Answers
37.5 degrees
we know angled like this always have 180 degrees total between the 2. which means we can set up a little equation to solve for x. The equation is (3x+22)+(x-4)= 180. Initially we can take the solid numbers (22 and -4) and get rid of them by taking them to the 180. 180- 22 is 158. 158 + 4 is 162. now we have 3x + x = 162. we combine like terms. means we end up with 4x =162. We now divide by 4 which means we get 40.5. Now we know x is 40.5. Now dbc is just 40.5- 4 which is 37.5.
The measure of angle ∠DBC is,
⇒ ∠DBC = 35.5°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Point D is in the interior of ∠ABC.
And, ∠ABD = (3x + 22)°
⇒ ∠DBC = (x - 4)°
Clearly, Both angle make a linear pair.
Hence, We get;
⇒ ∠ ABD + ∠DBC = 180°
⇒ (3x + 22) + (x - 4) = 180°
⇒ 3x + 22 + x - 4 = 180
⇒ 4x + 18 = 180
⇒ 4x = 180 - 18
⇒ 4x = 162
⇒ x = 162/4
⇒ x = 40.5
Hence, The measure of angle ∠DBC is,
⇒ ∠DBC = (x - 4)°
⇒ ∠DBC = (40.5 - 4)°
⇒ ∠DBC = 35.5°
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Related Questions
The following triangle is equilaterial triangle. Solve for the unknown variable.
Answers
Answer:
d
Step-by-step explanation:
Since the triangle is equilateral then the 3 sides are congruent, then
2x = 6 ( divide both sides by 2 )
x = 3
and
3y = 6 ( divide both sides by 3 )
y = 2
Thus x = 3 and y = 2 → d
Convert 7x - y = -9 to slope-intercept form. Simplify your answer.
Answers
7x - y = -9
-y = -9 - 7x
y = 9 +7x
y = 7x + 9
The equation of a line, 7x - y = -9, converted to slope-intercept form is: y = 7x + 9
Equation of a line in Slope-intercept FormIf "m" is the slope of a line and "b" is the y-intercept, the equation of the line in slope-intercept form is given as: y = mx + b.
Thus, given the equation, 7x - y = -9, rewrite/convert to slope-intercept form as follows:
7x - y = -9
-y = -7x - 9
Divide both sides by -1y = 7x + 9
Therefore, the equation of a line, 7x - y = -9, converted to slope-intercept form is: y = 7x + 9
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Take a factor out of the square root:
Answers
Answer:
[tex]-y\sqrt{3}[/tex]
Step-by-step explanation:
Under the radical there is a perfect square, one can take the perfect square out, and write it by its square root. The result of taking the principal square root is always positive, but it is given that the perfect square factor is negative, thus, one must multiply the square root by the negative sign to ensure that the result is positive.
Answer:
[tex]-y\sqrt{3}[/tex]
Step-by-step explanation:
4.
Your math test has 38 questions and is worth 200 points. The test consists
of multiple-choice questions worth 4 points each and open-ended questions
worth 20 points each. How many of each type of question are there?
... please solve this using if systems of equations
Answers
Answer:
Number of multiple-choice questions = x = 35 questions
Number of open-ended questions = y = 3 questions
Step-by-step explanation:
Let
Number of multiple-choice questions = x
Number of open-ended questions = y
x + y = 38 (1)
4x + 20y = 200 (2)
From (1)
x = 38 - y
Substitute x = 38 - y into (2)
4x + 20y = 200
4(38 - y) + 20y = 200
152 - 4y + 20y = 200
- 4y + 20y = 200 - 152
16y = 48
y = 48/16
y = 3
Substitute y = 3 into (1)
x + y = 38
x + 3 = 38
x = 38 - 3
x = 35
Number of multiple-choice questions = x = 35 questions
Number of open-ended questions = y = 3 questions
1. TEMPERATURE Suppose the temperature
outside is dropping 3 degrees each
hour. How much will the temperature
drop in 8 hour?
Answers
3x8=24
Plsssss help me this is urgent.
Which tank has the greater volume?
Tank A has a diameter of 10 ft and a height of 3 ft. Tank B has a diameter of 6 ft and a height of 8 ft
A.Tank B has a greater volume.
B.Tank A and Tank B have the same volume.
C.Tank A has a greater volume
Answers
Tank A has a greater volume.
From the set {5, 9, 12}, use substitution to determine which value of x makes the equation true. 12(x - 4) = 96
Answers
Answer:
12
Step-by-step explanation:
12(5-4)=96
60-48=12 means it's not five
12(9-4)=96
108-48=60 means it's not 9
12(12-4)=60
144-48=96 so answer is 12
Please help! Also how do you know?
Answers
Answer:
A. All four sides must be congruent.
Step-by-step explanation:
A quadrilateral has four sides. A rhombus has four equal sides, which are congruent. The angles can be different. It doesn't have four lines of symmetry. One triangles sums to 180 degrees not 4. 4 triangles would sum up to 720 degrees
8.)
1 point
Does (0,7) make the equation y = 3x + -7 true?
Answers
Answer:
YES
Step-by-step explanation:
The 7 in (0,7) is the y-intercept given in the equation y = 3x + 7
PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST
Answers
You just literally mark the graph, you see the 1st points (2,12) go on the X axis to 2, then go up to 12 and mark that as a point. and continue with this tactic with the rest.
Answer:
I think this is correct. <3
100 POINTS, MAHNIFIA PLEASE ANSWER!
SCAMMERS WILL NOT BE TOLERATED!
Answers
Answer:
- 3.4(21) = - 71.4
(- 2.3)(- 7.9) = 18.17
9.24 ÷ - 7 = -1.32
(- 8.5) ÷ (- 3.4) = 2.5
- 6.85 ÷ 0.5 = - 13.7
The graph represents the average heights of boys in the United States from age two to age ten. A line of best fit has been drawn through the data.
Which statement describes the correlation coefficient?
The correlation coefficient will have a value very close to 0.
The correlation coefficient will have a value very close to 1
The correlation coefficient will have a value very close to –1.
The correlation coefficient will have a value very close to 0.5.
Answers
Answer:
A gotchu Just took the test got 100
Step-by-step explanation:
B
Answer:
The answer is B
Step-by-step explanation:
As it is very close to one because all the points are close together
The circumference of the
wheel on Beyoncé's bicycle
is 63 inches. What is the
diameter of the bicycle
wheel to the nearest inch?
Use 3.14 for a.
Answers
To the nearest inch it'll be
d×3.14=63
= 20 inches
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.
Answers
Answer:
B
A=2
B=6
Step-by-step explanation:
The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.
Calculation of the expression:Since
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level.
So here the expression be like The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.
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Tyler invested $350 in an account paying an interest rate of 4.5% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $700?
Answers
Answer:
15.4 I did this on delta math
It would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
How to calculate compounding time?The formula for calculating the future value (FV) of an investment with continuous compounding is:
[tex]FV = Pe^{rt}[/tex]
Where P is the initial principal, r is the annual interest rate (expressed as a decimal), t is the time period (in years), and e is the mathematical constant e (approximately 2.71828).
In this case, we have P = $350, r = 4.5% = 0.045, and we want to find the time t when the FV is $700. Substituting these values into the formula, we get:
[tex]700 = 350e^{0.045t}[/tex]
Dividing both sides by $350, we get:
[tex]2 = e^{0.045t}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) = ln\times e^{0.045t}[/tex]
Using the properties of logarithms, we can simplify this to:
ln(2) = 0.045t ln(e)
Since ln(e) = 1, we can simplify further to:
ln(2) = 0.045t
Finally, solving for t, we get:
t = ln(2) / 0.045 ≈ 15.4
Therefore, it would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
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A castle has to be guarded 24 hours a day. 7 nights are ordered to split each day guard duty equally. How long will each night spend on guard duty in one day?
Answers
Answer:
3.43 hours
Step-by-step explanation:
A castle has to be guarded 24 hours a day. 7 knights are ordered to split each day guard duty equally. How long will each knight spend on guard duty in one day?
From the above question:
7 knights = 24 hours
1 knight = x hours
Cross Multiply
7 knights × x hours = 1 knight × 24 hours
x hours = 1 knight × 24 hours/ 7 knights
x hours = 3.4285714286 hours
Approximately = 3.43 hours
Therefore, each knight would spend 3.43 hours on guard duty in one day
Enter your solution without units below. 5cm 5cm 4cm 12cm 6cm
Answers
Answer: if ur looking 4 the surface area, then its 216 cm2.
Step-by-step explanation:
a= 1/2 b h
a= 1/2 (6) (4)
a= 12
12x2=24
a=lw
a= 12(5)
a= 60
60x2= 120
a=lw
a= 6(12)
a= 72
24+72+120= 216
You flip a coin 30 times, about how many times would you expect to tails to appear?
Answers
Answer:
15 heads out of 30
Step-by-step explanation:
The total number of possible sequences of coin flips can be determined by raising the number of outcomes, which is 2 for any coin (heads or tails), to the power of the number of times the coin is flipped, given by the question as 30. Therefore, 230 is the total number of different sequences for 30 coin flips.
We can use combinatorial math to find the number of sequences with exactly 15 heads, which is 30 choose 15 or (3015) . The probability we are looking for will be the number of sequences with 15 heads divided by the total possible sequences.
Now we can express the whole probability in math notation, and calculate an answer (rounded to 4 decimal places):
(3015)230=1551175201073741824≈0.1445≈14.45%
15 heads out of 30 is the most likely outcome when flipping 30 coins, if you run the same calculation with 14 or 16 heads you will get two equal, but smaller probabilities, same with 13 and 17 heads, and so on. If you graphed all of the outcomes, you will find it follows a normal distribution, or Bell curve, with the outcome of 15 heads, located at the peak.
If the coin is tossed 30 times then the expected value of the tails to appear is 15 which means tails will appear 15 times.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\[/tex]
You flip a coin 30 times then the expected value will be
The probability of getting tails is 0.5 then the expected value will be
[tex]E(X) = 0.5 \times 30\\\\E(X) = 15\\[/tex]
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If X = 2 units, Y = 9 units, and Z = 6 units, then what is the volume of the rectangular prism shown above?
Answers
Answer:
108 cubic units
Step-by-step explanation:
If X = 2 units, Y = 9 units, and Z = 6 units, then what is the volume of the rectangular prism shown above?
Volume of a rectangular prism XYZ = Length × Width × Height
= 2 unit × 9 unit × 6 unit
= 108 cubic units
the length of a rectangle is 7 cm more than its width and the area is 30 cm find the length, width and the perimeter
Answers
Answer:
Step-by-step explanation:
let width=x
length=x+7
x(x+7)=30
x²+7x-30=0
x²+10x-3x-30=0
x(x+10)-3(x+10)=0
(x+10)(x-3)=0
either x=-10 (rejected being negative)
or x=3
width=3 cm
length=3+7=10 cm
Perimeter=2(10+3)=2×13=26 cm
What is the distance between the points? Round to the nearest tenth if necessary.(-4,-8) (2,2)
Answers
Answer: [tex]2\sqrt{34}[/tex] or, as a decimal, 11.7.
Step-by-Step Explanation:
1. Use the distance formula and substitute the values of the two ordered pairs.
[tex]\sqrt{(2-(-4))^{2}+(2-(-8))^{2}}[/tex]...
2. Multiply -1 by -4.
[tex]\sqrt{(2+4)^2+(2-(-8))^2\\}[/tex] ...
3. Add 2 and 4.
4. Raise 6 to the power of 2.
[tex]\sqrt{36+(2-(-8))^2}[/tex]...
5. Multiply -1 by -8.
6. Add 2 and 8.
7. Raise 10 to the power of 2.
[tex]\sqrt{36+100}[/tex] ...
8. Add 100 and 36.
9. Rewrite 136 as 2² · 34.
10. After factoring 4 out of 136 and rewriting as ... [tex]\sqrt{2^{2}(34)}[/tex], pull out terms from under the radical. It should look like this now: [tex]2\sqrt{34}[/tex]. That is your final answer!!
Hope that helps! Note: the unrounded decimal is 11.66190378.
(P.S. Can I have Brainliest please? Once someone else answers, of course...)
Find the product. Express your answer as a mixed number in simplest form.
2 1/6 × 4 1/2
Answers
Answer: 1 1/2, 3/2, or 1.5
Step-by-step explanation: Convert expression into unproper fractions, 13/6, and 9/2. Then by changing 13/6 into a denominator with 2, you multiply and it equals 1 1/2.
A rectangular wall is 4x-5 units high and 2x+7 units long. Which polynomial best represents the area of the wall in square units?
Answers
Answer:
8x^2 + 18x - 35.
Step-by-step explanation:
Area = (4x - 5)(2x + 7)
= 8x^2 + 28x - 10x - 35
= 8x^2 + 18x - 35.
A bag of skittles contains only red, yellow, and green colors. The respective ratios are 1:3:5 for those three colors. If there are a total of 36 skittles in the bag, how many of each skittles red, yellow, and green are in the bag?
Answers
Answer:
Red skittles = 4 skittles
Yellow skittles = 12 skittles
Green skittles = 20 skittles
Step-by-step explanation:
A bag of skittles contains only red, yellow, and green colors.
The respective ratios are 1:3:5 for those three colors.
We have
red: yellow: green
1:3:5
The sum of the proportion = 1 + 3+ 5 = 9
If there are a total of 36 skittles in the bag, how many of each skittles red, yellow, and green are in the bag?
Hence,
Number of red skittles is calculated as:
1/9 × 36 skittles
= 4 skittles
Number of yellow skittles is calculated as:
3/9 × 36 skittles
= 12 skittles
Number of green skittles is calculated as:
5/9 × 36 skittles
= 20 skittles
Therefore, the number of
Red skittles = 4 skittles
Yellow skittles = 12 skittles
Green skittles = 20 skittles
what is the greatest common multiple of 96,48,84
Answers
Answer: 12
Step-by-step explanation: 96-84=12
I dont really know how i did it I just did.
01 Fill in the Blank Dropdown
The number that occurs the most in a set of data is called the
The middle number in a set of data that is in order from least to greatest is called
The average of a set of numbers is called
The
can be more than one number.
02 Fill in the Blank Dropdown
Answers
Answer:
Number that occurs the most: mode
Middle number in ordered set of data: median
average of a set of numbers: mode
More than one number: i think it is mode
Step-by-step explanation:
What is 1/12 divided by 36
Answers
Answer:
link to answer
https://visualfractions.com/calculator/divide-fractions/what-is-1-12-divided-by-36-36/
Answer:
This is 0.002 but I think you mean
36 divided by 1/12=
3
Can anyone help me out?????
Answers
Answer:
30
Step-by-step explanation:
12×5=60 60÷1/2=30
srry if I was wrong
12×5=60 60÷1/2=30 i hope it's right!! :)
what is the slope and y-intercept to -3x + y = 1
Answers
Answer:
Slope = 3
Y intercept = 1
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept.
So in your question
-3x+y=1
add 3x to each side to get
y = 3x+1
3 is m
1 is b
so the slope is 3
the y intecept is 1
can i please get some help
Answers
Answer: x=0
Step-by-step explanation: This is number 9
12=-4(-6x-3)
-4(-6x-3)=12
-4(-6x-3)/-4=12/-4
-6x-3=-3
-6x-3+3=-3+3
-6x/-6=0/-6
x=0