Anne and her husband are each starting a saving plan. Deshaun will initially set aside $750 and then add $165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=165N+750 , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $395 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=395N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N .
The equation relating T to N is T = 560N + 750
What is a function?
A function is defined as an expression or rule that explains or compares the relationship between two variables - the dependent and the independent variable.
From the information given, we have that;
Plan A = 165N + 750Plan B = 395NT is the total amount saved using both plan A and BThis is represented as;
T = A + B
Substitute the values
T = 165N + 750 + 395N
Collect like terms
T = 165N + 395N + 750
Add like terms
T = 560N + 750
Thus, the equation relating T to N is T = 560N + 750
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The cities of Raleigh, Durham, and Chapel Hill, North Carolina, form what is known as the Research Triangle. The approximate latitude and longitude of Raleigh are 35.82°N 78.64°W, of Durham are 35.99^°N 78.91°W , and of Chapel Hill are 35.92°N 79.04°W. Show that the triangle formed by these three cities is scalene.
We have proved that the triangle formed is scalene triangle.
It is given that latitude and longitude of three cities is given.
We have to prove that the triangle formed by the three cities is a scalene triangle.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
The Δ formed is a scalene triangle.
Raleigh has latitude and longitude (35.82°N , 78.64°W)
Durham has latitude and longitude (35.99°N , 78.91°W)
Chapel has latitude and longitude (35.92°N , 79.04°W)
Let's represent Raleigh as R , Durham as D and Chapel as C.
Let's check it.
Using the distance formula ;
RD = [tex]\sqrt{(35.99-35.82)^2 + (78.91 - 78.64)^2}[/tex]
RD = [tex]\sqrt{( 0.17^2+ 0.27^2)}[/tex]
RD = [tex]\sqrt{0.102}[/tex]
RD = 0.32
Similarly ;
DC = [tex]\sqrt{0.07^2 + 0.13^2}[/tex]
DC = [tex]\sqrt{0.0218}[/tex]
DC = 0.15
And
RC = [tex]\sqrt{0.10^2 + 0.40^2}[/tex]
RC = 0.41
The sides are all of different lengths, so , we can conclude that this is a scalene triangle.
Thus , the triangle formed by given latitude and longitude of three cities is scalene.
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Can yall help me with this
Answer:
Step-by-step explanation:
d
Simplify: 31−(5−3⋅4)2+26÷4
Answer:
51.5
Step-by-step explanation:
Simplify:
31−(5−3⋅4)*2+26÷4=
31-(5-12)*2+6.5=
31-(-7)*2+6.5=
31+14+6.5=
51.5
HELP PLEASE Use the substitution method to solve the given system of equations. Write your answer as an ordered pair, (x, y).
y - x = 4
6y + 2x = 4
Answer:
[tex] \sf \large \: x= \frac{−5}{2} \: and \: y = \frac{3}{2} [/tex]
Step-by-step explanation:
Let's solve your system by substitution.
y−x=4;6y+2x=4
Rewrite equations:
−x+y=4;2x+6y=4
Step: Solve−x+y=4for y:
−x+y=4
−x+y+x=4+x(Add x to both sides)
y=x+4
Step: Substitute x+4 for y in 2x+6y=4:
2x+6y=4
2x+6(x+4)=4
8x+24=4(Simplify both sides of the equation)
8x+24+−24=4+−24(Add -24 to both sides)
8x=−20
8x/8 = −20/8
(Divide both sides by 8)
x= −5/2
Step: Substitute −5/2 for x in y=x+4:
y=x+4
y=−5/2+4
y=3/2
(Simplify both sides of the equation)
Emily has a job where she earns $10.25 an hour. If she worked 11.5 hours last week, how much will she earn before taxes are taken out?
100.54
113.33
117.88
121.54
135.67
None of the Above
Answer:
C. $117.88
Step-by-step explanation:
$10.25 per hour
11.5 hours worked
$10.25 * 11.5 = $117.875
round $117.875 to $117.88
C. $117.88
You deposit $2000 and account that earns simple interest an annual rate of 4% how long must you leave the money in the account to warn $500 in interest?
Answer:
time = 6.25 years
Step-by-step explanation:
To calculate the simple interest earned, we can use the following formula:
[tex]\boxed{I = \frac{Prt}{100}}[/tex],
where:
I = simple interest ($500)
P = principal amount ($2000)
r = interest rate (5%)
t = time (? years)
To calculate the amount of time the money must be left, we have to substitute the given values into the equation, and solve for t:
[tex]500 = \frac{2000 \times 4 \times t}{100}[/tex]
⇒ [tex]500 \times 100 = 8000t[/tex] [Multiplying both sides by 100]
⇒ [tex]50000 = 8000t[/tex]
⇒ [tex]t = \frac{50000}{8000}[/tex]
⇒ [tex]t = \bf 6.25 \ \mathrm{\bf {years}}[/tex]
Therefore, the money must be left in the account for 6.25 years to earn $500 interest.
Name two angles that form a linear pair
Answer: [tex]\angle APC[/tex] and [tex]\angle CPB[/tex]
Step-by-step explanation:
See attached image.
. Find the equation of the line passing through the points (3, 7) and (5, -1). Your answer should be in point -slope form.
y-7=-4(x-3)
find the slope first
-1-7/ 5-3= -8/2
m= -4
put the slope into the point slope formula,
y-y1=m(x-x1)
to get
y-7=-4(x-3)
Answer: m= -4 y=-4x + 19
At a local print shop, 20 copies can be made for $8. At this rate, how how many copies could be made for $32?
80 copies could be made from $32 at a local print shop.
What is termed as the unitary method?The unitary method determines the value of a unit followed by the value of a necessary number of units.Increases or decreases in one quantity will result in a rise or decrease in that other quantity in direct variation. For example, a rise in the amount of goods will result in a higher price.Direct variation is its inverse. When we increase one quantity, the value of some other quantity decreases.For the given question;
$8 is cost for the 20 copies.
Then,
$8 ------> 20 copies.
Divide both side by 8.
$1 -------> 20/8 copies.
For $32, multiply both side by 32.
$32 ------->32×(20/8) copies
$32 -----> 80 copies.
Therefore, 80 copies will be prepared by the amount of $32 at the local print shop.
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Write an equation in point-slope form of the line having the given slope that contains the given point.
m:-1,(-2,3)
The equation in point-slop form of the line line having the slope m=-1 and that contains the point (-2,3) is y-3=-1(x+2)
Given,
The slope m = -1
The point = (-2,3)
We know the point-slope form,
[tex]y-y_{1}=m(x-x_{1})\\[/tex]
Substitute the values in the equation
y-3=-1(x-(-2))
y-3=-1(x+2)
Hence, the equation in point-slop form of the line line having the slope m=-1 and that contains the point (-2,3) is y-3=-1(x+2)
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if rectangle a is a 2 by 4 would a 4 by 8 be a scale factor
The required scale factor for the small rectangle is 8.
Given that,
Rectangle a is a 2 by 4 would a be 4 by 8,
To determine the scale factor,
The scale factor is defined as the ratio of modified change in dimensions to original dimensions
Area of the rectangle = product of dimensions = length * width
Area of the former rectangle = 2 * 4
= 8
Area of the later rectangle = 4 * 8 = 32
Scale factor = area of the later rectangle/area of the former rectangle
= 32 / 8
= 8
Thus, the required scale factor for the small rectangle is 8.
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Which of the following best describes the ordered pairs listed below? (-3, 2), (3, -10), (5, -14), (10, -24) A. both a relation and a function B. relation only C. function only D. neither a relation nor a function
Since each input is mapped to only one output, the best description of the ordered pairs is given by:
A. both a relation and a function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output.
For a point in the format (x,y), we have that:
x is the input.y is the output.The meaning is that the input x is mapped to the output y.For this problem, the points are given as follows:
(-3, 2), (3, -10), (5, -14), (10, -24)
Each input is mapped to only one input, that is, there are no repeated values of x, hence the best description of the ordered pairs is given by:
A. both a relation and a function.
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Round the decimal to the nearest whole number. 4.197.
Answer:
4
Step-by-step explanation:
Since 4 is the nearest whole number in 4.197, we need to look at the number next to it.
1 is less than 5, so 4 stays the same.
t is a positive whole number.
The expression 2f² + 5t + 2 can never have a value that is a prime number.
Can someone PLEASE explain why.
Since the given expression can be factored in the form (2t+1) and (t+2) so 2t² + 5t + 2 cannot be a prime number.
A whole number greater than 1 that has no factor other than 1 and the number itself is called a prime number.
Some examples of prime numbers are 3,11,19 ... all these numbers can only be divided by 1 or the number itself so they are called prime.
In the given expression 2t² + 5t + 2 , it is said that t is positive whole number. So if t is a positive whole number then the expression can be written as another positive whole number.
Now the expression 2t² + 5t + 2 can be factored into two smaller factors.
2t² + 5t + 2
= 2t² + 4t + t + 2
= 2t (t + 2 )+1 (t+2)
= (t+2) (2t+1)
If t is a positive whole number then t+2 is a whole number and 2t+1 is another positive whole number.
Hence these two numbers are factors of 2t² + 5t + 2 . But a prime number does not have any factors.
So 2t² + 5t + 2 is not a prime number.
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Your friend says the line y=-2 x+3 is perpendicular to the line x+2 y=8 . Do you agree? Explain.
I do not agree that the line y = -2x + 3 is perpendicular to the line x + 2y = 8.
Perpendicular lines are lines that form right angles at the point of intersection. The equation of the lines that are in perpendicular with each other have slopes that are negative reciprocal with one another.
If slope of A = a/b, and B is perpendicular to A, then slope of B = -b/a.
To check if the two given equation of the line is perpendicular with each other, get their slopes and see if they're negative reciprocal of one another.
Line 1 : y = -2x + 3
m = -2
slope of perpendicular line to line 1 = 1/2
Line 2 : x + 2y = 8 ⇒ 2y = -x + 8 ⇒ y = -1/2 x + 4
m = -1/2
1/2 ≠ -1/2
Since the negative reciprocal of the slope of the first line is not equal to the slope of the second line, then they are not perpendicular with each other.
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What is the value of the expression below?
12 + |7 - 10|
Answer: The answer is 15
Answer:
15 is the solution.
Step-by-step explanation:
Finding the value of expression,
→ 12 + |7 - 10|
→ 12 + |-3|
→ 12 + 3 = 15
Hence, the value is 15.
co effiecnet? what is it
The coefficient is defined as a coefficient is a number multiplied by a variable.
We need to define the term coefficient.
What is the coefficient?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it. It is assumed that the variables with no associated number have a coefficient of 1.
For example, in the expression 6x², 6 is the coefficient of x² but in the expression 2y² + 7, 2 is the coefficient of y².
In terms of a polynomial, a series, or any other expression, a coefficient is, in other words, a multiplicative factor.
Therefore, the coefficient is defined as a coefficient is a number multiplied by a variable.
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At a carnival, the object of a game is to throw a dart, at the board and hit region III.
a. What is the probability that it hits region I?
The probability that it hits region I is 15%.
Probability:
Probability means the possibility of the required event.
The formula for the probability is written as,
P(E) = n(E)/n(S)
Where,
P(E) is the probability of an required event
n(E) is the number of possible outcomes
n(S) is the total number of events.
Given,
At a carnival, the object of a game is to throw a dart at the board and hit region III.
Here we need to find the probability that it hits region I.
Consider the board was look like the following figure.
Then based on the given figure,
First, we have to find the total area of the board and the area of the required region.
And then we have to compare it to calculate the Probability.
So, the total area of the board is,
=> total area of the board = (10 + 30)(10 + 15)
=> total area of the board = 1000 in²
Now, the The area of the region I is
=> Area = (10)(15)
=> Area = 150 in²
Therefore, the probability that it hits region I is
=> P = 150/1000
=> P = 15/100
=> P = 15%
Therefore, the probability that it hits region I is 15%.
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can 4 x 2/3 be 2/1 ?
Answer:
noStep-by-step explanation:
can 4 x 2/3 be 2/1 ?
2/1 = 2
solve with an equation
4 * 2/3 = 2
8/3 = 2
or
2.66666666667 = 2
the equation is false, so your answer is no
1. What is the probability the marble is yellow? The probability it is blue? The
probability
it is red?
Answer:
What is the probability the marble is yellow? = 1/3
The probability it is blue? = 1/3
The probability it is red? = 1/3
As the sample size increases, the _____.a. standard error of the mean increasesb. population mean increasesc. standard deviation of the population decreasesd. standard error of the mean decreases
As the sample size increases, the standard error of the mean decreases.
How does the standard error change as the sample size grows?
Standard error diminishes as sample size grows because sample means tend to cluster more closely around the genuine population mean as sample size approaches the true population size.
What grows as the sample size grows?
Our estimate is more accurate since we have more information and hence more data. Our estimate is more certain, our uncertainty is lower, and our precision improves as our sample size grows.Learn more about Standard error
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If the measure of an interior angle of a regular polygon is 108, what type of polygon is it?
F octagon
G hexagon
H pentagon
J triangle
An interior angle of a regular polygon has a measure of 108°. It is a 5 sided polygon known as pentagon.
What shape does the Pentagon have?
A pentagon is a flat, 2D mathematical shape with five sides and five vertices. The Greek word "pentagonos," which means "five-angled," is where the name "pentagon" originates. There are five internal angles that create corners in a normal pentagon.What do you call a shape with five sides?
The geometric shape known as a pentagon has five sides and five angles. Penta here means five, and gon means angle. One of the different kinds of polygons is the pentagon. A regular pentagon's internal angles add up to 540 degrees.Learn more about Pentagon
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Find the value of c that completes the square. r^2+21r+c
Answer:
c = 110.25
(r + 10.5)²
Step-by-step explanation:
Hello!
Perfect Square Trinomial: [tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
21r is basically 2 times r and b, the missing number.
Solve for b21r = 2*r*b10.5 = bThe missing number, b, would be 10.5
Now c is basically b², so we just have to simplify 10.5²:
10.5²110.25c should be 110.25 for it to be a Perfect Square Trinomial. The factored form would be (r + 10.5)².
I don’t understand 15 through 18
Answer:
Step-by-step explanation:
15. True
16. False
17. True
18. True
Answer:
15 )true because they are opposite angles.
16) false 2 and 4 are opposite angles so should be the same value.
17 true ) because angle 4+1=180.
18 true) because the two angles make a 180 degree.
The table below shows the price of rolls at a bakery. A baker’s dozen includes 13 rolls for the price of a dozen rolls. How much money is saved by buying a baker’s dozen instead of 13 individual rolls?
Number of rolls
6
8
Baker’s dozen
Price ($)
$3.60
$4.80
$7.20
$0.55
$0.60
$0.70
$0.75
Based on the price to buy a baker's dozen, the money that the baker will save from buying a Baker's dozen instead of 13 individual rolls is $0.60.
What is the difference in cost?The price per roll is:
= 3.60 / 6
= $0.60
The price of 13 individual rolls is:
= 0.60 x 13
= $7.80
The amount saved is:
= Price of 13 rolls - Price of baker's dozen
= 7.80 - 7.20
= $0.60
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who needs special prayer
Answer: me man
Step-by-step explanation:
holy god
what is the quotient of 3/4÷1/5
At what rate is the amount of flour decreasing?
grams per minute ???
AnAt what rate is the amount of flour decreasing? 270- 180 90- grams per minute 2. As time increases, the amount of flour in the machine increases. Time (minutes)
LA and ZB are vertical angles. If mA = (6x - 26)° and m/B = (5x + 6)°,
then find the measure of ZB.
Answer:
∠ B = 166°
Step-by-step explanation:
since ∠ A and ∠ B are vertical angles then they are congruent, that is
∠ A = ∠ B
6x - 26 = 5x + 6 ( subtract 5x from both sides )
x - 26 = 6 ( add 26 to both sides )
x = 32
Then
∠ B = 5x + 6 = 5(32) + 6 = 160 + 6 = 166°
