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2 years ago

Which of the following sets of values is a soulution to the following system of liner expressions, 4x+y=24 x-y=-4

2 answers:

6 0

It is the first answer, x=4; y=8

Set up and add equations:
4x+y=24
+ x-y=-4

So 5x=20 (the y’s cancel)
X=4

Then substitute in 4(4)+y=24
16+y=24
Y=8

inessss [21]2 years ago

6 0

Answer:

x=4, y=8

Step-by-step explanation:

4x+y=24

x-y=-4

Add the two equations together to eliminate y

4x+y=24

x-y=-4

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

5x = 20

Divide by 5

5x/5 = 20/5

x = 4

We still need to find y

x-y = -4

4 -y = -4

Subtract 4 from each side

4-4-y = -4-4

-y = -8

Multiply by -1

-1 * y = -8 *-1

y= 8

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In the figure if angleACB = angleCDA, AC = 8 cm and AD= 3 cm, then BD is<br>

tatiyna

Answer:

AC = 8 cm,

AD = 3 cm and ∠ACB = ∠CDA

From figure,

∠CDA = 90°

∴ ∠ACB = ∠CDA = 90°

In right angled ∆ADC,

AC2 = AD2 + CD2

⇒ (8)2 = (3)2 + (CD)2

CD2 = 64 – 9 = 55

⇒ CD = √55 cm

In ∆CDB and ADC.

∠BDC = ∠AD [each 90°]

∠DBC = ∠DCA [each equal to 90°-∠A]

∴ ∠CDB ∼ ∆ADC

Then,

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2 years ago

Find the measure of the indicated angle to the nearest degree.

deff fn [24]

Given:

A right triangle with legs 5 units and 6 units.

To find:

The measure of angle opposite of side whose length is 5 units.

Solution:

In a right angle triangle,

$\tan \theta=\dfrac{Opposite}{Adjacent}$

Let $\theta$ be the missing angle. Then, for the given triangle,

$\tan \theta=\dfrac{5}{6}$

$\theta=\tan^{-1}\dfrac{5}{6}$

$\theta=39.805571^\circ$

Round the value to the nearest degree.

$\theta\approx 40^\circ$

Therefore, the measure of the required angle is 40 degrees.

8 0

3 years ago

Three consecutive integers have a sum of 132 . find the integers.

Jlenok [28]

N + n+1+n+2 = 132
3n = 129
n = 129/3 = 43 answer

the 3 integers are 43,44 and 45. Answer

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3 years ago

Christopher can paint the interior of his house in 15 hours. if he hires cynthia to help him they can do the same job together i

jenyasd209 [6]

If Christopher can paint his whole house in 15 hours, then he can get 1/15 of the job done in a single hour. If he hires Cynthia to help and they get the job done together (the sum of their efforts) in 9 hours, they can get 1/9 of the job done in a single hour. We are looking for how long Cynthia would take to do it on her own. Remember we are adding their efforts together and setting that equal to the total, so the equation is $\frac{1}{15}+\frac{1}{x}=\frac{1}{9}$ . What we are going to do here, what makes the most sense in solving for x, is to move the term with x in it to the other side of the equation and move the 1/9 over by subtraction. $\frac{1}{15}-\frac{1}{9}=-\frac{1}{x}$ . Of course before we can subtract those 2 fractions we need a common denominator, which happens to be 45: $\frac{3}{45}-\frac{5}{45}=-\frac{1}{x}$ and $-\frac{2}{45}=-\frac{1}{x}$ . We will cross multiply to get 2x = 45 and divide to find that it takes Cynthia 22.5 hours to do the job if she had to do it alone.