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Questions in mathematics

[Jawaban] The derivation for the equation of a parabola with a vertex at the origin is started below. [tex]\sqrt{(x-0)^2+(y-p)^2}=\sqrt{(x-x)^2+(y-(-p))^2}[/tex] 1. [tex](x)^2+(y-p)^2=(0)^2+(y+p)^2[/tex] 2. [tex]x^2+y^2-2 p y+p^2=y^2+2 p y+p^2[/tex] If the equation is further simplified, which equation for a parabola does it become? A. [tex]x^2=4 p y[/tex] B. [tex]x^2=2 y^2+2 p^2[/tex] C. [tex]y^2=4 p x[/tex] D. [tex]y^2=4 p y[/tex]

[Jawaban] Which reflection will produce an image of [tex]$\triangle RST$[/tex] with a vertex at (2,-3)? A. a reflection of [tex]$\triangle RST$[/tex] across the x-axis B. a reflection of [tex]$\triangle RST$[/tex] across the y-axis C. a reflection of [tex]$\triangle RST$[/tex] across the line y=x D. a reflection of [tex]$\Delta$[/tex]RST across the line y=-x

[Jawaban] Paper clips are sold in boxes of 1000. Each box costs £15.40. The table below shows the discount offered for large orders. | Total order | Discount | | :---------- | :------- | | £40-£54.99 | 5% | | £55-£79.99 | 6.5% | | £80 and above | 8% | Ethan orders 5 boxes of paper clips. Work out the amount of discount Ethan gets.

[Jawaban] Using the product and power properties of logarithms, expand $\ln \left(x^6 y^3\right)$. A. $6 \ln x-3 \ln y$ B. $6 \ln x+3 \ln y$ C. $3 \ln x+6 \ln y$ D. $18(\ln x+\ln y)$

[Jawaban] Which equation represents a line which is perpendicular to the line [tex]$3 x-8 y=-16$[/tex]? A. [tex]$y=\frac{8}{3} x+8$[/tex] B. [tex]$y=-\frac{3}{8} x+1$[/tex] C. [tex]$y=\frac{3}{8} x-4$[/tex] D. [tex]$y=-\frac{8}{3} x-2$[/tex]

[Jawaban] What is the exponential regression equation that fits these data? | x | y | |---|---| | 1 | 3 | | 2 | 8 | | 3 | 27 | | 4 | 85 | | 5 | 240 | | 6 | 570 | A. [tex]$y=102.54 x-203.4$[/tex] B. [tex]$y=2.93(1.03^x)$[/tex] C. [tex]$y=1.03(2.93^x)$[/tex]

[Jawaban] Which table represents the graph of a logarithmic function in the form [tex]y=\log _8 x[/tex] when [tex]b>1[/tex]? | x | y | |---|---| |$\frac{1}{8}$ | -3 | |$\frac{1}{4}$ | -2 | |$\frac{1}{2}$ | -1 | | 1 | 0 | | 2 | 1 | | x | y | |-1.9 | -2.096 | |-1.75 | -1.262 |

[Jawaban] A projectile is fired straight up from ground level with an initial velocity of $112 ft / s$. Its height, $h$, above the ground after $t$ seconds is given by $h=-16 t^2+112 t$. What is the interval of time during which the projectile's height exceeds 192 feet? A. $3 B. $3>t>4$ C. $t<4$ D. $t>4$

[Jawaban] Can you describe the distinguishing features of convex and non-convex polygons? How do these features affect the shapes and properties of each type of polygon?

[Jawaban] 1. Nadia is collecting stickers. On Monday, she got 1,245 stickers. On Tuesday, she collected 2,367 stickers. On Wednesday, she found another 1,789 stickers. How many stickers does Emma have in total after three days? 2. Aleena has 8,432 stickers in her collection. She decided to give 3,758 stickers to her friends. How many stickers does Emma have left? 3. Sarah is planting flowers in her garden. She wants to plant 8 rows of flowers, and each row will have about 15 flowers. About how many flowers will Sarah plant in total?