MATHEMATICS HIGH SCHOOL

Solve: y=6x-8 and y=-3x+10

Answers

Answer 1

Answer:

The solution to the system of equations is x = 2 and y = 4.

To solve the system of equations:

y = 6x - 8 ...(Equation 1)

y = -3x + 10 ...(Equation 2)

We can set the two equations equal to each other:

6x - 8 = -3x + 10

To solve for x,

6x + 3x = 10 + 8

9x = 18

Dividing both sides by 9:

x = 18/9

x = 2

So, y = 6(2) - 8

y = 12 - 8

y = 4

Therefore, the solution to the system of equations is x = 2 and y = 4.

Learn more about Equation here:

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Answer 2

Answer:

Answer:

x = 2

Step-by-step explanation:

hey there,

< If these two are together, then the problem would look like this:

$\left \{ {{y=6x-8} \atop {y=-3x+10}} \right.$

From the first equation, we can see that y = 6x-8. I am assuming in your problem you need to find what "x" is equal to, so plug in the first "y" value into the second one.

6x - 8 = -3x + 10

Bring all "x"s to one side and regular numbers to the other side.

6x + 3x = 10 + 8

9x = 18

x = 2

x = 2 is your final answer. >

Hope this helped! Feel free to ask anything else.

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What is 1 tenth of 3.0. as a decimal

Answers

Answer=0.3

1/10 of 3.0 is 0.3

3.0*(1/10)=0.3

Grant has 2/3 cup of ice cream in bowl. He then removes two 1/6 cups ice cream to share with his little brother. Whuch of the folliwing best explains the amount of ice cream left in grants bowl?

Answers

two 1/6 cups would be equal to 2/6 cups OR 1/3
subtract 1/3 from 2/3
grant has 1/3 cup left in this bowl

What is the negative reciprocal of 3/5

Answers

Answer:

-5/3

Step-by-step explanation:

To find the negative reciprocal

-1 /( number)

-1 ( 3/5)

-1 ÷ (3/5)

Copy dot flip

-1 * 5/3

-5/3

The negative reciprocal is -5/3

Answer:

-5/3

Step-by-step explanation:

Negative reciprocal of 3/5 is 5/3 * -1 = -5/3

Firewood is stacked in a pile. The bottom row has 20 logs, and the top row was 14 logs. Each row has one more log than the row above it. How many logs are in the pile?

Answers

Since, each row has one more log than the row above it

so, this is arithematic sequence

We are given that

First row is

$=14$

so,

$a_1=14$

Last row is

$=20$

so,

$a_n=14$

Each row has one more log than the row above it

so,

$d=1$

now, we can find number of rows

$a_n=a_1+(n-1)d$

we can plug values

$20=14+(n-1)1$

we can solve for n

$6=(n-1)1$

$n=7$

now, we can find total number of logs

$S=(n(a_1+a_n))/(2)$

now, we can plug values

$S=(7(14+20))/(2)$

$S=119$

So,

Number of logs in the pile are 119........Answer

The log in the pile is an illustration of arithmetic progression.

The number of logs in the pile is 119.

The first term of the progression is:

$\mathbf{a =14}$

The last term is:

$\mathbf{L =20}$

The common difference is:

$\mathbf{d =1}$

First, we calculate the number of terms using:

$\mathbf{L = a +(n - 1)d}$

So, we have:

$\mathbf{20= 14 +(n - 1) * 1}$

$\mathbf{20 = 14 +(n - 1) }$

Subtract 14 from both sides

$\mathbf{n - 1 = 6}$

Add 1 to both sides

$\mathbf{n = 7}$

The number of logs in the pile is calculated using the sum of n terms of an AP formula:

$\mathbf{S_n = (n)/(2)(a + L)}$

So, we have:

$\mathbf{S_n = (7)/(2)(14 + 20)}$

$\mathbf{S_n = 3.5(34)}$

$\mathbf{S_n = 119}$

Hence, the number of logs in the pile is 119.

Read more about arithmetic progressions at:

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Solve for x : 2x^2+4x-16=0

Answers

$2x^2+4x-16=0\ \ \ /:2\n\nx^2+2x-8=0\n\n\underbrace{x^2+2x\cdot1+1^2}_((*))-1^2-8=0\n\n(x+1)^2-1-8=0\n\n(x+1)^2-9=0\n\n(x+1)^2=9\iff x+1=-3\ or\ x+1=3\n\nx=-3-1\ or\ x=3-1\n\nx=-4\ or\ x=2\n\n\n(*)\ (a+b)^2=a^2+2ab+b^2$

$2x^2+4x-16=0\ \ \ /:2\n\nx^2+2x-8=0\n\na=1;\ b=2;\ c=-8\n\n\Delta=b^2-4ac\ if\ \Delta > 0\ then\ x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=2^2-4\cdot1\cdot(-8)=4+32=36;\ \sqrt\Delta=√(36)=6\n\nx_1=(-2-6)/(2\cdot1)=(-8)/(2)=-4;\ x_2=(-2+6)/(2\cdot1)=(4)/(2)=2$

in order to solve it, we need find the zero of the polynomial.

we find the zero of the polynomial by splitting the middle term method

2x2 -+ 4x - 16

= 2x2 + 8x - 4x -16

= 2x( x + 4)- 4(x + 4)
= (2x-)(x+4)

we find the zeroes of the factors

experimentally we find two values, 2 and -4.

Thus, values of x are 2 and -4

In one hour, a roadside stand sells 24 bouquets of flowers. The stand starts operating at 9:00 AM and closes at 12:30 PM for a 30 minute lunch break. If sales continue at the same rate, how many bouquets of flowers will the stand sell by 6:00 PM? A)216 B)96 C) 204 D)228