A triangle has angle measures that are related as follows:


• The largest angle is eight times the smallest angle.


• The middle angle is triple the smallest angle..


a) write an equation to model the relationship


b) solve the equation and then determine the measure of each angle. Sketch the triangle and label the angle measures.

Answers

Answer 1

Answer:

  a) a +8a +3a = 180°

  b) 15°, 45°, 120°

  c) see attached

Step-by-step explanation:

a)

Let 'a' represent the measure of the smallest angle. The largest angle is 8a, and the middle angle is 3a. The sum of angles, as always, is 180°.

  a +8a +3a = 180° . . . . . . equation modeling the relationship

__

b)

  12a = 180° . . . . . . collect terms

  a = 15° . . . . . . . divide by 12

  3a = 3×15° = 45°

  8a = 8×15° = 120°

The angle measures are 15°, 45°, and 120°.

__

c)

see attached. We have arbitrarily let the shortest side be 10 units.

A Triangle Has Angle Measures That Are Related As Follows: The Largest Angle Is Eight Times The Smallest

Related Questions

How many feet of fencing are needed to enclose the garden? 54 feet 68 feet 108 feet 140 feet.

Answers

Answer:

140

Step-by-step explanation:

30+30=60

40+40=80

60+80=140

Answer:

140

Step-by-step explanation:

I got it right on edge

HELP A store had apples on sale for $1.20 a pound. Joan spent $5.28 on apples. How many pounds did she buy?

Answers

Answer:

4.4 and almost a half

Step-by-step explanation:

Because he can't but 5 because if he bought 5 it would be 6$

But 4 he can if you add taxes.

1.20 for 1

2.40 for 2

3.60 for 3

4.80 for 4

A jar is full of 100 coins. All of the coins are either nickels or dimes.
a. The value of the coins is $6.35. Write a linear system representing this equation.
b. Solve the system to determine how many of each type of coin is in the jar.

Answers

Answer:

73 nickels, 27 dimes

Step-by-step explanation:

x+y=100

5x+10y=635

x=100-y

5(100-y)+10y=635

500-5y+10y=635

500+5y=635

5y=135

y=27

5x+10(27)=635

5x+270=635

5x=365

73

73+27=100

How are humans impacting Earth's climate?

Answers

Answer:

technology because of our building style or oil

Step-by-step explanation:

which math expression means 52 more than an unknown number

Answers

En expresiones algebraicas significaría x+52

Hi Everyone! Please draw a regular bar graph with x and y axis, along with all components of a bar graph!​

Answers

that the bar graph with all components

HELP (0,-3) and (5,-5) what is the slope

Answers

Answer:

-2/5

Step-by-step explanation:

To find the slope, we use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -5 - -3)/( 5 - 0)

   = ( -5+3)/( 5-0)

   = -2/5

Hi! I can help you with joy! :)

Use the slope formula:[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]Wherey2 is the y-coordinate of the second point (in this case, it's equal to -5)y1 is the y-coordinate of the first point (in this case, it's equal to -3)x2 is the x-coordinate of the 2nd point (in this case, x2=5)x1 is the x-coordinate of the 1st point (in this case, x1=0)Plug in the values:[tex]\displaystyle\frac{-5-(-3)}{5-0} \\\frac{-5+3}{5}[/tex][tex]\displaystyle\frac{-2}{5}[/tex][tex]\displaystyle-\frac{2}{5}[/tex]

Answer:

[tex]\huge\boxed{\bold{Slope=\displaystyle-\frac{2}{5} }}[/tex]

Hope it helps!

~Nature~

In terms of x, what is the length of the side of a square whose area is represented by the expression 25x^2 + 40x + 16?​

Answers

Answer:

Step-by-step explanation:

25x2 − 40x + 16 = (5x)² - 2*5*4  + 4²      { (a - b)² = a² - 2ab + b² }

                          = (5x - 4)²                      { here a = 50 and b = 4}

Side of the square = 5x - 4 units

Part B:

25x2 − 16y2 = (5x)² - (4y)²         { a² - b² = (a + b) * (a - b) }

                    = (5x + 4y) * (5x - 4y)    { here a = 5x and b = 4y}

Dimensions of Rectangle: (5x + 4y) ; (5x - 4y)

Answer:

Step-by-step explanation:

25x²+40x+16=25x²+20x+20x+16

=5x(5x+4)+4(5x+4)

=(5x+4)(5x+4)

=(5x+4)²

length of side=5x+4

What is the value for x?

Answers

This is an equilateral triangle, so all angles are 60 degrees, we can set 8y + 12 equal to 60, and 7x + 4 = 60
To simplify 8y + 12 = 60, subtract 12 from both sides to get 8y = 48, divide both sides by 8 and you have y = 6
To simplify 7x + 4 = 60, subtract 4 from both sides to get 7x = 56, divide both sides by 7 and you have x = 8

A car travels 625km using 25L of fuel (km/L) ​

Answers

Answer:

Step-by-step explanation:

625km divide by 25L =25

Hoped it helped u

Drag the tiles to the correct boxes to complete the pairs.
Simplify the mathematical expressions to determine the product or quotient in scientific notation. Round so the first factor goes to the tenths place.

Answers

1) (3.8 * 10^3) * (9.4 * 10^-5) = 0.3572 = 3.6 * 10^-1

2) (4.2 * 10^7) * (7.4 * 10^-2) = 3.1 * 10^6

3) (8.6 * 10^-6) * (7.1 * 10^9) / (4.1 * 10^ -2) * ( 2.8 * 10 ^-7) = 5.3 * 10^-6

4) 4.2 * 10^-1

Sorry for not putting my work for number 4. Hope this helps!

Pls somone help me pls

Answers

Answer:

This is a right answer. You can check it

Jojo likes to paint. She estimates the number of paintings she completes using the function P of w equals two thirds times w minus two, where w is the number of weeks she spends painting. The function J(y) represents how many weeks per year she spends painting. Which composite function would represent how many paintings Jojo completes in a year? P of J of y equals J times the quantity two thirds times w minus two P of J of y equals two thirds times J of y minus two J of P of w equals two thirds times J of y minus two J of P of w equals J times the quantity two thirds times w minus two.

Answers

Composite functions are functions of functions. The needed composite function for given context is: [tex]P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]

What are function of functions and how are they represented?

Function of function, as the name suggests, are functions applied over functions themselves. This is also called function composition.

We have input. We apply one function on that input. Then we apply another function on the output obtained by the first function. This whole function application on first input is called function of functions. The resultant function which maps the input x to the final output is called function of function.

If first function is g( and the other function is f, then we can write the resultant function of function as  [tex](f\circ g)(x)[/tex]input to first function.

Thus, we have;

[tex](f\circ g)(x) = f(g(x))[/tex]

For the given case, it is given that:

[tex]P(w) = \dfrac{2}{3}w - 2[/tex][tex]J(y)[/tex]

To evaluate how many paintings Jojo completes in a year, we need [tex]P(J(y))[/tex]  (since, we need number of paintings and input is year, so we convert year to number of weeks by function J, and then give the output to P function to evaluate number of paintings)

Thus,

[tex]P(w) = \dfrac{2}{3}w - 2\\\\P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]

Thus,

The needed composite function for given context is: [tex]P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]

Learn more about composite functions here:

https://brainly.com/question/24780056

growing from 1.4m to 1.6m in one year what’s the rate to change

Answers

Answer:

1.6 - 1.4 = 0.2

0.2 / 1.4 = 0.14 = 14%

Step-by-step explanation:

Three times a number is 24 less than the number. What is the number?

Answers

Answer:

Don't know the number.

Step-by-step explanation:

Tell me also.

3x=x-24
2x=-24
x=-12
aka the number is -12

Constance is drawing a map of the block on which she lives, using a scale of 1 inch to 160 feet. The actual length of her block is 1800 feet.

What is the exact length of the block on Constance's map

Answers

Answer:

788947

Step-by-step explanation:

I'm just here for answers

PLSSSSS HELP WILL MARK BRAINLIEST
If the expression is expanded, what is the coefficient of x?
4 (3x + 5)
Coefficient of x =

Answers

Answer:

12

Step-by-step explanation:

Start by expanding the expression:

4(3x+5)

Distribute the 4 to each of the numbers in the parentheses

12x+20

The coefficient of x is basically what is being multiplied by x. In this scenario, we can expand 12x to be...

12*x

Which means that the coefficient of x is 12

12x+20

12x+20=0

12x=-20.

12÷12x=-20÷12

x=-5/3

x=negative five over three

would - (-2) 4 be negative or positive

Answers

Would - (-2) 4 be negative or positive ?

- x - = +

Therefore -(-2)4 = 2*4= 8 which is positive

Positive

When you multiply a negative number to a positive number, your answer is a negative number. It doesn't matter which order the positive and negative numbers are in that you are multiplying, the answer is always a negative number.

Find the area of the shaded region. Use 3.14 as an approximation.​

Answers

Answer:

shaded area = 113.64 cm²

Step-by-step explanation:

To find the shaded area, subtract the area of the circle from the area of the triangle.

Area of a triangle = 1/2 x base x height

⇒ area of triangle = 1/2 x 25 x 21.4 = 267.5 cm²

Area of a circle = [tex]\pi r^2[/tex] (where r is the radius)

From inspection, we can see that the diameter of the circle = 14 cm

Therefore, as the diameter = 2r, then r = 14 ÷ 2 = 7 cm

⇒ area of circle = 3.14 x 7² = 153.86 cm²

Shaded area = area of triangle - area of circle

⇒ shaded area = 267.5 - 153.86 = 113.64 cm²

help please

Solve the problem and explain the steps taken.

There are four students working on a project in math class. Miguel has completed 1/8 of the project, Gina has completed 13% of the project, Jatziry has completed 0.10 of the project, and Kwa has completed 1/9 of the project. Make a list of the students in order from least to greatest by the amount of the project they have completed.

Answers

There are 3 ways you can solve this, you can convert these numbers into decimals, fractions, or percentages, so I’ll convert these into percentages. 1/8 as a percentage is 12.5%, 0.10 as a percentage is 10%, and 1/9 as a percentage is 11.1%, we have to take the 13 percent also, of all these percentages least to greatest in order would be, 10%, 11.1%, 12.5% and 13% hope it helps and im sorry if its incorrect!

Answer:

13%, 1/8, 1/9, 0.10  13>1/8>1/9>0.10

Step-by-step explanation:

What number is halfway between –3 and 4 ?

Answers

Answer:

0.5

Step-by-step explanation:

4-(-3)

4+3=

7

Half of 7 is 3.5

4-3.5=0.5

Answer:

The number 0.5 is halfway between -3 and 4.

Step-by-step explanation:

To find the halfway point between two numbers, add them together and divide by 2.

-3 + 4 = 1

1/2 = 0.5

Find the value of the power.
0.92 =

Answers

Answer:

hello the correct answer is x=6

Step-by-step explanation:

Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)

Answers

Answer:

  16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

  [tex]\displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}[/tex]

__

Additional comment

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

  area = 4.5 +3×4 = 16.5 . . . square units

Solve for x. The problem is in the picture!!

Answers

Answer:

According to the given Attachment

we know sum of all angles in a triangle is 180° .

Sum of all angles in = 180°

On substituting the given value we obtain

➥ x + 61° + 70° + 61° = 180°

➥ x + 192° = 180°

➥ x = 180° - 192°

➥ x = -12°

So, the value of x is -12°

Step-by-step explanation:

[tex]x + 61 + 70 + 61 = 180(sum \: of \\ \: triangle) \\ \\ x + 192 = 180 \\ \\ x = 180 - 192 \\ \\ x = - 12[/tex]

# be careful#

Write the next three terms of the arithmetic sequence.
0.2, 0.6, 1, 1.4,

Answers

The nth term of an arithmetic sequence is
a
+
(
n

1
)
d
where
a
is the first term and
d
is the common difference.
So
a
=
0.2
and
d
=

0.8
Hence, the nth term is
0.2

0.8
(
n

1
)

0.2

0.8
n
+
0.8
so
1

0.8
n

solve for X and y
60°
14 3

Answers

Answer:

X = 28

Y = 14

Step-by-step explanation:

+++++++++++++++++++++++++++++++++++++

John's bicycle covers 60 inches in one revolution. What
is the radius of his tire?

Answers

Answer:

The radius is equal to  [tex]\frac{30}{pi}[/tex]   or about 9.5 inches

Step-by-step explanation:

A revolution is the same as the circumference,

which can be found using C = 2πr

C = 2πr

60 = 2πr

(2π)r = 60

r = [tex]\frac{60}{2pi}[/tex]

r = [tex]\frac{30}{pi}[/tex] or about 9.5 inches

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Which equation does the graph below represent?

I kinda really need help with this lol
Thanks :)

Answers

Answer:

y-intercept, where the graph crosses y-axiss is 0. that means in the equation: y = mx + b

b = 0

the m, is slope. looking at the graph you can see the points on the line are connect up 4 right 1. rise/run = slope = 4

y = 4x

Step-by-step explanation:

Solve for f.

4 = fover3

Answers

Answer:

f = 12

Step-by-step explanation:

Step 1: Multiply both sides by 3.

4 × 3 = (f/3) × 3 12 = f

Step 2: Check if solution is correct.

4 = 12/34 = 4

Have a lovely rest of your day/night, and good luck with your assignments. ♡

Which ratio is larger, 18/5 or 72/25 ?​

Answers

18/5. Multiply the 5 as many times as you need to to get to 25. Then as many times as you multiplied the bottom multiply the top the same so it would be 5 times on both sides making the ratio. 90/25

Answer:

Step-by-step explanation:

LCM of 5 and 25=25

Now,

18/5=18x5/5x5=90/25

72/25=72/25

Since 90/25>72/25

Hence,

18/5 is greater than 72/75

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