A cable 27 feet long runs from the top of a utility pole to a point on the ground 16 feet from the base of the pole. How tall is the utility pole?

Step-by-step explanation:

The given equation is :

[tex]-2x^2+6x+1=-3x^2[/tex]

Taking all the terms to one side of the equation i.e.

[tex]-2x^2+6x+1+3x^2=0\\\\x^2+6x+1=0[/tex]

It is a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] whose solution is given by :

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here, a = 1, b = 6 and c = 1

Put all the values,

[tex]x=\dfrac{-6\pm \sqrt{6^2-4(1)(1)}}{2(1)}\\\\x=-0.171\ and\ x=-5.82[/tex]

Hence, this is the required solution.

Step-by-step explanation:

38 to 18 m square / videos 400

Answer:

EC = 28'

Step-by-step explanation:

Since ∆KAR ~ ∆ENC, therefore, their corresponding side lengths will be proportional to each other.

By implication, we have:

EN/KA = EC/KR

EN = 96'

KA = 24'

EC = ?

KR = 7'

Thus:

96/24 = EC/7

Cross multiply

EC*24 = 7*96

EC*24 = 672

Divide both sides by 24

EC = 672/24

EC = 28'

Answer:

Step-by-step explanation:

area =8*4 cm

=32 cm^2

Answer:

area of the figure=8×4

=32 cm²

9x =90

x=90/9

=10

4×10= 40

5×10=50

Answer:

[tex]y = \frac{-5}{3}\\\\y = \frac {4}{3}[/tex]

Step-by-step explanation:

[tex]y = \frac{2}{3} x + \frac{1}{3}\\\\when \ x = -3 \\\\y = \frac{2}{3}(-3) + \frac{1}{3} = -2 + \frac{1}{3} = \frac{-6 + 1}{3}= \frac{-5}{3} \\\\When \ x = 1 \frac{1}{2} = \frac{3}{2}\\\\y = \frac{2}{3} \times \frac{3}{2} + \frac{1}{3} = 1+ \frac{1}{3} = \frac{3 + 1}{3}= \frac{4}{3} \\\\[/tex]

Answer:

ans c hope it helps u take care have a nice day

Answer:

1. 1 cm

2. 7 and 2/16 (or 1/8) inches

Step-by-step explanation:

2. The distance from each small line on a ruler is 1/16 of an inch.

Answer: the answer is 48 inches

Step-by-step explanation:

Express 76% as decimal is 0,76

76/100 = 0,76

Answer:

there is not solution the the equation (graph)

Step-by-step explanation:

when the lines are parallel and do not intersect they is no solution.

Answer:

55°

Step-by-step explanation:

triangle= 180°

third angle= 180-90-35

= 55°

Answer:

80,000

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Hundreths

Step-by-step explanation:

Step-by-step explanation:

Write each decimal using a negative exponent. ... DNA contains the genetic code of an organism. ... meter. Which of the following represents the length of the DNA strand as a decimal?

Hi there!

[tex]\large\boxed{y = \pm \sqrt{x - 16}}[/tex]

To solve for the inverse, swap the x and y variables:

x = y² + 16

Isolate for y by subtracting both sides by 16:

x - 16 = y²

Square root both sides:

√(x - 16) = y

Add the plus/minus sign:

y = ±√(x - 16)

Answer:

c

Step-by-step explanation:

43-7= 36

Range is highest number minus smallest number

Given :

An equation, 2cos ß sin ß = cos ß .

To Find :

The value for above equation in (0, 2π ] .

Solution :

Now, 2cos ß sin ß = cos ß

2 sin ß = 1

sin ß = 1/2

We know, sin ß = sin (π/6)  or sin ß = sin (5π/6) in  ( 0, 2π ] .

Therefore,

[tex]\beta = \dfrac{\pi}{6}\ or\ \beta = \dfrac{5\pi}{6}[/tex]

Hence, this is the required solution.

Answer:

option no. D

Step-by-step explanation:

i+34j+14k

hope it helps

Answer:

13/16

Step-by-step explanation:

Answer:

Hello! answer: 10

Step-by-step explanation:

x = 10 because...

10 × 3 = 30 30 + 5 = 35 35 + 55 + 90 = 180 therefore x = 10 hope that helps!

Answer:

SAS. ( side, angle, side)

in option 2nd

Answer:

False

SAS = This stands for Side Angle Side congruency theorem

Step-by-step explanation:

Question 1.)

If any of the 2 angles of any triangle is congruent to any of the 2 angles of the other triangle, then this would be true. Let's find the measure of ∠R and ∠G:

=> ∠G = 180 - (98 + 30)

∠G = 52

=> ∠R = 180 - (98 + 26)

∠R = 56

Now we know that Angles of ΔHIG are 30, 98, and 52, and Angles of ΔSQR are 26, 98, and 56. 2 angles of 1 triangle are not congruent 2 angles of the other triangle, therefore the triangles aren't congruent.

Question 2.)

SAS congruency is used since an angle and it's 2 adjacent sides are given for each triangle.

Hope this helps!

Answer:

9901 / 2000

Step-by-step explanation:

might be wrong

Answer:

The vehicle travels 105.6 feet in one second.

Step-by-step explanation:

This question is solved by proportions.

72 mph

One hour has 3600 seconds.

Each mile has 5280 ft.

So in 3600 seconds, the vehicle travels 5280*72 = 380160 feet. In one second, how many feet?

3600 seconds - 380160 feet

1 seconds - x feet

Applying cross multiplication:

[tex]3600x = 380160[/tex]

[tex]x = \frac{380160}{3600}[/tex]

[tex]x = 105.6[/tex]

The vehicle travels 105.6 feet in one second.

Answer:

We can be 95% confident that the true proportion of listeners who will see a live music show in the next month is between 64% and 72%.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

A 95% confidence interval for the population proportion was 0.68 ± 0.04.

We are 95% sure that the true population proportion is between 0.68 - 0.04 = 0.64 and 0.68 + 0.04 = 0.72.

Thus, the correct answer is:

We can be 95% confident that the true proportion of listeners who will see a live music show in the next month is between 64% and 72%.

Answer:

14 units

Step-by-step explanation:

Side length of each square is 1 unit.

So, sum of the lengths of all the border edges = 14 units

Thus, the Perimeter of the figure = 14 units

Answer:

A=162.56in^2

Step-by-step explanation:

make sure u separate the different shapes

The area (A) of a trapezoid is calculated as follows:

A = 1/2 * sum of the parallel sides * height

In this case:

A = 1/2 * (23 + 5) * 12 = 168 yd^2.

Answer: it’s 168

Step-by-step explanation:

Answer:

B, C, D.

Step-by-step explanation:

These are all statistical questions since these can be answered by collecting data that vary.