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3 years ago

Find the coordinates of the points of intersection of the parabola y=x^2+3x-4 and the line y=2x+2

1 answer:

6 0

You can set the y values equal to each other and solve the system:

x^2+3x-4=2x+2
x^2+x-6=0
(x+3)(x-2)=0
x=-3,2

So, these are the x values of the intersection. To get the y values, you can just plug them back into either formula:

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

y2(2)+2
y=6

So the coordinates are (-3,-4) and 2,6).

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Find the amount to be paid at the end of 3years in each case. a) principal =1,200 at12% p.a

Viktor [21]

Answer:

$1632

Step-by-step explanation:

Given data

Principal= $1200

Rate= 12%

Time= 3 years

The simple interest expression is given as

A= P(1+rt)

substitute

A=1200(1+0.12*3)

A=1200(1+0.36)

A=1200*1.36

A=$1632

Hence the amount is $1632

4 0

3 years ago

A spherical cantaloupe is cut in half. The visible cross-section has an area of 5252 in2. The volume of the cantaloupe is _____

artcher [175]

Answer:

V = 286319.465 cm3

Step-by-step explanation:

First, you have to find the radius to be able to find the volume of a sphere.

The equation for the area of a circle is pi r^2 so you have to so some algebra.

5252 = pi r ^2

5252/pi = r^2

1671.76352 = r^2

sqrt(1671.76352) = r

r = 40.8872048

then you do the equation for the volume of a circle which is 4/3 pi r^3

4/3 pi (40.8872048)^3

4/3 pi 68353.7373

4/3 214739.599

286319.465

V = 286319.465 cm3

6 0

3 years ago

Find the quotient of n(x) = 6x^5y^7 and m(x) = 2x^3y

likoan [24]

Answer:

a. Yes

b. Yes

c. Yes

d. Degree 8

Step-by-step explanation:

a. Yes, n(x) is a polynomial of one single term (also called monomial) because it contains variables raised to positive integers.

b. Yes, m(x) is a polynomial of also one single term (also called monomial) because it contains variables raised to positive integers.

c. The quotient of n(x) / m(x) can be reduced to a polynomial of one single term as follows:

$\frac{n(x)}{m(x)} =\frac{6\,x^5\,y^7}{2\,x^3\,y} =3\,x^2\,y^6$

which as can be seen, also contains variables raised to positive integers.

d. The degree of the polynomial resultant is the addition of the powers of all variables present (x and y) which results in: 2 + 6 = 8

Therefore the degree of this polynomial is 8.

6 0

3 years ago

Decompose 5/15 and 8/12

AnnZ [28]

Answer:

Step-by-step explanation:

5/15 divided by 5 is equal to 1/3 and

8/12 divided by 2 is 4/6 divided by 2 is 2/3

You have to divide the numerator with the same number that you divide the denominator with.

6 0

2 years ago

What is the slope of the line? y + 5=2(x+1)

mel-nik [20]

Answer:

Step-by-step explanation:

So we have the equation:

$y+5=2(x+1)$

This is in the format point-slope form, where:

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

Here, m is the slope.

In our original equation, 2 replaces m.

Therefore, our slope is 2.

5 0

3 years ago

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