Answers
Answer:
m∠1 = 140°
m∠2 = 40°
m∠3 = 65°
m∠4 = 75°
m∠5 = 115°
Step-by-step explanation:
We will use a few different methods to find the angles:
A triangle's angles will always add up to 180°. With this information, we can find the last angle of the triangle on the left:
∠1+∠2+∠3=180°
60+80+∠3=180°
Let x represent the value of ∠3. Simplify addition:
[tex]140+x=180[/tex]
Subtract 140 from both sides:
[tex]140-140+x=180-140\\\\x=40[/tex]
The unknown angle is 40°. With this information, we can find the
m∠1:
m∠1 and the 40° we just found are supplementary angles, which means that their measures will add up to a total of 180°.
∠1+∠2=180°
Insert the value we know:
40°+∠2=180
Let x represent the value of ∠2. Subtract 40 from both sides:
[tex]40-40+x=180-40\\\\x=140[/tex]
There fore:
m∠1=140°
We can use this same rule to find the m∠2:
∠1+∠2=180°
or, we can use the vertical angles rule. The first angle we found (Which is 40°) is a vertical angle to m∠2, so they have the same value. Therefore:
m∠2=40°
To find m∠3, we need to find the other missing angle in the middle triangle. Use the supplementary angle rule, since the missing angle is supplementary to the angle that is 105°:
∠1+∠2=180°
Insert the known values, substituting x for the unknown angle:
[tex]x+105=180[/tex]
Subtract 105 from both sides:
[tex]x+105-105=180-105\\\\x=75[/tex]
The unknown angle is 75°. Now find m∠3, knowing that triangles add up to 180°:
m∠2+m∠3+75=180
Insert the m∠2, make m∠3 be x:
[tex]40+x+75=180[/tex]
Simplify addition:
[tex]115+x=180[/tex]
Subtract 115 from both sides:
[tex]115-115+x=180-115\\\\x=65[/tex]
Therefore:
m∠3=65°
To find m∠4, use the vertical angle rule.
Therefore:
m∠4=75°
To find m∠5, we could find all triangle measures of the least triangle, or we can use the following:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.
The m∠5 is the exterior angle, and the opposite interior angles are 75° and 40°:
[tex]75+40=115[/tex]
Therefore:
m∠5=115°
:Done
Related Questions
PLEASE HELP!!!!!
a,b,c,or d?!?!?
Answers
Answer:
A
Step-by-step explanation:
MARK BRAINLIEST
6.8x+9.3= -9.4+3.4(2-5x)
Answers
Answer: the answer to this is x=0.5
Step-by-step explanation:
In order to solve this you have to combine the multiplied terms into a single fraction so its going to look like this - 34x/5 + 9.3= -9.4+3.4(2-5x)
The reposition your terms and put together your multiplied terms into a fraction,Once you have that done distribute them
Subtract 9.3 on both sides.you may simplify and then multiply all the terms with the same value to get rid of the denominators from the fractions
also add 85x to both sides then finally divide both side by the same term which get you -59.5/119 and then simplify and you get -0.5
so x= -0.5
Answer:
x=-0.5
Step-by-step explanation:
step 1
6.8x+9.3=-9.4+3.4(2-5x)
6.8x+9.3=-9.4+(3.4)(2)+(3.4)(-5x) distribute
6.8x+9.3=-9.4+6.8+-17x
6.8x+9.3=(-17x)+(-9.4+6.8) combine like terms
6.8x+9.3=-17x+-2.6
6.8x+9.3=-17x-2.6
step 2
add 17x to both sides.
6.8x+9.3+17x=-17x2.6+17x
23.8x+9.3=-2.6
step 3
subtract 9.3 from both sides.
23.8x+9.3-9.3=-2.6-9.3
23.8x=-119
step 4
divide both sides by 23.8
23.8x/23.8= -11.9/23.8
The answer is =-0.5
23.21 to the nearest hundredth
Answers
Answer:
23.21
Step-by-step explanation:
The answer you have given is correct.
Tuition for one year at the University of Houston is about $12,300. Azul plans to attend this university and will save money each month for the next 4 years. His parents have saved $4,860 for his first year of tuition. Which plan shows the amount of money Azul will need to save in order to pay for his first year at the University of Houston?
A. Azul will need to save $1,860 per month for the next 4 years.
B. Azul will need to save $155 per month for the next 4 years.
C. Azul will need to save $620 per month for the next 4 years.
D. Azul will need to save $256.25 per month for the next 4 years
Answers
Answer:
It should be C. 620
Step-by-step explanation:
Using proportions, it is found that Azul will need to save $155 per month for the next 4 years, and the correct option is B.
The total price of one year of tuition is $12,300, while his parents have saved $4,860.Thus, the amount he has to save for the next 4 years is:
[tex]A = 12300 - 4860 = 7440[/tex]
4 years have 48 months, thus, he has to save $7440 in 48 months, which means that the monthly amount is:[tex]\frac{7440}{48} = 155[/tex]
And the correct option is:
B. Azul will need to save $155 per month for the next 4 years.
A similar problem is given at https://brainly.com/question/24342347
A textbook costs $65.49 before tax. The tax on the textbook is 6.5% what is the total costs of the textbook
Answers
Answer:
65.49*0.065 = 4.26
Step-by-step explanation:
65.49*0.065 = 4.26
65.49+4.26 = $69.75
Answer:
$69.75
Step-by-step explanation:
65.49x6.5%= 4.26
65.49+4.26= 69.75
Don't forget your label!
Hope this helps!
-AxekickNebulite
The vertex of a parabola is (6,2), and the equation of its directrix is x = 8. What is the equation of this parabola in standard form?
a. (y−2)2=8(x−6)
b. (y−2)2=−8(x−6)
c. (x−6)2=−8(y−2)
d. (x−6)2=8(y−2)
Answers
Answer:
The equation of this parabola in standard form is (y - 2)² = -8(x - 6) ⇒ B
Step-by-step explanation:
Let us revise the standard form of the equation of a parabola
The standard form of the equation is (y - k)² = 4p(x - h), where
(h, k) is the turning point (h + p, k) are the coordinates of the focus x = h - p is the equation of the directrix
∵ The vertex of a parabola is (6, 2)
→ From the fact above
∴ h = 6 and k = 2
∵ The equation of its directrix is x = 8
→ From the fact above
∴ h - p = 8
→ Substitute the value of h to find p
∵ 6 - p = 8
→ Subtract 6 from both sides
∴ - p = 2
→ Multiply both sides by -1
∴ p = -2
→ Substitute the values of h, k, and p in the form above
∴ (y - 2)² = 4(-2)(x - 6)
∴ (y - 2)² = -8(x - 6)
∴ The equation of this parabola in standard form is (y - 2)² = -8(x - 6)
On the last day of school, Davon surveys the students in his class to find out how many absences each had during the school year. The results are shown below.
{15, 0, 10, 1, 4, 4, 7, 6, 9, 9, 13, 11, 6, 5, 3, 8, 4, 3, 10, 17, 11, 4, 4, 3}
Represent these data on the histogram below.
!!!PLEASE HELP!!! To create the histogram, place your cursor over each interval on the x-axis then click and drag the bar up to graph the correct number of students. If you need to change the number of students you placed, click the top of the bar then drag the bar up or down to show the number of students you need. (there are 5 colums and it only goes up to 12)
Answers
Answer:
0-2 = 2. 3-5 = 9. 6-8 = 4. 9-11 = 6 12 & more = 3
What is the vertex of the graph of the function below?
y= x2 - 10x + 21
O A. (5,-4)
B. (3,0)
O C. (5,0)
OD. (3,-4)
Answers
Answer:
Step-by-step explanation:
A. (5,-4)
The vertex of the graph of the function is (5,-4).
The answer is option A.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the vertex of the function y = x² - 10x + 21,
We can use the formula:
x = -b/2a
where a is the coefficient of the x² term, b is the coefficient of the x term, and x is the x-coordinate of the vertex.
In this case,
a = 1 and b = -10, so:
x = -(-10)/(2 x 1) = 5
To find the y-coordinate of the vertex, we can substitute x = 5 into the function:
y = (5)² - 10(5) + 21 = -4
Therefore,
The vertex of the graph of the function is (5,-4).
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Which of the following explains the relationship between angles A and D?
Answers
Regroup the integers
Answers
Kai is looking for his first job as a pharmacy technician. He prepares for the job by memorizing household, metric, and apothecary abbreviations. In addition, he memorizes the methods for converting data between those measurement systems. Perform the following calculation using the ratio and proportion method. How many ounces (oz) are equal to 4 cups?
Answers
Answer:
Step-by-step explanation:
0.5: 4
pLZ NAME MEE THE brainliest thank u
I need help on this
Answers
Answer:
,b j,mbnlvj lcv
Step-by-step explanation:
nb ckhbv m
i just want want points sorry! :)
solve
log5(2)+log5(x)-log5(x-1)=log5(3)
Answers
Step-by-step explanation:
log5(2)+log5(x)-log5(x-1)=log5(3)
log5(2x) = log5(3)+log5(x-1)
log5(2x) = log5(3Xx-1)
2x = 3x-3
x= 3
Convert 1.05 to a percent.
Answers
Answer:
105%
Step-by-step explanation:
you would just move the decimal 2 places to the right
Who do u guys think will win National League MVP if ur right u'll get brainlyest
no idk
Answers
Answer:
Will Leitch
Step-by-step explanation:
*PLEASE SOLVE USING EQUATIONS*
How old am I if 200 reduced by 2 times my age is 46?
A) 89
B) 83
C) 77
D) 108
Answers
Answer:
C) 77
Step-by-step explanation:
77 times 2= 154
200-154= 46
Suppose Borman earned $148,000 last year. She calculates her self-employment tax by multiplying
$148,000 by 15.3%, which equals $22,644. Is Borman correct? Briefly explain.
Answers
Answer:
Yes Borman is correct.
Step-by-step explanation:
Borman moved the decimal point 2 spaces to the left which gave her 0.153
Then she multiplied that by $148,000 to get 15.3% of it which would give her $22,644 so therefore, she is correct.
When full, the gas tank of a car holds 22 gallons. It now contains 16.5 gallons. What percent represents how full the tank is?
Answers
Answer:
75%
Step-by-step explanation:
16.5/22 = 0.75
0.75 x 100 = 75
∴ 75% of the tank is full.
Add 1/2 + (-3/4)= show the work
Answers
Answer:
2/4 - 3/4 = -1/4
Step-by-step explanation:
2/4 is half
3/4 is a little more than half
2/4-3/4=1/4
Hope this helps!! :D
if z is the circumcenter of triangle qrs find each measure
Answers
Answer:
Step-by-step explanation:
Circumcenter of A triangle is the center of a circle passing through the vertices of the given triangle.
So, the distance of Z from the vertices Q, R and S will be the radii of the circle.
Therefore, ZQ = ZR = ZS
Since, circumcenter of a triangle is defined by the point of intersection of the perpendicular bisectors of the sides of the given triangle.
Therefore, points W, X and Y are the midpoints of sides QR, RS and QS.
Using these facts,
a). QR = 2(WQ)
= 2(25)
= 50
b). Apply Pythagoras theorem in ΔRXZ,
(RZ)² = (RX)² + (ZX)²
(RZ)² = (40)² + (9)²
RZ = √1681 = 41
c). XS = [tex]\frac{1}{2}(RS)[/tex]
= [tex]\frac{1}{2}(80)[/tex]
= 40
d). Since, ZQ = ZR = ZS
ZS = 41
e). By applying Pythagoras theorem in ΔRWZ,
(RZ)² = (WZ)² + (WR)²
(41)² = (WZ)² + (25)²
(WZ)² = (41)² - (25)²
WZ = √1056
WZ = [tex]4\sqrt{66}[/tex]
≈ 32.5
Applying the circumcenter theorem and the Pythagorean Theorem, the following measures are calculated as:
a. QR = 50
b. RZ = 41
c. XS = 40
d. ZS = 41
e. WZ = 32.5
Based on the circumcenter theorem of a triangle, the following holds true given that Z is the circumcenter of triangle QRS:
RZ, QZ, and ZS are equal (circumcenter Z is equidistant from the three vertices of ΔQRS).The perpendicular bisectors divides the three sides, RS, QS, and QR into equal parts each.Points X, Y, and W are at right angles.Given:
RS = 80WQ = 25XZ = 9a. Find QR:
QR = 2 × WQ = 2 × 25
QR = 50
b. Find RZ in right ΔXRZ:
XZ = 9 (given)
XR = 1/2(RS) = 1/2(80) = 40
Apply Pythagorean Theorem to find RZRZ = √(XZ² + XR²)
SubstituteRZ = √(9² + 40²)
RZ = 41
c. Find XS:
XS = 1/2(RS) = 1/2(80)
XS = 40
d. Find RZ:
RZ = ZS = QZ = 41 (equidistant)
ZS = 41
e. Find WZ in right ΔWRZ:
WR = WQ = 25
WR = 25
RZ = 41
Apply Pythagorean Theorem to find WZWZ = √(RZ² - WR²)
SubstituteWZ = √(41² - 25²)
WZ = 32.5
Learn more about the circumcenter theorem on:
https://brainly.com/question/8055762
An airplane is traveling with an airspeed of 500 mph in the direction N 60° E. A wind blows directly south at 50 mph. What is the plane’s drift angle?
3.84°
5.21°
60.00°
65.21°
Answers
Answer:
5.21
Step-by-step explanation:
Got it right on edg
Answer:
B) 5.21°
Step-by-step explanation:
got it right on edge :)
Simplify 3 square root of 512
Answers
Answer:
8
Step-by-step explanation:
not sure if this is what ur looking for sorry
The simplified form of 3√(512) using radical is 48√(2).
To simplify √(512), find the prime factorization of 512.
Prime factorization of 512:
512 = [tex]2^9[/tex]
Now, rewrite the square root as follows:
√(512) = √[tex](2^9)[/tex]
Next, use the property of square roots that states √(a * b) = √(a) * √(b):
√[tex](2^9)[/tex] = √([tex]2^8 * 2)[/tex]
= √[tex](2^8) * \sqrt(2)[/tex]
Since √[tex](2^8)[/tex] is equal to [tex]2^4[/tex] then
√(512) = [tex]2^4[/tex] * √(2)
Finally, simplify √(2) as it is not a perfect square:
√(512) = [tex]2^4[/tex]* √(2)
= 16 * √(2)
So, the simplified form is 48√(2).
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which expression is equivalent to 6-(-8)
○ -6+8
○ -6+(-8)
○ 6+(-8)
○ 6+8
Answers
Answer: 6 + 8
Step-by-step Explanation: When you're adding and subtracting positives and negatives and you see a minus a negative in a problem, you can change it to plus a positive.
So 6 - (-8) can be thought of as 6 + (+8).
Answer:6+8
Step-by-step explanation:
What is the 100th term in the sequence an= 4n-12
Answers
The hundredth term of the given sequence is 388.
What is a sequence?In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given that, we need to find the 100th term in the sequence an= 4n-12,
Put n = 100,
a₁₀₀ = 4 x 100 - 12
= 400 -12
= 388
Hence the hundredth term of the given sequence is 388.
Learn more about sequence, click;
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Find the scale factor to map ΔABC onto ΔA′B′C′.
Question 19 options:
A)
3
B)
1∕3
C)
1∕2
D)
4
Answers
Answer:
answer is 1/3 so B
Step-by-step explanation:
If ∠BAC ≅ ∠DCA, is ABE ≅ CDE? Explain.
A. Yes; the triangles are congruent by AAS.
B. Yes; the triangles are congruent by ASA.
C. Yes; the triangles are congruent by SAS.
D. No; the triangles are not congruent.
Answers
Answer:
The answer is A.
Step-by-step explanation:
It is A because both sides match up except for the last pair, where they are the same. Hope this helped!
Which transformation represents a reflection over the x-axis?
O (X,Y) - (-x, y)
O(x,y) → (X, -y)
O(x, y) (y,x)
(x, y) - (-y, x)
Answers
Find the value of x that makes u and v parallel
Answers
Answer:
3
Step-by-step explanation:
equate the two together to get the value of x
10+10 Chloe answer
Answers
Answer:
20
Step-by-step explanation:
Figure LMNO maps to L'M'N'O' by a 125° rotation about point T.
Quadrilateral L M N O is rotated 125 degrees about point T to form quadrilateral L prime M prime N prime O prime.
Which congruency statement is correct?
LMNO ≅ L'M'N'O'
LMNO ≅ O'M'N'L'
ONML ≅ M'O'N'L'
ONML ≅ O'M'N'L'
Answers
Answer:
A= LMNO ≅ L'M'N'O'
Step-by-step explanation:
just did it trust me
A= LMNO ≅ L'M'N'O'. Hope this helps!!