MATHEMATICS HIGH SCHOOL

Write the resultant of the two vectors as an ordered pair. <3, 6> and <5, –5>

Answers

Answer 1
Answer:

Answer: The resultant of the two vectors as an ordered pair is given by

<8,1>

Step-by-step explanation:

Since we have given that

There are two vectors :

\vec{a}=<3,6>=3\hat{i}+6\hat{j}\n\n\vec{b}=<5,-5>=5\hat{i}-5\hat{j}

So, we need to find the "Resultant of the two vectors":

\vec{a}+\vec{b}=(3+5)\ha{i}+(6-5)\hat{j}\n\n\vec{a}+\vec{b}=8\hat{i}+\hat{j}

Hence, the resultant of the two vectors as an ordered pair is given by

<8,1>

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A standard showerhead in Andrew's house dispenses 8 gallons of water per minute. Andrew changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead.y = 3xHow much water does Andrew save each day with the change in showerheads if he uses the shower for 8 minutes each day?5 gallons16 gallons24 gallons40 gallons

Change each mixed numeral to a fraction. 1 1/2, 1 7/8, 4 2/3, 5 5/6

Answers

3/2, 15/8, 14/3, 35/6

Find the x and y-intercepts of the equation 6x-2y+12=0

Answers

6x - 2y + 12 = 0
6x - 2y = -12
x = 0, -2
y = -6, 0 is what i got :)

Hi, anyone able to help with qn 7? Thanks :)!

Answers

Answer:

 

Step-by-step explanation:

I used the quadratic formula to find the roots of x^(2) + x -1

a=(-1-√(5))/(2) b=(-1+√(5) )/(2)

(1 )/(√(3) ) *((-1-√(5))/(2) )^(2) * (-1+√(5))/(2)

(1 )/(√(3) ) *((-1-√(5))/(2) ) * (-1+√(5))/(2)*((-1-√(5))/(2) )

(1 )/(√(3) ) *((-1-√(5))/(2) ) * (-1+√(5)-√(5) -4)/(4)

(1 )/(√(3) ) *((-1-√(5))/(2) ) * ( -4)/(4)

(1 )/(√(3) ) *((-1-√(5))/(2) ) * -1

(-1-1√(5) )/(2√(3) )*-1

(-1-1√(5) )/(2√(3) ) = (√(5)+1 )/(2√(3) )

Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

Answers

          f(x) = x² - 8x + 3
             y = x² - 8x + 3
           - 3                - 3
        y - 3 = x² - 8x + 16
y - 3 + 16 = x² - 8x + 16
     y + 13 = x² - 8x + 16
     y + 13 = (x - 4)²
         - 13      - 13
             y = (x - 4)² - 13
          f(x) = (x - 4)² - 13

At best buy they have a 42" TV that sells for $1250 and is on sale 15% and sales tax is 6%.What is the final cost?

Answers

ok so
sale is 15% off
and add 6% tax

100-15=85
100+6=106

therefor
1250 with 15% discount plus 6% tax means
1250 times 85% times 106% =
1250 times 0.85 times 1.06=1126.25
final cost=$1126.25
First Find 15% of the original price to find the sales price.

1250 x 0.15= 187.50

1250 - 187.50= 1062.5

Then to find your tax, multiply 1062.50 by 0.06.

1062.50 x 0.06= 63.75

Your total price would be: 1126.25 :)

-2(3x+9)=24 ( find the x )

Answers

Hello!! Let's solve this!

-2(3x+9)= 24

Distribute the 2 using the distributive property, which states: a(b + c) = ab + ac

-2(3x+9)= 24

-2(3x) + (-2)(9) = 24

Simplify it

-6x - 18 = 24

Add 18 on both sides

-6x - 18 + 18 = 24 + 18

-6x = 42

Divide -6 on both sides

-6x/-6 = 42/-6

x = -7

Your answer is x = -7.

Hope I helped! If you have any other questions or would like further explanation just let me know!! :)

Distribute -2 into parentheses for -6x-18=24
add 18 for -6x=42 for -7 so your answer is x=-7
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