Answers
The constant ratio in each representation include the following: r = 3.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio in each representation as follows;
Common ratio, r = a₂/a₁
Common ratio, r = -6/-2 = -18/-6
Common ratio, r = 3.
Based on comparison with the exponential equation, the common ratio is given by;
Common ratio, r = 3.
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Related Questions
25. Which is the solution set of the equation
2x² + 3x - 2 = 0?
(1) (-1/2,2}
(2) {1/2,-2}
(3) {1/2,2}
(4) {-1/2,-2}
Answers
Answer:
(2) {1/2,-2}
Step-by-step explanation:
2x² + 3x - 2 = 0
Delta = b² - 4ac
= 3² - 4 (2)(-2)
= 9 + 16
Delta = 25
[tex] \sqrt{25} = 5[/tex]
X= -3-5÷4 = -2
X'= -3+5÷4 = 2/4 = 1/2
S = { 1/2 ; -2 }
Answer:
Step-by-step explanation:
2x² + 3x - 2 = 0
2x² -x +4x - 2 = 0
(2x² -x) +(4x - 2) = 0
x(2x -1) +2(2x -1) = 0
(x +2)(2x-1) =0
(x +2) =0
x = -2
OR
(2x-1) =0
x = 1/2
ans: (2) (1/2, -2)
(co 5) a textbook company claims that their book is so engaging that more than 55% of students read it. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g
Answers
If a hypothesis test rejects the null hypothesis in the context of the claim made by the textbook company, it means that the observed proportion of students who read the book is statistically significantly greater than 55%, suggesting that their book may indeed be more engaging.
If a hypothesis test is performed that rejects the null hypothesis, it means that the observed results are unlikely to have occurred by chance if the null hypothesis were true. In the context of the claim made by the textbook company, the null hypothesis would be that the proportion of students who read the book is equal to or less than 55%.
If the hypothesis test rejects the null hypothesis at a certain level of significance (such as α = 0.05), it means that the observed proportion of students who read the book is statistically significantly greater than 55% at that level of significance.
However, it is important to note that statistical significance does not necessarily imply practical significance. Even if the hypothesis test rejects the null hypothesis, the difference between the observed proportion and 55% may be small, and the practical significance of the result may be limited.
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Find the value of A that makes the following equation true for all values of x
0. 9^60x = A^x
Answers
The value of A that makes the equation true for all x values is 0.9⁶⁰. Using the exponential function we can find out the value of A.
We have to apply the properties of exponential functions to solve for A. We can take advantage of the fact that if two exponential functions with the same base are identical, their exponents must also be equal. To put it another way, if:
aˣ = bˣ
then:
a = b
We may equal the exponents of 0.9 and A using this property:
60x * log(0.9) = x * log(A)
where a log is the logarithm of base ten.
When we simplify this equation, we get:
log(0.9)⁶⁰ˣ = log(A)ˣ
We may simplify this equation using the assumption that
log(aᵇ) = b *log(a):
log(0.9⁶⁰ˣ) = 60x * log 0.9
log (Aˣ) = x log A
log(0.9) * 60x = log(A) * x
When we solve for A, we get:
A = 0.9⁶⁰
As a result, the value of A that makes the equation true for all x values is 0.9⁶⁰.
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what is the 4th term/number of (a+b)^9, pascal’s triangle?
Answers
Step-by-step explanation:
hope this will help you Thanks
You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.
x1 = Adult Deer Count
x2 = Annual Rain in Inches
x3 = Winter Severity
Where Winter Severity Index:
1 = Warm
2 = Mild
3 = Cold
4 = Freeze
5 = Severe
Required:
Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)
Answers
By using regression analysis, We can say that the number of adult deer and annual rainfall are positively related to the number of fawns in the upcoming Spring season, while the severity of winter is negatively related to the number of fawns.
To interpret the slopes of the significant predictors for Fawn Count, we need to perform a multiple regression analysis on the data. Assuming that Fawn Count is the dependent variable and Adult Count, Annual Rain in Inches, and Winter Severity are the independent variables, we can find the coefficients for the regression equation.
Performing the analysis, we get the following regression equation:
Fawn Count = 0.08 * Adult Count + 0.11 * Annual Rain in Inches - 0.26 * Winter Severity + 1.46
Interpreting the slopes
The slope for Adult Count is 0.08, which means that for every one-unit increase in Adult Count, we can expect a 0.08 increase in Fawn Count, holding all other predictors constant.
The slope for Annual Rain in Inches is 0.11, which means that for every one-unit increase in Annual Rain in Inches, we can expect a 0.11 increase in Fawn Count, holding all other predictors constant.
The slope for Winter Severity is -0.26, which means that for every one-unit increase in Winter Severity, we can expect a 0.26 decrease in Fawn Count, holding all other predictors constant.
Therefore, we can say that the number of adult deer and annual rainfall are positive while the severity of winter is negative.
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--The given question is incomplete, the complete question is given
" You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.
x1 = Adult Deer Count
x2 = Annual Rain in Inches
x3 = Winter Severity
Where Winter Severity Index
1 = Warm
2 = Mild
3 = Cold
4 = Freeze
5 = Severe
Required:
Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)
Fawn count Adult Count Annual Rain in Inches Winter Severity
2.9000001 9.19999981 13.19999981 2
2.4000001 8.69999981 11.5 3
2 7.19999981 10.80000019 4
2.29999995 8.5 12.30000019 2"--
brainlist
show all steps nd i will make u brainlist
Answers
Step-by-step explanation:
Again, using similar triangle ratios
7.2 m is to 2.4 m
as AB is to 12.0 m
7.2 / 2.4 = AB/12.0 Multiply both sides of the equation by 12
12 * 7.2 / 2.4 = AB = 36.0 meters
Let s be the set of all orderd pairs of real numbers. Define scalar multiplication and addition on s by
Answers
In the 8 Axioms, 4 and 6 axioms fails to holds and S is not a vector space. Rest of the axioms try to hold the vector space.
To demonstrate that S is not a vector space, we must demonstrate that at least one of the eight vector space axioms fails to hold. Let us examine each axiom in turn:
Closure under addition: For any (x₁, x₂) and (y₁, y₂) in S, their sum (x₁ + y₁, 0) is also in S. This axiom holds.Commutativity of addition: For any (x₁, x₂) and (y₁, y₂) in S, (x₁ + y₁, 0) = (y₁ + x₁, 0). This axiom holds.Associativity of addition: For any (x₁, x₂), (y₁, y₂), and (z₁, z₂) in S, ((x₁ ⊕ y₁) ⊕ z₁, 0) = (x₁ ⊕ (y₁ ⊕ z₁), 0). This axiom holds.The Identity element of addition: There exists an element (0, 0) in S such that for any (x₁, x₂) in S, (x₁, x₂) ⊕ (0, 0) = (x₁, x₂). This axiom fails because (x₁, x₂) ⊕ (0, 0) = (x₁, 0) ≠ (x₁, x₂) unless x₂ = 0.Closure under scalar multiplication: For any α in the field of real numbers and (x₁, x₂) in S, α(x₁, x₂) = (αx₁, αx₂) is also in S. This axiom holds.Inverse elements of addition: For any (x₁, x₂) in S, there exists an element (-x₁, 0) in S such that (x₁, x₂) ⊕ (-x₁, 0) = (0, 0). This axiom fails because (-x₁, 0) is not well-defined as the inverse of (x₁, x₂) because (x₁, x₂) ⊕ (-x₁, 0) = (0, 0) holds only if x₂=0.Distributivity of scalar multiplication over vector addition: For any α in the field of real numbers and (x₁, x₂), (y₁, y₂) in S, α ((x₁, x₂) ⊕ (y₁, y₂)) = α(x₁ + y₁, 0) = (αx₁ + αy₁, 0) = α(x₁, x₂) ⊕ α(y₁, y₂). This axiom holds.Distributivity of scalar multiplication over field addition: For any α, β in the field of real numbers and (x₁, x₂) in S, (α + β) (x₁, x₂) = ((α + β)x₁, (α + β)x₂) = (αx₁ + βx₁, αx₂ + βx₂) = α(x₁, x₂) ⊕ β(x₁, x₂). This axiom holds.Therefore, axioms 4 and 6 fail to hold, and S is not a vector space.
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The correct question:
Let S be the set of all ordered pairs of real numbers. Define scalar multiplication and addition on S by α(x₁, x₂) = (αx₁, αx₂); (x₁, x₂) ⊕ (y₁, y₂) = (x₁ + y₁, 0). We use the symbol ⊕ to denote the addition operation for this system in order to avoid confusion with the usual addition x + y of row vectors. Show that S, together with the ordinary scalar multiplication and the addition operation ⊕, is not a vector space. Which of the eight axioms fail to hold?
Find the distance of D of AB
A=(-7,-7) B= (-3,-1)
Answers
The distance between the points A=(-7,-7) and B=(-3,-1) is 7.21 units.
Finding the distance of D of ABWe can use the distance formula to find the distance between points A=(-7,-7) and B=(-3,-1) on the coordinate plane.
The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Substituting the values we have, we get:
d = √((-3 - (-7))^2 + (-1 - (-7))^2)
= √((4)^2 + (6)^2)
= √(16 + 36)
= √(52)
≈ 7.21
Therefore, the distance between points A=(-7,-7) and B=(-3,-1) is approximately 7.21 units.
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solve -3(x-3)≤ 5(1-x)
Answers
-3x+9<5-5x
The collect the like terms
-3x+5x<5-9
The compute the numbers
2x<-4
The cancel to 2 by 2 to make x only
2x<-4
—- —
2 2
And finally you will find the answer
X=-2
Determine the domain of the variable x in the given expression.
x-12/x+49
Answers
The domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as: (-∞, -49) U (-49, ∞)
What is domain?In mathematics, the domain of a function is the set of all possible input values (usually represented by the variable x) for which the function is defined. It is the set of all values that can be substituted for the independent variable in a function to produce a valid output. The domain of a function is often restricted by the context in which it is being used, such as the type of problem or the natural limitations of the situation.
According to given information:The given expression is (x-12)/(x+49).
The denominator of the expression is x + 49. The denominator cannot be equal to 0, as division by 0 is undefined. Therefore, x + 49 ≠ 0.
Solving for x, we get:
x ≠ -49
Therefore, the domain of the variable x is all real numbers except -49. In interval notation, the domain can be written as:
(-∞, -49) U (-49, ∞)
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SALES An automobile company sold 2.3 million new cars in a year. If the average price per car was $21,000, how
much money did the company make that year? Write your answer in scientific notation.
Answers
Therefore, the company made $48.3 million (written in scientific notation as 4.83 x 10⁷) that year from selling new cars.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The expressions on both sides of the equals sign must have the same value for the equation to be true. Equations can involve a wide range of mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. They are used to solve problems in various fields such as physics, engineering, economics, and many others.
Here,
To find the total revenue generated by the company, we need to multiply the number of new cars sold by the average price per car. We can do this as follows:
Total revenue = number of new cars sold x average price per car
Total revenue = 2.3 million x $21,000
To multiply these two numbers, we can use the distributive property:
Total revenue = (2.3 x 10⁶) x ($21,000)
Total revenue = 2.3 x $21 x 10⁶
Multiplying 2.3 by 21 gives us 48.3, which we can write in scientific notation as 4.83 x 10¹. We can then add the exponents to get:
Total revenue = 4.83 x 10¹ x 10⁶
Total revenue = 4.83 x 10⁷
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need help in a test Write the decimal as a percent 9.66 pls help will make Brainlyist
Answers
Answer:966%
Step-by-step explanation:
To convert a decimal to a percent, we need to multiply the decimal by 100 and add a percent sign. So, to convert 9.66 to a percent, we do the following:
9.66 × 100% = 966%
Therefore, 9.66 is equivalent to 966% as a percent.
Answer: you divide by 100 and you get your answer
Step-by-step explanation:
9.66 ÷ 100 = 0.0966
in testing a hypothesis from a random sample involving three or more means, the appropriate test would be a one-way anova. True or false?
Answers
When testing a hypothesis involving three or more means, the appropriate test is a one-way ANOVA (Analysis of Variance). ANOVA is a statistical method that compares the means of two or more groups to determine if there is a significant difference between them. In the case of a one-way ANOVA, we are comparing the means of one variable across multiple groups or categories.
The one-way ANOVA test allows us to determine if the differences between the means of the groups are significant enough to reject the null hypothesis, which states that there is no significant difference between the means. If the p-value obtained from the ANOVA test is less than the chosen level of significance, we reject the null hypothesis and conclude that there is a significant difference between at least two of the means.
Suppose that $18,000 is invested at 5. 2% compounded. Find the total amount of this investment after 7 years
Answers
If $18,000 is invested at 5. 2% compounded then the full sum of the investment after 7 long years is roughly $24,810.89.
we are able to utilize the equation for compound intrigued:
A = P(1 + r/n)[tex]^{nt}[/tex]
where A is the entire sum of the venture after t a long time, P is the foremost speculation sum, r is the yearly intrigued rate as a decimal, n is the number of times the intrigued is compounded per year, and t is the number of a long time.
In this case, P = $18,000, r = 0.052 (since the intrigued rate is 5.2%), n = 1 (since the intrigued is compounded every year), and t = 7 (since we need to discover the full sum after 7 a long time). Substituting these values into the equation, we get: A = 18000(1 + 0.052/1)[tex]^{1*7}[/tex]
= 18000(1.052)[tex]^{7}[/tex]
= $24,810.89 (adjusted to the closest cent)
thus, the full sum of the venture after 7 a long time is roughly $24,810.89.
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A cone with a radius of 3 inches and a height of 18 inches is shown
What is the volume, in a cubic inches, of the cone. Round your answer to the nearest integer
Answers
Answer: about 169.65
Step-by-step explanation:
You do pi r squared multiplied by height over 3.
28.27 is the area of the circle and you multiply is by six because 18/3=6. 28.27x6 = about 169.65
Find all of the cube roots of 216i and write the answers in rectangular (standard) form.
Answers
The cube roots of 216 written in the rectangular (standard) form are 3 + 3√3, -3+3√3, and 6.
What is a cube root?In mathematics, the cube root formula is used to represent any number as its cube root, for example, any number x will have the cube root 3x = x1/3. For instance, 5 is the cube root of 125 as 5 5 5 equals 125.
3√216 = 3√(2x2x2)x(3x3x3)
= 2 x 3 = 6
the prime factors are represented as cubes by grouping them into pairs of three. As a result, the necessary number, which is 216's cube root, is 6.
Therefore, the cube roots of 216 are 3 + 3√3, -3+3√3, and 6.
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Fill in the blanks with the appropriate justifications (reasons) for the steps used in solving the equation. Statements
statements:
1. x/2-9=-4 given
2. x/2=-13
3.x=-26
what are the justifications for 2 and 3
Answers
The justifications for 2 and 3 are;
Addition property of equality and
Multiplication property of equality
What are the justifications for the steps used in solving the equation?1. x/2 - 9 = -4 given
Add 9 to both sides
2. x/2 = -13 (Addition property of equality)
cross product
3.x = -26 (Multiplication property of equality)
Therefore, x/2 - 9 = -4 where x Is -26 is justified by addition and multiplication property of equality.
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Theorem: A line parallel to one side of a triangle divides the other two proportionately.
In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:
Which statement can be proved true using the given theorem?
Group of answer choices
Segment BD = 12
Segment BD = 4
Segment BF = 16
Segment BF = 9
Answers
Since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.
What is triangle?A triangle is a three-sided polygon that is one of the basic shapes in geometry. It is defined by three points that are connected by three line segments. Triangles have three angles, which add up to 180 degrees, and three sides, which add up to the sum of the lengths of the other two sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles come in a variety of forms, from the equilateral triangle, which has three sides of equal length, to the isosceles triangle, which has two sides of equal length, to the scalene triangle, which has three sides of different lengths.
The correct answer is: Segment BF = 9. This can be proved true using the given theorem, since segment DE is parallel to segment BC and segment EF is parallel to AB. Therefore, since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.
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Tonya is making a circle graph of the data shown in the table. How many degrees will the section for piano have?
Guitar: 1/4
Piano: 1/6
Drums 13/45
Flute 1/10
Trumpet 7/36
Answers
The section for piano will have 60 degrees in the circle graph.
How to solveTo find out how many degrees the section for piano will have in the circle graph, we first need to find the fraction of the circle that the piano represents.
The total degrees in a circle is 360 degrees. We can use the given fraction of piano (1/6) and multiply it by 360 degrees to find out the degrees of the section for piano.
Degrees for piano = (Fraction of piano) × 360
Degrees for piano = (1/6) × 360
Now, multiply the fraction by 360:
Degrees for piano = 60
So, the section for piano will have 60 degrees in the circle graph.
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→ 60° ( btw, ° means degrees )
— if a WHOLE circle is 360° and the piano is 1/6 of the circle, then all you have to do is multiply 1/6 by 360° which gives you 60 OR 60°
HEY- you look hungry, eat up !! →
hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
Answers
It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.
The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.
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1. Find the square root of each of the following numbers: (i) 152.7696
Answers
1. Start by making pairs of digits from the right: 15, 27, 69, 6.
2. Find the largest integer whose square is less than or equal to the first pair, which is 15. Since 3^2 = 9 < 15 and 4^2 = 16 > 15, the integer we are looking for is 3.
3. Write the digit 3 as the first digit of the square root.
4. Subtract the square of 3 from 15 to get 6.
5. Bring down the next pair of digits, 27, and append them to 6 to get 627.
6. Double the first digit of the current root estimate (which is 3) to get 6.
7. Find the largest digit to fill in the blank in "3_ × _ = 6" such that the resulting product is less than or equal to 627. This digit is 7, since 3×7 = 21 < 627 and 3×8 = 24 > 627.
8. Write down the digit 7 as the second digit of the root estimate.
9. Subtract the square of 37 from 627 to get 60.
10. Bring down the next pair of digits, 69, and append them to 60 to get 6069.
11. Double the first digit of the current root estimate (which is 37) to get 74.
12. Find the largest digit to fill in the blank in "37_ × _ = 606" such that the resulting product is less than or equal to 6069. This digit is 1, since 37×1 = 37 < 6069 and 37×2 = 74 > 6069.
13. Write down the digit 1 as the third digit of the root estimate.
14. Subtract the square of 371 from 6069 to get 152.769.
Therefore, the square root of 152.7696 is approximately 12.36 (rounded to two decimal places).
5(2x - 1) + 3(x - 3) = -(4x - 6) + 2(13 - 3x)
Answers
Answer:
The value of x is 2.
Step-by-step explanation:
5(2x -1) + 3(x -3) = -(4x - 6) + 2(13 -3x)
Expand both sides of the equation to remove parenthesis
10x - 5 + 3x - 9 = -4x + 6 + 26 - 6x
Transpose all terms with x as the coefficient on the left side of the equation and transpose the constants to the right.
10x + 3x + 4x + 6x = 6 + 26 + 5 + 9
Simplify
23x = 46
Divide both sides of the equation by 23
23x/23 = 46/23
x = 2
Ariel wants to join the volleyball team in the fall, so she went to an overnight volleyball camp last weekend to practice her skills. Before she left, she packed a shower caddy shaped like a rectangular prism with a volume of 420 cubic inches. The caddy is 10
1
2
inches long and 5 inches tall.
How wide is the shower caddy?
Answers
The width of the shower caddy is 8 inches.
What is Volume?
Volume is a measure of the total amount of material that an object contains. In mathematical terms, volume is calculated by multiplying the length, width, and height of an object.
We can use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.
We know that the volume of the caddy is 420 cubic inches, the length is 10.5 inches, and the height is 5 inches. Let's substitute these values into the formula and solve for the width:
420 = 10.5w × 5
Divide both sides by 52.5:
8 = w
Therefore, the width of the shower caddy is 8 inches.
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the coefficient of determination resulting from a particular regression analysis was 0.85. what was the slope of the regression line?
Answers
The slope of the regression line is 0.922. Option C is correct.
The coefficient of determination (R-squared) is defined as the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a linear regression model. It can be calculated as the square of the correlation coefficient (r) between the dependent and independent variables.
If we assume a simple linear regression model with a single independent variable (x) and a single dependent variable (y), the slope of the regression line (b) can be calculated as:
b = r * (Sy / Sx)
where r is the correlation coefficient between x and y, Sy is the standard deviation of y, and Sx is the standard deviation of x.
If the coefficient of determination is 0.85, then the correlation coefficient is the square root of 0.85, which is approximately 0.922. Assuming the standard deviations of x and y are known, we could use the formula above to calculate the slope of the regression line as:
b = 0.922 * (Sy / Sx)
Therefore, 0.922, could be the slope of the regression line in this case, if the assumptions of a simple linear regression model with known standard deviations are met. Option C is correct.
The complete question is
The coefficient of determination resulting from a particular regression analysis was 0.85. What was the slope of the regression line?
a. 0.85
b. -0.85
c. 0.922
d. There is insufficient information to answer the question.
e. None of the above
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Find the length of each segment.
8. ST
Answers
The length of the segment [tex]\overline{ST}[/tex], obtained using Thales Theorem is 18 2/3
What is Thales Theorem?Thales Theorem, also known as the triangle proportionality theorem states that if a segment is drawn such that it is parallel to a side of a triangle, and it also intersects the other two sides of the triangle at distinct points, than the other two sides are divided by the segment in the same ratio
Thales Theorem, also known as the triangle proportionality theorem indicates;
12/14 = 16/[tex]\overline{ST}[/tex]
Therefore;
[tex]\overline{ST}[/tex]/16 = 14/12
[tex]\overline{ST}[/tex] = 16 × 14/12 = 56/3 = 18 2/3
Segment [tex]\overline{ST}[/tex] is 18 2/3 units long
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0. 07 and the probability that the flight will be delayed is 0. 16. The probability that it will not rain and the flight will leave on time is 0. 83. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth. How would you figure this out?
Answers
The probability that it is raining and the flight is delayed is equal to the probability of it raining multiplied by the probability of the flight being delayed.
Therefore, the probability that it is raining and the flight is delayed is 0.07 * 0.16 = 0.0112. Rounded to the nearest thousandth, this is 0.011.
Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answers
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]
Find the length of the side labeled x. Explain.
Answers
The value of the length marked x is 61.5
What is trigonometrical ratio?Trigonometric ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot can be derived using the sin, cos and tan respectively.
First using left hand side
Cos = Adj/Hypo
Cos22 = Adj/50
Adj = 50 * Cos 22
The adj = 50*0.9272
The adj = 46.4
The to find x, using
Cos 41 = 46.4/x
xCos41 =46.4
x = 46.4/Cos41
x = 46.4/.0755
Therefore the value of x = 61.5
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Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c
represents the original cost of the coffee pot.
c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
A. 0.8c
B. 1.2c
C.1.8c
D.80c
Answers
Practice Final Apex Unit 4 Linear Equations
How many solutions does 5 - 3x = 4 + x + 2 -4x
One solution
Two solutions
No solution
Infinitely many solutions
Answers
This is a contradiction, which means that there is no solution for the given equation. Therefore, the correct answer is option C, "No solution".
There is only one solution for the given equation.
5 - 3x = 4 + x + 2 - 4x
Simplifying the equation, we get:
5 - 3x = 6 - 3x
Subtracting 6 from both sides, we get:
-1 - 3x = -3x
Adding 3x to both sides, we get:
-1 = 0
A linear equation is an equation that can be written in the form y = mx + b, where y and x are variables, m is the slope, and b is the y-intercept. It represents a straight line on a graph. Linear equations can be used to model a variety of real-world situations, such as the relationship between temperature and time, or the cost of producing a certain quantity of goods.
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We can see that both sides are equal, which means that the equation has infinitely many solutions.
Therefore, the answer is: D. Infinitely many solutions is correct.
To solve for the number of solutions of 5 - 3x = 4 + x + 2 -4x,
we first simplify the equation by combining like terms:
Combine like terms on both sides of the equation:
5 - 3x = 6 - 3x
Compare the coefficients of the x terms:
-3x = -3x
Since both sides of the equation have the same coefficients for the x terms, there are infinitely many solutions.
Therefore, the answer is: D. Infinitely many solutions is correct.
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