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2 years ago

In a right-angled triangle, the hypotenuse is 113 and a leg is 112.

Mathematics

1 answer:

melomori [17]2 years ago

7 0

Answer: 15

Step-by-step explanation: Use the formula: $a^{2}+b^{2}=c^{2}$

Remember $c^{2}$ should always be the hypotenuse or the longest side.

$112^{2}+b^{2}=113^{2}$ ---> evaluate the exponents

$12544+b^{2}=12769$ ----> subtract 12544 to the other side

$b^{2}=225$ ---> take the square root of both sides

$b=15$

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What is 40% equivalent to?

olga_2 [115]

Answer:0.4

Step-by-step explanation:

3 0

3 years ago

Which inequality is represented by the graph? y≥35x−1.5 y≤35x−1.5 y<35x−1.5 y>35x−1.5

Setler79 [48]

Answer:

y > 0.6x - 1.5

Step-by-step Explanation:

We need two points, to get to the equation of the graph.

Since we've got the following equation for two points (x1, y1), (x2, y2):-

$\boxed{ \mathsf{ \red{y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1}) }}}$

okay soo

I found two points that lie on this graph, not on the shaded region but yeah the dotted line which defines the graph.

one point is <u>(0, -1.5)</u> which lies on the y axis(the point where the dotted line touches the y axis)

other point is <u>(2.5, 0)</u> and this lies on the x axis

placing these points in the place of (x1, y1) and (x2, y2) in the above mentioned equation

$\mathsf{\implies y - ( - 1.5) = \frac{0 -( - 1.5)}{2.5 -0 } (x -0 )}$

you can take any one as (x1, y1) or (x2, y2).

so upon solving the above equation we get

$\mathsf{\implies (y + 1.5) = \frac{0 + 1.5}{2.5 } (x )}$

$\mathsf{\implies y + 1.5 = \frac{ 1.5}{2.5 } x }$

$\mathsf{\implies y + 1.5 = \frac{ \cancel{1.5}\:\:{}^3}{\cancel{2.5}\:\:{}^5 } x }$

$\mathsf{\implies y + 1.5 = \frac{ 3}{5 } x }$

multiplying both sides by 5

$\mathsf{5y + 7.5 = 3x}$

okay so this is the required equation of the dotted line

now we'll find the inequality

for this check whether the origin (0,0) lies under the shaded region or not

in this case it does

replacing x and y with 0

$\mathsf{\implies5(0) + 7.5 = 3(0)}$

$\mathsf{\implies0 + 7.5 = 0}$

this is absurd, 7.5 is not equal to 0 so we're gonna replace that equals sign with that of inequality

7.5 is greater than 0! so,

$\mathsf{\implies7.5 > 0}$

this goes for the whole equation, since we didnt swap any thing from left to right side of the equation or vice versa we can use this sign, to obtain the required inequality

$\mathsf{5y + 7.5 > 3x}$

dividing this inequality by 5, since there's no co-efficient in front of y in the given answers

we get

y + 1.5 > 0.6x

taking 1.5 to the RHS

that is the last option

5 0

2 years ago

A rectangle has 3 square feet and width 1/2 foot. What is the length of the rectangle

Yakvenalex [24]

Answer:

We Know, Area = Length * Width

Here, A = 3

W = 1/2

Substitute it into the expression,

3 = L * 1/2

L = 3/ 1/2

L = 3/2 ft²

So, the length of the rectangle would be 3/2 ft²

<u>Hope this helps! :)</u>

<u></u>

8 0

3 years ago

Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?

sveticcg [70]

Answer:

y = 60 when x = 12

Step-by-step explanation:

Direct variation is

y = kx

15 = k3

Divide by 3

15/3 = k

5 =k

y = 5x

Let x = 12

y = 5*12

y = 60

5 0

2 years ago

How to find the maximum value of a quadratic function?

Iteru [2.4K]

Suppose
$y = a {x}^{2} + bx + c$
if a>0 it has min if 0>a it has max
$min \: y = (4ac - {b}^{2} ) \div 4a$

8 0

2 years ago