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3 years ago

Simplify. 10u -4u Please help

Mathematics

2 answers:

vovikov84 [41]3 years ago

8 0

Answer:

Step-by-step explanation:

The two terms 10u and 4u are like terms because they both carry the same variable (u) with the same degree (1). So, we can just subtract them as if they were normal numbers 10 - 4:

10u - 4u = 6u

Thus, the answer is 6u.

Hope this helps!

Morgarella [4.7K]3 years ago

8 0

Answer:

Step-by-step explanation:

10u - 4u

u(10 - 4)

u(6)

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Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

3 years ago

A dog won a race at the local fair by running 3 and one fourth miles in exactly 2 hours. At this constant rate, how long does i

Novosadov [1.4K]

Answer:

$\frac{4}{5}$ hour

Step-by-step explanation:

Let x represent time taken by dog to run the 1 and three tenths -mile state fair race.

We have been given that a dog won a race at the local fair by running 3 and one fourth miles in exactly 2 hours.

We will use proportions to solve our given problem as:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

We will equate both speeds as:

$\frac{1\frac{3}{10}}{x}=\frac{3\frac{1}{4}}{2}$

$\frac{\frac{13}{10}}{x}=\frac{\frac{13}{4}}{2}$

$\frac{13}{10\cdot x}=\frac{13}{4\cdot 2}$

Cross multiply:

$13\cdot 10\cdot x=13\cdot 4\cdot 2$

$10\cdot x=4\cdot 2$

$\frac{10\cdot x}{10}=\frac{4\cdot 2}{10}$

Therefore, it will take $\frac{4}{5}$ hour to complete $1\frac{3}{10}$ mile state fair race.

7 0

3 years ago

I need some tips and examples for subtracting integers. Appreciated!

Tcecarenko [31]

one tip:

Example: 4 - (-3)

it instantly becomes positive because the negatives are close to each other as shown.

hope that helps :)

5 0

3 years ago

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PLEASE ANSWER ME:

Natali [406]

Answer:

Q1=1 11/13 Q2= 1/4

Step-by-step explanation:

You estimate it to the nearest whole and from then on simplify it to the least possible.

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2 years ago

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A line has a slope of –5 and a y-intercept of (0, 3). What is the equation of the line that is perpendicular to the first line a

neonofarm [45]

Slope-intercept form:
y=mx+b
m=slope
b=y-intercept

Data of the first line:
m=-5
b=y-intercept=3 (y-intercept=it is the value of "y" when x=0)

y=-5x+3

A line perpendicular to the line y=mx+b will have the following slope:
m`=-1/m

Therefore: the line perpendicular to the line y=-5x+3 will have the following slope:
m´=-1/(-5)=1/5

Point-slope form of a line: we need a point (x₀,y₀) and the slope (m):
y-y₀=m(x-x₀)

We know, the slope (m=1/5) and we have a point (3,2) therefore:
y-y₀=m(x-x₀)
y-2=1/5(x-3) (point-slope form)
y-2=(1/5)x-3/5
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Answer: the line perpendicular to the first line will be: y=(1/5)x+7/5

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3 years ago

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