The sum of the measures of angles for a triangle is 180°. Find the value of x and then the measures of the 3 angles
Answers
Answer:
The value of x is 50
The measures of the 3 angles are 50°, 100°, 30°
Step-by-step explanation:
Let us solve the question
∵ The sum of the measures of the angles of a triangle is 180°
∵ The measures of the 3 angles of the given Δ are x°, 2x°, (x - 20)°
→ Add them and equate the sum by 180
∴ x° + 2x° + (x - 20)° = 180°
→ Add the like terms
∵ (x + 2x + x) + (-20) = 180
∴ 4x - 20 = 180
→ Add 20 to both sides
∵ 4x - 20 + 20 = 180 + 20
∴ 4x = 200
→ Divide both sides by 4 to find x
∴ x = 50
∴ The value of x is 50
To find the measures of the 3 angles substitute x by 50 in their expressions
∵ The measure of one angle is x
∴ The measure of the 1st angle is 50°
∵ The measure of the 2nd angle is 2x
∴ The measure of the 2nd angle = 2(50)
∴ The measure of the 2nd angle is 100°
∵ The measure of the 3rd angle is (x - 20)
∴ The measure of the 3rd angle = (50 - 20)
∴ The measure of the 3rd angle is 30°
∴ The measures of the 3 angles are 50°, 100°, 30°
Related Questions
Under his cell phone plan, Samuel pays a flat cost of $41.50 per month and $5 per gigabyte. He wants to keep his bill at $52.50 per month. Write and solve an equation which can be used to determine
x
x, the number of gigabytes of data Samuel can use while staying within his budget
Answers
Answer:
2.2 gigabytes
Step-by-step explanation:
Let us represent
x = the number of gigabytes of data Samuel can use while staying within his budget
Therefore, our equation is:
$41.50 + $5 × x = $52.50
41.50 + 5x = 52.50
Subtract 41.50 from both sides
41.50 - 41.50 + 5x = 52.50 - 41.50
5x = 11
x = 11/5
x = 2.2 gigabytes.
The number of gigabytes of data he need to keep his monthly cost at $52.50 is 2.2 gigabytes
Next door to me lives a man with his son. They both work in the same factory. I watch them going to work through my window. The father leaves for work ten minutes earlier than his son.one day I asked him about it and he told me that it takes 30 minutes for him to walk to his factory, whereas his son is able to cover the distance in only 20 minutes. If the father were to leave the house 5 minutes earlier then his son, then the son would catch up with his father in 2k minutes. where k is-----
Answers
9514 1404 393
Answer:
k = 5
Step-by-step explanation:
Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...
speed = distance/time = 1 / 30 . . . . units per minute
When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = 1/30(t +10)
Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...
d = (1/30)(t +5)
We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...
d = 1/20t
To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...
(1/30)(2k +5) = (1/20)(2k)
4k +10 = 6k . . . . . multiply by 60
10 = 2k . . . . . . . . . subtract 4k
5 = k . . . . . . . . . . . divide by 2
__
The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.
Under his cell phone plan, Elijah pays a flat cost of $64.50 per month and $5 per gigabyte. He wants to keep his bill at $87.50 per month
Answers
Given that $-3 \leq x \leq 2$ and $20x^{2} = y-24$, what is the least possible value for $y$?
Answers
Answer:
24
Step-by-step explanation:
The least possible value is when 20x^2 = 0. All other values give a larger value than 0. Thus, the minimum value for y = 24.
Answer:
24
Step-by-step explanation:
What's your biggest wish this Christmas?! :D <3
Answers
Answer:
To Get a new phone
Step-by-step explanation:
Change the following sentences as in dire
a. Let him write an email (into passive)
MA
Answers
Answer:
let the email be written by him.
An ice cream cone has a height of 11cm and a diameter of 4.5 cm. Which value best represents the amount of ice cream the cone can hold.
Answers
Answer:
D. 58cm
Step-by-step explanation:
Hi Alondra, umm... I looked this up and saw your name. This is on the final right.
Andrew Moreno
Answer:
An ice cream cone has a height of 11cm and a diameter of 4.5 cm. Which value best represents the amount of ice cream the cone can hold.
Step-by-step explanation:
If
s= t+7s/5 and s= -2 what is the value of t?
A) -24
B) -4
C) 4
D) 24
Answers
Answer:
C
Step-by-step explanation:
Given
s = [tex]\frac{t+7s}{5}[/tex] ← substitute s = - 2 into the equation
- 2 = [tex]\frac{t+7(-2)}{5}[/tex] ( multiply both sides by 5 to clear the fraction
- 10 = t - 14 ( add 14 to both sides )
4 = t → C
12. A plot of land measures 200m by 50m. Find its area in hectares. *
2 points
O A. 10ha
B. 100ha
C. 1ha
D. 10,000ha
Answers
Explanation:
200 x 50 = 10,000
10,000 square metres = 1 hectare
Food World sells a 6 lb. bag of potatoes for $5.70. Which of the following is NOT an equivalent price per pound of potatoes?
A 7 lb. bag for $6.65
B 20 lb. bag for $19.00
C 16 lb. bag of $14.45
B 9 lb. bag for $8.55
Answers
Darin has 3 pairs of tennis shoes, 4 pairs of pants, 6 shirts, 2 belts, and 3
hats. Darin makes an outfit by choosing one of each type of item. How
many unique outfits can Darin make?
A). 18
B). 42
C). 144
D). 432
Answers
When Sarah divided a number by 5, the quotient was 247 with a remainder. What is one possible dividend? With a complete sentence, explain how you found the dividend.
Answers
Answer:
One possible dividend is 1,237
Step-by-step explanation:
One possible dividend will be 1,237
This is because of we multiply 247 by 5, we get 1,235 and we can add 2 so we can have remainder 2
The difference between the next factor of 5 and the last one which has 247 as the multiple of 5 is 5
So adding 1,2,3 and 4 to the product will give a number that is not up to the next multiple of 5 and thus we can have our dividend with the remainder
HELP ASAP!!!!!!!! PLSSSSSSS HURRY!!!
Consider the function f(x) = 6 sine (x minus StartFraction pi Over 8 EndFraction) + 8. What transformation results in g(x)6 sine (x minus StartFraction 7 pi Over 16 EndFraction) + 1?
A.) Translate StartFraction 5 pi Over 16 EndFraction units left and 7 units up.
B.) Translate StartFraction 5 pi Over 16 EndFraction units right and 7 units up.
C.) Translate StartFraction 5 pi Over 16 EndFraction units left and 7 units down.
D.) Translate StartFraction 5 pi Over 16 EndFraction units right and 7 units down.
Answers
Answer:
D
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
used graphing calculator
Which of the following is equivalent to (2a + 5b) (a - 3b)?
A) 2a² - 2ab - 15b²
B) 2a² - ab 15b²
C) 2a² + 2ab - 15b²
D) 2a² + 11ab - 15b²
Answers
Answer:
Step-by-step explanation:
use foil and you will have
=2a^2-6ab+5ab-15b^2
=2a^2-ab-15b^2
i think is B, maybe you forgot a minus between ab and 15b^2
the area of a triangle is 84 CM2. find the altitude corresponding to the side measuring 14 cm?
Answers
Answer:
12 cm
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the altitude )
Here A = 84 and b = 14 , then
[tex]\frac{1}{2}[/tex] × 14 × h = 84
7h = 84 ( divide both sides by 7 )
h = 12
The altitude is 12 cm
plz help, The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answers
Answer:
The real solutions of f(x)=0 are: 0, 2, 5, 6
Step-by-step explanation:
We are given:
The graph of y = f(x)
We need to find all of the real solutions of f(x) = 0?
By looking at the graph we need to find the values of y when x =0
Looking at the graph, when x=0 we get
0, 2,5 and 6
So, the real solutions of f(x)=0 are: 0, 2, 5, 6
I am attaching the figure, that determines the answers.
Santa needs to hire extra help for the busy season. 9 elves can pack 27 toys in Santa's sleigh in an hour.
How many elves are needed to pack 240 toys each hour?
Answers
Answer:
Number of elves= 80 elves
Step-by-step explanation:
If 9 elves can pack 27 toys per hour. This means that each elf packs 3 toys per hour:
Toys per elf= 27/9 = 3
Now, we need to determine the number fo elves needed to pack 240 toys per hour:
Number of elves= number of toys/toys per elf
Number of elves= 240/3
Number of elves= 80 elves
What number could replace kkk below? \dfrac{k}{100} = \dfrac{1}{10} 100 k = 10 1 start fraction, k, divided by, 100, end fraction, equals, start fraction, 1, divided by, 10, end fraction k={}k=k, equals
Answers
Answer:
k = 10Step-by-step explanation:
Given the equation;
[tex]\dfrac{k}{100} = \dfrac{1}{10}[/tex]
We are to find the value of k.
Cross multiply;
[tex]\dfrac{k}{100} = \dfrac{1}{10} \\10 \times k = 100 \times 1\\10k = 100\\[/tex]
Divide both sides by 10
[tex]10k/10 = 100/10\\k = 10[/tex]
Hence the value of k is 10
Answer:
100/9
Step-by-step explanation:
On Khan
what is 32.23 + 4x?
ASAP
Answers
Answer:
cannot be simplified.
1. Solve the system of equations: 4x-y=14 and x=y+2
O (4,2)
O (2,4)
O (6,2)
0 (2,6)
Answers
Answer:
The second one
Step-by-step explanation:
4x-y=14
4(y+2) -y=14
4y+8-y=14
3y=14-8
3y=6
y=2
x=2+2
x=4
Answer:
y=2 x=4
a. (4,2)
simple. easy. awesome. xfinity
Answer please step by step would be helpful
Answers
Y = 1 + 2m
m = miles traveled
Replace y with 29
29 = 1 + 2m
2m = 28, divide by 2
m = 14
Solution: 14 miles
Answer:
The taxi ride was 14 miles long.
Step-by-step explanation:
So we know that he payed 29 $. Out of this 29$ 1$ was the pick up fee. So we know that 28$ were spend on distance that the taxi had to ride. We also know that Wyatt has to pay 2$ for each mile so in order to get the total number of miles the car drove we will have to divide the amount of money that was paid for the actually distance traveled by two. And so we get that our answer is........
28$ / 2$ = 14
Help with congruent angles - please----
State if the 2 angles are congruent.
If they are, state how you know- for example SSS or SAS.
Answers
Answer:
No, they are not congruent, see why belowStep-by-step explanation:
The red lines indicate corresponding angles. Here we see 2 corresponding congruent sides and 1 corresponding congruent angle. The SAS postulate states that we can conclude a triangle is congruent if we have 2 sides and 1 angle as being congruent. However, on closer inspection, we will notice that the angle is not actually corresponding. The first triangle has the angle between the two sides marked, but the second one has the angle on the other side marked. Because of this, we cannot conclude the triangles are congruent.
please help, i will mark you branniest :))
solve for k
3/k = 4/5
Answers
Answer:
3/k = 4/5
k = 3 divided by 4/5
k = 3.75
Step-by-step explanation:
pls help me 20 points
Answers
Answer:
the length of the minute hand is 36/100 . 150 = 54 (mm)
y is the distance between the minute hand and the hour hand now
x is the angle beween the minute hand and the hour hand, so we have:
cos x = 36/54 = 2/3 => sin x = [tex]\sqrt{1-(\frac{2}{3})^{2} }=\frac{\sqrt{5} }{3}=\frac{y}{54}[/tex] => y = 18√5 (mm)
a) see in the ques, u can see that in 45', the minute hand will move a distance equal to 2 times its length and a distance = 2.18√5 (mm)
=> the distance which the minute hand will move is 54.2 + 2.18√5 = 188,50 (mm)
b) the distance which the minute hand will move in 1h is 54.4 - 18√5 = 175,75(mm)
the distance which the hour hand will move in 1h is 36.4 = 144 (mm)
=> the minute hand will move: 175,75 - 144 = 31,75(mm) further than the hour hand
Step-by-step explanation:
Work out the percentage change to 2 decimal places when a price of £198 is increased to £209.99.
Answers
Answer:
The percentage change = 6.05%
Step-by-step explanation:
New value = £209.99
Old value = £198
Percentage change = [New Value - Old Value] / [Old Value] × 100
= [209.99 - 198] / [198] × 100
= [11.99] / [ 198] × 100
= 0.06 × 100
= 6.05%
Therefore, the percentage change = 6.05%
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!
Answers
Angle 1 is 112
Angle 2 is 68
Angle 3 is 90
Angle 4 is 90
Angle 5 is 22
Angle 6 is 158
You deposit $7,425 into a savings account
Answers
Answer:
wow then u saved $7425 in your savings account
Step-by-step explanation:
B is the midpoint of segment AC, What is the length of AC?
А
B
3X + 4
5X-6
Answers
Sarah made a certain number of bracelets for a craft show. Maria made 7 more than Sarah. Julie made 3 times as many as Maria.
Which expression represents the total number of bracelets Julie made if Sarah made s bracelets?
3s + 7
s + 21
21s
3(s + 7)
Answers
Answer:
D
Step-by-step explanation:
Write the equation for a parabola with a focus at (-7,-5) and a directrix at x = -4
Answers
Answer:
y² + 10y + 6x + 58 = 0
Step-by-step explanation:
Focus of the parabola has been given as (-7, -5) and directrix as x = -4
Let a point on the parabola is (x, y).
By the definition of a parabola, "distance of a point on parabola is equidistant from focus and directrix".
Distance from focus of the given point = [tex]\sqrt{(x+7)^2+(y+5)^2}[/tex]
Distance of the point from directrix = [tex]\sqrt{(x+4)^2}[/tex]
Therefore, equation of the parabola will be,
[tex]\sqrt{(x+7)^2+(y+5)^2}=\sqrt{(x+4)^2}[/tex]
[tex](x+7)^2+(y+5)^2=(x+4)^2[/tex]
x² + 14x + 49 + y² + 10y + 25 = x² + 8x + 16
y² + 14x + 10y + 74 = 8x + 16
y² + 10y + 6x + 58 = 0
Answer:
(y+5)^2/6 - 11/2
Step-by-step explanation: