MATHEMATICS HIGH SCHOOL

Help me find y........​
help me find y........​ - 1

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

a)

the sum of all angles in a quadrilateral must be 360º

y+88+25+35 = 360

y = 360=88-25-35

y = 212º

b)

the sum of all angles in an octagon must be 1080º

45+45+140+140+6y = 1080

6y = 1080-90-280

6y = 710

y = 710/6

y=~ 118,3º

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In triangle ABC, c = 8, b = 6, and ∠C = 60°. sin∠B = _____

Answers

Answer:

sin∠B=0.649°  

Step-by-step explanation:

Given: In triangle ABC, c = 8, b = 6, and ∠C = 60°.

To find: sin∠B

Solution: using the sine formula that is (SinA)/(a)=(SinB)/(b)=(SinC)/(c), we get

(SinA)/(a)=(SinB)/(6)=(Sin60^(\circ))/(8)

Taking the second and third  equality, we get

(SinB)/(6)=(Sin60^(\circ))/(8)

⇒(SinB)/(6)=((√(3))/(2))/(8)

⇒(SinB)/(6)=(√(3))/(16)

⇒SinB=\frac{√(3){*}6}{16}

⇒SinB=(3√(3))/(8)

⇒SinB=0.649^(\circ)

Thus, SinB=0.649^(\circ).
Hello,

sin B/b=sin C/c
==>sin B=√3 / 2 * 6/8=3√3 /8

how do I solve p-2 over 3 = 5 over 8?


Answers

(p-2)/(3)=(5)/(8)\ /\cdot24\n\n24\cdot(p-2)/(3)=24\cdot(5)/(8)\n\n8(p-2)=3\cdot5\n\n8p-16=15\n\n8p=15+16\n\n8p=31\ /:8\n\np=(31)/(8)\n\np=3(7)/(8)

a rainstorm produced a rainfall of 2 inches per hour how many hours would it take to get a rainfall amount of one foot

Answers

There are 12 inches in one foot.  If it rains 2 inches per hour, that means it would take 6 hours to rain 12 inches, or one foot.

6 hours x 2 inches/hour = 12 inches or 1 foot
12 inches in 1 ft. 2 inches per hour. 12 divided by 2 = 6hrs.

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent? Answers:
3 dramas, 5 comedies, and 3 documentaries
2 dramas, 6 comedies, and 3 documentaries
1 dramas, 4 comedies, and 6 documentaries
4 dramas, 3 comedies, and 4 documentaries

Answers

Answer:

Gina rent 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

Let Gina rented x movies of dramas , y movies of comedies and z movies of documentaries then , Gina rented total 11 movies.

\Rightarrow x+y+z=11   .........(1)

Also given Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries Gina, thus he rented 2x movies of dramas , 3y movies of comedies and 2z movies of documentaries. also, he rented a total of 27 movies.

\Rightarrow 2x+3y+2z=27 ............(2)

Also, Robby rented the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, thus, he rented x movies of dramas , 2y movies of comedies and 2z movies of documentaries also, he rented a total of 19 movies.

\Rightarrow x+2y+2z=19  ............(3)

Solving the three equation using matrix form,

\left[\begin{array}{ccc}1&1&1\n2&3&2\n1&2&2\end{array}\right] \left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c}11\n27\n19\end{array}\right]

This, system is in form of AX= b,

Where, A=\left[\begin{array}{ccc}1&1&1\n2&3&2\n1&2&2\end{array}\right] ,  X=\left[\begin{array}{c}x\ny\nz\end{array}\right] , b=\left[\begin{array}{c}11\n27\n19\end{array}\right]

Pre-mutiply by A inverse both sides,

X=A^(-1)b  ............(P)

First finding inverse,

\mathrm{Augment\:with\:a}\:3x3\:\mathrm{identity\:matrix}

=\begin{bmatrix}1&1&1&\mid \:&1&0&0\n 2&3&2&\mid \:&0&1&0\n 1&2&2&\mid \:&0&0&1\end{bmatrix}

\mathrm{Swap\:matrix\:rows:}\:R_1\:\leftrightarrow \:R_2

=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 1&1&1&\mid \:&1&0&0\n 1&2&2&\mid \:&0&0&1\end{bmatrix}

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_2\:\mathrm{\:by\:performing}\:R_2\:\leftarrow \:R_2-(1)/(2)\cdot \:R_1

=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 1&2&2&\mid \:&0&0&1\end{bmatrix}

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_3\:\mathrm{\:by\:performing}\:R_3\:\leftarrow \:R_3-(1)/(2)\cdot \:R_1

=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 0&(1)/(2)&1&\mid \:&0&-(1)/(2)&1\end{bmatrix}

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_3\:\mathrm{\:by\:performing}\:R_3\:\leftarrow \:R_3+1\cdot \:R_2

=\begin{bmatrix}2&3&2&\mid \:&0&1&0\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_1\:\mathrm{\:by\:performing}\:R_1\:\leftarrow \:R_1-2\cdot \:R_3

=\begin{bmatrix}2&3&0&\mid \:&-2&3&-2\n 0&-(1)/(2)&0&\mid \:&1&-(1)/(2)&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}

\mathrm{Multiply\:matrix\:row\:by\:constant:}\:R_2\:\leftarrow \:-2\cdot \:R_2

=\begin{bmatrix}2&3&0&\mid \:&-2&3&-2\n 0&1&0&\mid \:&-2&1&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}

\mathrm{Cancel\:leading\:coefficient\:in\:row\:}\:R_1\:\mathrm{\:by\:performing}\:R_1\:\leftarrow \:R_1-3\cdot \:R_2

=\begin{bmatrix}2&0&0&\mid \:&4&0&-2\n 0&1&0&\mid \:&-2&1&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}

\mathrm{Multiply\:matrix\:row\:by\:constant:}\:R_1\:\leftarrow (1)/(2)\cdot \:R_1

=\begin{bmatrix}1&0&0&\mid \:&2&0&-1\n 0&1&0&\mid \:&-2&1&0\n 0&0&1&\mid \:&1&-1&1\end{bmatrix}

Thus, A^(-1)=\begin{pmatrix}2&0&-1\n -2&1&0\n 1&-1&1\end{pmatrix}

Put values in equation (P),

X=A^(-1)b

\left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c,c,c}2&0&-1\n -2&1&0\n 1&-1&1\end{array}\right]\left[\begin{array}{c}11\n27\n19\end{array}\right]

\left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c,c,c}2\cdot \:11+0\cdot \:27+\left(-1\right)\cdot \:19\n \left(-2\right)\cdot \:11+1\cdot \:27+0\cdot \:19\n 1\cdot \:11+\left(-1\right)\cdot \:27+1\cdot \:19\end{array}\right]

\left[\begin{array}{c}x\ny\nz\end{array}\right]=\left[\begin{array}{c}3\n5\n3\end{array}\right]

Thus, Gina rent 3 dramas, 5 comedies, and 3 documentaries.
3 dramas, 5 comedies, and 3 documentaries

Which products are negative?Choose all answers that are correct.







A.

-1 1/4 · (-2 3/4) · (-3)






B.

1/2 · (-1/4) · (1/8)








C.

8 • (–1.1) • 5






D.

–3.1 • (–4.2) • (–6) • (–1.5)

Answers

A,B,and C because in when multiplying or dividing, + and - will be negative and if they are + and + or,  - and - then the answer will be positive.
all of them accept for d

Jacob’s recipe calls for 4 7/8 cups of raisins. He has 6/11 of the amount that he needs.About how many cups of raisins does Jacob have?

Estimate by first rounding each number to the nearest 1/2.

A.4 cups

B.5 1/2

C.2 1/2

D.3 1/2

Answers

If you would like to know how many cups of raisins does Jacob have, you can calculate this using the following steps:

6/11 ... 1/2
4 7/8 cups ... 5 cups

1/2 of 5 cups = 1/2 * 5 = 5/2 = 2 1/2 cups

The correct result would be C. 2 1/2.
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