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3 years ago

Chi has $11:30 in dimes and quarters. The number of dimes is three more

Mathematics

1 answer:

Oliga [24]3 years ago

6 0

Answer:

To solve this question, we first have to know that we are trying to assemble

and solve equations with two variables: x

and y.

Assuming x

is the number of dimes and y

is the number of quarters, we

can assemble the equations.

since the number of dimes is 3 more than three times the number of quarters,

we get x=3y+3.

Additionally, multiplying the number of dimes by 0.1 and the number of

quarters by 0.25,

we get the total value of x

and y

which appears by this

equation 0.1x+0.25y=11.30

Substituting the value of x

in the second equation, we get 0.1(3y+3)+

0.25y=11.30

Solving this equation, we get that the value of x,

we get x=3×20+3=

Using the first equation to get the value of x,

we get x=3×20+3=

60+3=63

dimes.

Chapter 9

Math Models and Geometry

Section 2

Solve Money Applications

Prealgebra

Step-by-step explanation:

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Identify all factors of the expression 〖4x〗^2+17x-15.

Basile [38]

The factors of given expression are: -5 and 3/4

Step-by-step explanation:

Given equation is:

$4x^2+17x-15$

Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15

$4x^2+20x-3x-15$

$= 4x(x+5) - 3(x+5)$

$=(4x-3)(x+5)$

Now

$4x-3 = 0\\4x = 3\\x = \frac{3}{4}$

$x+5 = 0\\x = -5$

Hence,

The factors of given expression are: -5 and 3/4

Keywords: Quadratic equation, factors

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3 years ago

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valentinak56 [21]

Answer:

$\dfrac{3x+4}{2x-2}$

Step-by-step explanation:

Invert and multiply the way you would any fraction division problem. Then cancel common factors from numerator and denominator.

$\displaystyle\frac{\left(\frac{4x^2+2x}{x^2+x-2}\right)}{\left(\frac{8x^2+4x}{3x^2+10x+8}\right)}=\frac{4x^2+2x}{x^2+x-2}\cdot\frac{3x^2+10x+8}{8x^2+4x}\\\\=\frac{2x(2x+1)(3x+4)(x+2)}{4x(2x+1)(x-1)(x+2)}=\frac{3x+4}{2(x-1)}\\\\=\frac{3x+4}{2x-2}$

4 0

3 years ago

Evaluate the surface integral. S xz ds, s is the part of the plane 2x 2y z = 4 that lies in the first octant

maksim [4K]

The value of the given surface integral is 4.

The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.

$S(u,v)=(1-u)((1-u)(2,0,0)+u(0,2,0)+u(4,0,0)\\S(u,v)=(2(1-u)(1-v),2u(1-v),4v)$

<h3>What is the surface integral?</h3>

A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.

with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to

$ds=\||\:\left(s_u\times \:\:S_v\right)||dudv=12\left(1-v\right)dudv$