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2 years ago

Which ordered pair is a solution of the equation?

Mathematics

1 answer:

levacccp [35]2 years ago

6 0

Step-by-step explanation:

both (1,11)and (_1,_5)

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What is the slope of the line shown below.

rusak2 [61]

slope = (y2-y1)/(x2-x1)

(2,4) (4,8)

m= (8-4)/(4-2)

m = 4/2

m=2

Answer: 2

8 0

2 years ago

Read 2 more answers

Of the 200 packages of bagels sold 15 of them were sesame seed bagels. What percent of the bagel packages sold are sesame seed b

Paladinen [302]

Answer:

.015%

Step-by-step explanation:

Hope it helps

~CoCo

6 0

2 years ago

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How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

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

3 0

4 months ago

The Green Corporation has 10,000 square feet of tile in their warehouse. Each day of manufacturing adds 1,250 square feet of til

Brut [27]

Answer:

8 days

Step-by-step explanation:

20,000-10,000=10,000

10,000/1,250= 8

so it would take 8 days

5 0

2 years ago

1. A heterozygous white-fruited squash plant is crossed with a yellow-fruited plant, yielding 200 seeds. of these seeds, 110 pro

garri49 [273]

Answer:

Part 1 , not significant

Part II, significant

Step-by-step explanation:

Given that a heterozygous white-fruited squash plant is crossed with a yellow-fruited plant, yielding 200 seeds. of these seeds, 110 produce white-fruited plants while only 90 produce yellow-fruited plants

$H_0: Both colours are equally likely\\H_a: Both colours are not equally likely$

(Two tailed chi square test)

We assume H0 to be true and find out expected

If H0 is true expected would be 100 white and 100 yellow

Chi square = $\Sigma \frac{(O-E)^2}{E} \\=\frac{(110-100)^2}{100} +frac{(90-100)^2}{100} \\=2$

df = 1

p value = 0.152799

Since p value > 0.05 at 5% level we accept that the colours are equally likely

Here observed are 1100 and 900

Expected 1000 & 1000

df = 1

Chi square = $\frac{20000}{100} =200$

p value <0.0001

These results are here statistically significant.

8 0

2 years ago