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2 years ago

16. Find the length of x.

Mathematics

2 answers:

otez555 [7]2 years ago

7 0

Answer:

Step-by-step explanation:

If two chords intersect inside a circle, then

DE * BE =AE * CE

10*x = 8*6

10x = 48

x = 48/10

x = 4.8

dimaraw [331]2 years ago

5 0

$\: \sf \: DE \times BE =AE \times CE \\ \\ \sf10 \times x = 8 \times 6 \\ \\ \sf10x = 48 \\ \\ \sf \: x = \dfrac{48}{10} \\ \\ \sf \: x = \cancel\dfrac{48}{10} \\ \\ \sf \red{x = 4.8}$

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Please help!! What is the solution to the quadratic inequality? 6x2≥10+11x

fredd [130]

Answer:

The solution of the inequation $6\cdot x^{2} \geq 10 + 11\cdot x$ is $\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)$ .

Step-by-step explanation:

First of all, let simplify and factorize the resulting polynomial:

$6\cdot x^{2} \geq 10 + 11\cdot x$

$6\cdot x^{2}-11\cdot x -10 \geq 0$

$6\cdot \left(x^{2}-\frac{11}{6}\cdot x -\frac{10}{6} \right)\geq 0$

Roots are found by Quadratic Formula:

$r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}$

$r_{1} = \frac{5}{2}$ and $r_{2} = -\frac{2}{3}$

Then, the factorized form of the inequation is:

$6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0$

By Real Algebra, there are two condition that fulfill the inequation:

a) $x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0$

$x \geq \frac{5}{2}\,\wedge\,x \geq-\frac{2}{3}$

$x \geq \frac{5}{2}$

b) $x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0$

$x \leq \frac{5}{2}\,\wedge\,x\leq-\frac{2}{3}$

$x\leq -\frac{2}{3}$

The solution of the inequation $6\cdot x^{2} \geq 10 + 11\cdot x$ is $\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)$ .

3 0

3 years ago

A snowball has a radius of 7cm. What is the volume of the snowball?

BabaBlast [244]

Answer:

The volume is 1436.8 $in^2$ .

Step-by-step explanation:

-To find the volume of a sphere, you need the formula:

$V = \frac{4}{3} \pi r^3$

-Use the radius for the formula:

$V = \frac{4}{3} \pi 7^3$

-Then, you solve:

$V = \frac{4}{3} \pi 7^3$

$V = \frac{4}{3}$ × $\pi$ × $7^3$

$V = \frac{4}{3} \pi$ × $343$

$V = \frac{1372}{3} \pi = 1436.755$

-Round the answer to the nearest tenth:

$V = 1436.8$

So, therefore the volume is 1436.8 $in^2$ .

7 0

3 years ago

I need help with this math problem

jenyasd209 [6]

Answer:

1:1.5 1 part lemon to 1.5 parts sugar

1.5 : 7 1.5 parts sugar to 7 parts water

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the equation of the line that passes through the point (-6,1) and has a slope of 1/6

anyanavicka [17]

Answer:y=1/6x+2

Step-by-step explanation:

Y=1/6x+b

Plug in (-6,1)

1=1/6(-6)+b

1=-1+b

Add 1 to both sides

1+1=b

2=b

Y=1/6x+2

8 0

3 years ago

I need help on these question ASAP!!!! This is Urgent

GarryVolchara [31]

Part 1: The equation of the line is $y=2x+1$

Part 2: The equation of the line in slope intercept form is $y=-3x-1$

Explanation:

Part 1: It is given that the point A is $(1,3)$ and the line B is $y=2 x-2$

To determine the line passing through the point A and parallel to line B, let us first determine the slope and y-intercept.

From the equation of line B, the slope is $m=2$

Substituting the point $(1,3)$ and $m=2$ in slope intercept form $y=mx+b$ , we have,

$3=2(1)+b$

$3=2+b$

$1=b$

Thus, the y-intercept is $b=1$

Let us substitute the values $m=2$ and $b=1$ in the slope intercept form $y=mx+b$ , we get,

$y=2x+1$

Thus, the equation of the line passing though point A and parallel to line B is $y=2x+1$

Part 2: The given two coordinates are $(-1,2)$ and $(1,-4)$

To determine the equation of line in slope intercept form, first we shall find the slope and y-intercept.

From the graph, we can see that the line touches the y-axis at -1.

Hence, the y-intercept is $b=-1$

The formula for slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the coordinates $(-1,2)$ and $(1,-4)$ , we have,

$m=\frac{-4-2}{1+1} =\frac{-6}{2} =-3$

Thus, the slope is $m=-3$

Substituting the values $b=-1$ and $m=-3$ in the slope intercept formula $y=mx+b$ , we get,

$y=-3x-1$

Thus, the equation of the line in slope intercept form is $y=-3x-1$

4 0

3 years ago