 square in.
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Simplify 5c - 8d - 4c + 3d
Simplify 6p - 2w + p + 5w
Answer:37c − 32d
2:7p+3w
Step-by-step explanation:
Answer:
1. c - 5d
2. 7p + 3w
Step-by-step explanation:
1.)
5c - 8d - 4c + 3d =
5c + -8d +-4c + 3d
Combine like terms:
(5c + -4c) +(-8d + 3d) =
c - 5d
2.)
6p - 2w + p + 5w =
6p + -2w + p + 5w
Combine like terms:
(6p + p) + (-2w + 5w) =
7p + 3w
find the smallest number that has1 ,2 ,3 ,4 ,5 and as factors. what is the special name for this number?
The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.
The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of these numbers. We can find the LCM of more than two numbers by following the below procedure:Firstly, find the LCM of two numbers.
This will be the smallest number that is a multiple of both these numbers. Then, find the LCM of this number and the third number. This will be the smallest number that is a multiple of all the three numbers. Repeat the same process for other numbers until we have found the LCM of all the given numbers.
Here, the given numbers are 1, 2, 3, 4, and 5.LCM of 1 and 2 is 2.LCM of 2 and 3 is 6.LCM of 6 and 4 is 12.LCM of 12 and 5 is 60.
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if the cost of 2 tables and 3 chairs is rs 3200 and the cost of 10 chairs and 4 tables is the same, what will be the cost of 5 tables and 6 chairs
The cost of 5 tables and 6 chairs would be Rs. 1200.
Algebraic problemLet the cost of one table be x and the cost of one chair be y.
From the given information, we have the following two equations:
2x + 3y = 3200 ... equation (1)
4x + 10y = 3200 ... equation (2)
To solve for x and y, we can multiply equation (1) by 2 and subtract it from equation (2) to eliminate x:
4x + 10y = 3200
(4x + 6y = 6400)
4y = -3200
Solving for y, we get:
y = -800
Substituting y = -800 into equation (1), we get:
2x + 3(-800) = 3200
Simplifying and solving for x, we get:
2x - 2400 = 0
2x = 2400
x = 1200
Therefore, the cost of one table is Rs. 1200, and the cost of one chair is Rs. -800 (which means the cost of one chair is Rs. 800 with a negative sign indicating a decrease from the original cost of Rs. 1200).
To find the cost of 5 tables and 6 chairs, we can simply multiply the cost of one table by 5 and the cost of one chair by 6 and add them:
Cost of 5 tables = 5 * Rs. 1200 = Rs. 6000
Cost of 6 chairs = 6 * Rs. (-800) = Rs. -4800 (or Rs. 4800 with a negative sign indicating a decrease from the original cost of Rs. 800)
Total cost = Rs. 6000 + Rs. (-4800) = Rs. 1200
Therefore, the cost of 5 tables and 6 chairs is Rs. 1200.
More on algebraic problems can be found here: https://brainly.com/question/30042644
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