Answer:
We can solve for y in the equation y = 2y - 2 by substituting y = 2x - 5.
Starting with y = 2y - 2, we substitute y = 2x - 5:
2x - 5 = 2(2x - 5) - 2
Expanding the right side:
2x - 5 = 4x - 12
Next, we isolate y by subtracting 2x from both sides:
-2x - 5 = 4x - 12
Adding 2x to both sides:
-5 = 6x - 12
Adding 12 to both sides:
7 = 6x
Finally, we divide both sides by 6 to solve for x:
x = 7/6
So, y = 2x - 5 = 2(7/6) - 5 = 7/3 - 5 = -14/3.
Therefore, y = -14/3 is the solution to the system of equations y = 2y - 2 and y = 2x - 5.
Step-by-step explanation:
30% of 750 using a table
A Ferris wheel has a radius of 218 feet. What is the
total distance covered if the Ferris wheel makes 6
rotations? Write an exact answer in terms of Pi.
The total distance covered by the Ferris wheel after 6 rotations is 2616π feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.
Perimeter = 2π * radius = 2π * 218 feet = 436π
For 6 rotations:
Total distance covered = 6 * 436π = 2616π
The total distance is 2616π feet
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Need help!
Use the Savings plan to find the amount A=? if monthly payments are $250 with APR=4% for 10 years.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The required formula is :
[tex] \qquad \dashrightarrow \sf \: A = P \times \dfrac{{\bigg(1 + \dfrac{APR}{n} \bigg) }^{ny} - 1}{\dfrac{APR}{n}}[/tex]
[tex] \textsf{A = Total accumulated savings } [/tex][tex] \textsf{P = regular deposit } [/tex][tex] \textsf{APR = annual percentage rate } [/tex][tex] \textsf{n = number of payment period per year} [/tex][tex] \textsf{y = number of years } [/tex]Now, plug in the values ~
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + \dfrac{0.04}{12} \bigg) }^{(12 \times 10)} - 1}{\dfrac{0.04}{12}}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + 0.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{1.4908- 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{0.4908}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.249[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A =\$ 36812.45[/tex]
That's the required value ~
What is terminal value formula ?
The terminal value formula helps estimate the value of a business beyond the explicit forecast period,
the terminal value formula = FCFF 6 / (WACC – Growth Rate)
We can say that in a DCF model with a five-year free cash flow projection, the terminal value formula = FCFF 6 / (WACC – Growth Rate)
It could be accountable that in finance, the terminal value (also known as “continuing value” or “horizon value” or "TV") of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most likely often used in multi-stage discounted cash flow analysis and also allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.
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When a number is increased by 5%, the result is 25. What is the original number to the nearest tenth?
Anwser : 23.8
Step 1: Subtract 5% from 25.
25 - (5% of 25) = 25 - (0.05 x 25)
Step 2: Simplify the equation.
25 - (0.05 x 25) = 25 - 1.25
Step 3: Subtract 1.25 from 25.
25 - 1.25 = 23.75
help me answer this pls
Since [tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex], the trigonometric expression [tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex] is proven.
How to prove the trigonometric expression?The trigonometric expression for this problem is defined as follows:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex]
The identity used for the proof is given as follows:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
Hence:
[tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex]
Replacing on the left side of the expression, we have that:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\sqrt{cos^{2}{\theta}}}[/tex]
Taking the square root:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
The tangent is given as the division of the sine by the cosine, hence:
[tex]\frac{\sin{\theta}}{\cos{\theta}} = \tan{\theta}[/tex]
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Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Evaluate each algebraic expression for the given values.
1. 9.8t^2 + 20t + 8 for t = -2, 0, 3.5
2. -3(2.1x - 7.9) for x = -18.1, -0.3, 14.4
The numeric values for each of the expressions are given as follows:
1. 9.8t² + 20t + 8:
t = -2: 7.2.t = 0: 8.t = 3.5: 198.05.2. -3(2.1x - 7.9):
x = -18.1: 137.73. x = -0.3: 25.59x = 14.4: -67.02.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
Then the numeric values are given as follows:
1. 9.8t² + 20t + 8:
t = -2: 9.8(-2)² + 20(-2) + 8 = 7.2.t = 0: 8. 9.8(0)² + 20(0) + 8 = 8.t = 3.5: 9.8(3.5)² + 20(3.5) + 8 = 198.05.2. -3(2.1x - 7.9):
x = -18.1: -3 x (2.1(-18.1) - 7.9) = 137.73.x = -0.3: -3 x (2.1(-0.3) - 7.9) = 25.59.x = 14.4: -3 x (2.1(14.4) - 7.9) = -67.02.Learn more about the numeric values of a function at brainly.com/question/28367050
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Use the Exterior Angle Theorem to find the measure of each angle.
mangleC =
°
mangleD =
°
mangleDEC
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. That means that the measure of angle DEF is equal to the sum of measure of angle C and measure of angle D. Substituting known values gives you 2y + 9 + 6y + 10 = 115, then you can solve
8y + 19 = 115
8y = 96
y = 12
The measure of angle C is 33 degrees, the measure of angle D is 82 degrees, and because the measure of angle DEF is 115 degrees, its supplement angle (DEC) measures 65 degrees.
5x+1=2x+10 (Please include the steps)
Answer:
x = 3
Step-by-step explanation:
5x + 1 = 2x + 10
1.) Subtract 2x from both sides to get 2x on the other side
5x - 2x + 1 = 10
2.) Subtract 1 from both sides to get 1 to the other side
5x - 2x = 10 - 1
3.) Combine like terms
3x = 9
4.) Divide 3 on each side to get x by itself
x = 3
Three numbers are given below. Use prime factorisation to determine the HCF and LCM 1848, 132 and 462
Answer:
The HCF is the highest common factor of 1848, 132 and 462, which is 14.Step-by-step explanation:
Prime factorisation is a mathematical method that breaks a number down into its prime factors, the smallest positive integers that are multiples of that number.The highest common factor of 1848, 132 and 462 is the smallest number that divides all three.The lowest common multiple is the smallest number that multiples all three numbers!Is 1/3(36m+12) and 12m+4 equivalent expressions
The expressions 1/3(36m+12) and 12m+4 are equivalent
What are equivalent expressions?
Equivalent expressions are defined as algebraic expressions that have the same solution but differ in the mode of the arrangement of values.
These expressions are known to have variables, constants, terms, coefficients, and factors.
They are also made up of mathematical operations.
We have the expression;
1/3(36m+12)
Now, expand the bracket
36m/3 + 12/3
Divide the values
12m + 4
Hence, the expression is 12m + 4
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If you flip a coin 8 times, what is the best prediction possible for the number of times it will land on tails?
which one of the following best describes the notion of the significance level of a hypothesis test?The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
The probability of the type I error
The probability of the type II error
The Hypothesis test of probability of the type I error is True.
The Hypothesis test probability of the type II error is False.
The notion of the significance level of a hypothesis test is best described by the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. This is also known as the "p-value." A significance level is often set beforehand, such as alpha (α) = 0.05, and if the p-value is less than alpha, the null hypothesis is rejected.
The probability of a type I error is related to the significance level. A type I error occurs when the null hypothesis is rejected when it is actually true. The probability of a type I error is represented by alpha (α) and is the level of significance that was set for the test.
The probability of a type II error is the probability of failing to reject a false null hypothesis. It is represented by beta (β) and depends on the sample size, the true value of the parameter being tested, and the level of significance set for the test.
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What is the sum of the distinct prime factors of the number 560?
A. 20
B. 14
C. 18
D. 16
E. 1488
The sum of the distinct prime factors is (b) 14
How to determine the sum of the distinct prime factorsFrom the question, we have the following parameters that can be used in our computation:
distinct prime factors of the number 560
The distinct prime factors of the number 560 are
Factors = 2, 5, 7.
When these numbers are added, we have
Sum = 2 + 5 + 7
Evaluate
Sum = 14
Hence , the sum is (b) 14
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What value for x makes the equation −13(x + 11) + 12x = -26 true
Answer:-117
Step-by-step explanation:
-13x-143+12x=-26
-x=-26+143=117
x=-117
based on each set of triangles or parallel lines crest a proportion and solve it to find the missing value
pls help
The value of the x in the given triangle is 7.5 units.
What is proportion?Proportion definition, comparative relation between things or magnitudes as to size, quantity, number.
Given is a triangle having sides, 12, 4 and 10 there is a missing side x we need to find is value,
Using the concept of parallel lines crest a proportion,
x / 10 = 12 / 16
x = 120 / 16
x = 7.5
Hence, the value of the x in the given triangle is 7.5 units.
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Help please the question is in the picture
Answer:
a) [tex]W(x) = 0.50 (3^x)[/tex]
W = tickets worth in $
x = number of balloons popped
b) For 8 balloons popped, number of tickets = 6,561
Tickets worth = [tex]\$ 3,280.50[/tex]
Step-by-step explanation:
The relation between number of balloons popped(x) and the number of tickets is
[tex]f(x) =3 ^ x\\\\f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\\\f(4) = 3^4 = 81[/tex]
each ticket is worth 50 cents
So for x tickets
[tex]W(x) = 0.50 (3^x)[/tex]
Number of tickets for 8 balloons popped
f(x) = 3^8
= [tex]f(x) = 3^8 = 6,561[/tex]
Ticket worth = [tex]0.5 \times 6,561 = \$ 3,280.50[/tex]
If the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees, what is the value of x?.
By the help of congruent , the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees and the value of x is 14
Things that have precisely the same size and shape are said to be congruent. The shapes and sizes need to hold true regardless of how we flip, spin, or rotate the forms. Two triangles that are identical in size and shape are said to be congruent triangles. Even if we flip, turn, or rotate one of two congruent triangles, the other two remain congruent.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.The equal sides and angles may not be in the same location if there is a turn or flip, but they are still there.
The are congruent So,
4x+8=64
Solve for x
X=14
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3/4 x ( z^3 x 4) equivalent expressions
The required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4). which is the correct answer .
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
her, we have,
We have been given expression as:
3/4 x ( z^3 x 4)
To determine the equivalent expression to the given expression
3/4 x ( z^3 x 4)
⇒ 3* z^3
Here the variable z has an exponent is 3 which is positive,
Rearrange the terms of variables z in the above expression
⇒3 · z³
Therefore, the required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4).
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What is the equation of this graph
In this equation, the value of x is fixed at 2, which means that every point on the graph will have the same x-coordinate value of 2. This creates a vertical line that passes through the point (2, y), where y can be any real number.
Therefore, the proper equation for the graph presented is:
[tex]x=2[/tex]
I NEED HELP ON THE FIRST QUESTION ASAP!!!!!!!!
Answer to question 1 is [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex]
=========================================================
Explanation:
The first task is to find the equation of the line through the given points in the table.
Pick any two points you want. I'll pick (0,100) and (50,80)
Determine the slope:
[tex](x_1,y_1) = (0,100) \text{ and } (x_2,y_2) = (50,80)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{80 - 100}{50 - 0}\\\\m = \frac{-20}{50}\\\\m = -\frac{2}{5}\\\\[/tex]
The slope is -2/5.
The y intercept is b = 100 because of the point (0,100)
We go from [tex]\text{y} = m\text{x}+b[/tex] to [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]
Each point from the table is found on this line. For instance, let's check the point (140,44)
[tex]\text{y} = -\frac{2}{5}\text{x}+100\\\\44 = -\frac{2}{5}*140+100\\\\44 = -56+100\\\\44 = 44\\\\[/tex]
This confirms (140,44)
I'll let you check the other points.
------------------
Any point on the line mentioned represents a scenario where César spends all of the $50.
If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.
This means we want to shade the region below the boundary line [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]
We'll replace the equal sign with a "less than or equal" sign
We arrive at [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex] as the final answer to question 1.
Answer: Answer to question 1 is =========================================================Explanation:The first task is to find the equation of the line through the given points in the table. Pick any two points you want. I'll pick (0,100) and (50,80) Determine the slope:The slope is -2/5.The y intercept is b = 100 because of the point (0,100)We go from to Each point from the table is found on this line. For instance, let's check the point (140,44)This confirms (140,44)I'll let you check the other points.------------------Any point on the line mentioned represents a scenario where César spends all of the $50.If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.This means we want to shade the region below the boundary line We'll replace the equal sign with a "less than or equal" signWe arrive at as the final answer to question 1.
Step-by-step explanation:
Find the asymptotes, domain and range.
For the given function,
Vertical asymptote = -5/4
Horizontal asymptote = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Range = (-∞,-5/4) ∪ (-5/4,∞)
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The given function is
[tex]f(x) = \frac{-5x+2}{4x+5}[/tex]
The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.
The horizontal asymptote of the function is when x tends to ∞ .
[tex]\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}[/tex]
The horizontal asymptote of function is at y = -5/4.
Since at x = -5/4, the function becomes undefined.
The domain is all real numbers except x = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Since the function is not defined at y = -5/4 as well, the range is also
(-∞,-5/4) ∪ (-5/4,∞) .
Therefore for the given function,
Vertical asymptote = -5/4
Horizontal asymptote = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Range = (-∞,-5/4) ∪ (-5/4,∞)
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What are the zeros of the function f(x) = x² - 4x² - 5?
+√5 ti
±2, ti
±5, ti
O +√2 ti
You must check the box below prior to submitting your exam!
The zeros of the function f(x) = x² - 4x - 5 are given as follows:
x = -1 and x = 5.
How to solve the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = x² - 4x - 5
The coefficients are given as follows:
a = 1, b = -4, c = -5.
Then the discriminant is given as follows:
D = b² - 4ac
D = (-4)² - 4(1)(-5)
D = 36
Hence the zeros are given as follows:
x = (4 + sqrt(36))/2 = 5.x = (4 - sqrt(36))/2 = -1.More can be learned about quadratic functions at https://brainly.com/question/1214333
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6) Brand X sells 25 kg bags of mixed nuts
that contain 41% peanuts. To make their
product they combine Brand A mixed nuts
which contain 35% peanuts and Brand B
mixed nuts which contain 45% peanuts.
How much of each do they need to use?
{10x + 7y= - 12
9x+ 5y = -16
Answer: x=-4, y=4
Step-by-step explanation:
We can use elimination method to solve this problem.
Let's eliminate y.
In equation 2, use the coefficient of y (i.e 5) to multiply equation 1. DO the same for other equation. Thus,
5(10x+7y=-12)
7(9x+5y=-16)
=> 50x+35y=-60
63x+35y= -112
clearly, y can be eliminated by subtraction.
Therefore,
-13x = 52 [-63+50 and 112-60)]
x = -4.
When x = -4,
9x+5y =-16
9(-4) +5y =-16
5y = 36-16
y=4.
Alexa earns 5% commission as a salesperson. She sold a gold necklace that cost $78. How much commission did Alexa earn?
Answer:
Step-by-step explanation:
= 5 /100 * 78 = 39 /10 = 3.9
$3.90
Which of the following values is a rational number?
A. O √²
B. O √49+√7
C. O √225+ √169
D. O √2x √121
E. O √11x16
The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
Let's check all the options, then we have
A. √(4)² = 4, is a rational number.
B. √49 + √7 = 7 + √7, is an irrational number.
C. √225+ √169 = 25 + 13, is a rational number.
D. √2 x √121 = 11√2, is an irrational number.
E. √11 x 16 = 4√11, is an irrational number.
The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.
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help help help help help help
What is 76 degree F in C?
76 degrees Fahrenheit was found to be equal to approximately 24.4 degrees Celsius using the formula of conversion.
To convert Fahrenheit to Celsius, you can use the following formula:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 76 degrees Fahrenheit, we get:
Celsius = (76 - 32) x 5/9
Celsius = 44 x 5/9
Celsius = 220/9
Celsius ≈ 24.4
Therefore, 76 degrees Fahrenheit is approximately 24.4 degrees Celsius.
On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.
On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.
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What is the distance d between the student and the mirror?
Using the fact that the two triangles must be similar, we will see that d = 7.5 ft
What is the distance between the student and the mirror?To find the distance d we will use the fact that the two triangles must be similar triangles.
That means that the quotients between the legs must be equal.
For the triangle on the left side, the quotient is:
50ft/30ft
For the triangle on the right side, the quotient is:
d/height of the student.
We know that the height of the student is 4.5ft, so that quotient is:
d/4.5ft
Now we can write the equation:
d/4.5ft = 50ft/30ft
Solving this for d, we will get:
d = 4.5ft*(50ft/30ft) = 7.5 ft
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