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2 years ago

In a sale, normal prices are reduced by 17%. The normal price of a washing machine is reduced by £42.50

Mathematics

1 answer:

Misha Larkins [42]2 years ago

8 0

Answer: The original price of washing machine is $250.

Step-by-step explanation:

Since we have given that

Rate of decline in normal prices = 17%

Amount of normal price reduced by = $42.50

Let the original price be x

According to question,

$\frac{17}{100}\times x=42.50\\\\x=\frac{100}{17}\times 42.50\\\\x=\$250$

Hence, The original price of washing machine is $250.

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X + y = –4<br> y = 3x + 16

babymother [125]

If
x+y=-4
y-3x=16 or we cn write as
x+y=-4
-3x+y=16
i multiply the first equation by 3
3x+3y=-12
-3x+ y=16
4y=4
y=1
x+1=-4
x=-5

6 0

2 years ago

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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

2 years ago

4. Stephanie breaks on average 1.5 pencils every school day. How many pencils can she expect to break in a week (5 days)?

olya-2409 [2.1K]

Answer:

7.5 pencils broken in a week (5 days).

Step-by-step explanation:

1.5 pencils broken a day

Now we just multiple this by 5 for each of the school day's.

1.5 pencils * 5 days = 7.5 pencils broken in a week.

Have a nice day! :)

Please mark this answer as brainiest!

7 0

2 years ago

Considera um quadrado de lado 2x e um rectângulo de comprimento x e largura x  2 . Qual é o valor de x para o qual as duas figu

ki77a [65]

Answer:

3 unidades de comprimento

Step-by-step explanation:

O perímetro é definido como a soma de todos os lados.

O perímetro de um quadrado de lado 2x é dado por:

$Q=4*2x=8x$

O perímetro de um retângulo de comprimento x e largura x² é dado por:

$R=2x+2x^2$

Para que ambos os perímetros sejam iguais:

$R=Q\\8x=2x+2x^2\\x^2=\frac{6}{2}x\\ x=3$

O valor de x é igual a 3 unidades de comprimento.

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2 years ago

A(n)=-6+3(n-1). Find the 16th term in the sequence

marshall27 [118]

Answer:

16th term = 39.

Step-by-step explanation:

Plug 16 into the formula -6 + 3(n - 1):

A(16) = -6 + 3(16-1)

= - 6 + 3*15

= -6 + 45

= 39.

6 0

2 years ago

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