Practice
Example 1
Use the graphs to determine the number of solutions the system
has. Then state whether the system of equations is consistent or
inconsistent and if it is independent or dependent.
1. y=x-1
y = -x + 1
3. y = x + 4
2x - 2y = 2
5. y = 0.5x
y=x+2
7. 2x - 2y = -4
-10x - 5y = 15
2. x-y=-4
y=x+4
4. y=2x-3
2x - 2y = 2
6. 4x+6y=12
2x + 3y = 6
8. 2x + 3y = 10
4x + 6y = 12
Period
GO Practice Spiral Review Extra Practice
Examples 2 and 3
Graph each system and determine the nu
.
2x+3y=6
y=x+4
x-y=-4
A
y=x-1
y=2x-3
2x+3y=10
y=x+2
Date
2x-2y=-4
.
2x-2y=2
y=-x+
y=0.5x
4x+6y=12
-10x-5y=15
Answers
Since the two equations are identical, they intersect in an infinite number of places. They are consistent and reliant as a result.
what is solution ?a value or set of values that, when used as a stand-in for one or more equation's variables, cause the equation to be true. a strategy or approach for resolving a problem, such as the solutions to the equation x2 = 4 being 2 and -2. a description of a resolution. to be more precise: a group of variable values that satisfy an equation. The equation 3(2)+5=11 states that 6+5=11 is accurate. So, the solution is 2.
given
y = 3x + 1
y = 3x + 1
The two equations are independent and consistent since they cross at a single precise location.
y = 3x + 1
y = x + 3
The two equations are independent and consistent since they cross at a single precise location.
y = x + 3
These two equations are incompatible because they do not intersect.
y = x + 3
To identify which line it is, rearrange the first equation into slope-intercept form.
Since the two equations are identical, they intersect in an infinite number of places. They are consistent and reliant as a result.
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Related Questions
What are the values of trigonometric ratios?
Answers
three main trigonometry ratios are sin ,cos and tan.
1- Sine or sin θ = perpendicular / Hypotenuse .
2- Cosines or cos θ = base of triangle / Hypotenuse .
3- Tangent or tan θ = perpendicular of triangle / base of triangle.
Trigonometry
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Trigonometric values are based on the angle theta and the values of the sides of triangle in which the theta angle is made.
for example - value of sin theta is equal to the side opposite to the theta angle divided by hypotenuse of the triangle and we will get the values of the sin trigonometric ratio.
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EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.
Answers
QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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You need to study the satisfaction of customers of a specific restaurant. You decide to order food and talk to those customers sitting next to you. This would most closely describe which type of sampling technique
Answers
This is how the Cluster of sampling technique is best described.
Describe cluster sampling.Cluster sampling divides a population into clusters, which are more compact groupings. From these clusters, they next randomly select a sample. Cluster sampling is a probability sampling approach that is frequently used to explore large populations, especially those that are widely geographically dispersed.Large, dispersed populations should be investigated using cluster sampling. This is because interviewing each individual is expensive, time-consuming, and in some cases impossible. Building more compact, comparable representations of the population under study is made possible by cluster sampling.For instance, if you wanted to investigate the consumption of soda in a certain city, you could use area sampling to divide the city into several regions, or clusters, and then choose out specific clusters to study.Learn more about cluster sampling refer to :
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The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
8:20 =
Ponies
3
Write the ratio of ponies to goats.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio,
possible.
T
123 f() ∞*E ABC αβγ
Rabbits
8
21
7
8
O
1.
Sheep
6
a
DG
Answers
Answer: 1:1
Step-by-step explanation:
We will write a ratio of ponies to goats;
ponies : goats
3 : 3
Next, 3:3 can be simplified to 1:1. This gives us our fully reduced ratio.
The perimeter of a square room is 80 feet. How many floor tiles 1 foot square would be needed to cover the area of the room
Answers
We would require 400 square tiles, each measuring one square foot, to cover the whole surface of the square room.
If the perimeter of the room is 80 feet, we know that all four sides of the square room have the same length. To find the length of each side, we can divide the perimeter by 4: 80 feet / 4 = 20 feet.
Now that we know the length of each side of the room, we can find the area of the room by squaring that measurement: 20 feet x 20 feet = 400 square feet.
To find the number of floor tiles needed to cover the area of the room, we divide the total area of the room by the area of each tile: 400 square feet / 1 square foot/tile = 400 tiles.
So, to cover the entire area of the square room, we would need 400 square tiles of one square foot each.
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please help solve this its for geometry
Answers
Answer:
Step-by-step explanation:
1.RS+ST=RT. so 9y+2+2y+7=15y-11
2.11y+9=15y-11
3.15y-11y=11+9
4.4y=20
finally we find the answer is y=5
solve the inequality. -7x < 35
Answers
[tex]-7x < 35[/tex]
Divide both sides by -7:
[tex]\dfrac{-7x}{-7} < \dfrac{35}{-7}[/tex]
Since we are dividing by a negative number, the sign will reverse.
[tex]\fbox{x} > \fbox{-5}[/tex]
The solution to the given inequality is x > -5 which represents a set of all real numbers x that are greater than -5.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question, as follows:
-7x < 35
To solve the inequality -7x < 35, we first need to isolate the variable (x) on one side of the inequality.
We will divide both sides of the inequality by -7 (since -7 is being multiplied by x on the left side).
However, when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality symbol. So the inequality becomes:
x > -5
This inequality can be read as "x is greater than -5." It is the solution set of all real numbers x that is greater than -5.
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Please help as soon as possible!
22. x=?
23. y=?
Answers
The unknown angles in the parallel lines are as follows;
x = 28
y = 23
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as linear angles, vertically opposite angles, interior angles, corresponding angles, alternate interior angles, alternate exterior angles etc.
using vertical angles and same side interior angles,
5y - 4 + 3y = 180 (same side interior angles are supplementary)
8y - 4 = 180
8y = 180 + 4
8y = 184
divide both sides by 8
y = 184 / 8
y = 23
Hence,
3y = 2x + 13(corresponding angles)
corresponding angles are congruent.
Hence,
3(23) = 2x + 13
69 - 13 = 2x
2x = 56
x = 56 / 2
x = 28
Therefore,
x = 28
y = 23
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Quantity (in lbs.) Value (per lb.) Total
Butterscotch x 2.15 2.15x
Peppermint y 2.35 2.35y
Mixture 10 2.20 22
Using the table, match the items in the following lists.
1 .
x
pounds of butterscotch candy
2 .
$2.35
pounds of peppermint candy
3 .
y
price per pound of butterscotch
4 .
$2.15
price per pound of mixture
5 .
$22.00
cost for ten pounds of mixture
6 .
$2.20
price per pound of peppermints
Answers
By using the table, each of the items in the lists should be matched as follows:
pounds of butterscotch candy: x.pounds of peppermint candy: y.price per pound of peppermint: $2.35.price per pound of butterscotch: $2.15.price per pound of mixture: $2.20.cost for ten pounds of mixture: $22.00.What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.
Based on the information provided in the table, we can reasonably infer and logically deduce that the variable x represent pounds of butterscotch candy while the variable y represent pounds of peppermint candy.
Additionally, a system of equations that models the information provided in the table is given by;
x + y = 10.
2.15x + 2.35y = 22.00.
In conclusion, the total quantity of candies in pounds (lbs.) is equal to 10.
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In deer, the gene $N$ is for normal coloring and the gene $a$ is for no coloring, or albino. Any gene combination with an $N$ results in normal coloring. The Punnett square shows the possible gene combinations of an offspring and the resulting colors from parents that both have the gene combination $Na$.
a. What percent of the possible gene combinations result in albino coloring?
$\%$
b. Show how you could use a polynomial to model the possible gene combinations of the offspring.
The gene combinations could be modeled by the polynomial
Answers
Using Punnett square we know that 25%of the possible gene combinations result in albino coloring.
What is Punnett square?The genotypes of a specific cross or breeding experiment are predicted using the Punnett square, a square diagram.
It bears Reginald C. Punnett's name, who developed the method in 1905.
Biologists use the figure to calculate the likelihood that a child will have a specific genotype.
So, there is only one gene combination that could result in albinism.
4 different gene pairings are possible.
The proportion of gene combinations that might result in albinism.
Coloring is, therefore:
Percentage = 1/4 * 100 = 25%
Therefore, using Punnett square we know that 25%of the possible gene combinations result in albino coloring.
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Correct question:
Genetics In deer, the gene N is for normal coloring and the gene a is for albino. Any gene combination with an N results in normal coloring. The Punnett square shows the possible gene combinations of an offspring and the resulting colors when both parents have the gene combination Na.
What percent of the possible gene combinations result in albino coloring?
Evaluate the expression 2^x- x^22
x
−x
2
2, start superscript, x, end superscript, minus, x, squared for x=5x=5
Answers
The evaluation of the expression 2ˣ - x² when x = 5 is 7
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: 2^x- x^2
Value x = 5
Rewrite the expression as
Expression: 2ˣ - x²
Substitute the known values in the above equation, so, we have the following representation
2ˣ - x² = 2⁵ - 5²
When the exponents are evaluated. we have
2ˣ - x² = 32 - 25
Evaluate the like terms in the equation
So, we have the following representation
2ˣ - x² = 7
Using the above as a guide, we have the following:
The solution is 7
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(-2) (-3) less greater than equal than 8- (-2)
Answers
The true statement is 6 less than 10
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
(-2) (-3) less greater than equal than 8- (-2)
We start by evaluating each expression
So, we have the following representation
(-2) (-3) = 6
8- (-2) = 10
Substitute the known values in the above equation, so, we have the following representation
6 less greater than equal than 10
6 is less than 10
So, we have
6 less than 10
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Solve the proportion.
8 / 3 = g / 3
a. 1 / 8
b. 9 / 8
c. 8
d. 8 / 9
Answers
Answer the questions. If you get stuck, consider using pattern blocks.
a. How many1/2s are in 4?
b.How many 2/3s are in 2?
c.How many 1/6s are in 1?
Answers
Eight 1/2s are in 4. This can be visualized with pattern blocks, as four triangles (each triangle is 1/2) would be needed to make up a square (4).
What is visualized?Visualization is the process of creating graphical representations of data and information. It can take the form of charts, graphs, diagrams, maps, and other visual representations of data and patterns. Visualization can be used to explore, analyze, and communicate data in an effective and meaningful way, helping to make complex data more accessible and easier to understand. Visualization can also help to uncover trends and relationships that might otherwise be difficult to detect.
b. Three 2/3s are in 2. This can be visualized with pattern blocks, as three hexagons (each hexagon is 2/3) would be needed to make up a rectangle (2).
c. Six 1/6s are in 1. This can be visualized with pattern blocks, as six rhombuses (each rhombus is 1/6) would be needed to make up a hexagon (1).
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Need the answer plsss!
Answers
By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.
what is polynomial ?The location on the y-axis where the slope of the line passes is known as the intersection point in mathematics. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to look like slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.
given
(4 - a) * ( a3 + 7a - 18 )
= 4a3 + 28a - 72 - a4 + 7a2 + 18 a
= a3 + 3a2 + 46a + 72
By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.
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Do the ratios 5/15 and 1/3 form a proportion?
Answers
Answer:
Step-by-step explanation:
We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.
5/15 = 1/3
5*3 = 15*1
15 = 15
as the left-hand side is equal to the right side. So, these fractions are in proportion.
Can I get help in number 6?
Answers
Answer:
Trim A
Inches = 36
Feet = 3
Yards = 1
Trim B
Inches = 216
Feet = 18
Yards = 6
Type in the missing values to complete the simplified form of the expression 4x-4+3y+ 6-2x+3y.
__ x +__ y + __
Answers
Answer:
2x+6y+2
Step-by-step explanation:
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What is a dual of a formula?
Answers
The dual formula is a formula which we get when we replace the symbol ∨ by ∧ , ∧ by ∨ , T by F or F by T.
Basically , we can say that it is obtained by replacing tautology by contradiction.
There are certain rules which are to be followed while applying dual formula which are,
Some symbols, example ¬ remains the same while finding dual.If we will find the dual of a dual we will get the original statement.T (tautology) and F (contradiction) are duals of each other.T is changed to F and vice-versa.S1 is a tautology if and only if S2 is a contradiction.
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Find the commission on a 1,250 sale with a commission rate of 5%.
Please help only if you know it and please explain the answer
Answers
The commission on the sale would be $62.5
To find the commission on a sale, you can use the following formula:
Commission = Sale Amount x Commission Rate
Sale Amount: the total value of the sale
Commission Rate: the percentage or decimal value of the commission rate (e.g. 5% = 0.05)
The commission on a sale can be calculated by multiplying the total sale amount by the commission rate.
In this case, the commission on a 1,250 sale with a commission rate of 5% would be:
= 1,250 x 0.05
= 62.5
So the commission on the sale would be $62.5
It's also worth noting that commission rate is given as a decimal and not a percentage. 5% is 0.05 as decimal.
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What is the equation of the line graphed below?
Answers
Answer: -2/3x is the slope and the beginning amount is 5 so the equation would be -2/3x+5.
Step-by-step explanation:
Once you find the slope using the formula rise/run you will get 2/3 but since the slope is going downwards it would be -2/3 which gives you the mx. Now to find the beginning amount look where the line intersects the graph which will give you the equation.
how to graph a parent function and describe the transformations it obtains?
Answers
The graph of the function f(x) = -2|x-3|+1 is attached below.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
f(x) = -2|x-3|+1
First |x-3| shows there is horizontal shift by 3 units.
Now, '+1' shows there is Vertical shift by 1 unit.
and, 2|x-3| shows there is Vertical stretch and the negative sign shows reflection over x- axis.
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Highschool Algebra: Indicated Operation.
(-ab2)(-6ab2)(3ab)
Answers
Answer:
-18a^3b^5
Step-by-step explanation:
First do -ab^2*-6ab^2=-6a^2b^4
Then multiply that by 3ab=-18a^3b^5
. In the cafeteria
3 out of every 5
students prefer
pizza. If there are
200 students in the
cafeteria how many
students prefer
pizza?
Answers
Answer:
120
Step-by-step explanation:
3/5 of 200 = 120
Step-by-step explanation: Write 3 out of every 5 students as a fraction, (3 over 5). Now divide 5 into 200. You get 40. Multiply that by 3, you get 120. (As a fraction it is 120 over 200). Therefore, 120 students prefer pizza.
What’s is the prime factorization of |-21|
Answers
Jack, Marta, Rand, Todd and 6 more students went apple picking. Every two of these 10 students pick a different number of apples. Combined, the ten students pick 45 apples. Suppose Jack and Marta pick a total of 16 apples; Marta and Rand pick a total of 15 apples; Rand and Todd pick a total of 13 apples. How many apples did Todd pick
Answers
So, Todd picked 1 apple.
We can use the information given to set up the following equations:
Let x be the number of apples Jack picked, and y be the number of apples Marta picked.
We know that x + y = 16 (Jack and Marta pick a total of 16 apples)
Let y be the number of apples Marta picked, and z be the number of apples Rand picked.
We know that y + z = 15 (Marta and Rand pick a total of 15 apples)
Let z be the number of apples Rand picked, and w be the number of apples Todd picked.
We know that z + w = 13 (Rand and Todd pick a total of 13 apples)
We know that the total number of apples picked is 45, therefore x + y + z + w = 45
We can use the equation x + y = 16 to express x in terms of y:
x = 16 - y
We can substitute this into the other equations
(16 - y) + y = 16
y + z = 15
z + w = 13
We can sum all the equations:
(16 - y) + y + y + z + z + w = 45
16 + 2y + 2z + w = 45
From the equation y + z = 15, we can substitute y = 15 - z
16 + 2(15 - z) + 2z + w = 45
16 + 30 - 2z + 2z + w = 45
46 + w = 45
w = 1
Therefore Todd picked 1 apple.
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Eric added up on a number line to find 4 over 5 minus 5 over 10
Answers
Answer: 4/5 minus 5/10 can be simplified as:
(4/5) - (5/10)
It can also be re-written as
(4/5) - (1/2)
To subtract these fractions, we need a common denominator, which is 10 in this case.
So it becomes
(4/5)(2/2) - (1/2)(5/5) = 8/10 - 5/10 = 3/10
So the result of 4/5 minus 5/10 is 3/10 on a number line.
Step-by-step explanation:
Erin is picking out some movies to rent, and he has narrowed down his selections to 5 documentaries, 5 mysteries, 5 dramas, and 7 action movies. How many different combinations of 9 movies can he rent if he wants all 5 mysteries
Answers
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
How are the various combinations determined?The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .
She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).
Five documentaries make up the total.
7 comedies total are available.
Four mysteries are present.
5 horror movies are there.
A total of 14 films, excluding comedies, are available.
If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.
1 * (14*13)/2 = 91
If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.
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evaluate the numerical expression
5^2/5^3
Answers
Answer:
The answer is 5⁻¹ or 1/5
Step-by-step explanation:
5²/5³
Here, we know that the base is the same i.e., 5 so, will use the property;
xᵐ ÷ xⁿ = xᵐ⁻ⁿ5² ÷ 5³
5² ⁻ ³ = 5⁻¹ = 1/5
Thus, The answer is 5⁻¹ or 1/5
What is the solution of
2+4/9x ≥ 4+x?
Answers
Answer:
x < -18/5
this is the answer of you problem