∠A=6x−18 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 18, degrees, end color #11accd \qquad \green{\angle B} = \green{14x +38^\circ}∠B=14x+38 ∘ start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 14, x, plus, 38, degrees, end color #28ae7b Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
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Using the properties of alternate angles, the value of x = 8 and ∠ A = 30
What are Alternate Angles?A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (four total angles) of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal.
For the given question,
∠A=6x−18
∠B=14x+38
As, both parallel lines are intersected by a transversal,
the value of angle ∠A and ∠180 - B is same as they are alternate angles,
⇒ 6x−18 = 180 - 14x - 38
⇒ 6x + 14x = 142 + 18
⇒ 20x = 160
⇒ x = 8
∠A = 6x−18
⇒ ∠ A = 30
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Correct question -
Related Questions
nothing changes with tangent
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hello
to solve this question, we have to use trigonometric ratios and in this case, it was specified to use tangent
from the image above, we can see that we have the value of angle and opposite and we need to look for adjacent
trigonometric ratio is given as SOH CAH TOA
[tex]\begin{gathered} \text{soh}=\text{sin}\theta=\frac{opposite}{\text{hypothenus}} \\ \text{cah}=\cos \theta=\frac{adjacent}{hypothenus} \\ \text{toa}=\tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]now, let's use the formula of tangent to solve this problem
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{opposite}=42 \\ \theta=64^0 \\ \text{adjacent}=x \\ \tan 64=\frac{42}{x} \\ x=\frac{42}{\tan 64} \\ x=20.48 \end{gathered}[/tex]from the calculations above, the value of x is equal to 20.48
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En la cerrada economía Chalupa, el consumo familiar triplica el de las unidades productivas y este supera en $2,500 al del gobierno, que tiene un equilibrio presupuestario y sus ingresos fueron $6,700. Si el consumo de capital fijo es 25% del PNB pm y el monto de impuestos netos de subsidios $1750 encuentre el ingreso nacional.
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Answer:
hola comasa due when 123 dfosb971 24
In the game of baseball, home plate is a pentagon.What is the measure of the angle at the bottom of home plate?A. 60°B. 90°C. 120°D. 135°
Answers
EXPLANATION
Since the figure is like a pentagon, we need to add the interior angles in order to get the needed angle.
The first part of the figure is composed of a square with two right angles of 90 degrees and two angles of 135, making a total of 90+90+135+135 = 450 degrees.
The left needed angle should add a total of 540 degrees, by the Sum of Interior Angles of a Pentagon Theorem, as follows:
450 + bottom angle = 540
Subtracting -450 to both sides:
bottom angle = 540 - 450
Subtracting angles:
bottom angle = 90 degrees
In conclusion, the value of the bottom angle is 90 degrees.
what is 3 1/2 x 4 1/2 x 5 ft * 5 1/6 x 5 1/4 x 3 1/3 x 4 1/2 in 5 ft x 5 1/3 * 2/3
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ANSWER
[tex]V=72\operatorname{cm}[/tex]EXPLANATION
h. We want to find the volume of the rectangular prism given.
The volume of a rectangular prism is given as:
[tex]V=l\cdot w\cdot h[/tex]where L = length
w = width
h = height
Therefore, we have that the volume of the prism is:
[tex]\begin{gathered} V=12\cdot2\cdot3 \\ V=72\operatorname{cm}^3 \end{gathered}[/tex]A straight highway is 100 miles long, and each mile is marked by a milepostnumbered from 0 to 100. A rest area is going to be built along the highwayexactly 6 miles away from milepost 57. If m is the milepost number of therest area, which of the following equations represents the possible locationsfor the rest area?O A. \m-6| = 57OB. 157+ ml = 6O C. Im + 61 = 57OD. 157-ml = 6SUBMIT
Answers
Given:
Few data is given
Required:
To calculate which option is correct
Explanation:
157+ ml = 6 means a rest area built along the highway exactly 6 miles away from milepost 57.Therefore this is the correct answer
Required answer:
Option D
12–15. Melvin Indecision has difficulty deciding whether to put his savings in Mystic Bank or Four Rivers Bank. Mystic offers 10% interest compounded semiannually. Four Rivers offers 8% interest compounded quarterly. Melvin has $10,000 to invest. He expects to withdraw the money at the end of 4 years. Which bank gives Melvin the better deal?
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The better deal between the offer at Mystic Bank and Four Rivers Bank is the deal at Mystic Bank.
What is the better deal?In order to determine which bank has the better offer, the future value of the investment options have to be determined.
The future value of an investment is a function of the amount investment, the number of compounding, the years of the investment and the interest rate.
When an investment is compounded semi-annually, it means that it grows exponentially twice in a year. When an investment is compounded quarterly, it means that is grows exponentially four times in a year.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsInterest rate at Mystic bank = 10% /2 = 5%
Interest rate at Four Rivers Bank = 8% / 4 = 2%
Future value of the investment at Mystic bank :
$10,000 x (1.05)^(2 x 4) = $14,774.55
Future value of the investment at Four Rivers Bank :
$10,000 x (1.02)^(4 x 4) = $13,727.86
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Triangles DEF and HJK are similar. DEF has side lengths DE=4, EF=6, FD=8. Which of the following could be the side lengths of HJK?• 2, 6, 7• 2, 5, 7• 8, 12, 16• 5, 7, 9
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Answer:
(c) 8, 12, 16
Step-by-step explanation:
You want to identify the side lengths that are proportional to lengths 4, 6, and 8.
RatiosReducing the ratios to lowest terms, we can compare them:
desired ratio: 4 : 6 : 8 = 2 : 3 : 42 : 6 : 7 — reduced, not equivalent2 : 5 : 7 — reduced, not equivalent8 : 12 : 16 = 2 : 3 : 4 . . . . . same as the desired ratios5 : 7 : 9 — reduced, not equivalentSide lengths 8, 12, 16 will form a triangle similar to ∆DEF.
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Rachel wants to buy the same number of gift bags and bows. Gift bags are sold in packs of 6. Bows are sold in packs of 9. What is the least number of gift bags and bows that Racheal can buy?
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The question wants the "lowest common multiple" of 6 and 9, so first, lets find some of the miltiples of 6 and 9:
[tex]\text{Multiple}(6)=\mleft\lbrace6,12,18,24,30,36,42,49,\ldots\mright\rbrace[/tex][tex]\text{Multiple}(9)=\mleft\lbrace9,18,27,36,45,54,\ldots\mright\rbrace[/tex]We can see that 18 is a commom multiple of 6 and 9, and is also the smallest, so the lowest common multiple of 6 and 9 is 18. So the least number of gift bags and bows that Rachel can buy is 18.
write the partial fraction decomposition of the rational expression 3x-5/x²-4x-32
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Denominator has been factorized on the right.
Now we need to write this fraction as a sum of two fraction.
[tex]\frac{3x-5}{(x+4)(x-8)}=\frac{A}{(x+4)}+\frac{B}{(x-8)}=\frac{A(x+4)+B(x-8)}{(x+4)(x-8)}[/tex][tex]A(x+4)+B(x-8)=3x-5\text{ at this stage we will find A B constants}[/tex]when x = 8 we have following
[tex]A(8+4)+B(8-8)=3\cdot8-5\rightarrow12A+0=19\rightarrow A=\frac{19}{12}\approx1.58[/tex]Similarly when x =-4 A = 17/12 these are the constants
QuestionIn ABC, C = 64°, c = 32, and b = 33. What are the two possible values for angle B to the nearest tenth of a degree?Select both correct answers.
Answers
Two possible diagrams of the triangle are shown below
To find angle B in each triangle, we would apply the law of sines which is expressed as
a/SinA = b/SinB = c/SinC
For either of the triangles, by applying the sine law, we have
33/Sin B = 32/Sin 64
By crossmultiplying, we have
32 SinB = 33 Sin 64
Sin B = (33 Sin 64)/32 = 0.9269
We would find angle B by finding the inverse of sine 0.9269
Thus,
B = Sin^-1(0.9269) = 68
This is an acute angle. B can also be an obtuse angle. Greater than 90 but less than 180 degrees). Thus, another value for B is
Questions 12-15. Data from Ivy Tech’s advising center shows that their wait times follow a normal distribution. Use theEmpirical Rule to answer the following questions. 5 10 15 20 25 30 3512. What percent of students will wait between 15 and 25 minutes? (round to the nearest whole number)13. What percent of students will wait less than 20 minutes? (round to the nearest whole number)14. What percent of students will wait more than 35 minutes? (round to the hundredths place)15. If 5,300 students come to the advising center, how many students would wait more than 35 minutes? (round to thenearest student)
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Answer:
12. 68%
13. 50%
14. 0.15%
15. 8 students
Step-by-step explanation:
Given a normal distribution with mean 20 and standard deviation 5, you want several probabilities based on the empirical rule.
Empirical ruleThe empirical rule tells you the percentages of a normal distribution that are within 1, 2, or 3 standard deviations of the mean. They are ...
within 1: 68%within 2: 95%within 3: 99.7%12. Between 15 and 25Wait times between 15 and 25 are within 20±5, so within 1 standard deviation of the mean. The percentage of students waiting 15–25 minutes is 68%.
13. Less than 20The mean of the distribution is 20, which is its line of symmetry.
50% of students will wait less than 20 minutes.
14. More than 3535 is 3 standard deviations above the mean, so the fraction in this group is half of the difference between 1 and 99.7%.
0.15% of students will wait more than 35 minutes.
15. How many?Of 5300, the number waiting more than 35 minutes is ...
0.15% × 5300 = 7.95 ≈ 8
About 8 students will wait more than 35 minutes.
__
Additional comment
These values are based on the empirical rule, as required by the problem statement. The actual number for P(Z>3) is about 0.0013499 (0.13%), and the number of students is about 7.15 ≈ 7. That is, the result using the empirical rule is slightly different than what you get using a calculator, spreadsheet, or table.
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Convert 103 degrees Fahrenheit to degrees Celsius. (Write your answer in fraction format)
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to convert Fahrenheit to Celcius we have to apply the next formula:
C°= (F°-32) x 5/9
Replacing:
C = (103-32)x 5/9
C = 71 x 5/9
C = (71 x5)/9 = 355/9
the last six days of August 2011 all time records for high temperatures in Austin Texas which of the following values that identifies the mean absolute deviation for these temperatures F. 4G. 107H. 103J. 3.3
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We have to calculate the mean absolute deviation (MAD) for these temperatures.
We can express the MAD as:
[tex]\text{MAD}=\frac{1}{n}\sum ^n_{i=1}|x_i-\bar{x|}[/tex]So first we have to calculate the mean of the sample. We can do this as:
[tex]\bar{x}=\frac{1}{n}\sum ^n_{i=1}x_i=\frac{1}{6}(103+110+112+109+105+103)=\frac{1}{6}\cdot642=107[/tex]Now we can calculate the MAD as:
[tex]\begin{gathered} \text{MAD}=\frac{1}{6}(|103-107|+|110-107|+|112-107|+|109-107|+|105-107|+|103-107|) \\ MAD=\frac{1}{6}(4+3+5+2+2+4) \\ \text{MAD}=\frac{1}{6}(20) \\ \text{MAD}\approx3.3 \end{gathered}[/tex]Answer: The MAD is approximately 3.3.
an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours.Wich has a graph that best represents this rate?
Answers
If an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H best represents this rate.
The graphs are attached
Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours,
hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour
Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per hour
The slope (rate of change) of a line (m) is given by:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:
Slope of the line , [tex]m = \frac{-20 - 0}{10 - 0}[/tex]
Slope of the line is - 2 meters per hour
b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:
Slope of the line, [tex]m = \frac{-70 - 0}{10 - 0}[/tex]
Slope of the line is -7 meters per hour
c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:
Slope of the line, [tex]m = \frac{-35 - 0}{10 - 0}[/tex]
Slope of the line is -3.5 meters per hour
d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:
Slope of the line, [tex]m = \frac{-3.5 - 3.5}{10 - 0}[/tex]
Slope of the line is 0 meters per hour.
Therefore, if an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H best represents this rate.
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Simplify the expression 2^5 +5^4
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Therefore
[tex]2^5+5^4=657[/tex]Arrange the quantities in order from smallest to largest.
2.6 km, 109,000 mm, 41.7 hm
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The order of the values using the basic unit of meters from smallest to largest. is: 109000 mm < 2.6 km < 41.7 hm
What are the units of measurement of distance or length?
Distance is the gap between any two points under consideration.
The basic unit for measuring distance is the meter.
There are larger as well as smaller units for measuring length or distance which are based on the unit of meter.
The units are as follows:
millimeter, mm = 0.001 m
centimeter, cm = 0.01 m
decimeters, dm = 0.1 m
meter, m = 1 m
kilometer, km = 1000 m
hectometer, hm = 100 m
Now to compare the given quantities making the units same as two quantities can only be compared only when there units are same :
Considering the given values;
2.6 km = 2600 m
109,000 mm = 109 m
41.7 hm = 4170 m
Therefore, after comparison arranging the quantities in order from smallest to largest is 109000 mm < 2.6 km < 41.7 hm
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graph the system below2x-3y=-183x+y=-5
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ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 2x-3y=-18 \\ \\ 3x+y=-5 \end{gathered}[/tex]To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:
[tex]\begin{gathered} \text{ For }2x-3y=-18 \\ \\ \text{The x-intercept} \\ \\ \:2x-3\cdot 0=-18 \\ \\ x=-9\rightarrow(-9,0) \\ \\ \text{The y -intercept} \\ \\ 2\cdot0-3y=-18 \\ \\ y=6\rightarrow(0,6) \\ \\ \\ \text{For }3x+y=-5 \\ \\ \text{The x-intercept} \\ \\ 3x+0=-5 \\ \\ x=-\frac{5}{3}\rightarrow\left(-\frac{3}{5},0\right) \\ \\ \text{The y- intercept} \\ \\ \:3\cdot 0+y=-5\: \\ \\ y=-5\rightarrow(0,-5) \end{gathered}[/tex]Now we graph:
help ................
Answers
Percentage of a number
Find a number which
its a 100% percentage
henW
When 232 is 290%
Then find
X = (100%/290)• 232
Divide 232/29 = 10% = 8 exactly
Now multiply by 10 = 10• 8 = 80
Then 100% = 80
what happens to a circle's circumference when the radius is doubled
Answers
ANSWER
The circumference doubles
EXPLANATION
Let the radius of the circle be r and the circumference be C.
The circumference of a circle is given as:
[tex]C=2\pi r[/tex]If the radius is doubled, the radius becomes:
[tex]2r[/tex]The circumference now becomes:
[tex]\begin{gathered} C^{\prime}=2\pi\cdot(2r) \\ C^{\prime}=2\cdot(2\pi\cdot r) \\ C^{\prime}=2\cdot(2\pi r) \\ C^{\prime}=2C \end{gathered}[/tex]Therefore, the circumference doubles when the radius is doubled.
is B the right answer? If not, which one is?
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Given the rational function;
[tex]f(x)=\frac{3x+4}{x(x-2)}[/tex]To determine the constraint for this function, we shall set the denominator equal to zero;
[tex]\begin{gathered} x(x-2)=0 \\ \text{Hence;} \\ x=0 \\ x-2=0 \\ x=2 \end{gathered}[/tex]This means the equation does not exist when x = 0, and when x = 2.
ANSWER:
The correct answer is option C.
18. A rectangular table cloth has a width of 3 yards 1 foot and a length of 4 yards. Part A. Debbie says that the width could also be written as 4 feet. Explain wether you agree or disagree with Debbie. Part B. The cost of the fabric used to make the tablecloth is $0.25 per square foot. Explain how to find the cost of the fabric needed to make the table cloth.
Answers
A)
In order to check this sentence, we need to convert the value from foot to yard.
Knowing that 1 yard is equal 3 feet, we have that:
[tex]3\text{ yards 1 foot}=3\cdot3\text{ feet + 1 foot}=9\text{ feet + 1 feet}=10\text{ feet}[/tex]So Debbie's affirmation is incorrect, therefore we disagree.
B)
First we need to calculate the area of the table cloth.
Converting the length to foot, we have:
[tex]4\text{ yards}=4\cdot3\text{ feet}=12\text{ feet}[/tex]Now, calculating the area (which is the product of the length and the width), we have:
[tex]\text{Area}=10\cdot12=120\text{ ft}^2[/tex]If each square foot is $0.25, we just need to multiply the area by the cost of one square foot in order to find the cost of the fabric for the table cloth:
[tex]\text{Cost}=120\cdot0.25=30[/tex]So the cost is $30.
Use the Law of Sines to find the indicated side x."(Assume c = 23.2. Round your answer to one decimal place.)
Answers
ANSWER
x = 21.6
EXPLANATION
We have that:
c = 23.2
To be able to solve this, we must first find angle
The sum of angles in a triangle is 180 degrees.
This means that:
=> 52 + 70 + 122+ =>
Sine Law says that the ratio of angle and side opposite the angle for any triangle equal.
This means that:
[tex]\frac{\sin A}{a}\text{ = }\frac{\sin B}{b}=\text{ }\frac{\sin C}{c}[/tex]So, we can say that:
[tex]\begin{gathered} \frac{\sin52}{x}=\text{ }\frac{\sin58}{23.2} \\ \text{Cross}-\text{multiply:} \\ 23.2\cdot\text{ sin52 = x }\cdot\text{sin58} \\ \Rightarrow\text{ x = }\frac{23.2\cdot\text{ sin52}}{\sin58} \\ x\text{ = }21.6 \end{gathered}[/tex]That is the value of x.
Given that bisects use the diagram above to complete the following statement.m∠AOB= m∠…
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A line is said to bisect an angle if it divides it in two equal parts.
Since the segment OB bisects the angle AOC, then the angles AOB and BOC have the same measure.
Therefore, the complete statement is:
[tex]m\angle AOB=m\angle BOC[/tex]Teri ran 8 kilometers. One mile is approximately equal to 1.6 kilometers. Which measurement is closest to the number of miles Teri ran?
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The closest distance or the number of miles Teri ran is equal to 5 miles.
What is the unitary method ?
The unitary method is a method in which you find the value of one unit and then the value of required no. of units.
It is given that Teri ran 8 kilometers.
It is also given that , 1 mile is approximately equal to 1.6 kilometers.
This is a question of unitary method. We know that value of one unit is given as 1 mile is equal to 1.6 kilometers approximately. We know have to calculate the no. of miles Teri ran , by converting 8 kilometers to miles.
So ,
1 miles = 1.6 kilometers
This implies :
8 kilometers = 8 / 1.6 miles
or
8 kilometers = 5 miles
or
8 kilometers is approximately equal to 5 miles.
Therefore , the closest distance or the number of miles Teri ran is equal to 5 miles.
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calculate the perimeter of kite ABCD where AB = 29 cm and CD = 47 cm
Answers
Answer:
152 cm
Step-by-step explanation:
Perimeter of kite= 2(a+b)
P= 2(AB+CD) = 2(29+47) = 2 *(76) = 152 cm.
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Paul needs to buy paint to cover all outside surfaces of his shed, depicted below. How much area, in square yards, does he need to cover?
2 sides of shed are rectangles with a base of 12ft and a side of 6 ft.
The other two sides are squares with sides of 6 ft.
The roof consists of four triangles, 2 of the triangles have a base of 6 feet and a height of 6 feet.
The other two triangles have a base of 12 ft and a height of 6 ft
Answers
The total surface area Paul is required to paint is 36 yard square.
How to find surface area?He needs to buy paint to cover all outside surfaces of his shed .
2 sides of shed are rectangles with a base of 12ft and a side of 6 ft.
Therefore,
area of a rectangle = lw
where
l = lengthw = widtharea of the rectangle = 12 × 6
area of the rectangle = 72 ft²
The rectangle are two.
Hence, area of the two rectangular faces = 72 + 72 = 144 ft²
The other two sides are squares with sides of 6 ft.
Therefore,
area of the two squares = 6² + 6² = 36 + 36 = 72 ft²
The roof consists of four triangles,
2 of the triangles have a base of 6 feet and a height of 6 feet.
Therefore,
area of the two triangles = 2 (1 / 2 × 6 × 6) = 36 ft²
The other two triangles have a base of 12 ft and a height of 6 ft.
area of the other triangle = 2(1 / 2 × 12 × 6) = 72 ft²
Hence,
total area the paint will cover = 72 + 36 + 72 + 144 = 324 ft² = 36 yard²
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Multiply 58*7 enter your answers in the boxes to complete the area model
Answers
We will get 406 after multiplication .
What does multiply mean?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. A multiplication issue has two factors, a product, and two factors. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.Calculating the outcome of adding a number several times is known as multiplication in elementary algebra. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.58 * 7 = 406
We will get 406 after multiplying .
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Need help with problems
Answers
You can write the relation between distance and time, as follow:
y = kx
where y is the distance, x is the time and k is the constant of proportionality.
k can be obtained with the given information, as follow:
k = 90/30 = 3
Then, the equation of the relationship is:
y = 3x,
for a time of 10 seconds, the distance traveled is:
y = 3(10) = 30
Hence, the answer is:
y = 3x , 30 feet
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Determine if the two expressions in each pair are equivalent.If they are equivalent,select the property that is illustrated.
Answers
Answer:
The second one is the Multiplicative Property of Zero.
The fourth one is the Commutative property.
Answer:
The second and third one
Step-by-step explanation:
Is the point (-255,76) on the line shown below
Answers
Answer:
yes it's is shown in the diagram below and prosperity more than your expectation for me too anymore I just