Answers
=======================================================
Explanation:
The smaller angles HGE and EGF combine to form the largest angle HGF.
This is an example of the angle addition postulate.
(angle HGE) + (angle EGF) = angle HGF
(3x+11) + (110) = 16x+4
3x+121 = 16x+4
121-4 = 16x-3x
117 = 13x
13x = 117
x = 117/13
x = 9 which is the final answer
We can stop here.
--------------------
Extra info (optional section)
Use this x value to find each angle shown below
angle HGE = 3x+11 = 3*9+11 = 27+11 = 38 degreesangle HGF = 16x+4 = 16*9+4 = 144+4 = 148 degreesThen notice how,
(angle HGE)+(angle EGF) = 38+110 = 148
which is exactly the measure of angle HGF
This confirms that the equation
(angle HGE) + (angle EGF) = angle HGF
is true for that x value of x = 9. Therefore, the answer is confirmed.
9514 1404 393
Answer:
11) x = 9°
13) x = -12°
Step-by-step explanation:
11) ∠HGE +∠EGF = ∠HGF
(3x +11) +(110°) = (16x +4)
117° = 13x . . . . . . . . . . . . . . . subtract 3x+4, collect terms
9° = x . . . . . . . . . . . . divide by 13
__
13) ∠BCF +∠FCD = ∠BCD
(x +78) +(x +41) = 95°
2x = -24°
x = -12°
Related Questions
The cost of hat, pants, and sweater is $225. The pant cost $10 more than hat, and the sweater cost $10 more than the pants. What is the cost of the hat ?
Answers
Answer:
$65
Step-by-step explanation:
Let x represent the cost of the hat.
Since the pants cost $10 more than the hat, the cost can be represented by x + 10.
Since the sweater cost $10 more than the pants, the cost can be represented by x + 20.
Create an equation adding these all together and setting it equal to 225, then solve for x:
(x) + (x + 10) + (x + 20) = 225
3x + 30 = 225
3x = 195
x = 65
So, the hat cost $65
Find the missing side of the triangle.
A. √226 ft
B. √17 ft
C. √329 ft
D. √346 ft
Answers
15^2 = x^2 + 11^2
225 = x^2 + 121
Subtract both sides 121
225 - 121 = x^2 + 121 - 121
104 = x^2
x = √104
x = √4 × 26
x = √4 × √26
x = 2 × √26
x = 2 √26
Choose the inequality that represents the following graph.
Answers
Answer:
it's most most probably option d becoz I studied In different way so... as per me d ... figure is quite diff but d
If the square of the hypotenuse of an isosceles right triangle is 98cm2 find the length of each side
Answers
Answer:
7
Step-by-step explanation:
Let the each leg be x so,
√(x²+x²)=√98
or, √(2x²)=√98
or, x√2=7√2
or, x=7
Mike traveled from the school to the mall and then from the mall to the library. Henry traveled from the school to the library. How many more miles did Mike travel than Henry?
Answers
Answer:
12 miles
Step-by-step explanation:
From the graph given :
Mike's travel :
School to Mall= 16 miles
Mall to Library = 30 miles
Total travel = 16 + 30 = 46 miles
Henry's travel :
From school to Library = Hypotenus :
Distance can be obtained using Pythagoras :
Hypotenus = √(opposite² + adjacent²)
Hypotenus = √(30² + 16²)
Hypotenus = √1156
Hypotenus = 34 miles
Difference in Distance covered :
(46 miles - 34 miles) = 12 miles
The greatest number which on dividing 1657 and 2037 leaves nemainder 6 ands respectively is?
Answers
Answer:
It would be 127
Step-by-step explanation:
We see that they only have 127 common in their prime factorization. Hence, HCF(1651, 2032) = 127. Hence, the greatest number which divides 1657 and 2037 leaves a remainder of 6 and 5 respectively is 127.
At age 20, to save for retirement, Rebecca decides to deposit 80$ at the end of each month in an IRA that pays 6.2% compounded monthly. Use the formula for the value of an annuity.
A=P[(1+r/n)^nt-1]/(r/n)
How much money will be in the IRA when Rebecca retires?
How much interest will the IRA have gained?
Answers
Answer:
159319.26 I Don't know the interest
What is the explicit formula for this sequence?
-9, - 3, 3, 9, 15, ...
Answers
Answer:
-15+6d
Step-by-step explanation:
The common difference of the sequence is -3+9=6
The formula is an=a+(n-1)d, an=-9+(n-1)*6=-15+6d
In the figure below, triangle ABC is similar to triangle PQR:
A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.
What is the length of side PQ?
48
24
40
18
Answers
Answer:
24
Step-by-step explanation:
Since the triangles are similar the side lengths must be proportional
2/12 = 4/PQ cross multiply expressions
2PQ = 48 divide both sides by 2
PQ = 24
Write each decimal as a fraction or mixed number in simplest form -0.4
Answers
Answer:
-2/5
Step-by-step explanation:
Help pls this is really hard
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
√2 ≈ 1.414 ≈ 1.4 +0.1(1/7)
The dot will be about 1/7 of the way between 1.4 and 1.5.
g(x) = x3 + 2x2 - x - 2 to answer all the questions in Part II. 1. Use synthetic division to show that x = -2 is a zero of the polynomial.
Answers
Answer:[tex]x^{2} -1[/tex]
Step-by-step explanation:
Given :[tex]g(x)=x^{3} +2x^{2} -x-2[/tex]
Factor x+2,x=-2
Using synthesis division:
-2 ) 1 2 -1 -2
-2 0 2
1 0 -1 0
[tex]x^{2} +0x-1[/tex]
Yes, x = -2 is a zero of the polynomial.
Given that,
The function g(x) = x³ + 2x² - x - 2 is divided by (x + 2)
Now apply the synthetic division to show that x = -2 is a zero of the polynomial.
When we divide by using synthetic division as shown in the attached image.
Remainder = 0
Hence, this shows that x = -2 is a zero of the polynomial.
Therefore, x = -2 is a zero of the polynomial.
To learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ4
The telephone numbers in a small town have two digits. They run from 00 to 99.
Of the 100 possible numbers, those that become smaller when reversed are not used, i.e. 21 is not used.
What is the maximum number of telephone numbers this town could have?
Answers
Answer:
[tex]55[/tex]
Step-by-step explanation:
We'll be using case-work to solve this problem. Let's call the ones digit of the telephone number [tex]B[/tex] and the tens digit [tex]A[/tex]. Each telephone number can be represented as [tex]AB[/tex].
Since the question states that numbers that are smaller when their digits are reversed are not used, we have the following inequality:
[tex]B\geq A[/tex]
This is because if [tex]A>B[/tex], the number would become smaller when [tex]A[/tex] and [tex]B[/tex] are switched in [tex]AB[/tex]. However, if [tex]A=B[/tex] or [tex]B>A[/tex], the number will not become smaller.
Let's work our way up starting with [tex]A=0[/tex]. If [tex]A=0[/tex], there are 10 other numbers (0-9) that we can choose for [tex]B[/tex] that adhere to the condition [tex]B\geq A[/tex]:
[tex]0B,\\01, 02, 03,...[/tex]
Therefore, there are 10 possible telephone numbers when the tens digit is 0.
Repeat the process, now assigning [tex]A=1[/tex]. Now, we only have the digits 1-9 to choose from for [tex]B[/tex], since [tex]B[/tex] needs to be greater than or equal to A. Therefore, there are 9 possible telephone numbers when the tens digit is 1.
This pattern continues. As we work our way up through the cases (when increasing [tex]A[/tex] by 1), the number of possible telephone numbers decreases by 1, since there becomes one less option for [tex]B[/tex].
The last case would be [tex]A=9[/tex] in which case there would only be one option for [tex]B[/tex] and that would be 9.
Since there are 10 cases (0-9), add up the possible telephone numbers for each case:
[tex]\displaystyle \sum_{n=1}^{10}n=1+2+3+4+5+6+7+8+9+10=\boxed{55}[/tex]
Alternatively, recall that the sum of this series can be found using [tex]\frac{n(n+1)}{2}[/tex], where [tex]n[/tex] is the number of values in the set. In this case, [tex]n=10[/tex], and we have:
[tex]1+2+3+4+5+6+7+8+9+10=\frac{10(11)}{2}=\frac{110}{2}=\boxed{55}[/tex]
The expression 8x2 − 176x + 1,024 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998. Choose the equivalent expression that is most useful for finding the year where the population was at a minimum.
Answers
B
Step-by-step explanation:
Might be wrong
Please help for brainliest!!
Answers
Answer:
108
Step-by-step explanation:
3(6*3*2)
Answer:
L x W x H is the formula to solving this problem.
It looks like 6 is the length, 3 is the width and 2 is the height!
6 x 3 x 2 = 36
BUT WAIT!
It seems like the 2 is on one of the tissues, if it isn't 36, the other answer is definitely something else...
2 + 2 + 2 = 6
6 x 3 x 6 = 108!
_ _ _ _ _
The answers could either be 36 or 108!
raise s to the 7th power, then find the sum of the result and 3
Answers
Answer:
s^7 + 3
Step-by-step explanation:
Brainliest, please!
PLZ HELP! I WILL PUT BRAINLIEST!
Find the three digit numbers which have the the following properties: all three digits are different, the first digit is the square of the second digit and the third digit is one more than twice the second digit.
Answers
Answer:
Step-by-step explanation:
1^2 = 1 This one is impossible. The digits have to be different.
2^2 = 4
3^2 = 9
so the first two digits can either be
4 and 2
9 and 3
The third clue is the one that decides. The third digit is odd and and 1 more than twice the second
The third digit can be 2 * 2 + 1 = 5 or 2*3 + 1 = 7. There is no way to choose between them.
So the answer is either 425 or 937. We cannot decide which. If there is another clue that will break the log jam, post it and I'll come back.
These are the only two answers possible. If the second digit is more than 3 then the first digit is no longer a single digit. It is more than 9.
1)a)write any three rational numbers .
Answer : 3/4,-2/6,1/2 is are called rational
number.
b)Explain rational numbers in your own words .
Answer: A number which can be written in the form p/q , where p and q are integers and q = 0 is called a rational number
Answers
Step-by-step explanation:
1)1/2,1/5 and 0
2)In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer
2, Nine people fit comfortably in a 3 ft. by 3 ft. area. Use this value to
estimate the size of a crowd that is 8 yards deep and 1 mile long.
Determine the Ratio? A
Ratio = 9 x (3x3). B
O Ratio = 9/3
C
Ratio = 9/(3x3)
D Ratio = 8/5280
Answers
The ratio for Nine people fit comfortably in a 3ft by 3ft area is [tex]\frac{9}{3X3}[/tex]
Option C [tex]Ratio =\frac{9}{3X3}[/tex]
Size of crowd: [tex]\frac{9}{3 \cdot 3} \cdot 24 \cdot 5280[/tex]
Given :
Nine people fit comfortably in a 3 ft. by 3 ft. area
To find : we need to estimate the size of a crowd that is 8 feet deep and 1 mile long. we need to determine the ratio as well
Ratio = number of people / total area
[tex]Raio=\frac{9}{3X3}[/tex]
To find the size of the crowd , convert yards into feet and mile into feet
1 yard = 3 miles
8 yards= 3 times 8 = 24 feet
1 mile = 5280 feet
Now we find the area in feet
[tex]24 \cdot 5280[/tex]
size of the crowd=ratio times the area in feet
[tex]\frac{9}{3 \cdot 3} \cdot 24 \cdot 5280[/tex]
Learn more : brainly.com/question/24367786
Simplify the following equation
4−8÷2+3
Answers
The correct order to evaluate it is:
4 - (8 / 2) + 3 = (4 - 4) + 3 = 0 + 3 = 3
Hi there!
»»————- ★ ————-««
I believe your answer is:
3
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying...}}\\\\4-8\div2+3\\\\---------------\\\text{Follow PEMDAS:}\\\\\\\rightarrow4-8\div2+3\\\\\rightarrow 4 - 4 + 3\\\\\rightarrow 0 + 3\\\\\rightarrow \boxed{3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Express 2³a²b in factor form
Answers
Answer:
In factor form, the answer is ---> 8a^2b
Step-by-step explanation:
2³a²b
= (2^3) (a^2) b
= 8a^2b
If the nth term of A.P. are 7, 12, 17, 22.....is equal to the nth term of another A.P. 27, 30, 33, 36. Find the value of n?
Answers
Answer:
[tex]n = 11[/tex]
Step-by-step explanation:
We are given two arithmetic sequences:
7, 12, 17, 22... and 27, 30, 33, 36...
And we want to determine n such that the nth term of each sequence is equivalent.
We can write a direct formula for each sequence. Recall that the direct formula for an arithmetic sequence is given by:
[tex]\displaystyle x_n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The first sequence has an initial term of 7 and a common difference of 5. Hence:
[tex]\displaystyle x_n = 7 + 5(n-1)[/tex]
The second sequence has an initial term of 27 and a common difference of 3. Hence:
[tex]x_n = 27 + 3(n-1)[/tex]
Set the two equations equal to each other:
[tex]7 + 5 (n-1) = 27 + 3(n-1)[/tex]
Solve for n. Distribute:
[tex]7 + (5n - 5) = 27 + (3n - 3)[/tex]
Combine like terms:
[tex]5n + 2 = 3n + 24[/tex]
Isolate:
[tex]2n = 22[/tex]
Divide. Hence:
[tex]n = 11[/tex]
In conclusion, the 11th term of the first A.P. is equivalent to the 11th term of the second.
Which is the graph of y = [x]-2?
PLEASE HELP TIMED PLEASE 20points
Answers
Answer:
3rd graph
Step-by-step explanation:
Answer:
it depends on the equation thats given
Step-by-step explanation:
you put the value of x in the brackets and then solve it so that u get the coordinates of y, then u can put the point on whichever values u get for x and y and continue like that until you get all the points (you can join them if the question asks)
Choose the model that correctly illustrates the division problem 2 3 ÷ 3 4 3 2 ÷ 4 3 .
Answers
23÷34÷32÷43
= 0.0001558519
Must click thanks and mark brainliest
Simplify 7 to the 6th power ⋅ 7 to the fifth power.
49 to the 11th power
49 to the 35th power
7 to the 11th power
7 to the 35th power
Answers
Answer:
7 to the 11th power
Step-by-step explanation:
7⁶×7⁵=7¹¹
because a¹×a¹=a¹+¹
Find the volume of a rectangular solid that
is 9 ft. by 12 ft. by 8 ft.
Help please
Answers
Answer:
864 ft³ is the volume
Step-by-step explanation:
Volume = width · height · length
= 12 · 9 · 8
= 864
Answer:
Step-by-step explanation:
Volume of rectangular solid = length * width * height
= 9 * 12 * 8
= 864 ft³
Need help with 1 and 2
Answers
Answer:
1a. 128
1b. 81
1c. 64
1d. 25
1e. 343
1f. 100000
1g. 64
1h. 0
1i. 13
1j. 1
2a. 243
2b. 64
2c. 36
2d. 625
2e. 1331
2f. 10000000
2g. 81
2h. 0
2i. 17
2j. 1
Pls help. I really suck at math.
Determine whether the following polygons are similar.
Answers
Answer:
They are not similar.
To easily check if they are similar, you only need to look at the degrees angles, since if the angles are the same, the lengths of the sides will always come out to be similar somehow.
Those triangles possess right angles as you can see the little square thingie in the corners.
Those are 90 degrees, and you can add the 30 degrees in the left shape to 90 to get 120.
There are 180 degrees in a triangle, so 180 - 120 = 60.
Therefore, the unknown angle is 60.
A 30 60 90 triangle is called a special right triangle since there are many useful ratios hidden inside.
The other triangle has a 55 degree angle which is not on the first, so they must not be similar.
Pls brainly dont delete this link, its useful.
https://blog.prepscholar.com/30-60-90-triangle-ratio-formula
This helps you understand the special triangles.
You don't suck at math, you suck at geometry imo, though only in this unit of geometry, probably good at others.
Step-by-step explanation:
Which situation is best represented using a negative integer?
Answers
Answer:
a
Step-by-step explanation:
If 150° and 3a are supplementary angles, find the value of a.
Answers
Answer:
a = 10
Step-by-step explanation:
Supplementary angles sum to 180° , so
150 + 3a = 180 ( subtract 150 from both sides )
3a = 30 ( divide both sides by 3 )
a = 10
