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3 years ago

In the box, type the number that will correctly complete the sentence.

Mathematics

1 answer:

grandymaker [24]3 years ago

5 0

Answer:

Step-by-step explanation:

The product of a number n and it's inverse $\frac{1}{n}$ is

n × $\frac{1}{n}$ = 1

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ABCD is a rectangle. Its diagonals meet at O. Find the value of x if BO = 3x + 4 andOC = x + 8 .Also find the length of its diag

scoundrel [369]

Step-by-step explanation:

the lengths OB, OC & BC together forms a isosceles triangle.

therefore,

OB=OC

3x+4=x+8

2x=4

x=2.

OB = 3x+4= 3.2+4=10cm.

OC= x+8= 2+8=10cm.

therefore, the diagonals are : 20cm each.

hope this helps you.

3 0

2 years ago

How many pairs of consecutive natural numbers have a product of less than 40000? I am in 5th grade. This is supposed to be easy

Ugo [173]

Answer:

There are 199 pairs of consecutive natural numbers whose product is less than 40000.

Step-by-step explanation:

We notice that such statement can be translated into this inequation:

$n \cdot (n+1) < 40000$

Now we solve this inequation to the highest value of $n$ that satisfy the inequation:

$n^{2}+n < 40000$

$n^{2}+n -40000$

The Quadratic Formula shows that roots are:

$n_{1,2} = \frac{-1\pm\sqrt{1^{2}-4\cdot (1)\cdot (-40000)}}{2\cdot (1)}$

$n_{1,2} = -\frac{1}{2}\pm \frac{1}{2} \cdot \sqrt{160001}$

$n_{1} = -\frac{1}{2}+\frac{1}{2}\cdot \sqrt{160001}$

$n_{1} \approx 199.501$

$n_{2} = -\frac{1}{2}-\frac{1}{2}\cdot \sqrt{160001}$

$n_{2} \approx -200.501$

Only the first root is valid source to determine the highest possible value of $n$ , which is $n_{max} = 199$ . Each natural number represents an element itself and each pair represents an element as a function of the lowest consecutive natural number. Hence, there are 199 pairs of consecutive natural numbers whose product is less than 40000.

6 0

2 years ago

Match the vocabulary word with the correct definition.

ki77a [65]

Answer:

equilateral triangle is a triangle with all three sides equal

isosceles triangle is a triangle with two sides of the same length

scalene triangle is a triangle in which no 2 sides have equal lengths

equiangular triangle is a triangle in which all angles are equal

triangle is the union of three segments determined by 3 noncolinear points

3 0

3 years ago

Read 2 more answers

Which probability is correct?<br> P(AB) = 1/2<br> P(BA) = 7/25<br> P(AC) = 6/23<br> P(CA) = 13/17

BartSMP [9]

I believe it is 1/2

5 0

3 years ago

Read 2 more answers

What is the inclination of a line through the points(5,14) and (9,18)

tia_tia [17]

Answer:

The inclination of the through the points (5, 14) and (9, 18) is 45°

Step-by-step explanation:

The given point has coordinates (5, 14) and (9, 18)

To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2, having coordinates (x₂, y₂), we have to look for the slope as follows;

The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate

$m = \dfrac{y_2 - y_1}{x_2-x_1}$

Where:

y₁ = The y-coordinate of point 1 = 14

x₁ = The x-coordinate of point 1 = 5

y₂ = The y-coordinate of point 2 = 18

x₂ = The x-coordinate of point 2 = 9

Substituting, we have;

$m = \dfrac{18 - 14}{9-5} = \dfrac{4}{4} = 1$

The inclination of the line is the angle the line makes with x-axis

Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;

$tan^{-1}m = tan^{-1} \left (\dfrac{y_2 - y_1}{x_2-x_1} \right) = \theta$

given that m = 1, we have;

tan⁻¹(m) = θ = tan⁻¹(1) = 45°.

8 0

3 years ago