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3 years ago

Share 126 in the ratio 2:5

Mathematics

1 answer:

maks197457 [2]3 years ago

4 0

Answer:

first share 2x=36

Second share=5x=90

Step-by-step explanation:

Ratio 2:5

Share=126

Let first share=2x

Second share=5x

So 2x+5x=126

7x=126

X=126/7

X=18

So first share 2x=36

Second share=5x=90

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The points (-10, 0) and (-5, 3) fall on a particular line. What is it’s equation in slope-intercept form?

yaroslaw [1]

Answer:

y = 3/5x + 6

Step-by-step explanation:

When given two points, it is convenient to start with the 2-point form of the equation of a line, then rearrange it to the form needed for the problem. For points (x1, y1) and (x2, y2), the equation is ...

y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

Filling in the given point coordinates, this is ...

y = (3 -0)/(-5 -(-10))·(x -(-10)) + 0

y = 3/5(x +10)

y = (3/5)x + 6

5 0

3 years ago

Please help!!! Brainliest?

Elena L [17]

I think the answer is b i hope this helps

7 0

3 years ago

Find m∠STU and m∠TUA

PIT_PIT [208]

Answers:

angle STU = 65 degrees
angle TUA = 123 degrees

=========================================================

Explanation:

Let's find the expression for angle TUS in terms of x

Angle TUA has the expression 11x+2. It will add to angle TUS to get 180 degrees

(angle TUS) + (angle TUA) = 180

angle TUS = 180 - (angle TUA)

angle TUS = 180 - (11x + 2)

angle TUS = 180 - 11x - 2

angle TUS = -11x + 178

Now focus on the interior angles of triangle TUS. We have these three angles

T = 5x+10
U = -11x+178
S = 58

For any triangle, the interior angles always add to 180, so,

T+U+S = 180

(5x+10) + (-11x+178) + (58) = 180

(5x-11x) + (10+178+58) = 180

-6x + 246 = 180

-6x = 180-246

-6x = -66

x = -66/(-6)

x = 11

Use this x value to find the angle measures we're after:

angle STU = 5x+10 = 5*11+10 = 55+10 = 65 degrees
angle TUA = 11x+2 = 11*11+2 = 121+2 = 123 degrees

--------------------------

As an alternative route, you can apply the remote interior angle theorem. This says that adding two interior angles leads to the exterior angle that isn't adjacent to either one.

In this case, we would say

(angle STU) + (angle TSU) = angle TUA

that leads to the equation

(5x+10) + (58) = 11x+2

Solving this should lead to x = 11 to generate the angles mentioned earlier.

6 0

3 years ago

A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag fo

defon

Answer:

a) The expected value is given by:

$E(X) =\frac{a+b}{2}= \frac{10+12}{2}= 11$

The variance is given by:

$Var(X) = \frac{(b-a)^2}{12}= \frac{(12-10)^2}{12}= 0.3333$

And the standard deviation is just the square root of the variance and we got:

$Sd(x) = \sqrt{0.3333}= 0.5774$

b) $P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a}, a \leq x \leq b$

And using this function we got:

$P(X$

c) $P(X>10.5)$

And using the complement rule and the cumulative distribution function we got:

$P(X>10.5)= 1-P(X$

Step-by-step explanation:

For this case we define the random variable X=quantity put in each bag , and we know that the distribution for X is given by:

$X \sim Unif (a= 10, b =12)$

Part a

The expected value is given by:

$E(X) =\frac{a+b}{2}= \frac{10+12}{2}= 11$

The variance is given by:

$Var(X) = \frac{(b-a)^2}{12}= \frac{(12-10)^2}{12}= 0.3333$

And the standard deviation is just the square root of the variance and we got:

$Sd(x) = \sqrt{0.3333}= 0.5774$

Part b

For this case we want this probability:

$P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a}, a \leq x \leq b$

And using this function we got:

$P(X$

Part c

For this case we want this probability:

$P(X>10.5)$

And using the complement rule and the cumulative distribution function we got:

$P(X>10.5)= 1-P(X$

3 0

3 years ago

Write the standard form of the line that passes through (-1,-3) and (2,1).

kobusy [5.1K]

Answer:

Step-by-step explanation:

$\mathrm{Line\:passing\:through\:}\left(-1,\:-3\right)\mathrm{,\:}\left(2,\:1\right)\\\\\mathrm{Find\:the\:line\:}\\\mathbf{y=mx+b}\mathrm{\:passing\:through\:}\left(-1,\:-3\right)\mathrm{,\:}\left(2,\:1\right)\\\\\mathrm{Compute\:the\:slope\:}\left(-1,\:-3\right),\:\left(2,\:1\right):\quad \\m=\frac{4}{3}\\\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-1,\:-3\right),\:\left(x_2,\:y_2\right)\\\left\\$

$\\m=\frac{1-\left(-3\right)}{2-\left(-1\right)}\\\\Refine\\\\m=\frac{4}{3}\\\\\mathrm{Compute\:the\:}y\mathrm{\:intercept}:\quad b=-\frac{5}{3}\\\\y=\frac{4}{3}x-\frac{5}{3}\\$

Convert equation to standard form

$y - \frac{4}{3} x + \frac{5}{3} = 0\\\\Multiply \:through\: by\: 3;\\\\3\times (y - \frac{4}{3} x + \frac{5}{3} )=0\\\\3y -4x+5 = 0\\Arrange\:n\:form\:of \:;\\Ax +By = C\\\\-4x +3y =-5$

5 0

4 years ago