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2 years ago

Simplify this expression 8n/17n

Mathematics

2 answers:

Olenka [21]2 years ago

7 0

Answer:

$\frac{8n^{2}}{17}$

Andrei [34K]2 years ago

4 0

hence it can be further simplified to 8/17 or 0.4

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Solve for c in the equation 32c = 128.

pishuonlain [190]

<u>Answer</u>

A. c = 4

<u>Explanation</u>

In algebra, what you do to one side of the equation, the same has to be done on the other side.

32c = 128

divide both sides by 32

32c = 128.

32c ÷ 32 = 128 ÷ 32

c = 128/32

= 4

7 0

2 years ago

Question 1

12345 [234]

Answer:

A). Surface area = 222 cm²

Volume = 180 cm³

B). Surface area = 375 cm²

Volume = 360 cm³

C). % increase in surface area = 67.57%

% increase in volume = 100%

Step-by-step explanation:

In the figure attached base of a prism has been given.

A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)

Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8

= 30

Area of the base = 8×5 - 2×2 = 36 cm²

Surface area of the prism = 30×5 + 2×(36)= 222 cm²

Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off

= 8×5×5 - 2×2×5

= 200 - 20

= 180 cm³

B). Surface area of the prism if it's height is 10 cm,

Surface area = 30×10 + 2×(36) = 372 cm²

Volume of the prism = 8×5×10 - 2×2×10

= 400 - 40

= 360 cm³

C). Increase in surface area = 372 - 222 = 150 cm²

% increase in the surface area = $\frac{150}{222}\times 100$ = 67.57%

Increase in volume = 360 - 180 = 180 cm³

% increase in volume = $\frac{180}{180}\times 100$ = 100%

4 0

2 years ago

Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial

Mariulka [41]

Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

b = -3

c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

-3/2 = - 3/2

LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

7 0

3 years ago

I’m confused on this one

GenaCL600 [577]

The slope of CD is

$m = \dfrac{6 - -4}{2 - 0} = 5$

The slope of the perpendicular bisector is the negative reciprocal,

$n = -1/m = - \dfrac 1 5$

The perpendicular bisector passes through M, the midpoint of CD

M =( (0+2)/2, (-4 + 6)/2) = (1, -1)

So point slope form for the perpendicular bisector is

$y - -1 = - \frac 1 5(x - 1)$

Solving for y gives slope intercept form.

$y = - \frac 1 5 x - \frac 4 5$

Not sure how to type that without spaces; we didn't have online homework back then.

Answer: y=(-1/5)x-4/5

3 0

3 years ago

Express 24 as a fraction of 60

seraphim [82]

Answer:

24/60 = 2/5

Step-by-step explanation:

24/60

Divide both the numerator and denominator by a common factor, 6

4/10

Divide both the numerator and denominator by a common factor, 2

2/5

7 0

3 years ago

Read 2 more answers