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3 years ago

find the smaller of 2 consecutive integers,x, if the sum of the smaller and 6 times the larger is -29

Mathematics

1 answer:

AnnyKZ [126]3 years ago

3 0

Answer:- The smaller integer is -5.

Explanation:-

Let the first consecutive integer be x and the second consecutive integer be x+1.

According to the given question:-

x+6(x+1)= -29

⇒x+6x+6= -29 [distributive law]

⇒x+6x= -29-6 [subtract 6 on the both sides]

⇒7x= -35 [combining like terms ]

⇒x= -5 [dividing 7 on both sides]

Thus the smaller integer =x= -5

larger integer =x+1= -5+1= -4

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2 years ago

Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer.

Sonja [21]

<h3>Answer: Rhombus</h3>

======================================================

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\$

Segment AB is exactly $\sqrt{17}$ units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

-------------------------

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\$

Segment AB has a slope of 1/4.

Do the same for BC

$B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\$

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a <u>rhombus</u>.

4 0

1 year ago

Read 2 more answers

A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an

Nataly [62]

Answer:

The distance between the walls is 70 m.

Step-by-step explanation:

Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is

BE ⊥ ED and CD ⊥ ED

AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m

AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.

The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°

The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°

As shown is figure attached below.

WE have to find the distance between the walls that is Length of ED

Length of ED = EA + AD

Consider the Δ AEB,

Using trigonometric ratio,

$\tan\theta=\frac{perpendicular}{base}$

Here $\theta=45^{\circ}$ , perpendicular = 30 m and base we can find.

thus,

$\tan 45^{\circ}=\frac{30}{EA}$

We know $\tan 45^{\circ}=1$

thus, EA = 30 m

Consider the Δ AEB,

Using trigonometric ratio,

$\cos\theta=\frac{base}{hypotenuse}$

Here $\theta=60^{\circ}$ , hypotenuse = 80 m and base we can find.

thus, $\cos 60^{\circ}=\frac{base}{80}$

We know, $\cos 60^{\circ}=\frac{1}{2}$

thus, Base = 40 m

AD = 40 m

Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m

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3 years ago

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Step-by-step explanation:

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2 years ago