Question
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 five
times the measure of the first angle. The third angle is 30 more than the second. Let T. y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
Provide your answer below:

Answers

Answer 1

Answer:

t = 30°y = 60°z = 90°

Step-by-step explanation:

The given relations can be used to write three equations for the angle values.

Setup

  t + y + z = 180 . . . . . sum of all angle measures

  y + z = 5t . . . . . . . . second and third total 5 times the first

  y + 30 = z . . . . . . third angle is 30 more than the second.

__

Solution

Using the third equation to substitute for z in the first two equations gives ...

  t + y + (y +30) = 180   ⇒   t +2y +30 = 180

  y + (y +30) = 5t   ⇒   2y +30 = 5t

Using the second of these equations to substitute for (2y+30) in the first, we have ...

  t +5t = 180

  t = 180/6 = 30 . . . . . . divide by the coefficient of t

Using this value in our equation for 5t gives ...

  2y +30 = 5(30)

  2y = 120

  y = 60

Then the value of angle z is ...

  y +30 = z = 60 +30

  z = 90

The first, second, and third angles are 30°, 60°, and 90°, respectively.


Related Questions

An exam consists of 50 multiple choice questions. Based on how much you studied, for
any given question you think you have a probability of
p = 0.70 of getting the correct answer. Consider the
sampling distribution of the sample proportion of the 50
questions on which you get the correct answer.

Answers

Using the Central Limit Theorem, it is found that the sampling distribution of the sample proportion of the 50 questions on which you get the correct is approximately normal, with mean of 0.7 and standard error of 0.0648.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem, we have that p = 0.7, n = 50, hence the mean and the standard deviation are given as follows:

[tex]\mu = p = 0.7[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648[/tex]

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

a survey of lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of 4 pounds. if a random sample of 36 lobster fishermen is selected, what is the possibility that their average catch is less than 31.5 pounds? assume the distribution of weights of lobster is normal

Answers

There is a probability of 22.66% that their average catch is less than 31.5 pounds

What is z score?

The z score is used to determine by how many standard deviations the raw score is above or belaw the mean. It is given by:

z = (raw score  - mean)/ (standard deviation ÷ √sample)

Given that, mean = 32, std = 4, sample = 36, hence:

For 31.5:

z = (31.5 - 32) / (4 ÷√36) = -0.75

P(z < -0.75) = 0.2266

There is a probability of 22.66% that their average catch is less than 31.5 pounds

Find out more on z score at: https://brainly.com/question/25638875

Evaluate x^3-3y when x=-3 and y=4

Answers

Answer:

If you would like to solve x^3 - 3 * y when x = - 3 and y = 4, you can do this using the following steps:

x = - 3

y = 4

x^3 - 3 * y = (-3)^3 - 3 * 4 = -27 - 12 = - 39

The correct result would be A -39.

Step-by-step explanation:

pa answer PO Ng question ko plss BRAINLYES Naman dyan

GEOMETRY: VOLUME & SURFACE AREA!! HELP PLEASE WITH ANY ONE OF THEM!!

Answers

Answer:

1) 728

2) 274.89

Step-by-step explanation:

Find the volume and surface formulas for each shape attached.

I'll do a couple for you. For rest just use the formulas and input the values and solve.

1) It is a pyramid.

V  = 1/3 * b * h, where b is the area of base, which is a rectangle so,

b = l * w

so,

V = 1/3 * l * w * h

V = 1/3 * 8 * 21 * 13

V = 1/3 * 2184

V = 2184 / 3

V = 728

2) It is a cylinder

[tex]V = \pi *r^2*h[/tex]

V = π * 5^2 * 3.5

V = π * 25 * 3.5

V = 87.5 π

V = 274.89

if the area of a circle is 36 x 3.14 inches squared find its diameter

Answers

Answer:

36

Step-by-step explanation:
36 x 3.14 = 113.04

Since to find a diameter from the area, you need to divide by 3.14

113.04 divided by 3.14 = 36


But since its already there you can just figure out that 36 is the diameter and you don't have to do any calculating

3. What function can be used to model data pairs that have a common ratio? (1 point)

O linear
O quadratic
Oexponential
Onone of the above

Answers

Answer:

The function that can be used to model data Paris that have a common ratio is exponential.

common ratio exponential

A small pizza costs $4.50, and a salad costs $3.75. You plan to buy two small pizzas and four salads. Write and solve an inequality to find the additional amounts x you can spend to get free delivery.

Answers

The inequality in the total amount of purchase is the greater than inequality

The inequality to find the additional amounts x you can spend to get free delivery is 24.00 + x > y

How to determine the inequality?

The given parameters are:

Small pizza = $4.50

Salad = $3.75

The cost of two small pizzas and four salads is:

Total = 2 * 4.50 + 4* 3.75

Evaluate

Total = 24.00

Let the amount to get free delivery be y.

So, the inequality would be:

24.00 + x > y

Read more abput inequalities at:

https://brainly.com/question/11234618

HELP MEEEEEE PLESEEE

Answers

Answer:

648 cubic centimeters

Step-by-step explanation:

6×9×12=648

Answer:

648 cubic centimeters

Step-by-step explanation:

All you need to do is multiply all of the measures that they show you.

6 x 9 x 12 which equals 648

A jar of 36 coins contains 9 pennies. What percent of the coins are Pennies

Answers

9/36= .25


The answer is 25%

Answer:

25%

Step-by-step explanation:

The fraction of coins which are pennies

= 9/36

= 1/4.

As a percent this is 1/4 * 100

= 25%.

help pls! The pair of figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas.

Answers

Step-by-step explanation:

the scaling ratio is 12/20 = 3/5.

this always applies only to one-dimensional distances, lengths.

the perimeter is calculated as the sum of individual lengths. so while each length is scaled by the same ratio, also the sum is then scaled by that ratio.

p_old = a + b + c

p_new = ra + rb + rc = r(a + b + c) = r×p_old

so, the ratio for the perimeter is also 3/5.

for the area this is a bit different, as an area is always calculated by multiplying 2 lengths (other unscaled factors can be ignored for that consideration of relative change), and that means the scaling ratio has to be multiplied in twice.

a_old = a × b

a_new = ra × rb = r² × a×b = r² × a_old

so, the ratio for the area is

(3/5)² = 9/25

complete the squares​

Answers

i wanted to ask what exactly the question is

??

Please help me I’ll mark brainly

Answers

Answer:

Step-by-step explanation:

First box: (3/4)*b

Second box (3/4 * -8)

third box (3/4b)

fourth box: -6

5th box: 12

If someone can help me step by step exactly

Answers

1) fill the numbers into your equation
2) 130-135=-5
3) now you should have -5 divided by 5, divided by the square root of 28
4) simplify the equation to -1 divided by the square root of 28
5) you now need to multiply both the numerator and the denominator by the square root of 28 divided by the square root of 28
6) you have now got the square root of 784 and you can now simplify the denominator to 28
7) your equation should be Z= -1 multiplied by the square root of 28 over 28
8) depending on how your teacher wants you to simplify your answer can stop there or go even farther to -5.29/28

The value of z using the information and the formula provided in the question is -5.292.

What is the value of z?

Subsituting for the missing values in the formula, the formula becomes: [tex]\frac{130 - 135}{\frac{5}{\sqrt{28} } }[/tex]

Solving for the numerator, the number becomes -5. Solving for the denominator, the number becomes 0.94491

z = -5/0.94491

z = -5.292

To learn more about mathematical equations, please check: https://brainly.com/question/26427570

for a standard distribution, which of the following variables always equals 0?

Answers

Second option I believe

please help me thank u :)

Answers

Answer:

The answer would be 17

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

15^2 + 8^2 = c^2 (15^2 = 225 and 8^2 = 64)

225 + 64 = 289

[tex]\sqrt{289}[/tex] = 17

Calculate the percent

Answers

Answer:

95% of 28 is 26.6

Step-by-step explanation:

28 * 0.95 = 26.6

Answer:

•SEE ABOVE ATTACHMENT•

HOPE IT HELPS!

MARK AS BRAINLIAST.

Part 1 , i really need help if anyone have the items for these please help

Answers


That’s should help you with that!!

Help my sister please don’t delete she needs help

Answers

Inches of yarn needed = 4 ( Inches on one side )

In short: y = 4(L)

0)

What is the greatest side length Sarah could make with 48 inches of yarn?

4(L) = 48

divide both sides by 4

L = 12 inch

→ the greatest side length she could make is 12 inch.

1)

Inches on one side       ||   2     ||    3    ||     4      ||     5      ||   6

Inches of yarn needed ||   8     ||   12    ||   16     ||    20      ||   24

2)

pattern:

inches need = one side + one side + one side + one side inches need = 4 ( one side )

PLEASE HURRY What is the surface area of this right rectangular prism?

Enter your answer as a mixed number in simplest form

Answers

first off, let's change all the mixed fractions to improper fractions.

Check the picture below.

[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{left and right}}{2\left( \frac{4}{3}\cdot \frac{5}{2} \right)}~~ + ~~\stackrel{\textit{front and back}}{2\left( 3\cdot \frac{4}{3} \right)}~~ + ~~\stackrel{\textit{top and bottom}}{2\left( 3\cdot \frac{5}{2} \right)}} \\\\\\ \cfrac{20}{3}+8+15\implies \cfrac{89}{3}\implies 29\frac{2}{3}[/tex]

precio antes de impuestos 1563.60 impuesto 5.4%

Answers

Answer:

precio antes De impuestos 1563.60 impuestos 5.4%

FIRST GET BRAINIEST PERIODTT TYSMMSMSMMSM

Answers

4+4+6+6=12+8=20

hope this helps

height: 6-2=4 units

length: 9-3=6 units

4×6=24

-> 24 units

Which expression is approximately equal to 5 5/8 x 4 5/6?

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5 \dfrac{5}{8}\times 4\dfrac{5}{6}}\\\\\mathsf{= \dfrac{5\times6+5}{8}\times\dfrac{4\times6+5}{6}}\\\\\mathsf{= \dfrac{45}{8}\times \dfrac{29}{6}}\\\\\mathsf{= \dfrac{45\times29}{8\times6}}\\\\\mathsf{= \dfrac{1,305}{48}}\\\\\mathsf{= \dfrac{1,305\div3}{48\div3}}\\\\\mathsf{= \dfrac{435}{16}\approx 27 \dfrac{3}{16}}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{27\dfrac{3}{16}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

On a map 0.5 inches is equal to 5 miles. Suppose Washington, D.C. is 1.25 inches from Baltimore Maryland. How far are the two cities apart ?

Answers

The two cities would be 12.5 miles apart.

What is the T VALUE and confidence interval of this data set? 68, 70, 70, 70, 70, 71, 71, 71, 72, 72, 72, 72, 72, 73, 73, 73, 73, 74, 74, 74, 74, 75, 76, 76, 76, 76, 76, 77, 78, 78


Sample Size: 30

alpha: .05

Confidence: 95%

Answers

Answer:

its 2 all of those are in the 2 time tables unwelcome

-1/2 (-3 / 2x + 6x + 1) -3 x

Answers

Answer: here

Step-by-step explanation:

−21−24

Answer: negative 21 Negative 224


-21-24

292.9 divided by 29 how do u work that out

Answers

Answer:

10.1

Step-by-step explanation:

 292.9

   29

since there is one decimal place, you'll multiply both e' numerator and denominator by a number with ONE ZERO. i.e- 10.           SO:      292.9  ×  10

                                 29     ×  10

               2929

                290    This is the same as: 2929 / 290  or  2929 ÷ 290

                               = 10.1

WELL UNDERSTOOD????

   

Hemos comprado 3 kg de manzanas y nos han cobrado $ 3.45. ¿Cuánto nos cobrarían por 1, 2, 5 y 10 kg?

Answers

Answer:

Por 1 kg: $1.15

Por 2 kg: $2.30

Por 5 kg: $5.75

Por 10 kg: $11.50

Lo siento si esta respuesta no es correcta, si lo es o no, por favor dímelo en los comentarios!

Step-by-step explanation:

Primero, divida $ 3.45 por 3, lo que le dará $ 1.15.

Luego, multiplique $ 1.15 a 1, 2, 5 y 10.

(Respondí esto usando un traductor, por lo que mi gramática podría estar un poco desviada. ¡Espero que esto ayude!)

Find the area of the polygon

Answers

Answer:

40

put some efforts dude...they are so easy

Answer:

40

Step-by-step explanation:

area of a triangle= ½×base× height½×4×6=10since the polygon ha four equal triangles with the same measurement,multiply by four10×4=40ans=40

hope that helps

Please help me solve this problem​

Answers

Answer:

See below

Step-by-step explanation:

Since all graphs pass throught the origin, they all have the form of:

y = ax², where a- coefficient

The coefficient of each graph's equation can be calculated based on the given pairs of points.

Each of them calculated for you and attached below.

Acontainer ship left Hawaii and traveled
toward Tahiti at an average speed of 25
km/h. An aircraft Cimier left sometime
later traveling in the opposite direction
with an average speed of 25 km/h. After
the container ship had traveled for six
hours the ships 200 km apart Find
the number of hown heraft carrien
hohe

Answers

Answer:

Step-by-step explanation:

-lukelaws

did i help?

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