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3 years ago

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Determine the absolute value of -11.

1 answer:

joja [24]3 years ago

8 0

The absolute value of any number is positive...even if it says negative.
Examples :
|5| = 5
| -5 | = 5

so ur answer is : 11

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Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian

777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\B=30^o$

Applying the law of sines

Find the measure of angle A

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(A)}=\frac{2}{sin(30^o)}$

$sin(A)=1$

so

$A=90^o$

Find the measure of angle C

In a right triangle

we know that

$B+C=90^o$ ----> by complementary angles

$B=30^o$

therefore

$C=60^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}$

$c=2\sqrt{3}\ units$

therefore

The dimensions of the triangle are

$A=90^o$

$B=30^o$

$C=60^o$

$a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units$

<em>Second case</em>

In the triangle ABC

Let

$a=4\ units\\b=2/ units\\A=30^o$

Applying the law of sines

Find the measure of angle B

$\frac{a}{sin(A)}=\frac{b}{sin(B)}$

substitute the given values

$\frac{4}{sin(30^o)}=\frac{2}{sin(B)}$

$sin(B)=0.25$

so

using a calculator

$B=14.48^o$

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$A+B+C=180^o$

$A=30^o\\B=14.48^o$

therefore

$30^o+14.48^o+C=180^o$

$C=135.52^o$

Find the length side c

Applying the law of sines

$\frac{c}{sin(C)}=\frac{a}{sin(A)}$

substitute the given values

$\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}$

$c=5.61\ units$

therefore

The dimensions of the triangle are

$A=30^o$

$B=14.48^o$

$C=135.52^o$

$a=4\ units\\b=2\ units\\c=5.61\ units$

see the attached figure to better understand the problem

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3 years ago

A bank paid 2.3% interest on a money market account. What is 2.3% written as a decimal

DochEvi [55]

$1\%\ \ \rightarrow\ \ \frac{1}{100}=0.01 \\\\2.3\%\ \ \rightarrow\ \ x\\\\x= \frac{2.3\%\cdot0.01}{1\%} \ \ \ \Rightarrow\ \ \ x=0.023$

7 0

3 years ago

Read 2 more answers

Which statement best describes the function below?

Illusion [34]

A it is a many to one function

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3 years ago

PLEASE HELP NOW!!!!!!!!!!!!!!!!!!!

Dahasolnce [82]

Answer:

8 + k² - 6 > 8(k + 2) - 4k when k = 7

Step-by-step explanation:

8 + k² - 6 = 8 + 7² - 6 = 51

8(k + 2) - 4k = 8(7 + 2) - 4(7) = 8(9) - 28 = 44

8 + k² - 6 > 8(k + 2) - 4k when k = 7

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3 years ago

Use the substitution method to solve the following system of equations: 3x + 5y = 3 x + 2y = 0 (1 point) (1, 1) (6, −3) (6, 1) (

PtichkaEL [24]

Step-by-step explanation:

Given.

$3x+5y=3$

$x+2y=0$

Take the second equation and subtract 2y to both sides.

$(x+2y)-2y=0-2y$

$x=-2y$

Substitute x into the first equation and simplify.

$3x+5y=3$

$3(-2y)+5y=3$

$-6y+5y=3$

$-y=3$

Invert.

$y=-3$

Substitute Y into your second equation.

$x+2y=0$

$x+2(-3)=0$

$x-6=0$

Add -6 to both sides.

$(x-6)+6=0+6$

$x=6$

Answer:

(6, -3)

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3 years ago