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3 years ago

Solve the system of linear equations by substitution. 5x+2y=9 x+y=-3

1 answer:

8 0

Step 1: subtract x from -3. New equation should be y=-3-x.
Step 2: plug that equation into top equation. Should be 5x + 2(-3-x) = 9.
Step 3: use distribitive properties on 2(-3-x). New equation is 5x - 6 - 2x = 9.
Step 4: combine like terms. New equation 3x - 6 = 9.
Step 5: work it out. Divide 3x and 9 by 3. New equation is x - 6 = 3. Add 6 to -6 and 9. Final eqaution is x = 9.
Step 6: swap 9 for x in second equation. New equation is 9 + y = -3
Step 7: subtract 9 from 9 and -3. New equation is y = -12
: = = -

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AB = 3 + x

strojnjashka [21]

Answer:

Option A) 4, 2

Step-by-step explanation:

We are given that quadrilateral ABCD is a parallelogram with sides:

$AB = 3 + x\\DC = 4x\\AD = y + 1\\BC = 2y$

Since the opposite sides of a parallelogram are equal, we can write:

$AB = DC\\AD=BC$

Equating the sides we get,

$\Rightarrow 3+x = 4x\\4x-x = 3\\3x = 3\\x = 1\\\Rightarrow y + 1 = 2y\\y = 1$

Putting the values of x and y, we get:

$AB = 3 + x =4\\DC = 4x =4\\AD = y + 1=2\\BC = 2y=2$

Thus, the lengths of the opposite side pairs is 4,2.

4 0

3 years ago

Convert 5.6 into vulgar fraction

zheka24 [161]

Answer:

The answer is 28/5

Step-by-step explanation:

5.6 can be written as 56/10 into vulgar fraction.

Thus, The answer is 56/10 = 28/5

<u>-TheUnknownScientist 72</u>

8 0

2 years ago

A 14.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall (above the fire truck)

UkoKoshka [18]

Answer:

h = 7.47 m

Step-by-step explanation:

According to the question, we have a right triangle formed by the ladder with the wall and the floor.

The length of the ladder is the hypotenuse and the desired height is the opposite. This is due to the fact that "the ladder makes an angle of 21" 27" with the horizontal". Then, the trigonometric ratio to use is sine:

$sin(\theta)=\frac{opposite}{hypotenuse}$

Using the values given:

$sin(\21"27")=\frac{h}{14.5}$

Multiplying both sides by 14.5:

$14.5*sin(\21"27")=14.5*\frac{h}{14.5}$

$14.5*sin(\21"27")=h$

Then h = 7.47 m

8 0

3 years ago

I need help with questions 1,2, and 3. Would gratefully appreciate it (:

motikmotik

Answer:

Step-by-step explanation:

(2):

First let's organise the data:

33 miles ... x mph ... 4h - downstream

33 miles ... y mph ... 7h - up the stream

x = 33/4 = 8.25 mph

y = 33/7 = 4.71 mph

(3)

P(x) = $x^2 - 2x - 3$

To find the amount of key rings sold when the profit is 5000$ we have to equate P(x) with 5, because in the problem the profit of the key rings is displayed in terms of thousands.

$x^2 - 2x - 3 = 5\\x^2 - 2x - 8 = 0\\x_1 = 4, x_2 = -2$