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LuckyWell [14K]
2 years ago
11

Find the equation of the line with a slope of -3, passing through the point (2,5).

Mathematics
1 answer:
Alexxx [7]2 years ago
8 0
Y = -3(2) + 11
y = -6 + 11
y = 5

Answer is a) y = -3x + 11 , when x is 2 y is 5
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-2(3y - 6) + 4(5y - 8) = 92
Whitepunk [10]

Answer:

y = 8

Step-by-step explanation:

-2(3y - 6) + 4(5y - 8) = 92\\\\\mathrm{Expand\:}-2\left(3y-6\right)+4\left(5y-8\right):\quad 14y-20\\14y-20=92\\\\\mathrm{Add\:}20\mathrm{\:to\:both\:sides}\\14y-20+20=92+20\\\\Simplify\\14y=112\\\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14y}{14}=\frac{112}{14}\\\\Simplify\\y= 8

3 0
2 years ago
Read 2 more answers
9 t-shirts and a hat costs £93 4 t-shirts and a hat costs £43 how much does the hat and t-shirt cost
alexandr402 [8]

Answer:

T-shirt costs £10

Hat costs £3

Step-by-step explanation:

£93-£43=£50

9-4=5

£50/5=10

1 t-shirt=£10

£10x9=£90

£93-£90=£3

T-shirt = £10

Hat= £3

4 0
3 years ago
Read 2 more answers
Identify the interval on which the quadratic function is positive.
Alenkasestr [34]

Answer:

\textsf{1. \quad Solution:  $1 < x < 4$,\quad  Interval notation:  $(1, 4)$}

\textsf{2. \quad Solution:  $-2 < x < 4$,\quad  Interval notation:  $(-2, 4)$}

Step-by-step explanation:

<h3><u>Question 1</u></h3>

The intervals on which a <u>quadratic function</u> is positive are those intervals where the function is above the x-axis, i.e. where y > 0.

The zeros of the <u>quadratic function</u> are the points at which the parabola crosses the x-axis.  

As the given <u>quadratic function</u> has a negative leading coefficient, the parabola opens downwards.   Therefore, the interval on which y > 0 is between the zeros.

To find the zeros of the given <u>quadratic function</u>, substitute y = 0 and factor:

\begin{aligned}y&= 0\\\implies -7x^2+35x-28& = 0\\-7(x^2-5x+4)& = 0\\x^2-5x+4& = 0\\x^2-x-4x+4& = 0\\x(x-1)-4(x-1)&= 0\\(x-1)(x-4)& = 0\end{aligned}

Apply the <u>zero-product property</u>:

\implies x-1=0 \implies x=1

\implies x-4=0 \implies x=4

Therefore, the interval on which the function is positive is:

  • Solution:  1 < x < 4
  • Interval notation:  (1, 4)

<h3><u>Question 2</u></h3>

The intervals on which a <u>quadratic function</u> is negative are those intervals where the function is below the x-axis, i.e. where y < 0.

The zeros of the <u>quadratic function</u> are the points at which the parabola crosses the x-axis.  

As the given <u>quadratic function</u> has a positive leading coefficient, the parabola opens upwards.   Therefore, the interval on which y < 0 is between the zeros.

To find the zeros of the given <u>quadratic function</u>, substitute y = 0 and factor:

\begin{aligned}y&= 0\\\implies 2x^2-4x-16& = 0\\2(x^2-2x-8)& = 0\\x^2-2x-8& = 0\\x^2-4x+2-8& = 0\\x(x-4)+2(x-4)&= 0\\(x+2)(x-4)& = 0\end{aligned}

Apply the <u>zero-product property</u>:

\implies x+2=0 \implies x=-2

\implies x-4=0 \implies x=4

Therefore, the interval on which the function is negative is:

  • Solution:  -2 < x < 4
  • Interval notation:  (-2, 4)
3 0
11 months ago
I need help with all of them and if you can't help with all of them just answer one of them please. Look at the picture
likoan [24]
All you have to do is substitute the y value from the 1st equation into the second equation and solve...

a) y= 2-x
5x + 4y = 5

Substitute (2-x) into the second equation anywhere there is a y...

5x + 4y = 5
5x + 4(2-x) = 5

Now solve

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

Now that you have a solution for x, substitute -3 into either of the original equations anywhere there is an x then solve for y...

y = 2 - x
y = 2 - (-3)
y = 2+3 = 5

You solved for x and got -3 and solved for y and got 5, so your solution set is
(-3, 5).

Now check it by substituting both numbers into one of the original equations and you should have a true statement if it is correct...

y = 2 - x
5 = 2 - (-3)
5 = 2+3
5 = 5

True statement... it checks!


note* during the check, if the equation would have worked out to something like 2 = 5, then that is a false statement therefore the solution set would be wrong and you'd have to go back and find the mistake.
5 0
3 years ago
Lamar has a summer job. He gets paid $7.25 an hour and a $150 bonus at the end of summer. The total Lamar earns can be modeled b
Alex17521 [72]
B. 

Slope is the first number and intercept is the second 
4 0
3 years ago
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