(y - yo) = m.(x - xo)
Let's go
(-1/n - (-1/m)) = s.(1 - n/m)
(-1/n + 1/m) = s.(1 - n/m)
(-m+n)/mn = s.(m - n)/m
If we multiply both sides by m
(-m + n)/n = s.(m - n)
If we take the (-1) from the left side we have
(-1.(m - n))/n = s.(m - n)
And if we divide both sides by (m - n)
-1/n = s
So our slope is -1/n
5.43 x 10^1 In scientific notation
Answer:
Step-by-step explanation:
= 5.43 × 101
(scientific notation)
= 5.43e1
(scientific e notation)
= 54.3 × 100
(engineering notation)
(one)
= 54.3
(real number
Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?
They are independent because P(X) x P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) x P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).
Answer: The correct option is
(A) [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]
Step-by-step explanation: We are given to consider a situation in which X and Y are two events such that
[tex]P(X)=\dfrac{4}{5},~P(Y)=\dfrac{1}{4},~P(X\cap Y)=\dfrac{1}{5}.[/tex]
We are to select the statement that best describes the events X and Y.
We know that
any two events A and B are said to be independent if
[tex]P(A)\times P(B)=P(A\cap B).[/tex]
We have, for events X and Y,
[tex]P(X)\times P(Y)=\dfrac{4}{5}\times\dfrac{1}{4}=\dfrac{1}{5}=P(X\cap Y)\\\\\\\Rightarrow P(X)\times P(Y)=P(X\cap Y).[/tex]
Thus, X and Y are independent because [tex]P(X)\times P(Y)=P(X\cap Y).[/tex]
Option (A) is CORRECT.
What is the answer to use an integer to describe sea level
Answer:
an integer is any whole number
if it is 5 below sea level then it is -5
Step-by-step explanation:
think of sea level like 0
Your friend is making a pattern for quilt pieces. Her pattern is a right angle with two acute angles that complementary. The measure of one of the angles is to be 12° more than half the measure of the other angle. Find the measure of each angle of the triangle. Show your work using the format above.
Answer:
The measure of angle 1 is 52° and the measure of angle 2 is 38°
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x ----> the measure of angle 1
y ----> the measure of angle 2
we know that
[tex]x+y=90\°[/tex] -----> equation A
[tex]y=\frac{x}{2}+12[/tex] ----> equation B
Substitute equation B in equation A and solve for x
[tex]\frac{x}{2}+12+x=90\°[/tex]
[tex]\frac{x}{2}+x=90\°-12\°[/tex]
[tex]\frac{3x}{2}=78\°[/tex]
[tex]x=(2)78/3=52\°[/tex]
Find the measure of y
[tex]y=\frac{52}{2}+12=38\°[/tex]
therefore
The measure of angle 1 is 52° and the measure of angle 2 is 38°
The two acute angles in the triangle are 52° and 38°. This is found by setting up and solving two equations based on the problem's conditions.
Explanation:This question is about solving an equation related to two acute angles in a triangle. Let's denote the smaller angle as 'x' and the larger angle as 'y'. Since the two angles are complementary, we can write an equation like 'x + y = 90'. The problem states that one angle is 12° more than half the other. We can formulate this as 'y = x/2 + 12'. To solve for 'x' and 'y', we need to substitute 'y' from the second equation into the first one to get 'x + x/2 + 12 = 90'. Multiplying through by 2 to eliminate the fraction gives '2x + x + 24 = 180', which simplifies to '3x = 156'. Solving for 'x' gives 'x = 52'. Substitute 'x' into either of the original equations gives 'y = 52/2 + 12 = 38'. Thus, the two acute angles in the triangle are 52° and 38°.
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sam and meena share sweets in the ratio 4:5 meena gets 40 sweets wok out how many sweets sam gets
Answer:
Same gets 32 sweets.
Step-by-step explanation:
We have by proportion 4/5 = x/40 where x is the number of sweets that Sam gets.
5x = 4*40
5x = 160
x = 160/5 = 32 sweets.
500 principal earning 3% compound monthly, after 10 years.
A. A bazillion dollars
B. $671,96
C. $512,64
D. $674,68
Answer:
D. $674.68
Step-by-step explanation:
We will use the well known equation for compound interest
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where
[tex]A[/tex] is the final total[tex]P[/tex] is the principal amount (starting total)[tex]r[/tex] is the interest rate as a decimal[tex]n[/tex] is the number of times the interest is compounded each year[tex]t[/tex] the number of yearsPlugging in what we know from the question:
[tex]A = 500(1+\frac{0.03}{12})^{12 \times 10}\\A = 500(1.34935355)\\A = 674.68[/tex]
So the answer is D.
Hope this helps!
3/4x-5/6=2/3x how to solve?
Answer:
The answer is 10.
Step-by-step explanation:
Multiply both sides of the equation by 12.
12( 3/4x - 5/6) = 12 times 2/3x.
Distribute 12 through the parenthesis.
12 times 3/4x - 12 times 5/6 = 12 times 2/3x.
Reduce the numbers with greatest common divisor 3.
12 times 3/4x - 12 times 5/6 = 4 times 2x.
Reduce the numbers with greatest common divisor 4.
3 times 3x - 12 times 5/6 = 4 times 2x.
Reduce the numbers with greatest common divisor 6.
3 times 3x - 2 times 5 = 4 times 2x.
Calculate the product, 4 times 2x.
3 times 3x - 2 times 5 = 8x.
Calculate the product 3 times 3x.
9x - 2 times 5 = 8x.
Multiply the numbers - 2 times 5.
9x -10 = 8x.
Move the constant to the right by adding its opposite to both sides.
9x - 10 + 10 = 8x + 10.
Eliminate the opposites, -10 + 10.
9x = 8x + 10.
Move the variable to the left by adding its opposite to both sides.
9x -8x = 8x -8x + 10.
Now eliminate the opposites
9x - 8x = 10.
Collect the like terms by subtracting their coefficients.
(9-8)x
Subtract the numbers.
1x.
When the term has a coefficient of 1, it doesn't have to be written, so it's basically x.
Then, x will equal to 10!
4321342345670
+22347968
the Answer is
4.3213647e+12
Solve -3 1/2 = 1/2x + 1/2x + x
Answer:
-1.75 I apologize if that is not right but i am 99% sure
Step-by-step explanation:
When you add like terms on the right side you end up with 2x, then all you di is divide both sides by 2 and you end up with -1.75
(Apex Question, Help?)
Which polynomial represents the difference below
2x^2+7x+6
-
(3x^2-x)
A. -x^2+6x+6
B. 2x^2+4x+6
C. 2x^2+5x+6
D. -x^2+8x+6
The required difference between polynomial 2x^2+7x+6-(3x^2-x) is,
-x^2+8x+6.
To simplify 2x^2+7x+6-(3x^2-x)
Polynomial is defined as the sum of more than one variable in terms of their power.
Here,
[tex]=2x^2+7x+6-(3x^2-x)\\=2x^2-3x^2+7x+x+6\\=-x^2+8x+6[/tex]
Thus, the required difference between polynomial 2x^2+7x+6-(3x^2-x) is, -x^2+8x+6.
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Linda entered an elevator on floor 9. She rode down 8 floors. Then she rode up 11 floors and got off. What floor was she on when she left the elevator?
so she started on 9 then she went down 8 so 9 - 8 = 1. then she went up 11 floors.so 1 + 11= 12. that's your answer. 12
4.5+1.5x=18-3x
a)1.5 b)3 C)6 D)9
Answer:
b) 3
Step-by-step explanation:
4.5+1.5x=18-3x
1) Subtract 4.5 from both sides:
1.5x=13.5-3x
2) Add 3x to both sides:
4.5x=13.5
3) Divide both sides by 4.5:
x=3
What is the approximate circumference of the circle shown below
Answer:
A. 48.7cm
Reason:
The way to find circumference is Pi times the diameter so simply do this:
[tex]15.5 \times \pi = 48.694686[/tex]
round it and you'll get to 48.7cm
Hope it helps :)
Sorry if not :(
Answer: A. 48.7 cm
Step-by-step explanation:
The circumference of circle is given by :_
[tex]\text{Circumfernce}=\pi d[/tex] , where d= diameter of the circle .
In the given [picture , we are given that the diameter of the circle = 15.5 cm
Then, the circumference of the circle will be :-
[tex]\text{Circumfernce}=\pi (15.5)\ cm[/tex]
Substitute [tex]\pi =3.14[/tex] , we get
[tex]\text{Circumfernce}=(3.14) (15.5)\ cm[/tex]
[tex]\text{Circumfernce}=48.67\approx48.7\ cm[/tex]
Hence, the approximate circumference of the circle = 48.7 cm
Thus , the correct answer is 48.7 cm .
Solve the formula C= Rd for d
Answer:
d = C/R.
Step-by-step explanation:
You Divide both sides by R:
C = Rd
C / R = Rd / R
C/R = d.
Marcus is 5 19/24 feet tall. Ben is 5 9/16 feet tall. Which of the two boys is taller?
well, Marcus and Ben are both 5 feet tall and a little bit more, Marcus is 19/24 more and Ben is 9/16 more, so the 5's in the fraction are the same, so which one is larger, 19/24 or 9/16?
we can simply put both fractions with the same denominator, by multiplying one by the other's denominator, so let's proceed,
[tex]\bf \stackrel{\textit{\large Marcus is taller}}{5~feet + \left( \cfrac{19}{24}\cdot \cfrac{16}{16}\implies \boxed{\cfrac{304}{384}} \right)}\qquad \qquad \qquad \stackrel{\textit{\large Ben}}{5~feet + \left( \cfrac{9}{16}\cdot \cfrac{24}{24}\implies \boxed{\cfrac{216}{384}} \right)}[/tex]
1-2+3-4+5-6+..+99-100.
"twice a number plus 4 is 8"
Answer:
2n + 4 = 8
Step by Step explanation:
"twice a number" means to multiply 2 by a number
"plus 4" is telling you to add 4 to 2n
"is 8" means equals 8
so, that means 2n + 4 = 8
I hope i helped :)
The sum of three integers is 228. The second integer is 1 more than the first,
and the third integer is 2 more than the first. Write an equation to determine
the integers. Solve your equation. Show your work.
Please help
Answer: The integers are 75,76,77
Step-by-step explanation:
Answer: first ingeter is 75, second is 76, and third 77
Step-by-step explanation: 75 + 76 + 77 = 228
2 1/2+3 3/4+1 1/2 plz hep me plz thanks you
Answer:
7.75 or 7 3/4
Step-by-step explanation:
2 1/2 + 1 1/2 = 4
4 + 3 3/4 = 7 3/4
7 3/4 = 7.75
either works
Round 725,390 to da nearest thousand
Answer:725000
Step-by-step explanation:in thousands you have 5,390. Sound you’re rounding down from the hundredth position of 390. 390 is below 500 so go down a thousand.
Help with number 16 (15 points!)
Answer:
-5≥x≤-1
Step-by-step explanation:
comment if you would like an explanation for this.
gcf of 80, 16 and 96
Answer:20
Step-by-step explanation: hard to explain
Answer:
16
Step-by-step explanation:
Which algebraic expression is a trinomial?
Answer:
A trinomial is a mathematic expression which includes 3 terms. An example would be 5 + 2 - 6. Hope this helps!
Two dams, when opened, release water at different rates. The following functions represent the amounts of water the dams release over t minutes:
Dam A f(t) = 5t – 7t – 1
Dam B g(t) = 3t 2 + 4t + 9
Which function represents the difference in the amounts of water released, h(t) = f(t) – g(t)?
Options:
h(t) = 3t 2 – 5t + 11t + 10
h(t) = 2t 2 – 11t – 10
h(t) = 5t – 3t 2 – 3t + 8
h(t) = 5t – 3t 2 – 11t – 10
Answer:
Step-by-step explanation:
h(t) = 2t 2 – 11t – 10 is the answer
The value of h(t) is h(t) = 2t^2 – 11t – 10.
To add or subtract functions, just add or subtract the values at each point where it makes sense.
How to find h(t) = f(t) – g(t)?
Two dams, when opened, release water at different rates. The following functions represent the amounts of water the dams release over t minutes:
Given : Dam A f(t) = 5t^2 – 7t – 1
Dam B : g(t) = 3t ^2 + 4t + 9.
Then f(t) – g(t) = (5t^2-7t-1) -(3t^2+4t+9)
=> 2t^2 – 11t – 10.
Thus, h(t) = 2t^2 – 11t – 10.
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What is the value of the expression with base 3 and exponent 6
Answer:
729
Step-by-step explanation:
3 x 3 x 3 x 3 x 3 x 3 = 729
what is the answer for this question
Answer:
Symmetry
Step-by-step explanation:
Because the two sides are equally the same. Basically identical.
PLEASE HELP QUICK !!!!!!Point B is in the interior of ∠AOC, m∠AOC = 108°. Find m∠AOB, if m∠AOC = 3m∠AOB.
Answer:
The measure of angle AOB is 36°
Step-by-step explanation:
- Point B is in the interior of ∠AOC
- That means angle AOB is a part of angle AOC
- Measure of angle AOC is 108°
- Measure of angle AOC is 3 times measure of angle AOB
- We need to find measure of angle AOB
* Lets solve the problem
∵ m∠ AOC = 3 m∠ AOB
∵ m∠ AOC = 108°
- Substitute m ∠AOC in the equation above
∴ 108 = 3 m∠ AOB
- Divided both sides by 3
∴ 36° = m∠ AOB
The measure of angle AOB is 36°
Answer: The measure of ∠AOB = 36°.
Step-by-step explanation:
Since we have given that
m∠AOC = 108°
and we need to find the measure of ∠AOB.
As we know that
[tex]m\angle AOC=3m\angle AOB\\\\108=3\angle AOB\\\\\dfrac{108}{3}=\angle AOB\\\\36^\circ=\angle AOB[/tex]
Hence, the measure of ∠AOB = 36°.
Simplify each expression
Keep in mind you are NOT solving for the letters!!!
Please answer both of these questions (problems attached)
I’m really confused haha please help explain and answer (there are two)
Answer:
-5n-172b+56Step-by-step explanation:
Q: -(5n-1)-2-5n+1-2-5n-1Q: -8b+8 (10b+7)-8b+80b+5672b+56What is an equation of the line that passes
thrcugh the point (-2,5) and is parallel to the
line x - 2y = 6?
what is the solution of the proportion -27 = m/9
Answer:
m= -243
Step-by-step explanation:
1. inverse operations so division into multiplication: 9 x (-27)=
remember negative times positive is negative
therefore u get -243