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2 years ago

12

|2x + 3| = 15 what is x?

2 answers:

Gre4nikov [31]2 years ago

3 0

Answer:

x = 6, -9

Step-by-step explanation:

prisoha [69]2 years ago

3 0

Answer:

x=6

Step-by-step explanation:

2x+3=15

Subtract 3 from both sides (3-3), 15-3

2x=12

Divide by 2 on both sides (2/2), 12/2=6

x=6

ISOLATE THE VARIABLE

Hope that helps

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Using the distance formula, calculate how far Tre threw the ball. (4 points: 2 points for setup, 1 for calculation, 1 for the an

sergij07 [2.7K]

Answer:

$D = 63.717$

Step-by-step explanation:

The details that complete the question are:

$(x_1,y_1) = (0,42.78)$

and

$(x_2,y_1)=(90,42.78)$

Required

Determine how far the ball travelled

Distance is calculated using:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute values for x's and y's

$D = \sqrt{(42.78 - 0)^2+(42.78-90)^2}$

$D = \sqrt{42.78^2+(-47.22)^2$

$D = \sqrt{1830.1284+2229.7284$

$D = \sqrt{4059.8568$

$D = 63.717$

<em>Hence, the ball travelled a distance of 63.717 units</em>

6 0

3 years ago

What is the length of the hypotenuse? If necessary, round to the nearest tenth.

exis [7]

Answer:

<h2><u><em>3.5 Km</em></u></h2>

Step-by-step explanation:

the length of the hypotenuse is 4 Km, it is probable that you are looking for the value of the cathetus a.

it is a right triangle and we use Pythagoras

a² = 4² - 2²

a² = 16 - 4

a² = 12

a = √12

a = 3.46 (round 3.5)

4 0

1 year ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

A circle has a diameter of 20 inches and a central angle AOB that measures 160°. What is the length of the intercepted arc AB? U

juin [17]

Calculate the circumference of the full circle:

circumference = PI x diameter = 3.14 x 20 = 62.8 inches
the arc length is 160 degrees of the full circle

divide 160 by 360 (full circle) and multiply by the circumference:

160/360 x 62.8 = 27.9 inches

5 0

3 years ago

Fofino [41]

1. Z=4 10-6
2 y= 6 48/8
3. Q= 13 12+1
6 m=15 11+4
7. 21 19+2
8. S=2 3-1
9. C=6 24/4

8 0

2 years ago