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3 years ago

The sun of 3 less than 5 times a number and the number increased by 9 is 24. What is the number.?

Mathematics

1 answer:

puteri [66]3 years ago

8 0

Answer:

let the number be x

(5x-3) + (x+9)=24

6x +6= 24

6x=18

x=3

The number is 3

Step-by-step explanation:

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Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Taya2010 [7]

Answer:

Segment DE is half the length of segment AC. -- Substitution property of equality

Step-by-step explanation:

Here is given a proof for proving line joining mid segment is parallel and half the length of third side.

Stepwise proof is given in two columns

We find that for every line there is a justification as

STatement Justification

D and E coordinates found out MId point formula

DE and BC are measured Distance formula

DE=1/2 BC Substitution property of equality

This justification was missing in the given proof and with this included proof would be complete

4 0

3 years ago

Read 2 more answers

Use the given information to find (a) sin(s+t), (b) tan(s+t), and (c) the quadrant of s+t. cos s = - 12/13 and sin t = 4/5, s an

Anton [14]

Answer:

Part a) $sin(s + t) =-\frac{63}{65}$

Part b) $tan(s + t) = -\frac{63}{16}$

Part c) (s+t) lie on Quadrant IV

Step-by-step explanation:

[Part a) Find sin(s+t)

we know that

$sin(s + t) = sin(s) cos(t) + sin(t)cos(s)$

step 1

Find sin(s)

$sin^{2}(s)+cos^{2}(s)=1$

we have

$cos(s)=-\frac{12}{13}$

substitute

$sin^{2}(s)+(-\frac{12}{13})^{2}=1$

$sin^{2}(s)+(\frac{144}{169})=1$

$sin^{2}(s)=1-(\frac{144}{169})$

$sin^{2}(s)=(\frac{25}{169})$

$sin(s)=\frac{5}{13}$ ---> is positive because s lie on II Quadrant

step 2

Find cos(t)

$sin^{2}(t)+cos^{2}(t)=1$

we have

$sin(t)=\frac{4}{5}$

substitute

$(\frac{4}{5})^{2}+cos^{2}(t)=1$

$(\frac{16}{25})+cos^{2}(t)=1$

$cos^{2}(t)=1-(\frac{16}{25})$

$cos^{2}(t)=\frac{9}{25}$

$cos(t)=-\frac{3}{5}$ is negative because t lie on II Quadrant

step 3

Find sin(s+t)

$sin(s + t) = sin(s) cos(t) + sin(t)cos(s)$

we have

$sin(s)=\frac{5}{13}$

$cos(t)=-\frac{3}{5}$

$sin(t)=\frac{4}{5}$

$cos(s)=-\frac{12}{13}$

substitute the values

$sin(s + t) = (\frac{5}{13})(-\frac{3}{5}) + (\frac{4}{5})(-\frac{12}{13})$

$sin(s + t) = -(\frac{15}{65}) -(\frac{48}{65})$

$sin(s + t) =-\frac{63}{65}$

Part b) Find tan(s+t)

we know that

tex]tan(s + t) = (tan(s) + tan(t))/(1 - tan(s)tan(t))[/tex]

we have

$sin(s)=\frac{5}{13}$

$cos(t)=-\frac{3}{5}$

$sin(t)=\frac{4}{5}$

$cos(s)=-\frac{12}{13}$

step 1

Find tan(s)

$tan(s)=sin(s)/cos(s)$

substitute

$tan(s)=(\frac{5}{13})/(-\frac{12}{13})=-\frac{5}{12}$

step 2

Find tan(t)

$tan(t)=sin(t)/cos(t)$

substitute

$tan(t)=(\frac{4}{5})/(-\frac{3}{5})=-\frac{4}{3}$

step 3

Find tan(s+t)

$tan(s + t) = (tan(s) + tan(t))/(1 - tan(s)tan(t))$

substitute the values

$tan(s + t) = (-\frac{5}{12} -\frac{4}{3})/(1 - (-\frac{5}{12})(-\frac{4}{3}))$

$tan(s + t) = (-\frac{21}{12})/(1 - \frac{20}{36})$

$tan(s + t) = (-\frac{21}{12})/(\frac{16}{36})$

$tan(s + t) = -\frac{63}{16}$

Part c) Quadrant of s+t

we know that

$sin(s + t) =negative$ ----> (s+t) could be in III or IV quadrant

$tan(s + t) =negative$ ----> (s+t) could be in III or IV quadrant

Find the value of cos(s+t)

$cos(s+t) = cos(s) cos(t) -sin (s) sin(t)$

we have

$sin(s)=\frac{5}{13}$

$cos(t)=-\frac{3}{5}$

$sin(t)=\frac{4}{5}$

$cos(s)=-\frac{12}{13}$

substitute

$cos(s+t) = (-\frac{12}{13})(-\frac{3}{5})-(\frac{5}{13})(\frac{4}{5})$

$cos(s+t) = (\frac{36}{65})-(\frac{20}{65})$

$cos(s+t) =\frac{16}{65}$

we have that

$cos(s+t)=positive$ -----> (s+t) could be in I or IV quadrant

$sin(s + t) =negative$ ----> (s+t) could be in III or IV quadrant

$tan(s + t) =negative$ ----> (s+t) could be in III or IV quadrant

therefore

(s+t) lie on Quadrant IV

4 0

2 years ago

Please help due today Geometry

Stolb23 [73]

<F=180-106+29=180-135=45°

In both triangles

<F=<H
<S=<A

Hence both triangles are similar by AA congruency

6 0

2 years ago

The slope of the line passing through ( – 5,0) and ( – 4, y) is - 1. What is the value of y?

Rudiy27

Answer:

$y = -1$

Step-by-step explanation:

Given

Points: (-5,0) and (-4, y)

Slope: $m = -1$

Required

Find y

The slope (m) of a line is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$-1 = \frac{y - 0}{-4 - (-5)}$

$-1 = \frac{y }{-4 +5}$

$-1 = \frac{y }{1}$

$-1= y$

$y = -1$

8 0

2 years ago

−2x + y = 1 −4x + y = −1 (3, 1) (−1, 3) (−1, −3) (1, 3)

babunello [35]

(1, 3) are the correct coordinates of the intersection (or solution) of this system.

6 0

3 years ago

The sun of 3 less than 5 times a number and the number increased by 9 is 24. What is the number.?​

The sun of 3 less than 5 times a number and the number increased by 9 is 24. What is the number.?