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Questions in mathematics

[Open]Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

[Open]Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

[Open]What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

[Open]The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

[Open]If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]

[Open]Use the distributive property to write an equivalent expression. $7(q-4 r+1)$

[Open]Simplify completely. $(r s)^{-2}(2 s)^3(2 r)^3$

[Open]A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. Let $y$ = quarts of water left in the tub and $t$ = time in minutes. | Time (t) | Quarts of water (y) | |---|---| | 0 | 50 | | 2 | 45 | | 4 | 40 | Choose the correct answers. Which equation models the relationship? Is there a viable solution when time is 30 minutes?

[Open]The degree of the polynomial [tex]10 x^2+2 x^m y-4 y[/tex] is 3. What is the value of [tex]m[/tex]?

[Open]Write down the number of parts of a nest that has exactly the same size. (2) Determine the width of the small nest to the width of the large nest as a ratio in its simplest form. ( Calculate the selling price per breeding pair if the input cost is $R 95,00$. Select the step from column B to match the correct assembly instruction of the Budgie nest in column A.