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sergiy2304 [10]
2 years ago
12

Find the equation of the line with slope 1 and y-intercept (0,−1).

Mathematics
1 answer:
DedPeter [7]2 years ago
7 0

We will build the equation in the form of y = mx + b where 'm' is the slope and 'b' is the y-intercept.

We know the slope and we know the where the line intercepts the y-axis.

The answer:

y = 1x + -1

Because the coefficient of "1x" is just one we can simplify to the final answer:

y = x + -1

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Paul deposits $5000 in a bank which pays a compound interest rate of 5% per
disa [49]

Answer:

$4866.61

Step-by-step explanation:

3 0
3 years ago
The formula for the volume V of a cylinder is , where r is the radius of the base and h is the height of the cylinder. Select th
m_a_m_a [10]

Answer:

<h2>h = 4 cm</h2><h2 />

Step-by-step explanation:

V = π r² h

where r = 3 cm

V = 36π cm³

solve for h

plugin values into the formula:

36π = π 3² h

h = <u> 36π </u>

      π 3²

h = 4 cm

6 0
3 years ago
Calculate (A⃗ ×B⃗ )⋅C⃗ for the three vectors A⃗ with magnitude A = 5.08 and angle θA = 25.6 ∘ measured in the sense from the +x
alexgriva [62]

Answer:

(A⃗ ×B⃗ )⋅C⃗ = - 76.415

Step-by-step explanation:

First we need to calculate (A⃗ ×B⃗ ) :

(A⃗ ×B⃗ ) = A.B.sin (α).n

Where A is the magnitude of A⃗

Where B is the magnitude of B⃗

Where α is the angle between A⃗ and B⃗ = 63.9 - 25.6 = 38.3

Finally n is the vector orthogonal to A⃗ and B⃗

n magnitude is 1 and his direction is given by the right hand-rule

so n = ( 0 , 0 , 1 )

(A⃗ ×B⃗ ) = A.B.sin (α).n = 5.08 . 3.94 . sin (38.3) . (0 , 0 , 1 ) = (0,0,12.4)

C⃗ can be written as C.(0,0,-1) because of his +z - direction

C.(0,0,-1) = 6.16.(0,0,-1) = (0,0,-6.16)

(A⃗ ×B⃗ )⋅C⃗ = (0,0,12.4).(0,0,-6.16) = -76.41480787 = -76.415

8 0
3 years ago
Jane needs to buy mulch to cover a circular garden
scoray [572]

Answer:

$3089.4

Step-by-step explanation:

A circle is a locus of a point such that its distance from a point known as the center is always constant.

The area of a circle is given by the formula:

Area = πr²; where r is the radius of the circle.

From the image attached, we can see that the garden is circular with a radius of 5.5 yard. Hence:

Amount of mulch needed to cover garden = area of garden = πr² = π(5.5)²  = 95 yd²

Since mulch cost $32.52 per square yard, hence:

Cost of mulch needed = $32.52 per yd² * 95 yd² = $3089.4

7 0
3 years ago
Which of the following sets contain all roots of the polynomial
Zarrin [17]

All these given roots are contained in option C.

The given equation is :

9x^{3}+9x^{2}-4x-4=0

9x^{2}(x+1)-4(x+1)=0

(9x^{2}-4)(x+1)=0

9x^{2}-4=0,x+1=0

x^{2}=\frac{4}{9},x=-1

x=\frac{2}{3},x=-1

Roots = -1,\frac{-2}{3} ,\frac{2}{3}

Hence these lie in between (\frac{-3}{2} ,\frac{3}{2})


8 0
3 years ago
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