Point X is the incenter of ΔABC. Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed. If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures. GX = mABX =
Answers
The Measurement of Line GX will be 13 and ∠ABX will be 22°
What is the right-angle triangle?
A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given, Point X is the incenter of ΔABC. Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X.
Also Given :
EX = 4z + 1 and XF = 2z + 7
Solution :
Take EX and XF equal time each other and then solve for z and then you will get GX because EX = XF = GX is congruent.
EX = XF
4z + 1 = 2z + 7
2z = 6
z = 3
As, EX = XF = GX
EX = 4(3) + 1
EX = 13
Thus, GX = 13 ------ ( EX = XF = GX )
To find the ∠ABX, divide ∠ABC them by 2 you will get
∠ABX = 22°
Therefore, The Measurement of Line GX will be 13 and ∠ABX will be 22°.
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Answer:
The first one is 13.
The second one is 22.
Step-by-step explanation:
I took the test I know this is correct. :)
Related Questions
The width of a rectangle is 5 feet more than its length. The perimeter is, at most,50 feet. What is the largest possible width of the rectangle?(write and solve inequality)
GIVING BRAINLIEST PLLZ SHOW WORK
1. Triangle STU is shown on the coordinate plane below. Triangle STU is transformed using the rule (x, y) -> (x+4, y-2). In the image of the transformation, triangle S'T'U', what is the x-coordinate of S'?
Find the prime factors of 60 by dividing by prime numbers.
2) x²+10x+21=0
3) x²+8x+15=0
4) x²+9x+14=0
5) x²-2x35=0
Answers
Answer:
Step-by-step explanation:
To solve these quadratic equations by factoring, you need to find two numbers that multiply to the constant term (the number without x^2) and add up to the coefficient of the linear term (the number with x). Here are the solutions for each of the equations:
1. x² + 5x + 6 = 0
We need two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.
So, we can factor the equation as (x + 2)(x + 3) = 0.
Now, set each factor equal to zero and solve for x:
x + 2 = 0 => x = -2
x + 3 = 0 => x = -3
So, the solutions are x = -2 and x = -3.
2. x² + 10x + 21 = 0
We need two numbers that multiply to 21 and add up to 10. The numbers are 7 and 3.
So, we can factor the equation as (x + 7)(x + 3) = 0.
Now, set each factor equal to zero and solve for x:
x + 7 = 0 => x = -7
x + 3 = 0 => x = -3
So, the solutions are x = -7 and x = -3.
3. x² + 8x + 15 = 0
We need two numbers that multiply to 15 and add up to 8. The numbers are 5 and 3.
So, we can factor the equation as (x + 5)(x + 3) = 0.
Now, set each factor equal to zero and solve for x:
x + 5 = 0 => x = -5
x + 3 = 0 => x = -3
So, the solutions are x = -5 and x = -3.
4. x² + 9x + 14 = 0
We need two numbers that multiply to 14 and add up to 9. The numbers are 7 and 2.
So, we can factor the equation as (x + 7)(x + 2) = 0.
Now, set each factor equal to zero and solve for x:
x + 7 = 0 => x = -7
x + 2 = 0 => x = -2
So, the solutions are x = -7 and x = -2.
5. x² - 2x - 35 = 0
To factor this equation, we need two numbers that multiply to -35 and add up to -2. The numbers are -7 and 5.
So, we can factor the equation as (x - 7)(x + 5) = 0.
Now, set each factor equal to zero and solve for x:
x - 7 = 0 => x = 7
x + 5 = 0 => x = -5
So, the solutions are x = 7 and x = -5.
Answers
Math problem
Hey
Answers
Answer:
10.91
Step-by-step explanation:
40.54-29.63= 10.91
BRAINLIEST ARE ALWAYS APPRECIATED :)
Answer:
10.91
Step-by-step explanation:
40.54
- 29.63
_______________
10.91
Answers
The next term in the pattern is 22.5.
To find the next term in the pattern, it's essential to identify the underlying rule or mathematical operation that governs the progression of the given numbers.
In this case, we can observe that the sequence is increasing by a consistent difference of 4.5 between each consecutive term.
Starting from 4.5 and adding 4.5 successively, we get:
4.5 + 4.5 = 9
9 + 4.5 = 13.5
13.5 + 4.5 = 18
The next term would be:
18 + 4.5 = 22.5
So, the next term in the pattern is 22.5.
In this sequence, each term is obtained by adding 4.5 to the previous term, resulting in an arithmetic progression.
If you continue this pattern, you will keep adding 4.5 to each subsequent term to find the following numbers in the sequence.
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22.5
note that the difference (d ) between each term is
d = 9 - 4.5 = 13.5 - 9 = 18 - 13.5 = 4.5
to obtain the next term add 4.5
next term = 18 + 4.5 = 22.5
Answers
Answer:
AC = BD = 1 unit
Step-by-step explanation:
Given : length of diagonal of rectangle ABCD and
We have to find the length of diagonal.
We know In rectangle diagonal are of equal lengths.
Therefore, for rectangle ABCD diagonals AC= BD
Substitute the values, we get,
Cross multiply , we get
On simplyfy , we get
Solve for y , we get
Divide both side by 12, we get,
Thus, put the values of y in AC and BD to find the length of diagonals , we get,
Similarly for BC, we get,
Thus, AC = BD = 1 unit
Answers
Final answer:
Everett made 3/5 of his shots which is 36 made baskets out of 60 shots. We calculated this by multiplying 3/5 (the fraction of shots he made) by 60 (total number of shots) and simplified it to whole numbers.
Explanation:
The subject matter of this question is fraction multiplication, a fundamental topic in mathematics. To find out how many baskets Everett made, we must use multiplication of fractions and whole numbers. Since Everett made 3/5 of his shots and he shot 60 baskets, we need to multiply these two numbers together.
You would do this calculation: 3/5 * 60. Here's a step-by-step breakdown:
- Temporarily ignore the denominator (5) and multiply the numerator (3) by 60. That's 180.
- Then, divide this number by the denominator: 180 divided by 5. The result is 36.
Therefore, Everett made 36 baskets out of 60 shots.
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