In Δ A B C, the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. What is the measure of the middle angle?
Answer:
52degrees
Step-by-step explanation:
Let the measure of the largest angle be x
middle angle be y
smallest angle be z
Since the sum of angle in a triangle is 180 degrees, hence;
x + y + z = 180 .... 1
If the measure of the largest angle is 32 less than 3 times the smallest angle, then;
x = 3z - 32
3z = x+ 32
z = x+32/3 ..... 2
If he measure of the middle angle is 8 more than half the measure of the largest angle, then;
y = x/2 + 8 .... 3
Substitute 2 and 3 into 1;
x + x/2 + 8 + (x+32)/3 = 180
multiply through by 6
6x + 3x + 48 + 2(x+32) = 1080
9x + 48 + 2x + 64 = 1080
11x + 112 = 1080
11x = 1080-112
11x = 968
x = 968/11
x = 88 degrees
Get the middle angle y;
Since y = x/2 + 8
y = 88/2 + 8
y = 44 + 8
y = 52 degrees
Hence the measure of the middle angle is 52degrees
The angles in a triangle add up to 180 degrees.
The middle angle is 52 degrees
Let the largest, middle angle and the smallest angle be x, y and z
From the question, we have:
[tex]\mathbf{x = 3z -32}[/tex]
[tex]\mathbf{y = 8 + \frac 12x}[/tex]
Make z in [tex]\mathbf{x = 3z -32}[/tex]
[tex]\mathbf{z =\frac{x + 32}{3}}[/tex]
The angles in a triangle add up to 180 degrees.
So, we have:
[tex]\mathbf{x + y + z = 180}[/tex]
Substitute the expressions for y and z in [tex]\mathbf{x + y + z = 180}[/tex]
[tex]\mathbf{x + 8 + \frac 12x + \frac{x+32}{3} = 180}[/tex]
Multiply through by 6
[tex]\mathbf{6x + 3x + 48 + 2(x+32) = 1080}[/tex]
[tex]\mathbf{9x + 48 + 2(x+32) = 1080}[/tex]
Open brackets
[tex]\mathbf{9x + 48 + 2x + 64 = 1080}[/tex]
Evaluate like terms
[tex]\mathbf{11x + 112 = 1080}[/tex]
Subtract 112 from both sides
[tex]\mathbf{11x = 968}[/tex]
Divide both sides by 11
[tex]\mathbf{x = 88}[/tex]
Substitute 88 for x in [tex]\mathbf{y = 8 + \frac 12x}[/tex]
[tex]\mathbf{y = 8 + \frac{88}2}[/tex]
[tex]\mathbf{y = 8 + 44}[/tex]
[tex]\mathbf{y = 52^o}[/tex]
Hence, the middle angle is 52 degrees
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5. Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your reasoning?
Answer:
andre
Step-by-step explanation:
there is 100 cm in a meter. So diego would be 1.65 meters
Answer:
Andre
Step-by-step explanation:
1.7 meters is 170 centimeters because 1 cm is 100 meters. 165 centimeters is less than 170 meters,so Andre is taller.
Latrell took one of his friends out to lunch. The lunches cost $60 and he paid 5% sales tax. If Latrell left a 15% tip on the $60, how much in total did he pay?
Answer:
$72
Step-by-step explanation:
Cost of the lunch = $60
Sales tax = 5% of $60
= 5/100 × 60
= 0.05 × 60
= $3
Tip = 15% of $60
= 15/100 × 60
= 0.15 × 60
= $9
how much in total did he pay?
Total amount paid = cost of the lunch + sales tax + tip
= $60 + $3 + $9
= $72
Latrell paid $72 in total for the lunch
3x^2 - 8 = 67
Solve for X
Answer:
x=5
Step-by-step explanation:
3x^2=75
x^2=25
x=5
Andrew had a collection of 300 baseball cards at the beginning of the summer After the summer Andrew had traded some of his baseball cards and know he only has 213 baseball cards What percent is the decrease of his baseball cards collected
Answer:
The percentage decrease is 29%
Step-by-step explanation:
Given
[tex]Initial = 300[/tex]
[tex]Final = 213[/tex]
Required
Determine the percentage decrease
This is calculated as thus:
[tex]\%Percentage = \frac{|Final - Initial |}{Initial} * 100\%[/tex]
Substitute values for Final and Initial
[tex]\%Percentage = \frac{|213 - 300|}{300} * 100\%[/tex]
[tex]\%Percentage = \frac{|-87|}{300} * 100\%[/tex]
Get absolute value of -87
[tex]\%Percentage = \frac{87}{300} * 100\%[/tex]
[tex]\%Percentage = \frac{87* 100\%}{300}[/tex]
[tex]\%Percentage = \frac{8700\%}{300}[/tex]
[tex]\%Percentage = 29\%[/tex]
Hence, the percentage decrease is 29%
√-8 . √-32 show work
Answer:
-16
Step-by-step explanation:
the sum of three consecutive odd numbers is 57. Find the product of the numbers.
Answer:
17, 19, 21. Hope this helps.
Which of the following statements best explains why this graph represents a relation that is not a function
Answer:
i think it’s “ the x values between 1 & 3 are each paired with multiple y values “
Step-by-step explanation:
The given relation is not a function because input value 1 and 3 have more than one value
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
As, we know if the relation is function then it's input value is distinct.
From the graph we can se that the input value 1 and 3 have more than one value
As, input 1 ----> {1.1, -1.1}
and, input 3 ----> {0, -2.5}
Hence, the given relation is not a function.
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The formula used to convert Fahrenheit (°F ) to Celsius (°C
5(F - 32) : 9
Which represents the Celsius conversion of 77af?
19°C
O 25°C
O 109°C
Answer:
25°C
Explanation:
My mom uses Celsius and she told me, even though I was still doing the math-
How is 400, 000 + 8000 + 500 + 6 written in standard form ?
Answer:
408,506
Step-by-step explanation:
Answer:
408,506
UwU
hope this helps
HELP ASAP!!! please, I need help
Your answer would be be subtract 3
hope it helps
A triangle has 2 angles that each measure 83°. What kind of triangle is it? A. equiangular triangle B. right triangle C. obtuse triangle D. isosceles triangle
Answer:
D. isosceles triangle
Step-by-step explanation:
The two angles are equal but the third angle will not be. Therefore, a triangle with two equal angles and one not is isosceles.
What is 2+2??? PLS HELP ASAP WILL MARK BRAINLIEST IF CAN
Answer:
2+2=?
Step-by-step explanation:
well 2+2=4
bc idek but i got a pair of fuzzy socks and i love them
Jake scored 2 goals in soccer this season. Jaime scored 4 times as many goals as Jake. Edgar scored 3 times as many goals as Jaime. How many goals did Edgar score?
Answer:
Edgar scored 24 goals in soccer this season.
Step-by-step explanation:
Proportions
We can calculate the number of goals scored by Edgar this season if we follow the relationships given in the problem.
First, we know jake scored 2 goals. Also, we know Jaime scored 4 times as many goals as Jake.
This means Jaime scored 2*4 = 8 goals.
Finally, we know Edgar scored 3 times as many goals as Jaime.
Then, Edgar scored 8*3 = 24 goals.
Edgar scored 24 goals in soccer this season.
Solve for the -2(3)+12
answer correctly pls lol kk
Answer: y= -4x-2
Step-by-step explanation:
glad i could help!
Helppppppp helpppppppp
Answer:
8^12
Step-by-step explanation:
8^7×8^5
add the exponents
7+5=12
keep the base
8^12
Can u plz finish the rest show all the work
Answer:
1/12 is the answer
Answer:
12
Step-by-step explanation:
[tex]\frac{5}{6} - \frac{4}{3} (\frac{3}{4})[/tex]²
⇒ [tex]\frac{5}{6} - \frac{4}{3}[/tex] × [tex]\frac{9}{16}[/tex]
⇒ [tex]\frac{5}{6} - \frac{36}{48}[/tex]
⇒ [tex]\frac{5}{6} - \frac{3}{4}[/tex]
LCM of 4 and 6 is 24
⇒ 5 × 4/6 × 4 - 3 × 6/4 × 6
⇒ 20/24 - 18/24
⇒ 20-18 /24
⇒ 2/24
⇒12
hope this helps you^^
What is the perimeter of the rectangle?
A 30 cm
B. 60 cm
C. 200 cm
D. 400 cm
Answer:
60 cm
B.)60 cm
Answer:
B: 60 cm
Step-by-step explanation:
Because the perimeter you have to add all sides
so it would be 20+10+20+10 = 60
A police officer drives 191 miles in 152 minutes. What is the officer's average speed in miles per hour?
Answer: I think I would be about 1.323 miles per Hour
Step-by-step explanation:
Brian purchased 4 items that were $1.00 each. The sales tax rate is 5.5%. How much was Brian's total bill including sales tax?
Please Help I’m in a test!!!!!
What is the slope of the line that passes through the points (-8, 3) and (-8, 5)?
(A) 0
(B) 1/8
(C) 2
(D) undefined
Answer:
undefined
Step-by-step explanation:
The x coordinates didn't change so the line is vertical and vertical lines have undefined slope
The radius of an airplane propeller is 24 inches. What is the circumference of the propeller?
Answer:
48π
Step-by-step explanation:
the circumference is dπ and the diameter is 2 of the radius
Answer:
48
Step-by-step explanation:
solve this fast! ill give brainliest and a thank you and 5 stars
Answer: now i hav to walk my fish
1 -20
2. 200
3. -6
4. 5
5. -60
6. 45
Step-by-step explanation:
How to walk fish um u see go scuba diving in mariana trench then u find fish (hint) avoid kraken and megaladon or tell them corpse jr sent u. the put leash on fish boom u walked him (another hint) bring extra oxygen tanks u will run out then u die, to leave the kraken throws u out of water and to ur home.
- me
toodles
A fruit stand sells 2 oranges for two dollars and fifty cents.
What is the unit price for each orange?
Answer:
the answer would have to be 1.25
Step-by-step explanation:
Answer:
1 orange= $1.25
2 oranges= $2.50
There are 2.5 oranges per pound, and 1.2 grapefruit per pound. With $50 you can buy 36 pounds of oranges or 45 pounds of grapefruit. If you have enough money to buy 29 pounds of grapefruit, how many oranges (to the nearest whole orange) could you buy instead? is it A.B.C.D OR E
A)23
B)28
C)90
D)58
E)91
help me find p.....
Answer:
the angle size in an nonagon is 140°
Step-by-step explanation:
HELP!!! WILL GIVE BRAINLIEST!!!!
Answer:
c. 12
Step-by-step explanation:
F(x) = (3x - 2)/6 which of the following is the inverse of F(x) ? O A O B. F ^ 1 * (x) = (6x + 2)/3 F ^ - 1 * (x) = (2x - 3)/6 F ^ 1 * (x) = (6x - 2)/3 F ^ - 1 * (x) = (2x + 3)/6 O D.
NEED THIS ASAP!!
Answer:
A
Step-by-step explanation:
The inverse of the given function is (6x + 2)/3.
What is the inverse of a function?"The inverse of a function is a function that undoes the operation of that function. The inverse of a function exists if and only if the function is bijective"
Given function is
F(x) = (3x - 2)/6
⇒ y = (3x - 2)/6
If we write 'x' instead of 'y' and 'y' instead of 'x', then we get:
x = (3y - 2)/6
⇒ 6x = (3y - 2)
⇒ 3y = 6x + 2
⇒ y = (6x + 2)/3
Therefore, F⁻¹ (x) = (6x + 2)/3
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A total of 20 families participate in a car wash. Each family brings two cars. Mr. Gonzales notices that 35% of the cars were minivans. How many minivans were washed?
Answer:
14 minivans
Step-by-step explanation:
From the question
A total of 20 families participate in a car wash. Each family brings two cars.
Hence, the total number of cars brought to the car wash is:
20 × 2
= 40 cars.
Mr. Gonzales notices that 35% of the cars were minivans.
The number of minivans were washed is :
35% of the total number of cars
= 35/100 × 40
= 14 minivans
Hence, 14 minivans were washed