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3 years ago

Determine the slope between the points (-3, 0) and (0, 5)

Mathematics

2 answers:

Alex787 [66]3 years ago

5 0

The slope is approximately 1.7x+5

Georgia [21]3 years ago

5 0

The slope is 5/3 hope this helps

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Factorise the expression fully; 72ab-36bc+48bd

Serggg [28]

72ab-36bc+48bd

Factor out 12b from the expression

12b x(6a-3c+4d)

Answer : 12b x(6a-3c+4d)

4 0

3 years ago

A rectangle has the length of 2x+7 and the width of 9x find the area and the perimeter

seraphim [82]

Answer:

see explaination

Step-by-step explanation:

length (l) = 2x+7

width (b) = 9x

area of rectangle = l×b

=(2x+7)(9x)

=18x^2+63x

perimeter of rectangle = 2(l+b)

=2(2x+7)(9x)

=2(18x^2+63x)

=36x^2+126x

3 0

2 years ago

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d is 0.15 per second of time, t.

garik1379 [7]

Here the function given by

f(d)=0.15t

Now

f(1):-

$\\ \sf\longmapsto f(1)=0.15(1)=0.15m$

$\\ \sf\longmapsto f(2)=0.15(2)=0.3m$

6 0

2 years ago

Given the quadratic equation <img src="https://tex.z-dn.net/?f=y%20%3D%202%28x%20-1%29%5E%7B2%7D%20%2B%208" id="TexFormula1" tit

Sunny_sXe [5.5K]

Answer:

Part 1) "a" value is $2$

Part 2) The vertex is the point $(1,8)$

Part 3) The equation of the axis of symmetry is $x=1$

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is $y=2x^{2}-4x+10$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

if a > 0 then the parabola open upward (vertex is a minimum)

if a < 0 then the parabola open downward (vertex is a maximum)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

$x=h$

In this problem we have

$y=2(x-1)^{2}+8$ -----> this is the equation in vertex form of a vertical parabola

The value of $a=2$

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point $(1,8)$

$(h,k)=(1,8)$

The equation of the axis of symmetry is $x=1$

The equation of a vertical parabola in standard form is equal to

$y=ax^{2}+bx+c$

Convert vertex form in standard form

$y=2(x-1)^{2}+8$

$y=2(x^{2}-2x+1)+8$

$y=2x^{2}-4x+2+8$

$y=2x^{2}-4x+10$

see the attached figure to better understand the problem

7 0

3 years ago

Money Flow The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4 years. Find the

77julia77 [94]

Answer:

Present value = $4,122.4

Accumulated amount = $4,742

Step-by-step explanation:

Data provided in the question:

Amount at the Start of money flow = $1,000

Increase in amount is exponentially at the rate of 5% per year

Time = 4 years

Interest rate = 3.5% compounded continuously

Now,

Accumulated Value of the money flow = $1000e^{0.05t}$

The present value of the money flow = $\int\limits^4_0 {1000e^{0.05t}(e^{-0.035t})} \, dt$

= $1000\int\limits^4_0 {e^{0.015t}} \, dt$

= $1000\left [\frac{e^{0.015t}}{0.015} \right ]_0^4$

= $1000\times\left [\frac{e^{0.015(4)}}{0.015} -\frac{e^{0.015(0)}}{0.015} \right]$

= 1000 × [70.7891 - 66.6667]

= $4,122.4

Accumulated interest = $e^{rt}\int\limits^4_0 {1000e^{0.05t}(e^{-0.035t}} \, dt$

= $e^{0.035\times4}\times4,122.4$

= $4,742

8 0

2 years ago