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damaskus [11]
3 years ago
10

HELP PLEASE!!!!! Solve each system.

Mathematics
2 answers:
Ede4ka [16]3 years ago
7 0

15.\ \text{Elimination method}\\\underline{+\left\{\begin{array}{ccc}y=-3x+9\\y=3x+3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2y=12\qquad\text{divide both sides by 2}\\.\qquad \boxed{y=6}\\\\\text{put the value of y to the second equation}\\\\6=3x+3\qquad\text{subtract 3 from both sides}\\3=3x\qquad\text{divide both sides by 3}\\1=x\to\boxed{x=1}\\\\Answer:\ x=1,\ y=6\to(1,\ 6)


16.\ \text{Substitution method}\\\left\{\begin{array}{ccc}y=11x+4\\y=7x-16\end{array}\right\Rightarrow11x+4=7x-16\\\\11x+4=7x-16\qquad\text{subtract 4 from both sides}\\11x=7x-20\qquad\text{subtract 7x from both sides}\\4x=-20\qquad\text{divide both sides by 4}\\\boxed{x=-5}\\\\\text{Put the value of x to the first equation}\\\\y=11(-5)+4\\y=-55+4\\\boxed{y=-51}\\\\Answer:\ x=-5,\ y=-51\to(-5,\ -51)

gogolik [260]3 years ago
7 0
15. -3x+9=3x+3
6x=-6
x=1
y=3x+3
y=6

16. 7x-16=11x+4
-20=4x
-5=x
y=-35-16
y=-51

do you understand? sorry if my english is bad i am Indonesian please corect me if i do some false
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The length of the hypotenuse of the right triangle is 25 cm, the length of one of the legs is 10 cm. What is the length of the s
sergejj [24]

Answer:

\large\boxed{AD=21\ and\ CD=2\sqrt{21}}

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem for calculate the length of CA:

CA^2+CB^2=AB^2

We have

CA=x,\ CB=10,\ AB=25

Substitute:

x^2+10^2=25^2

x^2+100=625             subtract 100 from both sides

x^2=525\to x=\sqrt{525}\\\\x=\sqrt{25\cdot21}\\\\x=\sqrt{25}\cdot\sqrt{21}\\\\x=5\sqrt{21}\ cm

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

\dfrac{AD}{AC}=\dfrac{AC}{AB}

We have:

AD=y,\ AC=5\sqrt{21},\ AB=25

Substitute:

\dfrac{y}{5\sqrt{21}}=\dfrac{5\sqrt{21}}{25}

\dfrac{y}{5\sqrt{21}}=\dfrac{\sqrt{21}}{5}              cross multiply

5y=5(\sqrt{21})^2            divide both sides by 5

y=21\ cm

If you mean the length of segment CD, then use the proportion:

\dfrac{CD}{AD}=\dfrac{CB}{CA}

Substitute:

\dfrac{CD}{21}=\dfrac{10}{5\sqrt{21}}\\\\\dfrac{CD}{21}=\dfrac{2}{\sqrt{21}}\qquad\text{cross multiply}\\\\CD\sqrt{21}=42\qquad\text{multiply both sides by}\ \sqrt{21}\\\\21CD=42\sqrt{21}\qquad\text{divide both sides by 21}\\\\CD=2\sqrt{21}\ cm

3 0
3 years ago
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IceJOKER [234]

9514 1404 393

Answer:

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Step-by-step explanation:

In expanded form, the number is ...

  4×16^4 +10×16^3 +9×16^2 +14×16^1 +13

  = (((4×16 +10)×16 +9)×16 +14)×16 +13 = ((74×16 +9)×16 +14)×16 +13

  = (1193×16 +14)×16 +13 = 19102×16 +13 = 305,645 base 10

_____

If you want to convert this to base 8, that is easily done by writing the binary equivalents of the hex digits, then regrouping them by 3s.

  4A9ED₁₆ = 0100 1010 1001 1110 1101₂ = 01 001 010 100 111 101 101₂

  = 1124755₈

5 0
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Aleonysh [2.5K]

The question seems incomplete but that could just be my perception.

The slope of y = -4x is -4 as it's the value just in front of the x value. This equation is in the form y = mx+b where m = -4 and b = 0. The m is the slope.

Anything parallel to y = -4x will also have a slope of -4. Parallel lines have equal slopes (but different y intercepts)

Anything perpendicular to y = -4x will have a slope of 1/4. Notice how multiplying the original slope (-4) and the perpendicular slope (1/4) gets you -1. To go from -4 to 1/4, we flip the fraction and the sign. Think of -4 as -4/1 to flip the fraction to -1/4 and then flip the sign to +1/4 or just 1/4.

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Sholpan [36]

Answer:

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Step-by-step explanation:

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