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Find two numbers if their sum is 91 and the ratio is 6:7.

sammy [17]

Answer:

42:49

Step-by-step explanation:

6x + 7x = 91

13x = 91

x = 7

6 x 7 = 42

7 x 7 = 49

then 42:49

5 0

3 years ago

Read 2 more answers

Given the diagram below with line DE║ line AC. Find BC.

Karolina [17]

Answer:

13.5

Step-by-step explanation:

In triangle ABC, DE || AC

Therefore by basic proportionality theorem:

$\frac{BD}{DA} = \frac {BE}{EC} \\\\\therefore \frac{4}{8} = \frac {BE}{9} \\\\\therefore \frac{1}{2} = \frac {BE}{9} \\\\\therefore BE = \frac{9}{2} \\\\\therefore BE = 4.5\\\because BC = BE + EC \\\therefore BC = 4.5 + 9\\\huge \red {\boxed {\therefore BC = 13.5}} \\$

8 0

3 years ago

Can someone help me with these

Trava [24]

Short answer
For 6: 72 ft^2
For 7: 650 m^2

Six
The base is a square. It's measurement is s = 4
Base = 4^2
Base = 16 ft^2

One triangle
A = 1/2 * b * h
A = 1/2 * 4 * 7
A = 14 tt^2

Four triangles
A = 4 * 14
A = 56 ft^2

Total Area = 56 + 16 = 72 ft^2
Answer 72 square feet

Seven
Triangles
Area of 1 triangle = 1/2 * 10 * 13
Area of 1 triangle = 65

Area of 6 triangles
Area of 6 triangles = 6 * area of 1 triangle
Area of 6 triangles = 390

Base
As near as I can tell, the base is a hexagon. It's using a rather out of the way method of drawing it. I will assume it is a regular hexagon. The area of a regular hexagon is 3 sqrt(3)/2 * S^2 where s is the side of the hexagon.

Area = 3sqrt(3)/2 s^2
s = 10
Area = 3sqrt(3)/2 10^2
Area = 5.1962 * 100 /2
Area = 259.81

Total area
Total area = area of the base + area of the triangles
Total area = 259.81 + 390
Total area (rounded ) = 650

Answer C <<<< answer

I'll do one more in this batch and then you'll need to repost again.

Eight

If you draw two diagonals on the base of the figure, the intersection point will meet the base of the height. Read that a couple of times.
Join the intersection to the midpoint of the length of the square bottom. You should get 3.5

x is found by using the pythagorean theorem.
h = 6
s = 3.5
x = ????

x^2 = 6^2 + 3.5^2
x^2 = 36 + 12.25
x^2 = 48.25
x = sqrt(48.25)
x = 6.95

C <<<< answer

8 0

3 years ago

Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations: