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3 years ago

What is sum of two mixed numbers of 5.815+6.021

Mathematics

1 answer:

Julli [10]3 years ago

3 0

5.815+6.021= 11.836

good luck!

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Find the area of a triangle bounded by the y-axis, the line f(x)=9−4/7x, and the line perpendicular to f(x) that passes through

Setler79 [48]

<u>ANSWER: </u>

The area of the triangle bounded by the y-axis is $\frac{7938}{4225} \sqrt{65} \text { unit }^{2}$

<u>SOLUTION:</u>

Given, $f(x)=9-\frac{-4}{7} x$

Consider f(x) = y. Hence we get

$f(x)=9-\frac{-4}{7} x$ --- eqn 1

$y=9-\frac{4}{7} x$

On rewriting the terms we get

4x + 7y – 63 = 0

As the triangle is bounded by two perpendicular lines, it is an right angle triangle with y-axis as hypotenuse.

Area of right angle triangle = $\frac{1}{ab}$ where a, b are lengths of sides other than hypotenuse.

So, we need find length of f(x) and its perpendicular line.

First let us find perpendicular line equation.

Slope of f(x) = $\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-4}{7}$

So, slope of perpendicular line = $\frac{-1}{\text {slope of } f(x)}=\frac{7}{4}$

Perpendicular line is passing through origin(0,0).So by using point slope formula,

$y-y_{1}=m\left(x-x_{1}\right)$

Where m is the slope and $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$

$y-0=\frac{7}{4}(x-0)$

$y=\frac{7}{4} x$ --- eqn 2

4y = 7x

7x – 4y = 0

now, let us find the vertices of triangle, one of them is origin, second one is point of intersection of y-axis and f(x)

for points on y-axis x will be zero, to get y value, put x =0 int f(x)

0 + 7y – 63 = 0

7y = 63

y = 9

Hence, the point of intersection is (0, 9)

Third vertex is point of intersection of f(x) and its perpendicular line.

So, solve (1) and (2)

$\begin{array}{l}{9-\frac{4}{7} x=\frac{7}{4} x} \\\\ {9 \times 4-\frac{4 \times 4}{7} x=7 x} \\\\ {36 \times 7-16 x=7 \times 7 x} \\\\ {252-16 x=49 x} \\\\ {49 x+16 x=252} \\\\ {65 x=252} \\\\ {x=\frac{252}{65}}\end{array}$

Put x value in (2)

$\begin{array}{l}{y=\frac{7}{4} \times \frac{252}{65}} \\\\ {y=\frac{441}{65}}\end{array}$

So, the point of intersection is $\left(\frac{252}{65}, \frac{441}{65}\right)$

Length of f(x) is distance between $\left(\frac{252}{65}, \frac{441}{65}\right)$ and (0,9)

$\begin{aligned} \text { Length } &=\sqrt{\left(0-\frac{252}{65}\right)^{2}+\left(9-\frac{441}{65}\right)^{2}} \\ &=\sqrt{\left(\frac{252}{65}\right)^{2}+0} \\ &=\frac{252}{65} \end{aligned}$

Now, length of perpendicular of f(x) is distance between $\left(\frac{252}{65}, \frac{441}{65}\right) \text { and }(0,0)$

$\begin{aligned} \text { Length } &=\sqrt{\left(0-\frac{252}{65}\right)^{2}+\left(0-\frac{441}{65}\right)^{2}} \\ &=\sqrt{\left(\frac{252}{65}\right)^{2}+\left(\frac{441}{65}\right)^{2}} \\ &=\frac{\sqrt{(12 \times 21)^{2}+(21 \times 21)^{2}}}{65} \\ &=\frac{63}{65} \sqrt{65} \end{aligned}$

Now, area of right angle triangle = $\frac{1}{2} \times \frac{252}{65} \times \frac{63}{65} \sqrt{65}$

$=\frac{7938}{4225} \sqrt{65} \text { unit }^{2}$

Hence, the area of the triangle is $\frac{7938}{4225} \sqrt{65} \text { unit }^{2}$

8 0

3 years ago

A road sign has the shape of an equilateral triangle with a side length of 48 inches. What is the height of the sign? The road s

Ivenika [448]

The height of the equilateral triangle is 41. 6 inches. Option C

<h3>How to determine the height</h3>

The formula for finding the height of an equilateral triangle is given as;

h = (a√3)/2

we have a = 48 inches

Let's substitute the value

Height, h = $\frac{48\sqrt{3} }{2}$

Height = $\frac{48 * 1. 732}{2}$

Height = $\frac{83. 14}{2}$

Height = $41. 6$ Inches

Thus, the height of the equilateral triangle is 41. 6 inches. Option C

Learn more about equilateral triangles here:

brainly.com/question/1399707

#SPJ1

5 0

1 year ago

Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. Which triangle did Tim draw?

d1i1m1o1n [39]

Answer:

Isocoles (I can't spell)

Step-by-step explanation:

180-70=110. 110-40=70.

Two angles are 70

3 0

2 years ago

(Please help)Choose the correct answer and please explanation each (Brainliest)

Vesnalui [34]

Answer:

1. C

2. D

3. C

Explanation:

1. Girls = 12 plus twice the number of boys, so C. y = 12 + 2x.

2. You have to see which point has the second value being greater than the first value:

A) -1 > -2 is not true

B) 0 > 1 is not true

C) 2 > 3 is not true

D) 8 > 4 is true, so it's D

3. Add the two values and see if it's less than 5

A) -1-4 < 5 is true

B) 0 + 4 < 5 is true

C) 1 + 7 < 5 is not true, so this is the answer

D) 2 + 2 < 5 is true

3 0

2 years ago

What percent of 4 is 1?

Flauer [41]

Lets take 100 and divide it by 4 to get 25, this means that 1 first part of 100 is 25 these means that the porcentage of 1 in 4 is 25%

Hope this helps

8 0

3 years ago