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3 years ago

Mason plans to use a strategy to find the product of 32 * 250. Write a strategy Mason could use to find the product.

Mathematics

1 answer:

Romashka [77]3 years ago

5 0

I think Mason could use a calculator

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What 3 equations equal to 120

Elanso [62]

Answer: 119+1=120

121-1=120

60*2=120

Step-by-step explanation:

It is what it is

8 0

3 years ago

Read 2 more answers

What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

3 years ago

Kelso sold digital cameras on her website. She bought the cameras for $65 each and included 60% markup to get the selling price.

Butoxors [25]

Find 60% of 65 then add it to 65

0.6 x 65 = 39

now add it to 65:

39 + 65 = 104

They are selling them for 104$

6 0

3 years ago

kow [346]

Answer:

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 7)² + (y - 5)² = 16 ← is in standard form

with centre = (- 7, 5 ) and r = $\sqrt{16}$ = 4 → B

5 0

3 years ago

Hong is a software salesman. His base salary is $2500 , and he makes an additional $110 for every copy of Math is Fun he sells.

nalin [4]

Pn=? 2500 +110×22=4920

4 0

3 years ago