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3 years ago

Please help me out!!!!!!!!!!! :)

Mathematics

1 answer:

Harman [31]3 years ago

6 0

Answer:

y + 20 = 1(x + 10)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 10, - 20) and (x₂, y₂ ) = (1, - 9)

m = $\frac{-9+20}{1+10}$ = $\frac{11}{11}$ = 1

Using (a, b) = (- 10, - 20), then

y - (- 20) = 1 (x - (- 10)), that is

y + 20 = x + 10

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Barry bought 21 stamps from a hobby shop. he gave 3/7 of them to his sister, how many stamps did he have left?

Alex17521 [72]

He gave away 9 (20 x (3/7) =9) so 21-9=12

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3 years ago

Given: measure of angle KJ = 124°, measure of IC =38°<br><br> Find: m∠CQJ, m∠LIJ.

VLD [36.1K]

Answer:

Part 1) $m$

Part 2) $m$

Step-by-step explanation:

Part 1) Find the measure of angle CQJ

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite.

$m$

$arc\ IK+arc\ CJ=360\°-(arc\ IC+arc\ KJ)$

substitute the values

$arc\ IK+arc\ CJ=360\°-(38\°+124\°)=198\°$

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Part 2) Find the measure of angle LIJ

step 1

Find the measure of angle IJL

we know that

The inscribed angle is half that of the arc it comprises.

$m$

substitute the values

$m$

step 2

Find the measure of angle ILJ

we know that

The measurement of the external angle is the semi-difference of the arcs it encompasses.

$m$

substitute the values

$m$

step 3

Find the measure of angle LIJ

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

In the triangle LIJ

$m$

substitute the values

$m$

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3 years ago

Tami spins a spinner with seven sections. The sections are

tia_tia [17]

Answer:

Step-by-step explanation:

if all sides are equal and there are 7 sides than each side has and equal opportunity to be landed on.

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3 years ago

Read 2 more answers

one hose can fill a goldfish pond in 14 minutes, and the two hoses can fill the same pond in 10 minutes, find how long it takes

likoan [24]

Answer:

Step-by-step explanation:

$\frac{1}{14} +\frac{1}{t} =\frac{1}{10}$

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3 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

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3 years ago