Answers
Answer:
9. x = 31°
10. m∠ABC = 62°
11. m∠BCA = 60°
Step-by-step explanation:
We are given the following values for ΔABC, and its exterior angle, ∠ACD:
In ΔABC, the two nonadjacent interior angles are:
m∠A = 58° m∠B = 2x°While the exterior angle, m∠ACD = (5x - 35)°.
In order to solve for questions 9 through 11, we must apply the Exterior Angle Theorem which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent or remote interior angles.
Question 9:In order to find the value of x, we can use the Exterior Angle Theorem:
m∠ACD = m∠A + m∠B
(5x - 35)° = 58° + 2x°
5x° - 35° = 58° + 2x°
Subtract 2x from both sides:
5x° - 2x - 35° = 58° + 2x° - 2x
3x - 35° = 58°
Next, add 35° to both sides:
3x° - 35° + 35° = 58° + 35°
3x° = 93°
Divide both sides by 3 to isolate x:
[tex]\displaystyle\mathsf{\frac{3x}{3}\:=\:\frac{93}{3} }[/tex]
x = 31°
Therefore, the value of x = 31°.
Question 10:In order to find m∠ABC, we must first substitute the value of x into m∠B:
m∠B = 2x° = 2(31)° = 62°
Therefore, m∠ABC = 62°.
Question 11:In order to find m∠BCA, we must first find the value of its supplement, m∠ACD, by substituting the value of x derived from question 9.
m∠ACD = 5x° - 35° = 5(31)° - 35° = 120°
Next, substitute the value of m∠ACD into the following equation:
m∠BCA + m∠ACD = 180°
m∠BCA + 120° = 180°
Subtract 120° from both sides:
m∠BCA + 120° - 120° = 180° - 120°
m∠BCA = 60°
Therefore, m∠BCA = 60°.
Verify:In order to verify whether we have the correct values for each interior angles, we can apply the Triangle Sum Theorem which states that the sum of all interior angles of a triangle is equal to 180°. In other words:
m∠A + m∠B + m∠C = 180°.
58° + 62° + 60° = 180°
180° = 180° (True statement).
Related Questions
Find the equation for the line bellow
Answers
Y=x+3 please helppppppppppol
Answers
Answer:
(-1, 2), (0,3), (1,4)
slope= 1
y-intercept= (0,3)
Step-by-step explanation:
3.8×102+1.7×103 giving answer in standard form
Answers
Answer: 5.15 x 10^2
Step-by-step explanation:
3.8 x 103 + 1.7 x 103 = 5 x 103 = 515 = 5.15 x 10^2
There are some red and blue balls in a bag of 21 balls and the probability of picking 2 red balls out in a row is 1/14 how many red balls are there?
Answers
Answer:
6 red balls
Step-by-step explanation:
The probability in the first pick
6/21
The probability in the second pick (without replacement)
5/20
the requested probability
(6/21)(5/20) = 30/420
simplification
30/420 = 3/42 = 1/14
Hope this helps
Answer:
6 red balls.
Step-by-step explanation:
If there are x red balls then
probability of 2 red balls
= x/21 * (x - 1)/20 = 1/14
x^2 - x / 420 = 1/14
x^2 - x = 30
x^2 - x - 30 = 0
(x - 6)(x + 5) = 0
x = 6.
14.9 x 100 PLS HELP
Answers
Answer:
just move the decimal to the right two place, for two zeroes. The answer is 1490.
Step-by-step explanation: Just simply multiply 14.9 by 100.
Answer:
1490.Step-by-step explanation:multiply 14.9 by 100
Help me please ill mark as the brainiest if correct. I don't know how so please tell me
Answers
Answer:
:)))))
Step-by-step explanation:
<3
Luis and Erin are playing a game. They each start with 0 points. At the end of the game, Luis has 250 points, and Erin has -250
Which statement about the game is true?
A. Erin and Luis have a total of 500 points.
B. Erin has lost 250 points.
C. Luis has 250 more points than Erin.
D. Erin and Luis have an equal number of points.
Answers
Answer:
B
Step-by-step explanation:
Can someone help Pleasaseee
Answers
Answer:
i think it's 1.8.
Step-by-step explanation:
why? bc if u add 6/20 + 1.5 = 1.8
i think it's 1.8, im not sure, hopefully it's correct!!
Answer:
1.8
Step-by-step explanation:
you just simplify -6/20 into a decimal and you get .3 then you add it to 1.5.
2/7 divided by 3/4
Amanda
Answers
Answer:
2/7÷3/4=2/7×4/3=8/21
[tex] \rm \ \blue{ \overbrace{ \underbrace{ \tt \color{hotpink} \: \: \: \: \: \: \: \: \: \: answer \: \: \: \: \: \: \: \: \: }}}[/tex]
[tex]\large \color{pink} \frac{8}{21} [/tex]
Step-by-step explanation:
[tex] \huge \color{brown} \frac{2}{7} \div \frac{3}{4} [/tex]
divide by a fraction, multiply by the reciprocal of that fraction[tex] \large \color{hotpink} \frac{2}{7} \div \frac{4}{3} [/tex]
multiply the fraction[tex] \huge \color{darkblue} \frac{8}{21} [/tex]
hope it helpsCalculator
6 mm
What is the area of this figure?
6 mm
Enter your answer in the box.
8 mm
8 mm
mm
Answers
Answer:
[tex] {84mm}^{2} [/tex]
Step-by-step explanation:
Area of square= l×l
Area of square= 6mm × 6mn
Area if square = 36 mm²
Area of triangle 1= ½b ×h
Area of triangle 1= ½ (6mm)(8mm)
Area of triangle 1 = 24 mm²
Area of triangle 2 is the same as area of traingle 1 because they have the same base and hight
: . area of triangles is 48mm²
Area of the figure= Area of square + Area of triangles
A of figure = 36+48
A of figure = 84 mm²
Option 2
Use trapezium formula
Area of trapezium= (a+b)/2 * h
a=6 mm (base)
b=8+6=14 mm (Base)
h= 6mm (height)
[tex]area \: of \: trapezium = ( \frac{6 + 14}{2} )(6) \\ = 60mm ^{2} [/tex]
Therefore the area of triangle= 24mm² as calculated in option 1
Area of the figure= Area of trapezium +Area of triangle
Area of figure = 60+24
= 84 mm²
What is the probability of randomly selecting a month pf year and not getting a month that ends in y?
Answers
Answer:
2/3
Step-by-step explanation:
The months whose names end in 'y' include Jan, Feb, May, Jul. The probability of randomly selecting a month whose name ends in 'y' is 4/12 (remember that there are 12 months in a year), or 1/3.
Thus, the probability of selecting a month whose name does NOT end in 'y' is 8/12, or 2/3. Note that this event is the 'complement' of the first event:
P(name does not end in 'y') = 1 - P(name does not end in 'y') = 1 - 1/3 = 2/3
An angle measures 157.2° more than the measure of its supplementary angle. What is the measure of each angle?
Answers
Two supplementary angles equal 180 degrees
Subtract the difference from 180:
180-157.2 = 22.8
Divide by 2:
22.8 /2 = 11.4
One angle is 11.4
Now add the difference to 11.4
11.4 + 157.2 = 168.6
The second angle is 168.6
Answer: 11.4 and 168.6
simplify 8+2(5-×) thanks
Answers
Answer:
=8+2(5-x)
=8+10-2x
=18-2x
Answer:
hey am
I think that's be the answer
if you think it's not right
don't write
The following stock prices reflect the closing price for the past five days. Find the 3 day SMA
(Simple Moving Average) for days 2-4.
$44.25, $44, $41.75, $40, $39.75
Answers
Answer:
solution
Step-by-step explanation: total=209.75
A certain forest can support a population of 800 deer. There are currently 200 deer in the forest and their population is growing at a rate of 2% per year. Complete the sequence below that models this population growth.
Answers
It would take 70 years for the deer population to reach 800.
An exponential function is in the form:
y = abˣ
where b is the multiplier, y, x are variables and a is the initial value.
Let y represent the population and x represent the time in years.
a = 200, b = 100% + 2% = 102% = 1.02
y = 200(1.02)ˣ
For a population of 800:
800 = 200(1.02)ˣ
ln(4) = xln(1.02)
x = 70 years
It would take 70 years for the deer population to reach 800.
Find out more on exponential function at: brainly.com/question/2456547
Answer: 200, 0.02, and 800
Step-by-step explanation:
Resuelve la siguiente ecuación lineal: 13-4(5x+1)=3(7-5x)-15
Answers
.........................
Help help hep hep math
Answers
Answer:
f(3) = 2
Step-by-step explanation:
f(3) = 2(3) - 4
f(3) = 2
19z+12=20z–8
help i dont really understanddd!!!
Answers
Answer:
z = 20
Step-by-step explanation:
subtract 19z from 20z, and add 8 to 12. you will be left with 20 = 1z. Divide 1 by 20 and you will have Xz =20.
I hope this helps!
The large rectangle below represents one whole. What percent is represented by the shaded area? %
Answers
Answer:
Step-by-step explanation:
would help a lot if you show the picture or describe it very well.
2 FOR 2.20 UNIT RATE
Answers
Answer: (if your asking for the unit rate of that)
the unit rate is 1.10
Answer:
1.10
Step-by-step explanation:
2 /2 = 1
20/ 2 = 10
1.10 is the unit rate
find the greatest common factor GCF and the least common multiple LCM of these Numbers. 8and 9
Answers
Answer:
LCM is [tex]72[/tex]
GCF is [tex]1[/tex]
Step-by-step explanation:
LCM is least common multiplier
LCM of
[tex]8,9=8\times 9\\\\=72[/tex]
GCF is greatest common factor
Factors of [tex]8=1,2,4,8[/tex]
Factors of [tex]9=1,3,9[/tex]
Greatest common factor is [tex]1[/tex]
GCF is [tex]1[/tex]
Multiply and fill in the blanks
a) 5pq(p2+ q2+pq)
b) -7pr (pq – qr - rq)
c) (4x-3y) (5x-4a)
with explanation pls !
Answers
The solution to the simplification of the algebraic expressions are;
A) 5p³q + 5pq³ + 5p²q
B) 14pqr² - 7p²qr
C) 20x² - 15xy - 16ax + 12ay
A) We have the expression;
5pq(p² + q² + pq)
Multiplying out using the concept of distributive property, we have;
(5pq × p²) + (5pq × q²) + (5pq × pq)
>> 5p³q + 5pq³ + 5p²q
B) We have the expression;
-7pr(pq – qr - rq)
Multiplying out using the concept of distributive property, we have;
-7p²qr + 7pqr² + 7pqr²
>> 14pqr² - 7p²qr
C) (4x - 3y)(5x - 4a)
By quadratic expansion, we have;
(4x * 5x) - (3y * 5x) - (4x * 4a) + (4a * 3y)
>> 20x² - 15xy - 16ax + 12ay
Read more about simplification of algebra at; https://brainly.com/question/4344214
Carla waters the flowers every other day and
pulls weeds every 5th day. If she did both
chores today, how many days until she has to
do both chores again on the same day?
Answers
Answer:
Using the number 4 as a place holder I think it would be 20 days before she has both chores on the same day
LOOK AT THE PICTURE ATTACHED AND HELP QUICKLLYYYYY PLZZZ!!!!
Answers
Answer: √490
Step-by-step explanation:
suppose Amaya wants to bake cookies that require 4.5 cups of flour for a recipe that makes 4 dozen cookies. how much flour would Amaya need to make 126 cookies?
Answers
Answer:
11.8125 cups of flour
Step-by-step explanation:
4 dozen = 48 cookies
126/48=2.625 batches of 48 cookies
2.625 x 4.5 = 11.8125 cups of flour
Three (3) is a common factor of 21 and 22.
O A. True
B. False
SUBMIT
Answers
Answer:
false.
Step-by-step explanation:
Factors for 21: 1, 3, 7, and 21. Factors for 22: 1, 2, 11, and 22.
Answer:
B false
hello hope this helps
PLEASE HELP!!!
Bob and Sue are 12 miles apart and moving toward each other. Bob is running at a constant speed of 5mph, and Jada walks at a constant speed of 3mph How long does it take until Bob and Sue meet?
Answers
Answer:
34 miles
Step-by-step explanation:
jn
A man buys an article for $600 and sells it for $710. what is his profit or loss
Answers
Answer:
Profit of $110
Step-by-step explanation:
$710-$600=$110
Don’t know where to start
Answers
Step-by-step explanation:
C = 2πr = 2 x π x 6 = 37.69911
Which description best describes the association between variables x and y?
picture is below
Answers
Answer:
The dots have a weak positive correlation.
Step-by-step explanation:
The values on the graph, or dots, are generally going upwards, meaning they are positive. If they were generally going downwards, or from the top left to bottom right, they would be negative.
The values are not tightly packed together. If they were, they would have a strong positive correlation. Instead, they are loosely around each other. But because they are not completely random all over the graph, the correlation is weak.
Hence, the values on the graph have a weak and positive correlation.