MATHEMATICS HIGH SCHOOL

Given the equation4x + 2y = 10 (standard form), what is the slope-intercept form of this equations?

Answers

Answer 1

Answer:

Answer:

Y=2x+5

Step-by-step explanation:

Move the variable (x) to the right

2y= 10-4x

divide both sides of the equation by 2

y=5-2x

and then reorder the terms

y=-2x+5

Answer 2

Answer:

y=-2x+5

Step-by-step explanation:

hope i helped

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If a right angle triangle has a hypotenuse of length 13 units and a leg of length 7 units, what would be the length of the other leg?

Answers

The length of the other leg of a right angle triangle is, 10.95 units

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A right angle triangle has a hypotenuse of length 13 units and a leg of length 7 units.

Now, By the Pythagoras theorem, we get;

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ 13² = 7² + Base²

⇒ 169 = 49 + Base²

⇒ Base² = 169 - 49

⇒ Base² = 120

⇒ Base = √120

⇒ Base = 10.95 units

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Pythagorean theorem: A² + B² = C²
(7)² + B² = 13²;
49 + B² = 169;
B² = 130;
B = 11.40
The length of the other leg is 11.40.

Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)

Answers

Answer: y = -x + 5 and y = -x - 7 (see attached graph)

Step-by-step explanation:

y = $(9)/(x + 1)$

= 9(x + 1)⁻¹

Use the product rule to find the derivative

a = 9 a' = 0

b = (x + 1)⁻¹ b' = -(x + 1)⁻²

ab' + a'b

= 9[-(x + 1)⁻²] + 0[(x + 1)⁻¹ ]

= $(-9)/((x + 1)^(2))$

Set the derivative equal to the desired slope of -1 to solve for x

-1 = $(-9)/((x + 1)^(2))$

-(x + 1)² = -9

(x + 1)² = 9

√(x + 1)² = √9

x + 1 = +/- 3

x + 1 = 3 x + 1 = -3

x = 2 x = -4

Plug those values into the original equation to solve for y:

y = $(9)/(x + 1)$

= $(9)/(2 + 1)$

= 3

(2, 3)

y = $(9)/(x + 1)$

= $(9)/(-4 + 1)$

= -3

(-4, -3)

Next, plug in the given slope (-1) and the coordinates above into the Point-Slope formula y - y₁ = m(x - x₁) to find the equations:

m = -1, (x₁ y₁) = (2, 3) m = -1, (x₁ y₁) = (-4, -3)

y - 3 = -1(x - 2) y + 3 = -1(x + 4)

y - 3 = -x + 2 y + 3 = -x - 4

y = -x + 5 y = -x - 7

Answer:

$f(x)=\frac9{x+1}\n f'(x)=-\frac9{(x+1)^2}\n f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\n |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\n x_1=2\ \vee\ x_2=-4\n f(x_1)=f(2)=\frac9{2+1}=3\n f(x_2)=f(-4)=\frac9{-4+1}=-3$

First tangent line:

$y=f'(x_1)\cdot (x-x_1)+f(x_1)\ \to \ y=-1(x-2)+3\ \to \ y=-x+5$

Second tangent line:

$y=f'(x_2)\cdot (x-x_2)+f(x_2)\ \to \ y=-1(x+4)-3\ \to \ y=-x-7$

Notice: slope of -1 means that both $f'(x_1), \ f'(x_2)$ are equal to -1, so $f'(x_1)=-1 \ and \ f'(x_2)=-1$

Create a list of steps, in order, that will solve the following equation.3(x + 1)2 = 108

Solution steps:

- Add 1 to both sides

- Divide both sides by 3

- Multiply both sides by 3

- Subtract 1 from both sides

- Square both sides

- Take the square root of both sides

PLSS HELP!!

Answers

Take a to be the first choice and so on
The order is b,f,d
Umm...I could really use up all the steps but hope it helps
Please mark as brainliest

Please someone help me with this question and show working! Thank you.

Answers

Answer:

Below;)

Step-by-step explanation:

We know force = mass * acceleration

So Given, mass = 0.6 mg

We know 1mg = 10^-3 g
and 1g = 1/1000 kg
So 1mg = 10^-6 kg

Hence, Mass: 0.6 mg = 10^-6 * 0.6 kg

Also Acceleration = 7.5 km/s²

We know 1km = 1000 m

Acceleration = 7.5*1000 m/s²
Acc = 7500 m/s²

Putting values, we get Force as:

F = ma
F = 0.6*10^-6 kg* 7500 m/s²
F = 4500 * 10^-6 N
F = 4.5 * 10^-3 N

Susie is solving the quadratic

Answers

Answer:

Option (D)

Step-by-step explanation:

Standard equation of a quadratic function is,

ax² + bx + c

Comparing this function with the given quadratic function,

f(x) = 2x² - 4x - 3

a = 2, b = -4 and c = -3

By using quadratic formula to get the value of x,

x = $(-b\pm √(b^2-4ac) )/(2a)$

= $(-(-4)\pm √((-4)^2-4(2)(-3)) )/(2(2))$

= $(4\pm√(16+24))/(4)$

= $(-4\pm √(40))/(4)$

= $(-2\pm √(10))/(2)$

Therefore, Susie made a mistake in step IV.

Option (D) is the answer.

3c - 9d + 5d
simplify this