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2 years ago

The sum of two prime numbers is 85. What is the product of these two prime numbers?

1 answer:

8 0

Prime numbers are numbers that can only be evenly divided into 1 and itself.

Sum= add

so, 83 and 2 are the prime numbers.
83 + 2= 85

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Hurrrryyyyy plllzzz. Determine the equation of the line that passes through the given points

pashok25 [27]

<h2>Answer:</h2>

y = 2

<h2>Step-by-step explanation:</h2>

To determine the equation of the line that passes through (10,2) and (-3,2), we need to determine the slope of the line. Then substitute the slope and any given point in point slope form to obtain the equation of the line.

<h3>Finding the Slope of the line:</h3>

$\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }$

$\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }$

<u>Substitute the coordinates of the given points:</u>

$\implies \text{Slope} = \dfrac{2 - 2}{-3 - 10 }$

<u>Simplify the equation to determine the slope:</u>

$\implies \text{Slope} = \dfrac{0}{-3 - 10 }$

∴ 0 divided by ANY number is ALWAYS 0.

$\implies \text{Slope} =0$

<h3>Finding the equation of the line:</h3>

Point slope form formula: y - y₁ = m(x - x₁)

x₁ and y₁ are the coordinates of any given point.
m is the slope

<u>Substitute the values in the point slope form:</u>

$\implies \text{Equation of line:} \ y - y_{1} = m(x - x_{1} )$

$\implies \text{Equation of line:} \ y - 2 = 0(x - 10)$

<u>Simplify the equation to determine the equation of the line:</u>

∴ Any number multiplied by 0 is 0.

$\implies \text{Equation of line:} \ y - 2 = 0$

$\implies \text{Equation of line:} \ y = 0 + 2$

$\implies \text{Equation of line:} \ y = 2$

Thus, the equation of the line is y = 2.

5 0

2 years ago

Stephanie had a total of 80 pieces of $ 2 and $ 10 notes. After spending 2/5 of her $ 2 notes and 8 pieces of her $ 10 notes, sh

Ghella [55]

Answer:

$440

Step-by-step explanation:

notes $2 - n

notes $10 - m

n + m = 80 ----------> m = 80 - n

1 - 2/5 = 3/5

$\frac{3}{5} * n = m - 8$

$\frac{3}{5} * n = 80 - n - 8 \\\\\frac{3}{5} * n + n = 72\\\\\frac{8}{5} * n = 72\\n = 45 \\m = 35\\$

45 * $2 + 35 * $10 = 90 + 350 = $440

3 0

2 years ago

Can someone help me with this question please

postnew [5]

Answer:

which ones do you need??

7 0

3 years ago

Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marb

Umnica [9.8K]

Answer:

It would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.

Since

$z = ax^2 + by^2$

For this case, the gradient of your function would be

$\nabla z = (2ax , 2by)$

And -1 times the gradient of your function would be

$-\nabla z = (-2ax , -2by)\\$

Then, at

$(1,1,a+b),\\x = 1 \\y = 1$

So it would go towards

$v = (-2a,-2b)$

The magnitud of that vector is

$|v| = 2\sqrt{a^2+b^2}$

and to conclude it would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

6 0

2 years ago

I need answers for Question 1 and 2

Xelga [282]

Answer: The answer to your first question would be A. 1. This is simply because anything raised to the power of 0 is 1 no matter what. The answer to your second question would be B. 1, for the same reason as above, anything to the power of 0 is 1. Hope this helped and make sure to remember that rule, it is important and easy to remember!

4 0

2 years ago