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2 years ago

What are the solutions to 5x^2 - x - 1 < 0

1 answer:

5 0

5x^2 - x - 1 > 0
Using the equation to find x,
x= 1/10 +- 1/10sqrt21

Answer is
1/10 - 1/10sqrt21 < x < 1/10 + 1/10sqrt21

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I need help on some geometry questions

kupik [55]

Answer: x = 40

Step-by-step explanation:

3x + x + 20 = 180 same side (consecutive) interior angles

4x + 20 = 180

4x = 160

x = 40

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Answer: x = 24

Step-by-step explanation:

6x - 24 + 2x + 12 = 180 linear pair (supplementary angles)

8x - 12 = 180

8x = 192

x = 24

****************************************************************************

Answer: x = 16

Step-by-step explanation:

base angles of an isosceles triangle are congruent

2(2x + 15) + 6x - 10 = 180 triangle sum theorem

4x + 30 + 6x - 10 = 180

10x + 20 = 180

10x = 160

x = 16

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Let ∠1 and ∠2 represent the exterior angles in the diagram and "x" represent the same side (consecutive) interior angle with ∠1.

Then m∠1 + x = 180 same side interior angle theorem

and m∠2 + x = 180 linear pairs are supplementary

m∠1 + x = m∠2 + x transitive property

m∠1 = m∠2 subtraction property of equality

∠1 ≈ ∠2 definition of congruency

8 0

3 years ago

The tee for the sixth hole on a golf course is 305 yards from the tee. On that hole, Marsha hooked her ball to the left, as sket

EleoNora [17]

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

$a =255\ yd\\c = 305\ yd\\\angle B =17^\circ$

To find:

Side $b = ?$

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Putting all the values:

$cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd$

So, the distance between the Ball and hole is 96.42 yd

Correct answer is option D. 96.4 yd.

8 0

3 years ago

Each of the

Allisa [31]

To find median . . . list the number in order from least to greatest

10 , 11, 12, 12 13, 15

Then cross of a number from each side until you get to the middle number or middle 2 numbers.
IF there are 2 numbers add them together and divide by 2

12 + 12 = 24
24 / 2 = 12

Your median is 12

To find mean (this is the same as average) add all the numbers to get a total.

10 + 11 + 12 + 12 + 13 + 15 = 73

Then count the number of items added . . .6

Take the total and divide by the items counted

73 / 6 = 12.1666

Your directions say to round to the nearest tenth place.

12.166 = 12.2

8 0

4 years ago

Read 2 more answers

For y = 3x - 2x^2 +5x^3 show how to find the value for y, when x = 3. Show your work

Mnenie [13.5K]

$y \: = \: f(x) \: = \: 3x \: - \: 2 {x}^{2} \: + \: 5 {x}^{3}$
Here, y is a cubic function of x.
When x = 3,
$y \: = \: f(3) \: = \: 3(3) \: - \: 2 {(3)}^{2} \: + \: 5 {(3)}^{3}$
$y \: = \: 9 \: - \: 18 \: + \: 135$
$y \: = \: f(3) \: = \: 126$
Hence, when x = 3, y = 126.

8 0

3 years ago

Read 2 more answers

Will someone please help me

Rufina [12.5K]

Answer:

The filled table for each equation by using the exact values in the table is

10x+2y=56

x y

______________________

0 28

$\frac{56}{10}$ 0

________________________

8x+3y=49

x y

_________________________

0 $\frac{49}{3}$

$\frac{49}{8}$ 0

_________________________

Step-by-step explanation:

Given equations are 10x+2y=56 and 8x+3y=49

To fill the table for each equation by using the exact values in the table :

10x+2y=56

put x=0 in above equation we get

10(0)+2y=56

2y=56

$y=\frac{56}{2}$

$y=28$

Therefore (0,28)

put y=0 in the given equation 10x+2y=56 we get

10x+2(0)=56

10x=56

$x=\frac{56}{10}$

Therefore ( $\frac{56}{10}$ ,0)

10x+2y=56

x y

_________________________

0 28

$\frac{56}{10}$ 0

__________________________

For

8x+3y=49

put x=0 in above equation we get

8(0)+3y=49

3y=49

$y=\frac{49}{3}$

Therefore (0, $\frac{49}{3}$ )

put y=0 in the given equation 8x+3y=49 we get

8x+3(0)=49

8x=49

$x=\frac{49}{8}$

Therefore ( $\frac{49}{8}$ ,0)

8x+3y=49

x y

_________________________

0 $\frac{49}{3}$

$\frac{49}{8}$ 0

________________________

7 0

4 years ago