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3 years ago

If the first term in an arithmetic sequence is –3 and the tenth term is 15, what is the common difference?

Mathematics

1 answer:

Triss [41]3 years ago

6 0

Given that the First term of the Arithmetic sequence = -3

⇒ a = -3

We know that nth term of a Arithmetic sequence is : Tn = a + (n - 1)d

where a is the first term and d is the common difference

Given that 10th term is 15

⇒ T₁₀ = -3 + (10 - 1)d

⇒ -3 + (10 - 1)d = 15

⇒ 9d = 18

⇒ d = 2

⇒ Common difference of given Arithmetic Sequence is 2

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Find a point-slope form for the line that satisfies the stated conditions.

Yakvenalex [24]

Answer:

y=6x+41

Step-by-step explanation:

y-5=6(x+6)

y=6x+41

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3 years ago

Do the diagonals of a rhombus bisect and are congruent?

umka2103 [35]

Answer:

All the properties of a rhombus apply (the ones that matter here are parallel sides, diagonals are perpendicular bisectors of each other, and diagonals bisect the angles). All the properties of a rectangle apply (the only one that matters here is diagonals are congruent). All sides are congruent by definition.

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3 years ago

3) x2+ y2 - x + 3y - 42 = 0<br> X+y=4

REY [17]

The solution is $(-1,5)$ and $(7,-3)$

Step-by-step explanation:

The expression is $x^{2} +y^{2} -x+3y-42=0$ and $x+y=4$

Using substitution method we can solve the expression.

Let us substitute $x=4-y$ in $x^{2} +y^{2} -x+3y-42=0$

$(4-y)^{2} +y^{2} -(4-y)+3y-42=0$

Expanding and simplifying the expression, we get,

$\begin{array}{r}{16-8 y+y^{2}+y^{2}-4+y+3 y-42=0} \\{2 y^{2}-4 y-30=0}\end{array}$

Let us use the quadratic equation formula to solve this equation,

$\begin{aligned}y &=\frac{4 \pm \sqrt{16-4(2)(-30)}}{2(2)} \\&=\frac{4 \pm \sqrt{16+240}}{4} \\&=\frac{4 \pm 16}{4} \\y &=1 \pm 4\end{aligned}$

Thus, $y=5$ and $y=-3$

Substituting y-values in the equation $x+y=4$ , we get the value of x.

For $y=5$ ⇒ $x=4-5=-1$

For $y=-3$ ⇒ $x=4+3=7$

Thus, the solution set is $(-1,5)$ and $(7,-3)$

7 0

4 years ago

. Fill in the blank with the most accurate definition.

Zigmanuir [339]

Two distinct points are $\boxed{{\text{collinear}}}.$ Option (C) is correct.

Further Explanation:

Given:

The options are as follows,

(A). Coplanar.

(B). Equidistant.

(C). Collinear.

(D). Complementary.

Explanation:

A point is a location on the graph or at any surface.

A line is the distance between the two points that extends to infinite in both directions.

The points that are on the same plane is known as coplanar points.

Ifdistance to the points from a particular point is same then the points are equidistant.

The points that are on the same line is known as collinear points.

Two distinct points are $\boxed{{\text{collinear}}}$ . Option (C) is correct.

Option (A) is not correct.

Option (B) is not correct.

Option (C) is correct.

Option (D) is not correct.

Learn more:

1Learn more about product of binomial and trinomial brainly.com/question/1394854.
Learn more about equation of circle brainly.com/question/1506955
Learn more about range and domain of the function brainly.com/question/3412497.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Line and Rays

Keywords: ray, line, definition, accurate, coplanar, equidistant, collinear, complementary, two, two distinct, points line segment, point, two dimension, plane, parallel lines, intersecting lines, location, distance, undefined, defined, pair, pair of lines, intersection point, never intersect.

7 0

3 years ago

Read 2 more answers

Can you guys please help me with on this cause I’m really confused?

Bezzdna [24]

A = l * w
3/2km^2 = 3/2km * w
3/2 = 3/2 * w
w = 1

To check:
3/2 =?= 3/2 * w
3/2 =?= 3/2 * 1
3/2 = 3/2

Hope this helps

3 0

3 years ago