10x + 4x 3 – 4 Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.

In △PKQ, PK = KQ = 12, m∠P = 35º. Find PQ.

Neporo4naja [7]

The length of PQ is 19.66 units

Step-by-step explanation:

The given is:

1. PK = KQ = 12

2. m∠P = 35º

We need to find the length pf PQ

∵ PK = KQ

∴ m∠P = m∠Q

∵ m∠P = 35°

∴ m∠Q = 35°

The sum of measures of the angles of a triangle is 180°

∴ m∠P + m∠Q + m∠K = 180°

∴ 35 + 35 + m∠K = 180

∴ 70 + m∠K = 180

- Subtract 70 from both sides

∴ m∠K = 110°

Let us use cosine rule to find the length of PQ

∵ PQ = $\sqrt{(KP)^{2}+(KQ)^{2}-2(KP)(KQ)cos(K)}$

∵ PK = 12 , KQ = 12 , m∠K = 110°

- Substitute these values in the rule

∴ PQ = $\sqrt{(12)^{2}+(12)^{2}-2(12)(12)cos(110)}$

∴ PQ = 19.66

The length of PQ is 19.66 units

Learn more:

You can learn more about triangle in brainly.com/question/12985572

#LearnwithBrainly

4 0

3 years ago

In parallelogram LMNO, what is the measure of angle N? 50° 70° 110° 130°

belka [17]

we know that

In a parallelogram opposite angles are congruent and consecutive angles are supplementary.

So

m∠O=m∠M

m∠L=m∠N

m∠O+m∠L= $180$

Step $1$

Find the value of x

$(x+20)+(2x+10)=180\\ 3x+30=180\\ 3x=180-30\\ x=\frac{150}{3} \\ \\ x=50\ degrees$

Step $2$

Find the value of angle L

m∠L $=(2x+10)$

m∠L $=(2*50+10)$

m∠L $=110\ degrees$

Remember that

m∠N=m∠L

m∠N= $110\ degrees$

therefore

the answer is

the measure of the angle N is equal to $110\ degrees$

4 0

2 years ago

Read 2 more answers

There are 36 ribbons of which 1/5 are yellow, 7/15 are pink and the remaining ribbons are

Kay [80]

Step-by-step explanation:

Let there be x blue ribbons

$\therefore \: \frac{1}{5} + \frac{7}{15} + x = 36 \\ \therefore \: \frac{1 \times 3}{5 \times 3} + \frac{7}{15} + x = 36 \\ \therefore \: \frac{3}{15} + \frac{7}{15} + x = 36 \\ \therefore \: \frac{3 + 7}{15} + x = 36 \\ \therefore \: \frac{10}{15} + x = 36 \\ \therefore \: x = 36 - \frac{10}{15} \\ \therefore \: x = \frac{36 \times 15 - 10}{15} \\ \therefore \: x = \frac{540 - 10}{15} \\ \therefore \: x = \frac{530}{15} \\ \therefore \: x = 35\frac{5}{15} \\ \\ \therefore \: x = 35\frac{1}{3} \: are \: blue. \\$

5 0

3 years ago

Please answerrrrr Thank you!!!!!!!!!!!!

dlinn [17]

The correct answers are:

_________________

" (x − 13) ° = 53 ° " ;

_________________

" x = 66 " ;

_________________

" m∠2 = 55° " ;

_________________

" m∠1 = 55° " .

__________________

Step-by-step explanation:

Note: The following "given values/answers" within the attached image:

Specifically:

(x − 13)° = 72° ; and;

x = 85° ;

_________________

are: "incorrect"—and are "arbitrarily assigned values"

_________________

The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.

_________________

Let's start by finding the measure of ∠2 ; that is: " m∠2 " :

To find m∠2:

_________________

Note that: both: "∠2 " ; and the angle that measures "175" with the attached image:

→ both form a straight line—that is;

→ they are "supplementary angles" ;

→ which means they add up to "180° " ;

_________________

So: To solve for: "m∠2" :

_________________

→ m∠2 = 180 − (125) = 55° ,

_________________

Now; to solve for: " m∠1 " :

_________________

Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;

{since: vertical angles are congruent; which means that vertical angles are equal.} ;

_________________

→ As such, m∠1 = m∠2 = 55 °.

_________________

Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;

And combine with angle with the given measurement of 72° ;

And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

_________________

All three of these angles form a straight line—that is;

→ they are "supplementary angles" ;

→ which means they add up to "180° " ;

So, 55° + 72° + (x − 13)° = 180° ;

Let us solve for "x" ; and for "(x − 13)" ;

_________________

55 + 72 = 127 ;

→ 127 + (x − 13) = 180 ;

Now, subtract "127" from each side of the equation:

_________________

→ 127 + (x − 13) − 127 = 180 − 127 ;

to get:

" (x − 13) = 53 " ; → which is one of our answers;

Now, to solve for "x" ; we add "13" to Each Side of the equation;

to isolate "x" on one side of the equation; & to solve for "x" :

_________________

x − 13 + 13 = 53 + 13 ;

to get:

_________________

x = 66 ;

_________________

So: The correct answers are:

_________________

" (x − 13) ° = 53 ° " ;

→ Double check by substituting our value of "66" for "x" :

" (66 − 13) =? 53 ? Yes! ;

_________________

" x = 66 " ;

_________________

" m∠2 = 55° " ;

_________________

" m∠1 = 55° " .

_________________

Hope these answers—and explanations—are helpful!

Best wishes!

_________________

3 0

2 years ago

What is the answer to 2/5(10p-15)=14?

satela [25.4K]

Answer:

P = 5

Step-by-step explanation:

2/5(10p) - 2/5(15)= 14

20p/5 - 30/5= 14

4p - 6= 14

4p = 20

p=5

8 0

3 years ago