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2 years ago

Write 14/√2 + √50 in the form b√2 where b is an integer.

Mathematics

2 answers:

fenix001 [56]2 years ago

6 0

Answer:

Step-by-step explanation:

14/√2 +√50= 14*√2/√2*√2+ √25*2= 7√2+5√2= 12√2

12√2= b√2

b=12

kifflom [539]2 years ago

3 0

Answer:

$12 \sqrt{2}$

Step-by-step explanation:

Taking the terms one at a time,

$\frac{14}{ \sqrt{2} } \\ \frac{14 * \sqrt{2} }{ \sqrt{2} * \sqrt{2} } \\ \frac{14 \sqrt{2} }{2} \\ 7 \sqrt{2}$

$\sqrt{50} \\ \sqrt{25 * 2} \\ \sqrt{25}* \sqrt{2} \\ 5 * \sqrt{2} \\ 5 \sqrt{2}$

Adding the terms, you have;

$7 \sqrt{2} + 5 \sqrt{2} =(7 + 5) \sqrt{2} = 12 \sqrt{2}$

Hope it helps!

I'm out!

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The equation of line f is y − 9 = -5(x + 7) . Line g is parallel to line f and passes through (3, -8) . What is the equation of

Kisachek [45]

Answer:

The slope intercept form: y = - 5x + 7

Step-by-step explanation:

The equation of line f is y − 9 = -5(x + 7)

You need to find the slope of line f

y - 9 = -5(x + 7)

In point slope form: y - y1 = m(x - x1) where m = slope

In the line f, slope m = -5

Parallel lines, slope is the same so slope of line g is also equal - 5

Line g passes through (3, - 8) so equation in point slope form:

y + 8 = -5(x - 3)

y + 8 = -5x + 15

y = -5x + 7 <-----this is slope intercept form

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3 years ago

The altitude of a triangle is 1cm shorter than the base. If the area of the triangle is 15cm2, calculate the altitude.

WITCHER [35]

Answer:

5 cm

Step-by-step explanation:

We khow that the altitude of this triangle is 1cm shorter than the base

Let H be our altitude and B our base and A the area of the triangle
A= (B*H)/2 ⇒ 15=(B*H)/2
H is 1cm shorter than B ⇒ B=H+1
H*(H+1)/2=15 ⇒ H*(H+1)=30⇒ H²+H=30⇒H²+H-30+0

that's a quadratic equation . Let's calculate the dicriminant .

Let Δ be the dicriminant

a=1
b=1
c= -30
Δ=b²-4*a*c = 1²-4*1*(-30)=1+4*30=121≥0
Δ≥0⇔ that we have two solutions x and y
x= (-1- $\sqrt{121}$ )/2= (-1-11)/2= -6
y= (-1+ $\sqrt{121}$ )/2= 10/2 = 5

We have a negative value and a positive one

The altitude is a distance so it can't be negative

H= 5cm

6 0

3 years ago

Need help for question 8 and 9. I need the equation that’s passes through the points!

dsp73

Answer:

Step-by-step explanation:

Question 8

Let the equation of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

y = mx + b

Here, m = slope and y-intercept = b

Since, m = $\frac{y_2-y_1}{x_2-x_1}$

For two points (1, 4) and (5, 8),

m = $\frac{8-4}{5-1}$

m = 1

Equation will be,

y = (1)x + b

y = x + b

Since, this line passes through (1, 4),

4 = 1 + b

b = 3

Therefore, equation of the line will be,

y = x + 3

Question 9

Let the equation is y = mx + b

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For two points (2, 10) and (6, 4)

m = $\frac{10-4}{2-6}$

m = $-\frac{3}{2}$

By substituting the value of 'm' in the equation,

y = $-\frac{3}{2}x+b$

Since, this line passes through (2, 10)

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3 years ago

A linear set of points with a unique starting point and extending infinitely in one direction what term matches the definition?

bija089 [108]

Answer:- Option A "ray" is the right term which matches with the definition.

Explanation:-

A ray is a line that has one fixed endpoint, and extends infinitely along the line from the fixed endpoint.

Therefore, the term which matches with the given definition is "ray".

Thus A linear set of points with a unique starting point and extending infinitely in one direction is called a ray.

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3 years ago

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What is the equation of the line that passes through the point (-4,8) and has a slope of -1/4

iragen [17]

Answer:

Step-by-step explanation:

When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.

It is given by:

$(y - y_1) = m (x - x_1)$

where $m$ is the slope of the line and

$(x_1, y_1)$ is the point passing through it.

Here, $m = \frac{-1}{4}$ and $(x_1,y_1) = (-4,8)$

Substituting in the equation:

$y - 8 = \frac{-1}{4} (x + 4)$

$\implies 4y - 32 = -x - 4$

$\implies x + 4y - 28 = 0$

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2 years ago