Answer: x=3
Step-by-step explanation:
divide by the common factor 3
3x ÷ 3 = x
9÷3 = 3
hence the reason we get x=3
Answer: 3
Step-by-step explanation:
To solve for x, you need to divide 9 by 3 which equals 3.
Since 3x = (3 ⋅ 3), x = 3.
Define units for the time that Marshall has the beans and the amount of coffee beans that Marshall has left.
After 4 weeks the amount of coffee that Marshall will have left would be = 20 ounces.
How to calculate the amount of coffee left?The amount of ground coffee that Marshall bought for his office machine = 40 ounces
The quantity of coffee he uses per week in his office = 5 ounces.
Therefore for 4 weeks would be= ?
But, 1 week = 5 ounces
4 weeks = X
make X the subject of formula;
X = 5×4 = 20 ounces
The amount of ground coffee that will remain = 40-20 = 20 ounces.
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. Find m/P. M (7x+31) (21x-19).
The value of the angle P is 107°
What are consecutive angles?Consecutive angles, also called contiguous or adjoining angles, are angles that have a common side and the same vertex.
They are located next to each other and share a side and vertex. The sum of the consecutive angles is equal to the angle formed by the non-common sides of the angles.
Consecutive angles are also adjacent angles, which means that the other two sides are opposite rays.
Given that, a figure, we need to find the measurement of the angle P,
We know that, the consecutive angles between the parallel lines are supplementary, so,
∠M + ∠P = 180°
7x+31 + 21x-19 = 180
28x = 180-12
28x = 168
x = 6
Therefore,
∠P = 21(6)-19 = 107
Hence, the value of the angle P is 107°
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in a bag of 10 marbles, there are 4 blue, 3 red, 2 green, and 1 yellow. What is the probability that you draw one marble that is green, replace it, and draw another marble that is red? Enter your answer as a fraction in lowest terms. Do not add spaces to your answer.
The probability of drawing a green marble and replacing it is 2/10 = 1/5.
Since the marble is replaced, the probability of drawing a red marble on the second draw is still 3/10.
The probability of both events occurring is the product of their individual probabilities:
1/5 * 3/10 = 3/50
So the probability of drawing a green marble, replacing it, and drawing a red marble is 3/50.
If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?
f of x is equal to the square root of the quantity 4 times x plus 3 end quantity and g of x is equal to the square root of the quantity 4 times x plus 3 end quantity
f of x is equal to the square root of the quantity 4 times x plus 3 end quantity and g of x is equal to the square root of 2
f (x) = 8x + 6 and g of x is equal to the square root of x
f of x is equal to the square root of x and g(x) = 8x + 6
The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:
[tex]f(x) = \sqrt{x}[/tex]g(x) = 8x + 6.What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The functions for this problem are defined as follows:
[tex]f(x) = \sqrt{x}[/tex]g(x) = 8x + 6.As the composition of the functions is then given as follows:
[tex]h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}[/tex]
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The length of a rectangle l is 4 units longer than its width. What is the area of the rectangle?
Answer:
Assuming you are looking for an expression to represent the area of the rectangle, as you didn't provide any values for the length or width, the area of the rectangle is [tex]x^{2} +4x[/tex] [tex]un^{2} .[/tex]
Step-by-step explanation:
The formula for the area of a rectangle is [tex]a=lw[/tex], where [tex]l[/tex] represents the length of the rectangle, and [tex]w[/tex] represents the width. We are given that the length of the rectangle is 4 units longer than its width, so we can set the width to be represented by the variable [tex]x[/tex], and we get that the length and width are [tex]x+4[/tex] and [tex]x[/tex] respectively. As we are trying to find the area of the rectangle, we have to multiply the length and width of the rectangle together, which then we will get that the area of the rectangle is [tex]x(x+4)=x^{2} +4x[/tex] [tex]un^2.[/tex]
If your teacher or whatever website you're using requires a specific variable, you can just replace the [tex]x[/tex] in the expression to whatever you need.
Have a great day! Feel free to let me know if you have any more questions :)
Now you will attempt to copy your original triangle using one of its angles:
Draw a line segment, DE of any length anywhere on the coordinate plane, but not on top of ∆ABC.
Choose one of the angles on ∆ABC. From point D, create an angle of the same size as the angle you chose. Then draw a ray from D through the angle. You should now have an angle that is congruent to the angle you chose on ∆ABC.
Create a point anywhere outside the mouth, or opening, of the angle you created. The point will initially be named F by the tool, but you should rename it point G. Now draw a ray from E through G such that it intersects the first ray. Your creation should be a closed shape resembling a triangle.
Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.
Click on point G, and move it around. By moving point G, you can change
DEF and EFD while keeping FDE fixed.
Take a screenshot of your results for one position of G, save it, and insert the image in the space below.
The construction of similar triangles are given in attached figure.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Similar shapes are shapes whose lengths are in an equivalent ratio. Triangle ABC and triangle DEF are similar because the side lengths of both triangles are in an equivalent ratio (refer to the attachment).
Step 1: Draw a random triangle ABC
The lengths of two sides and an angle are:
AB=10
BC=6
C=90
Step 2: Draw and measure the length of DE
DE=15
Step3: Calculate the ratio
The corresponding line segment to DE is line segment AB.
So, the ratio (k) is:
k= DE/AB
k= 15/10
k=1.5
Step 4: Multiply the ratio by the other line segment in step 1
In (1), we have:
BC=6
So,
EF=k*BC
EF=1.5*6
EF=9
Step 4: Draw a circle with center F and radius EF
The center of the circle is point F and the radius of the circle is 9 units
Step 5: Draw a ray from the center (i.e. point F) to DE
Refer to the attached image for
Triangle ABC
Triangle DEF
Circle with center F and radius 9
Ray from F to DE
Therefore, construction of similar triangles are given in attached figure.
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12d + 8r is___ to 2(5d+4r)+4d
Answer: equivalent
To determine if two expressions are equal, we can set them equal to each other and simplify if possible.
12d + 8r = 2(5d + 4r) + 4d
Expanding the right-side expression:
12d + 8r = 10d + 8r + 4d
Combining like terms:
12d + 8r = 14d + 8r
Subtracting 8r from both sides:
12d = 14d
Subtracting 12d from both sides:
0 = 2d
Dividing both sides by 2:
d = 0
So the expressions are equal if d = 0, meaning if the coefficient of the variable d is 0 in both expressions. If d is not 0, then the expressions are not equal.
Step-by-step explanation:
I don’t get how to do this please help!
Answer:
Length = 5 cm
Width = 3 cm
Step-by-step explanation:
Part (a)
Length L = c
(i) Width W = c- 2 (width is 2 cm less than width)
(ii) Area of the rectangle = L x W
= c(c - 2) = c² - 2c
Part (b)
Area is given as 15 cm²
Therefore, c²- 2c = 15
Part (c)
The equation for area from part (b) is
c² - 2c = 15
Carry 15 to the left side by subtracting 15 from both sides:
c²- 2c - 15 = 15 - 15
c²- 2c - 15 = 0
This is a quadratic equation which can be solved easily by factoring
The factors of the constant 15 are 5 and 3
The constant is product of the factors is -15; so one of the numbers is negative
The sum of the numbers is the coefficient of c
Since this -2, the numbers are -5 and 3
Therefore the factorization of the equation
c² - 2c - 15 = (c + 3)(c - 5)
And since c² - 2c - 15 = 0 this means (c + 3)(c - 5) = 0
So either c + 3 = 0 ==> c = -3 which can be rejected because length cannot be negative
This gives us
c - 5 = 0
Or c = 5
So length = 5 cm
Since width = c - 2
width = 5 - 2 = 3
Length = 5
Width = 3
Let g(x) be the indicated transformation of f(x). Write the rule for g(x).
7. f(x)=2x, shift the graph vertically 2 units
8. f(x)= x-3; horizontal stretch by a factor of 3
9. f(x)=X: vertical compression by a factor of
Let g(x) be the indicated combined transformation of f(x) = x. Write
the rule for g(x).
10. horizontal stretch by a factor of 5 followed by a horizontal
shift right 2 units
11. vertical shift down 3 units followed by a vertical compression
by a factor of
12. reflection across the y-axis followed by
a vertical shift up 4 units
Solve.
13. Tia's earnings can be represented by the function f(x) = 5x + 120,
where x is the number of hours she works. If she works 3 additional
hours, her earnings function is g(x) = 5(x + 3) + 120. What type of
transformation can be applied to the graph of fto get the graph of g?
Answer:
g(x) = 2x + 2
g(x) = 3(x-3)
g(x) = 1/3x
g(x) = 5(x + 2)
g(x) = 1/3(x - 3) + 3
g(x) = -x + 4
Vertical shift of 3 units to the right.
Step-by-step explanation:
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0)
The statement that are true about the function and its graph is "The graph of the function is a parabola " , the correct option is (b) .
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
In the question ,
it is given that ,
the quadratic function is f(x) = x² – 5x + 12 .
for x = -10 ,
f(-10) = (-10)² – 5(-10) + 12
= 100 + 50 + 12
= 162
option(a) is false .
the graph of the quadratic function is shown below .
form the graph we can see that the graph is a parabola ,
and the function opens upwards ,
the graph does not contain the points (20,-8) and (0,0)
Therefore , The statement that are true about the function and its graph is "The graph of the function is a parabola " , the correct option is (b) .
The given question is incomplete , the complete question is
Consider the quadratic function f(x) = x² – 5x + 12. Which statement is true about the function and its graph?
(a) The value of f(–10) = 82
(b) The graph of the function is a parabola.
(c) The graph of the function opens down.
(d) The graph contains the point (20, –8).
(e) The graph contains the point (0, 0).
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your friend shows u a coin collection. In it, 45/50 of the coins are quarters. what percent of the coins are quarters?
Answer:
90.00%
Step-by-step explanation:
Answer:
90% is quarters
y varies as t. If y = 6 when t =4, calculate:
a) the value of y, when t = 6
b) the value of t, when y = 4
Answer:
see explanation
Step-by-step explanation:
given y varies as t , then the equation relating them is
y = kt ← k is the constant of variation
to find k use the condition y = 6 when t = 4
6 = 4k ( divide both sides by 4 )
[tex]\frac{6}{4}[/tex] = k , that is
k = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{3}{2}[/tex] t ← equation of variation
(a)
when t = 6 , then
y = [tex]\frac{3}{2}[/tex] × 6 = 3 × 3 = 9
(b)
when y = 4 , then
4 = [tex]\frac{3}{2}[/tex] t ( multiply both sides by 2 to clear the fraction )
8 = 3t ( divide both sides by 3 )
[tex]\frac{8}{3}[/tex] = t
13.
In circle A, secant EC and tangent BC intersect at C.
mEB = 166° and mBD = 80°
B
А.
С
What is mZBCD ?
we are given that circle A has a secant EC and a tangent BC that intersect at point C. We are also given that mEB = 166° and mBD = 80°. Our task is to find the measure of angle ZBCD, which is formed by the intersection of secant EC and tangent BC.
To find mZBCD, we first need to find mECB. Since EC is a secant and BC is a tangent to circle A, and EC and BC intersect at C, we know that:
mECB = mBEC (because they are opposite angles formed by intersecting lines)
Also, mBEC = 180° - mEB (because BEC is a straight line)
So, mECB = 180° - mEB = 180° - 166° = 14°
Since mBD is 80°, we have:
mZBCD = mECB + mBD = 14° + 80° = 94°
So, mZBCD = 94°. This means that angle ZBCD is 94°.
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Could you please help me with 1, 2, 3, 4, 6, and 8 please it will mean a lot
After rewriting the expression [tex]4 ^ {( 2x -4)}[/tex] using distributive property, [tex]4^{2x} . 4^{-4}[/tex] is the equivalent expression.
Describe expression.In mathematics, it is acceptable to multiply, divide, add, or negate. The construction of an expression looks like this: Amount, a mathematical operator, and an expression A mathematical expression's variables can be numbers, amounts, or functions (such as addition, subtraction, multiplication or division etc.)
Contrasting concepts and language is typical practice. Any mathematical statement that rates systems, numbers, and then an arithmetic operation between them is referred to as an expression, sometimes known as a formula. For instance, the arithmetic operator + separates the word m from the terms 4m and 5 in the balanced formula, just as it does for the variable m in the phrase 4m + 5.
given
Expressions that are equivalent do the same thing even when they have distinct appearances.
Two quadratic expressions that are analogous have the same value when we use the same value for the variable.
[tex]4 ^ {( 2x -4)}[/tex]
[tex]4^{2x} . 4^{-4}[/tex]
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One way to establish validity of a questionnaire is by measuring:
A) the correlation between the score on the questionnaire and another measure of the same concept
B) The alpha value of the reliability coefficient
C) How well subjects perform on the questionnaire at one time compared to another time
D) The consistency by which multiple subjects are able to complete the questionnaire without error
B) The alpha value of the reliability coefficient is one way to establish the validity of a questionnaire.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
The alpha value of the reliability coefficient, also known as Cronbach's alpha, measures the internal consistency of a questionnaire. It indicates how well the items on the questionnaire are related to each other and form a consistent measure of the concept being assessed. A high alpha value indicates that the items on the questionnaire are measuring the same underlying concept and that the questionnaire is reliable.
Correlation between the score on the questionnaire and another measure of the same concept (Option A) and consistency by which multiple subjects are able to complete the questionnaire without error (Option D) can also provide information about the reliability of a questionnaire.
The alpha value of the reliability coefficient is one way to establish the validity of a questionnaire.
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What is the sum of 17.25 and 1.725 , to the nearest integer?
The sum of 17.25 and 1.725, to the nearest integer, is 19.
First, let's add the two numbers together: 17.25 + 1.725 = 19.975
Next, we need to round the sum to the nearest integer. To do this, we need to look at the tenths place of the number. Since the tenths place is a nine, we need to round up to the nearest integer.
In this case, the nearest integer is 19.
To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 19.
To make sure we understand how to round to the nearest integer, let's look at another example. If we add 3.45 + 2.735, the sum is 6.185.
Looking at the hundredths place, we see that it is a five. Since five is greater than or equal to five, we need to round up to the nearest integer.
In this case, the nearest integer is 7.
To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 7.
In summary, to round a number to the nearest integer, we need to look at the tenths place. If the tenths place is greater than or equal to five, we round up to the nearest integer. If it is less than five, we round down to the nearest integer.
Therefore, the sum of 17.25 and 1.725, to the nearest integer, is 19.
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The sum of 17.25 and 1.725 is 18.975. To the nearest integer, this number is rounded up to 19.
Rounding to the nearest integer involves finding the closest whole number to a decimal or fractional number. When the decimal portion of a number is greater than or equal to 0.5, the number is rounded up to the next whole number. When the decimal portion of a number is less than 0.5, the number is rounded down to the previous whole number. In this case, the decimal portion of 18.975 is greater than 0.5, so the number is rounded up to 19.
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Question in picture.
Answer:
Since you are looking for an equation to represent the pattern, the correct equation in y = mx + b form would be y = 4x - 3.
Step-by-step explanation:
It's important to look for two things in order to write a slope-intercept form equation: the rate of change, and the beginning value.
First thing we can start with is the rate of change, which can be found by simply selecting any two points - or in this case terms - and find the difference between term values and term number, and then divide them by each other to find the rate of change. To make things easy, we can just use terms 1 and 2. Term 1 has a term 1 value of 1 block, while term 2 has a value of 5 blocks. In order to find the rate of change, we first find the difference in term value (5 - 1 = 4 blocks), then find the difference in term numbers (2 - 1 = 1 term), and lastly divide the difference in term value by the difference in term number (4 ÷ 1 = 4 blocks per term), which is your rate of change. Note that 4 is the number of blocks each term increases by when the term number increases by 1, and not the total number of blocks in each term.
Now that we know the rate of change, we can input it into the base equation, which will become y = 4x + b. Now we only need to find b. The simple way to solve for b would be to use a single term as reference, and plug in its term number and value into the equation and calculate b. Once again, it's easier to just use the lowest one, which would be term 1, with a term number of 1, and a term value of 1. By inserting these values, we'll get an algebraic equation to solve for b, which is 1 = 4(1) + b or 1 = 4 + b. Now, we just need a value for b that would make 4 + b equal to 1, which would be b = 1 - 4 = -3, so b would equal -3. Which means the final equation to represent this situation would be y = 4x - 3.
Have a great day! Feel free to let me know if you have any more questions :)
What do I have to do
Answer:
Could you upload the whole picture? I think I can help but I don't understand what's it's asking.
Step-by-step explanation:
..
another aleks question,,, pleas and thank u
According to algebra properties, the following properties are used in the resolution of a linear equation:
Step 2: compatibility with multiplication.
Step 3: existence of multiplicative inverse, associative and modulative properties and definition of multiplication.
Step 4: existence of additive inverse.
Step 5: associative and modulative properties and existence of additive inverse.
How to solve a linear equation
Herein we find the case of a linear equation with one variable, that must be cleared by algebra properties. First, write the entire equation:
8 · (y + 3) = - 16 / 8
Second, use compatibility with multiplication:
8 · (y + 3) / 8 = - 16 / 8
Third, apply existence of multiplicative inverse, associative and modulative properties and definition of multiplication:
y + 3 = - 2
Fourth, use existence of additive inverse:
y + 3 - 3 = - 2 - 3
Fifth, use associative and modulative properties and existence of additive inverse:
y = - 5
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2(5+3(10+5(12-3))) como la resuelvo?
Answer:
340
Step-by-step explanation:
[tex]2(5 + 3(10 + 5(12 - 3)))[/tex]
let's start with:
The most inner brackets[tex]5(12 - 3)[/tex]
[tex](12 - 3) = 9[/tex]
[tex]5(9) = 45[/tex]
let's rewrite the question now while removing the solved brackets and substituting it with 45
[tex]2(5 + 3(10 + 45))[/tex]
let's solve the current inner brackets[tex]3(10 + 45)[/tex]
[tex](10 + 45) = 55[/tex]
[tex]3(55) = 165[/tex]
let's rewrite the question and do the same thing as before
[tex]2(5 + 165)[/tex]
Lastly let's solve the last brackets[tex]2(5 + 165)[/tex]
[tex](5 + 165) = 170[/tex]
[tex]2(170) = 340[/tex]
you created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. does the graph show any trend? if
A scatterplot of miles per gallon (MPG) against weight can reveal the relationship between the two variables. If there is a trend in the graph, it can help us understand the relationship between the two variables.
For example, if the graph shows a negative correlation, meaning that as the weight of the vehicle increases, the MPG decreases, this trend may be what is expected, as heavier vehicles typically have lower fuel efficiency. On the other hand, if the graph shows no trend or a positive trend, it would indicate that weight and MPG are not significantly related, which might not be what was expected.
It is important to keep in mind that a scatterplot can only show the relationship between two variables and cannot provide a definitive explanation of the cause-and-effect relationship between them
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Complete Question: you created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. does the graph show any trend? if yes, is the trend what you expected? why or why not?
Use the figure below to answer the following questions.
10.
Name the vertex of the angles.
11.
12.
Name a point in the interior of ZCOB.
Name the sides of 22.
B
Q.
57°
2
43°
°F
A
1) Vertex - A,B,C,O,Q,F
2) Points in the interior of ∠COB - Q,F
3) Sides of ∠2 - side OC and side OA.
What is Interior angles?
Interior angles can be generated in two methods in geometry. The first occurs within a polygon, whereas the second occurs when parallel lines are cut by a transversal. Angles are classified into many sorts based on their measurements.
1) Vertex of angles would be A,B,C,O,Q,F
2) The points in the interior of ∠COB would be, Q,F
3) The sides of ∠2 would be, side OC and side OA.
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given the following frequency table of values, is the mean or the median likely to be a better measure of the center of the data set? value232425262728frequency434424
The Mean likely to be a better measure of the center of the data set.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Since Median represents the middle value of the given data when arranged in a particular order.
The measure of central tendency is the value that best describes a data set.
The measure of central tendency could be the mean, mode, and median
Recall that the best measure of central tendency is the mean
In this exercise, since the data values and the frequency of occurence, the measure of center that best describes the set of data in the table is the mean (Average).
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help me: A circle has a diameter of 140 cm.
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.
Answer:
440cm (to 3 s.f.)
Step-by-step explanation:
circumference= πd
= π×140
= 440cm (to 3 s.f.)
A ladder leans against the wall of a building. The ladder measures
41 inches and forms an angle of 42° with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.
We can use trigonometry to solve this problem. Let's call the height of the ladder "h" and the distance from the wall to the base of the ladder "d".
From the problem, we know that the ladder forms a 42° angle with the ground. This means that the sine of the angle is equal to the opposite side (h) over the hypotenuse (41 inches):
sin(42°) = h/41
We can solve for h by multiplying both sides by 41 and taking the sine of 42°:
h = 41 × sin(42°)
h ≈ 28.61 inches
So the top of the ladder is about 28.61 inches from the ground.
To find the distance from the wall to the base of the ladder, we can use the cosine of the angle:
cos(42°) = d/41
We can solve for d by multiplying both sides by 41 and taking the cosine of 42°:
d = 41 × cos(42°)
d ≈ 31.15 inches
So the base of the ladder is about 31.15 inches from the wall.
The equation of line g is y = 6x - 7. Line h, which is parallel to line g, includes the point
(1, 1). What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
DjO
Answer:
y = 6x -5
Step-by-step explanation:
You want the equation of the line through (1, 1) that is parallel to the line y = 6x -7.
Parallel lineThe parallel line will have the same slope. In this slope-intercept form, that means the x-term is the same. The constant is chosen to make the line pass through the given point:
y = 6x +b . . . . . . . . . . . . . . where 'b' is the new y-intercept
b = y -6x = 1 -6·1 = -5 . . . . solve for b, use (x, y) = (1, 1)
The desired equation is ...
y = 6x -5
how many different rational numbers between $\dfrac{1}{1000}$ and $1000$ can be written either as a power of $2$ or as a power of $3$, where the exponent is a (possibly negative) integer?
The number of different rational numbers between [tex]$\dfrac{1}{1000}$[/tex] and 1000 that can be written either as a power of 2 or as a power of 3, where the exponent is a (possibly negative) integer, is 33.
To find all of the possible rational numbers, we need to find all the integer exponents for 2 and 3 that satisfy the conditions. [tex]2^0 = 1, 2^{-3} = 1/8, 2^{-2} = 1/4, 2^{-1} = 1/2, 2^1 = 2, 2^2 = 4, 2^3 = 8[/tex], and so on.
Similarly, for 3, we have [tex]3^0 = 1, 3^{-3} = 1/27, 3^{-2} = 1/9, 3^{-1} = 1/3, 3^1 = 3, 3^2 = 9, 3^3 = 27[/tex], and so on.
By combining the positive and negative exponents of 2 and 3, we get 33 different rational numbers that satisfy the conditions.
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consider a linear system with the same number of equations as variables. when does this system have a unique solution?
The two system of linear equation with two variables has unique solution if and only if ( a₁ / a₂ ) ≠ ( b₁ / b₂ ) ≠ ( c₁ / c₂ ).
Let us consider two linear equation with two variables 'x' and 'y'.
Number of equations are same as number of variables
⇒We have two system of linear equation that is :
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Condition for system of linear equation has unique solution is:
( a₁ / a₂ ) ≠ ( b₁ / b₂ ) ≠ ( c₁ / c₂ )
⇒ lines intersect at one point gives unique solution.
Therefore, the linear system of equation with two variables representing it has unique solution by ( a₁ / a₂ ) ≠ ( b₁ / b₂ ) ≠ ( c₁ / c₂ ).
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puja limbu did 8 out of 10 math problem and raju lama did
11 out of 15 similar math problem express the number of problem solved by each of the them in fraction and identify who did better performance
The equivalent fractions for their ratios are given as follows:
Puja Limbu: 24/30.Raju Lama: 22/30.Hence, due to the higher numerator, Puja Limbu had the better performance.
What are equivalent fractions?Equivalent fractions are fractions that have the same denominator.
The fractions for this problem are given as follows:
Puja Limbu: 8/10.Raju Lama: 11/15.The common denominator is the least common multiple of 10 and 15, which is of 30, hence the equivalent fractions are given as follows:
Puja Limbu: 24/30. -> multiply numerator and denominator by 3, as 30/10 = 3.Raju Lama: 22/30. -> multiply numerator and denominator by 2, as 30/15 = 2.More can be learned about equivalent fractions at https://brainly.com/question/24372153
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A house painter knows that he can cover 400 square feet with a gallon of paint.
Write an equation that shows how the number of square feet the painter can cover, y, depends on the number of gallons of paint available, x
The equation that shows how the number of square feet the painter can cover, y, depends on the number of gallons of paint available, x is y = 400x.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
A house painter knows that he can cover 400 square feet with a gallon of paint.
Let x be the number of gallons of paint.
Let y be the number of square feet the painter can cover.
Number of square feet the painter can cover with 1 gallon of paint = 400
Number of square feet the painter can cover with x gallon of paint = 400x
So y = 400x
Hence the required equation is y = 400x
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