All categories

1 year ago

If m<3 =54°. find each measure.

Mathematics

1 answer:

weqwewe [10]1 year ago

6 0

Answer/Step-by-step explanation:

Given:

m<3 = 54°

m<2 = right angle

a. m<1 + m<2 + m<3 = 180° (angles in a straight line)

m<1 + 90° + 54° = 180° (substitution)

m<1 + 144° = 180°

m<1 = 180° - 144°

m<1 = 36°

b. m<2 = 90° (right angle)

c. m<4 = m<1 (vertical angles)

m<4 = 36° (substitution)

d. m<5 = m<2 (vertical angles)

m<5 = 90°

e. m<6 = m<3 (vertical angles)

m<6 = 54°

f. m<7 + m<6 = 180° (same side interior angles)

m<7 + 54° = 180° (substitution)

m<7 = 180 - 54

m<7 = 126°

g. m<8 = m<6 (alternate interior angles are congruent)

m<8 = 54°

h. m<9 = m<7 (vertical angles)

m<9 = 126°

i. m<10 = m<8 (vertical angles)

m<10 = 54°

j. m<11 = m<4 (alternate interior angles are congruent)

m<11 = 36° (substitution)

k. m<12 + m<11 = 180° (linear pair)

m<12 + 36° = 180° (substitution)

m<12 = 180° - 36°

m<12 = 144°

l. m<13 = m<11 (vertical angles)

m<13 = 36°

m. m<14 = m<12 (vertical angles)

m<14 = 144° (substitution)

You might be interested in

Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $

Hitman42 [59]

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

50x+150y=600

x=3y

Solve for y in each equation:

1) 50x+150y=600

150y=−50x+600

y=-1/3x+4

2) x=3y

y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

4 0

1 year ago

Given two vectors a⃗ =4.00i^+7.00j^ and b⃗ =5.00i^−2.00j^ , find the vector product a⃗ ×b⃗ (expressed in unit vectors). what is

FinnZ [79.3K]

The vector product of $\boxed{a \times b = - 43\hat k}$ and the magnitude of $a \times b$ is $\boxed{43}.$

Further explanation:

Given:

Vector a is $\vec a = 4.00\hat i + 7.00\hat j.$

Vector b is $\vec b = 5.00\hat i - 2.00\hat j.$

Explanation:

The cross product of a \times b can be obtained as follows,

$\begin{aligned}a \times b &= \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k} \\4&7&0\\5&{ - 2}&0 \end{array}}\right|\\&= \hat i\left( {0 - 0} \right) - \hat j\left( {0 - 0} \right) + \hat k\left( { - 9 - 35} \right)\\&= 0\hat i - 0\hat j - 43\hat k\\&= - 43\hat k\\\end{aligned}$

The vector can be expressed as follows,

$a \times b = - 43\hat k$

The magnitude of $a \times b$ can be obtained as follows,

$\begin{aligned}\left| {a \times b} \right| &= \sqrt {{0^2} + {0^2} + {{\left( { - 43} \right)}^2}}\\&= \sqrt {{{43}^2}}\\&= 43\\\end{aligned}$ 43404

The vector product of $\boxed{a \times b = - 43\hat k}$ and the magnitude of $a \times b$ is $\boxed{43}.$

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Vectors

Keywords: two vectors, vector product, expressed in unit vectors, magnitude, vector a, vector b, a=4.00i^+7.00j^, b=5.00i^-2.00j^, unit vectors, vector space.

8 0

1 year ago

Read 2 more answers

If the federal reserve decreases the reserve rate from 2.5% to 1.25% how does this affect the amount of money that would result

kirza4 [7]

The correct answer for this question is this one: "D it increases by $1,800,000"
<span>If the federal reserve decreases the reserve rate from 2.5% to 1.25%, this affect the amount of money that would result because of fractional reserve banking from an initial deposit in a bank of $45,000 is that </span><u>it increases by $1,800,000</u>Hope this helps answer your question and have a nice day ahead.

3 0

2 years ago

A biased die has a probability of 1/4 of showing a 5, while the probability of any of 1, 2, 3, 4, or 6 turning up is the same .

just olya [345]

Possibilities of outcomes:
5, 5, 5
5, 5, 4

P(sum at least 14) = P(5,5,4) + P(5,5,5)
= 1/4 x 1/4 x 3/20 + 1/4 x 1/4 x 1/4
1/40

7 0

1 year ago

: adam and melissa went fly-fishing and caught a total of 32 salmon. melissa caught three times as many salmon as adam. how many

nadya68 [22]

A=Adam
m= Melissa

a+m = 32
m= 3a
Then 3a + a = 32 or 4a =32 then a = 8

5 0

1 year ago