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3 years ago

Rove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero.

Mathematics

2 answers:

liubo4ka [24]3 years ago

8 0

Answer:

$\frac{ad+bc}{bd}$

Step-by-step explanation:

$Greetings!$

$I'm~Isabelle~Williams~and~I~will~be~answering~your~question!$

$Let,\frac{a}{b} ~and ~\frac{c}{d}~be~two~rational~numbers, ~where~ b ~and~ d ~are~ not~ zero ~and~ a, ~b, ~c ~and \\~d ~are~ integers.$

$1.~Given:$

$\frac{a}{b} +\frac{c}{d}$

$2.~Now,~we~multiply~to~get~a~common~denominator:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}$

$3.~Then~simplify:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}=\frac{ad+bc}{bd}$

$4.~Since,b\neq 0,~d\neq 0,~then,~bd,~ad,~bc~and~ad+bc~are~integers~too.~So~the\\ fraction~will~be:$

$\frac{ad+bc}{bd}$

$Thus,~making~it~a~rational~number!$

$Hope~this~answer~helps!~and~have~an~amazing~day~ahead!$

$-Isabelle~Williams$

Brut [27]3 years ago

8 0

Answer:

ad + cb / bd

Step-by-step explanation:

The answer is ad plus cb over bd

(Took test)

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Find the value of −12 + 8 −(−9). Question 20 options: 5 −13 −5 13

larisa86 [58]

Answer:

-12 + 8 = -4

-4 - (-9) = -4 + 9 = 5

Step-by-step explanation:

3 0

3 years ago

Either use technology to find the P-value or use

Akimi4 [234]

Answer:

The first step is calculate the degrees of freedom, on this case:

$df=n-1=21-1=20$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(20)}$

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation

$\bar X$ represent the mean

$s$ represent the sample standard deviation

$n=21$ sample size

$\mu_o =140$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t=-0.024 would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:

Null hypothesis: $\mu \geq 140$

Alternative hypothesis: $\mu < 140$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

The statistic is given by: $t = -0.024$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=21-1=20$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(20)}$

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected $\alpah=0.01,0.05,0.1$

7 0

3 years ago

Share a reward of $140 in a ratio of 2:5

storchak [24]

So first we divide 140 by 7 because our ratio is a total of 7 dollars to get 20
So we multiply both sides of the ratio by 20 to get a ratio of 40:100
We can check our answer and it is right because 100+40=140

3 0

3 years ago

How do I do this? please detail steps.

vladimir2022 [97]

Define
${x} = \left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right]$

Then
x₁ = cos(t) x₁(0) + sin(t) x₂(0)
x₂ = -sin(t) x₁(0) + cos(t) x₂(0)

Differentiate to obtain
x₁' = -sin(t) x₁(0) + cos(t) x₂(0)
x₂' = -cos(t) x₁(0) - sin(t) x₂(0)

That is,
$\dot{x} = \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right] x(0)$

Note that
$\left[\begin{array}{ccc}0&1\\-1&09\end{array}\right] \left[\begin{array}{ccc}cos(t)&sin(t)\\-sin(t)&cos(t)\end{array}\right] = \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right]$

Therefore
$x(t) = \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] x(t)$

7 0

3 years ago

Help pls ty in advance

svetoff [14.1K]

$\bold{\huge{\underline{ Solution\: 2 }}}$

The name of the circle is IJKL
The name of central Angle
$\sf{\underline{= {\angle} IHJ }}$
The name of the secant = KL

${\bigstar}$ Circle :- It is a round figures, which has no end points.

${\bigstar}$ Central angle :- It the angle ,which lie in the middle of the circle.

Here, H is the mid point of the circle .So, Angle IHJ is the central angle.

${\bigstar}$ Secant :- A line drawn in circle in such a way that it intersect the circle from two distinct points. Then, It is called secant .

Here, KL is the line which acts as a secant because it intersect the circle from point K and point L.

$\bold{\huge{\underline{ Solution\: 3 }}}$

Semicircle = FGH and FIH
Minor Arc :- FG or GH
Major Arc :- FHG or GFH

${\bigstar}$ Semicircle :- Semicircle is nothing but the half of the circle.

Here, In second diagram 

FGH and FIH are acting as two semicircles which simulatineously forming one circle.

${\bigstar}$ Minor Arc :- Minor Arc is nothing but the smaller arc of the circle and it is always smaller than the half of the circle that is semicircle.

Here, 

FG or GH are the minor arc of the given circle.

${\bigstar}$ Major Arc :- Major Arc is nothing but the largest arc of the circle and it is always larger than the half of the circle that is semicircle.

Here, 

FHG or GFH is the major arc as it is larger than the semicircle of the given circle .

7 0

2 years ago