in rectangle abcd measure of angle d =(3x+15) measure b =(6x-42) find measure of angle a
Answers
So, we have that m∠B = m∠D. Therefore,
[tex]6x-42=3x+15\\3x=57\\x=19[/tex]
Now, let's substitute for x back into the expression for either ∠B or ∠D to find it's angle measure.
m∠B = [tex]6(19)-42=72[/tex]
Now, remember that ∠B or ∠D are supplements of ∠A.
So, m∠B + m∠A = 180°.
That means m∠A = 180° – 72° = 108°.
That seems reasonable, because A appears to be an obtuse angle.
Related Questions
When translating a figure using a combination of two translations, is the resulting figure congruent to the original figure?
Answers
When translating a figure using two translations, the end result is a figure that is congruent to the original. This is due to the fact that translations move the shape without altering its size or orientation.
Explanation:Yes, when translating a figure using a combination of two translations, the resulting figure is congruent to the original figure. When a figure is translated, it is moved without being turned or flipped, the size and shape remains the same, hence making it congruent. For example, consider a parallelogram. If two different vectors A and B are chosen to translate it, following the rules of vector summation, the figure moved, known as the resultant vector retains the dimensions and angles of the original parallelogram, albeit in a different location.
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PLEASE HELP WILL GIVE 30 POINTS
Add or subtract. Show your work for each problem
a. (x^2-4x+5)+(7x^2+2x-3) b. (7x^2+4x-6)-(2x^2-3x+1)
Answers
To solve this problem you must apply the proccedure shown below:
a) You must sum terms with same exponents, therefore, you have that the sum of these two polynomials is:
[tex] (x^{2}-4x+5)+(7x^{2}+2x-3) [/tex]
[tex] 8x^{2} -2x+2 [/tex]
b) First, you must mulitply the signs of the second polynomial by the negative sign, and them, you apply an algebraic sum. Therefore, the result is:
[tex] (7x^{2}+4x-6-2x^{2}+3x-1) \\ 5x^{2} +7x-7 [/tex]
The answers are: a)[tex] 8x^{2} -2x+2 [/tex]; b) [tex] 5x^{2} +7x-7 [/tex]
a)
x² - 4x + 5 + 7x² + 2x - 3
8x² - 2x + 2
b)
7x² + 4x - 6 - (2x² - 3x + 1)
7x² + 4x - 6 - 2x² + 3x - 1
5x² + 7x - 7
Please help for number 2!
Answers
What is Eleven less than two times a number is equal to 27
Answers
If you want me to solve 2x - 11 = 27 than its below:
2x = 11 + 27
38 = 2x
38/2 = x
19 = x
-Love, live, and watch anime.
11 less implies: -11
two times a number (x) implies: 2x
equal to 27 implies: = 27
Set the equation together.
2x - 11 = 27 is your equation.
Solve for x. Note the equal sign. What you do to one side you do to the other. Add 11 to both sides
2x - 11 (+11) = 27 (+11)
2x = 38
Isolate the x. Divide 2 from both sides.
2x/2 = 38/2
x = 19
hope this helps
HEEEEEEEEEEEEEEEEEEEEEEELP
Answers
y = 3x - 8
Explanation:
The equation in slope-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept
We are given that the slope = 3
Therefore, the equation becomes:
y = 3x + c
Now, we need to get the value of c. We are given that the point (6,10) belongs to the line. Therefore, we will substitute with this point in the equation of the line and solve for c as follows:
y = 3x + c
10 = 3(6) + c
10 = 18 + c
c = 10 - 18
c = -8
Based on the above, the equation of the line is:
y = 3x - 8
Hope this helps :)
a plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour.if the plane resultant speed due to the wind is 180 miles/hour,what is the plane's actual speed. rounded to the nearest integer
Answers
I hope this helped!
The plane's actual speed is 135 miles/hour if the plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour option (C) 135 miles/hour is correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
The question in incomplete.
The complete question is:
A plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour. If the plane's resultant speed due to the wind is 180 miles/hour, what is the plane's actual speed, rounded to the nearest integer?
120 miles/hour130 miles/hour135 miles/hour140 miles/hourFrom the data given in the question:
Using Cosine Law:
c² = a² + b² - 2 ac cos C
180² = 50² + x² - (2×50)x cos 150°
32400 - 2500 - x² = 86.6x
29,900 - x² = 86.6 x
x² + 86.6x - 29900 = 0
After solving the above quadratic equation:
x = 135 miles/hour
Thus, the plane's actual speed is 135 miles/hour if the plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour option (C) 135 miles/hour is correct.
Learn more about the angle here:
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Each box of Fred’s Fudge is constructed from 2 triangles and 3 rectangles. What is the shape of each box?
Answers
The answer is a rectangular prism
The boxes of Fred's Fudge, made of 2 triangles and 3 rectangles, are most likely shaped as triangular prisms.
Each box of Fred's Fudge is constructed from 2 triangles and 3 rectangles. The shape of each box can be determined by visualizing how the triangles and rectangles are assembled. In most cases, packaging that includes triangles would imply the presence of triangular prism shapes, where the triangles serve as the ends and the rectangles connect the corresponding sides of the triangles. Hence, it's reasonable to conclude that the shape of each box is likely a triangular prism.
Carmela randomly selected 65 stamps from a stamp collection. Eleven of these were commemorative stamps. What is the interval estimate for the proportion of commemorative stamps in the entire collection if the sampling method had a margin of error of ±0.025?
Answers
p = 11/ 65 = 0.1692
This will make it easier to compute for the interval estimate. Interval Estimate = probability ± margin of error
upper limit = 0.1692 + 0.025 = 0.1942
lower limit = 0.1692 - 0.025 = 0.1442
So the interval estimate is 0.1442 < x < 0.1942
PLEASE HELP!
The manager of a sawmill wants to find out what percentage of the boards that the mill produced are defective.
Which sampling methods are likely to be biased?
Select each correct answer.
The manager selects 20 boards at random each day for 5 days and examines them.
Every 40th board produced over the course of 1 week is selected and examined.
On 1 day, an hour after the sawmill begins production, 30 boards in a row are selected and examined.
The manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week were defective. Results from the first 5 customers to respond are tallied
Answers
The third and fourth methods described are more likely to yield unbiased results, whereas the first and second methods are prone to bias.
The manager of a sawmill wants to find out what percentage of the boards that the mill produced are defective. To determine this accurately, the manager must use unbiased sampling methods.
Biased Sampling Methods
On 1 day, an hour after the sawmill begins production, 30 boards in a row are selected and examined: This method is likely to be biased because it only considers boards produced during a specific timeframe, which might not represent the entire production cycle.
The manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week were defective. Results from the first 5 customers to respond are tallied: This method is biased due to its reliance on customer self-reporting and the fact that only the first few respondents are considered, which might not be representative.
Possibly Unbiased Sampling Methods
The manager selects 20 boards at random each day for 5 days and examines them: This sampling method is likely to be unbiased as it involves random selection across multiple days, covering a broader production span.
Every 40th board produced over the course of 1 week is selected and examined: This method is less likely to be biased as it systematically covers the production over a week, though it might miss defects that occur in clusters shorter than 40 boards.
In summary, the third and fourth methods described are more likely to yield unbiased results, whereas the first and second methods are prone to bias.
Write an algebraic expression that illustrates the multiplicative identity.
Answers
Ex: 1(m) or 1 x m.
The reason for thusbis that when you are multiplying you are representing groups of something, so 1 group of anything or m, would just be that anything or m in this case!
Answer:
The multiplicative identity shows us that any time you multiply something by the number 1, the result would be what you started with.
Ex: 1(m) or 1 x m.
The reason for thusbis that when you are multiplying you are representing groups of something, so 1 group of anything or m, would just be that anything or m in this case!Step-by-step explanation:
A popular brand of running shoes costs a local store $68 for each pair. If the store sells the shoes for $119, what is the percent of increase in the price?
Answers
help please and thank you.
Answers
.. 8, 10, 14, 15, 18, 22, 22, 30, 33
b) min: 8
.. med: 18
.. max: 33
.. Q1: med of first 4: 12
.. Q3: med of last 4: 26
Is a product of a rational and irrational number, rational or irrational? Give an example
Answers
A picture measuring 2.5" high by 6" wide is to be enlarged so that the width is now 18 inches. How tall will the picture be?
Answers
2.5 to 6 so if 6 is raised to 18 thats times 3 so just times 2.5 by 3 and you would 7.5
2.5" long/6" wide = t/18 " wide
6t = 18*2.5
6t = 45
t = 45/6
t = 7.5 inches
The probability that an event will occur is fraction 7 over 8. Which of these best describes the likelihood of the event occurring? a.Likely b.Certain c.Unlikely d.Impossible
Answers
Answer:
A
Step-by-step explanation:
A is the correct answer because, 7/8 is very likely. It isn't certain though. There is a 12.5 % chance that it can occur.
What is 3/4 of a year ? Write in months.
Answers
To make this a bit simpler, first, we should convert a year into months:
1 yr = 12 mo
Now, we multiply 12 by 3/4, since we're trying to find 3/4 of a year.
12 * 3/4 = 9
So, our answer would be 9 months.
Hope this helps!
Find the first term of the arithmetic sequence in which t22=1008 and d= -8
Answers
t22 = 22nd term
d = common difference
d = -8
n = number of terms
n = 22
.
tn = t1 + (n - 1)d
t22 = t1 + (n - 1)d
1008 = t1 + (22 - 1)-8
1008 = t1 + (21)-8
1008 = t1 + 168
1008 - 168 = t1
840 = t1
Please need help on this any clue any one
Answers
Answer:
A
Step-by-step explanation:
it makes the most sense
Which of the following represents “the sum of the abscissa and the ordinate is negative four”?
A. x + y = -4
B. xy = 4
C. 4x + 4y = 0
Answers
When you are working with coordinate points, the x-value in the point is called the abscissa. The y-value in the point is called the ordinate.
Therefore all you have to do is add the x and y of the coordinates to get our equation. Don't forget that the sum has to be -4 according to the problem.
The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
The area of this triangle, A, is equal to the perimeter of this triangle.
Create a system of equations to model this situation. Determine if there are any solutions, and, if possible, whether or not they are viable.
How many total possible solutions are there to this system?
Of any possible solutions, how many are viable solutions for this situation?
Answers
y = 1/2(x²) - (7/2)x
The equation to represent the perimeter of the triangle would be:
y = 3x - 6
The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).
Explanation
The area of a triangle is found using the formula
A = 1/2bh
For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x
We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x
The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)
Combining like terms we get:
P = 3x - 6
We will replace P with y, so we have:
y = 3x - 6
Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:
3x - 6 = 1/2(x²) - (7/2)x
It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x
We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x
When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12
This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)
Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.
Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)
We cannot have a negative perimeter, so the only viable solution is (12, 30).
Answer:
two possible and one viable
Step-by-step explanation:
hope this helps!
0.000309 in scientific notation
Answers
Writing in scientific notation means a should be
0 ≤ a < 10
Therefore, 0.000309 will be written as
3.09 x 10ⁿ
3 is the 4th decimal place value
so n = - 4
3.04 x 10⁻⁴
Can anyone PLEASE help me with this? Will mark brainliest
Simplify the expression.
2 1/4x+(4 1/3x-7 4/5) divided by 2 3/5
Answers
hope this helps
Question
--------------------------------------
[tex]2 \dfrac{1}{4} + ( 4\dfrac{1}{3} x - 7 \dfrac{4}{5} ) \div 2 \dfrac{3}{5} [/tex]
--------------------------------------
Start with the bracket
--------------------------------------
--------------------------------------
Change to improper fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + ( \dfrac{13}{3} x - \dfrac{39}{5} ) \div 2 \dfrac{3}{5} [/tex]
--------------------------------------
Make into single fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{15}} \div 2 \dfrac{3}{5} [/tex]
--------------------------------------
Now do the divide
--------------------------------------
--------------------------------------
Convert to improper fraction
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[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{15}} \div \dfrac{13}{5} [/tex]
--------------------------------------
Change to multiplication fraction
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[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{15}} \times \dfrac{5}{13} [/tex]
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Multiply the fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{39}} [/tex]
--------------------------------------
Now do the addition
--------------------------------------
--------------------------------------
Change to improper fraction
--------------------------------------
[tex] \dfrac{9}{4} + \dfrac{65x-117}{39}} [/tex]
--------------------------------------
Put into single fraction
--------------------------------------
[tex] \dfrac{351 + 260x -468}{156} [/tex]
--------------------------------------
Combine like terms
--------------------------------------
[tex] \dfrac{260x -117}{156} [/tex]
The sum of two numbers is 76. The first number is 4 more than twice the other. How much is the first number?
Answers
Since their sum is 76, then x+y=76.
Since x is 4 more than twice y, then x=4+2y.
Now, since you have a definition for x (x=4+2y), you can substitute that equation in for x in the first equation.
This gets you (4+2y)+y=76.
Now, simplifying that out, you get the solution for y: y=24. Since you know what y is, you can substitute that in for y in the first equation and find x:
x+24=76
x=76-24
x=52
How can you estimate to find the percent of a number? Please give a full explanation.
(do not use an example to demonstrate)
Answers
I hope this helped! :-)
how many square feet of outdoor carpet will we need for this hole
Answers
Answer: 36 sq
Step-by-step explanation: you add 24 to 12 and get 36
Answer:
[tex]36\text{ inch}^2[/tex]
Step-by-step explanation:
We have been given an image of outdoor carpet needed for a hole. We are asked to find the area of outdoor carpet needed for this hole.
We can see that there are two pieces needed to cover the given hole.
One pieces equal 24 square inches and another pieces equal 12 square inches.
[tex]\text{Area of carpet needed to cover the hole}=24\text{ inch}^2+12\text{ inch}^2[/tex]
[tex]\text{Area of carpet needed to cover the hole}=36\text{ inch}^2[/tex]
Therefore, [tex]36\text{ inch}^2[/tex] of carpet is needed to cover the given hole.
last month you swim the 50m freestyle in 28.38 seconds. Today you swim it in 27.33 seconds what is your percent of change round to the nearest tenth of a percent if necessary
Answers
Making it a percent and rounding it to the nearest tenth it’ll be 96.3%
how do you find the slope intercept form if you are given two triangles with one point over laped?
Answers
If one edge of both of the triangles form a straight line, you take the units of rise (y values) and divide it by the run (x values) of any one of the triangles.
Hope this helps!
A flagpole that is 30 feet tall casts a shadow that extends 42 feet from the base of the flagpole. What is the distance from the top of the flagpole to the end of the shadow?
Answers
HOW DO u do this?? Plz help!!!! Question 2
Answers
HEEEEEEEEEEEEEEEEELP
Answers
y = -5x + 6
Explanation:
The equation of line in slope-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept
We are given that the slope = -5. Therefore, the equation becomes:
y = -5x + c
Now, we need to get the value of c. To do so, we will substitute with the given point (3,-9) in the equation and solve for c as follows:
y = -5x + c
-9 = -5(3) + c
-9 = -15 + c
c = -9 + 15 = 6
Based on the above, equation of line is:
y = -5x + 6
Hope this helps :)