Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F
Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24
Subtract both sides of the equation by 3x
6x + 12 = 24
Subtract 12 from both sides
6x = 12
Divide both sides by 6
x = 2
This should be your answer. Have an awesome day! :)
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.
Which plot description is the best example of a tragedy?
A. A young married couple begins to grow apart as work and family obligations take their toll on the marriage, causing them to split up.
B. A puppy gets lost during a cross-country move and experiences many dangerous situations as he finds his way back to his family.
C. A billionaire oilman loses his fortune and his family after he fails to see the damage his company is doing to the environment.
D. An old man recounts his amazing experiences during the war, remembering all of the friends he made as well as those he lost.
How many liters are in 2.751 ounces?
Use the conversion factor: 1 liter = 33.814 ounces
Rounded to the result to the correct number of significant figures. Express your answer in scientific notation.
Format your answer using the following template to earn credit:
"XXX.XXXX x 10^-+XX units"
Replace the X's with digits, as necessary Replace "units" with the correct unit abbreviation
Replace "-+" with either "+" or "-", as necessary
A ball is thrown vertically upward from the top of a 200 foot tower, with an initial velocity of 5 ft/sec. Its position function is s(t) = –16t2 + 5t + 200. What is its velocity in ft/sec when t = 3 seconds?
Answer:
The velocity would be - 91 ft/sec.
Step-by-step explanation:
Given,
The function that shows the position of the ball after t seconds,
[tex]s(t) = -16t^2 + 5t + 200[/tex]
Since, velocity is the changes in position with respect to time,
That is, if v(t) is the velocity of the ball after t second,
[tex]\implies v(t)=\frac{d}{dt}(s(t))[/tex]
[tex]=\frac{d}{dt}(-16t^2 + 5t + 200)[/tex]
[tex]=-32t+5[/tex]
Hence, the velocity after 3 seconds is,
[tex]v(3)=-32(3)+5=-96+5=-91\text{ ft per seconds}[/tex]
2. Draw the image of ∆RST under the dilation with scale factor ⅓ and center of dilation at the origin. Label the image ∆R’S’T’.
Natalie uses a 15% off coupon when she buys a camera.The original price of the camera is $45.00.How much money does Natalie save by using the coupon?
The money saved by Natalie if, Natalie uses a 15% off coupon when she buys a camera, The original price of the camera is $45.00, is $6.75.
What is percentage?The percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given:
Natalie uses a 15% off coupon when she buys a camera, The original price of the camera is $45.00,
Calculate the money saved by Natalie as shown below,
The money saved by the Natalie = 15% of the original price
The money saved by the Natalie = 15 / 100 × 45
The money saved by the Natalie = 0.15 × 45
The money saved by the Natalie = 6.75
Thus, the money saved by Natalie is $6.75.
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in this right triangle LMN L and M are complentary angles and sin (L) is 19\20 what is cos (M)
Answer:
19/20
Step-by-step explanation:
If you know the ratio of inches to centimeters is 1 to 2.54, how can you find the number of centimeters equivalent to 9 inches? What is the relationship between centimeters and inches?
Ratios are used to show the relationship of variables that are in proportions.
The equivalent of 9 inches is 22.86 centimeterThe relationship between them is: [tex]Centimeter= 2.54 \times Inches[/tex]Given that:
[tex]Inches : Centimeter = 1: 2.54[/tex]
Multiply the ratio by 9, to calculate the equivalent of 9 inches
[tex]Inches : Centimeter = 1 \times 9: 2.54 \times 9[/tex]
[tex]Inches : Centimeter = 9: 22.86[/tex]
Hence, the equivalent of 9 inches is 22.86 centimeter
The relationship between both is as follows:
[tex]Inches : Centimeter = 1: 2.54[/tex]
Rewrite as:
[tex]\frac{Inches}{Centimeter} = \frac{1}{2.54}[/tex]
Cross multiply
[tex]Centimeter \times 1 = 2.54 \times Inches[/tex]
[tex]Centimeter= 2.54 \times Inches[/tex]
Hence, the relationship between them is: [tex]Centimeter= 2.54 \times Inches[/tex]
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The function f(x) = is shown on the graph.
Which statement is correct?
Answer:
c.
Step-by-step explanation:
What is the maximum number of consecutive positive integers that can be added together to create a sum less than 400?
To find the maximum number of consecutive positive integers that sum to less than 400, solve the inequality n(n+1)/2 < 400. The largest integer n that satisfies the inequality is 28, meaning up to 28 consecutive integers can be used.
Explanation:To solve the question on the maximum number of consecutive positive integers that can be added together to create a sum less than 400, we can use the formula for the sum of an arithmetic series. The sum of the first n integers is n(n+1)/2. We want this sum to be less than 400, so we need to solve the inequality n(n+1)/2 < 400 for n.
The inequality simplifies to n^2 + n - 800 < 0. The roots of the equation n^2 + n - 800 = 0 can be found using the quadratic formula or by factoring when possible. The largest integer n that satisfies the inequality will give us the answer. Upon solving, we can find that n = 28 will be the largest integer before the sum exceeds 400. Therefore, we can add up to 28 consecutive positive integers to stay under the limit of 400.
Which shows the factored form of M^2+ 40m + 400
The factored form of the given quadratic equation M² + 40M + 400 is (M + 20)², achieved by noticing that the equation is a perfect square trinomial.
Explanation:The question asks you to find the factored form of the polynomial equation M² + 40M + 400. We can factor this equation by grouping. Factoring is the process of breaking down a complex equation into its simplest terms or variables.
Factoring the Equation
The first step to factoring is to look for a common factor among all the terms. In this case, we don't have one, so we move to the next step: factoring quadratics. A quadratic is an equation where the highest exponent is 2.
The equation given, M² + 40M + 400, it is a perfect square trinomial because 20² equals 400. Factored form of perfect square trinomial (a + b)² = a² + 2ab + b².
Setting a=M and b=20 (since (20)²=400), hence this polynomial factors to be (M + 20².
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determine the equation of the graph and select the correct answer below.
Use the square root property of equality to solve (x – 3)2 = –4. The solutions are a. -1 or 7 b. 1 or 5 c. 3+- 2i d. 3+-4i
Answer:
The solution is 3 ± 2i . The correct option is C.
Step-by-step explanation:
using the square root property of equality to solve (x - 3)² = -4
we have;
(x - 3)² = -4
Take the square root of both-side
√(x - 3)² = ±√-4
x - 3 = ±√4 × √-1
Not that square root of -1 is i
x - 3 = ±2i
Add 3 to both-side of the equation
x -3 + 3 = 3 ± 2i
x = 3 ± 2i
Therefore, the solution are 3 ± 2i
I really need help please.......
The steps to the simplifying the expression (3x^2 −2)(2x^2 +5x+7) are are listed below. Write out an explanation of how it is being simplified from one step to the next. Use at least 4 -5 complete sentences. Be sure that your explanation includes the following words:
-distribute or distribution or distributive property
-like terms
-binomial
-trinomial
-simplify
(3x^2-2)(2x^2+5x+7)
Step 1: (3x^2*2x^2)+(3x^2*5x)+(3x^2*7)-(2*2x^2)-(2*5x)-(2*7)
Step 2: (6x^4)+(15x^3)+(21x^2)-(4x^2)-(10x)-(14)
Step 3-answer:6x^4+15x^3+17x^2-10x-14
Soo.. I'm stuck. On this problem as well :((
The diagonals of a rectangle measures 18.2 inches. the width of the rectangle is 6.7 is 6.7 inches. find the length of the rectangle.
What's the value of X and the measure of angles B and C ? Please help
Jessica is stacking items on a shelf. She has large books that weigh 5 pounds each and medium books that weigh 3 pounds each. The shelf should hold at most 50 pounds. Let x represent the number of large books. Let y represent the number of medium books. Which inequality represents this situation?
Answer:
5x + 3y ≤ 50
Step-by-step explanation:
Given,
The weight of each large book = 5 pounds,
And, the weight of each medium book = 3 pounds,
Thus,
The total weight in pounds of x large books and y medium books = x × weight of each large book + y × weight of each medium book
= 5x + 3y
According to the question,
Total weight ≤ 50 pounds
( Note : at most = less than equal )
⇒ 5x + 3y ≤ 50
Which is the required inequality.
the total surface area of a cube is 726 in^2 what is the length of each side of the cube? it is. in
Paul plans to put concrete on a rectangular portion of his driveway. The portion is 12 feet long and six inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Paul needs is $108.89. Which of the following is closest to the width of the portion of the driveway on which Paul plans to put concrete?
[1 foot = 12 inches; 1 yard = 3 feet]
a) 3 feet
b) 5 feet
c) 8 feet
d) 10 feet
A cube with a side length of 6 mm has a surface area to volume ratio of
What is the value of 4p − 2, when p = 8
The value of the expression 4p − 2, when p = 8 is 30.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
The expression is :
4p -2
The number p is the variable, 4 is the coefficient of the variable and 4,2 are constants.
The variables are the unknown parameters, whose value is not known.
The coefficients of the variables are the numbers multiplied to the variable.
The constants are integers.
The number p is multiplied by 4 and then 2 is subtracted from it.
Subtraction is the basic mathematical operation.
The value of the expression has to be determined at p =8.
To determine, the value of the p will be substituted in the expression.
=> 4 * 8 -2
=> 32 -2
=> 30
The value of the expression when p=8 is obtained.
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The cost of tuition at Johnson Community College is $200 per credit hour. Each student also has to pay $70 in fees. Write an equation that represents the tuition cost C for x credit hours taken.
a. C = 200x + 70
c. C = 200 + 70x
b. C = 70x
d. C = 200x
The equation that represents the tuition cost C for x credit hours taken is C = 200x + 70 thus, option (A) is correct.
What is the equation?There are many different ways to define an equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
As per the given,
Fixed cost = $70
Per credit hour fee = $200
For x credit hour = 200x
Tuition cost C = 200x + 70
Hence "The equation that represents the tuition cost C for x credit hours taken is C = 200x + 70".
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Answer:A) C = 200x + 70
Step-by-step explanation:
If the average of 7 consecutive numbers is 43 what is the largest number
the average is 43, which would be the middle number, since 7 is odd, there would be 3 numbers below 43 and 3 numbers above 43
43 +3 = 46
The largest number is 46
Using the graph below, calculate the average rate of change for f(x) from x = 0 to x = 2.
exponential function going through points 0, negative 2 and 2, 6
x = −4
x = −2
x = 2
x = 4
Answer:
The correct answer is D.) x = 4
I just took the 07.06 quiz
which of the following functions have graphs that contain vertical asymptotes?
power; y=x^n
reciprocal; y=1/x
exponential; y=b^x
logarithmic;y=logb x
root;y=^n sqrt x
could you please explain? I know that two of these answers are correct but I don't fully understand.
Thank you!
If the population of a country grows at a rate of approximately 5 percent per year, the number of years required for the population to double is closest to
The population of the country will double its population in approximately 14 years at a rate of 5 % growth rate every year
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the population be = x
Let the number of years be time = t
Let the percentage of increase be = 5 %
Now , dx / dt = rate of increase of population per change in time
Here, ( dx/dt ) ∝ x
where , x is the population at any time t
Then ( dx/dt ) = Ax
where A is the proportionality constant.
Now , the equation is dx / x= A dt
On , Integrating with respect to x , we get
ln x = At + c
where c is the integration constant
So , on simplifying the equation , we get
Taking exponents on both sides of the equation ,
[tex]x=e^{rt + c}[/tex]
Let [tex]k=e^{c}[/tex]
So , the equation is
[tex]x= ke^{rt}[/tex]
Now , r is the rate of increase, and k is the initial population be x₀
And to find the time t taken to attain double population, so x = 2x₀
[tex]x= ke^{rt}[/tex]
Substituting the values in the equation , we get
[tex]2x_{0} =x_{0} e^{0.05t}[/tex]
[tex]2 = e^{0.05t}[/tex]
Taking logarithm on both sides,
[tex]ln 2=ln ( e^{0.05t} )[/tex]
0.69314=0.05t
t = 0.69317 / 0.05
t = 13.86294 years
Therefore , it takes 13.86294 years to double population
And , 13.86294 ≈ 14 years
Hence , The population of the country will double its population in approximately 14 years at a rate of 5 % growth rate every year
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Arnold walked 3 miles each day for the past 5 days. What is the reasonable range for the total number of miles he walked during this time
Faye’s bank charges her a $2.25 service fee every time she uses an out-of-network ATM. If Faye uses an out-of-network ATM twice a week, how much money does she pay in service fees every year?
a.
$240.25
b.
$225.00
c.
$200.75
d.
$234.00
The amount of money that is being paid by Faye as service fee every year is: d. $234.00.
Given the following data:
Service fee = $2.25Number of times = 2Time = 1 yearTo determine the amount of money that is being paid by Faye as service fee every year:
How to solve a world problem.First of all, we would calculate the amount of money she pays for the service in a week as follows:
[tex]Cost = 2.25 \times 2[/tex]
Cost per week = $4.50
Note: There are 52 weeks in a year.
Thus, we would multiply the cost per week by 52:
[tex]Total \;cost = 52 \times 4.5[/tex]
Total cost = $234.00
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The 100-meter race times at a state track meet are normally distributed with a mean of 14.62 seconds and a standard deviation of 2.13 seconds. Using the Standard Normal Probabilities table, what is the approximate probability that a runner chosen at random will have a 100-meter time less than 15.5 seconds? a.0.1894
b. 0.3409
c. 0.6591
d. 0.7910
e. 0.8106
To solve this problem, we use the t statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = 15.5 seconds or below, u is the sample mean = 14.62 seconds, s is standard dev = 2.13 seconds
z = (15.5 – 14.62) / 2.13
z = 0.41
Using standard distribution tables at z = 0.41, the value of P is:
P = 0.6591 = 65.91%
Hence there is a 65.91% chance the runner will have less than 15.5 seconds of time
answer:
c. 0.6591
Answer:
c. 0.6591
Step-by-step explanation: