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3 years ago

(08.01)Consider the following pair of equations:

Mathematics

2 answers:

Nana76 [90]3 years ago

8 0

Answer:

from the first equation

-x-y=-5

-x=y-5

: x=5-y. eqn 3

y= x+1

subtitute x in this equation

:- y= 5-y+1

y+y= 6

2y = 6

y=3

subtitute y in eqn 3

x=y-5

:- x=3-5

x= -2

Nat2105 [25]3 years ago

6 0

Answer:

(2,3)

Step-by-step explanation:

this is the only coordinate that can be plugged in and still be true. therefore, this is the only value that intersect and creates a point.

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Answer:

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2 years ago

A rock falls off a balcony. It’s height(in feet)is given by the formula f(x)= -16t^2+12.5t+150, where t is measured in seconds.

ELEN [110]

Answer: $3.47\ seconds$

Step-by-step explanation:

Given the following function:

$f(x)= -16t^2+12.5t+150$

You need to follow these steps in order to solve the exercise:

1. Substitute $f(x)=0$ :

$0= -16t^2+12.5t+150$

2. Now you need to apply the Quadratic formula. This is:

$x=t=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

In this case, you can identify that:

$a=-16\\b=12.5\\c=150$

Then, you can substitute these values into the formula:

$t=\frac{-12.5\±\sqrt{(12.5)^2-4(-16)(150)}}{2(-16)}$

3. Evaluating, you get:

$t_1=3.47\\\\t_2=-2.69$

4. You must choose the positive value. Then:

$t=3.47\ seconds$

7 0

4 years ago

please do the steps Solve for d: 1/6d-8=5/8 2. Solve for x: 3x-4+5x=10-2z 3. Solve for c: 7(c-3)=14 4. Solve for m: 11(m/22+3/44

xeze [42]

Answer:

d = 55.5

x = 1

c = 11

m = $\frac{1}{122}$

k = $\frac{a}{(c + 5)}$

Step-by-step explanation:

Sorry, the formatting is slightly hard to understand, but I think this is what you meant.

Q1.

$\frac{1}{6}$ d - 8 = $\frac{5}{8}$ x 2

Step 1. Simplify.

$\frac{5}{8}$ x 2 = $\frac{5}{8}$ x $\frac{2}{1}$ = $\frac{10}{8}$

Step 2. Cancel out the negative 8.

$\frac{1}{6}$ d - 8 = $\frac{10}{8}$

+ 8 to both sides (do the opposite: $\frac{1}{6}$ d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)

$\frac{1}{6}$ d = $\frac{10}{8}$ + 8

Step 3. Simplify.

$\frac{10}{8}$ + 8 = $\frac{10}{8}$ + $\frac{8}{1}$ = $\frac{10}{8}$ + $\frac{64}{8}$ = $\frac{74}{8}$ = $\frac{37}{4}$

Step 4. Cancel out the $\frac{1}{6}$ .

$\frac{1}{6}$ d = $\frac{37}{4}$

÷ $\frac{1}{6}$ from both sides (do the opposite: d is multiplied by $\frac{1}{6}$ right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)

÷ $\frac{1}{6}$ = x 6

So....

x 6 to both sides

d = $\frac{37}{4}$ x 6 = $\frac{37}{4}$ x $\frac{6}{1}$ = $\frac{222}{4}$ = $\frac{111}{2}$ = 55.5

Step 5. Write down your answer.

d = 55.5

Q2.

3x - 4 + 5x = 10 - 2x × 3

Step 1. Simplify

3x - 4 + 5x = 3x + 5x - 4 = 8x - 4

10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x

Step 2. Cancel out the negative 6x

8x - 4 = 10 - 6x

+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)

14x - 4 = 10

Step 3. Cancel out the negative 4

14x - 4 = 10

+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)

14x = 14

Step 4. Divide by 14

14x = 14

÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])

x = 1

Step 5. Write down your answer.

x = 1

Q3.

7(c - 3) = 14 × 4

Step 1. Expand the brackets

7(c - 3) = (7 x c) - (7 x 3) = 7c - 21

Step 2. Simplify

14 x 4 = 56

Step 3. Cancel out the negative 21

7c - 21 = 56

+ 21

7c = 56 + 21

7c = 77

Step 4. Cancel out the ×7

7c = 77

÷ 7

c = 77 ÷ 7

c = 11

Step 5. Write down your answer.

c = 11

Q4.

11( $\frac{m}{22}$ + $\frac{3}{44}$ ) = 87m + m × 5

Step 1. Expand the brackets

11( $\frac{m}{22}$ + $\frac{3}{44}$ ) = (11 x $\frac{m}{22}$ ) + (11 x $\frac{3}{44}$ ) = ( $\frac{11}{1}$ x $\frac{m}{22}$ ) + ( $\frac{11}{1}$ x $\frac{3}{44}$ ) = $\frac{11m}{22}$ + $\frac{33}{44}$ = $\frac{m}{2}$ + $\frac{3}{4}$