Answer:
Therefore [tex]m_{2}[/tex] = -3.
Step-by-step explanation:
i) let us say the slope of the line passing through (-2,7) and (4,9) is [tex]m_{1}[/tex].
ii) to find the slope of the line passing through two points ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) we use the formula m = [tex]\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]. Therefore we can say that [tex]m_{1}[/tex] = [tex]\dfrac{9 - 7}{4 - (-2)}[/tex] = [tex]\dfrac{1}{3}[/tex].
iii) let us say the slope of the perpendicular line to the line passing through (-2,7) and (4,9) is [tex]m_{2}[/tex]
iv) from the formula for the slopes of a line and the line perpendicular to it which is given by [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = -1, therefore [tex]m_{2}[/tex] = -1 ÷ [tex]m_{1}[/tex] = -3. Therefore [tex]m_{2}[/tex] = -3
What is it equivalent expression for 3(x+9)-2
========================================
Work Shown:
3(x+9)-2
3*x+3*9 - 2 ..... distribute
3x+27-2 .... multiply
3x+25 .... combine like terms
Answer:3x+25
Step-by-step explanation:
In ΔDEF,{EF}\cong{DE} EF ≅ DE and m∠E = 104°. Find m∠D.
The 3 inside angles need to equal 180.
Subtract E from 180 to find the sum of the other two angles:
180 - 104 = 76
Now because EF ≅ DE , angle D and F would be the same so divide 76 by 2
Angle D = 38
What is a formula for the nth term of the given sequence?
-17, -8, 1...
−17,−8,1...
a_{n}=-8+9(n-1)a
n
=−8+9(n−1)
a_{n}=-17(9)^{n}a
n
=−17(9)
n
a_{n}=9n-26a
n
=9n−26
a_{n}=-17-9(n-1)a
n
=−17−9(n−1)
Answer:
The nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]
Step-by-step explanation:
Given sequence is -17,-8,1,...
To find the nth term of the given sequence :
Let [tex]a_1=-17,a_2=-8,a_3=1,...[/tex]
To find the common difference d :
[tex]d=a_2-a_1[/tex]
[tex]=-8-(-17)[/tex]
[tex]=-8+17[/tex]
Therefore d=9
[tex]d=a_3-a_2[/tex]
[tex]=1-(-8)[/tex]
[tex]=1+8[/tex]
Therefore d=9
The common difference d is 9
Therefore the given sequence is an arithmetic sequence
The nth term of an arithmetic sequence is given below
[tex]a_n=a_1+(n-1)d[/tex]
Substitute [tex]a_1=-17[/tex] and d=9 in the above equation we get
[tex]a_n=-17+(n-1)9[/tex]
Therefore the nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]
The formula for the nth term of the sequence -17, -8, 1 is a_n = 9n - 26, where n is the position of the term in the sequence.
Explanation:The sequence provided is -17, -8, 1, which suggests that there is a common difference between terms since it is an arithmetic sequence. To find the nth term of an arithmetic sequence, we use the formula a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference. In this case, the common difference is 9 (since -8 - (-17) = 9).
So, using the formula for the nth term of an arithmetic sequence:
a_1 = -17 (the first term)d = 9 (the common difference)Our formula becomes a_n = -17 + (n - 1) × 9. Simplifying this:
a_n = -17 + 9n - 9
a_n = 9n - 26
Therefore, the formula for the nth term of the given sequence is a_n = 9n - 26.
Find the average rate of change for f(x) = x2 + 9x + 18 from x = −8 to x = −2.
A) −1
B) −3
C) 1
D) 3
Answer:
c
Step-by-step explanation:
c
You work as a tailor. You are provided with 5 3/4 yards of cloth for making curtains. You use 4 1/4 yards of cloth for that purpose.
How many yards of cloth remain?
Final answer:
After using 4 1/4 yards out of 5 3/4 yards of cloth to make curtains, 1 1/2 yards of cloth remain.
Explanation:
You are provided with 5 3/4 yards of cloth and you use 4 1/4 yards for making curtains. To find out how much cloth remains, you need to subtract the amount used from the total amount provided. You perform the subtraction by converting the mixed numbers to improper fractions or by subtracting the whole numbers and fractions separately.
First, subtract whole numbers:
5 yards - 4 yards = 1 yardNext, subtract the fractions:
3/4 yard - 1/4 yard = 2/4 yard, which simplifies to 1/2 yard.Combine the whole number and the fraction for the final answer:
1 yard + 1/2 yard = 1 1/2 yards of cloth remain.How to write 21 less than n equal 31 in a equation promblem
Answer:
n-21=31
Step-by-step explanation:
Just read it carefully, it is worded weirdly, but just think about it.
Answer:
52
Step-by-step explanation:
n-21=31
n=31+21
n=52
please help asap I also need it in my own words
Step-by-step explanation:
so to find out how long you would first do 60-30 as this is how many extra minutes they workout. the answer is 30.
then you would divide 30 by 2 that makes 15 as there is 2 people then you would add 15 to 30 and you get 45
45mins on treadmill
freehand=60-45=15
60-30=30
30÷2=15
15+30=45
60-45=15
part A:
freehand=f
treadmill=t
x=y+30
that is what i believe the eqation is
Evaluate a + (-b) where a = 4 and b =2
Answer:
The answer is 2
Step-by-step explanation:
4 + (-2) = 2
Answer:
2
Step-by-step explanation:
Given the expression : a + (-b)
where a = 4 and b = 2
Therefore: a + (-b) = 4 + (-2)
=4 - 2
= 2
A fraction that is a terminating decimal between 1.25 and 1.5
Answer:
13/10
Step-by-step explanation:
13/10 = 1.30 is a number between 1.25 and 1.50.
x/5 = -10 What is the value of X
Answer:
[tex]x=-50[/tex]
Step-by-step explanation:
we have
[tex]\frac{x}{5} =-10[/tex]
Solve for x
That means ----> isolate the variable x
Multiply by 5 both sides to remove the fraction
[tex]\frac{x}{5}(5) =-10(5)[/tex]
Simplify
[tex]x=-50[/tex]
which expressions are equivalent?
Answer:
C none of the above
Step-by-step explanation:
x + z + y
is not going to be equal to x + y - z
Its like saying 10 + 5 - 4 = 11
To 10 + 5 + 4, they are not going to be equal
Answer:
C none of the above
Step-by-step explanation:
What is the quotient?
StartFraction 2 y squared minus 6 y minus 20 Over 4 y + 12 EndFraction divided by StartFraction y squared + 5 y + 6 Over 3 y squared + 18 y + 27 EndFraction
The quotient is [tex]\frac{3(y-5)}{2}[/tex]
Explanation:
The expression is [tex]\frac{2 y^{2}-6 y-20}{4 y+12} \div \frac{y^{2}+5 y+6}{3 y^{2}+18 y+27}[/tex]
Now, reciprocal the term [tex]\frac{y^{2}+5 y+6}{3 y^{2}+18 y+27}[/tex] and convert ÷ to ×
[tex]\frac{2 y^{2}-6 y-20}{4 y+12} \times \frac{3 y^{2}+18 y+27}{y^{2}+5 y+6}[/tex]
Taking the common terms out, we get,
[tex]\frac{2\left(y^{2}-3 y-10\right)}{4(y+3)} \times \frac{3\left(y^{2}+6 y+9\right)}{y^{2}+5 y+6}[/tex]
Factorizing each numerator and denominator, we get,
[tex]\frac{2(y-5)(y+2)}{4(y+3)} \times \frac{3(y+3)(y+3)}{(y+3)(y+2)}[/tex]
Multiplying the terms, we have,
[tex]\frac{6(y-5)(y+2)(y+3)^{2}}{4(y+3)^{2}(y+2)}[/tex]
Cancelling the common factors, we get,
[tex]\frac{3(y-5)}{2}[/tex]
Thus, the quotient is [tex]\frac{3(y-5)}{2}[/tex]
Answer:
B
Step-by-step explanation:
On edge 2021
PLEASEE I’m failing math with a 57 I need help
4. take 110-80/4-2, this gives you 30/2, which is then 15. Therefore it is 15 dollars per hour
Complete the statement using always, sometimes, or never.
A quadrilateral is
a trapezoid.
a.) always
b.) sometimes
c.) never
it had to be b cuz now all quadrilateral have straight sides
how many soulutions does the system of equations have x-3y=15. and 3x-9y=45
Answer:
Infinitely many solutionsStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-3y=15\\3x-9y=45\end{array}\right\\\\\text{Divide both sides of the second equation by 3}\\\\\dfrac{3x}{3}-\dfrac{9y}{3}=\dfrac{45}{3}\\\\x-3y=15\\\\\text{We received the same equation as the first.}\\\\\bold{CONCLUSION}\\\\\text{The system of equations has infinitely many solutions.}[/tex]
[tex]\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2x=c_2\end{array}\right\\\\\text{If}\ a_1=a_2,\ b_2=b_2,\ c_1=c_2,\ \text{then the system of equations}\\\text{ has infinitely many solutions}\\\\\text{If}\ a_1=a_2,\ b_1=b_2,\ c_1\neq c_2,\ \text{then the system of equations}\\\text{has no solutions}\\\\\text{Other the system of equations has one solution.}[/tex]
What percent of 18 is 24?
Answer:
133%
Step-by-step explanation:
24/18=4/3=1.33...=133%
Answer:
75%
Step-by-step explanation:
because it = 18/24 or 75%
jackie can spell 83% of her words correctly. if she attempted 23 words, about how many did she make
Solve for x. 11x+4< 15 OR 12x–7>-25
please help!! brainliest!!
Identify the sets of lines to which the given line is a transversal.
line a
Answer:
I think the answer is C
Step-by-step explanation:
from looking at the graph and how the lins intercept
Answer:
C is the correct answer.
Step-by-step explanation:
On average shawnte drinks 1/2 of a 6-ounce glass of water in 2/3 hour how much watee does she drink in a hour
she drinks 9/2 ounces of water in 1 hour
Step-by-step explanation:
On average, the person drinks 1/2 of a 6-ounce glass of water in 2/3 hour.
First of all, we have to rewrite the amount of water in a single fraction: we have
[tex]\frac{1}{2}\cdot 6 = \frac{6}{2}=3[/tex]
This means that the person drinks 3 ounces of water every 2/3 hours.
In order to find how much water she drinks in one hour, we use the following proportion:
[tex]\frac{3}{2/3}=\frac{x}{1}[/tex]
where
x is the amount of water she drinks in one hour.
Solving the equation for x,
[tex]x=\frac{3\cdot 1}{2/3}=\frac{3\cdot 1 \cdot 3}{2}=\frac{9}{2}[/tex]
Therefore, she drinks 9/2 ounces of water in 1 hour.
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How do you write the difference of a number and eight, divided by ten
Answer:
(x-8)/10
Step-by-step explanation:
-------
(X - 8)/10 or (8 -X)/10
The unknown number can be given as X
The difference between the number and 8 can be given as 8 -X or X - 8
The dividing it by 10 will give (x-8)/10 or (8-x)/10 depending on the value of the unknown number X
Three bags of sweets weigh 6 3/4 kg. Two of them have the same weight and the third bag is heavier than each of the bags of equal weight by 1 1/5 kg. Find the weight of each bag.
Final answer:
The weight of each bag of equal weight is 1 17/20 kg and the weight of the third bag is 1 41/20 kg.
Explanation:
Let's assume the weight of each bag of equal weight is x kg. According to the question, the third bag is heavier than each of the equal bags by 1 1/5 kg, which can be written as 6/5 kg.
So, the weight of the third bag is x + 6/5 kg.
Now, we can set up an equation based on the given information:
2x + (x + 6/5) = 6 3/4
Simplifying the equation, we get:
3x + 6/5 = 27/4
Now, we can solve for x by multiplying both sides of the equation by 5 to get rid of the fraction:
15x + 6 = 135/4
15x = 135/4 - 6
15x = 135/4 - 24/4
15x = 111/4
Now, divide both sides of the equation by 15 to solve for x:
x = (111/4) / 15 = 111/60 = 37/20 = 1 17/20
Hence, the weight of each bag of equal weight is 1 17/20 kg and the weight of the third bag is 1 17/20 + 6/5 = 1 17/20 + 24/20 = 1 41/20 kg.
A cat weighs 3.5 ounces when born. The cat grows 0.5 ounces each week. After
how many weeks does the cat way 16.5 ounces?
Answer:
10 weeks
Step-by-step explanation:
Answer: 26 weeks
Step-by-step explanation:
This is an example of an arithmetic sequence.
The first term = 3.5
common difference = 0.5
Using the formula for calculating the nth term of an arithmetic sequence :
[tex]t_{n}[/tex] = a + (n - 1 ) d
Therefore :
16.5 = 3.5 + ( n - 1 ) x 0.5
16. 5 = 3.5 + 0.5n - 0.5
16.5 = 3 + 0.5n
16.5 - 3 = 0.5n
13.5 = 0.5n
n = 13.5/0.5
n = 27
Therefore , it will take the cat (n-1) weeks to weigh 16.5 ounce, which will be 27 - 1 = 26
check:
3.5 + 26 ( 0.5)
= 3.5 + 13
= 16.5
Anna wants to buy a house at $67,000. She will need at down payment of 15%. What is the down payment amount
Answer:
67000*.15=10,050
Step-by-step explanation:
The required down payment would be the amount of $10,050.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Anna wants to buy a house for $67,000.
She will need a down payment of 15%.
We have to determine the evaluation of 15% of $67,000.
⇒ 15% of 67,000
15% is expressed as 15/100 in fractional form
⇒ (15/100)(67,000)
15/100 is expressed as 0.15 in decimal form
⇒ (0.15)(67,000)
Apply the multiplication operation, and we get
⇒ 10,050
Therefore, the down payment would be $10,050.
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Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1/12 miles long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?
Answer:
6 seconds
Step-by-step explanation:
1/12 mile * 5280 feet/mile = 440 feet per train
50 miles/hour * 1/3600 hr/sec * 5280 ft/mile = 73 1/3 ft/second
one train has to travel 440 feet to pass the other train
440 feet * 1/(73 1/3) sec/ft = 6 seconds
The time it will take for the two trains to pass each other's rear car is 6 seconds.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Two passenger trains travelling in opposite directions meet and pass each other. Each train is 1/12 miles long and is traveling 50 mph.
Therefore, the total distance that the two train needs to cover is twice the size of a train.
Distance = 2 × 1/12miles = 1/6 miles
Also, the relative speed of the two trains moving in opposite directions is,
Speed = 50 mph + 50 mph = 100 mph
Now, the time that the two trains need to cover the entire distance is,
Time = (1/6 miles)/ 100mph = 1/600 hours
Converting the time to seconds,
Time = 1/600 hours × 3600 = 6 seconds
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The world record for the 100 meter sprint is 9.77 seconds. How long would it take to run 1 meter at the speed
Answer:
Step-by-step explanation:
Time taken = 9.77/100 = 0.0977 seconds
Can someone please help me with this? Thank you!
Answer:
[tex]\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]
Step-by-step explanation:
In the first equality
[tex]5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],[/tex]
the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so
[tex]5=\dfrac{2}{5}m\Rightarrow m=5\times \dfrac{5}{2}=\dfrac{25}{2}[/tex]
For the second equality
[tex](H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),[/tex]
if [tex]H=[-2\ 3\ -1][/tex], then this equality represents the assotiative property of matrix addition.
Hence,
[tex]m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]
the consecutive odd integers have a sum of 36. find the integers
how many consecutive odd integers are there, or else I can't help you
==================================================
Work Shown:
x = some integer
2x = even integer
2x+1 = odd integer
(2x+1)+2 = 2x+3 = odd integer just after 2x+1
The integers 2x+1 and 2x+3 add to 36
(2x+1)+(2x+3) = 36
2x+2x+1+3 = 36
4x+4 = 36
4x+4-4 = 36-4 ... subtract 4 from both sides
4x = 32
4x/4 = 32/4 .... divide both sides by 4
x = 8
With x = 8, we can say
2x+1 = 2*8+1 = 17 is the first odd integer
2x+3 = 2*8+3 = 19 is the next odd integer
17+19 = 36, so the answer is confirmed
--------------------
A non-algebraic way to get the answer is to divide 36 in half to get 18
Then try odd integers around 18, so 19+21 = 40 but thats too high
then maybe try 15+17 = 32, thats too low
17+19 = 36 is right on the money
The following table shows the consumer price index(CPI) for a fictional country from 1992-2000.during which of these time periods was there a period deflation?
A.1992-1994
B.1994-1996
C.1996-1998
D.1998-2000
D.1998-2000
Step-by-step explanation:
Deflation describes the drop of prices for goods and services leading to slowing down of economic growth.During economic uncertainty, prices of goods and services can get very low causing the inflation rate to go lower than zero.CPI index shows inflation when it rises over a short period of time.CPI declines to mean deflation where there is a steady decrease in prices of goods and services.
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Keywords : table, CPI, country, period, deflation
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Math question please help :)
Question 3
Answer: Choice A) {(3,4) (3,5)}-----------
Explanation:
Note how in choice A we have repeated x values
x = 3 pairs up with y = 4 and y = 5 at the same time.
The input x = 3 must only pair up with one output only if we want a function to happen.
If you plotted the points (3,4) and (3,5), it is possible to draw a vertical line through them. So this fails the vertical line test.
The other answer choices do not have repeated x values, so they are all functions.
==========================================
Question 4
Answer: choice A) 2x+3y = 10 and choice D) y = 18-----------
If you plotted choice A and choice D on an xy coordinate system, you should see straight lines forming.
2x+3y = 10 turns into y = (-2/3)x+10/3 which is y = mx+b form.
Choice D's equation is equivalent to y = 0x+18, so its slope here is 0, making it a flat horizontal line.
Choice B does not count as an answer because while it is a linear vertical line, it is not a function for similar reasons back in question 3. The fact that x = 16 pairs up with infinitely many y values is what makes this not be a function.
Choice C is not a linear equation. Instead it is a quadratic equation because the largest exponent is 2.