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3 years ago

The width of a rectangular frame is 6 in. shorter than its length. The area of the frame is 216 in?

Mathematics

1 answer:

Veronika [31]3 years ago

3 0

Answer:

18 in

Step-by-step explanation:

len = y

width= y - 6

the area of rectangle is len x width

(Y) x (Y-6) = 216

Y^2 - 6Y = 216, Y^2 - 6y -216 = 0

y = (36 /2) or (-24 /2)

len couldn't be negative so 18

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On a coordinate plane, triangle A has points (3, 3), (6, 3), (6, 9). Triangle A prime has points (negative 2, negative 1), (nega

IrinaVladis [17]

Answer:

A. dilation by a scale factor of 1/3

B. translation to the left 4 units

C. translation down 3 units

Step-by-step explanation:

On a coordinate plane,

triangle A has points (3, 3), (6, 3), (6, 9).

Triangle A prime has points (negative 2, negative 1), (negative 2, negative 2), (negative 3, negative 2).

Determine all the transformations needed to transform the pre-image, A, to the image, A'.

Select all that apply, given

A=(3,3),(6,3),(6,9)

A'=(-2,-1),(-2,-2),(-3,-2) possible typo, should read

A'=(-2,0),(-2,-2),(-3,-2)

dilation by a scale factor of 1/2

dilation by a scale factor of 1/3

reflection over the x-axis

translation to the left 4 units

translation down 3 units

If the typo correction is valid, then the transformatitons are:

A. dilation by a scale factor of 1/3

B. translation to the left 4 units

C. translation down 3 units

6 0

4 years ago

Read 2 more answers

Write the following as an inequality.

Dimas [21]

Answer:
-9 < w ≤ 5

Explanation:
W is bigger than -9 so the symbol has the bigger end towards the W.
W is also less than or equal to 5 so the smaller end of the sign is towards the W.

7 0

3 years ago

A hyperbola centered at the origin has verticies at (add or subtract square root of 61,0 and foci at (add or subtract square roo

deff fn [24]

Answer:

$\frac{x^2}{61}-\frac{y^2}{37} =1$

Step-by-step explanation:

The standard equation of a hyperbola is given by:

$\frac{(x-h)^2}{a^2} -\frac{(y-k)^2}{b^2} =1$

where (h, k) is the center, the vertex is at (h ± a, k), the foci is at (h ± c, k) and c² = a² + b²

Since the hyperbola is centered at the origin, hence (h, k) = (0, 0)

The vertices is (h ± a, k) = (±√61, 0). Therefore a = √61

The foci is (h ± c, k) = (±√98, 0). Therefore c = √98

Hence:

c² = a² + b²

(√98)² = (√61)² + b²

98 = 61 + b²

b² = 37

b = √37

Hence the equation of the hyperbola is:

$\frac{x^2}{61}-\frac{y^2}{37} =1$

6 0

3 years ago

James works in a flower shop. He will put 60 tulips in vases for a wedding. He must use the same number of tulips in each vase.

Lina20 [59]

Answer: a. 1, 3, 5, 15

Step-by-step explanation:

If he needs to put an equal number of tulips in each vase he uses, the number of vases will have to be multiples of 15.

The multiples of 15 are;

1, 3, 5, and 15.

James can therefore put;

1 tulip in 15 vases
3 tulips in 5 vases
5 tulips in 3 vases
15 tulips in 1 vase

5 0

3 years ago

The intercepts of the line Y=-2x-21

alexgriva [62]

Answer:

-21

Step-by-step explanation:

GIven data

We are given the equation of a line as

Y=-2x-21

let us compare this with the general equation of a line

y=mx+c

from the comparison, we can see that the intercept is -21

Therefore, the intercept is -21

3 0

3 years ago