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3 years ago

Need help with a math question

Mathematics

2 answers:

OLEGan [10]3 years ago

8 0

Answer:

7.0711

= 7.1 (rounded to nearest tenth)

Step-by-step explanation:

see attached.

laila [671]3 years ago

8 0

For this case we have by definition, that the distance between two points is given by:

$d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}$

According to the given data, we have the following points: $(x_ {1}, y_ {1}) = (6, -5)\\(x_ {2}, y_ {2}) = (- 1, -4)$

Substituting the points in the formula we have:

$d = \sqrt {(- 1-6) ^ 2 + (- 4 - (- 5)) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (- 4 + 5) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (1) ^ 2}\\d = \sqrt {49 + 1}\\d = \sqrt {50}\\d = 7.0711$

Rounding off we have to:

$d = 7.1$

ANswer:

$d = 7.1$

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Step-by-step explanation:

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2 years ago

Find either of the values of x<br> 2x^2+3x-2=3

Serjik [45]

Answer:

x = 1 or x = -5/2

Step-by-step explanation:

Solve for x over the real numbers:

2 x^2 + 3 x - 2 = 3

Divide both sides by 2:

x^2 + (3 x)/2 - 1 = 3/2

Add 1 to both sides:

x^2 + (3 x)/2 = 5/2

Add 9/16 to both sides:

x^2 + (3 x)/2 + 9/16 = 49/16

Write the left hand side as a square:

(x + 3/4)^2 = 49/16

Take the square root of both sides:

x + 3/4 = 7/4 or x + 3/4 = -7/4

Subtract 3/4 from both sides:

x = 1 or x + 3/4 = -7/4

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8 0

3 years ago

A number when divided 6 is diminished by 40

wolverine [178]

Answer:

Let x be the number

given x/6=x-40

x=6(x-40)

x=6x-240

x-6x=-240

-5x=-240

x=-240/-5=48

4 0

3 years ago

What is the value of x?

Nikolay [14]

Answer: 7 centimeters

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,

$\frac{BC}{CD} = \frac{AC}{CE} 


$ (1)

Since $AC = 6, CD = 42, CE = 36, BC = x$ , we can substitute these values to equation (1). So, equation (1) becomes

$\frac{x}{42} = \frac{6}{36}$
$\frac{x}{42} = \frac{1}{6}$ (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters

8 0

3 years ago