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3 years ago

The points (0,2) and (1,5) are on a line which of these points is on the same line

Mathematics

1 answer:

katrin [286]3 years ago

6 0

Answer:

y = 3x + 2

Step-by-step explanation:

The equation for two points on a line is generated from the straight line equation y = mx + b ---------------- eqn (i)

where m, the slope = (y2 - y1) / (x2 - x1)

therefore for (0,2) and (1,5) m = (5 - 2)/(1 - 0) = 3

This implies that eqn (i) can be rewritten as:

y = 3x + b ------------------- eqn (ii)

pickintg the point (0,2) and substituting into eqn (ii)

2 = 3(0) + b

this implies that b = 2

for confirmation with (1,5)

5 = 3(1) + b

b = 5 - 3 = 2

hence m = 3, b = 2

the equation is y = 3x + 2

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In the figure below what is the value of x?

vazorg [7]

Answer:

The value of x is 106

Step-by-step explanation:

Let us solve the question

In the given figure

∵ The triangle in the given figure has two sides equal

→ That means the triangle is an isosceles triangle

∴ The triangle is isosceles

∵ In the isosceles triangle, the base angles are equal in measures

∵ The measure of one base angle is 37°

∴ The measure of other base angle is 37°

→ The sum of the measures of the interior angles of a Δ is 180°

∵ 37° + 37° + x = 180°

→ Add the like terms

∴ 74° + x = 180°

→ Subtract 74 from both sides

∵ 74 - 74 + x = 180 - 74

∴ x = 106

∴ The value of x is 106

7 0

2 years ago

In the diagram, ∠4 and ∠5 are what type of angles?

igomit [66]

Answer:

B. Alternate interior angles

Step-by-step explanation:

<4 and <5 are inside the parallel lines on alternate sides of the third line.

6 0

3 years ago

Point C is on line segment \overline{BD} BD . Given CD=x,CD=x, BC=5x-5,BC=5x−5, and BD=2x+7,BD=2x+7, determine the numerical len

NARA [144]

Answer:

$CD = 3$

Step-by-step explanation:

Given

$CD = x$

$BC = 5x - 5$

$BD = 2x + 7$

Required

Determine CD

Since, C is a point on BD, the relationship between the given parameters is;

$BD = BC + CD$

Substitute the values of BD, BC and CD

$2x + 7 = 5x - 5 + x$

Collect Like Terms

$2x - 5x - x = -5 - 7$

$-4x = -12$

Divide both sides by -4

$\frac{-4x}{-4} = \frac{-12}{-4}$

$x = 3$

To determine the length of CD;

Substitute 3 for x in $CD = x$

Hence;

$CD = 3$

3 0

3 years ago

In triangle ABC, a = 4, b = 6, and cos C = − 1/4. What is the length of side c?

shusha [124]

The length of side c would be 8.

Step-by-step explanation:

Given that,

a = 4

b = 6

cosC = -1/4

If we are given two sides and angle, the law of Cosines can be used to find the third side:

$c^{2} = a^{2} + b^{2} - 2ab (cos(c))$

By inserting the values in the formula, we get

$c^{2} = 4^{2} + 6^{2} - 2.4.6 (-\frac{1}{4} )$

$c^{2} = 16 + 36 + 12$

$c^{2} = 64$

$\sqrt{c^{2} } = \sqrt{64}$

c = 8.

Therefore, the length of side c would be 8.

7 0

3 years ago

The perimeter of △CDE is 55 cm. A rhombus DMFN is inscribed in this triangle so that vertices M, F, and N lie on the sides CD ,

ivanzaharov [21]

Answer:

CD = 14 cm; DE = 21 cm

Step-by-step explanation:

The perimeter is the sum of side lengths (in centimeters), so ...

CD + DE + CF + EF = 55

CD + DE + 8 + 12 = 55 . . . . . . . substittute for CF and EF

CD + DE = 35 . . . . . . . . . . . . . . subtract 20

___

The segment DF is a diagonal of the rhombus, so bisects angle D. That angle bisector divides ΔCDE into segments that are proportional. That is, ...

CD/DE = CF/EF = 8/12 = 2/3

___

So, we have two segments whose sum is 35 (cm) and whose ratio is 2 : 3. The total of "ratio units is 2+3=5, so each must stand for a length unit of 35/5 = 7 (cm). The sides are ...

CD = 2·7 cm = 14 cm

DE = 3·7 cm = 21 cm

<em>Check</em>

CD + DE = (14 +21) cm = 35 cm . . . . . matches requirements

7 0

3 years ago