a = -2 is the value of linear equation .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Step 1 - Write the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 2 - rewrite the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 3 - Take the LCM.
3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4
Step 4 - Further simplify the above expression
3a - 6 - a - 2/a² - 4 = 6a/a² - 4
Step 5 - Cancel out the denominator of both sides and then further simplify.
2a - 8 = 6a
a = -2
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The complete question is -
A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.
3/a + 2 − 6a/a2 − 4 = 1/a − 2
What is the slope of the line that passes through the points
(
−
9
,
−
7
)
(−9,−7) and
(
−
11
,
−
6
)
(−11,−6)? Write your answer in simplest for
Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:
m= (y₂ - y₁)÷ (x₂ -x₁)
Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.
Equation of the line in this case
Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:
m= (-6 - (-7))÷ (-11 -(-9))
m= (-6 +7)÷ (-11 +9)
m= (1)÷ (-2)
m= -1/2
Considering point 1 and the slope m, you obtain:
-7= (-1/2)×(-9) + b
-7= 9/2 +b
-7 -9/2= b
-23/2= b
Finally, the equation of the line is y= -1/2x -23/2.
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A cylindrical can without a top is made out of metal material with a total area of 1500π cm2. Find the dimensions that will maximize the volume held by the can.
The dimensions of the cylinder will be r = 8.92 cm and h = 17.86 cm.
What is dimensions ?
Dimensions refer to the length or width of an area, region, or space in one direction.
Main Body:
Volume of cylinder = πr²h
Surface area = 2πr² + 2πrh
Given surface area = 1500 cm²
1500 = 2πr²+2πrh
h= (750/πr)-r ----(1)
V= πr²{(750/πr)-h}
V =750r - πr³
V' = 750- 3πr²
Put V' =0
0 = 750 - 3πr²
r≈ 8.92 cm
substituting the value of r in equation (1)
we get h= 17.86 cm
Hence the dimension of cylinder are r = 8.92 cm and h = 17.86 cm
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Determine the degree measure of one angle of a 30-sided regular polygon. 5,400° 5,040° 180° 168°
To determine the degree measure of one angle of a 30-sided regular polygon.
The degree measure of one angle of a 30 sided regular polygon is 168°.
What is a regular polygon?
A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.
The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.
We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is
(Side - 2) × 180°
(30 - 2) × 180°
= 5040°
Measure of each angle of 30-gon
= 5040°/30
= 168°
Thus, the degree measure of One angle of a 30 sided regular polygon is 168°
Hence the answer is, The degree measure of one angle of a 30 sided regular polygon is 168°.
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Solve using the quadratic formula.
x² - 4x + 2 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
X =
or x =
The factors of the equation x²-4x+2=0 by using quadratic formula is x=3.414 and 0.585.
Given that,
The quadratic equation is x²-4x+2=0
We have to find the factor by using quadratic formula.
What is the quadratic formula?The word "quadratic," which meaning square, is derived from the word "quad." A quadratic equation is a "equation of degree 2," to put it another way.
A quadratic equation is a second-degree algebraic equation in x. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, x's coefficients are a and b, and c is just a constant.
x=[tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Take the equation,
x²-4x+2=0
Here,
a=1, b=-4 and c=2
Substitute the values in the formula.
x=[tex]\frac{-(-4)\pm\sqrt{(-4)^{2}-4(1)(2) } }{2(1)}[/tex]
x=[tex]\frac{4\pm\sqrt{16-8 } }{2}[/tex]
x=[tex]\frac{4\pm\sqrt{8 } }{2}[/tex]
x=[tex]\frac{4\pm\sqrt{4 \times 2 } }{2}[/tex]
x=[tex]\frac{4\pm2\sqrt{2 } }{2}[/tex]
x=2±√2
x=2+√2 or x=2-√2
x=3.414 or x=0.585
Therefore, The factors of the equation x²-4x+2=0 by using quadratic formula is x=3.414 and 0.585.
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What is the answer of 3 power 5?.
Find - 18 + 27 +13 + (− 8)
Answer:
14
Step-by-step explanation:
Correct me if I'm wrong
Answer:answer is 14
Step-by-step explanation:
hope this helps
PLS HELP
Angel is renting a meeting room at a college. There is a reservation fee of $41 and an additional fee of $4 per hour. She needs to spend no more than $65. What is the possible number of hours for which Angel can rent the meeting room? Use h for the number of hours.
pls explain
Answer:
She can rent the room for 6 hours.
Step-by-step explanation:
65 - 41 = 24
So she has left 24$ to use
24 divided by 4 = 6
She can rent the room for 6 hours.
Graph the line: 6 - 3y = 2x
6-3y=2x
-3y=2x-6
y=(2x-6)/-3
y=-(2/3)x+2
No me deja adjuntar la imagen de la gráfica, te recomiendo una página de internet llamada Desmos
X=0
y=-(2/3)(0)+2=2
(0,2)esmos
x=3
y=-(2/3)(3)+2=-2+2=0
(3,0)
x=-3
y=-(2/3)(-3)+2=2+2=4
(-3,4)
A cout mater bough 45 meter of rope he ued two nine of the rope for knot tying. How many meter of rope were ued for knot tying
The meters of rope used for knot tying is 10 meters.
According to the question,
We have the following information:
A cout mater bough 45 meter of rope he used two-ninth of the rope for knot tying.
So, we have the following expression for the rope used for knot tying:
45 of 2/9
We know that the word of is replaced by multiplication.
45*2/9
Now, we will first multiply the numbers in the numerator and then we will divide the obtained result by denominator.
90/9
Dividing 90 by 9:
10 meters
Hence, the meters of rope used for knot tying is 10 meters.
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a prism is made up of 120 equal cubes. if the volume of the prism is 25, 920cm3, then what is the length of each cube?
The side length of a single cube will be 6 centimeters.
What is the formula to calculate the volume of a cube of side length 'a' units?The volume of the cube will be -
V = (a x a x a) cubic units
We have the volume of Prism as V[P] = 25920 cm³ which is made up of [n] = 120 cubes of the same volume.
The volume of a single cube will be -
V[c] = V[P]/n
V[c] = 25920/120
V[c] = 216 cm³
Volume of a cube = V[c] = (a x a x a)
Equating volume, we get -
a³ = 216
a = 6 cm
Therefore, the side length of a single cube will be 6 centimeters.
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Solve for X
HELP PLS
Determine which quadratic equation has complex solutions
a) 15x² - 10 = 0
b) 1/2x² + 12 = 4
15x² - 10 = 0 is a quadratic equation which has complex solutions.
Define quadratic equation.The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. There should be two solutions to quadratic equations. If you think about the discriminant formula, two roots can be real, equal, or imaginary.
Given,
Quadratic equation:
15x² - 10 = 0
15x² = 10
x² = 10/15
Roots:
x = ±√10/15
15x² - 10 = 0 is a quadratic equation which has complex solutions.
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How do i find the area if the x is 25. i broke the shape into a rectangle and a triangle, the area of the smaller rectangle is 40 and the area of the bigger rectangle is 250. I am trying to find the area of the whole complex figure
Answer:
See the picture below
Step-by-step explanation:
Based on the graph, can this be a proportional relationship? Why or why not?
Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
What is a proportional relationship?A proportional relationship exists when each pair of data values is related in the same way, by multiplying by a factor. A proportional relationship can be identified by looking at data, an equation, or a graph. A proportional relationship with a constant of proportionality k between two quantities y and x is represented by the equation y = kx.
They pass through the source. They are linear (straight lines) and pass through the origin as well. The x to y ratio is a proportionality constant. For example, consider the following number pairs with a ratio of 2.5: 5 and 2; 10 and 4; 100 and 40; 2.5 and 1. These number pairs are all proportional to one another.
Note that an overview was his as the information is incomplete.
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Jenny made $234 for 18 hours of work. At the same rate, how many hours would she have to work to make $156?
Answer:
The answer is 12 hours
Step-by-step explanation:
Jenny would have to work 12 hours to make $156
234/18 = 13
156/13 = 12
Ross drives 315 miles in 5 hours. If Ross continues to drive at the same rate, how many miles can he drive in 10 hours?
OA. 630
OB. 610
OC. 1,260
OD.
252
2 of 10 Answered
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What are the respective names of the points of concurrency?.
The respective names of the point of concurrency is:
1. Circumcenter
2. Incenter.
3. Centroid
4. Orthocenter
Point of concurrency:
The point of concurrency is a point where three or more lines or rays intersect with each other.
Circumcenter:
The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.
Incenter:
The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle.
Centroid:
The point where three medians of the triangle meet is known as the centroid.
Orthocenter:
The point where three altitudes of the triangle meet is known as the orthocenter.
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a club has 58 members, 38 men and 20 women. a committee must consist of 8 people. in how many ways can the committee consist of at most 1 woman?
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
6C1 * 7C5 = 6 * 21 = 126 1 man6C2 * 7C4 = 15 * 35 = 525 2 men6C3 * 7C3 = 20 * 35 = 700 3 men6C4 * 7C2 = 15 * 21 = 315 4 men6C5 * 7C1 = 6 * 7 = 42 5 men6C6 = 1 6 mennumber of different committees with at least 1 man126+525+700+315+42+1= 1,709or13C6 = 1716 number of committees with 6 people7C6 = 7 number of committees with no men1716 - 7 = 1,709 number of committees with at least 1 manlearn more about probability click here:
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What is the answer of this question
The number of shelves is x/20.
From the question, we have
You collect miniature cars and display them on shelves that hold 20 cars each.
Number of shelves = x/20
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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Write an exponential function y=ab^x whose graph passes through the points (2,6.4) and (5,409.6)
[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=6.4 \end{cases}\implies 6.4=ab^2\implies \cfrac{6.4}{b^2}=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} x=5\\ y=409.6 \end{cases}\implies 409.6=ab^5\implies \stackrel{\textit{substituting from the 1st equation}}{409.6=\left( \cfrac{6.4}{b^2} \right)b^5} \\\\\\ 409.6=6.4b^3\implies \cfrac{409.6}{6.4}=b^3\implies 64=b^3\implies \sqrt[3]{64}=b\implies \boxed{4=b} \\\\\\ \cfrac{6.4}{b^2}=a\implies \cfrac{6.4}{4^2}=a\implies \boxed{0.4=a}~\hfill {\Large \begin{array}{llll} y=0.4(4)^x \end{array}}[/tex]
I need help ASAP!!!!!!!!!!!!!
It’s due today!
Answer:
Step-by-step explanation:
briefly explain the goal for defining and measuring variability. a measure of variability describes the degree to which the scores in a distribution are . variability also measures the .
Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out to clustered together. The purpose for measuring variability is to obtain an objective measure of how the scores are spread out in a distribution
What is variability ?Variability also measure how accurately individual score or sample represent the entire population
When the standard deviation is 0 , the scores have no variability.
Variability describes how far the data points are from each other and from the center of the distribution. In addition to measures of central tendency, measures of variability provide descriptive statistics that summarize the data.
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Find the slope and the y-intercept of the line. y = - 4x + 3 Select the correct choice below and fill in any answer boxes within your choice. A. The slope is (Simplify your answer. Type an integer or a fraction.) B. The slope is undefined.
with simple explanation, please!!
Answer:
A- the slope is -4 and y-intercept is 3
Step-by-step explanation:
The standard form is y=mx+c (for straight line graph) while m is slope(gradient) and c is y-intercept.
So, slope is -4 and y-intercept is 3
if you buy one ticket in the virgina lottery, then the probability that you will win a prize is 0.22. if you buy one ticket each month for six months, what is the probability that you will win at least one prize?
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How would the median change for this set of data, if the 6 was swapped for a 10?
Thank you for helping.
Answer:
it will increase
Step-by-step explanation:
6 is bigger than 10
solve the system of equation and choose the correct ordered pair \
3x+4y=38
5x-5y=-30
Answer:
Step-by-step explanation:
3x+4y=38
Line p has an equation of y = x-4. Line q includes the point (-10, -3) and is perpendicular
to line p. What is the equation of line q?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = - x - 13
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 4 ← is in slope- intercept form
with slope m = 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1 , then
y = - x + c ← is the partial equation of line q
to find c substitute (- 10, - 3 ) into the partial equation
- 3 = 10 + c ⇒ c = - 3 - 10 = - 13
y = - x - 13 ← equation of line q
Solve the system of equations. 8x-3y = 3 3x - 2y = -5
The solution of the system of equations is x = 1 and y = -1.
What is a two-variable linear equation?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equivalent to zero, it then is said to be a linear equation in 2 factors. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
SOLUTION TO WORK OUT
the equations are resolved
8x + 3y = 5 & 3x − 2y = 5
EVALUATION
The equations in the given system are
8x + 3y = 5 - - - - - - - (1) (1)
3x − 2y = 5 - - - - - - - (2) (2)
Equation 1's two sides multiplied by two gives us
16x + 6y = 10 - - - - - - (3) (3)
Equation 2's two sides are multiplied by three to get
9x - 6y = 15 - - - - - - (4) (4)
Equation 3 and Equation 4 together give us
25x = 25
⇒ x = 1
Equation 1 is completed when x = 1.
8 + 3y = 5
⇒ 3y = 5 - 8
⇒ 3y = - 3
⇒ y = - 1
FINAL RESPONSE
Consequently, the needed answer is x = 1 and y = - 1.
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What is the slope intercept form equation of the line that passes through 3 4 and 5/16 )? Y 6x − 14 y − 6x 14 y − 6x − 14 y 6x 14?.
The correct option is (a) i.e. the slope intercept form of the given line is y = 6x-14.
What is the slope and slope-intercept form?The slope of the line through two points (x₁ ,y₁) and (x₁ ,y₂) can be found by using the formula below.
m = (y₂ - y₁) / (x₂ - x₁).
The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.
Here we have a line that passes through two points (x₁ ,y₁) = (3 ,4) and (x₁ ,y₂) =(5 ,16).
The slope of the line m = (y₂ - y₁) / (x₂ - x₁) = (16 -4) /(5 -3) = 12/2 = 6.
⇒ slope m = 6.
And we know the slope intercept form is
y = mx + b
⇒ 4 = 6*3 + b {with points (3 ,4)}
⇒ b =4 - 18 = -14 ⇒ b = -14.
So the slope intercept form is y = 6x-14.
The slope-intercept form of the equation with m =6 and y-intercept as -14 was found to be
y = 6x -14.
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NOTE : The question given here is not complete. The complete question is given below.
Question: What is the slope intercept form equation of the line that passes through (3 ,4)and (5,16)?
(a) y = 6x − 14
(b) y = −6x +14
(c) y = −6x − 14
(d) y = 6x + 14?
jason is working as chief financial officer for a global finance company based in melbourne. he is planning to have a video-conference call with his counterpart in london. when it is 5pm in melbourne, he found out that its 8am in london. if the counterpart likes to have a video call with him 5pm on friday london time, what time will it be in melbourne?
If the counterpart likes to have a video call with him 5 pm on Friday London time, it will be 2 am on Saturday in Melbourne.
Given in ques,
When it is 5 pm in Melbourne, he found out that its 8 am in London.
The time difference is of 9 hours with Melbourne's time being ahead.
So, when its 5 pm on Friday in London, Melbourne's time will be ahead by 9 hours which would be 2 am on Saturday.
Hence, it would be 2 am in the morning on Saturday in Melbourne when its 5 pm in the evening on Friday in London.
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