Answer:
The top angle of the triangle is, X = 68°.
Step-by-step explanation:
Let there is a triangle named PQR with bottom corner angles ∠ P and ∠ Q and the ∠ R is the angle at the top.
Now, given that ∠ P = 31° and ∠ Q = 81° and we have to find out ∠ R i.e. X.
In Δ PQR, we know, ∠ P + ∠ Q + ∠ R = 180°
⇒ 31° + 81° + X = 180°
⇒ X = 68°
Therefore, the top angle of the triangle is 68°. (Answer)
Solve by using substitution. Express your answer as an ordered pair.
3x+y=10
Y=x+2
A.) 8,10
B.) 8/3,2
C.) 2,4
D.) 4,2
Answer:
c. 2,4
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure of the first angle. The third angle is 12 more than the second.
Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
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
jacob qnd jordan are training for track season. jacob did 39 sit-ups in 30 secs. jordan did 59 sit-ups in 50 secs. who will likely do more sit-ups in 2 1/2 mins
Jordan it a bigger number
Mark as Brainliest
ASAP
Of 450 lunches sold at school on Thursday, 40% were hamburgers
and the rest were pizza. How many more pizza lunches were sold than
hamburgers? Explain how you found your answer.
Answer: 90
Step-by-step explanation:
Total number of lunches sold = 450
Number of hamburgers = 40% of the total , that is
number of hamburgers = 40/100 x 450 = 180
number of pizza = 450 - 180 = 270
Therefore , the number of pizza lunches sold more than hamburgers will be
270 - 180 = 90
Therefore : 90 more pizza lunches were sold than hamburgers.
What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
A: y=-1/4x +33
B: y=-1/4x + 36
C: y = 4x - 16
D: y = 4x + 16
Answer:
Option D: y = 4x + 16
Step-by-step explanation:
Given the line: y - 1 = 4(x + 3) ⇒ y = 4x + 13
The slope of the given line = m = 4
The required line is parallel to the given line
So, the slope of the required line = m = 4
So, the general equation of the required line: y = 4x + c
Where c is constant represents y-intercept
To find the value of c, substitute with the point (4,32)
At x = 4 y = 32
∴ 32 = 4 * 4 + c
∴ c = 32 - 16 = 16
∴ y = 4x + 16
The answer is option D: y = 4x + 16
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1?
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
–8
–5
0
6
Answer: 0 on edge
Step-by-step explanation:
got it correct
Answer: C
Step-by-step explanation:
took quiz
3,562,185 What is the value of 3?
Answer: 3 millions
Explanation: To determine what the digit "3" means in 3,562,185, if we put 3,562,185 into the place value chart, we can see that the 3 appears in the units column of the millions period so in this problem 3 refers to 3 millions.
ASAP PLEASE !!!!!
Two trains leave a station on different tracks. The tracks make an angle of 130°, with the station as a vertex. The first train
travels 100 km and makes its first stop at point A, while the second train travels 200 km and makes it first stop at point B.
How far apart are the trains when both are at their first stop? Round the answer to the nearest integer.
The trains are 275 km apart when both are at their first stop
Solution:
The tracks make an angle of 130°, with the station as a vertex
Therefore, from given figure in question,
Angle at station = 130 degree
Let "c" be the point at station
The first train travels 100 km and makes its first stop at point A
Distance between A and station c = 100 km
Let a = 100 km
The second train travels 200 km and makes it first stop at point B
Distance between B and station c = 200 km
Let b = 200 km
We have to find the value of "d"
We can use the law of cosine
The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
From given figure in question,
Side opposite "d" to 130 degree is equal to sum of square of other sides a and b minus twice the product of those sides and the cosine of the angle between them which is 130 degrees
Therefore,
[tex]d^2 = a^2 + b^2 - 2ab\ cos\ d[/tex]
[tex]d^2 = 100^2 + 200^2 - 2(100)(200)cos 130\\\\d^2 = 10000 + 40000 - 40000cos 130\\\\d^2 = 50000 - 40000 \times -0.6427\\\\d^2 = 50000 + 25711.5\\\\d^2 = 75711.5\\\\\text{Take square root on both sides }\\\\d = 275.15 \approx 275[/tex]
Thus trains are 275 km apart when both are at their first stop
Answer:
D. 275 km
Step-by-step explanation:
Find fifth roots of z⁵ + 32 = 0 and draw its graph?
Answer:
Step-by-step explanation:
How can I use fractions tiles to help divide a whole number by a unit fraction
Final answer:
To divide a whole number by a unit fraction using fraction tiles, treat the division as multiplication by the reciprocal of the unit fraction and then split the whole number tiles accordingly.
Explanation:
To use fraction tiles to help divide a whole number by a unit fraction, you can follow these steps:
Understand that dividing by a unit fraction is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as multiplying by 2, since 2 is the reciprocal of 1/2.Start with fraction tiles that represent the whole number you want to divide. For instance, if the whole number is 6 and you're dividing by 1/2, use 6 whole tiles.Since you're multiplying by the reciprocal of the unit fraction, convert the action of dividing into multiplication. Each whole tile would be split into the number of pieces that are equivalent to the denominator of the unit fraction. If dividing by 1/2, split each whole into 2 pieces.Count all the new pieces. The result is the number of pieces you have after dividing by the unit fraction. In our example with 6 whole tiles and dividing by 1/2, you'd end up with 12 pieces since each whole tile is split into 2 pieces.Angle 1 and angle 2 are vertical angles.
Angle 2 has a measure of 93°
What is the measure of angle 1 ?
Enter your answer in the box
Answer:
<1 = 93 (vertical opposite angle are equal)
Step-by-step explanation:
Answer: I can confirm, Josshyaby is correct I took the test
Step-by-step explanation:
What is 3 5/8 ÷14 please answer this
Answer:
29/112
Step-by-step explanation:
3 5/8=29/8
(29/8)/14
(29/8)(1/14)=29/112
Which of the following points is a solution of the inequality y < -|x|?
a) (1, -2)
b) (1, -1)
c) (1, 0)
Answer:
a) (1, -2)
Step-by-step explanation:
The given inequality is y < -|x|
We substitute the point to see which points satisfy the inequality.
For a) (1, -2), we substitute x=1 and y=-2 to get:
-2 < -|1|---------->-2<-1--------->True
For b) (1, -1), we substitute x=1 and y=-1 to get:
-1 < -|1|---------->-1<-1--------->False
For a) (1, 0), we substitute x=1 and y=0 to get:
0 < -|1|---------->0<-1--------->False
The first choice is correct.
Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?
Answer:
20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
elizabeth can run 5 mils in 24 1/2 minutes Dez can run 8 miles in 32 1/3 minutes. who can run faster?
Equivalent ratio 1:
Equivalent ratio 2:
Answer:
Des can run faster than Elizabeth.
Des can run 1 mile in 4.037 minutes while Elizabeth can run 1 Mile in 4.9 minutes
Step-by-step explanation:
If Elizabeth can run 5 miles in 24.5 minutes. Elizabeth will run 1 mile in 24.5/5=4.9 minutes.
If Dez can run 8 miles in 32 1/3 minutes. Then Dez will run 1 mile in 32.3/8=4.037 minutes
Therefore if Dez can run 1 mile in 4.037 minutes and Elizabeth can run 1 mile in 4.9 minutes then Dez can run faster than Elizabeth.
If sin A is negative and cos A is positive, what
is the number of the quadrant in which angle A
terminates?
Answer:
Quadrant 4
Step-by-step explanation:
sinA < 0 in quadrants 3 and 4
cosA > 0 in quadrants 1 and 4
Thus sinA < 0 and cosA > 0 in quadrant 4
Common factor and HCF of 10m squared,15mk
Answer:
Step-by-step explanation:
10m^2 and 15mk
common factor is 5m
HCF is 5m
Can some one help me please and explain it
Answer:
c= -2
Step-by-step explanation:
Perpendicular lines imply that the product of the gradient of the two lines is -1.
So let's find the gradient of each lines.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Gradient of 1st line
= 1-(-4)/ -3-2
= 5/-5
= -1
(gradient of 1st line)(gradient if 2nd line)= -1
(-1)(gradient of 2nd line)= -1
gradient of 2nd line= -1 ÷ (-1) =1
Now make use of the gradient formula to find an expression of the gradient of the second line.
Gradient of 2nd line= c-1/ -2-1
subst. gradient of second line and simplify:
1= c-1/-3
c-1= -3 (multiply by -3 on both sides)
c= -3+1 (add 1 on both sides)
c= -2
The line passing through (11,y) and (2,0)is parallel to the line joining (7,5) and (-2,2). Find y.
Answer: y = 3
Step-by-step explanation:
Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
For the first line
[tex]x_{1}[/tex] = 11
[tex]x_{2}[/tex] = 2
[tex]y_{1}[/tex] = y
[tex]y_{2}[/tex] = 0
substituting into the formula , we have
m = [tex]\frac{0 - y}{2 - 11}[/tex]
m = [tex]\frac{-y}{-9}[/tex]
m = [tex]\frac{y}{9}[/tex]
Also Finding the slope of the second line we have
[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]
Since the two lines are parallel , we will equate their slope , that is
[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]
3y = 9
y = 3
What is the equation of the line that has a slope of -4 and goes through (-1,6)
Answer:
y = - 4x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 4, thus
y = - 4x + c ← is the partial equation
To find c substitute (- 1, 6) into the partial equation
6 = 4 + c ⇒ c = 6 - 4 = 2
y = - 4x + 2 ← equation of line
If 5/8 = x/16 , then x is equal to
Answer:
10/16
Step-by-step explanation:
Factor each expression.
17. 5x -25
Hii!
_________________________________________________________
Answer:
5(x-5)
Step-by-step explanation:
Both terms, 5x and -25, have something in common. This "something" is called the greatest common factor, or g.c.f.
The g.c.f. of 5x and -25 is 5, so we factor 5 out by dividing 5x and -25 by 5. Upon doing this we obtain
x-5
Now we need to put parentheses around x-5.
(x-5)
Next, we put 5 outside the parentheses.
5(x-5)
--
Hope that this helped! Best wishes.
--
What is the value of n?
Answer:
What is n?
Step-by-step explanation:
what should be added to both sides of the equation to solve for the variables? 45=30+m
Answer: m = 15
Step-by-step explanation:
45 = 30 + m
subtract 30 , from both sides , that is , -30 should be added to both sides to find the variable
45 - 30 = 30 + m - 30
15 = m
Therefore : m = 15
The friends now To go on the loop D loop and the roller coaster. Explain why only 1 of the friends can go on both of these rides
Are there any more instructions or information?
Due to requirements such as height and ride capacity, only one friend can go on both the loop and the roller coaster at the same time.
Explanation:In order to go on the loop and the roller coaster, the friends need to meet certain requirements. For example, they need to be tall enough to ride the roller coaster and meet any age restrictions. Additionally, the roller coaster may have a limited number of seats or ride capacity. Due to these factors, it's possible that only one friend can go on both of these rides at the same time.
Learn more about Requirements for riding the loop and roller coaster here:https://brainly.com/question/32081951
#SPJ12
What are the like terms in this expression?
9a - 3b + 4ab
Answer:
There are no like terms for all 3 variables for 9a-3b+4ab
Michelle sets up a lemonade stand to make some extra money.She spends $4.75 purchasing supplies.She earns $16.50 selling lemonade.How much money does she make after she subtracts her expenses?
Linda's start up cost for her online jewelery store was $250, as she has to pay an additional $60per month to keep it running. Write an expression or equation modeling the real world
Total Cost = 250 + 60x is the equation that models the given situation
Solution:
Given that, Linda's start up cost for her online jewelery store was $250
She has to pay an additional $60 per month to keep it running
To find: Equation that models this situation
From given,
Start up cost = $ 250
Let "x" be the number of months she keeps the store running
Additional pay per month = $ 60
Thus, the total cost Linda spend to keep the store running is given as:
Total Cost = Startup cost + (Additional pay per month)(number of months)
[tex]Total\ Cost = 250 + 60x[/tex]
Thus the equation that models the given situation is found
find the value of m<1 m<2 and m<3
Answer:
i don't know
Step-by-step explanation:
it took Bob 55 minutes to clean the garbage. How many seconds did it take bob?there are 60 seconds in one minute please help me .
Answer:
3,300 sec
Step-by-step explanation: