Step-by-step explanation:
Let's denote the length of the rectangle to be L and the width to be W.
The first sentence tells us that the length, L, is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. What is that quantity? Well that's "twice the width." We can rewrite this sentence in terms of L and W as: L = 2W - 4.
Now we know the length of the rectangle in terms of the width.
The area of a rectangle is given by A = L x W. Using this equation, we can substitute our values for area and length:
A = L x W
96 = (2W - 4) x W
From this we can solve for W and subsequently solve for L using algebra:
96 = (2W - 4) x W
96 = 2W^2 -4W
96 = 2(W^2 - 2W)
48 = W^2 - 2W
W^2 - 2W - 48 = 0
(W - 8)(W + 6) = 0
W = 8 or W = -6
Since W is the side-length of a rectangle, we can disregard the negative solution. Therefore W = 8 ft.
If W = 8, then L = 2W - 4 = 2(8) - 4 = 12 ft.
Lastly, we know the Perimeter of a rectangle is given as P = 2L + 2W. Substituting into this equation we solve for the perimeter:
P = 2L + 2W = 2(12) + 2(8) = 40 ft.
The width of the rectangle will be 38 inches.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches.
L = 2W - 4
Then the equation is given as,
P = 2(L + W)
220 = 2W - 4 + W
110 = 3W - 4
3W = 114
W = 38 inches
The width of the rectangle will be 38 inches.
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Jeff, Gene, and Mike need to eat an entire cake before it goes bad. The cake is cut into 8 pieces.
- Jeff could eat 6 pieces of cake in 2 hours
- Gene can eat 2 pieces of cake in 30 minutes
- Mike can eat 4 pieces of cake in 48 minutes
The pieces can be divided into smaller pieces as necessary - the rates are based on the size of pieces that result when dividing the cake into 8 equal pieces.
Answer these questions below:
1) How many pieces of cake can jeff eat in 1 hour? _________________
2) How many pieces of cake can Gene eat in 1 hour? _____________________
3) How many pieces of cake can Mike eat in 60 minutes? ____________________
4) Will it take Mike, Gene, and Jeff more than 1 hour to each eat the cake, or less that an hour to eat the cake? Explain how you know.
The pieces of cake that Jeff will eat in 1 hour is 3
The pieces of cake that Gene will eat in 1 hour is 4
The pieces of cake that Mike will eat in 1 hour is 5
It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake
How many pieces of cake would they eat in 1 hour?In order to determine the pieces of cake that Jeff can eat in 1 hour, divide 6 by 2.
6/2 = 3 pieces of cake
In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 2 pieces of cake by 2.
2 x 2 = 4 pieces of cake
In order to determine the pieces of cake that Gene can eat in 1 hour, multiply 4 pieces of cake by 60 minutes and divide the result by 48 minutes.
(4 x 60) / 48 = 5 pieces of cake
It will take Mike, Gene, and Jeff more than 1 hour to each eat the cake, because they all eat less than 8 slices of cake in one hour.
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If a rectangular garden is 35 ft. by 25 ft., how many feet of fence are needed to enclose it?
You can find the equation of a line through two points even if one point is not the y -intercept. Find the slope m of the line passing through the two points.Using either point, substitute for x, y , and m into y=m x+b . Solve for b and rewrite y=m x+b for the values of m and b . Write an equation in slope-intercept form for the line passing through each pair of points.
b. (-4,16) and (3,-5)
16 = -4(-3) + 4 is an equation in slope-intercept form for the line passing through points (-4,16) and (3,-5)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We have been asked to write an equation in slope-intercept form for the line passing through (-4,16) and (3,-5)
First we will find the slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-4,16) and (3,-5)
⇒ m = [tex]\frac{-5- 16}{3 - (-4)}[/tex]
⇒ m = [tex]\frac{-21}{7}[/tex]
⇒ m = -3
We know that the equation for slope(m) and y - intercept(b) of a line is given by :
y = mx + b
Here lets take equation 16 = -4(-3) + b .Here x and y is substituted with the second two points.
⇒ 16 = -4(-3) + b
⇒ 16 = 12 + b
⇒ b = 16 - 12
⇒ b = 4
The equation in the slope intercept is as follows:-
16 = -4(-3) + 4
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A bolt of fabric is a large rectangular strip of fabric. Starr-Lyn designs her own fabric. The design is then produced and placed on a bolt that is 81.5 meters (m) long and 1.32 m wide. Part A: Determine the area in Square meters of a bolt of fabric with Starr- Lyn's design.
The area of the rectangle according to the given length and width is 107.58m².
What do we mean by a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal, or a parallelogram with a right angle. A square is a rectangle with four equal-length sides. A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width.The formula of the area of a rectangle: l × w
Now, substitute the values in the formula:
l × w81.5 × 1.32107.58m²Therefore, the area of the rectangle is 107.58m².
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50 PTS - functional notation (yes or no)
Can someone explain what I have to do for this? Do I just plug them in or what also yes or no for what?? Thanks!
The solution to the functional notations would be either yes or no if the function on the left hand side and right hand side are the same. Hence we would have:
c. No: f ( x ) ≠ f ( -x )
d. Yes: ( - x ) = - f ( x )
What is function notation?Function notation is way of writing functions so that they can easily be understood in the mathematical sense. This method is applied in the question to help read the meaning in the question without much explanations.
Given data
f ( x ) = x^3
f ( -x ) = - x^3
How to solve the function notationsc. No f ( x ) ≠ f ( -x )
f ( x ) = x^3 and f ( -x ) = - x^3
f ( x ) is not equal to f ( -x )
plugging the values for the left hand side of the equation gives
x^3
and plugging the values for the right hand side of the equation gives
- x^3
since the left hand side of the equation is not equal to the right hand side of the equation it means that the both sides of the equation are not equal hence equation sated in c is not correct
f ( x ) ≠ f ( -x ) ( take note of the sign )
d. Yes ( - x ) = - f ( x )
( - x ) is equal to - f ( x )
This represents odd functions where the negative sign persists at the left hand side and the right hand side of the equation. Odd function do appear for functions which have negative signs and have odd exponents too.
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If an analysis of variance is used for the following data, what would be the effect of changing the value of ss1 to 50? sample data m1 = 10 m2 = 20 ss1 = 90 ss2 = 70
The decreases SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.
What are the population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
It is given that:
Sample Data
M1 = 10 M2 = 15
SS1 = 90 SS2 = 70
As we know,
The F ratio:
F = S²(x)/S²(y)
From the data given we can say:
Reduce SSwithin and boost the F-magnitude. ratio's
Thus, the decrease SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.
The question is incomplete.
The complete question is attached in the picture.
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Alexandra and her children went into a bakery where they sell cupcakes for 3.25 each and donuts for 1.25 each. Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether. If x represents the number of cupcakes purchased and y represents the number of donuts purchased, write and solve a system of inequalities graphically and determine one possible solution.
explanation up top:) that's the explanation I hope you understand
The number of maximum cupcakes and cookies sold is 6 and 5 respectively.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Alexandra sell cupcakes for 3.25 each and donuts for 1.25 each.
let x be the number of cupcakes purchased and y be the number of donuts purchased.
Now, Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether.
So, x+ y ≥11
and, 3.25x + 1.25y ≤ 25.
Thus, x= 5.625 and y= 5.375
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Can someone explain how I’d solve this?
Answer:
please upload a picture of your question
Please help with problem 25, part a and b Algebra 1, In the attachment.
The equation to represent the number of people that can attend the event will be 18500 +/- 1200.
How to calculate the value?Based on the information, equation to represent the number of people that can attend the event will be 18500 +/- 1200.
The maximum number will be:
= 18500 + 1200
= 19700
The minimum number will be:
= 18500 - 1200
= 17300
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4 is subtracted from the product of 5 and a number.
Answer:
5x-4
Step-by-step explanation:
Product of a number, x , and 5 = 5x
subtract 4 5x -4
gina wilson unit 3 homework 1
Solve for R
60 = -12r
c. Find the exact lengths of the altitudes of triangles B and C.
The length of the altitude of triangle B is
The length of the altitude of triangle C is
The right triangle B and c altitude length are same that is 6.
Given that,
In the given picture there are 2 right triangles.
They are B and C.
2 sides of the triangle B is 3 and [tex]3\sqrt{3}[/tex].
2 sides of the triangle C is 6 and [tex]6\sqrt{2}[/tex].
The angle for both the right triangle B and C is 90°.
We have to find the length of the altitude of right triangles B and C.
By using the Pythagorean theorem we can find the length of the altitude of the right triangle B and C.
The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where the sides of the right triangle are a, b, and c.
First, We will find for the right triangle B.
Here, a=[tex]3\sqrt{3}[/tex] and b=3
Now, substitute in the formulae
[tex](3\sqrt{3})^{2} +3^{2}=c^{2}[/tex]
[tex]27+9=c^{2}[/tex]
[tex]36=c^{2} \\[/tex]
[tex]c^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{c^{2} } =\sqrt{36}[/tex]
[tex]c=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
Now, We will find for the right triangle C.
Here, b=6 and c=[tex]6\sqrt{2}[/tex]
Now, substitute in the formulae
[tex]a^{2} +6^{2}=(6\sqrt{2}) ^{2}[/tex]
[tex]a^{2} +36=72[/tex]
[tex]a^{2}=72-36 \\[/tex]
[tex]a^{2} =36\\[/tex]
Taking square root on both sides
[tex]\sqrt{a^{2} } =\sqrt{36}[/tex]
[tex]a=6[/tex]
Therefore, the length of the altitude of right triangle B is 6.
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Which expression best represents a simpler form of 4m+3(m+n) ?
A 7m+3n
B 4m+3mn
C 3m+4n
D 7m²+3n
The expression 7m+3n best represents a simpler form of 4m+3(m+n).
The Simplified Algebraic Expression is defined as the expression that do not have any like terms and also it cannot be simplified further.
For Example : 2x+5y+6x , the simplified form will be 8x+5y as it cannot be simplified further.
In the given question,
=4m+3(m+n)
=4m+3m+3n ...(multiplying 3 with m and n)
Now Combining the like terms ,
We get ;
=7m+3n
Therefore , the expression that best represents a simpler form of 4m+3(m+n) is 7m+3n.
The correct option is (A) 7m+3n.
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State the property that justifies the following statement.
If 12=2 x+8 and 2x+8=3y, then 12=3y.
The property that justifies the following statement, if 12=2 x+8 and 2x+8=3y, then 12=3y is the transitive property.
Transitive property is one of the properties of equality which states that if there is an equality sign between two values or numbers and one of these numbers is equal to a third numerical value then the other number is also equal to that third numerical value.
Therefore this property can be described as,
if x = y and y = a, then x = a
The transitive property also justifies that if two values x and y are not equal, but y is equal to a, then x cannot be equal to a. That is if x ≠ y, but y = a, then x ≠ a.
So, according to the transitive property, the statement, If 12=2x+8 and 2x+8=3y, then 12=3y is valid.
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Find the measures of the sides of Δ X Y Z and classify
triangle by its sides.
X(-5,9), Y(2,1), Z(-8,3)
The measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ = 6.7 and the triangle XYZ must be an acute triangle
In this questions we have been given the the coordinates of the triangle XYZ.
X(-5, 9), Y(2, 1), Z(-8, 3)
We need to find the measures of the sides of ΔXYZ .
We find the the measures of the sides using distance formula.
XY = √[(1 - 9)² + (2 + 5)²]
XY = √[-8² + 7²]
XY = √(64 + 49)
XY = √(113)
XY = 10.6
Now side YZ
YZ = √[(3 - 1)² + (-8 - 2)²]
YZ = √[(2)² + (-10)²]
YZ = √4 + 100
YZ = √104
YZ = 11.2
And the length of side XZ would be,
XZ = √[(3 - 9)² + (-8 + 5)²]
XZ = √(-6² + -3²)
XZ = √(36 + 9)
XZ = √45
XZ = 6.7
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 6.7² + 10.6²
= 44.89 + 115.54
= 160.43
= 12.67²
And 11.2² = 125.44
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, the measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ = 6.7 and the triangle XYZ must be an acute triangle
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i need to know how to solve this please
Step-by-step explanation:
8z^3+z^2+3z-1/z-1 you can use long division to get 8z^2+(9z^2+3z-1)/(z-1). You can keep dividing this equation until you get 8z^2+9z+12+11/z-1.
By using synthetic division, you can divide it into
1 -1. 8 1 3 -1 (a.k.a their coefficients)
Then bring the 8 down three, 1 down two, and 3, down one. Take that and multiply the one by each, and put it down. 8, 1, and 2. Then, do that with -1, to get -1, -2, and 1. So, the answer is 8z^2+9z+12+11+z-1. But since it's division, and there are 4 terms on one side, and 2 terms on the other, you have to divide it so it's 8z^2+9z+12+11/z-1.
Hope this makes sense!
The formula for simple interest is I=Prt
a. Solve the formula for t, when r is the simple interest per year.
t=_
b. Use the new formula to find the value of t in the table.
The value of t in the table is _ years
a. The formula solved for t when r is the simple interest per year is t = I/Pr
b. Using the new formula, the value of t in the table is 3 years
Simple InterestFrom the question, we are to solve the given formula for t
The given formula is
I = Prt
To solve for t, we will divide both sides of the equation by Pr
I/Pr = Prt/Pr
I/Pr = t
∴ t = I/Pr
b.
I = $75
P = $500
r = 5% = 0.05
t = 75/(500×0.05)
t = 75/25
t = 3 years
Hence, the value of t in the table is 3 years
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Name the property of 8(9 + 0 ) = 8(9)
The property of 8(9 + 0 ) = 8(9) is the identity property of addition.
How to illustrate the information?It should be noted that the identity property of addition states that the sum of 0 and any number will be equal to that number.
In this case, the property of 8(9 + 0 ) = 8(9) is the identity property of addition. This was illustrated as 9 + 0 equals to 9.
Therefore, the property is the identity property of addition.
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Which expression equals 5x/x² - 9 - 4 x / x² + 5x + 6?
(A) 7 x/(x-3)(x+3)(x+2) (B) x²-2 x / (x-3)(x+3)(x+2)
(C) x²+22x / x-3)(x+3)(x+2)
(D) 9x² - 2 x / (x-3)(x+3)(x+2)
The expression that is equal to [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex] is [tex]\frac{x^{2}+22x }{(x+2)(x+3)(x-3)}[/tex].
In the given question
[tex]=\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex].....(i)
First solving the denominator of both the terms ,
=x²-9
=x²-(3)²
=(x+3)(x-3) ...using identity a²-b²=(a+b)(a-b) .....(ii)
=x²+5x+6
=x²+3x+2x+6 ...by splitting the middle term
=x(x+3)+2(x+3)
=(x+2)(x+3) ....(iii)
Substituting the value of (ii) and (iii) in (i)
we get,
[tex]=\frac{5x}{(x+3)(x-3)} -\frac{4x}{(x+2)(x+3) }[/tex]
taking LCM as (x+2)(x+3)(x-3) we get ,
[tex]=\frac{5x(x+2)-4x(x-3)}{(x+2)(x+3)(x-3)} \\ \\ =\frac{5x^{2} +10x-4x^{2} +12x}{(x+2)(x+3)(x-3)}[/tex]
Simplifying the like terms in the numerator we get
[tex]=\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex]
Therefore , the expression that equals [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex] is [tex]\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex].
The correct option is (c).
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The quotient of a number X and 7
Answer: x / 7
Step-by-step explanation:
"the quotient of" represents division, or /.
"a number" represents a variable, in this case, it's x.
while "7" just means the number 7.
Hope this helps!
1. (1.2 × 10³) + (8.3 × 10³)
Answer:
9,500
Step-by-step explanation:
first, remove the parentheses
1.2 x 10^3 + 8.3 x 10^3
Collect the like terms
take 1.2x10^3 + 8.3x10^3 and you will get 9.5 x 10^3
Evaluate the power of 10^3 = 1,000
then do 9.5x1000 = 9,500
Using a calculator, what is the solution of 1080=15³ˣ⁻⁴ ? Round the answer to the nearest hundredth.
The solution of the given equation 1080 = 15³ˣ⁻⁴ is (x = 2.19), round to the nearest hundredth.
What is defined as the logarithmic functions?A logarithmic term represents a number in logarithmic form. A log term is another name for it.
A quantity can also be the sum of two or even more quantities. As a result, a term can consist of the product of two or more quantities, one of which must be in logarithmic form. For such cases, this same terms are known as log terms.
A quantity can also be defined as the quotient of two quantities. But, if a term includes a quotient of quantities, or at least one of the quantities can also be expressed in log form, this same terms are known as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, consider the given equation given in the question;
1080=15³ˣ⁻⁴
Take log on the both sides;
㏒1080 = ㏒15³ˣ⁻⁴
Using the power rule on the second side of the equation;
㏒1080 = (3x - 4)㏒15
Taking log on one side and other variables on other side.
3x - 4 = ㏒1080/㏒15
Use calculator to find the values of both log.
3x - 4 = 2.57
3x = 6.57
x = 2.19
Therefore, the solution of the given function 1080=15³ˣ⁻⁴ is (x = 2.19), rounded up to nearest hundredth.
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In order to design an appropriate touchscreen for a computer, the manufacturer has to consider the average size of the fingers and hands that will be touching the screen. One lab found that the average width of the index ( or pointing ) finger for adults is from 1.6 cm to 2 cm wide.
1. All the measurements on this page are inclusive. Explain what that means for the inequality symbols you will use.
2. Write the average width as an inequality using centimeters.
3. One centimeter = 0.39 inches. Write the average width as an inequality using inches.
The range of the average width of the index finger which is between 1.6 centimeters and 2 centimeters gives;
1. The symbols to use for the inequality are ≤ and ≥
2. The average width expressed as an inequality is; 1.6 ≤ w ≤ 2
3. The inequality for the average width in inches is 0.624 ≤ w ≤ 0.78
How can the inclusive range be expressed as an inequality?1. With regards to working with number ranges or intervals, the term inclusive means that the endpoints of the (closed) interval are included in the range.
The inequality symbol to be used in an inclusive interval are ≤ and ≥ (the symbols < and > are used for an exclusive measurements)
2. The minimum width = 1.6 centimeters
Maximum width = 2 centimeters
The average width in centimeters, w, written as an inequality is therefore;
1.6 ≤ w ≤ 23. The given conversion factor is 1 cm. = 0.39 inches.
Therefore;
1.6 cm = 1.6 × 0.39 in. = 0.624 in.
2 cm = 2 × 0.39 in. = 0.78 in.
The inequality for the average width in inches is therefore;
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Determine whether each relation is a function. (1,1),(2,0),(3,1),(4,3),(0,2)
Range - { 1 , 0, 1 , 3 , 2 } is relation is a function.
What is domain and range ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Definitions of domain and example?
The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .
function. (1,1),(2,0),(3,1),(4,3),(0,2)
Domain - { 1,2, 3 , 4 , 0 }
Range - { 1 , 0, 1 , 3 , 2 }
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On a construction crane, the amount of force needed to move objects is directly proportional to the weight of the objects. If 4 Newtons of force is needed to move an object that is 1200 pounds, how much force would be needed to move an object that is 900 pounds?
Based on the fact that the force needed to move object is directly proportional to the weight of the objects, the force needed to move and object that is 900 pounds is 3 newtons of force.
How much force is needed?When things are directly proportional, it means that they increase by a given amount together and also decrease by the same amount.
If 4 Newtons are needed for 1,200 pounds, the newtons needed for 1 pound is:
= 4 / 1,200
= 1/300 newtons
If there are 900 pounds to be moved, the newtons needed are:
= 1/300 x 900
= 3 newtons of force
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Q2 The length of a roll of ribbon is 30 metres, correct to the nearest half-metre. A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll. Work out the maximum possible length of ribbon left on the roll.
The maximum possible length of ribbon left on the roll is 24.5 m.
Find bounds, Roll
30 → nearest half metre.
0.5 ÷ 2 = 0.25
LB = 30 – 0.25 = 29.75
GB = 30 + 0.25 = 30.25
Piece
5.8 → nearest 10cm or 0.1m
(10÷100=0.1)
0.1÷2 = 0.05
LB = 5.8 – 0.05 = 5.75
GB = 5.8 + 0.05 = 5.85
Max length left = GB roll – LB piece
=30.25 – 5.75
=24.5m
The metric system's default unit of measurement for length. 100 centimeters equal to 1 metre. A meter is a common metric unit that is around 3 feet, 3 inches long. It measures 100 times more than a Centimetre, or 0.01 meters, in size. 1000 meters make up one kilometre.
Hence, the maximum possible length of ribbon left on the roll is 24.5 m.
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a question with a single correct answer
data that consists of numbers
a question that can have a variety of answers
:: statistical
III
:: numerical
nonstatistical
Answer:
a question with a single correct answer: non statistical
data that consists of numbers: numerical
a question that can have a variety of answers: statistical
Step-by-step explanation:
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need help fast !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The correct location of the system of equations are;
Single solution;
y = 11 - 2•x
4•x - y = 7
x + y = 15
2•x - y = 15
No solution;
2•x + y = 7
-4•x = 2•y + 14
x = 12 - 3•y
3•x + 9•y = 24
Infinite solution;
2•x + y = 7
-6•x = 3•y - 21
What are the types of solutions to linear system of equations?The possible system of equations and their solution are presented as follows;
System of equations
y = 11 - 2•x4•x - y = 7Solution;
4•x - y = 7
Therefore;
11 - 2•x = 4•x - 7
6•x = 18
x = 3; Single solution;
System of equations
2•x + y = 7-4•x = 2•y + 14Solution;
2•x + y = 7 gives;
y = 7 -2•x
-4•x = 2•y + 14 gives;
y = -2•x - 7
7 -2•x = -2•x - 7
0 = 14, no solution
System of equations
x = 12 - 3•y3•x + 9•y = 24Solution;
x = 12 - 3•y gives;
3•x + 9•y = 24 gives;
x = (24 - 9•y) ÷ 3 = 8 - 3•y
Which gives;
12 - 3•y = 8 - 3•y
12 = 8 no solutionSystem of equations
2•x + y = 7-6•x = 3•y - 21Solution;
2•x + y = 7 gives;
y = 7 - 2•x
-6•x = 3•y - 21 gives;
3•y = 21 - 6•x
y = 7 - 2•x
7 - 2•x = 7 - 2•x Infinitely many solutions
System of equations
x + y = 152•x - y = 15Solution;
x + y = 15 gives;
y = 15 - x
2•x - y = 15 gives;
y = 2•x - 15
Which gives;
15 - x = 2•x - 15
3•x = 15 + 15 = 30
x = 30 ÷ 3 = 10 Single solution
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Solve for the missing exponent
(4a^3)^2=16a
Step-by-step explanation:
= 16 a^6=16a divide for 16
a^6=a there are only two solutions 1 and 0 cause:
1^6=1 and 0^6=0
