All categories

4 years ago

Triangle abc has angle measures as shown What is the value of x? Show your work.

Mathematics

1 answer:

VikaD [51]4 years ago

7 0

Answer:

x=31

<c = 93

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

<a +<b + <c = 180

35+ 52+3(x+2) = 180

Combine like terms

87+3(x+2) = 180

Subtract 87 from each side

87-87 +3(x+2) = 180-87

3(x+2) =93

Divide each side by 3

3(x+2)/3 = 93/3

x+2 = 31

Subtract 2 from each side

x+2-2 = 31-2

x = 29

Substitute x into the expression for angle c

<c = 3(x+2)

=3(29+2)

= 3(31)

=93

You might be interested in

A frying pan has a radius of 14 centimeters. What is the circumference of the frying pan? Use 22 over 7 for 3.14

katen-ka-za [31]

To find the circumference calculate pi x the diameter of the circle.
Since the radius is 14, the diameter is 28. 3.14 x 28 = about 87.96

3 0

4 years ago

The eccentricity e of an ellipse is defined as the number c/a, where a is the distance of a vertex from the center and c is the

Anna71 [15]

Answer:

Check below, please.

Step-by-step explanation:

Hi, there!

Since we can describe eccentricity as $e=\frac{c}{a}$

a) Eccentricity close to 0

An ellipsis with eccentricity whose value is 0, is in fact, a degenerate one almost a circle. An ellipse whose value is close to zero is almost a degenerate circle. The closer the eccentricity comes to zero, the more rounded gets the ellipse just like a circle. (Check picture, please)

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1 \:(Ellipse \:formula)\\a^2=b^2+c^2 \: (Pythagorean\: Theorem)\:a=longer \:axis.\:b=shorter \:axis)\\a^2=b^2+(0)^2 \:(c\:is \:the\: distance \: the\: Foci)\\\\a^2=b^2 \\a=b\: (the \:halves \:of \:each\:axes \:measure \:the \:same)$

b) Eccentricity =5

$5=\frac{c}{a} \:c=5a$

An eccentricity equal to 5 implies that the distance between the Foci has to be five (5) times larger than the half of its longer axis! In this case, there can't be an ellipse since the eccentricity must be between 0 and 1 in other words:

$If\:e=\frac{c}{a} \:then\:c>0 , and\: c>0 \:then \:1>e>0$

c) Eccentricity close to 1

In this case, the eccentricity close or equal to 1 We must conceive an ellipse whose measure for the half of the longer axis a and the distance between the Foci 'c' they both have the same size.

$a=c\\\\a^2=b^2+c^2\:(In \:the\:Pythagorean\:Theorem\: we \:should\:conceive \:b=0)$

$Then:\\\\a=c\\e=\frac{c}{a}\therefore e=1$

7 0

3 years ago

I am stuck on how to do 10 percent of $55.86

faust18 [17]

Answer:

read step by step

Step-by-step explanation:

.10×55.86 = 5.58

then subtract $5.58 from your total .

and that will give you the answer

8 0

3 years ago

mike's condo has a market value of 310000. the property in mikes area is assessed at 40% of the market value. the tax rate is 14

Svetradugi [14.3K]

If you would like to know Mike's tax, you can calculate this using the following steps:

a market value ... 310000
the property ... 40% of the market value = 40% * 310000 = 40/100 * 310000 = 124000

the tax rate ... 145.10 per 1000 of assessed valuation
145.10 ... 1000 of assessed valuation
x ... 124000 of assessed valuation
____________________________
145.10 * 124000 = 1000 * x /1000
x = 145.10 * 124000 / 1000
x = 17992.4 (Mike's tax)

The correct result would be: Mike's tax is 17992.4.

6 0

3 years ago

Farmer Brown has 42 animals, which are cows and chickens. They have a total of 120 legs. Write a system of equations, show your

SCORPION-xisa [38]

Answer:

The system of equations is:

x + y = 42

4x + 2y = 120

And there are 24 chickens.

Step-by-step explanation:

We know that the total number of cows (x) plus the total number of chickens (y) is 42, because Farmer Brown has 42 animals.

We also know that cows (x) have 4 legs and so 4 times the number of cows is the number of cow legs. And chickens (y) have 2 legs, so the number of chickens times two represents the total chicken legs. The sum of 4x + 2y is 120 because there are 120 legs in total.

To solve the system of equations, first solve each equation for y.

In the first equation:

x + y = 42

Subtract x from both sides to isolate y.

y = 42 - x

Second equation:

4x + 2y = 120

Subtract 4x from both sides

2y = 120 - 4x

Divide both sides by 2

y = 60 - 2x

Now that the y's are isolated in both equation, you can put them into 1 equation. Where y = y:

y = 42 - x

y = 60 - 2x

42 - x = 60 - 2x

Add 2x to both sides

42 + x = 60

Subtract 42 from both sides

x = 18

Since x is the number of cows, we know that Farmer Brown has 18 cows.

Now we can substitute the x value into one of the equations:

y = 42 - x

y = 42 - (18)

y = 24

The number of chickens is represented by y, so there are 24 chickens.

3 0

3 years ago