Answer:
The slope for the given points is - 2 , and y- intercept is 5
Step-by-step explanation:
Given points as :
( - 1 , 7 ) and ( 0 , 5 )
Now slope of line in points form as
Slope = m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
or, m = [tex]\dfrac{5 - 7}{0 + 1}[/tex]
or, m = - 2
so, Slope of line is - 2
Now equation of line is given as
y - [tex]y_1[/tex] = m × ( x - [tex]x_1[/tex] )
or, y - 7 = ( - 2 ) × ( x + 1)
or, y - 7 = - 2 x - 2
Or, equation of line is
y = - 2 x + 5
Now, for y - intercept , x = 0
So, from line equation
y = - 2 × 0 + 5
Or, y = 0 + 5
∴ y = 5
Hence The slope for the given points is - 2 , and y- intercept is 5 Answer
1+9i and 5-3i midpoint
Answer:
[tex]3+3i[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two complex numbers (a+bi) and (c+di) points is equal to
[tex](\frac{a+c}{2})+(\frac{b+d}{2})i[/tex]
we have
(1+9i) and (5-3i)
substitute the given values
[tex](\frac{1+5}{2})+(\frac{9-3}{2})i[/tex]
[tex]3+3i[/tex]
Final answer:
The midpoint of the complex numbers 1+9i and 5-3i is calculated using the average of their real and imaginary parts, resulting in the midpoint of 3 + 3i.
Explanation:
To find the midpoint of two complex numbers, 1+9i and 5-3i, we use the midpoint formula for complex numbers which is the average of the real parts and the average of the imaginary parts separately. The formula for the midpoint M is given by:
M = ½(x1 + x2) + ½(y1 + y2)i
For our complex numbers, the real parts are 1 and 5, and the imaginary parts are 9 and -3. Applying the midpoint formula, we get:
M = ½(1 + 5) + ½(9 - 3)i = ½(6) + ½(6)i = 3 + 3i
Therefore, the midpoint of the complex numbers 1+9i and 5-3i is 3 + 3i.
A price was first decreased by 12%, then it was decreased again by an additional 5%. What is the percent of the total decrease?
Answer:
The answer is 16.4%
Step-by-step explanation:
The total decrease of price percentage is 16.4% when the price was decreased by 12% .
Evaluating decrease price :
The first discount reduces the price to (100 - 12)%
= 88% which is 0.88 times the original price.
The second discount reduces the already discounted price to
(100 - 5)% =
95% of the discounted price
(0.95 times the discounted price). Get 2 discounts combined
Final Price = (0.95)(0.88) x (Original Price)
= 0.836 x (Original Price)
This is 83.6% of the original price, so the total discount rate is
(100 - 83.6)%
= 16.4%.
Buttons are sold in packets and in boxes.
There are 6 buttons in a packet.
There are 15 buttons in a box.
Nomusa buys packets of buttons and boxes of buttons.
She buys a total of buttons.
Write a formula for in terms of and .
Answer:
Let the number of packets be x and the number of boxes be y.
Then, the formula is 6x + 15y
Step-by-step explanation:
The formula for the total number of buttons Nomusa buys, represented by t, in terms of the number of packets, p, and boxes, b, she buys is: t = 6p + 15b.
Explanation:In this mathematical context, let's suppose that Nomusa buys p packets and b boxes of buttons. The total number of buttons can be represented by the letter t. Since there are 6 buttons in a packet and 15 buttons in a box, the total number of buttons Nomusa buys will be the sum of all buttons in the packets and boxes she buys. Thus, the formula in terms of p (packets) and b (boxes) will be: t = 6p + 15b.
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What is a benefit of getting an Associate Degree?
Answer:
you can qualify for more jobs and make more money
Step-by-step explanation:
Final answer:
One benefit of getting an Associate Degree is gaining specialized knowledge and skills, which can increase job prospects. Additionally, it can be a stepping stone towards earning a higher degree, leading to more opportunities. Lastly, earning an Associate Degree can provide personal fulfillment and a sense of accomplishment.
Explanation:
One benefit of getting an Associate Degree is that it provides students with the opportunity to gain specialized knowledge and skills in a specific field. This can make them more competitive in the job market and increase their chances of finding employment. For example, someone with an Associate Degree in Business Administration may have a better understanding of business operations and management principles, which can be valuable in entry-level positions or when starting their own business.
Another benefit is that an Associate Degree can serve as a stepping stone towards earning a higher degree. Many universities and colleges accept transfer credits from associate degree programs, allowing students to continue their education and earn a bachelor's degree or beyond. This can open up more career opportunities and potentially lead to higher salaries.
Lastly, getting an Associate Degree can also provide personal fulfillment and a sense of accomplishment. It shows that you have successfully completed a program of study and have attained a certain level of expertise in a subject area. This can boost self-confidence and motivate you to pursue further education or career goals.
Least common denominator of 7/9 and 2/3
Answer: 9
Step-by-step explanation: The common denominator will be the least common multiple for the two denominators.
To find the least common multiple or lcm of 3 and 9, begin by listing the first few multiples for each number.
Multiples of 6
1 × 9 = 9
2 × 9 = 18
3 × 9 = 27
Notice that we skipped 0 × 9 in our list of multiples. That's because 0 × 6 is 0 according to the zero property of multiplication and our least common multiple can't be 0.
When listing the multiples of 3, it's a good idea to keep an eye on the list of multiples for 9 so that we will notice when we find a least common multiple.
Multiples of 3
1 × 3 = 3
2 × 3 = 6
3 × 3 = 9
Notice that in both lists, we have the least common multiple which is 9.
Therefore, the least common denominator of 9 and 3 is 9.
O
The distance between the library and the station is 15 km, while
the station and the school are 33 km apart. How many kilometers
do you have to walk from the library to get to the school if you go
via the station?
18 km apart
You subtract 33 and 15
find the area of the shaded region
Answer:
21 centimeters is the answer
A bacteria culture has an initial population of 25. This bacteria reproduces at a daily rate of 1.28 percent. How long will it take for the population to grow to 375 bacteria?
Answer:
212.9 days
Step-by-step explanation:
The bacteria culture initial population is 25 represented by Po and the population after t days is represented by P(t).
Using growth formula:
P(t) = Po ( 1 + r)^t where r is rate in percent and t is time in days
r = 1.28%, P(t) = 375, and Po = 25
substituting this values into the equation above yields
375 = 25 (1 + 1.28/100)^t
375÷25 = ( 1 + 0.0128)^t
15 = (1.0128)^t
take logarithm of both sides
log 15 = log (1.0128)^t remember the law log a^b = b log a
applying the same law gives
log 15 = t log 1.0128
divide both side by log 1.0128
log 15 ÷ log 1.0128 = t log 1.0128 ÷ log 1.0128
t = 212.9 days
Answer:
211 days
Step-by-step explanation:
Select all statements that are true about the linear equation.
y= 1/3x + 2
The graph of the equation is a single point representing one solution to the equation.
The point (9,5) is on the graph of the equation.
The graph of the equation is the set of all points that are solutions to the equation.
The point (-3,-1) is on the graph of the equation.
Answer:
The point (9,5) is on the graph of the equation
The graph of the equation is the set of all points that are solutions to the equation
Step-by-step explanation:
we have the linear equation
[tex]y=\frac{1}{3}x+2[/tex]
This is the equation of the line in point slope form
where
the slope is [tex]m=\frac{1}{3}[/tex]
the y-intercept is [tex]b=2[/tex]
Remember that
If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation
The graph of the equation is the set of all points that are solutions to the equation
Verify each statement
case 1) The graph of the equation is a single point representing one solution to the equation
The statement is false
Because the graph of the equation is the set of all points that are solutions to the equation
case 2) The point (9,5) is on the graph of the equation
The statement is true
Because
For x=9, y=5
substitute the value of x and the value of y in the linear equation
[tex]5=\frac{1}{3}(9)+2[/tex]
[tex]5=3+2[/tex]
[tex]5=5[/tex] ----> is true
so
the ordered pair satisfy the linear equation
therefore
The point is on the graph of the equation
case 3) The graph of the equation is the set of all points that are solutions to the equation
The statement is true
case 4) The point (-3,-1) is on the graph of the equation
The statement is false
Because
For x=-3, y=-1
substitute the value of x and the value of y in the linear equation
[tex]-1=\frac{1}{3}(-3)+2[/tex]
[tex]-1=-1+2[/tex]
[tex]-1=1[/tex] ----> is not true
so
the ordered pair not satisfy the linear equation
therefore
The point is not on the graph of the equation
Order the numbers from
least to greatest.-7/5 -1 5/11
-1.45
-1 91/200
Answer:
-1 91/200, -1.45, -7/5, -1 5/11
Step-by-step explanation:
Lowest Common Denominator:
LCD = 2200
Equivalent Fractions with the LCD
-7/5 = -3080/2200 (-7/5)
-15/11 = -3000/2200 (-1 5/11)
-145/100 = -3190/2200 (-1.45)
-291/200 = -3201/2200 (-1 91/200)
help with math again *10 pts* asap
Answer:
[tex]a_n=2n+5[/tex]
Step-by-step explanation:
we have the sequence
[tex]7,9,11,...[/tex]
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant and this term is called a common difference
Let
[tex]a_1=7\\a_2=9\\a_3=11[/tex]
we know that
[tex]a_2-a_1=9-7=2[/tex] ----> [tex]a_2=a_1+2[/tex]
[tex]a_3-a_2=11-9=2[/tex] ----> [tex]a_3=a_2+2[/tex]
The common difference is 2
This is an arithmetic sequence
The general formula for an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex]
where
d is the common difference
n is the number of terms
substitute the given values
[tex]a_n=7+2(n-1)[/tex]
[tex]a_n=7+2n-2[/tex]
[tex]a_n=2n+5[/tex]
The two figures shown are congruent. Which statement is true?
Help me :(
Answer:
i think it is the second answer
Step-by-step explanation:
i think this because the upside down ? is reflecting the ?
Answer:
One figure is a reflection of the other.
Step-by-step explanation:
Each point of the shape of one figure is equidistant to the equivalent point of the other, observing a symmetry line which perpendicular to the distance between each corresponding pair of points.
30 pt, easyish
PLEASE HELP AND WRITE SOMETHING GOOD.
HELP PLEASE
What is the starting point and rate of change for
a(x) = 210(1.12)x
please help FAST
The starting point is (0 , 210) and the rate of change is 1.12
Step-by-step explanation:
The form of the exponential function is [tex]f(x)=a(b)^{x}[/tex] , where
a ix the initial value ⇒ (at x = 0)b is the factor of growth/decay of the function ⇒ (rate of change)If b > 1, then the function is growthIf 0 < k < 1, the the function is decay∵ The function is [tex]a(x)=210(1.12)^{x}[/tex]
∵ At the starting point x = 0
- Substitute x in the function by 0
∴ [tex]a(0)=210(1.12)^{0}[/tex]
- Remember any number to power of zero = 1 except 0
∴ [tex](1.12)^{0}=1[/tex]
∴ a(0) = 210(1) = 210
∵ a(x) = y
∴ The starting point is (0 , 210)
∵ The from of the exponential equation is [tex]f(x)=a(b)^{x}[/tex]
∵ [tex]a(x)=210(1.12)^{x}[/tex]
- Compare the two function
∴ b = 1.12
∵ b is the rate of change of the function
∴ The rate of change of the function is 1.12
The starting point is (0 , 210) and the rate of change is 1.12
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What is the absolute value of 2.84
Answer:
2.84
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
if you sleep 8 hours of each day what fraction of the day do you not sleep
Answer:
16/24 which can then be simplified to 2/3
Answer:
8/24 = 1/3
Step-by-step explanation:
6. Leo earns $16/h as a gardener in a city
park. For time worked above 35 h in a
week, he earns time-and-a-half. How much
does he earn for each of the following
numbers of hours worked in a week?
a) 36 h b) 39 h c) 42 h
h
a) He will earn $584 for working 36 hours.
b) He will earn $656 for working 39 hours.
c) He will earn $728 for working 42 hours.
Step-by-step explanation:
Amount per hour = $16
Time and a half means 1.5 times more than the original payment.
Therefore, above 35 hours, the earning for one hour,
Extra time per hour = 16*1.5 = $24
A) 36 h
For the first 35 hours, he will get $16 per hour, therefore,
Amount of 35 hours = [tex]35*16= \$560[/tex]
Amount of one hour = $24 (as calculated above)
Total = 560+24 = $584
He will earn $584 for working 36 hours.
B) 39 h
39 h = 35h + 4h
Amount of 35 hours = $560
Amount of extra 4 hours = $24*4 = $96
Total = 560+72 = $656
He will earn $656 for working 39 hours.
C) 42 h
42 h = 35h + 7h
Amount of 35 hours = $560
Amount of extra 7 hours = 24*7 = $168
Total = 560+168 = $728
He will earn $728 for working 42 hours.
Keywords: addition, multiplication
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Find the Percent Change.
TV was reduced from $300 to $200.
it's either 2/3 or 66.6 (neverending 6s)
Answer:it changed from $100
Step-by-step explanation:
help!!!!!!!!!!!!!!!
Answer:
First Option.
Step-by-step explanation:
I recommend using the app Photomath for these types of math problems. It gives a detailed explanation as to how you should solve them.
Write the equation of the line passing through (-2,5) and parallel to the line y=2x+6
Answer:
y=2x+9
Step-by-step explanation:
Which point could be removed in order to make the relation a function?
{(0, 2), (3, 8), (-4,-2), (3, 6), (-1, 8), (8, 3)}
O (8,3)
O (3,6)
0 (-1,8)
0(-4,-2)
Answer:
(3,6)
Step-by-step explanation:
the x input cannot repeat in order for it to be a function
Please help with 11c!?
Answer:
"To the nearest year, it would be about 9 years"
Step-by-step explanation:
11c)
This is compound growth problem. It goes by the formula:
[tex]F=P(1+r)^t[/tex]
Where
F is the future amount
P is the present (initial) amount
r is the rate of growth, in decimal
t is the time in years
Given,
P = 20,000
r = 8% = 8/100 = 0.08
F = double of initial amount = 2 * 20,000 = 40,000
We need to find t:
[tex]F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t[/tex]
To solve exponentials, we can take Natural Log (Ln) of both sides:
[tex]2=(1.08)^t\\Ln(2)=Ln((1.08)^t)[/tex]
Using the rule shown below we can simplify and solve:
[tex]Ln(a^b)=bLn(a)[/tex]
We can write:
[tex]Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064[/tex]
To the nearest year, that would be about 9 years
the perimeter of a rectangle is 46m. the length is 3 m more than 3 times the width find the length and the width of the rectangle
Answer:
width =5m
length=18m
Step-by-step explanation:
w=x
l=3x+3
perimeter =2(l+w)
46=2(x+3x+3)
46=2(4x+3)
46=8x+6
46-6=8x
40=8x
x=40/8
x=5
l=3x+3=3*5+3=15+3=18
Final answer:
To find the length and width of a rectangle with a given perimeter, use algebra to solve for the width first, then use that value to find the length. The width is 5 meters and the length is 18 meters based on the given perimeter and the relationship between length and width.
Explanation:
The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. According to the problem, the perimeter is 46 meters, and the length is 3 meters more than 3 times the width. Therefore, we can express the length as l = 3w + 3. Let's set up the equation using the perimeter formula:
P = 2l + 2w46 = 2(3w + 3) + 2w46 = 6w + 6 + 2w46 = 8w + 640 = 8ww = 5Now that we've found the width to be 5 meters, we can find the length:
l = 3w + 3l = 3(5) + 3l = 15 + 3l = 18 metersThe width of the rectangle is 5 meters and the length is 18 meters.
Somebody please help me with this
Answer:
see the explanation
Step-by-step explanation:
Part 1) Record the coordinates of the given triangle
Looking at the graph
Let
A(-4,2)
B(-2,5)
C(3,2)
Part 2) Translate the given triangle down 2 units and right 5 units. Graph the translation
we know that
A translation of 5 units at right means (x+5)
A translation of 2 units down means (y-2)
so
The rule of the translation is equal to
(x,y) -----> (x+5,y-2)
Apply the rule of the translation at each vertices
A(-4,2) ----->A'(-4+5,2-2)
A(-4,2) ----->A'(1,0)
B(-2,5) -----> B'(-2+5,5-2)
B(-2,5) -----> B'(3,3)
C(3,2) -----> C'(3+5,2-2)
C(3,2) -----> C'(8,0)
using a graphing tool
The graph in the attached figure
What is the relationship between the place-value position of
the 7 and the 5 in the number 462,903.75?
of the place
The place value of the 7 represents
value of the 5
The place value of the 5 represents 10 times the place
Value of the 7
The place value of the 7 represents 100 times the place
value of the 5
of the place value
D The place walue of the 5 represents
of the 7
Answer:7
Step-by-step explanation:
Because it’s the place value of 5
Stephen invests $2,000 in a savings account paying 6% annual interest. Find the balance after 5 years if the interest is compounded quarterly.
Final answer:
The balance in the savings account after 5 years, with quarterly compounded interest, will be $2,699.80.
Explanation:
To find the balance after 5 years when the interest is compounded quarterly, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
Where:
- A is the final amount
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
Plugging in the given values:
[tex]A = $2,000(1 + 0.06/4)^(4*5)[/tex]
[tex]A = $2,000(1.015)^20[/tex]
A = $2,000 * 1.3499
A ≈ $2,699.80
After 5 years, the balance in the savings account will be approximately $2,699.80.
the Parks and recreation department in your town offers a season pass for $150.
With the season pass you pay $5 per session to use the town's tennis courts. Without the season pass you pay $15 per session to use the tennis courts.
Write a system of equations to represent the situation
The system of equations are p = 150 + 5n and p = 15n
Solution:
Given that, The Parks and recreation department in your town offers a season pass for $150.
With the season pass you pay $5 per session to use the town's tennis courts.
Without the season pass you pay $15 per session to use the tennis courts.
We have to write a system of equations to represent the situation
Now, let the number of sessions be "n" and total paying amount be "p"
Then in case of taking season pass
total amount = season pass cost + $5 per session
p = 150 + 5 x n
p = 150 + 5n
And in case of no season pass
total amount = 15 per session
p = 15 x n
p = 15n
Hence, the system of equations are p = 150 + 5n and p = 15n
Final answer:
To represent the cost of using the town's tennis courts with and without a season pass, we use two equations: C = 150 + 5x for with a pass, and C = 15x for without a pass, where C is the total cost and x is the number of sessions.
Explanation:
The Parks and Recreation Department offers two options for using the town's tennis courts: with a season pass and without a season pass. We need to write a system of equations to represent the cost for each option depending on the number of sessions a person attends.
Equations
With Season Pass: C = 150 + 5x
Without Season Pass: C = 15x
In these equations, C represents the total cost of using the tennis courts for a given number of x sessions. For the pass option, there is an upfront cost of $150 plus $5 per session. Without the pass, each session costs $15.
These equations can help determine the point at which purchasing a season pass becomes more cost-effective than paying per session.
Can someone help me find the value of x?
Thanks!
Answer:
x = 7
Step-by-step explanation:
The segment joining the midpoints of the 2 sides of the triangle is one half the length of the third side, that is
2x - 6 = 8 ( add 6 to both sides )
2x = 14 ( divide both sides by 2 )
x = 7
the length of a rectangle is 4 meters less than twice the width the perimeter is 34 Meters find the length and width in meters
The width and length of the rectangle are 7 meters and 10 meters, respectively, as determined by using algebraic expressions to relate the given perimeter with the width and length formulas.
Explanation:To solve for the length and width of a rectangle given the perimeter, we can use algebra. Since we know the length (L) is 4 meters less than twice the width (W), we can write this relationship as L = 2W - 4. The formula for the perimeter (P) of a rectangular shape is P = 2L + 2W. We are given that the perimeter is 34 meters.
Substituting the expression for L into the perimeter formula gives us:
P = 2(2W - 4) + 2WP = 4W - 8 + 2WP = 6W - 8Since the perimeter is 34 meters, we set 6W - 8 = 34.
Add 8 to both sides: 6W = 42Divide by 6: W = 7 metersNow, we find the length using the expression L = 2W - 4:
L = 2(7) - 4L = 14 - 4L = 10 metersTherefore, the width is 7 meters and the length is 10 meters.
Antoine made $33,284 last year. He receives a 4.5% annual raise. What will his new salary be
Answer:
$34781.78
Step-by-step explanation:
$33,284 * 1.045 = $34781.78
The new salary will be $34781.78
Last year salary = $33284
Annual raise = 4.5%
Therefore, based on the above figures the new salary will be:
= $33284 + (4.5% × $33284)
= $33284 + (0.045 × $33284)
= $33284 + $1497.78
= $34781.78
Based on the calculation above, the new salary will be $34781.78
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The price of a car was decreased by 10% to £729. What was the price before the decrease?
Answer:
810
Step-by-step explanation:
90/100=729/x
100×729= 90x
72900=90x
810 = x
Answer:
£810
Step-by-step explanation:
100% - 10% = 90%
£729 is 90 % after the price was decreased by 10%. Therefore, Divide £729 by 90% to get the original price.
£729/90% = £810