x = first angle
y = second angle
z = third angle
x + y + z = 180
The sum of the measures of the second and third angles is twice the measure of the first angle. ----> y + z = 2x
The third angle is 12 more than the second. ----> z = y + 12
Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation
y + z = 2x Plug in (y + 12) for z
y + (y + 12) = 2x Simplify
2y + 12 = 2x Divide 2 on both sides
y + 6 = x Isolate "y"
y = x - 6 Next you could plug this into z = y + 12, so that z has the x variable
z = y + 12
z = x - 6 + 12
z = x + 6
Now that you have y and z, you can do this:
x + y + z = 180
x + (x - 6) + (x + 6) = 180 Simplify
3x = 180 Divide 3 on both sides
x = 60 Now that you found x, plug it into the other equations to find y and z
y = x - 6
y = 60 - 6
y = 54
z = x + 6
z = 60 + 6
z = 66
x = 60°
y = 54°
z = 66° [sorry if this is confusing]
PROOF
x + y + z = 180
60 + 54 + 66 = 180
180 = 180
The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.
Explanation:To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:
The sum of the angles of a triangle is 180 degrees, so x + y + z = 180.The sum of the measures of the second and third angles is twice the measure of the first, so y + z = 2x.The third angle is 12 more than the second, so z = y + 12.First, let's substitute z = y + 12 into the other two equations:
In x + y + z = 180, replace z with y + 12 to get x + y + y + 12 = 180; or, simplifying further, x + 2y = 168.In y + z = 2x, replace z with y + 12 to get y + y + 12 = 2x or, simplifying further, 2x = 2y + 12 or x = y + 6.We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.
Learn more about system of equations here:https://brainly.com/question/35467992
#SPJ3
si p+ 2p+3p=12, ¿cual es el valor de 5p -1
For this case we have the following equation:
[tex]p + 2p + 3p = 12[/tex]
To solve we follow the steps below:
We add similar terms from the left side of the equation:
[tex]6p = 12[/tex]
We divide between 6 on both sides of the equation:
[tex]p = \frac {12} {6}\\p = 2[/tex]
Finally, we have to:
[tex]5p-1 = 5 (2) -1 = 10-1 = 9[/tex]
Answer:
[tex]p = 2\\5p-1 = 9[/tex]
what’s 12.3+0.61+100
Answer:
12.3 + 0.61 +100= 112.91
Step-by-step explanation:
All you have to do is make all the values have two place values and then add.
16.3k + 19.2 + 7.5k = -64.1
You need to find "k", by isolating/getting "k" by itself in the equation
16.3k + 19.2 + 7.5k = -64.1 First combine like terms, 16.3k and 7.5k
23.8k + 19.2 = -64.1 Subtract 19.2 on both sides
23.8k = -83.3 Divide 23.8 on both sides to get "k" by itself
k = - 3.5
Quotient of 4 and a number increased by 10
Answer:
x+10/
Step-by-step explanation:
Quotient of 4 =divide by 4
a number increased by 10= x+10
The statement 'Quotient of 4 and a number increased by 10' can be translated into a mathematical expression as 4/x + 10, where x is the unknown number.
Explanation:If you mean the quotient of 4 and a number, we call that unknown number 'x'. So, the quotient of 4 and a number x is written as 4/x. Then, according to your question, that quotient is increased by 10. In mathematics, 'increased by' typically equates to the operation of addition. Thus, the entire expression translates into mathematical terms as 4/x + 10.
Learn more about Mathematical Expression here:https://brainly.com/question/34902364
#SPJ3
Which is the simplified form of n-6p3
The simplified form of n-6p³ is n-6p³.
Explanation:To simplify the expression n-6p³, we need to combine like terms. Since n and 6p³ do not have any common factors, the simplified form of the expression is n-6p³.
Convert 2671, to base 3 without first converting to base 10.
I do not understand the second half of the question but 2671 in base 3 is 10122221
Answer:
10122221 base 3
Step-by-step explanaUrtion:
Will brought a 144-ounce cooler filled with water to soccer practice. He used 16 ounces from the cooler to fill his water bottle. He then took out 16 plastic cups for his teammates and poured the same amount of water into each cup.
Find the number of ounces of water, x, that Will could have poured into each cup.
Answer:
x ≤ 8
Step-by-step explanation:
The number of ounces of water x that Will could have poured into each cup is 8 or less than 8. by solving through inequality.
What is inequality?Inequality is just like equation which expresses relationship between two or more variables but it is in greater than or less than form. It is just like:
x+ y<c.
How to form inequality?Let the capacity of each cup be x.
According to question
16x+16<=144
16x<=144-16
16x<=128
x<=8.
Hence the number of ounces of water that Will could have poured into each cup is 8 or less than 8.
Learn more about inequality at https://brainly.com/question/11613554
#SPJ2
Max takes a taxi to work one day. The taxi charges. A $6 flat fee plus $0.25 per mile. Max wants to spend exactly $12.50. How many miles will he travel in the taxi for this amount?
Determine the general form of the equation for the circle x^2 + (y + 1)^2 = 2.
Answer:
x² + y² + 2y - 1 = 0
Step-by-step explanation:
The general form of the equation for the circle:
x² + y² + ax + by + c = 0
Where: a, b and c are constants.
For the given equation:
x² + (y + 1)² = 2
∴ x² + (y + 1) (y+1) = 2
∴ x² + y² + 2y + 1 = 2 ⇒ subtract 2 from both sides
∴ x² + y² + 2y + 1 - 2 = 2 - 2
∴ x² + y² + 2y - 1 = 0
So, the general form of the equation for the circle:
x² + y² + 2y - 1 = 0
PLEASE I NEED TO KNOW ASAP
i know this is probably easy but i don’t understand it.
1.666666667x10^3 in 1 decimal place not in standard form
would it be something like 1.06
3,400,000
I thaink but not shore if wrong i'm sorry
Answer:
666.6
Step-by-step explanation:
1.666666667*10^10^3= 666.6
a plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works. if he charges hayden $122 for the house visit how long did the plumber work
Answer:
The plumber worked for 43 minutes.
Step-by-step explanation:
A plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works.
Now, the total amount to be paid to the plumber C(x) as a function of x number of minutes that he works can be modeled by the equation
C(x) = 70 for x ≤ 30 minutes and C(x) = 70 + (x - 30)4 for x > 30 minutes.
Now, the plumber charges Hayden $122 for the house visit. In that case, x must be greater than 30 minutes.
So, we can write
122 = 70 + (x - 30)4
⇒ 122 = 70 + 4x - 120
⇒ 4x = 172
⇒ x = 43 minutes.
Therefore, the plumber worked for 43 minutes. (Answer)
The volume of industrial production increased ten times. What was this increase in percent?
Answer:
1000%
Step-by-step explanation:
Think of 1x10. This is kinda hard to explain but if lets say 1 is 100% of the total number then you mutiply it by 10 you also mutiply the percent which in this case was 100% of 1.
900 % is the correct answer UvU
Have a good day!
91 tiles to make 13 hot plates. how many tiles to make 1 hot plate?
Answer:
7 tiles
Step-by-step explanation:
91/13=7
Answer:
7
Step-by-step explanation:
if 91 tile = 13 hot plate
X tile = 1 hot plate
(let X represent the number of tiles for one plate)
cross miltiply: 91×1 =13×X
X = 91/13
X =7 tiles
What is the constant of this proportionality for 1 4, 2 8, 3 12, 4,16
Answer:
k = 4
Step-by-step explanation:
The constant of proportionality is found by starting with y = kx, then finding k.
We can just use one point (such as the first one, (1,4) ) and substitute these values of x and y into the equation y = kx, to get:
4 = k x1
k = 4.
So y = 4x
(we can also check that all the other points also satisfy this equation - which they do, as each y value is 4 times the corresponding x value)
Answer:
4
Step-by-step explanation:
A 40ft tall building cast a shadow of 10ft. At the same time another building cast a shadow of 24 ft. How y’all is the second building?
Answer:
Every 4 feet in height would be 1 foot in length, so I want to say about 96ft
Step-by-step explanation:
What is the solution of the system?
10x−2y=24
6x+2y=8
Enter your answer in the box, as an ordered pair
Answer:
The solution is (2, -2)
Step-by-step explanation:
Let's find out the solution of the system:
10x − 2y = 24
6x + 2y = 8
Describing x in terms of y in the first equation, this way:
10x − 2y = 24
10x = 24 + 2y
x = 2 * (12 + y)/10 (Dividing by 10 at both sides)
x = (12 + y)/5 (Simplifying)
Solving for y in the 2nd equation:
6x + 2y = 8
6 * (12 + y)/5 + 2y = 8
(72 + 6y)/5 + 2y = 8
72 + 6y + 10y = 40 (Multiplying by 5 at both sides)
16y = 40 - 72
16y = -32
y = -2
Solving for x in the 1st equation:
10x − 2y = 24
10x - 2 * -2 = 24
10x + 4 = 24
10x = 24 - 4
10x = 20
x = 20/10
x = 2
The solution is (2, -2)
the mean of 100 numberical observations is 37.53. what’s the value of the sum of all 100 numbers
Answer: 3753
explanation: Mean is the average so divide 3753 by 100 to get 37.53.
3x 2 - 6 = 10 - x 2
{±1}
{±2}
{±4}
Answer:
x = ± 2
Step-by-step explanation:
Given
3x² - 6 = 10 - x² ( add x² to both sides )
4x² - 6 = 10 ( add 6 to both sides )
4x² = 16 ( divide both sides by 4 )
x² = 4 ( take the square root of both sides )
x = ± [tex]\sqrt{4}[/tex] = ± 2
b {+2}
1111111111111111111111
Which polygon has exactly one pair of parallel sides? A. rectangle B. trapezoid C. parallelogram D. square
Answer:
B. trapezoid
Step-by-step explanation:
The other three have two pairs of parallel sides
Answer:
B
Step-by-step explanation:
slope of (0,3) and (-4,-1)
The perimeter of a rectangle is 30 inches. Its length is three times its width. Write an equation to represent the problem
Answer:
Eqn of the problem: 2(3x + x) = 30
Solution: Width = 3.75 inches and Length= 11.25 inches
Step-by-step explanation:
We are given;
The perimeter of the rectangle as 30 inches Length is 3 times its widthWe are required to represent the equation of the problem;
Assuming the width = x inches, then;Length = 3x inchesThe formula for getting the perimeter of a rectangle is;
Perimeter = 2 (l+w)
In this case;
2(3x + x) = 30
Therefore;
The equation for the problem is;
2(3x + x) = 30
8x=30
Thus;
8x = 30
x = 3.75 inches
3x = 11.25 inches
Hence, the with is 3.75 inches while the length is 11.25 inches
which expression is equivalent to 3y-8+(-7y)+8
Answer:
I believe the answer to this question is: -4Y
Find the missing angle in the following right triangle with a second angle that measures 32degrees
Check the picture below.
The last line of a proof represents
PLEASE HELP ME MAKE HONOR ROLL PLEASE NEED HELP
Translate this phrase into an algebraic expression.
71 less than twice Julie's age
Use the variable j to represent Julie's age.
Answer:
71 < 2 · j
Step-by-step explanation:
71 less than twice Julie's age
Use the variable j to represent Julie's age.
71, less than (<) twice (2) and j represents the age
|1/2(16−6^3)| plz help
Answer:
I believe the answer to this question is: 100.
the weight of 80 screws in a jar of identical screws is 2 ounces. what is the weight, in ounces, of 4 screws
The weight of 4 screws is 0.1 ounces
Step-by-step explanation:
The problem can be solved by setting up a proportion.
In fact, we know that:
- The weight of 80 screws is 2 ounces
- So we want to find the weight of 4 screws
We can write the following proportion:
[tex]\frac{80}{2}=\frac{4}{x}[/tex]
where
x is the weight of 4 screws
Solving the equation, we find:
[tex]x=\frac{4\cdot 2}{80}=0.1[/tex]
So, the weight is 0.1 ounces.
Learn more about relationship between variables:
https://brainly.com/question/10708697
#LearnwithBrainly
Evaluate the expressions 3x-2 and 4x+4 for the following value of x.
Question:
Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2
Answer:
Part a: [tex]4x+4>3x-2[/tex]
Part b: [tex]4x+4=3x-2[/tex]
Part c: [tex]4x+4>3x-2[/tex]
Part d: [tex]4x+4>3x-2[/tex]
Explanation:
Part a: Substituting [tex]x=0[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(0)-2 \\&=-2\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(0)+4 \\&=4\end{aligned}[/tex]
The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]
Thus, [tex]4x+4>3x-2[/tex]
Part b: Substituting [tex]x=-6[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(-6)-2 \\&=-18-2 \\&=-20\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(-6)+4 \\&=-24+4 \\&=-20\end{aligned}[/tex]
The value of [tex]3x-2[/tex] and [tex]4x+4[/tex] are equal.
Thus, [tex]4x+4=3x-2[/tex]
Part c: Substituting [tex]x=5[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(5)-2 \\&=15-2 \\&=13\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(5)+4 \\&=20+4 \\&=24\end{aligned}[/tex]
The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]
Thus, [tex]4x+4>3x-2[/tex]
Part d: Substituting [tex]x=-2[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(-2)-2 \\&=-6-2 \\&=-8\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(-2)+4 \\&=-8+4 \\&=-4\end{aligned}[/tex]
The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]
Thus, [tex]4x+4>3x-2[/tex]
Final answer:
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Explanation:
Part a: 4x+4>3x-2
Part b: 4x+4=3x-2
Part c: 4x+4>3x-2
Part d: 4x+4>3x-2
Part a: Substituting x=0, we get,
[tex]\begin{aligned}3 x-2 &=3(0)-2 \n&=-2\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(0)+4 \n&=4\end{aligned}[/tex]
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Part b: Substituting x=-6, we get,
[tex]\begin{aligned}3 x-2 &=3(-6)-2 \n&=-18-2 \n&=-20\end{aligned}\begin{aligned}4 x+4 &=4(-6)+4 \n&=-24+4 \n&=-20\end{aligned}[/tex]
The value of 3x-2 and 4x+4 are equal.
Thus, 4x+4=3x-2
Part c: Substituting x=5, we get,
[tex]\begin{aligned}3 x-2 &=3(5)-2 \n&=15-2 \n&=13\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(5)+4 \n&=20+4 \n&=24\end{aligned}[/tex]
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Part d: Substituting x=-2, we get,
[tex]\begin{aligned}3 x-2 &=3(-2)-2 \n&=-6-2 \n&=-8\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(-2)+4 \n&=-8+4 \n&=-4\end{aligned}[/tex]
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
PLEASE HELP < I NEED HELP, TRYING TO MAKE HONOR ROLL
Translate the sentence into an equation.
Twice the difference of a number and 7 equals 2 .
Use the variable x for the unknown number.
Answer:
2(x-7) = 2
Step-by-step explanation:
First, let's look at the first part -- "Twice the difference of a number and 7". The difference between a number (x) and 7 means x-7. It also says twice the difference, so we are going to multiply x-7 by 2. So that ends us with 2(x-7)
The last part -- "equals 2" means we will set what we currently have to 2. 2(x-7) = 2
Answer:
2(x-7)=2
Step-by-step explanation:
The difference of a number and 7 is x-7 (difference means subtract)
Now the question says twice so that is what we do 2(x-7) now equal that to two 2(x-7)=2
if there are 60 chocolate bars and they are one dollar each and I have 19 left how much money will I have
Answer:
60(if you sell all)
Right now you have: 41 dollars
Step-by-step explanation:
Answer: you will have 41 dollars.
Step-by-step explanation:
because if you had 60 chocolate and now you had 19 left you sold 41 chocolate bars and you multiply that by how much there are which is 1 dollar and 41 time 1 is 41.