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3 years ago

14

Find the slope of the line containing the given pair of points. If the slope is undefined state this. (-5,9) and (2,3) can someo

ne please help me solve this and if all possible show me your work

2 answers:

zavuch27 [327]3 years ago

6 0

Slope between (x1,y1) and (x2,y2) is
(y1-y2)/(x1-x2)

given
(-5,9) and (2,3)
(x,y)
x1=-5
y1=9
x2=2
y2=3

slope=(9-3)/(-5-2)=6/-7=-6/7

slope=-6/7

cricket20 [7]3 years ago

4 0

Slope equals y1-y2/x1-x2 so 9-3/-5-2 = -6/7

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Find the next three terms in the pattern 9,4,-1,-6,-11 then describe the pattern

Yanka [14]

You would be subtracting by 5 so the next three would be -16, -21, -26

6 0

3 years ago

ANSWER ASAP The ratio of red marbles to blue marbles in a jar is 3 to 8. There are 40 blue marbles in the jar. How many red marb

bogdanovich [222]

If the ratio of red marbles to blue marbles in a jar is 3 to 8, the meaning is for every 3 red marbles there are 8 blue marbles.
3 red marbles------------------8 blue marbles.

ratio=3/8

we have 40 blue marbles; we have to compute the number of red marbles.

1) Method 1; by the rule three.

3 red marbles-----------------8 blue marbles
x----------------------------------40 blue marbles

x=(3 red marbles * 40 blue marbles) / 8 blue marbles=15 red marbles.

answer: B. 15

Method 2: the ratio of red marbles to blue marbles is
ratio=number of red marbles / number of blue marbles
ratio=3/8

if we want to compute the number of red marbles we have to multiply the number of blue marbles by this ratio.

number of red marbles=ratio (red/blue)* number of blue marbles
number of red marbles=(3/8)*40=15

Answer: B.15

5 0

3 years ago

Margaret [11]

Use long subtraction to evaluate.
$418.51

3 0

3 years ago

Convert,the complex number into polar form: 4+4i

kow [346]

Z = a + bi
z = 4 + 4i

r² = a² + b²
r² = (4)² + (4)²
r² = 16 + 16
r² = 32
r = 4√(2)
r = 4(1.414)
r = 5.656

$cos\theta = \frac{a}{r}$
$cos\theta = \frac{4}{4\sqrt{2}}$
$cos\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$cos\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
$cos\theta = \frac{4\sqrt{2}}{4(2)}$
$cos\theta = \frac{4\sqrt{2}}{8}$
$cos\theta = \frac{\sqrt{2}}{2}$
$2(cos\theta) = 2(\frac{\sqrt{2}}{2})$
$2cos\theta = \sqrt{2}$
$2cos\theta = 1.414$

$sin\theta = \frac{b}{r}$
$sin\theta = \frac{4}{4\sqrt{2}}$
$sin\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$sin\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
$sin\theta = \frac{4\sqrt{2}}{4(2)}$
$sin\theta = \frac{4\sqrt{2}}{8}$
$sin\theta = \frac{\sqrt{2}}{2}$
$2(sin\theta) = 2(\frac{\sqrt{2}}{2})$
$2sin\theta = \sqrt{2}$
$2sin\theta = 1.414$

z = a + bi
z = rcosθ + (rsinθ)i
z = r(cosθ + i sinθ)

z = 4 + 4i
z = 5.656cosθ + (5.656sinθ)i
z = 5.656(cosθ + i sinθ)
z = 5.656(cos45 + i sin45)

$\theta = tan^{-1}\frac{b}{a}$
$\theta = tan^{-1}\frac{4}{4}$
$\theta = tan^{-1}(1)$
$\theta = 45$

The polar form of 4 + 4i is approximately equal to 5.656(cos45 + i sin45).

5 0

3 years ago

Solve for x in the equation x2 - 4x-9 = 29.

erastova [34]

Answer:

$x=2+\sqrt{21}\\\\x=2-\sqrt{21}$

Step-by-step explanation:

One is given the following equation;

$x^2-4x-9=29$

The problem asks one to find the roots of the equation. The roots of a quadratic equation are the (x-coordinate) of the points where the graph of the equation intersects the x-axis. In essence, the zeros of the equation, these values can be found using the quadratic formula. In order to do this, one has to ensure that one side of the equation is solved for (0) and in standard form. This can be done with inverse operations;

$x^2-4x-9=29$

$x^2-4x-38=0$

This equation is now in standard form. The standard form of a quadratic equation complies with the following format;

$ax^2+bx+c$

The quadratic formula uses the coefficients of the quadratic equation to find the zeros this equation is as follows,

$\frac{-b(+-)\sqrt{b^2-4ac}}{2a}$

Substitute the coefficients of the given equation in and solve for the roots;

$\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}$

Simplify,

$\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}\\\\=\frac{4(+-)\sqrt{16+152}}{2}\\\\=\frac{4(+-)\sqrt{168}}{2}\\\\=\frac{4(+-)2\sqrt{21}}{2}\\\\=2(+-)\sqrt{21}$

Therefore, the following statement can be made;

$x=2+\sqrt{21}\\\\x=2-\sqrt{21}$

8 0

3 years ago