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1 year ago

Ava bought 7.73 pounds of fruit for a class party. the class ate 3.59 pounds of the fruit. how much fruit is left?

1 answer:

6 0

Ava bought $7.73$ pounds of fruit for a class party , class ate $3.59$ pounds fruits then $4.14$ pounds fruit left after party.

How can we find how much fruit is left after party ?

Ava bought $=7.73$ pounds fruit

ate by class $=3.59$ pounds fruit

fruit left after party $= total fruit -fruit ate by class$

$= 7.73-3.59\\=4.14$

So $4.14$ pound fruit is left .

Learn more about the fruit left here :

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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]

ANSWER:

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

SOLUTION:

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

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2 years ago

Which set is closed under the operation multiplication?

oee [108]

I have another set of choices here:

A. {0.5, 1, 2}

B. {1, 2, 4}

C. {1, 2, 3, 4, 5}

D. {0}

If you multiply two numbers from a closed set the answer is in the set.
So A is not closed because 2 x 2 = 4 which isn't in the set. Only 0.5, 1, and 2 are in set A. 

Try multiplying the largest numbers in sets B, C, and D by themselves. You will soon discover the closed set.

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2 years ago

Evaluate (1/3)(m) - 1 - (1/2)(n) m=21 and n=12

Aneli [31]

Answer:

the answer is 0

Step-by-step explanation:

(1/3)(21)-1-(1/2)(12)

The first thing you do is that you multiply 1/3 times 21/1 which equal 7 then you multiply 1/2 times 12/1 which that equal 6 then you solve 7-1-6 and you get 6-6 which equal 0 i hope this help you and i hope you have a goood day.

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2 years ago

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musickatia [10]

Answer:

Step-by-step explanation:

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2 years ago

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If Happie had ridden exactly 100 feet in 25

Strike441 [17]

Answer:

The speed rate is 100 feet per 25 seconds, or 20 feet every 5 seconds, (100 / 5 = 20)

Every minute is 60 seconds long, this means that to find out how fast she would roll in one minute we just need to do 60 / 5 = 12 and then do 12 x 20

12 x 20

10 x 20 = 200 feet per second

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200 + 40 = 240 feet per second

Happie would roll 240 feet in a minute at the speed of 100 feet per 25 seconds

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