the sum of the internal angles of a triangle are equal to 180 degrees.
once i remembered that the problem became a lot easier.
let a, b, and c be the angles of the triangle.
-----
let a = 2*b
-----
let c = a+b-12
-----
the above two statements are given.
since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is
-----
a + b + c = 180
-----
we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.
-----
it looks like the easiest thing is to solve for b. once we find b, the rest should fall into place very nicely.
-----
since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.
that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.
looking at the equation c = a + b - 12, we solve for b as follows:
since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.
-----
the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.
we can substitute 3*b - 12 for c and the equation becomes
3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.
dividing both sides of the equation by 6 and we get b = 32 degrees.
-----
we have b = 32 degrees.
we have a = 2 * b so a = 64 degrees.
we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.
-----
substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.
-----
answer is:
a
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 71 brakes using Compound 1 yields an average brake life of 41,628 miles. A sample of 31 brakes using Compound 2 yields an average brake life of 36,379 miles. Assume the standard deviation of brake life is known to be 4934 miles for brakes made with Compound 1 and 4180 miles for brakes made with Compound 2. Determine the 98% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval.
Answer:
98% Confidencce Interval is ( 3030.6, 7467.4 )
Step-by-step explanation:
Given that:
Sample size [tex]n_1 =[/tex] 71
Sample size [tex]n_2 =[/tex] 31
Sample mean [tex]\overline x_1 =[/tex] 41628
Sample mean [tex]x_2 =[/tex] 36,379
Population standard deviation [tex]\sigma_1[/tex] = 4934
Population standard deviation [tex]\sigma_2 =[/tex] 4180
At 98% confidence interval level, the level of significcance = 1 - 0.98 = 0.02
Critical value at [tex]z_{0.02/2} = 2.33[/tex]
The Margin of Error = [tex]z \times \sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2} }[/tex]
= [tex]2.33 \times \sqrt{\dfrac{4934^2}{71}+\dfrac{4180^2}{31} }[/tex]
= [tex]2.33 \times \sqrt{\dfrac{24344356}{71}+\dfrac{17472400}{31} }[/tex]
= [tex]2.33 \times \sqrt{906504.06 }[/tex]
= 2218.40
The Lower limit = [tex]( \overline x_1 - \overline x_2) - (Margin \ of \ error)[/tex]
= ( 41628 - 36379 ) - ( 2218.40)
= 5249 - 2218.40
= 3030.6
The upper limit = [tex]( \overline x_1 - \overline x_2) + (Margin \ of \ error)[/tex]
= ( 41628 - 36379 ) + ( 2218.40)
= 5249 + 2218.40
= 7467.4
∴ 98% Confidencce Interval is ( 3030.6, 7467.4 )
enter an inequality that represents the graph
PLEASE HELP QILL GIVE BRAINLIEST
Enter the mixed number as a decimal 3 and 1 over 10
I really need help with this question
Answer: my sis helped me a little so i think its right try 1,500
Step-by-step explanation:
if she gets paid 849000 a year then i would divide 849000 by 12 cause theres that meany months in a year then with that number subtract the Christmas plus witch is 5500 and thats the answer i think
Can someone do this for me? I will give brainliest!
Answer:look it up on quizlet
Step-by-step explanation:
what is the simplified expression for -2a^2b+a^2-5ab+3ab^2-b^2+2(a^2b+2ab)
Answer:
Step-by-step explanation:
Hello,
[tex]-2a^2b+a^2-5ab+3ab^2-b^2+2(a^2b+2ab)\\\\=-2a^2b+a^2-5ab+3ab^2-b^2+2a^2b+4ab\\\\=a^2+3ab^2-ab-b^2[/tex]
Thanks
3) At a barbecue, there are 68 hotdogs being grilled, and there are 34 people. How many hotdogs does each person get? (You can use a calculator) 68 II 8 Hotdogs People 34 Answer: hotdogs for each person
Answer:
2 hotdogs for each person
Step-by-step explanation:
Luke Skywalker mixes bantha milk that is 16% protein with tauntaun milk that is 9% protein. How many pounds of each should he mix to get a 350-pound mixture that is 12% protein?
b = amount of bantha milk
t = amount of tauntaun milk
b + t = 350
0.16 b + 0.09 t = 0.12(b + t) = 42
t = 350 - b
0.16 b + 0.09 (350 - b) = 42
0.16 b + 31.5 - 0.09 b = 42
0.07 b = 10.5
b = 150
t = 200
Use function notation to represent the average speed of the car on the interval from t = 2 to t = 7 .
Answer:
[tex]Average\ Speed = \frac{s(7) - s(2)}{5}[/tex]
Step-by-step explanation:
Given
t = 2 to 7
Required
Find the average speed over these intervals
The function is not given; so, I'll represent the function as s(t)
When [tex]t = 2;[/tex]
[tex]s(t)= s(2)[/tex]
When [tex]t = 7[/tex]
[tex]s(t) = s(7)[/tex]
[tex]Average\ Speed = \frac{Change\ in\ Distance}{Change\ in\ Time}[/tex]
This gives:
[tex]Average\ Speed = \frac{s(7) - s(2)}{7 - 2}[/tex]
[tex]Average\ Speed = \frac{s(7) - s(2)}{5}[/tex]
Help please thanks.
Answer:
Step-by-step explanation:
[tex]\sqrt{1}[/tex] -2 / 6 = (1-2)/6= -1/6= .2 (rounded to tenth)
How hard is 6th grade math?
Answer:
super easy i can help you whenever
Step-by-step explanation:
im in high and i had As in 6th
Answer:
a little hard you just have to understand it
Step-by-step explanation:
Speed limit signs are placed every 58 mi on the highway. How many signs are there on a 75 mi stretch of highway? Which operation should be used to solve the problem? division multiplication
Answer:
you should use multiatication
Step-by-step explanation:
Answer:
lol u got the answer it's multiplication i need POOOIIIIINNNNTTTTSSS
Step-by-step explanation:
In the diagram of circle A, what is the measure of
ZXYZ?
35°
70°
75°
140°
Using the intersecting secant theorem:
Angle xyz = 1/2( wz- XX)
Xyz = 1/2(175-105)
Xyz = 1/2(70)
Xyz= 35
The answer is 35 degrees
The measure of <XYZ is 35 degrees
Circle geometryTo find the measure of<XYZ, we will use the expression as shown below:
The angle at the vertex is half the difference of the intercepted arcs
<XYZ = 1/2(175 - 105)
<XYZ = 1/2(70)
<XYZ = 35 degrees
Hence the measure of <XYZ is 35 degrees
Learn more on geometry here: https://brainly.com/question/24375372
I really need help on this question
Answer:
Answer:answer is 6.5
Answer: so please mark as brainlestA store offers customers a 40% discount on the price of x of selected items. Then, the store takes off an additional 16% at the cash register. Write a price function P(x) that computes the final price of the item in terms of the original price x.
P(x) = ?
Answer:
x-40%-16%
Step-by-step explanation:
help me please. 15 POINTS BRAINLEST ANSWER EVER (y+4)–(y–1)=6y
Answer:
5/6
Step-by-step explanation:
y+4-y+1=6y
5=6y
y=5/6
Solution for (y+4)-(y-1)=6y equation:
Simplifying
(y + 4) + -1(y + -1) = 6y
Reorder the terms:
(4 + y) + -1(y + -1) = 6y
Remove parenthesis around (4 + y)
4 + y + -1(y + -1) = 6y
Reorder the terms:
4 + y + -1(-1 + y) = 6y
4 + y + (-1 * -1 + y * -1) = 6y
4 + y + (1 + -1y) = 6y
Reorder the terms:
4 + 1 + y + -1y = 6y
Combine like terms: 4 + 1 = 5
5 + y + -1y = 6y
Combine like terms: y + -1y = 0
5 + 0 = 6y
5 = 6y
Solving5 = 6y
Solving for variable 'y'.Move all terms containing y to the left, all other terms to the right.
Add '-6y' to each side of the equation.
5 + -6y = 6y + -6y
Combine like terms: 6y + -6y = 0
5 + -6y = 0
Add '-5' to each side of the equation.
5 + -5 + -6y = 0 + -5
Combine like terms: 5 + -5 = 0
0 + -6y = 0 + -5
-6y = 0 + -5
Combine like terms: 0 + -5 = -5
-6y = -5
Divide each side by '-6'.
y = 0.8333333333
Simplifying
y = 0.8333333333
4 5 6 7 8 9 10 TIME REMAINING 35:22 Triangle KNM is shown. Triangle K N M is shown. Angle M K N is 25 degrees. Angle K N M is 130 degrees. Angle N M K is 25 degrees. What is true about the sides of KNM? KN = NM KN + NM = KM KM = 2(NM) KN = One-halfKM Mark this and return
Answer:
KN = NM
Step-by-step explanation:
Given that:
In a triangle KNM
angle ∠ MKN = 25°
angle ∠ KNM = 130°
angle ∠ NMK = 25°
The objective is to determine what is true about the side of KNM.
The correct option is:
KN = NM
From the above, we will see that two angles are equal, which implies the triangle is likely to be an isosceles triangle. An isosceles triangle is a triangle that has two equal angles and sides.
Thus, the intersection of NK with KM is at an angle of 25°, so do NM and KM. We can thereby conclude that the two sides are equal in length provided that they possess the same angles and they intersect at the line at the same angle.
Answer: (A)
Step-by-step explanation: trust me!
AN = 16CM; AC = 18CM & CN = (4X -6) CM. Find the value of X
Answer:
x = 6
Step-by-step explanation:
Since <A is congruent to <N, they are both an isosceles base angles. ∆CAN is an isosceles ∆.
Therefore, one of the properties of an isosceles ∆ is that two sides are equal, aside the base of the isosceles. This implies that: CN = AC
AC = 18cm
CN = (4x - 6)cm, therefore, we can generate an equation for solve for x as follows,
4x - 6 = 18 (two sides of an isosceles ∆ are congruent)
Add 6 to each side of the equation.
4x - 6 + 6 = 18 + 6
4x = 24
Divide both sides by 4
4x = 24/4
x = 6
which sign makes the statement true?
Answer:
Less than sign
Step-by-step explanation:
3/4 is greater than 3/5 because its 3 out of 4 making it 75% and 3/5 is 60%
Nathaniel mowed 18 lawns in 3 hours. What was his rate of mowing in hours per lawn?
Answer:
1/6 hours for every 1 lawn:)
Step-by-step explanation:
Nathaniel mow 18 lawns in 3 hours, then the rate of mowing will be 0.16 or 1/6 hours per lawn.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the information given in the question,
Total lawns mowed by Nathaniel = 18
Total time taken by Nathaniel to mow 18 lawns = 3 hours.
Then, the time required to mow each lawn is,
= 18/3
= 1/6 hrs. Or 0.16 hrs.
To know more about arithmetic operations:
https://brainly.com/question/25277954
#SPJ2
What is one equivalent ratio for 1/3
Answer: 2/6
Step-by-step explanation:
Answer:
[tex]\frac{2}{6}[/tex]
Step-by-step explanation:
In order to create an equal ratio to [tex]\frac{1}{3}[/tex], we need to find a constant to multiply both the numerator and the denominator by.
Let's do 2.
[tex]1\cdot 2 = 2\\\\3\cdot 2 = 6\\\\[/tex]
So:
[tex]\frac{2}{6}[/tex]
Hope this helped!
Jaden bought extra chicken because they’re on sale he wants to store them in the freezer which is such a -2°F he decided to turn the freezer down to another 5° to be sure they don’t spoil
Answer:
-2 - 5
-(2+5)
=7
Answer: -7 °F
118 meters in 2 seconds, how many meters in 11 seconds?
Answer:
It would be 649
Step-by-step explanation:
118 ÷ 2= 59
59 x 11= 649
Answer:
649m
Step-by-step explanation:
[tex]\frac{118m}{2s} =\frac{59m}{s}[/tex]
so that 59m/s we multiply by 11s
[tex]\frac{59m}{s} (11s)=649m[/tex]
What is the number of solutions in this system?
one solution
no solution
infinitely many solutions
First answer is Brainlyist
1
7) What equation is missing in the steps to solvex+6=27
2
Equation
Steps
1
-x+6=2
Original equation
1
2
Multiplication property of equality
8) You have no more than $60 to spend. You want a drink that costs $1.50 including tax, and you
want to buy a pair of pants, which will have 4% sales tax. What is the inequality that represents
the pre-tax price of a pair of pants that you can afford if you buy the drink?
a. +0.04% +1.50 > 60
C. X+0.04x + 1.50 < 60
b. +0.04x +1.50 2 60
d. 1+0.04x + 1.50 S 60
Answer:
I'll answer it
Step-by-step explanation:
do you need it now
As a cube what is -1/64 ________ to the power of ^3
Answer:
(-1/64)= (-1/4)^3
Explanation:
[tex]\sqrt[3]{-\frac{1}{64} }=-\frac{1}{4}[/tex]
[tex](-\frac{1}{4})^3=-\frac{1}{64}[/tex]
whats - 1/64 as cubed
Answer: 1/4
Step-by-step explanation:
Suppose you invest $1000 in an account paying 8% interest per year.
a) What is the balance in the account after 3 years? How much of this balance corresponds to ‘interest on interest’?
Answer:
wasdStep-by-step explanation:
For which values of a the system has no solution: x≤5, x≥a
Given:
The system of inequalities is
[tex]x\leq 5[/tex]
[tex]x\geq a[/tex]
To find:
The values of a for which the system has no solution.
Solution:
We have,
[tex]x\leq 5[/tex] ...(1)
It means the value of x is less than or equal to 5.
[tex]x\geq a[/tex] ...(2)
It means the value of x is greater than or equal to a
Using (1) and (2), we get
[tex]a\leq x\leq 5[/tex]
But if a is great than 5, then there is no value of which satisfies this inequality.
Therefore, the system has no solution for a>5.
5.1436 rounded to the nearest tenth
Answer:
5.1
Step-by-step explanation:
we have
5.1436
since 4 is less than five we cannot pass the 1 to 2
so it stays like
5.1