Standard Form is ...
ax + by = c
where a ≥ 0, b > 0 (if a=0), and {a, b, c} are mutually prime integers (unless irrational numbers are involved).
You can get there from where you're starting in a couple of steps. Multiply by the least common denominator of any fractions. (Here, you multiply by 4.) Then put the variable terms on the opposite side from the constant term. Make sure the leading coefficient is positive.
... 4y -4 = x -12
... x -4y = 8 . . . . add 12-4y
whats the product of 3x(-6)?
1) Switch the negative sign with the three= -(3x6)
2) Multiply= -18
3) Your answer is -18
Hope I could help! :)
4+2p_< 3p -1 can somebody answer this for me
Answer: p ≥ 5
Step-by-step explanation:
Subtract 4 from both sides :
4+ 2p - 4 ≤ 3p-1 - 4
Simplify :
2p ≤ 3p -5
Subtract 3 p from both sides
2p - 3p ≤ 3p - 5 - 3p
Simplify:
- p ≤ - 5
Multiply both sides by -1 (reverse the inequality right) :
( - p ) * ( - 1 ) ≥ ( -5 ) * ( - 1 )
Simplify :
p ≥ 5
Hope that helps!
You earn the same amount each week at your part-time job. The total amount you earn in 4 weeks is $460. How much do you earn per week?
according to the 2010 United States census the population of a town was 89154 roughly a 12% increase from 79601 in 2000 constructing Expo Neo model to predict the town's population Each decade use your model to predict the population of the town in 2040
Final answer:
To predict the population of the town in 2040 using an exponential growth model, we can use the formula P(t) = P₀ * (1 + r)^(t - t₀), where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t₀ is the initial time. Given the population in 2010 and 2000, we can calculate the growth rate and substitute the values into the formula to predict the population in 2040.
Explanation:
To construct an exponential growth model to predict the population of the town in 2040, we can use the formula P(t) = P₀ * (1 + r)^(t - t₀), where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t₀ is the initial time.
Given that the population in 2010 was 89154 and in 2000 was 79601, we can calculate the growth rate as follows:
Growth rate = (Population in 2010 - Population in 2000) / Population in 2000 * 100%
Growth rate = (89154 - 79601) / 79601 * 100%
Growth rate ≈ 11.98%
Now we can substitute the values into the exponential growth model and predict the population in 2040, which is 30 years after 2010:
P(2040) = 89154 * (1 + 0.1198)^(2040 - 2010)
P(2040) ≈ 89154 * 1.1198^30 ≈ 89154 * 4.676
P(2040) ≈ 417204.504
How can I find the area of this?
Find the area of each triangle and then add them together.
Bottom Triangle
A = [tex]\frac{1}{2}[/tex]b * h
= [tex]\frac{1}{2}[/tex](160)(120)
= 80(120)
= 9600 m²
Top Triangle
First we need to find the side length. We can calculate the length of the hypotenuse using Pythagorean Theorem for the bottom triangle.
a² + b² = c²
120² + 160² = c²
14400 + 25600 = c²
40000 = c²
200 = c
Now we can use Pythagorean Theorem on the top triangle to find the missing side length.
a² + b² = c²
100² + b² = 200²
10000 + b² = 40000
b² = 30000
b ≈ 173
A = [tex]\frac{1}{2}[/tex]b * h
= [tex]\frac{1}{2}[/tex](100)(173)
= 50(173)
= 8650 m²
Top Triangle + Bottom Triangle = Total Area
8650 + 9600
18250
Answer: Area = 18,250 m²
Which of the following is a mathematical statement showing that one ratio is equal to another ratio?
Answer:
Proportion
Step-by-step explanation:
took test
The sum of three consecutive integers is 171. What is the largest integer ?
According to the Triangle Inequality, the length of the longest side of a triangle must be less than the sum of the length of the other two sides. The two shortest sides of a triangle measure 3/10 and x + 1/5, and the longest side measures 3/2x
x has to equal 1. 3/10 + 1/5 = 1/2
the equation is now 1/2 + x = 1 1/2x
x = 1
1 1/2 = 1 1/2
Final answer:
The Triangle Inequality Theorem is applied to determine the range of values for x that would make the side lengths given form a valid triangle.
Explanation:
Understanding the Triangle Inequality Theorem
The Triangle Inequality Theorem states that in any triangle, the length of any side must be less than the sum of the other two sides. For the given question, we need to use this principle to analyze the side lengths. With the two shorter sides given as [tex]\( \frac{3}{10} \) and \( x + \frac{1}{5} \)[/tex], and the longest side given as [tex]\( \frac{3}{2}x \)[/tex], we can establish the inequality:
[tex]\( \frac{3}{2}x < \frac{3}{10} + \left( x + \frac{1}{5} \right) \).[/tex]
By solving this inequality, we can find the range of possible values for x that makes the configuration a valid triangle. This problem is an application of basic geometric principles and inequalities.
The sum of twelve times p and d
[tex]Sum =[/tex] [tex]add (+)[/tex]
[tex]Twelve =[/tex] [tex]12[/tex]
[tex]p[/tex] & [tex]d = [/tex] [tex]p[/tex] & [tex]d[/tex] (since they are unknown numbers)
SO, this means that your answer SHOULD look like this: [tex]12p[/tex] [tex]+ d[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
A) 30
B) 2.5
C)1.5
D)2
Larry is 10 and his sister is 7 years old. In how many years time will their total age be 25 years?
What is the value of t=1
Answer:
???
Step-by-step explanation:
Do you not have the full equation posted because t=1 is t=1
Given A= {(2,3),(5,1),(-3,-2),(0,3)} A is a subset of
A. N X R
B. R X N
C. N x N
D. R X R
[tex]A=\{(2,\ 3),\ (5,\ 1),\ (-3,\ -2),\ (0,\ 3)\}\\\\X=\{2,\ 5,\ -3,\ 0\}\\\\Y=\{3,\ 1,\ -2}\\\\-3\ and\ -2\ are\ not\ a\ natural\ numberss.\\\\Therefore\ your\ answer\ is\ D.\ \mathbb{R}\ \times\ \mathbb{R}[/tex]
The set A= {(2,3),(5,1),(-3,-2),(0,3)} is a subset of 'R x R', the cartesian product of Real numbers and Real numbers because both elements of all pairs in the set A are real numbers.
The given set A contains ordered pairs where each pair is constituted of two elements. An ordered pair is always in the form of (a, b) where 'a' is from the first set and 'b' is from the second set in a Cartesian product.
In the given subsets:
A. N X R(Cartesian product of Natural numbers and Real numbers)
B. R X N(Cartesian product of Real numbers and Natural numbers)
C. N X N(Cartesian product of Natural numbers and Natural numbers)
D. R X R(Cartesian product of Real numbers and Real numbers)
Looking at the subset A= {(2,3),(5,1),(-3,-2),(0,3)}, we can observe the first element of each pair in the set, we have 2, 5, -3, and 0. Negative numbers and zero are not natural numbers. Therefore it can't be a subset of 'N x R' or 'N x N'. But they are real numbers. Hence, it could be either 'R x N' or 'R x R'. However, if we look at the second element of each pair, we see that they are 3, 1, -2, and 3. Among these, -2 is a negative number and is not a natural number, but is a real number. Therefore, the set A must be a subset of 'R x R', which is the cartesian product of Real numbers and Real numbers.
Learn more about Cartesian Product here:
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Which number is bigger 1/8,,,,,,,,0.065,,,3/100,,,,0.105
1/8 = 0.125
0.065
3/100 = 0.03
0.105
the bigger is 1/8
what letter represents the initial value in y=a(b)^x
The letter "a" represents initial value. "b" is the rate, and "x" is time. Hope I could help!
6x4=8xN
How can I solve this
6×4=24 right so than how many 8 can get you to 24, so you do 8,16,24 or 8×3 So it's 8×3=24 (Your welcome ^.^)
6x4=8xN is the same as 24=8N
Divide both sides by 8 and there's your answer
Please help ‼️‼️‼️
Write an equation of the line containing the given point and perpendicular to the given line
what is the product of -2 1/4 and -4 1/2 as a mixed number and in simplest form
Bryce rides his bike 4 blocks west to school after school he rides six blocks East to the grocery store how many blocks past his house is Bryce when he arrives at the grocery store
He rode 6 blocks to the East than he rode 4 blocks to the West, so that means after he rode 6 blocks to the east he went backwards 4 blocks.
The equation is, 6-4=2 Because he only past 2 blocks from his home to arrive at the grocery store.
Bryce is 2 blocks past his house when he arrives at the grocery store.
Explanation:To find out how many blocks past his house Bryce is when he arrives at the grocery store, we need to calculate the total distance he has traveled from his house to the grocery store. He rides 4 blocks west to school and then 6 blocks east to the grocery store. To find the total distance, we can subtract the distance traveled west from the distance traveled east: 6 blocks - 4 blocks = 2 blocks past his house.
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How many ounces of a 40% alcohol solution must be mixed with 16 ounces of a 45% alcohol solution to make a 44% alcohol solution
If f(x)=5x+4, which of the following is the inverse of f(x)?
[tex]Solution,\mathrm{Inverse\:of}\:5x+4:\quad \frac{x-4}{5}[/tex]
[tex]Steps:[/tex]
[tex]y=5x+4[/tex]
[tex]\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y, x=5y+4[/tex]
[tex](\mathrm{Solve}\:x=5y+4\:\mathrm{for}\:y),(x=5y+4)[/tex]
[tex]\mathrm{Switch\:sides}, 5y+4=x[/tex]
[tex]\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}, 5y+4-4=x-4[/tex]
[tex]\mathrm{Simplify}, 5y=x-4[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5, \frac{5y}{5}=\frac{x}{5}-\frac{4}{5}[/tex]
[tex]\mathrm{Simplify}, y=\frac{x-4}{5}[/tex]
[tex]\mathrm{The\:Correct\:Answer\:is\:\frac{x-4}{5}}[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]\mathrm{-Austint1414}[/tex]
To find the inverse of f(x) = 5x + 4, swap x and y to get x = 5y + 4, solve for y to get y = (x - 4)/5, which is the inverse.
With the given function f(x) = 5x + 4, we first replace f(x) with y to get y = 5x + 4. We then swap x and y to get x = 5y + 4. To solve for y, we subtract 4 from both sides, giving us x - 4 = 5y. Then, we divide both sides by 5, yielding (x - 4)/5 = y. Therefore, y = (x - 4)/5, which is the inverse of the function f(x).
A triangle has the perimeter of 31". The longest side is 1" less than twice the shortest side and the 3rd side is 4" longer than the shortest site. Find the lengths of the sides
Please help !! :) I am offering 20 points !!
(2,3) is the ordered pair because both lines meet at this direct point on the graph.
x=2
y=3
Is Ralph's ran 15 miles in 5 days how far will he be expected to run in 8 days
24 miles because, s Ralph runs 15 miles in 5 days, so 5 times 3 =15 so 3 times 8 = 24 miles
I need help with this equation
A(x+b)-c=d
Which statement about the equation is true?
3+x=2–3x
The equation has no solution.
The equation has one solution.
The equation has infinitely many solutions.
If I did it correctly the there would be one solution for the equation.
3+x=2-3x
3=2-4x
1=-4x
x=-1/4
Answer:
Step-by-step explanationn:
two-thirds a number less than four is negative seven.
4 - 2/3x = -7 would be the equation to represent this.
how much does the medium smoothie cost?
2 jumbo + 1 medium = 4 med + 0.15
Multiply 2 jumbo smoothies by 2 which is >> 9.90+m =4 m+0.15
9.75=3m
Divide and it'll be 3.25
3.25=m
I Actually spent a hour trying to write an answer as it also challenged me, then i saw how simple it is i wish i could take back my time
Anyways, to find out the amout a medium smoothie cost we need to find the equation for it. With the given information we can find out that the cost of 4 medium smoothies is the same as 2 jumbos and one smoothie.So first lets find out the cost of 2 smoothies, 4.95 * 2 = 9.9.Now lets plot them into an equation.
4x+0.15=9.9+x
Simplyfy the equation by removing the x from the right side
4x-x=3x x-x=0
so now our new equation is
3x+0.15=9.9
Next lets remove the 0.15
0.15-0.15 = 0 9.9-0.15=9.75
so our new equation is now
3x=9.75
Then, we simplify the x by dividing the amount of x's it has
3x/3=x 9.75/3=3.25
So, after doing all that math, we found out that x=3.25
So each smoothie costs $3.25
so, the equation would be 4x+0.15=9.9+x
We can test it out by plotting in the situation
(3.25*4)+0.15=13.15 9.9+3.25=13.15
Don't forget to add the extra amount.
I am so glad i was able to find this out, and hope this helps you, as i had trouble with it myself, and thats coming from someone who's taking honors!
about 47% of the 15152 samples researchers found were bacteria. what number of dna samples were not bacteria
To find what number of DNA samples were not bacteria we have to find what was 47% of the 15,152 samples first.
We can do this by multiplying 0.47 x 15,152 = 7,121.44
Now 7,121.44 is 47% of the samples that DOES have bacteria. To find out how many do not we must subtract.
15,152 - 7,121.44 = 8,030.56
So the number of DNA samples that were not bacteria were 8,030.56.
GOOD LUCK! :)
Determine the slope of the line that passes through the points (-5, -4) and (0, 10).
so the equation for slope is y2-y1/x2-x2
so this would be -4-10/-5-0 which equals -14/-5 which is the same thing as 14/5
so the answer is 14/5 or if its mixed then 2 4/5
Hope this helps!
m=y2-y1/x2-x1
m=1-1/10-(-5)
m=1-1/10 + 5
m=0/15
Slope: m=0