if the lines a and b in the diagram below are parallel why do angles 1 nd 8 measure 120 degree angles
A) Because they are alternate interior angles.
B) Because they are corresponding angles.
C) Because they are alternate exterior angles.
D) Because they are same-side interior angles.
Answers
C) Because they are alternate exterior angles.
Related Questions
. The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.77 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
A . c=g/1.77
B. c=1.77g
C. g=1.77c
D. c=g+1.77
Answers
The cost equals $1.77 times the number of gallons purchased.
Which expression is equivalent to (2x^4y)^3
Answers
The equivalent expression to the given expression is [tex]8x^12y^3[/tex].
We have given that,
The expression (2x^4y)^3
We have to determine the,
Which expression is equivalent to (2x^4y)^3
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
The answer is D.
2^3 is 8.
(x^4)^3 is x^12 and y^3 is simply y^3.
Put them together to get the final answer.
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The number of hours (H) that a candle will burn increases when the length of the candle (L) increases. Write the correct equation for this scenario, and solve for the number of hours when the length is 2. Length Hours 15 3 20 4
Answers
[tex]\bf \textit{H increases as L increases}\implies H=kL \\\\\\ \textit{from the table above, we also know that } \begin{cases} L=15\\ H=3 \end{cases} \\\\\\ 3=k15\implies \cfrac{3}{15}=k\implies \cfrac{1}{5}=k\quad thus\quad \boxed{H=\cfrac{1}{5}L} \\\\\\ \textit{now, what is H when L = 2}\qquad H=\cfrac{1}{5}\implies \cdot 2[/tex]
Answer:
H = .2L; H = .4
Step-by-step explanation:
Which side has an equal measure to BC?
A.DE
B.AB
C.EF
D.DF
PLEASE HELP
Answers
In the given diagram, we are given two triangles, triangle ABC and triangle DEF.
And we are given a line or reflection l.
Triangle DEF is the mirror image of triangle ABC.
Therefore, all sides of the triangle ABC would be congruent to sides of triangle DEF.
AB = DF
AC = DE and
BC = EF.
We can see than BC is the smallest side of triangle ABC and EF is the smallest side of triangle DEF.
Therefore, correct option is C option.C.EFWhich symbol creates a true sentence when x equals 6? 42 + (x – 3)2 __ 28
Answers
Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?
Answers
A = (x - 1)^2
A = (x - 1)(x - 1)
A = x^2 - 2x + 1
Area of rectangle = L * W
A = x(x - 2) = x^2 - 2x
The greater area would be the square <==
An equilateral triangle and a square have the same perimeter of 12 inches. what is the ratio of the side length of the triangle to the side length of the square? express your answer as a common fraction.
Answers
Length of one side of the triangle = 12/3 = 4
2) Perimeter of the square: 12
Length of one side of the square = 12/4 = 3
Ratio of Triangle side to the square side = 4/3
A triangle has measurements of 39, 52, and 65 units. Is it a right triangle?
Yes
No
Not enough information to tell
Answers
We can use the Pythagorean Theorem to see if it is a right triangle.
The Pythagorean Theorem is a² + b² = c².
c = the longest side, or the hypotenuse. In this case, the hypotenuse should be 65.
39 can be a, and 52 could be b, or 52 could be a, and 39 could be b. It doesn't matter.
39² + 52² = 65²
Is this equation true?
Yes! This equation is true.
The answer is Yes, this is a right triangle.
Hope this helps! :)
Shyla used a probability simulator to pull 3 colored marbles from a bag and flip a coin 50 times. The results are shown in the tables below:
16 blue
20 green
14 yellow
heads 18
tails 32
Using Shyla's simulation, what is the probability of pulling a blue marble and the coin landing tails up?
Answers
P( getting a tail) = 32/50 = 16/25
The 2 events are independent so you multiply the probabilities:-
Required probability = 8/25 * 16/25 = 108/625
Answer:
512/2500
Step-by-step explanation:
Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant
Answers
(x - 2)^2 - 4 = 5
(x - 2)^2 = 9
x- 2 = +/- sqrt9 = +/- 3
x = 3 + 2 or -3 + 2
solution set is {-1 , 5}
The solution of the given equation is -1 or 5
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given is an equation, x²-4x = 5,
we need to transform it into a perfect square,
The equation is =
x²-4x = 5
Add 4 to each side,
x²-4x+4 = 5+4
x²-4x+4 = 9
(x-2)² = 9
Solving for x,
x-2 = √9
x-2 = ±3
x = -1 or x = 5
Hence, the solution of the given equation is -1 or 5
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a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days
Answers
Initial mass, m₀ = 23 g
Decay constant, k = 0.13
Exponential decay obeys the equation
[tex]m(t)=m_{0} e^{-kt}[/tex]
where t = time, days
For half life, the mass is m = m₀/2.
Therefore
[tex]e^{-0.13t} = \frac{1}{2} \\ -0.13t = ln(0.5)\\t= \frac{ln(0.5)}{-0.13} =5.33[/tex]
Answer: The half life is 5.33 days
Answer:
5.3 is the right answer.
Step-by-step explanation:
how many solutions does this system have -3x+6y=10 -3x+6y= -4
Answers
-3x+6y=10
0x+0y=14
Mike wants to make meatloaf. His recipe uses a total of 6 pounds of meat. If he uses a 3 to 1 ratio of beef to pork how much pork will he use? Enter your answer as a mixed number in simplest terms
Answers
5/4 = 1.25
3 * 1.25 = 3.75 of beef
1 * 1 .25 = 1.25 pounds of pork
Mike will use 1 1/2 pounds of pork for his meatloaf recipe, which calls for a 3 to 1 ratio of beef to pork and a total of 6 pounds of meat.
Mike's meatloaf recipe has a total of 6 pounds of meat and uses a 3 to 1 ratio of beef to pork. To find out how much pork he will use, we can express the total amount of meat as the sum of beef and pork parts.
First, we know that there are 3 + 1 = 4 parts in total because of the given ratio. Since the ratio is 3 to 1, for every 4 parts of meat, 1 part is pork. Therefore, we calculate the weight of each part by dividing the total weight by the number of parts:
6 pounds ÷ 4 parts = 1.5 pounds per part
Since one part is pork, Mike will use 1.5 pounds of pork for his meatloaf. Expressed as a mixed number, that's 1 1/2 pounds of pork in simplest terms.
PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOURE RIGHT!!
Find the greatest possible error for each measurement.
9 g
a.
1/2 g
b.
1/4 g
c.
1/6 g
d.
1/8 g
Answers
gpe = 1/2 of the unit measures
since 9 is a whole number the gpe would be 1/2 g
Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy
Answers
In general, if x is the number of days to eat 50 pounds of food, then x/50 is the expression representing the amount eaten per day (in pounds). Finally 365*(x/50) is the expression representing the total amount eaten over the whole year.
This is why the final answer is choice C
Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^2
Answers
V=(4πr^3)/3 multiply both sides by 3
3V=4πr^3 divide both sides by 4π
r^3=3V/(4π) take the cube root of both sides
r=((3V)/(4π))^(1/3)
The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
Answers
The two x-intercepts are x = 5 and x = 15, which are the two values of x where f(x) = 0. The vertex is located halfway between these two points, so where x = 10. When x = 10, f(x) = 25, so the vertex of this graph is (10, 25).
Part A: The vertex is (10, 25). The vertex represents the point where the profit is a maximum. When 10 photos are printed, the profit is $25.
Part B: The two x-intercepts are x = 5 and x = 15. This shows where the profit is $0. When 5 photos or 15 photos are printed, the profit is $0.
The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.
Answers
lw=252, using l from above
(w+4)w=252
w^2+4w=252, now halve the linear coefficient, square it, then add that to both sides, ie (4/2)^2=4
w^2+4w+4=256
(w+2)^2=256
w+2=±16
w=-2±16
w=14 or 18, but since w<l
w=14in and l=18in
Thank you very much for your help!
Answers
[tex]x^2+y^2=25[/tex]
For b.
[tex](x-4)^2+(y-3)^2=25[/tex]
For c.
[tex](x-5)^2+(y-4)^2=9[/tex]
Hope that helps
.help me with this please thanks
Answers
They are not like terms because they are not all the same
ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP
Answers
^
whole number
if 3.xxx... < .5, round to 3.
If 3.xxx... > or = .5, round to 4.
Because .059 < .5, it is therefore rounded to 3.
I need help learning how to do these problems some how whenever I do them I always get it wrong please help I have a test Wednesday!
Answers
After that, we have -4x+5y=6 and -6x-12y=-14. You can multiply the second equation by -2/3 and add on to get -3y=(-28/3)+6 and y=-((-28/3)+6)/3. Solve from there by plugging it in for variables as shown, then with z after x. The next two are similar, but feel free to ask if you have any issues with those!
The base of the parallelogram, b, can be found by dividing the area by the height. If the area of the parallelogram is represented by 6x2 + x + 3 and the height is 3x, which represents b, the length of the base
Answers
A = 6x² + x +3
h = 3x
where ''A'' is area and ''h'' is height. From the statement above,
length of base, b = A / h
b = (6x² + x + 3)/3x
Thus, the expression for the length of the base is 6x²+x+3 / 3x.
Answer:
[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
Step-by-step explanation:
Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
To find: The base of the given parallelogram.
Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.
Now, area of parallelogram is given as:
[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.
Substituting the given values, we have
[tex]6x^2+x+3=b{\times}3x[/tex]
⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]
⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]
⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]
which is the required expression for the base of the given parallelogram.
Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m
Answers
2/3 = y /(xz) = y/(5*12)
= y/60
so y / 60 = 2/3
y = (2*60)/3
= 40
Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?
Answers
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after t seconds is given by the following.
h=7+23t-16t^2
Find all values of t for which the ball's height is 15 feet.
Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
Answers
You get the quadratic equation: [tex]-16t^2+23t-8[/tex]
You can solve it with the quadratic equation: [tex] \frac{-b+ \sqrt{b^2-4ac}}{2a} and \frac{-b- \sqrt{b^2-4ac}}{2a}[/tex]
From here you solve and get the given numbers as your answers!
As per quadratic equation, all values of 't' for which the ball's height is 15 feet are 33.25 and (- 31.813).
What is a quadratic equation?"Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x)."
Given, [tex]h = 15[/tex] feet.
Therefore, the quadratic equation for [tex]h = 15[/tex] will be:
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 feet per second.
The ball's height h (in feet) after t seconds is:
[tex]h = 7+23t-16t^{2}[/tex]
[tex]15 = 7+23t-16t^{2}[/tex]
⇒ [tex]15-7-23t+16t^{2} = 0[/tex]
⇒ [tex]16t^{2} -23t - 8 = 0[/tex]
⇒ [tex]t = [- (-23)[/tex] ± [tex]\sqrt{(23)^{2} - 4(16)(- 8)}[/tex] ]/(2 × 16)
⇒ [tex]t =[/tex] [23 ± 1041]/32
⇒ [tex]t =[/tex] [23 + 1041]/32, [23 - 1041]/32
⇒ [tex]t =[/tex] 33.25, - 31.813
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The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is
Answers
[tex]\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &7500\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4\\ t=years\to &3 \end{cases} \\\\\\ A=7500\left[ \cfrac{\left( 1+\frac{0.12}{4} \right)^{4\cdot 3}-1}{\frac{0.12}{4}} \right][/tex]
Answer:
$180,997.50.
Step-by-step explanation:
1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.
2. Select the rate-per-period column corresponding to the period interest rate.
3. Locate the value in the cell where the periods row intersects the rate-per-period column.
4. Multiply the annuity payment by the table value from step 3.
Future value = annuity payment × table value
FV = $7500.00 * 24.133 = $180,997.50
HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5
a (3x-1)(2x+5)
b (3x-5)(2x-1)
c (3x-1)(2x-5)
d (3x-5)(2x+1)
Answers
You have to try whatever factoring method you've been taught, but this is the answer.
The solution is: the following expression factored completely,
6x^2-13x=5 is: c (3x-1)(2x-5)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, we have,
we have,
6x² - 13x = +5
6x² - 13x - 5 = 0
6x² - 15x + 2x - 5 =0
so, we get,
(3x-1)(2x-5) = 0
The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.
When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.
The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is
... C (3x-1)(2x-5)
Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c (3x-1)(2x-5)
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Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?
Answers
then the rate of Steve is 2 (c/h) , because Steve works faster, he can wash twice the number of cars, for the same amount of time.
Thus If Steve and Sue work together, they can wash 1 + 2 = 3
(cars per hour).
That is, the rate of Steve and Sue working together, is 3 (c/h).
In the first 30 minutes, Sue washes half of the car.
The remaining half will be washed at a rate of 3 (c/h)
The main formula is Work = Time * Rate
where Work is washing (1/2)c, and rate is 3(c/h)
Time=Work/Rate = [tex] \frac{ \frac{1}{2} c}{3 \frac{c}{h} }= \frac{1}{6}h [/tex]
1/ 6 h =(1/6)*60 min = 10 min
Answer: 10 min
Solve 2x2 + 5x + 5 = 0. Round solutions to the nearest hundredth.
Answers
Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
To solve the quadratic equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex], we can use the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
where [tex]\(a = 2\), \(b = 5\)[/tex], and [tex]\(c = 5\)[/tex].
Substituting the values into the quadratic formula:
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 5}}}}{{2 \cdot 2}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 40}}}}{{4}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{-15}}}}{{4}}\][/tex]
Since the discriminant [tex](\(b^2 - 4ac\))[/tex] is negative, the solutions will involve imaginary numbers.
Using the imaginary unit [tex]\(i\)[/tex], where [tex]\(i^2 = -1\),[/tex] we can rewrite [tex]\(\sqrt{{-15}}\)[/tex] as [tex]\(i\sqrt{{15}}\):[/tex]
[tex]\[x = \frac{{-5 \pm i\sqrt{{15}}}}{{4}}\][/tex]
So, the solutions to the equation [tex]\(2x^2 + 5x + 5 = 0\)[/tex] are complex numbers. Rounded to the nearest hundredth, they are:
[tex]\[x_1 \approx -0.63 + 1.35i\][/tex]
[tex]\[x_2 \approx -0.63 - 1.35i\][/tex]
These solutions represent the points where the graph of the quadratic equation intersects the x-axis. They lie on the complex plane.