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3 years ago

Anyone know? pls help!

Mathematics

1 answer:

Effectus [21]3 years ago

4 0

Answer:

Step-by-step explanation:

The angles (6x - 7) and (4x + 7) are the vertical angles.

The vertical angles are congruent, therefore have the same measure.

We have equation:

6x - 7 = 4x + 7 subtract 4x from both sides

6x - 2x - 7 = 4x - 2x + 7

2x - 7 = 7 add 7 to both sides

2x - 7 + 7 = 7 + 7

2x = 14 divide both sides by 2

2x : 2 = 14 : 2

x = 7

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A sequence is defined by the recursive function f(n + 1) = f(n). If f(3) = 9 , what is f(1) ?

Andre45 [30]

Assuming that f(n+1) = f(n) is the full recursive definition, and that there are no typos, then this means that the nth term is equal to the (n+1)th term for any n where n is a positive whole number.

So
f(1) = f(2)
f(2) = f(3)
f(3) = 9

By the transitive property, f(1) = f(3) = 9. Therefore the answer is 9.

4 0

4 years ago

Mr. Jackson traveled to a city 170 miles from his home to attend a meeting. Due to car trouble, his average speed returning was

Umnica [9.8K]

Answer: the average speed at which he traveled to the city is 52.9 mph

Step-by-step explanation:

Let x represent the average speed at which he traveled to the city. Due to car trouble, his average speed returning was 8mph less than his speed going. It means that the speed at which he returned is (x - 8) mph.

Time = distance/speed

Assuming the distance travelled to and from the city is the same(170 miles), then

Time spent in travelling to the city is

170/x

Time spent in travelling back from the city is

170/(x - 8)

If the total time for the round trip was 7 hours, it means that

170/x + 170/(x - 8) = 7

Multiplying both sides of the equation by x(x - 8), it becomes

170(x - 8) + 170x = 7x(x - 8)

170x - 1360 + 170x = 7x² - 56x

7x² - 56x - 170x - 170x + 1360 = 0

7x² - 396x + 1360 = 0

Applying the general formula for solving quadratic equations which is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 7

b = - 396

c = 1360

Therefore,

x = [- - 396 ± √(- 396² - 4 × 7 × 1360)]/2 × 7

x = [396 ± √(156816 - 38080)]/14

x = [396 ± √118736]/14

x = (396 + 344.58)/14 or x = (396 - 344.58)/14

x = 52.9 or 3.7

Checking both values of x,

For x = 52.9

170/52.9 + 170/(52.9 - 8) = 7

= 3.2 + 3.8 = 7

Therefore, x = 52.9 mph

4 0

3 years ago

What could you use to show that opposite sides are congruent? Which quadrilaterals does it work for?

slega [8]

Square
as the sides are all equal

4 0

3 years ago

A rectangle has vertices E(4,8), F(2,8), G(2,-2) and H(-4,-2). The rectangle is dilated with the origin as the center of dilatio

Leona [35]

Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).

Given:

The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).

The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).

To find:

The algebraic representation that represents this dilation.

Solution:

If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:

$(x,y)\to (kx,ky)$ ...(i)

Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,

$G(2,-2)\to G'(k(2),k(-2))$

$G(2,-2)\to G'(2k,-2k)$

The image of G after dilation is G'(5,-5). So,

$(2k,-2k)=(5,-5)$

On comparing both sides, we get

$2k=5$

$k=\dfrac{5}{2}$

So, the scale factor is $k=\dfrac{5}{2}$ .

Substituting $k=\dfrac{5}{2}$ in (i), we get

$(x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)$

Therefore, the required algebraic representation to represents this dilation is $(x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)$ .

3 0

3 years ago

9x+5=8x+15 solve for x

timurjin [86]

9x+5=8x+15
9x-8x=15-5
X=10

5 0

4 years ago

Read 2 more answers