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OlgaM077 [116]
3 years ago
14

How many pieces of carpet can be cut from the roll if each piece is 3/4 meter long

Mathematics
1 answer:
Mkey [24]3 years ago
7 0
3 meters is the same thing as 12/4 meters so divide 12/4 by 3/4 to get 4. 
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At an archeological site, the remains of two ancient step pyramids are congruent. If ABCD= EFGH find EF
Pani-rosa [81]

Answer:

EF = 44 ft

Step-by-step explanation:

Given that ABCD is congruent to EFGH, it follows that their corresponding lengths and angles would be congruent to each other.

This means, for the sides:

AB = EF,

BC = FG,

CD = GH

AD = EH.

Therefore, if AB = 44 ft, corresponding side, EF = 44 ft

4 0
2 years ago
Read 2 more answers
Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).
KonstantinChe [14]

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

2x^2-3x-6=0

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}

We have to find the value of (a+2)(b+2).

Putting the values:

(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4

3 0
3 years ago
Jamie took 7 maths tests and got a score of 68,71,71,84,53,62 and 67 .What was Jamie's mode score?
Taya2010 [7]
The modal score would be 71. 71 appears the most in the list.
6 0
2 years ago
Penny's garden has alength of 16ft. and the width is 5 ft. with a rectangular fountain in the middle that measures 5 ft by 9 ft.
lilavasa [31]

First we need the whole garden:

16 x 5 = 80

Now we need to fountain:

5 x 9 = 45

Now to find our answer:

80 - 45 = 35

So our answer is B. 35ft²

4 0
3 years ago
(a) The function k is defined by k(x)=f(x)g(x). Find k′(0).
Brut [27]

Answer:

(a) k'(0) = f'(0)g(0) + f(0)g'(0)

(b) m'(5) = \frac{f'(5)g(5) - f(5)g'(5)}{2g^{2}(5) }

Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e., \frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}

this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ m(x)=\frac{1}{2}\times\frac{f(x)}{g(x)} ]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows : \frac{\mathrm{d} \frac{f(x)}{g(x)}}{\mathrm{d} x}=\frac{\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}}{g^{2}(x)}

this will give <em>m'(x) = \frac{1}{2}\times\frac{f'(x)g(x) - f(x)g'(x)}{g^{2}(x) }</em>

on substituting the value x=5, we will get the value of m'(5).

{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}

{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }

{ NOTE : \frac{\mathrm{d} f(x)}{\mathrm{d} x}=f'(x) }

4 0
3 years ago
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