Part A: Solve the following system of authentically showing your work: 3x + 2y = 4 4x + 3y = 7.

Matt is playing a game. He gains 7 points, loses 10 points, and then loses 8 points. What is his final score? *

Juli2301 [7.4K]

Answer:

-11

Step-by-step explanation:

7-10-8 = -11

8 0

2 years ago

Read 2 more answers

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

Hello, I'm new! I need help

melamori03 [73]

The interest in the first month is given as $ 97.1. The principal balance in the second question is $15,030.02

<h3>How to solve for the interest in the first month</h3>

1. We have to solve for the cost of the car

This would be = 19,725*(1.0475)

= 20,661.9375

There is a Down payment = 2,175

balance would be 20661.9375-2,175 = 18,486.94

average rating interest of new car = 6.30%

So the interest accrued in first month = 18,486.94x0.063/12 = $ 97.1

2. cost = 15867

sales tax = 5.25%

10 percent down payment

5.25/100 = 0.0525

cost of car = 15867 + (15867 * 0.0525)

= 16700 dollars

10% of 16700 dollars

= 1670 dollars

principal balance = 16700 - 1670

= $15,030.02

Read more on interest rate here

brainly.com/question/25793394

7 0

1 year ago

How do i solve this? <br><br> 7 < 3 - 2x<br><br><br> It's linear inequalities

Natasha2012 [34]

Hello from MrBillDoesMath!

Answer:

x < -2

Discussion:

7 < 3 - 2x => Add 2x to both sides

7 + 2x < 3 - (2x - 2x) => As 2x -2x = 0

7 + 2x < 3 => Subtract 7 from both sides

(7-7) + 2x < 3 - 7 => As 7-7 = 0 and 3-7 = -4

2x < -4 => Divide both sides by 2

x < -4./2 = -2

Thank you,

MrB

7 0

3 years ago

A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) af

Lunna [17]

Here the answer is: 0.76 and 1.84

I hope I don't have to explain it again.

4 0

3 years ago