Answer:
A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2
Step-by-step explanation:
The equation of the given line is 8·x - 4·y = 12
Which gives;
8·x- 12= 4·y
y = 2·x - 3
Given that the line passes through the points (0, -3) and (1, -1), we have;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;
[tex]Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2[/tex]
y - (-3) = 2×(x - 0)
y = 2·x - 3 which is the equation of the given line
For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x - 6 to have no solution, the slope of the two lines should be equal that is m = 2
Given that the line passes through the point (1.5, 0), we have;
y - 0 = 2×(x - 1.5)
y = 2·x - 3...................(1)
For the equation, y = m·x - 6, when m = 2, we have;
y = 2·x - 6..................(2)
Solving equations (1) and (2) gives;
2·x - 3 = 2·x - 6, which gives;
2·x - 2·x= - 3 - 6
0 = 9
Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.
Answer:
short answer is 2 or d
Step-by-step explanation:
A number is 30% of 20% of the number x.
Answer:
6/100x
Step-by-step explanation:
Answer:6/100x
Step-by-step explanation:
In triangle $ABC$, $AB = BC = 25$ and $AC = 40$. What is $\sin \angle ACB$?
Answer:
Sine angle of <ACB = 38.68°
Step-by-step explanation:
Hello,
To solve this problem, we need a good representation of the sides and the angle.
See attached document for better illustration.
Assuming it's a right angled triangle,
AC = hypothenus
AB = opposite
BC = adjacent
AC = 40
BC = 25
AB = 25
From trigonometric ratios
Sinθ = opposite/ hypothenus
Sinθ = AB / AC
Sinθ = 25 / 40
Sinθ = 0.625
θ = sin⁻¹0.625
θ = 38.68°
Sine angle of <ACB = 38.68°
For a chemical reaction to occur, at least one-third of the solution must be an acid. If there are five liters of acid, in interval form, how much solution is present?
A. [5,8)
B. (3/5,5]
C. (5/3,5]
D. [5,15]
Answer:
Amount of solution = 15 liter
Step-by-step explanation:
Given:
One third of solution is acid
Amount of acid = 5 Liter
Find:
Amount of solution
Computation:
Amount of solution = Amount of acid (1 / One third of solution is acid)
Amount of solution = Amount of acid (3)
Amount of solution = (5)(3)
Amount of solution = 15 liter
Last season, a softball team played 18 games. The team won 15 of these games. What is the ratio of the softball team's wins to its total number of games played ?
Answer:
5:6Step-by-step explanation:
Given the total number of games played by the softball team = 18 games
Total games won = 15 games
Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played
Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]
[tex]Ratio = \frac{15}{18}[/tex]
Expressing the ratio in its lowest term
[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]
Hence, the ratio of the softball team's wins to its total number of games played is 5:6
1. Which financial statement reports the amount of cash paid for acquisitions of property, plant, and equipment? In which section (operating, investing, or financing) of this statement is the information reported? 2. Indicate the amount of cash paid for acquisitions of property and equipment in the year ended September 30, 2017.
Answer:
1. Cash flow statements; the investing section
Step-by-step explanation:
The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.
The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.
A 6 inch-y’all plant grew 3/4 of an inch one week and twice as much the following week. How tall is the plant now?
Answer:
8 inches
Step-by-step explanation:
3/4+(3/4*2)=3/4+6/4=9/4=2 1/4
2 1/4+6=8 1/4=8.25
Answer: 8.25 inches
Step-by-step explanation:
PLEASE HELP! I WILL GIVE BRAINIEST! Look at the figure below: A triangle ABC is drawn. D is a point on BC such that BD is equal to DC. A straight line joins points A and D. This line extend Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? a Triangle ABD and triangle ECD b Triangle ABC and triangle ECD c Triangle ABD and triangle ADC d Triangle ADC and triangle ABC
Answer:
ADB and ADC
Step-by-step explanation:
SAS is side angle side. so, which 2 triangles have same side, then angle, then side. We have to have it in that specific order.
Answer:
ABD and ECD
Step-by-step explanation:
EDC and ADB are vertical angles, so that is the angle we need for the SAS postulate. The markings on each of the corresponding sides is the same, which means we have 2 congruent sides, as well as an angle.
What number :Increased by 130% is 69 i rlly need help!!!
Answer:
53.076923
Step-by-step explanation:
130% as a decimal is 1.3
Divide 69 by 1.3:
69 /1.3 = 53.076923
Answer:
30
Step-by-step explanation:
The unknown number is x.
Start with x.
To increase x by 130%, you need to add 130%of x to x.
x + 130% of x
The sum equals 69.
x + 130% of x = 69
x + 130% * x = 69
1x + 1.3x = 69
2.3x = 69
x = 30
Answer: The number is 30.
Use the distributive property to remove the parentheses -5(2x-3w-6)
Answer:
15w - 10x + 30.
Step-by-step explanation:
-5(2x - 3w - 6)
= (-5 * 2x) + (-5 * -3w) + (-5 * -6)
= -10x + 15w + 30
= 15w - 10x + 30.
Hope this helps!
Answer:
[tex] - 10x + 15w + 30[/tex]Step-by-step explanation:
[tex] - 5(2x - 3w - 6)[/tex]
Multiply each term in the parentheses by -5
[tex] - 5 \times 2x - 5 \times ( - 3w) - 5 \times ( - 6)[/tex]
Calculate the product
[tex] - 10x - 5 \times ( - 3x) - 5 \times ( - 6)[/tex]
Multiplying two negatives equals a positive [tex]( - ) \times ( - ) = ( + )[/tex]
[tex] - 10x + 5 \times 3w - 5 \times ( - 6)[/tex]
Calculate the product
[tex] - 10x + 15w - 5 \times ( - 6)[/tex]
Multiply the numbers
[tex] - 10x + 15w + 30[/tex]
Hope this helps..
Best regards!!
Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
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simplify. Remove all perfect squares from inside the square root. V180=
Answer:
6√5
Step-by-step explanation:
We have to solve the expression [tex]\sqrt{180}[/tex]
Break 180 into its factors which are in the perfect square form.
Since, 180 = 9 × 4 × 5
= 3² × 2² × 5
Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]
= [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]
= 3 × 2 × √5
= 6√5
Therefore, solution of the given square root will be 6√5.
find the hypo when the opposite is 36 and the adjacent is 27
Answer:
45
Step-by-step explanation:
Given the legs of the right triangle.
Then using Pythagoras' identity
The square oh the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is
h² = 36² + 27² = 1296 + 729 = 2025 ( take the square root of both sides )
h = [tex]\sqrt{2025}[/tex] = 45
Answer:
45
Step-by-step explanation:
When you are given the opposite and adjacent sides of a triangle, the easiest way to find the hypotenuse is through the Pythagorean theorem!
The formula is a^2 + b^2= c^2
Plugging in the values, your formula would now look like 36^2 + 27^2= c^2
Once you do square your values and add them up, the result would end up being 2025, but since that is squared, to find the actual value of c you have to take the square root of this number, this will result in 45.
There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After that, Susan took half of the remaining pieces of candy. In the end there were 8 pieces of candy left in the bowl. How many candies were there in the bowl at the beginning?
Answer:
Number of pieces of candy in the bowl=64
Step-by-step explanation:
Let
x=number of pieces of candy in a bowl
Shirley took=1/2 of x
=1/2x
Remaining
x-1/2x
= 2x-x/2
=1/2x
Rose took half of the pieces left in the bowl=1/2 of 1/2x
=1/2*1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x
=1/2*1/4x
=1/8x
Remaining 8
1/8x=8
x=8÷1/8
=8*8/1
=64
x=64
sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues
Answer:
[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}[/tex]
[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]
[tex]\bold{METHOD\ 2}[/tex]
[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]
[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]
An exterior angle of a triangle is equal to the sum of________ opposite angle
Answer:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Answer:
Two remote interior angles.
Which situation can be represented by 80x > 150 + 50x?
Answer:
All numbers greater than 5, i.e., [tex]x>5[/tex] .
Step-by-step explanation:
The given inequality is
[tex]80x>150+50x[/tex]
Isolate variable terms on one side to find the solution.
Subtract 50x from both sides.
[tex]80x-50x>150+50x-50x[/tex]
[tex]30x>150[/tex]
Divide both sides by 30.
[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]
[tex]x>5[/tex]
It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a nut chocolate followed by a caramel chocolate.
Answer:
16/117Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given the total amount of chocolate in a box = 39chocolates
Amount of nuts = 16
Mount of caramel = 13
Amount of solid chocolate = 10
If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39
IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3
The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117
100 points timed Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer: A
Step-by-step explanation:
The answer is A. It accurately describes the equation shown. Negative values are represented by negative tiles and positive values are represented by positive tiles.
Hope it helps <3
Using leaner combination method what is the solution to the system of linear equations 7x-2y=-20 and 9x+4y=-6
Answer:
x = -2 and y = 3
Step-by-step explanation:
In linear combination method we try one of the variables from bopth of equations by
first making the variable equal in vlaue
then either subtracting or adding the two equation as required to eliminate the variable.
_____________________________________________
7x-2y=-20 equation 1
and 9x+4y=-6 equation 2
we see that y has
has value -2 and +4
4 = 2*2
thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.
7x-2y=-20
multiplying the LHS and RHS with 2
2(7x-2y)=-20 *2
=> 14x - 4y = -40 eqaution 3
now that we have got 4y
lets add equation 2 and equation 3
9x +4y= -6
+14x - 4y = -40
________________________________
=> 23x + 0 = -46
x = -46/23 = -2
Thus, x = -2
substituitinng x = -2 in 7x-2y=-20
7*-2 -2y=-20
=> -14 -2y = -20
=> -2y = -20+14 = -6
=> y = -6/-2 = 3
Thus, y = 3
solution is x = -2 and y = 3
A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π .
Answer:
12π inches
Step-by-step explanation:
s = rθ
s = (21) (4π/7)
s = 12π
The length of the arc will be;
⇒ Arc = 37.68 inches
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The central angle = 4π/7
And, A circle has a radius of 21 inches.
Now,
We know that in circle;
⇒ Arc = Radius × Angle
Substitute all the values, we get;
⇒ Arc = 21 × 4π/7
⇒ Arc = 3 × 4 × 3.14
⇒ Arc = 37.68 inches
Thus, The length of the arc will be;
⇒ Arc = 37.68 inches
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Triangle RST was dilated with the origin as the center of dilation to create triangle R'S'T'. The triangle was dilated using a scale factor of 34. The coordinates of the vertices of triangle RST are given. You can use the scale factor to find the coordinates of the dilated image. Enter the coordinates of the vertices of triangle R'S'T' below. (Decimal values may be used.)
Answer:
Multiply every coordinate from the old one by 0.75
Step-by-step explanation:
I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.
The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.
Answer:
x, y ----> 3/4x, 3/4y
Step-by-step explanation:
John wants to nail a thumbtack on his circular board, pictured below. If the thumbtack is equally likely to be placed anywhere on the board, what is the probability that the thumbtack will be placed on the inner circle? Use 3.14 for , and round your answer to the nearest whole percent. A. 51% B. 55% C. 57% D. 60%
Answer:
[tex]Probability = 51\%[/tex]
Step-by-step explanation:
Given
Radius of inner circle = 5ft
Radius of outer circle = 7ft
Required
Determine the probability that the thumbtack will be placed on the inner circle
We start by calculating the area of both circles;
Inner Circle
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14 * 5^2[/tex]
[tex]Area = 3.14 * 25[/tex]
[tex]Area = 78.5[/tex]
Outer Circle
[tex]Area = \pi R^2[/tex]
[tex]Area = 3.14 * 7^2[/tex]
[tex]Area = 3.14 * 49[/tex]
[tex]Area = 153.86[/tex]
At this point, the probability can be calculated;
The probability = Area of Inner Circle / Area of Outer Circle
[tex]Probability = \frac{78.5}{153.86}[/tex]
[tex]Probability = 0.51020408163[/tex]
Convert to percentage
[tex]Probability = 0.51020408163 * 100\%[/tex]
[tex]Probability = 51.020408163\%[/tex]
Approximate
[tex]Probability = 51\%[/tex]
the sum of the first term of an ap is 240 and the sum of the next 4 term is 220 find the first term of the ap
Answer:
The common difference is -5/4
T(n) = T(0) - 5n/4,
where T(0) can be any number. d = -5/4
Assuming T(0) = 0, then first term
T(1) = 0 -5/4 = -5/4
Step-by-step explanation:
T(n) = T(0) + n*d
Let
S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240
S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220
S2 - S1
= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)
= (5+6+7+8 - 1 -2-3-4)d
= 4(4)d
= 16d
Since S2=220, S1 = 240
220-240 = 16d
d = -20/16 = -5/4
Since T(0) has not been defined, it could be any number.
11.1/0.01= what is the answer
Answer:
1,110
Step-by-step explanation:
calculator
Algebra 2 help needed!
Answer:
(g + f) (x) = (2^x + x – 3)^1/2
Step-by-step explanation:
The following data were obtained from the question:
f(x) = 2^x/2
g(x) = √(x – 3)
(g + f) (x) =..?
(g + f) (x) can be obtained as follow:
(g + f) (x) = √(x – 3) + 2^x/2
(g + f) (x) = (x – 3)^1/2 + 2^x/2
(g + f) (x) = (x – 3)^1/2 + (2^x)^1/2
(g + f) (x) = (x – 3 + 2^x)^1/2
Rearrange
(g + f) (x) = (2^x + x – 3)^1/2
What is the circumference of a circle with a diameter of 100m. A 100m B 157m C 300 m D 314m
Answer:
C = 314 m
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
Using 3.14 for pi
C = 3.14 * 100
C = 314 m
Answer:
The answer is option D.
314mStep-by-step explanation:
Circumference of a circle = πd
Where d is the diameter
From the question
d = 100m
Circumference of the circle is
100π
= 314.2
Which is 314m to the nearest whole number
Hope this helps you
how do i wright this as a expression? seven and the quotient of z and eight
8÷7=z and z is the answer you got when you divided,that's how I understand the question
Please answer this in two minutes
Answer:
u = [tex]\sqrt{6}[/tex].
Step-by-step explanation:
This is a 45-45-90 triangle.
That means that there are two side lengths with lengths of x, and a hypotenuse with a length of xsqrt(2). We can then set up a proportion.
[tex]\frac{1}{\sqrt{3} } =\frac{\sqrt{2} }{u}[/tex]
1 * u = [tex]\sqrt{3} * \sqrt{2}[/tex]
u = [tex]\sqrt{6}[/tex].
Hope this helps!
please solve this using quadratic formula :")
Answer:
Step-by-step explanation:
The given equation is expressed as
(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12
Simplifying the right hand side of the equation, it becomes
[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)
x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)
(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)
4x/(x - 1)(x + 1)
Therefore,
4x/(x - 1)(x + 1) = 7/12
Cross multiplying, it becomes
4x × 12 = 7(x - 1)(x + 1)
48x = 7(x² + x - x - 1)
48x = 7x² - 7
7x² - 48x - 7 = 0
Applying the quadratic formula,
x = - b ± √(b² - 4ac)]/2a
from our equation,
b = - 48
a = 7
c = - 7
Therefore
x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)
x = [48 ± √(2304 + 196]/14
x = (48 ± √2500)/14
x = (48 ± 50)/14
x = (48 + 50)/14 or x = (48 - 50)/14
x = 98/14 or x = - 2/14
x = 7 or x = - 1/7
Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7
Step-by-step explanation:
Name an inscribed angle
Answer:
BHF
Step-by-step explanation:
Definition of inscribed