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4 years ago

Pls help and show work

Mathematics

1 answer:

Artist 52 [7]4 years ago

5 0

2 since it ends with two
6 since it is divisible by 2
3 since their sum gives a number divisible by three
3 since their sum gives a number divisible by 3
3
5 since it ends with 5
5
2
2

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Find all points on the x-axis that are 14 units from the point (6,-7) All points on the x-axis that are 14 units from the point

Maksim231197 [3]

Answer: $(6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)$ are the required points.

or (18.124,0) and ( -6.124,0) are the required points.

Step-by-step explanation:

Let (x,0) be the point on x -axis that are 14 units from the point (6,-7) .

Then by distance formula , we have

$\sqrt{(x-6)^2+(0-(-7))^2}=14\ \ \ [\ \because distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}]$

Taking square on both the sides , we get

$(x-6)^2+7^2=14^2\\\\\Rightarrow\ x^2+6^2-2(6)x+49=196\\\\\Rightarrow\ x^2+36-12x=147\\\\\Rightarrow\ x^2-12x=111\\\\\Rightarrow\ x^2-12x-111=0$

Using quadratic formula : $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{12\pm\sqrt{(-12)^2-4(1)(-111)}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{144+444}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{588}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm\sqrt{2^2\times7^2\times3}}{2}\\\\\Rightarrow\ x=\dfrac{12\pm14\sqrt{3}}{2}\\\\\Rightarrow\ x=6\pm7\sqrt{3}$

so, $(6+7\sqrt{3},0)\text{ and }(6-7\sqrt{3},0)$ are the required points.

since $\sqrt{3}=1.732$

so, $(6+7(1.732),0)\text{ and }(6-7(1.732),0)$ are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

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3 years ago

Which of the following equations is nonlinear?

Mice21 [21]

Answer:

D)y=5x³ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌

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3 years ago

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What represent the relationship between the total mass of a crate

sineoko [7]

9514 1404 393

Answer:

(a) M = 0.25n +100

Step-by-step explanation:

The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).

The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...

slope = rise/run = 25/100 kg/CD = 0.25

Then the equation describing the points on the graph will be ...

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3 years ago

Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

hammer [34]

Answer: option d.

Step-by-step explanation:

If y varies directly as x and z, the form of the equation is:

$y=kxz$

Where k is the constant of variation.

If y=4 when x=6 and z=1 then substitute these values into the expression and solve for k:

$4=k(6)(1)\\4=6k\\k=\frac{4}{6}\\\\k=\frac{2}{3}$

Substitute the value of k into the expression. Then, the equation is:

$y=\frac{2}{3}xz$

To find the value of y when x=7 and z=4, you must substute these values into the equation. Therefore you obtain:

$y=k=\frac{2}{3}(7)(4)$

$y(7,4)=\frac{56}{3}$

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3 years ago

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State the slope of the line. A:undefined B:1 C:-2 D:0 Help ASAP

Nikitich [7]

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slope = rise/run = 0/2 = 0

The slope is 0

Answer: D) 0

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3 years ago

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