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2 years ago

Help due in 45 minutes!!

Mathematics

1 answer:

Nat2105 [25]2 years ago

3 0

Answer:

(14,-1)

Step-by-step explanation:

okay so first you need to use the "x=4y+10" in the first equation.

Rewrite as

3(4y+10) +11y=7

Distribute the 3(4y+10)

Rewrite as

12y+30

You'll have the equation

12y +30 +11y= 7

Subtract the 7 from both sides

12y+30+11y-7= 0

Combine like terms

23y+23=0

the best thing to do here is divide the equation by 23.

23/23 = 1

you'll have

y + 1 = 0

this simplifies to

y= -1

use this y value to solve for x

the easiest way to do this is start with the equation

x = 4y +10

Substitute the y for -1

x = -4(-1) +10

x = 4 +10

x = 14

the solution point is

(14,-1)

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4. The length of a rectangle is one more than twice the width. The area is 105 in?.

Zanzabum

9514 1404 393

Answer:

7 in

Step-by-step explanation:

For width w in inches, the length is given as 2w+1. The area is the product of length and width, so we have ...

A = LW

105 = (2w +1)w

2w^2 +w -105 = 0

To factor this, we're looking for factors of -210 that have a difference of 1.

-210 = -1(210) = -2(105) = -3(70) = -5(42) = -6(35) = -7(30) = -10(21) = -14(15)

So, the factorization is ...

(2w +15)(w -7) = 0

Solutions are values of w that make the factors zero:

w = -15/2, +7 . . . . . negative dimensions are irrelevant

The width of the rectangle is 7 inches.

7 0

2 years ago

Please help!! i’m stuck

eduard

Answer:

Step-by-step explanation:

8 0

2 years ago

Mary bought a handbag for 15.00naira. if she sold it for 18.00,what was her percentage gain?

melomori [17]

Answer:

total profit gained = 20%

Step-by-step explanation:

profit = SP - CP = 18 - 15 = 3 naira

total profit percentage =

( profit / CP ) × 100
3 / 15 × 100
20%

hence her total percentage gain was 20%

8 0

2 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

2 years ago

If m= 7x and m = 3x + 20, what is the value of x? a 10 4 7 5

Ipatiy [6.2K]

Equate the expressions for m.
7x = 3x + 20
4x = 20 . . . . . . . subtract 3x
x = 20/4 = 5 . . . divide by 4

The value of x is 5.

5 0

2 years ago