Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.
Answers
Maggie made a mistake while combining similar terms of x using vertical angles; the result is -3x rather than 3x, hence the right answer is x = 9.
How do vertical angles work?When two lines intersect, vertical angles are two angles that are opposed by the same vertex and are congruent, meaning they have the same measure.
The vertical angles for this issue are as follows:
4x + 2.
7x - 25.
Since they agree, the following equation may be used to determine the variable x:
4x + 2 = 7x - 25.
The following results from shifting all terms with x to the left side of the equality and all terms that are constant to the right side, with the opposite signal:
4x - 7x = -25 - 2
Combining similar phrases yields the following results:
-3x = -27.
Maggie made a mistake here since 4x - 7x = -3x, thus the proper answer is as follows:
3x = 27
x = 27/3
x = 9.
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Related Questions
Using the function, y = 2x-1
generate a coordinate pair for an x value of 7.
A (13,7)
B (7,13)
C (7.26)
D (7.8)
Answers
This is because if you substitute x into the equation (2 x 7 - 1), you get 13, which is the Y value.
A sixth grade class recorded the number of letters in each students first name. The results are shown in the dot plot.Which is the best representation of the center of this data set?A. 8B. 5C. 7D. 6
Answers
Center of a data set is a single number that sumarizes the entire data, the median is the best measure of center to use in this distribution.
Median is the midpoint value of a data set, where the values are arranged in ascending or descending order:
As a first step let's organize the data in ascending order:
3, 4, 5, 6, 7, 8, 9, 10, 11
The median is 7.
PLS HELP!!!!!!!!!!!!!!!!!!
Answers
Answer: a.) Circle B
b.) 9.42
Step-by-step explanation:
A diameter of 9 cm means that the circumference of Circle A is approximately 28.26 cm.
Circumference = Diameter x π
9 x 3.14 = 28.26
A radius of 6 cm means the circumference of Circle B is approximately 37.68 cm.
Circumference = 2 x Radius x π
2 x 6 x 3.14 = 37.68
37.68 > 28.26
37.68 - 28.26
For these types of problems, I recommend numbermaniacs.com .
Have a nice day!
I need some help on my math, i have a image of it.
Answers
Answer:
[tex]a_{n}[/tex] = 4 - 3(n - 1) and a₈ = - 17
Step-by-step explanation:
a recursive formula is of the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( d is the common difference )
compare to
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3
then d = - 3
the explicit formula for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term
here a₁ = 4 and d = - 3 , then
[tex]a_{n}[/tex] = 4 - 3(n - 1) ← explicit formula
then
a₈ = 4 - 3(8 - 1) = 4 - 3(7) = 4 - 21 = - 17
Kira the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 2 clients who did Plan A and 3 who did Plan B. On Thursday there were 5 clients who did Plan A and 6 who did Plan B. Kira trained her Wednesday clients for a total of 3 hours and her Thursday clients for a total of 7 hours. How long does each of the workout plans last?
Answers
The length of Plan A is 1 hour. The duration of Plan B is 1/3 hours
How long does each of the workout plans last?The first step is to formulate a set of linear equations :
2a + 3b = 3 equation 1
5a + 6b = 7 equation 2
Where:
a - duration of Plan A b = duration of Plan BIn order to determine the value of a, take the following steps:
Multiply equation 1 by 2:
4a + 6b = 6 equation 3
Subtract equation 3 from equation 2
a = 1
In order to determine the value of b, substitute for the value of a in equation 3:
4(1) + 6b = 6
4 + 6b = 6
6b = 6 - 4
6b = 2
b = 2/6
b = 1/3 hours
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Please solve this problem and show work.
Answers
Option c) 4.8 is solution to this equation.
Define cube root.The factor we multiply by itself three times to obtain a number is its cube root. 3 cube root of, end cubic root is the symbol for the cube root. The definition of a cube is the process of multiplying a number by itself three times, and a cube root is the opposite of a cube. Alternately, we could state that a number's cube root gives us a number that, when cubed, gives us the same number and is referred to as a perfect cube. Both the prime factorization approach and the long division method can be used to get a number's cube root.
Given Data
x³ + 9 = 117
x³ = 117 - 9
x³ = 108
x =∛108
Cube root:
x = 4.76
Option c) 4.8 is solution to this equation.
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20 points !!
Which equation describes the
relationship shown in the table?
Ay=1.2(500)*
Oy=500+100
Oy=500(1.2)"
Oy 100+500x
Answers
Answer:
this is a rip off there at no 20 points it only 10
Step-by-step explanation:
Helpppp this assignment is due in like 30 minutessss
Answers
Define two variables and translate the sentence into an inequality.
The savings are at lest 14000 more than the costs
Answers
The two variables are x and y as savings and cost, respectively. The inequality that represents the given sentence is x ≥ 14000 + y.
To represent an unknown number, letters and symbols are used which is known as variables.
The amount of savings and the costs are the unknowns, hence, we can assign a variable to each to represent them.
Let x = savings and y = cost.
Inequality demonstrates the relationship between quantities that are different from each other. The expressions in comparison can be separated by the symbol <, >, ≤, or ≥.
Let x = savings and y = cost.
The given sentence can be expressed as
x ≥ 14000 + y
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What number multiplied by 3/4has a product of 1
Answers
Answer:
4/3
Step-by-step explanation:
We multiply the factors, and we get the answer of 1.
3 x 4 = 12
_ _ _
4 x 3 = 12
12/12 is 1.
The answer is 4/3.
Hope this helps!
Btw, could I get Brainliest? Thanks!
(it took me so long just to type out that equation-)
Answer:
One of these is the answer you want. If you have choices, please list them.
Step-by-step explanation:
Solution and answer
Let x be the number that can be multiplied by 3/4 and get 1.
(3/4)*x = 1 Multiiply both sides by 4
4*(3/4)x = 4*1 Combine
3x = 4 Now divide by 3
3x/3 = 4/3
x = 1 1/3 or x = 4/3 or x = 1.3333333
1/3+2/3x=-5/6x-1/24
step by step pls
Answers
Answer:
x = -1/4, or -0.25
Step-by-step explanation:
1/3 + 2/3x = -5/6x - 1/24
first lets write everything in the common denominator of 24
8/24 + 16/24x = -20/24x - 1/24
now we take all our x's onto 1 side, and all our numbers onto the other side
36/24x = -9/24
lets cancel out all the 24's
36x = -9
x = -9/36
now lets simplify
x = -1/4, or -0.25
Please help
Solve for r
3r - -2 = 20
(The two minus’s wasn’t a mistake it’s minus negative 2)
Answers
Answer: r = 6
Step-by-step explanation:
3r - (-2) = 20
The double minus sign makes it a +2 so lets rewrite
3r + 2 = 20
3r = 18
r = 6
Product a requires 5 hr on machine m, while product b needs 7 he on the same machine. the machine is available for at most 40 hr per week. let x be the number of product a made and y be the number of product b.
Answers
The required linear equation is 5x + 7y = 280
Product A requires = 5 hours on machine
Product B requires = 7 hours on machine
Time when machine is available = 40 hours per week
this means it is available for 40 × 7 = 280 hours
Given ; let x be the number of product a made
and y be the number of product b.
Thus the linear equation can be obtained as
5x + 7y = 280
where x is for the number of product A makes
and y is for the number of product B makes.
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Can I have the food truck she sells tacos and burritos she tells each taco for $3.75 each burrito for $7.75 Hannah Montana less than 430 of worth of tacos and burritos each day write an equity possible values for the number of tacos sold in the number of burrito sorry that was satisfy the constraint
Answers
The inequality for the possible value of the number of tacos sold in the number of burrito will be;
⇒ $3.75x + $7.75y < 430
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Cost of each taco = $3.75
Cost of each burrito = $7.75
And, Hannah Montana less than 430 of worth of tacos and burritos each day.
Now,
Let the number of taco = x
Let the number of burrito = y
So, Cost of taco = $3.75x
Cost of burrito = $7.75y
Since, Hannah Montana less than 430 of worth of tacos and burritos each day.
So, we can formulate the inequality as;
⇒ $3.75x + $7.75y < 430
Therefore,
The inequality for the possible value of the number of tacos sold in the number of burrito will be;
⇒ $3.75x + $7.75y < 430
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Use the following scenario for questions 12-14Alison has $5.10 in quarters and dimes in her piggy bank. She has 27 coins in all.12 Write a system of linear equations to represent the situation.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
piggy bank:
quarters and dimes = $5.10
# quarters and dimes = 27
Step 02:
system of equations:
quarters = q
dimes = d
equation 1:
q + d = 27
equation 2:
0.25q + 0.10d = 5.10
The answer is:
q + d = 27 eq.1
0.25q + 0.10d = 5.10 eq.2
work out the area of a circle with radius of 7.5cm take pi to be 3.142 and give your answer to 2.d.p
Answers
The area of the circle is found to be 176.74 cm² up to two decimal points.
What is defined as the term circle?A circle is a round figure with no corners as well as edges.A circle is defined in geometry as a closed, 2-dimensional curved shape.The center of the a circle is the point in such a circle from which all distances to the circle's points are equal. This distance is known as the circle's radius.Semicircle is ½ a circle because semi means half. It is made by cutting a complete circle across a line segment that passes through the circle's center. This line segment has been known as the circle's diameter.For the given question,
The radius of the circle is 7.5 cm.
The formula for the area of the circle is;
Area = πr²
π = 3.142 and r is the radius.
Put the values.
Area = 3.142 × 7.5²
Area = 176.74
Thus, the area of the circle is found to be 176.74 cm² up to two decimal points.
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9
7
(Simplify your answer.)
Answers
Answer: 9/7 is already in the simplest form.
Find the length of side BC.
Give your answer to 3 significant figures.
C
A
63°
7.4 cm
B
Answers
The length of hypotenuse BC is 19.4 cm.
What is the hypotenuse?A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a specific angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we use specific terminology. The side opposite the right angle is always the hypotenuse of a right triangle.So, a triangle with a right angle and a side.
We must determine the hypotenuse BC.We receive the neighboring side.Let's use the trigonometric cos:
cos(B) = adjacent/hypotenuse cos(71) = AB/BCcos(71) = 6.3/BCBC cos(71) = 6.3BC = 6.3/cos(71)BC = 19.3508Rounding to 3 significant figures: 19.4
Therefore, the length of hypotenuse BC is 19.4 cm.
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The correct question is given below:
Find the lengths of side BC. Give your answer to 3 significant figures.
Log (2x+1) - log(3x -1) =1
Find x
Answers
Answer:
11/28
Step-by-step explanation:
[tex]\log \left(\frac{2x+1}{3x-1} \right)=1 \\ \\ \frac{2x+1}{3x-1}=10 \\ \\ 2x+1=30x-10 \\ \\ 11=28x \\ \\ x=11/28[/tex]
On checking this solution in the original equation, we see it works.
At Sunny's Pizza Parlor, 5 out of every 9 pizzas sold are
pepperoni. Out of the next 144 pizzas, how many would
not be pepperoni?
Answers
====================================================
Work Shown:
5 out of 9 are pepperoni, so 4 out of 9 are not pepperoni
(4 not pepperoni)/(9 pizzas) = (x not pepperoni)/(144 pizzas)
4/9 = x/144
4*144 = 9x
576 = 9x
9x = 576
x = 576/9
x = 64
------------------
Slightly alternative route:
(5 pepperoni)/(9 pizzas) = (y pepperoni)/(144 pizzas)
5/9 = y/144
5*144 = 9y
720 = 9y
9y = 720
y = 720/9
y = 80
Out of the next 144 pizzas, 80 are expected to be pepperoni. That means there should be 144-80 = 64 pizzas that aren't pepperoni.
if i toss a fair coin five times and the outcomes are ttttt, then the probability that tails appears on the next toss is (a) 0.5. (c) greater than 0.5. (e) 1. (b) less than 0.5. (d) 0.
Answers
If there are a total of two probabilities, then the chance of one probability of happening is 0.5, no matter what.
Therefore, A (0.5), is correct.
I need it (ASAP) can some body help me!!!!!!
Answers
Answer:
5. N
6. ?
7. M, L, J
8. JL
Step-by-step explanation:
Graph AFGH with vertices F(- 2, 2) , G(- 2, - 4) and H(- 4, - 4) and its image after the similarity transformation.
Dilation: (x, y) -> (3/4 * x, 3/4 * y)
Reflection: in the x-axis
Answers
The reflection over the x- axis are F" (-3/2 , -3/2), G" (-3/2 , 3) ,
H" (-3 , -3).
Given,
Dilation: (x, y) -> (3/4 * x, 3/4 * y)
From the graph,
Angle FGH with vertices F(- 2, 2) , G(- 2, - 4) and H(- 4, - 4)
To find the reflection.
Now, According to the question:
Let's know the Reflection over x - axis:
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Come to the solution:
F(- 2, 2) , G(- 2, - 4) and H(- 4, - 4)
Dilation: (x, y) -> (3/4 * x, 3/4 * y)
F' (3/4 × -2 , 3/4 × 2) = (-3/2 , 3/2)
G' (3/4 × -2 , 3/4 × -4) = (-3/2 , -3)
H' (3/4 × -4 , 3/4 × -4) = (-3 , -3)
Reflection in the x -axis of FGH are:
F" (-3/2 , -3/2)
G" (-3/2 , 3)
H" (-3 , -3)
Hence, The reflection over the x- axis are F" (-3/2 , -3/2), G" (-3/2 , 3) ,
H" (-3 , -3).
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2/5 of the fish in Gary’s fish tank are guppies. 1/4 of the guppies are red. What fraction of the fish in Gary’s tank are red guppies? What fraction of the fish In Gary’s tank are not red guppies? Please show all steps! I am so confused!
Answers
If 2/5 of the fish in Gary’s fish tank are guppies. 1/4 of the guppies are red. The fraction of the fish in Gary’s tank that are red guppies is 1 / 10. The fraction of the fish In Gary’s tank that are not red guppies is 9 /10.
FractionGiven data:
Fish in Gary's fish tank that are guppies = 2 / 5
Guppies that are red = 1 / 4
Fraction of the fish in Gary's tank that are red guppies = ?
Now let find the fraction
Fraction = 2 /5 × 1 / 4
Fraction = 2 / 20
Simplifying 2/20 to lowest terms = 1 / 10 (red)
b. Fraction of guppies that are not red
Fraction = 1 - 1 /1 0
Fraction = 9 / 10
Therefore 1 /1 10 are red guppies and 9 / 10 are not red guppies.
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2. Task: 6 1/3 yards = ? feet Rule: (number) (unit)
help asap!
Answers
Answer:
18.3 yards
Step-by-step explanation:
6 yards = 18 feet
1/3 yards = 0.3333...
-5y+4=-11 what does y equal
Answers
Answer:
y=3
Step-by-step explanation:
-5y = -15
divide by -5 on both sides to get y=3
Answer: y= -7/5
steps in the picture below!
Calculate the theoretical yield (in grams) of potassium trioxalatoferrate (iii) trihydrate, k3[fe(c2o4)3]â‹…3h2o. trihydrate, k 3 [ fe ( c 2 o 4 ) 3 ] â‹… 3 h 2 o .
Answers
k3[fe(c2o4)3]â‹…3h2o. trihydrate, k 3 [ fe ( c 2 o 4 ) 3 ] â‹… 3 h 2 o . ?
Festival A will be in a rectangular field with an area of 80 000 m²
The greatest number of people allowed to attend Festival A is 425
Festival B will be in a rectangular field 700 m by 2000 m.
The greatest number of people allowed to attend Festival B is 6750
The area per person allowed for Festival B is greater than the area per person allowed
for Festival A.
(a) How much greater?
Give your answer correct to the nearest whole number.
Answers
The area per person allowed for Festival B is 19 m² greater than the area per person allowed for Festival A.
How is the area per person determined?To compute the area per person for each festival, we determine the total areas for Festival A and Festival B.
The total area for each festival is then divided by the most significant number of persons allowed.
Remember that the area is the product of length and width squared.
The area of the rectangular field for Festival A = 80,000 m²
The length of the field for Festival B = 2,000 m
The width of the field for Festival B = 700 m
The area of the rectangular field for Festival B = 1,400,000 m² (700 x 2,000)
The most significant number of persons attending Festival A = 425
The greatest number of persons attending Festival B = 6,750
The area per person for Festival A = 188 m² (80,000 m²/425)
The area per person for Festival B = 207 m² (1,400,000 m²/6,750)
The difference between the area per person for Festival A and Festival B = 19 m² (207 - 188).
Thus, we can conclude that Festival B has 19 m² areas per person allowed than Festival A.
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The ratio of men to women working for a company is 5 to 6. If there are 102 women working for the company, what is the total number of employees?
Answers
Answer:
187 people
Step-by-step explanation:
5 to 6 is the same as 5/6. 5 is the men and 6 is the women. We know that there are 102 women so we can arrange this equation.
[tex]\frac{5}{6}[/tex] = [tex]\frac{x}{102}[/tex]
Re-arrange the equation to find x, or the number of men in the company.
[tex]\frac{(102*5)}{6}[/tex] = x
x = 82
We have found the number of men in the company. Now add the number of men and women.
102 + 82 = 187
187 total people!
Answer: 187 employees
Step-by-step explanation:
ratio of men to women: 5:6
number women working for company: 102
to work out the number of men working for the company, you must first find out what you have to multiply 6 by to get to 102
therefore you do 102/6 which is 17
now you do 17x5 to work out how many men are working for the company which is 85
total number of employees: 102+85=187
Suppose that a restaurant chain claims that its bottles of ketchup contain 24
ounces of ketchup on average, with a standard deviation of 0.2 ounces. If you
took a sample of 49 bottles of ketchup, what would be the approximate 95%
confidence interval for the mean number of ounces of ketchup per bottle in
the sample?
A. 24 ± 0.229
B. 24±0.114
C. 24 +0.029
D. 24 ± 0.057
Answers
The approximate 95% confidence interval for the sample's mean number of ounces of ketchup per bottle is 24 ± 0.029
Explain about the confidence interval mean?Based on the margin of error, the confidence interval is created. The size of the confidence interval for a specific confidence level is determined by three variables. These are population size, sample size, and percentage.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Therefore,
The sample's average bottle contains 24 ounces of ketchup, with a 96% confidence interval of 0.029.
Detailed explanation:
Given
The average is 24 ounces.
0.2 ounces is the standard deviation.
Sample Size, n = 49 ketchup bottles
95% confidence interval (0.95)
The actions that must be taken in order to compute the confidence at this level are as follows:
1. Determining the degree of freedom
You may compute the degree of freedom (d f) by taking 1 out of the sample size.
d f = n - 1
d f = 49 - 1
d f = 48
2. Divide by two after subtracting the confidence level from 1.
α = (1 – .95) / 2 = 0.025
3. Consult the t-distribution table to get the solutions to (1) and (2).
When = 0.025 and there are 48 degrees of freedom (df),
We get 2.0106
4. Separate
=0.2/√49
=0.2/7
=0.028
=0.029
5. The following example is used to compute the 95% confidence interval.
As a result of step 5, X.
in which x = 24
Thus, we have
24 ± 0.029
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