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4 years ago

15

A given line has the equation 10x+2y=-2. What is the equation, in the slooe-intercept form, of the line that is parallel to the

given line and passes through the point (0,12) ?

1 answer:

nexus9112 [7]4 years ago

5 0

10x+2y=2 or give us the options

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If the hypotenuse is c=a√2, then 6=a√2. In inches, what is the value of a?

Aloiza [94]

The value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2. This can be obtained by using Pythagoras' theorem.

<h3>Calculate the value of a:</h3>

This question can be solved using Pythagoras' theorem,

If in a right angled triangle, hypotenuse is the longest side of the triangle and always opposite to the angle 90°, height and base are the two shorter sides which are adjacent to the angle 90°.

If hypotenuse = c, height = a and base = b then,

⇒ hypotenuse² = height² + base²

⇒ c² = a² + b²

Here in the question it is given that,

Hypotenuse of the triangle is c = a√2
6 = a√2 in inches ⇒ c = 6

Height and base is equal and both has the value of a ⇒ height = a and base = a

By using the Pythagoras' theorem we can write that,

⇒ hypotenuse² = height² + base²

⇒ 6² = a² + a²

⇒ 36 = 2a²

By dividing both sides of the equation by 2,

⇒ 18 = a²

⇒ a² = 18

By taking square on both side of the equation,

⇒ a = 3√2 inches

Hence the value of a is 3√2 inches if it is given that the hypotenuse is c = a√2 and 6 = a√2.

Learn more about Pythagoras' theorem here:

brainly.com/question/9005379

#SPJ1

3 0

2 years ago

A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=

Romashka [77]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after <em>t</em> seconds is modeled by the function:

$h(t)=-16t^2+104t+56$

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, <em>a</em> = -16, <em>b</em> = 104, and <em>c</em> = 56.

Find the <em>x-</em> (or rather <em>t-</em>)<em> </em>coordinate of the vertex. So:

$\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}$

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

$\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}$

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for <em>t: </em>

$0=-16t^2+104t+56$

We can simplify a bit. Divide both sides by -8:

$0=2t^2-13t-7$

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

$\displaystyle 0=2t^2-14t+t-7$

Factor out a 2<em>t</em> from the first two terms and group the last two terms:

$0=2t(t-7)+(t-7)$

Factor by grouping:

$0=(2t+1)(t-7)$

Zero Product Property:

$2t+1=0\text{ or } t-7=0$

Solve for each case:

$\displaystyle t=-0.5\text{ or } t=7$

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

6 0

3 years ago

(Picture) MULTIPLYING MONOMIALS AND BINOMIALS

lilavasa [31]

Answer:

Second option: B and C

Step-by-step explanation:

A is the product of 4x and -2x: A=(4x)(-2x)→A=-8x^2 (x^2)

B is the product of 4x and 3: B=(4x)(3)→B=12x (x^1)

C is the product of 1 and -2x: C=(1)(-2x)→C=-2x (x^1)

D is the product of 1 and 3: D=(1)(3)→D=3 (constant)

Then, the like terms are B and C

6 0

3 years ago

Is the statement {0}=ø true or false

Schach [20]

Answer:

False

Step-by-step explanation:

This statement is false

{0}=ø

The first parts {0} says there is a zero in the set

The second item says it is an empty set

5 0

4 years ago

Please help me answer this !!!!

Studentka2010 [4]

Answer:

d = 101

Step-by-step explanation:

t = 11

11 x 11 = 121

-20 + 121 = 101

check: 101- 121 = -20 (correct)

4 0

3 years ago