MATHEMATICS HIGH SCHOOL

Find the length of side xx in simplest radical form with a rational denominator.

Answers

Answer 1

Answer:

The length of side is √10/2

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a 45-90-45 so if the sides are x then the hypotenuse will be x√2

From the figure the hypotenuse of triangle is √5

SO equation it to x√2

We get √5=x√2

Divide both sides by √2

√5/√2=x

As the denominator should be a whole number we have to rationalize the denominator.

Multiply numerator and denominator with √2

√5/√2×√√2/√2

√10/2

Hence, the length of side is √10/2

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Answer 2

Answer:

Answer:

$(√(10) )/(2)$

Step-by-step explanation:

on a 45 - 45 - 90 triangle if the sides are x then the hypotenuse is x $√(2)$

so,

$√(5)$ = x $√(2)$ (Divide by $√(2)$ )

$(√(5) )/(√(2) )$ = x (rationalize the denominator)

$(√(5) )/(√(2) )$ · $(√(2) )/(√(2) )$ = $(√(10) )/(√(4) )$ = $(√(10) )/(2)$

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Assign two variables for each problem, and write the equations. Solve.In five years, Kate will be twice as old as Joey. Right now, Kate is 11 years older than Joey. How old is Joey right now?

I need two variables and two equations. And please solve it.

Answers

lets make k equal to Kate's age and j equal to Joey's age. If in 5 years Kate will be twice as old as Joe, you can write the equation k+5=2(j+5) and then simplify it to make it easier to work with.
k+5=2(j+5)
k+5=2j+10
k+5-2j=10
k-2j=5
since we know that right know Kate is 11 years older than Joey, you can write the equation k+j=11. Since you know have two equations with with the same variable, you can make a system of equations as fallows:
k-2j=5
k+j=11

Since you need to figure out how old Joey is, you need to somehow get k to cancel out. The easiest thing to do for this problem is to is multiply the top equation by -1 to get:
-k+2j=-5 (you have to add the bottom equation to the top equation)
k+j=11 (-k+k=0, 2j+j=3j, and -5+11=6)
Since k got canceled out, you are left with the equation 3j=6 which means j=2.
Therefore, Joey's current age is 2.

I hope this helps.

(4/3)d^2+5=2a). d= -2/3 or d= 2/3
b). d= -3/2 or d= 3/2
c). d= -36 or d=36
d). NO REAL SOLUTION

Answers

d. no real solution.

(4/3)d² + 5 = 2
(4/3)d² = 2 - 5
(4/3)d² = -3
d² = -3 / (4/3)
d² = -3 * 3/4
d² = -9 / 4
d = √-9 / √4
d = -3/2

Even though I got the value of d, when I substituted the value to the equation, the equation is not equal to 2.

I got 8 = 2. not equal. no real solution.

Explain: How could you use cubes to act out a problem

Answers

From breaking up the problems and sorting them out

to break the problem apart to make it easier to understand

What is the solution to the system of equations

Answers

Step-by-step explanation:

$5x + 3y = 13 \n 7x + 8y = - 16 \n 5x = 13 - 3y \n x = (13 - 3y)/(5) \n 7( (13 - 3y)/(5) ) + 8y = - 16 \n 18.2 - 4.2y + 8y = - 16 \n 3.8y = - 34.2 \n y = - 9 \n$

$x = (13 - 3( - 9))/(5) = (13 + 27)/(5) = (40)/(5) = 8 \n x = 8 \n y = - 9$

Match the sequence (term) with the correct type of sequence (definition).Match Term Definition
128, 32, 8, 2, ... A) Arithmetic, common difference is 5
1, 3, 9, 27, ... B) Arithmetic, common difference is -3
5, 10, 15, 20, ... C) Geometric, common ratio is 0.25
20, 17, 14, 11, ... D) Geometric, common ratio is 3

Answers

The correct answer among all the other choices is 20, 17, 14, 11, ... D) Geometric, common ratio is 3. This is the sequence (term) with the correct type of sequence (definition) among the examples given. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

What is the solution to the following system of equations?y = -x2 - 5x - 4
y = -x2 + 9x - 18 (2 points)

(-1, -10)
(1, -10)
(-1, 10)
(1, 10)

Answers

The answer is (1,-10)

You solve this by equating the two equations:
-x2 -5x -4 = -x2 +9x -18
-14x = -14
x =1

You then substitute 1 to either of the equations to find y:
y = -(1)2 -5(1) -4
y = -10

Therefore, the solution is (1,-10)

Answer:

It's B

Step-by-step explanation:

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Solve for X in 5x/10=2