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3 years ago

Solve by using elimination.express answer as an ordered pair 2x-5y=-7 5x-3y=11

1 answer:

8 0

$2x-5y=-7 \ \ \ \ \ \ |\times (-5) \\
5x-3y=11 \ \ \ \ \ \ \ |\times 2 \\ \\
-10x+25y=35 \\
\underline{10x-6y=22 \ \ \ \ \ \ } \\
25y-6y=35+22 \\
19y=57 \\
y=\frac{57}{19} \\
y=3 \\ \\
2x-5y=-7 \\
2x-5 \times 3 =-7 \\
2x-15=-7 \\
2x=-7+15 \\
2x=8 \\
x=\frac{8}{2} \\
x=4 \\ \\ \boxed{(x,y)=(4,3)}$

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Which of these expressions shows like terms?

Katen [24]

Answer:

the answer is 2× + 3×

Step-by-step explanation:

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4 0

3 years ago

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

8. In right triangle LMN shown below, altitude MK is drawn to LN from M. IF LM = 12 and LK =10, then

Elena-2011 [213]

The length of the KN is 4.4

Step-by-step explanation:

We know from Pythagoras theorem

In a right angle ΔLMN

Base² + perpendicular² = hypotenuse ²

From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.

Hence ∠LKM = ∠NKM = 90 °

Given values-

LM=12

LK=10

Let KN be “s”

⇒LN= LK + KN

⇒LN= 10+x eq 1

Coming to the Δ LKM

⇒LK²+MK²= LM²

⇒MK²= 12²-10²

⇒MK²= 44 eq 2

Now in Δ MKN

⇒MK²+ KN²= MN²

⇒44+s²= MN² eq 3

In Δ LMN

⇒LM²+MN²= LN²

Using the values of MN² and LN² from the previous equations

⇒12² + 44+s²= (10+s) ²

⇒144+44+s²= 100+s²+20s

⇒188+s²= 100+s²+20s cancelling the common term “s²”

⇒20s= 188-100

∴ s= 4.4

Hence the value of KN is 4.4

8 0

3 years ago

Kindlyy solve this question..

Bas_tet [7]

Answer:

Volume = 21688.37 in.³

Step-by-step explanation:

Volume of a sphere : V=4/3πr³

4/3π17.3³ ≈ 21688.37025

hope this helps :D

3 0

3 years ago

Mixed Applications

Orlov [11]

The solution to the given question will be:-

A) If a number, n, divided by 8 equals 2.5, what is n: n = 20

B) The sum of a number, n, and 6.05 is 12.4. What is n: n = 6.35

C) Stacy is one-fourth as old as her mother. If Stacy's mother is

36, how old is Stacy: 9 years

<h3>What is an expression?</h3>

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

A) If a number, n, divided by 8 equals 2.5, what is n?

n / 8 = 2.5

n = 8 x 2.5 = 20

B) The sum of a number, n, and 6.05 is 12.4. What is n?

n + 6.05 = 12.4

n = 12.4 - 6.05 = 6.35

C) Stacy is one-fourth as old as her mother. If Stacy's mother is

36, how old is Stacy?

(1 / 4) M $_{age}$ = S $_{age}$

S $_{age}$ = ( 36 / 4)

S $_{age}$ = 9 years

Therfore the answers are n = 20 ,n = 6.35, S $_{age}$ = 9 years

To know more about Expression follow

brainly.com/question/723406

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6 0

2 years ago