MATHEMATICS MIDDLE SCHOOL

Can someone please help me

Answers

Answer 1

Answer: You would add 50% of 8, which is 4,
then add 8+4 to get 12.
Bianca will be 12

Answer 2

Answer: The answer is 12 years old

x > 5

Step-by-step explanation:

We know:

If a, band care length of sides of a triangle, then

a + b > c

a + c > b

b + c > a

We have a = x, b = x, c = 10.

Substitute:

x + x > 10

2x > 10 divide both sides by 2

2x : 2 > 10 : 2

x > 5

Find the cube root of 2^6*3^6*5^3

Answers

Answer:

180

Step-by-step explanation:

Given that :

2^6*3^6*5^3

To Find :

The cube root of 2^6*3^6*5^3

Solution :

First of all let clear this term,

$\bigstar$ Cube root :

Cube root is the number which produces a given number when cubed.

Now,

Your Answer :

$\sf \n \n\implies 2^6*3^6*5^3= 2^6* 3^6*5^3\n \n\implies 64* 729* 125\n \n \implies 5832000\n \n \bigstar\textbf{Cube root of 5832000= 180}$

Answer:

180

Step-by-step explanation:

2^6*3^6*5^3= 2⁶× 3⁶×5³

=64×729×125

=5832000

cube root of 5832000= 180

Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find the value of x.

Answers

Answer:

x=4

Step-by-step explanation:

Step 1:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

$AC^2 = AB^2 + BC^2$

step 2:-

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

$(a + b)^2 = a^2 +2ab+b^2$

289 = 4x^2 +9(x^2+2x+1)

$13x^2 +18x-280 = 0$

finding factors 70 X 52 = 3640

$13x^2 +70x-52x-280 = 0$

$13x^2 -52x+ 70x-280 = 0$

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and $13x =-70$

x=4 and $x=(-70)/(13)$

we can not choose negative value so x value is 4

Final answer:- x = 4

verification:-

$AC^2 = AB^2 + BC^2$

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

Answer:

x = 4

Step-by-step explanation:

The length of two legs of a right angle triangle are 2x and 3(x+1).

The length of longest side is 17 units. It means measure of hypotenuse is 17 units.

According to the pythagoras theorem,

$leg_1^2+leg_2^2=hypotenuse^2$

$(2x)^2+(3(x+1))^2=(17)^2$

$4x^2+9(x^2+2x+1)=289$

$4x^2+9x^2+18x+9=289$

$13x^2+18x-280=0$

On splitting the middle terms we get

$13x^2+70x-52x-280=0$

$x(13x+70)-4(13x+70)=0$

$(13x+70)(x-4)=0$

Using zero product property we get

$13x+70=0\Rightarrow x=-(70)/(13)$

$x-4=0\Rightarrow x=4$

The value of x can not be a negaive number, because for negative value of x the value of 2x is negative and side can not be negative.

Therefore, the value of x is 4.

Write an equation of a line whose slope is 10 and y-intercept is (0,-20)(0,−20)

Answers

y = 10x - 20
................................

y = 10x - 20Hope this helps

5/4 gallons of water fill 5/6 of a bucket how many gallons of water fill the entire bucket

Answers

Answer:

$(3)/(2)$ gallons

Step-by-step explanation:

If $(5)/(4)$ gallons fill $(5)/(6)$ of a bucket.

Then we can write the ratio;

$(5)/(4):(5)/(6)$

Let $x$ gallons fill the entire bucket which is equivalent to $1$ .

Then we can again write the ratio;

$x:1$

We can write the following equation of proportion to solve for $x$ .

$(5)/(4):(5)/(6)=x:1$

This implies that;

$((5)/(4) )/((5)/(6) )=(x)/(1)$

We simplify to get;

$(5)/(4)* (6)/(5) }=x$

$x=(6)/(4) =(3)/(2)$

Therefore $(3)/(2)$ gallons will fill the entire bucket

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