Substituting x-4=y and -5y+8x=29
Answers
-5x+20+8x=29
3x+20=29
3x=9
X=3
Related Questions
In the figure, the horizontal lines are parallel and AB = BC = CD. If LM = 3 Find JM? A. 12 B. 6 C. 3 D. 9
Answers
The value of JM is 9, the correct option is D.
What are Parallel Lines?
The lines that always have a constant distance between them and never intersect each other are called Parallel Lines.
The slope of parallel lines is equal to each other.
The parallel lines, AM, BL, CK, DJ can be seen in the figure.
As the distance between AB = BC = CD is equal,
The parallel line runs at same distance from each other and so, the distance between LM= LK = KJ,
The value of LM is 3.
Then the value of JM = LM + KL + KJ
JM = 3 + 3 + 3
JM = 9 units.
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Eric plans to rent a Beach House for a week. He has a coupon for 20% off the daily base rate of $200. He will also have to pay an additional $20 a day for utilities. Which expression represents the situation. (d represents the number of days)
Answers
Answer: 180 d is the required expression.
Step-by-step explanation:
Since, He has a coupon for 20% off the daily base rate of $200.
Therefore, His daily base cost = 80 % of 200 = [tex]\frac{20\times 80}{100}[/tex] = $ 160
Additional cost he pay in a day = $20
Therefore, his total cost of one day = 160 + 20 = 180
Thus, his total cost in d days = 180 d
Which is the required expression.
Answer:
180d C)
Step-by-step explanation:
40 is 20 percent of 200, if you remove 40 from 200 you get 160. then add 20 and you have 180.
The graph represents the piecewise function
Answers
the slope seems to be 2 and y intercep tis -1 so 2x-1
right equation is x is greater than or equal to 1
slope is 1 and y intercept is 4 so x+4
top left blank is x+4, top right blank is x is greater than or equal to 1
bottom left blank is 2x-1, bottom right blank is x is less than or equal to -1
Hence, we have:
f(x)= 2x-1 when x ≤ -1
x+4 when x ≥ 1
Step-by-step explanation:After looking at the graph we observe that in the region: x ≤ -1The graph is a straight line that passes through (-1,-3) and (-2,-5)
Hence, the equation of line is:
[tex]f(x)-(-3)=\dfrac{-5-(-3)}{-2-(-1)}\times (x-(-1))\\\\\\f(x)+3=\dfrac{-5+3}{-2+1}\times (x+1)\\\\\\f(x)+3=2(x+1)\\\\\\f(x)=2x+2-3\\\\\\f(x)=2x-1[/tex]
Also, in the interval x ≥ 1The graph is a straight line that passes through (1,5) and (2,6)
Hence, the equation of line is:
[tex]f(x)-5=\dfrac{6-5}{2-1}\times (x-1)\\\\\\f(x)-5=x-1\\\\\\f(x)=x-1+5\\\\\\f(x)=x+4[/tex]
Find the cost of twelve $1,000 bonds at a quotation of 84.50.
Answers
*12 bonds
*1 bond = $1,000
*Quotation of 84.50% per bond ($845 each).
What to find:
*QT - Quotation Total. QT = (12 x $1,000) x Quotation
*TC - Total Cost. TC = (12 x $1,000) + QT
Solution:
Finding QT:
QT = (12 x $1,000) x Quotation
QT = (12 x $1,000) x 84.50%
QT = $12,000 x 84.50%
QT = $10,140
Finding TC:
TC = (12 x $1,000) + QT
TC = (12 x $1,000) + $10,140
TC = $12,000 + $10,140
TC = $22,140 <--- What we are looking for.
Therefore, the total cost of twelve $1,000 bonds at a quotation of 84.50% is: $22,140.
What is the slope of this line y + 3 = -4(x - 5)?
Answers
y=-4x+17
Final answer: Slope=-4
Just a side note: This is written in point slope form or y-y1= m(x-x1). You could just look at the m value to find slope.
WILL MAKE BRAINLIEST!!! A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims, that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.
Answers
We can use the cosine rule when we know the length of two sides and the angle opposite the side that is unknown. For example, referring to the second diagram, we know the length of side a and side b and we are looking for the length of side c. We also know the angle that is located on the opposite of side c, then to solve this we can use the cosine rule
c² = a² + b² - 2ab(cos(C°))
The third diagram shows a scenario when sine rule can be used. Say we need the length of the side c. We know the length of side a, the size of angle A° and angle C° then we can use the sine rule
[tex] \frac{c}{sin(C)} = \frac{a}{sin(A)} [/tex]
We can also use sine rule if we know length of side b and the size of angle B° instead of side a and angle A°
A city’s population, P (in thousands), can be modeled by the equation P = 130( 1.03)^x where x is the number of years after January 1, 2000. For what value of x does the model predict that the population of the city will be approximately 170,000?
Answers
To find the value of x for which the model predicts a population of approximately 170,000, solve the equation P = 130(1.03)^x. Divide both sides by 130, take the logarithm of both sides, and solve for x. The approximate value of x is 9.855.
Explanation:To find the value of x for which the model predicts a population of approximately 170,000, we need to solve the equation:
170 = 130(1.03)x
To solve for x, we can start by dividing both sides of the equation by 130:
170/130 = (1.03)x
1.3077 = (1.03)x
Next, take the logarithm of both sides of the equation:
log(1.3077) = x * log(1.03)
Using a calculator, we can find that x is approximately 9.855.
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Firstly, we need to clarify that the population given in the question, 170,000, is represented in 'thousands' in the modelling equation. Therefore, for simplicity, it is referred to as '170' in the equation.
We know from the problem that the population model is:
P = 130 * (1.03 ^ x),
where P is the population (in thousands) and x is the number of years since the start point (January 1, 2000). Given that we're looking for the point in time where the population is approximately 170,000 (or '170' in the terms of the equation), we can set P = 170 and solve for x:
170 = 130 * (1.03 ^ x)
Solving an equation in terms of x with an exponent can be handled neatly with logarithms. You can isolate the variable by taking the natural log (ln) of both sides. So we can transform our equation like this:
ln(170 / 130) = ln(1.03 ^ x)
Next, we use the property of logarithms that says the log of a number raised to an exponent is equal to the exponent times the log of the number:
ln(170 / 130) = x * ln(1.03)
Solving for x gives:
x = ln(170 / 130) / ln(1.03)
Calculating the value gives x ≈ 9.075604092564975. However, since the population is generally reported on an annual basis, we round the value of x up to the nearest whole number. That gives us:
x_rounded ≈ 10 years.
So, according to the model, the city's population will reach approximately 170,000 around 10 years after January 1, 2000.
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David wants to buy a game system and his favorite game.The game costs $25 and is 1/5 of the price of the game system.How much does the game system cost?
Answers
multiply 25 by 5 = 125
the game system cost 125
As per linear equation, the game system costs $125.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given, the cost of the game is $25.
The cost of of the game is [tex]\frac{1}{5}[/tex] of the price of the game system.
Therefore, the cost of the game system is
= 5 × cost of the game
= $(5 × 25)
= $125
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what is the smallest positive integer that is divisible by each of the integers from 3 to 7, inclusive
Answers
{3, 4, 5, 6, 7}
these numbers can be written as multiplication of prime factors as :
{3, 2*2, 5, 2*3, 7}
The smallest common multiple of these numbers must have factors which divide all the factors of these 5 numbers.
So the multiple must have these factors: 3, 2*2 (one two is not enough to divide 4), 5 and 7. We do not need to write 2 and three again, because we already have them.
so the smallest common multiple is 3*2*2*5*7=420
Answer: 420
Janet wins the lottery and receives $100 the first year. In the following years, she receives $50 more each year. (That is, Janet receives $150 the second year, $200 the third year, and so on.) How much will Janet receive, in total, after 10 years?
A) $2,500
B) $3,250
C) $1,450
D) $1,500
Answers
What is the simplified form of √ 2160x^8/60x^2
Answers
------------ =
60 x^2
The correct answer I found is 6x³
Helppppp! Which answer choice correctly describes the relationship between two of the lines in the figure?
Answers
_____________________________________________________________
Take note of the "right angle" — which indicates that "a" is perpendicular to "c" .
_____________________________________________________________
Which of the numbers listed below are solutions to the equation? Check all that apply. x2 = -36 A. 6 B. 1296 C. 18.0 D. 72 E. -6 F. None of these
Answers
So, to find the x square root both terms. But you can't. Why? Because we have a negative number, and you can't do the sqrt of a negative number. So, none of the above is the answer. Non-solvable
Malik solved this system of equations.
2x+4y=24
5x+y=15
As the first step, he decided to solve for x in the first equation because it has a small, even number for the coefficient. Jill told him there was a more efficient way. What reason can Jill give for her statement?
A.The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.
B. The variable x in the second equation has a coefficient of 5 so it will be easy to divide 15 by 5.
C. The variable y in the first equation is divisible by 2 so it will be the most efficient way to start.
D. The variable y in the first equation has a larger even number. When dividing by 4, the solution will be a smaller number.
Answers
The variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.
System of equationsGiven the simultaneous equation
2x+4y=245x+y=15The best way to solve this kind of equation is by the substitution method. To do that in an easy way, you can locate which of the variables in the equations has a coefficient of 1.
From equation 2, we can see that the variable "y' has a coefficient of 1, hence the reason that Jill can give for her statement is that the variable y in the second equation has a coefficient of one so there will be fewer steps to the solution.
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Factor x2a2 + 3xa2 + 2a2
Answers
You factor out the common term, which is a^2.
You would then get a^2(x^2+3x+2) as the answer.
Factor out (x^2+3x+2)
a^2(x+1)(x+2)
Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a downward sloped line crossing the y axis at two that ends at the open point 2, 1.3, a closed point at 2, -1, and an upward sloped line starting at the open point 2, 4. Find = limit as x approaches two from the right of f of x..
Answers
-------------------------------
Start on the right side of the value x = 2. In other words, start at some value larger than 2, say x = 4. Starting at x = 4, move closer to x = 2. Move as close as you can. The closer x gets to 2, the closer y gets to 4. You'll never actually get to x = 2 or y = 4 because of the hole. However, the right-hand limiting value is 4 assuming you can keep getting closer and closer.
Note: if you approach x = 2 from the left side, you arrive at a different y value So this suggests that overall, the limit at x = 2 doesn't exist. But the right hand limit (RHL) does exist as described above.
Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make?
Answers
so 100 cookies and 20 brownies
what is the greatest number you can divide them both by?
find the GCF
factor them
100=2*2*5*5
20=2*2*5
so the GCF is the common group to both or 2*2*5 or 20
100/20=5
20/20=1
there are 20 groups, each wit 5 cookies and 1 brownie
20 groups
what is the surface area of a square pyramid with a base of 12cm and a slanted height of 8cm?
Answers
12*12= 144 cm^2
Triangle sides:
12*8/2= 48 cm^2 each
Multiply by 4 because there are four of them
48*4= 192 cm^2
Add the base
192+144=336 cm^2
Final answer: 336 cm^2
An angle whose vertex is at the center of a circle is a middle angle of that circle.
A. True
B. False
Answers
Because n angle whose vertex is at the center of a circle is a CENTRAL angle of that circle
An angle whose vertex is at the center of a circle is a middle angle of that circle.
This is false because there can be numerous angles in the center of a circle. Moreover, the angle whose vertex is at the center is called a central angle. The two endpoints of this angle and located at the circumference or outline of the circle and the vertex is located at the center of that circle.
There are 325 students in ping pong club. There are 5 girls for every 7 boys in the club. Which is the correct proportion that can be used to determine the number of girls in the club?
Answers
Answer: D
Hope this helps :)
Please give brainliest
To find the number of girls in the club, you can set up a proportion using the given information. Cross-multiply the proportion and solve for the number of girls. The approximate number of girls in the club is 232.
Explanation:To determine the number of girls in the club, we can set up a proportion using the given information. Since there are 5 girls for every 7 boys in the club, the proportion can be written as:
Girls/Boys = 5/7
To find the number of girls, we can solve the proportion by cross-multiplying:
Girls = (5/7) * Total Number of Students
Substituting the given total number of students as 325, we can calculate the number of girls in the club as:
Girls = (5/7) * 325
Girls = 232.14
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staircase of steps in a swimming pool has a vertical rise of 14 inches per step and a landing of 20 inches.
Answers
Therefore, the slope of the stair case is
Slope = rise/run = 14/20 = 0.7
Which of the following graphs best represents the solution to the pair of equations below? y = −x + 6 y = 2x − 3 A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and through the x axis at 6. The other line passes through the y axis at negative 3 and the x axis at 1.5. The lines intersect at the point 3 comma 3. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and the x axis at 6. The other line passes through the y axis at 3 and the x axis at negative 1.5. The lines intersect at 1 comma 5. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and the x axis at negative 6. The other line passes through the y axis at negative 3 and the x axis at negative 1.5. The lines intersect at negative 3 and 3. A coordinate plane is shown with two lines graphed. One line passes through the y axis at 6 and the x axis at negative 6. The other line passes through the y axis at 3 and the x axis at 1.5. The lines intersect at negative 1 comma 5.
Answers
i) y=-x+6
ii) y=2x-3
The solution of the system of equations is found by equalizing the 2 equations:
-x+6=2x-3
-2x-x=-6-3
-3x=-9
x=-9/(-3)=3
substitute x=3 in either i) or ii):
i) y=-3+6=3
ii) y=2(3)-3=6-3=3
(the result is the same, so checking one is enough)
This means that the point (3, 3) is a point which is in both lines, so a solution to the system.
In graphs, this means that the lines intersect at (3, 3) ONLY
Answer: The graph where the lines intersect at (3, 3)
The point of intersection of the lines y = −x + 6 and y = 2x − 3 is (3, 3)
Linear function
A linear function is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Given the equations:
y = −x + 6 (1)
y = 2x − 3 (2)
Solving the equations 1 and 2 simultaneously gives:
x = 3, y = 3
The point of intersection of the lines y = −x + 6 and y = 2x − 3 is (3, 3)
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What's an equation for "Six more then twice a number is 72?"
Answers
the equation would be:
2x+6 = 72
what is the most efficient first step in the process to factor the trinomial 3x^3-24x^2+36x
Answers
the answer is factor out 3x on apex.
Answer:
Factor out 3x
Step-by-step explanation:
A P E X answer
By how much does a^3 - 2a exceed a^2 + a - 6?
Answers
Answer
a³ - a² - 3a + 6
Explanation
The equation requires you to subtract the two expressions.
(a³ - 2a) - (a² + a - 6)
In such an expression we subtract the like term only.
(a³ - 2a) - (a² + a - 6) = a³ - 2a - a² - a + 6
= a³ - a² -2a - a + 6
= a³ - a² - 3a + 6
The length of a rectangle is twice its width. if the perimeter of the rectangle is 36 cm , find its area.
Answers
W = Width
L x W = area
Length = 2w
Lets find the width by solving for w.
2w + w = 36
3w = 36
3w/3 = 36 / 3
w = 12
So
L = 2 x 12 = 24
W = 12
L X W = area
24 x 12 = 288 cm^2
Find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5
A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)
Answers
every term increases by d amount
so [tex]a_n+d=a_{n+1}[/tex]
therefor
[tex]a_{15}+d=a_{15+1}=a_{16}[/tex]
-53+d=-5
add 53 both sides
d=48
alright
an=a1+d(n-1)
an=a1+48(n-1)
use a15=-53
a15=-53=a1+48(15-1)
-53=a1+48(14)
-53=a1+672
minus 672 both sides
-725=a1
the equation is
an=-725+48(n-1)
answer is C
posting a screenshot my loves
Answers
For (x-7)^2, we have -7 because it's -14/7. Next, 7^2=49, so we have to add 49 to the right, getting (x-7)^2+43=49. Subtract 43 from both sides to get
(x-7)^2=6, and square root both sides to get x-7=sqrt(6) and add 7 to both sides to get x=sqrt(6)+7, which is approximately 9.45. I challenge you to do the next one on your own, using the techniques stated here :)
Help? Sampling
A toy bin has twenty toys in it, five of each type. Storm wants to know which type of toy he would pick if he pulled out one.
Which of the following would be the most appropriate sampling technique?
A. He could use a spinner with four equal-sized sections, one for each toy.
B. He could make a chart to show all of the toys that other people pulled out. <<?
C. He could use a spinner with five equal-sized sections, one for each toy.
D. He could use a random number generator with the total number of toys as the top number.
Answers
Answer:
Option (C) is correct choice.
Explanation:
The most appropriate sampling technique for Storm to determine which type of toy he would pick from the bin is option C. He could use a spinner with five equal-sized sections, one for each type of toy.
Option A (using a spinner with four equal-sized sections) does not accurately represent the distribution of toys in the bin, as there are five types of toys.
Option B (making a chart of toys that other people pulled out) relies on the data from others and does not involve Storm directly selecting a toy.
Option D (using a random number generator) is not as straightforward and intuitive as directly selecting a toy from the bin.
Therefore, option C provides Storm with a fair and simple method to randomly select one type of toy from the bin.
What is the graph of x = -5?
Answers
the graph is the line parralle of axis- y passing by the point : (-5 , 0 )