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3 years ago

Identify the terms and like terms in the expression. 10x2 – y + 12 - 3x2

Mathematics

1 answer:

Alexandra [31]3 years ago

6 0

Answer:

Terms: $10x^2, -y, 12\ and\ -3x^2$

Like Terms: $10x^2\ and\ -3x^2$

Step-by-step explanation:

Given

$10x^2 - y + 12 - 3x^2$

Required

List out the terms and like terms

The terms of a mathematical expression:

$a + b - c + d$ are a, b, c and d

Using the same yardstick as above;

The terms of $10x^2 - y + 12 - 3x^2$ are

$10x^2, -y, 12\ and\ -3x^2$

To get the like terms, we look for terms with the same variable

$10x^2\ and\ -3x^2$ have the same variable of x^2

Hence, they are like terms

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

2 years ago

Pls answer me this all question

Scorpion4ik [409]

Answer:

a. $5 \frac{21}{40}$

b. $\frac{1}{42}$

Step-by-step explanation:

$a. \: 12 \frac{2}{5} - 6 \frac{7}{8}$

$\frac{62}{5} - \frac{55}{8}$

$\frac{62}{8} \times \frac{8}{8} - \frac{55}{8} \times \frac{5}{5}$

$\frac{62 \times 8 - 55 \times 5}{40}$

$\frac{221}{40}$

$5 \frac{21}{40}$

$b. \: \frac{3}{14} - \frac{4}{21}$

$\frac{3}{14} \times \frac{3}{3} - \frac{4}{21} \times \frac{2}{2}$

$\frac{3 \times 3}{42} - \frac{4 \times 2}{42}$

$\frac{1}{42}$

Hope it is helpful....

5 0

2 years ago

Read 2 more answers

Surface area of solid figures

Lilit [14]

Answer:

C. 468mm²

Step-by-step explanation:

The formula for the surface area of rectangular prism is:

$A=2(wl+hl+hw)$

Let's break down our variables.

L = 12mm

W = 6mm

H = 7mm + 2mm = 9mm

Now we substitute our values in the formula:

$A=2((6)(12)+(9)(12)+(9)(6))$

$A=2(72+108+54)$

$A=2(234)$

$A=468mm^{2}$

6 0

2 years ago

Write the equation of a rational function g(x) with vertical asymptotes at x = -3 and x = 3 , a horizontal asymptote at y = -4 a

Bezzdna [24]

Answer:

The equation for rational function for given asymptotes is

f(x)=(-4x^2-6)/{(x-3)(x+3)}

Step-by-step explanation:

Given:

vertical Asymptotes at x=3 and x=-3 and a horizontal asymptote at

y=-4 i.e parallel to x axis.

To find:

equation of a rational function i.e function in form p/q

Solution;

the equation should be in form of p/q

Numerator :denominator.

Consider f(x)=g(x)/h(x)

as vertical asymptote are x=-3 and x=3

denominator becomes, (x-3) and (x+3)

for horizontal asymptote to exist there should have same degrees in numerator and denominator which of '2'

when g(x) will be degree '2' with -4 as coefficient and dont have any real.

zero.

By horizontal asymptote will be (-4x^2 -6)

The rational function is given by

f(x)=g(x)/h(x)

={(-4x^2-6)/(x-3)(x+3)}.

3 0

2 years ago

Rani, Anita, Jassi and Zoyz are each given a piece of wire of the same length. They bend the wire into different shapes as shown

LenKa [72]

Answer:

Saw this question before. The answer is Anita' square.

Square has only four sides while the others more than four so make sense for the square to have longer sides

3 0

2 years ago