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3 years ago

Finding the proportion using the figure below

Mathematics

1 answer:

Serjik [45]3 years ago

5 0

The ratio of the figure is $\frac{a}{j} =\frac{c}{k} .$

Step-by-step explanation:

Step 1:

The given figure of two triangles. A smaller triangle and a larger triangle. The smaller triangle has sides measuring a and c. The second and larger triangle has sides measuring (a + b) and (c + d).

From the given diagram, we have

$j = a+b$ and $k=c+d.$

So the second larger triangle has sides measuring j and k.

Step 2:

If a ratio is given, both sides of the ratio must have the corresponding side lengths of the given triangles.

On the left side of the ratio, we have the terms a and j, which are the side lengths of the smaller and larger triangles respectively.

Similarly, the right side has a ratio of c and an unknown term. The term c is the length of the smaller triangle whereas k is the length of the larger triangle.

So the ratio of the figure is $\frac{a}{j} =\frac{c}{k} .$

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3 years ago

A flagpole casts a shadow that is 85 feet long. Paul is 6 feet tall, and while standing next to the flagpole, casts a shadow tha

hammer [34]

Answer:

51m

Step-by-step explanation:

-Paul is 6ft, and has a 10ft shadow. The pole has a 85ft shadow:

-Using ratios:

$\frac{Height\ of \ object}{Height\ of \ shadow}$

Let h be the height of the flagpole:

$=>\frac{6}{10}=\frac{h}{85}\\\\h=\frac{6\times 85}{10}\\\\h=51$

Hence, the height of the pole is 51m

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3 years ago

Graph f(x)=2^x+1 and g(x)=−x+4 on the same coordinate plane.

12345 [234]

Given f(x)= 2^x +1

g(x)= -x +4

We have to find the value of x which satisfy the condetion : f(x)= g(x)

Solution : let us place expression given for f(x) and g(x) equal to each other

This gives us : 2^x + 1 = -x+ 4

Let us bring all x terms on left side only

we add x on both sides this makes : 2^x +1 +x = -x+ 4 +x

on the right side -x and +x becomes a "0"

we get : 2^x + 1 + x = 4

* let us nopw bring all the numeric terms on left side only

subtract 1 from both sides : 2^x + 1 + x - 1 = 4- 1

on the left side +1 and -1 becomes a "0"

on the rigth side 4-1 becomes a "3"

equation look like : 2^x + x = 3

We can see the right side is an odd number

on the left side there is sum of two terms one of them is 2^x which is an even number always .

we know that sum of an even number with an even number result out an even number

but we want a result as an odd number (3)

this suggest that x should be an odd number .

Also the sum of 2^x and x is 3 so 2^x should be smaller than 3

the smallest value ( x being an integer )

2^x can have is : 2^1= 2 which is for x=1

let us check plugging x= 1 . 2^1 + 1 = 3 which is TRUE

Hence answer is x= 1

8 0

3 years ago

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