In a triangle, the measure of the middle angle
is triple the measure of the smallest angle, and
the measure of the largest angle is 55° greater
than the measure of the smallest angle. Find
the measures of the
angles.

Answers

Answer 1

Let the smallest angle in a triangle be = x

Largest angle in a triangle = 55 + x

The middle angle in a triangle = 3x ( triple the measure of the smallest angle )

Their sum = 180° ( according to the angle sum property all the angles of a triangle sum up to 180° )

This can be written as :

= x + 55 + × + 3x = 180

Let us find each angle by solving the equation .

= x + 55 + x + 3x = 180°

= x + x + 3x + 55 = 180°

= 5x + 55 = 180°

= 5x = 180 - 55 ( transposing +55 from LHS to RHS changes +55 to -55 )

= 5x = 125

= x = 125 ÷ 5 (transposing ×5 from LHS to RHS changes ×5 to ÷5 )

= x = 25

Using this let us find the measure of each angle .

Smallest angle = x = 25

Smallest angle = 25°

Middle angle = 3x = 3 × 25 = 75

Middle angle = 75°

The largest angle = x + 55 = 25 + 55 = 80

Largest angle = 80°

Therefore , the measure of the smallest angle = 25° , the measure of the middle angle = 75° and the measure of the largest angle = 80° .

Answer 2

We have that the measures of the  angles are as follows

[tex]\theta_1=80 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

[tex]\theta_3=25 \textdegree[/tex]

From the question we are told that:

The measure of the middle angle  is triple the measure of the smallest angle

The measure of the largest angle is 55° greater  than the measure of the smallest angle

Let

[tex]\theta_1=Largest\ angle[/tex]

[tex]\theta_2=Middle\ angle[/tex]

[tex]\theta_3=Smallest\ angle[/tex]

Therefore

[tex]\theta_1=55 \textdegree+\theta_3\\\\\theta_2=3*\theta_3[/tex]

Generally, the equation for the angle of a triangle is mathematically given by

[tex]\theta_1+\theta_2+\theta_3=180[/tex]

Therefore

[tex]55 \textdegree+\theta_3+3*\theta_3+\theta_3=180[/tex]

[tex]\theta_3=25 \textdegree[/tex]

Therefore

Substitute [tex]\theta_3[/tex] into equations of [tex]\theta_1[/tex] and [tex]\theta_2[/tex]

For [tex]\theta_1[/tex]

[tex]\theta_1=55 \textdegree+25 \textdegree\\\\\theta_1=80 \textdegree[/tex]

For [tex]\theta_2[/tex]

[tex]\theta_2=3*\theta_3[/tex]

[tex]\theta_2=3*25 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

in conclusion

The measures of the  angles are as follows

[tex]\theta_1=80 \textdegree[/tex]

[tex]\theta_2=75 \textdegree[/tex]

[tex]\theta_3=25 \textdegree[/tex]

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Related Questions

You traveled 52 miles. Then, your avg rate is 12 mph. What algebraic exp.
models the distance?

Answers

Answer:y=12x

Step-by-step explanation:

The algebraic equation that models the distance will be d = 12 * t ,

where d = distance traveled and t = time taken to travel.

What is the average speed?

The total distance traveled by the object in a given time interval is the average speed. A scalar quantity is an average speed. It is represented by the magnitude and lacks direction.

        Avg. speed = [tex]\frac{Total distance travelled}{Total Time Taken}[/tex]

Given :

Total distance traveled = 52 miles.

Average Speed =  12 mph

Let the time taken by t hours.

Therefore, according to the formula:  12 = 52 / t

52 = 12 * t

in order to convert it into algebraic form, let d = 52

Hence, The algebraic equation that models the distance will be

d = [tex]12 *t[/tex]

where d = distance traveled and t = time taken to travel.

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Solve: 4 − 2(2x − 7) = −6.
A) −6
B) −5
C) −3
D) 6

Answers

Answer:

x = 6

Step-by-step explanation:

4 − 2(2x − 7) = −6.

Distribute

4 -4x +14 = -6

Combine like terms

18-4x = -6

Subtract 18 from each side

18 -4x-18 = -6-18

-4x = -24

Divide each side by -4

-4x/-4 = -24/-4

x = 6

Suppose x, y, and z are all rational numbers. Is LaTeX: \frac{z}{\sqrt{x^2-y^2}}z x 2 − y 2 a rational number? Explain your answer.

Answers

Answer:

The square root of 2 is not rational, i.e. it is irrational. Explanation: We can think of a rational number as that which can be expressed as a fraction or ratio of two integers. Irrational numbers do not terminate or repeat, and cannot be represented by a finite … Suppose √2 is rational.

Step-by-step explanation:

a computer shop charges 20 pesos per hour (or a fraction of an hour) for the first two hours and additional 10 pesos per hour for each succeeding hour. find how much you would pay if you used one of their computers for 40 minutes. show solutions.​

Answers

Answer:

The equation for the price, as a function of time in hours is:

P(x) = 20*x    for 0 ≤ x ≤ 2

P(x) = 40 + 10*(x - 2)  for  2 ≤ x

Now, we want to evaluate this function in 40 mins.

we know that 1 hour = 60mins.

Then 40 mins = (40/60) hours = 0.67 hours.

Then we input this in our function, and because this is smaller than 2, we use the first piece of our function:

P(0.67) = 20*0.67 = 13.4

So in 40 mins, the charge will be 13.4 pesos.

3(x + 4) = 2x + 4x - 6 Please help i'll give 90 pts and I only have 113.

Answers

Answer:

x= 6

Step-by-step explanation:

3(x + 4) = 2x + 4x - 6

3x + 12 = 2x + 4x - 6

3x + 12 = 6x - 6

-3x = -18

x= 6

hope it helps

if it helps you, pls give me the brainliest.

Answer:

x = 6

Step-by-step explanation:

3(x + 4) = 2x + 4x - 6

~Distribute the left side

3x + 12 = 2x + 4x - 6

~Combine like terms on the right side

3x + 12 = 6x - 6

~Subtract 12 to both sides

3x = 6x - 18

~Subtract 6x to both sides

-3x = -18

~Divide -3 to both sides

x = 6

Best of Luck!

The cost for children under twelve at a certain buffet restaurant is a base charge of a dollar plus twenty-five cents for each year of the child's age. Represent this cost as an expression, using y to stand for the child's age in years. Then use the expression to find the cost for a child who is nine.

Answers

Answer:

[tex]Cost = 1 + 0.25y[/tex]

[tex]Cost =3.25[/tex]

Step-by-step explanation:

Given

[tex]Base\ Amount = \$ 1[/tex]

[tex]Additional = 25cents[/tex] of child's age

Solving (1):

Determine the cost function.

Represent the years as y.

So, we have:

[tex]Additional = 25cents[/tex] * y

Convert 25 cents to dollars.

[tex]25 cents = 25 * \$0.01[/tex]

[tex]25 cents = \$0.25[/tex]

So, we have:

[tex]Additional = \$0.25 * y[/tex]

The cost amount is then:

[tex]Cost = Base\ Amount + Additional[/tex]

[tex]Cost = 1 + 0.25y[/tex] --- This is the cost function

Solving (b): Cost of 9 years old.

In this case;

[tex]y = 9[/tex]

Substitute 9 for y in [tex]Cost = 1 + 0.25y[/tex]

[tex]Cost =1 + 0.25 * 9[/tex]

[tex]Cost =1 + 2.25[/tex]

[tex]Cost =3.25[/tex] --- This is the cost for a child of 9

Answer:

1+0.25y, 2.25

Step-by-step explanation:

You would express the added 25 cents times the age of the child since the age is represented by the variable y, you would put 0.25y

then to find what the cost is for a nine year old you would multiply 9 by 25 and at the end of multiplying you would move the decimal from zero two times to the left. In case you don't understand how you could move the decimal from zero, there is always a decimal to the right of a whole number where the number ends its just not seen because there is no decimal in the number to represent. The decimal would still be there just it would be invisible but it becomes visible when there is a decimal number to represent.

hope this helps someone, keera

Find the surface area of the cube shown below

Answers

Answer:

the answer is 37.5cm^2

what are all the fractions that are equivalent to 1/7​

Answers

2/14, 3/21, 4/28. just multiply 1 and 7 by the same number to come up with an equivalent fraction

Answer:

Some include: 3/21, 4/28, 5/35.

Step-by-step explanation:

You multiply the bottom by a number and then you multilpy the top by that same number!

1/7=3/21

1 times 3=3

7 times 3=21

Find the slope of each line.

Line A: (6,4) & (-3,-1)

Line B: (-6,0) & (3,5)


a) line a= 5/9 line b= 5/9

b) line a= 9/5 line b= 9/5

c) line a= -5/9 line b= -5/9

d) line a= -9/5 line b= -9/5

Answers

Answer:

a) line a= 5/9 line b= 5/9

Step-by-step explanation:

Use the slope formula:

m =    y2 - y1  

         x2 - x1

Plug-in the known values for each line:

Line A:     -1 - 4 = -5    =  5  

               -3 - 6      -9         9

Line B:     5 - 0  =  5  

               3 - (-6) =   9

A 24ft flagpole has a shadow of 9ft. A soldier standing next to the flagpole has a shadow of 2.25 feet. How tall is the soldier?

Answers

Answer:

6 feet

Step-by-step explanation:

Let's form a proportion;

24                    x

____    =      _____ ,

 9                   2.25

24(2.25) = 9x,

54 = 9x,

x = height of soldier = 6 feet

Answer:

6 feet

Step-by-step explanation:

[tex]\frac{height of object}{length of shadow}[/tex]

Let the hight of the soldier be x

[tex]\frac{24}{9}[/tex] = [tex]\frac{x}{2.25}[/tex]

x = (24×2.25)/9 = 6ft

John sold 32 poster prints of his artwork in September for a total of $126. In October, he sold 48 prints of his artwork for $240. If the relationship between the number of poster prints and total earnings is linear, what was the cost per print expressed as a slope(# of posters sold, $posters sold for)?(complete sentence answer

Answers

Given:

In September, John sold 32 prints of his artwork for $126.

In October, he sold 48 prints of his artwork for $240.

To find:

The cost per print expressed as a slope.

Solution:

Let y be the cost of x prints.

The relationship between the number of poster prints and total earnings is linear.

In September, John sold 32 prints of his artwork for $126. So, the line passes through (32,126).

In October, he sold 48 prints of his artwork for $240. So, the line passes through (48,240).

Now, the slope of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{240-126}{48-32}[/tex]

[tex]m=\dfrac{114}{16}[/tex]

[tex]m=7.125[/tex]

The slope of the linear function 7.125.

Therefore, the cost of per print is $7.125.

Monique made several batches of soup for a potluck supper each batch requires 3/4 of a pounds of potatoes and she used a total of six 1/2 pounds of potatoes how many batches of sifted Monique make which division and multiplication problems could represent this scenario check all that apply

Answers

Answer:

The answer is below

Step-by-step explanation:

Monique made several batches of soup for a potluck supper. Each batch required 3\4 of a pound of potatoes, and she used a total of 6 1/2 pounds of

potatoes. Solve the division problem.

What is 13/2 ÷ 3/4

Answer:

a) 3\4 of a pound of potatoes can make a batch of potluck supper. Monique used 6 1/2 pounds of  potatoes in total. Let n represent the number of batches of soup that was made, hence:

[tex]n=\frac{total\ number\ of\ potatoes\ used}{6 1/2 pounds ofpotatoes\ to\ make\ a\ batch\ of\ soup} \\\\n=\frac{6\frac{1}{2} }{\frac{3}{4} } =\frac{\frac{13}{2} }{\frac{3}{4} } =\frac{13}{2}*\frac{4}{3} =8.67[/tex]

Therefore Monique made about 8 batches of soup

b) [tex]\frac{\frac{13}{2} }{\frac{3}{4} } =\frac{13}{2}*\frac{4}{3} =\frac{26}{3} =8.67[/tex]

Answer:

b and e are the best options and are true

Evaluate the following expressions for m=-3 n=4 p=2

Answers

Answer:

-8

Step-by-step explanation:

Given:

m=-3 n=4 p=2

Missing Equation:

p2 + mn

Find:

Value of equation

Computation:

p2 + mn

⇒ (2)2 + (-3)(4)

⇒ 4 + (-12)

⇒ 4 - 12

-8

What is the solution to the system of equations?

Answers

Answer:

(2, - 4 )

Step-by-step explanation:

Given the 2 equations

x + 2y = - 6 → (1)

3x + y = 2 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the term in y

- 6x - 2y = - 4 → (3)

Add (1) and (3) term by term to eliminate y

- 5x = - 10 ( divide both sides by - 5 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (1)

2 + 2y = - 6 ( subtract 2 from both sides )

2y = - 8 ( divide both sides by 2 )

y = - 4

Solution is (2, - 4 )

whixh equation shows the negative one property of division ​

Answers

Answer:#3

Step-by-step explanation:

Ur welcome

Given A(2,14), B(2,3), C(4,2) and D(14,2) what about AB?

Answers

Answer - 11

I’m assuming you’re trying to find the line AB (basically the distance between point A and B). If that’s the case, since they both have the same x vale, subtract their y values. 14-3 gives you 11, which is the length of line AB

there are 11 pieces of pie left over in the cafeteria. if the 6 pieces are apple and 5 are cherry , what fraction of the remaining are apple

Answers

Answer:

6/11

Step-by-step explanation: If not this try 12/22

The answer is 6 over 11 (6/11)

This is because 11 is the denominator and both 5 and 6 are numerators. If you were to ask for what the fraction of remaining pie would be cherry, then you would say 5/11

pls respond ,.... 25 points

Answers

The answer is B, hope this helped you!

I need help ASAP !!!!!

Answers

Answer:

a is 12, p is 9.

Step-by-step explanation:

No matter what letters or numbers you use you have to come out with the exact number that sums up with the queston provided which means you have to come out with the sum 21 either way, no matter what letters, numbers youu use.

Facts:

help me yo!

A bag held 2 orange marbles, 3 black marbles, and 5 pink marbles. I drew a pink marble and did not replace it. What is the probability of drawing a pink marble next?

A) 2/5
B) 4/9
C) 1/2
D) 5/9

A bag held 3 white marbles, 1 orange marble, and 2 green marbles. Anna drew a white marble and did not replace it. What is the probability of drawing a green marble next?

A.) 1/6
B.) 1/5
C.) 1/3
D.) 2/5

A locker combination has three nonzero digits, and digits cannot be repeated. If the first digit is 3, what is the probability that the next digit is odd?

A.) 4/9
B.) 1/5
C.) 1/2
D.) 5/9

My locker combination has three digits. None of the digits are zero. What is the probability that the first digit of my locker combination is less than 4?

A.) 3/10
B.) 1/3
C.) 2/5
D.) 4/9

Answers

Answer:

1 is B 2 is D

Step-by-step explanation:

5+3+2=10

but since you took a pink one out its now 9 you also need to subtract 1 from the 5 since you didn't replace it

so your chances of getting a pink one are 4/9

Caryn Dexter susie and Vinny filled 24 grocery bags with total of 177 cans to bring to the recycling center. Each person had the same number of cans in every one of his or her bags but that number differed from person to person. How many bags did each person fill How many cans were in each of their bags?

Answers

Answer:201

Step-by-step explanation:

177+24=201

PLEASE HELP I ONLY NEED# 8,10,12,19,20 AND 22 DONE ​

Answers

This is the answer hope you get it :)

The 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively. ​What is the 1st term of the sequence.

Answers

Answer:

            a₁ = -1

Step-by-step explanation:

[tex]a_n=a_1+d(n-1)\\\\a_8=a_1+d\cdot7\\\\a_{20}=a_1+d\cdot19\\\\a_{20}-a_8=a_1+19d-(a_1+7d)=12d\\\\56-20=2d\\\\12d=36\\\\d=3\\\\\\ a_1+3\cdot7=20\\\\a_1=20-21=-1[/tex]

If the 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively, then the 1st term of the sequence is -1

The nth term of an arithmetic sequence is given by the formula:

[tex]a_n=a+(n-1)d[/tex]

The 8th term of the arithmetic sequence is 20

[tex]a_8 = 20\\\\a_8=a+(8-1)d\\\\a+7d=20.......................(1)[/tex]

The 20th term of the arithmetic sequence is 56

[tex]a_{20} = 56\\\\a_{20}=a+(20-1)56\\\\a+19d=56.......................(2)[/tex]

Subtract equation (1) from equation (2)

12d  =  36

d  =  36/12

d  =  3

Substitute d = 3 into equation (1)

a  +  7d  =  20

a  +  7(3)  =  20

a  +  21  =  20

a   =  20  -  21

a  =  -1

The first term of the arithmetic sequence is -1

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What is the equation of the line that passes through the point (5, - 2) and has a slope of - 2/5

Answers

Answer:

Y=-2/5x

Step-by-step explanation:

Y-int: (0,0)

x-int:(-2,5)

Peyton recorded her height twice a year. She grew 5 1/4 inches in 3 1/2 years. What was Peyton’s average growth rate per year?

Answers

Height in which Peyton grew in 3 ½ years = 5 ¼ inches

Height Peyton grows each year =

= 5 ¼ ÷ 3 ½

= 21/4 ÷ 7/2

= 21/4 × 2/7 ( division of fractions is the same as multiplication with reciprocal )

= 42/28

Let us simplify this by dividing the numerator and denominator by 2 .

= 42 ÷ 2 / 28 ÷ 2

= 21/14

= 1 7/14 inches

Peyton's average growth rate per year was 1 7/14 per year . Let us simplify it .

= Both 7 and 14 are divisible by 2 .

So , 1 whole 7 ÷ 2 / 14 ÷ 2

= 1 whole 1/2

= 1 1/2

Therefore , Peyton's average growth rate per year was 1 1/2 inches .

A box contains 10 tags, numbered 1 through 10, with different numbers on each tag. A second box contains 8 tags, numbered 20 through 27 with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?

Answers

Answer:

29

Step-by-step explanation:

Given that:

Bag 1 : Bag contains 10 tags numbered 1 - 10 with different numbers on each

Bag 2: Another bag with 8 tags numbered from 20 - 27

Two Tags are drawn at random, one from each bag; Expected value of the sum of numbers on the two selected tags :

Expected value = mean of numbers in bag 1 + mean if numbers in bag 2

E(X) = (bag 1 minimum + maximum) / 2 + (bag 2 minimum + maximum) / 2

E(X) = [(1 + 10) / 2] + [(20 + 27) / 2]

E(x) = (11/ 2) + (47/2)

E(x) = 5.5 + 23.5

E(x) = 29

Hence, expected value of sum if numbers from each draw = 29

36÷2/3

pls help i no understand

Answers

It would be 54.
Easiest way to do this is to put 36 over 1. Then cross multiply and get 3(36)/2(1) which is 108/2 and that comes out to 54.

Ian purchased cans of soda for a party he was having. For every 12 cans of soda she payed $4.98. What is the cost per can of soda?



The cost of each can of soda is $
i need this quik and now

Answers

$.40

Step-by-step explanation:

if you want the full one it's .415

alex toby and samual are playing a game together

Answers

Answer:

sorry I don't mean to be rude but where is the question what you've written is a statement

Add a picture or the equations

Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select all of the true statements. Original Segment EF is twice as long as segment AB. Segment CD is twice as long as segment FG The Measure fo Angle HEF is twice the measure of Angle DAB. The area of EFGH is twice the area of ABCD

Answers

The question is incomplete. Here is the complete question.

Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select all of the true statements.

A. Segment EF is twice as long as segment AB.

B. Segment CD is twice as long as segment FG

C. The measure of angle HEF is twice the measure of angle DAB

D. The length of segment EH is 16 units.

E. The area of EFGH is twice the area of ABCD.

Answer: A. Segment EF is twice as long as segment AB

              D. The length of segment EH is 16 units

              E. The area of EFGH is twice the area of ABCD

Step-by-step explanation: One quadrilateral which is scaled copy of another quadrilateral means both quadrilateral are similar, i.e., they have congruent angles (same angles) but different sides lengths.

Comparing side GH with side CD, you notice GH's length is twice the side CD. This relationship between each corresponding sides is called scale factor.

Analysing statements above:

A. This statement is correct because segments EF and AB are corresponding sides, so EF will be twice as much as AB;

B. This is incorrect because they are not corresponding sides, so they are not related;

C. Is incorrect because measure of angle in similar quadrilateral has the exact same angle;

D. Statement is correct because if segment AD is 8 units, the corresponding segment EH will be:

EH = 2 x 8 = 16 units

E. Tis statement is correct because area of quadrilateral ABCD is proportional to the area of quadrilateral EFGH by the scale factor, therefore, area of EFGH is twice the area of ABCD.

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