Answer:
(8.21, -20.79)
Step-by-step explanation:
Given the simultaneous equation;
[tex]\frac{a}{b} - \frac{b}{2} = 10\\a - b = 29[/tex]
From 2;
a = 29 + b ....3
Substitute 3 into 1;
[tex]\frac{29+b}{b} - \frac{b}{2} = 10\\\frac{2(29+b)-b^2}{2b} = 10\\\frac{58+2b-b^2}{2b} = 10\\58+2b-b^2 = 20b\\b^2-2b-58 = -20b\\b^2-2b+20b -58 = 0\\b^2+18b-58 = 0\\[/tex]
Factorize
b = -18±√18²-4(-58)/2
b = -18±√324+232/2
b = -18±√556/2
b = -18±23.58/2
b = -18-23.58/2 and -18+23.58/2
b = -41.58/2 and 5.58/2
b = -20.79 and 2.79
Since a = 29 + b
when b = -20.79
a = 29 - 20.79
a = 8.21
Hence the solution to the system of equation is (8.21, -20.79)
What is the slope of the line that passes through the points (5, 1) and (2, -7)?
Answer:
m [ slope ] = 8/3
Step-by-step explanation:
What is the slope of the line that passes through the points (5, 1) and (2, -7)?
m = ∆y / ∆x
m = y₂ – y₁ / x₂ – x₁
| (5, 1) → (x₁, y₁) | (2, -7) → (x₂, y₂) |
[each coordinate will correspond (directly go to) to the variables shown]
m = (-7) – (1) / (2) – (5)
m = -8 / -3
m = 8 / 3
This means that this line has a rise of 8 and a run of 3.
Up 8 and right 3 proportionally, it would touch the opposite corners of a plane that was 8 by 3 units.
Slope can be thought of as the steepness of a line, the greater the slope, the greater the steepness.
These points are generally known as cartesian coordinates.
____________
Once you have the slope, you can back track from one of the coordinates to find the equation of the line.
Just multiply the slope by the x of either coordinate, make it opposite, and then add that to the y of that coordinate to get b [the y-intercept; where it crosses the y axis, x is always 0]
Since (2, -7) is closer to the y axis than (5, 1) it is more convenient.
In (2, -7), 2 is the x variable and -7 is the y variable.
-mx + y = (-8/3)(2) + (-7) = -16/3 + (-21/3)
21/3 is the same as 7 [so it will have a common denominator].
-16 + -21 / 3 = -37/3 = b
Thus this line has an equation of
y = mx + b
↓ ↓
y = 8/3x – 37/3.
__________________________
Or you can refer to point slope which is what is taught:
y – y₁ = m(x – x₁).
You can tell that there are some similarities to this and the slope formula.
m = ( y₂ – y₁ / x₂ – x₁ ) →
m × ( x₂ – x₁ ) =
( y₂ – y₁ / x₂ – x₁ ) × ( x₂ – x₁ )
[multiply the denominator by both sides]
m ( x₂ – x₁ ) = y₂ – y₁
[x₂, and y₂ can just be x and y since you only need the initial coordinate and slope, because the second coordinate can be anything along that line]
m ( x – x₁ ) = y – y₁ →
y – y₁ = m(x – x₁)
[symmetric property of equality]
if a = b, b = a.
1. You bought a digital camera for your birthday. The original cost was $555.
It is marked "15% off". What is the sale price? *
Answer:
$471.75
Hope this helps!
Express 9 hours as a percentage of 3 days.
Step-by-step explanation:
3(days) × 24(hours) = 72(hours)
9/72 ×100 = 12.5 %
Rearrange W=3(2a+b)-4 to make a the subject
Step-by-step explanation:
Answer aboove in the photo
Have a nice dayy
i need to know the answer
plzzzz help me i beg u this is a major test
I will even drop 50 points
Jordan invests £12500 into
His bank account.
He receives 8.5% per year simple interest.
How much will Jordan have after 3years?
Give your answer to the nearest penny
where appropriate.
Answer:
Jordan will have $15687.50 after 3 years.
Step-by-step explanation:
First, we have to find the amount of interest Jordan has by using the following formula,
simple interest = $12,500 * 8.5% * 3
since the interest rate is obviously a percentage, we convert it into a decimal.
simple interest = $12,500 * 8.5% * 3
simple interest = $12,500 * 0.085 * 3
now that the numbers are the way it's supposed to be, we multiply them all together.
simple interest = $12,500 * 0.085 * 3
simple interest = $1062.50 * 3 (here, we multiply the first two numbers before multiplying it by 3 so we will have two numbers remaining which is easier to deal with without all three numbers together)
simple interest = $3187.50
Jordan has $3185.50 simple interest.
however, this is not the final answer since it asks how much he has AFTER 3 years. think about it.. would you really have $3187.50 AFTER 3 years with investing $12,500 into your account? no, since the values have such big difference to each other. we have to add the amount of interest by the principal by using the following formula,
total amount = principal + simple interest
now, we substitute the numbers in.
total amount = principal + simple interest
total amount = $12,500 + $3185.70
total amount = $15.687.50
Therefore, Jordan will have $15,687.50 after 3 years.
Rachel’s credit card billing statement says she owes $350 for purchases last month. Her minimum monthly payment is $25. If she doesn’t have the full $350 to pay it off, but has more than the $25 minimum, what should she do?
1) Pay more than the monthly payment amount.
2) Pay the $350 by using a different credit card.
3) Wait until she has the $350 before paying the credit card bill even though she will get a late fee.
4) Only pay the minimum payment.
4-4=3-3 true or false
Answer:
True
Step-by-step explanation:
4-4=0
3-3=0
Answer:
True
Step-by-step explanation:
First you would have to find what is 4-4=0
Second it would be 3-3=0
so it’s true
It have the same answer
Please help with this i am not sure if it is b
Answer: Yes its B sorry if im wrong
Step-by-step explanation:
have a nice day
Reasoning Solve the system of linear equations using substitution. Use pencil and paper. Which
expression would be easier to substitute into the other equation, in order to solve this problem?
Explain your reasoning.
X = 3y -9
X + 3y = 2
The solution is
(Simplify your answer. Type an ordered pair.)
Answer:
Lol I’m doing the same thing
Step-by-step explanation:
BRANLIEST+20Pts In each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained.
Help me pls anything helps
Answer:
Step-by-step explanation:
This is a function as there is only one unique value of y for any unique value of x. It passes the ‘vertical line test’.
So insert ‘F’ as this is a function.
Answer:
F
Step-by-step explanation:
this is a function because it is just a reflection over the x-axis
the function is f(x) = -(x - 1)^2 + 3
What is the best buy?
6 shirts for $252.42
4 shirts for $116.00
5 shirts for $90
what are the base pairing rules in terms of DNA
Answer:
The rules of base pairing (or nucleotide pairing) are:
A with T: the purine adenine (A) always pairs with the pyrimidine thymine (T)
C with G: the pyrimidine cytosine (C) always pairs with the purine guanine (G)
Step-by-step explanation:
Simplify the expression.
StartFraction 0.5 (negative 14 + 12.6) over 9.32 + (negative 7.92) EndFraction
Answer:
[tex]\frac{0.5(-14 + 12.6)}{9.32 + (-7.92)} = \frac{-0.7}{1.4} = -0.5[/tex]
Step-by-step explanation:
Answer:
Its B
Step-by-step explanation:
I checked it on EDGE 2020!
The measures of the three interior angles of a triangle are 85°, 20°, and 75º. Determine the
measures of the three exterior angles
Answer:
The measures of the three exterior angles would be 95, 160 and 105.
Matt and 6 of his friends went out to eat.
They decided to split the bill evenly. Each
person paid $14. What was the total bill?
Answer:
The total bill was $98.
Step-by-step explanation:
Matt and 6 of his friends = 7 people
Each person paid $14
$14 x 7 = $98 in total
f (2) if f(x)=x+4
?????????
Answer:
if f(x)=x+4
f(2)=2+4=6 is your answer
really easy....plz help if u can..will mark
Answer:
The distributive property.
Step-by-step explanation:
The distributive property is when you distribute a number to different numbers in a parentheses. For example...
2*x would be 2x, and 2*4 would be 8.
What property is illustrated in: IF ∠A ≅ ∠B, ∠B ≅ ∠C then ∠A ≅ ∠C
Answer:
true
Step-by-step explanation:
x=-3 is a zero of multiplicty one and x=3 is a zero multiplicty of two while the lead co efficient is one
don't understand sorry
Answer this correctly, and you'll be awarded as brainliest.
Answer:
Possible
plz give brailiest
What is the area of the polygon below?
Answer:
B.84 sq.units
Step-by-step explanation:
Adding both rectangles
12 + 72
84sq.units
pls Mark as brainliest
Kelly ordered birthday pencils. It cost $25 per box plus $3 for shipping. If Kelly can spend up to at most $200, what is the greatest number of boxes she can purchase?
Answer:7
Step-by-step explanation: 25 x 7 = 175 now 3 x 7 = 21 175 + 21 =196 r 4 :)
Portia worked 2 part-time jobs and earned $233.00 for working a total of 26 hours at both jobs. She is paid $7.00 per hour at job A and $10.00 per hour at job B. How many hours did Portia work at job A?
PLEASE HELP!!!!!!
Answer:
9 hours for job A, 17 hours for job B please brainliest :>
Step-by-step explanation:
A+B = 26
7A+10B = 233
A = 9
B = 17
Heyyyy!
Here's your answer!
She worked 14 hours at Job A and worked 12 hours at Job B
Step-by-step explanation:
14 × 6.40 = 89.60 and 12 × 7 = 84
84 + 89.60 = 173.60
Hoped I helped!
Please help with this question it’s freaking me out
Answer:
20 cm²
Step-by-step explanation:
see picture. count the number of squares.
If 2x-7y=12 and -3x+7y=-11 then find the value of the x and y
The model below represents an equation.
Which represent like terms in the model of the equation?
and
Question:
The model below represents an equation.
2 long x tiles and 3 square y tiles = 3 long x tiles
Which represent like terms in the model of the equation?
Answer:
2 long x tiles and 3 long x tiles are like terms
Step-by-step explanation:
Given
2 long x tiles and 3 square y tiles = 3 long x tiles
Required
Identify the like terms
Represent long with a and square with b.
So, we have:
2a x and 3b y = 3a x
and, as used here means addition
So:
[tex]2a x + 3b y = 3a x[/tex]
Collect like terms
[tex]3by = 3ax - 2ax[/tex]
[tex]3by = ax[/tex]
See that 3ax and 2ax are evaluated without any barrier.
This means that they are like terms
An 11-ft ladder leans agalnst the side of a house. The bottom of the ladder Is 9 ft from the side of the house. How high Is the IS top of the ladder from the ground?
If necessary, round your answer to the nearest tenth.
Answer:
The top of the ladder is 6.3 feet high from the ground.
Step-by-step explanation:
The given question can be expressed by the three sides of a right angled triangle. Let the height of the top of the ladder from the ground be represented by h.
Thus, applying the Pythagoras theorem to determine h, we have;
[tex]/hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]11^{2}[/tex] = [tex]h^{2}[/tex] + [tex]9^{2}[/tex]
121 = [tex]h^{2}[/tex] + 81
[tex]h^{2}[/tex] = 121 - 81
= 40
h = [tex]\sqrt{40}[/tex]
= 6.325
h = 6.325 feet
The top of the ladder is 6.3 feet high from the ground.