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2 years ago

Find the 60th term of the arithmetic sequence -29, -49, -69, ...

Mathematics

1 answer:

WARRIOR [948]2 years ago

7 0

Answer:

-1209 is the answer

Step-by-step explanation:

Trust me, I took Algebra last year and did a similar problem.

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Write an equation of the line passing through the point (5, 8) that is parallel to the line 7x+5y=3

zepelin [54]

Answer:

y = (-7/5) x + 15

Step-by-step explanation:

Let's name the line whose formula we'll calculate as line A. The other line is line B.

Rewrite the equation of line B:

7x+5y=3

y = -7x/5 + 3/5

A parallel line has to have the same slope (-7/5). With that information in mind, we only need to calculate b (following the basic equation for a line, y=mx+b).

Line A passes through the point (5,8), so we can express the slope as:

m = $\frac{y_2-y_1}{x_2-x_1}=\frac{8-y_1}{5-0} =-\frac{7}{5}$

So we solve for y₁:

8-y₁ = -7

y₁ = 15

That is the value in the Y-axis line A crosses when x=0. In other words, it is b.

The equation is y = (-7/5) x + 15

6 0

3 years ago

Simplify the expression state any excluded values 2a^2-4a+2 --------------- 3a^2-3

chubhunter [2.5K]

Answer:

The simplified form is $\dfrac{2(x-1)}{3(x+1)}$ .

$x =1$ is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

$\dfrac{2a^2-4a+2}{3a^2-3}$

Let us simplify the numerator and denominator separately.

The numerator is given as $2a^2-4a+2$

2 is a common factor in all the three terms. So, we factor it out. This gives,

$=2(a^2-2a+1)$

Now, $a^2-2a+1=(a-1)(a-1)$

Therefore, the numerator becomes $2(a-1)(a-1)$

The denominator is given as: $3a^2-3$

Factoring out 3, we get

$3(a^2-1)$

Now, $a^2-1$ is of the form $a^2-b^2=(a-b)(a+b)$

So, $a^2-1=(a-1)(a+1)$

Therefore, the denominator becomes $3(a-1)(a+1)$

Now, the given expression is simplified to:

$\frac{2a^2-4a+2}{3a^2-3}=\frac{2(x-1)(x-1)}{3(x-1)(x+1)}$

There is $(x-1)$ in the numerator and denominator. We can cancel them only if $x\ne1$ as for $x=1$ , the given expression is undefined.

Now, cancelling the like terms considering $x\ne1$ , we get:

$\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}$

Therefore, the simplified form is $\dfrac{2(x-1)}{3(x+1)}$

The simplification is true only if $x\ne1$ . So, $x =1$ is the excluded value for the given expression.

8 0

4 years ago

Solve 6 - 2/3(x+5)=4x algebraically

Alexandra [31]

Answer:

4/7 =x

Step-by-step explanation:

6 - 2/3(x+5)=4x

Multiply each side by 3 to clear the fraction

3(6 - 2/3(x+5))=4x*3

Distribute

18 -2(x+5) =12x

Distribute the 2

18 -2x-10 = 12x

Combine like terms

8 -2x = 12x

Add 2x to each side

8-2x+2x =12x+2x

8 = 14x

Divide by 14 on each side

8/14 =14x/14

4/7 =x

4 0

3 years ago

PLEASE HELP! NO ONE HAS BEEN HELPING WITH MY QUESTIONS SO IT WOULD MEAN A LOT IF YOU DID!

kvv77 [185]

Answer:

80 m²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = $\frac{1}{2}$ h (a + b)

where h is the perpendicular height between bases and a, b are the bases

Here h = 8, a = 14 and b = 6, thus

A = $\frac{1}{2}$ × 8 × (14 + 6) = 4 × 20 = 80 m²

3 0

3 years ago

How many of each type ticket were sold

Anastasy [175]

I can't answer if I dont see anything

7 0

3 years ago