MATHEMATICS HIGH SCHOOL

Which value could be substituted for x in order to make the inequality true? 8 < x < 8.5

Answers

Answer 1
Answer:

Answer:

8 < 8.2 <8.5

Step-by-step explanation:

Pick a number that is greater than 8 but less than 8.5.

Ex: 8.1, 8.2, 8.3, 8.4

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Using zero product. let y = 0. y=2x^2 - 11x + 5
The urgency is real!!!

Answers

Simple...

the solution is the intersection of the graph with the x-axis.

x=5, (1)/(2)

Another way you can solve is by using the quadratic formula...

First, find a, b, c...

a=-2

b=11

c=-5

Then just plug it into your quadratic formula.

Thus, your answer.

What does ( 7.8 x 10 to the 3rd) x (1.0 x 10 to the 4th) equal?

Answers

Answer:

7.8 * 10^7

Step-by-step explanation:

Group coefficients together and exponents together to multiply numbers in scientific notation.

(7.8  *  1)  (10^3  * 10^4)

Multiply  7.8 times 1.

7.8 * (10^3 * 10^4)

Use the power rule  a^m * a^n = a^(m+n) to combine exponents. So, add 3 and 4

7.8 * 10^7

A sphere has a volume of 4500pi cubic inches. find the surface area of the sphere.

Answers

V=(4 \pi r^3)/(3)\n \n 4500\pi=(4 \pi r^3)/(3)\n \n 13500 \pi=4 \pi r^3\n \n r^3=(13500 \pi)/(4 \pi)\n \n r^3=3375 \n \n \boxed{r=15 in}

S=4 \pi r^2\n \n S=4 \pi 15^2\n \n \boxed{S=900 \pi \ in^2}
Cube : \ V=4500 \ \pi \ in^3\n\nV=(4)/(3)\pi r^3 \n \n4500 \pi =(4)/(3)\pi r^3 \ \ / \cdot ((3)/(4\pi))\n \n(3)/(4\pi)\cdot 4500 \pi =(3)/(4\pi)\cdot (4)/(3) \pi r^3\n \nr^3 =3*1125

r^3 = 3375 \n\nr=\sqrt[3]{3375}\n \nr=15 \ in \n \n the \ surface \ area : \n\nSA = 4 \pi r^2 \n \nSA=4 \pi \cdot 15^2 = 4\cdot 225 \pi = 900 \pi \ in^2
 

Ax+by=1
bx-ay=a+b
solve in linear equation in 2 variables

Answers

\left\{\begin{array}{ccc}ax+by=1&/\cdot a\nbx-ay=a+b&/\cdot b\end{array}\right\n\n+\left\{\begin{array}{ccc}a^2x+aby=a\nb^2x-aby=ab+b^2\end{array}\right\n------------\n.\ \ \ \ \ a^2x+b^2x=a+ab+b^2\n.\ \ \ \ \ \ (a^2+b^2)x=a+ab+b^2\n.\ \ \ \ \ \ \ \ \ \ \ \ x=(a+ab+b^2)/(a^2+b^2)\n\na\cdot(a+ab+b^2)/(a^2+b^2)+by=1\n\n(a^2+a^2b+ab^2)/(a^2+b^2)+by=1\n\nby=1-(a^2+a^2b+ab^2)/(a^2+b^2)

by=(a^2+b^2)/(a^2+b^2)-(a^2+a^2b+ab^2)/(a^2+b^2)\n\nby=(a^2+b^2-a^2-a^2b-ab^2)/(a^2+b^2)\n\nby=(b^2-a^2b-ab^2)/(a^2+b^2)\n\ny=(b^2-a^2b-ab^2)/(a^2b+b^3)

y=(b(b-a^2-ab))/(b(a^2+b^2))\n\ny=(b-a^2-ab)/(a^2+b^2)\n\nAnswer:\n\nx=(a+ab+b^2)/(a^2+b^2)\ and\ y=(b-a^2-ab)/(a^2+b^2)
ax+by=1
bx-ay=a+b
The solution in attached file

What’s the triangle congruence shortcut

Answers

Answer:

Side-Side-Side [SSS]

Step-by-step explanation:

You know this since the little bars sticking outside of the triangle show that those 2 lines are congruent. Then you know of one line being the same for both, so you then know all of the sides. And since all of the side lengths are equal, this triangle is congruent by Side-Side-Side.

D) Vivek is 30 years younger than his father. After 10 years their ages will be in the ratio 1:2. Find their present ages.​

Answers

Answer:

I think Vivek is 20 and his father is 50

Because 30 + 30 equals 60 as he has to be half his age he'll be 30 but that's in 10 years time. you just subtract 30 and 60 by 10 and you'll get 20 and 50

Answer:

Vivek:20 years

Father:50 years

Step-by-step explanation:

Since it is a age question, their difference do not change, so

2-1=1 (difference in ratio)

1u=30

Vivek now:30-10=20 years

Father: 30x2=60

60-10=50 years

Hope this helps! Thanks.
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