MATHEMATICS HIGH SCHOOL

Find the solution set of the following quadratic equations using the quadratic formula.1.) x^2 - 7x + 9 = 0
2.) 3x^2 + 10x = -3

Answers

Answer 1

Answer:

Answer:

1) $x_1=\frac{7+√(13)}2\,,\quad x_2=\frac{7-√(13)}2$

2) $x_1=-\frac13\,,\quad x_2=-3$

Step-by-step explanation:

1)

$x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\n\nx=(-b\pm√(b^2-4ac))/(2a)=(-(-7)\pm√((-7)^2-4\cdot1\cdot9))/(2\cdot1)=\frac{7\pm√(49-36)}2\n\nx_1=\frac{7+√(13)}2\,,\quad x_2=\frac{7-√(13)}2$

2)

$3x^2 + 10x=-3\n\n3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\n\nx=(-b\pm√(b^2-4ac))/(2a)=(-10\pm√(10^2-4\cdot3\cdot3))/(2\cdot3)= \frac{-10\pm√(100-36)}6\n\nx_1=\frac{-10+√(64)}6=\frac{-10+8}6=-\frac13\,,\qquad x_2=\frac{-10-8}6=-3$

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What set of reflections would carry triangle ABC onto itself? triangle ABC on the coordinate plane with point A at 1, 2, point B at 2, 4, and point C at 3, 0.

Answers

Your answer is Y-axis, X-axis, Y-axis, X-axis.
The A y-axis , B y-axis and C would also be reflected over the Y-axis. When you think about the coordinates on a graph, and with that also being said there all positive.

Answer:

y-axis, x-axis , y-axis and x-axis

Step-by-step explanation:

Given : In triangle ABC

The coordinates are

A = (1,2) , B=(2,4) and C =(3,0)

Rule of reflection:

*Reflecting a point (x, y) across the y-axis will map it to (-x, y).

*Reflecting a point (x, y) across the x-axis will map it to (x, -y).

If you do a reflection on coordinate point A = (1,2) across y-axis we get $(-1 ,2)$

then, reflecting a point (-1 , 2) across x -axis we get, (-1, -2)

then, reflecting a point (-1 , -2) across y-axis we get, (1 , -2)

and

reflecting a point (1, -2) across x- axis we get the result same i.e, A =(1,2)

Similarly,

For B = (2,4) across y-axis $\rightarrow$ (-2, 4) across x- axis $\rightarrow$ (-2, -4) across y -axis $\rightarrow$ (2 , -4) across x axis $\rightarrow$ ( 2, 4) = B

for C = (3, 0) across y-axis $\rightarrow$ (-3, 0) across x- axis $\rightarrow$ (-3, 0) across y -axis $\rightarrow$ (3 , 0) across x axis $\rightarrow$ (3, 0) = C

Therefore, the set of reflection would carry triangle ABC onto itself is:

y-axis, x-axis , y-axis and x-axis

Jordan takes 50% of the cherries from a bowl. then Mei takes 50%of the remaining cherries. Finally Greg takes 50 %of the remaining cherries. There are 3 cherries left. How many cherries were in the bowl before Jordan arrived

Answers

Answer:

Step-by-step explanation:

Let total cherries in a bowl=x

Jordan takes cherries=50% of x= $(50)/(100)x$

Remaining cherries= $x-(50)/(100)x=(50)/(100)x=(x)/(2)$

Mei takes cherries=50% of $(50x)/(100)=(x)/(4)$

Now, remaining cherries= $(x)/(2)-(x)/(4)=(x)/(4)$

Greg takes cherries=50% of $(x)/(4)=(x)/(8)$

Now, remaining cherries= $(x)/(4)-(x)/(8)=(x)/(8)$

Now,remaining cherries in a bowl=3

We have to find total cherries in a bowl before Jordan arrived.

According to question

$(x)/(8)=3$

$x=3* 8=24$

Hence, total cherries in a bowl=24

So in the final smallest bowl when half are removed there are 3 so the total amount was double 3 which is 6 before greg removed some.
Mei had removed half of the cherries which left 6 cherries so the total amount before Mei removed half was 12.
Jordan took half of the cherries which left 12. If you follow the same logic you double 12 which makes....
Good luck, hope this helped you understand the question more, feel free to comment and ask for help :)

F(x) = 3x + 9, g(x) = 5x2

Find (f + g)(x).

Answers

(f-g)(x) is a shorthand way of saying that you need to get the difference of the two functions: f(x) and g(x). so essentially, (f-g)(x) = f(x) - g(x) = 5x+2 - (-3x+4) = 8x-2 (f/g)(-2) = f(-2)/g(-2) = -4/5 or -0.8 Hope this helps.

If f(x) = x2 − 2x + 9 and g(x) = 8 − x, what is (f o g)(−4)?

Answers

I hope this helps you

How many different (non-conguerent) triangles have integer side lengths and perimeter 2014

Answers

Take all the possible triangles. That is, all triplets of numbers a,b,c that have a total sum of 2014 and obey the conditions: a<b+c;b<c+a;c<a+b. All triangles have been taken 3 times, so divide the count by 3.

Find the area of a sector with a central angle of 32° and a radius of 8.5 millimeters. Round to the nearest tenth.

Answers

You use the formula:
A = angles/360*pi*r^2
A = 32/360pi*8.5^2 = 0.279* 72.25= 20.15775 rounded to 20.2
I hope that this is the answer that you were looking for and it has helped you.

Answer:

The area of sector is 20.2 millimeter².

Step-by-step explanation:

The formula for area of sector is

$A=\pi r^2* ((\theta)/(360))$