Answers
One of the interior angles of the triangle, angle y is equal to 67° and the exterior angle x is equal to 113°.
Sum of interior angles of a triangle.The interior angles of a triangle have a total sum of 180°.
Considering the triangle with interior angles: y, 51°, and 62° we have that;
y + 51° + 62° = 180°
y + 113° = 180°
y + 113° - 113° = 180° - 113° {subtract 113° from both sides}
y = 67°
the exterior angle x and the angle y lie on a straight line, so they sum up to 180°.
x + 67° = 180°
x + 67° - 67° = 180° - 67° {subtract 67° from both sides}
x = 113°
Therefore, the interior angle y = 67° and the exterior angle x = 113°.
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Related Questions
what's 0.4 divided by 0.242
Answers
Answer:
the answer is 1.65
Step-by-step explanation:
i hope this helps
Answer:
1.65289
Step-by-step explanation:
Homework Progress 9 / 12 Marks The same honey is sold in two different size jars. Large Jar Small Jar 540g for £4.10 360g for £2.81 By considering the amount of honey per penny, work out which jar is the best value for money. Working must be shown.Homework Progress 9/ 12 Marks The same honey is sold in two different size jars. Large Jar Small Jar 540g for £4.10 360g for £2.81 By considering the amount of honey per penny, work out which jar is the best value for money. Working must be shown.
Answers
Answer:
Step-by-step explanation:
If the large Jar is $4.10 for 540g
and small jar $2.81 for 360 g
You need to show how much it cost for 1 g,so you can compare how much it cost per gram. You would divide the total cost by the grams to see how much it is for 1 g.
Large jar. $4.10/540 = $.0076 for 1 gram
Small Jar. $2.81/360 =$.0078 for 1 gram
Because the large jar is cheaper to buy per gram, the large jar is the best value for the money.
3 1/3 divided by 1 1/5
Answers
Answer:
25/9
Step-by-step explanation:
3 1/3 ÷ 1 1/5
3 1/3 = 10/3
1 1/5 = 6/5
10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9
So, the answer is 25/9
What is (x-2)-(x-5)? Plz I will mark u brainliest.
Answers
Answer: 3
This is the simplified way
The driving distance between Denver
and Chicago along Interstate 80 is
about 1020 miles. About how long
would it take to drive that distance
at 60 miles per hour?
Answers
Answer:
17
Step-by-step explanation:
divide 1020 by 60
1020 ÷ 60 = 17
meaning that you go 17 mph
Answer:
17 hours.
Step-by-step explanation:
Formula
d = r * t
Givens
t = ?
d = 1020 miles
r = 60 miles per hour
Solution
1020 = 60 * t Divide by 60
1020/60 = t
17 hours.
Please help me the question
Answers
The polynomials completely factorized have the following expressions;
50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)
51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)
52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)
53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)
How to factorise the polynomials completelyFor the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;
(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2
x² + 3x + 2 = (x + 1)(x + 2)
so;
x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)
For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;
(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8
x² - 2x - 8 = (x + 2)(x - 4)
so;
x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)
For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;
(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14
x² - 9x + 14 = (x - 2)(x - 7)
so;
x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)
For the polynomial x³ - x² + 21x + 45 divisible by x + 5;
(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9
x² - 6x + 9 = (x - 3)(x - 3)
so;
x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)
Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.
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Make a frequency table using five classes.
class 31-38 39-46 47-54 55-62 63-70
f
11
24
15
7
3
Then estimate the mean and sample standard deviation using the frequency table. (Round s to two decimal places.)
Answers
Answer: C
Step-by-step explanation:
A card is randomly selected from a standard
deck of playing cards. Find the probability
that it is a face card, given that a black card
is drawn.
Answers
Answer:
3 / 13
Step-by-step explanation:
Hello!
There are 52 cards in a deck with half being red and half being black. The question ask for when a black card is drawn so we divide the total by 2
52/ 2 = 26
There are 6 black face cards in a deck so to get the probability one will be drawn we put how many there are over the total amount
6/26 we can simplify this
3 / 13
The answer is 3 / 13
Hope this helps!
Answer:
3/13
Step-by-step explanation:
In a standard 52-card deck, there are 26 black cards and 26 red cards. Of the 26 black cards, 13 are spades and 13 are clubs. Each suit has 3 face cards, Jack, Queen, and King. Therefore, there are 6 black face cards out of a total of 26 black cards.
p(face given black) = 6/26 = 3/13
This morning, Kendall drank a cup of coffee that had 95 milligrams of caffeine in it. She didn't have any more caffeine for the rest of the day. Kendall read online that the amount of caffeine in her body will decrease by approximately 13% each hour. Write an exponential equation in the form y=a(b)x that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = ____. To the nearest milligram, how much caffeine will be in Kendall's body after 12 hours?
Answers
An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is
The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.
What is an exponential function?In Mathematics, an exponential function can be modeled by using the following mathematical equation:
f(x) = a(b)^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:
Rate of change (decay rate) = 100 - 13 = 87% = 0.87.
By substituting the parameters into the exponential equation, we have the following;
\(f(x) = 95(0.87)^x\)
When x = 12, we have;
\(f(12) = 95(0.87)^{12}\)
f(12) = 17.86 ≈ 18 milligrams.
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Use the following information to answer the next question. In the process, what is the total distance that Jeremy covers?Use the following information to answer the next question.
In the process, what is the total distance that Jeremy covers?
Answers
The total distance covered by Jeremy is 1320 m
What is a line segment ?
A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.
For sapling 1 = No distance is covered.
For sapling 2, distance covered = 10 m
Return distance=10 m
For sapling 3, distance covered =20 m
Return distance=20 m and so on
Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...
Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12
Total distance covered = 122 [2(0) + (12 − 1) 20 ]
Total distance covered = 6 (11)(20) = 1320 m
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Complete question:
There are 12 saplings to be planted in a straight line at an interval of 10 m between
two consecutive saplings. Jeremy can carry only one sapling at a time and he has to
come back to the original point to take the next sapling. He plants 12 saplings in this
manner, planting the first sapling at the original point. After planting all the saplings,
he comes back at the original point,
In the process, what is the total distance that Jeremy covers?
Identify the values of the variables. Give your answers in simplest radical form. HELP!
Answers
The value of the variables in the right triangle are as follows;
\(v = \frac{3\sqrt{2} }{2}\)\(w=\frac{3\sqrt{6} }{2}\)How to find the side of a right tringle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side of a right triangle can be found by using trigonometric ratios.
Therefore, let's find the variable length of the right triangle as follows;
sin 30 = opposite / hypotenuse
sin 30 = v / 3√2
1 / 2 = v / 3√2
cross multiply
3√2 = 2v
divide both sides by 2
v = 3√2 / 2
Let's find the variable w.
cos 30 = adjacent / hypotenuse
cos 30 = w / 3√2
√3 / 2 = w / 3√2
cross multiply
√3 × 3√2 = 2w
3√6 = 2w
divide both sides by 2
w = 3√6 / 2
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You visit the tallest building in a city and drop a penny off the edge of the observation deck. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and then it will continue falling at the same rate. How many feet will the penny fall during the 8th second?
384 feet
272 feet
256 feet
240 feet
Answers
The distance that an object falls due to gravity is given by the equation:
d = 1/2 * g * t^2
where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed.
In this case, we are given that the penny falls 16 feet during the first second, 48 feet during the second second, and 80 feet during the third second. From this, we can see that the penny is falling with a constant acceleration of 32 feet per second per second (since the distance is increasing by 32 feet each second).
To find the distance that the penny falls during the eighth second, we can use the same equation as before, but with a value of t equal to 8 seconds:
d = 1/2 * g * t^2
d = 1/2 * 32 * 8^2
d = 1/2 * 32 * 64
d = 1024 feet
Therefore, the penny will fall 1024 feet during the eighth second.
Question 3 Write a method that solves for x in the quadratic equation. The parameters are a, b, c, and boolean flag that indicates whether it will solve the equation with addition or subtraction in the numerator. 2-4ac ㄨㄧ- 2a Source: Wikipedia The method will return the value of x
Answers
On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )
What is quadratic equation?A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.
public static double solve(double a, double b, double c, boolean flag)
{ double d = Math.sqrt(b*b - 4*a*c); if(flag)
{ return (-b + d) / (2*a); }
else { return (-b - d) / (2*a); } }
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Mr. Charles bought dinner for his family
The dinner cost $46.95.
He left a 15% tip.
Answers
Hope it helps!!!!!!!!!
HELP NEED SOON!! A store receives a shipment of 5,000 MP3 players. In a previous shipment of 5,000 MP3 players, 300 were
defective. A store clerk generates random numbers to simulate a random sample of this shipment. The
clerk lets the numbers 1 through 300 represent defective MP3 players, and the numbers 301 through
5,000 represent working MP3 players. The results are given.
4,942 368 110 4,758 4,452 610 773 171 460 2,699
Based on this sample, how many of the MP3 players might the clerk predict would be defective?
The manager would expect
defective players in the shipment.
Answers
Answer:
2?
Step-by-step explanation:
From my understanding, all numbers 300 and below represent defective mp3s, so there's two.
What is the image point of (-6,8) after a translation right 4 units and up 2 units?
Answers
Answer:
(-2, 10)
Step-by-step explanation:
Right 4 units means add 4 units to the x axis value, which is negative 2. So -6+4 is -2. Up 2 units means add 2 units to the y axis value, which is 8. If we add 2 to 8, we get 10. So our new value is (-2,10)
The image point of (-6,8) after a translation right 4 units and up 2 units is (-2,10).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The transformation that moves a point right 4 units and up 2 units is called a translation. The translation moves each point in the plane by the same distance and direction. In this case, the distance moved was 4 units to the right and 2 units up.
The image point of (-6,8) after a translation right 4 units is (-2,8).
After a translation up to 2 units, the image point becomes (-2,10).
Hence, the image point of (-6,8) after a translation is (-2,10).
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25. Which of the following is a correct way
of calculating 0.63 ÷ 0.015?
A. 63 15
B. 630 - 15
C. 630 1.5
D. 63
0.15
Answers
Answer: (Maybe) B
Step-by-step explanation:
The answer for this problem would be 42. However, if you take 630 and divide it by 15 (630/15) you'll get 42 as well. I'm not sure if you accidentally typed the hyphen in there (choice B) or if it's supposed to represent a negative sign. But, I believe B would be correct.
A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 8. Find the numbers.
Answers
Answer:
Let your two numbers be n and n-1. Then: 2n+n²-2n+1=51 n²=50 n=5√2 n-1=5√2-1
Hope that helps <3
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AB=34 and EB=38, solve for EA. Round to the nearest tenth if necessary
Answers
The value of side EA is,
EA = 16.9
We have to given that;
Circle E with diameter CD and radius EA.
And, AB is tangent to E at A.
Here, AB = 34 and EB = 38
Hence, By using Pythagoras theorem we get;
AB² + AE² = EB²
34² + AE² = 38²
1156 + AE² = 1444
AE² = 1444 - 1156
AE² = 288
AE = √288
AE = 16.9
Thus, The value of side EA is,
EA = 16.9
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Please help! Anyone who knows about SSS, SAS, ASA, and AAS theorems.
Answers
Answer:
Step-by-step explanation:
Given:
∠C ≅ ∠E
Statements Reasons
1). ∠C ≅ ∠E 1). Given
2). ∠ABC ≅ ∠DBE 2). Vertically opposite angles
3). ΔABC ~ ΔDBE 3). By AA postulate of similarity.
Question provided in attachment.
Answers
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.
How to calculate the valueSample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18
= 480 / 18
≈ 26.667
Sample Standard Deviation (s):
= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))
≈ ✓(319.778 / 17)
≈ ✓(18.81)
≈ 4.336
Confidence level = 99%
Sample Size (n) = 18
Sample Mean = 26.667
Sample Standard Deviation (s) = 4.336
Degrees of Freedom (df) = n - 1 = 18 - 1 = 17
Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.
Margin of Error (E) = 2.898 * (4.336 / ✓18))
≈ 3.748
Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)
= (22.919, 30.415)
We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.
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Which equation is the inverse of 5y+4= (x+3)²+12?
O y = x²+x+1100
y=3± √√5x+ 7/2
O-5-4--(x+3)²--1/
O
O y=-3± √5x+
7
Answers
The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
Which equation is the inverse of 5y+4= (x+3)²+12?From the question, we have the following parameters that can be used in our computation:
5y+4= (x+3)²+12
Swap x and y in the equation
So, we have
5x + 4= (y + 3)² + 12
When we make the vairiable y the subject, we have
y = -3 ± √(5x - 8)
Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
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how to find the missing angle when given two sides of a right triangle?
Answers
Answer:
Step 1 The two sides we know are Opposite (300) and Adjacent (400).
Step 2 SOHCAHTOA tells us we must use Tangent.
Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
Step 4 Find the angle from your calculator using tan-1
Find the grade Juniper Would have to make on his fifth test if after four tests he has an average of 90,  and he must have a 92.5 in order to get a new four wheeler. 
Answers
Answer:102.5
Step-by-step explanation:
The first four tests are 2.5 short of the desired average.
2.5 x 4 = 10
The fifth test must be 92.5 + 10 points more to make up for the other tests being lower.
102.5
please help me please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please
Answers
Answer:
1a: 16
1b: 25
1c: 36
1d: 49
1e: 64
1f: 91
1g: 100
2a: 4
2b: 5
2c: 6
2d: 7
2e: 56 is not a perfect square
2f: 9
2g: 10
Halp how to factor 4x-2
Answers
Answer:
2(2−1)
Step-by-step explanation:
4−2
Grouping
Common factor
4−2
2(2−1)
Solution
2(2−1)
To factor, you do the opposite of what you would in distributive property. You have to find the greatest common factor, or GCF, of 4 and -2.
4 2
------ -------
1 | 4 1 | 2
2 | 2
So the GCF is 2. Now we factor the expression.
4x-2
2(2x-1)
---
hope it helps
Find the quotient. 64 ÷ 32 =
Answers
Answer:
64÷32=2.
Step-by-step explanation:
if you add 32+32 it's 64, so that means 32x2=64 and yeahhh
What is X?
I’m at a loss
Answers
Answer:
9
Step-by-step explanation:
5x-3= 2x+24
5x=2x+27
3x=27
X=9
Answer: A. 9
Step-by-step explanation:
The diagonal is bisected by the other diagonal. So the 2 parts of the diagonal are equal
5x - 3 = 2x + 24 >Bring like terms to 1 side
3x = 27 >Divide both sides by 3
x = 9
explain 3 factors that should be considered in the construction of index numbers
Answers
1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.
2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.
3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`
construction of index number is also available in two parts:
1. simple
2. weighted
1. simple: the simple method is classified into simple aggregative and simple relative.
2. weighted: the weighted method is classified into a weighted aggregative and weighted average.
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Which of the following is a perfect cube?
a. 100
b. 216
c. 80
d. 65
Answers
Explanation dont let 100 trick you, the factors of 216 in a pair of three and write in the form of cubes.
Answer:
216
Step-by-step explanation:6x6x6