Please help with these math questions

Answers

Answer 1

Answer: 1.
a^2+b^2=c^2
easy
a=a
b=13
c=21
a^2+13^2=21^2
a^2+169=441
minus 169 both sides
a^2=272
sqrt both sides
a=16.4924
D is answer

2. same thing
a=18
b=26
18^2+26^2=c^2
324+676=c^2
1000=c^2
sqrt both sides
31.6228=c
C is answer

3.
one way is to plug them in
remember that hypotonuse is longest side
A. 7^2+24^2=25^2, is that true?, yes it is treu
answer is A

4.
legs are 6 and 4
a=6
b=4
c=x
4^2+6^2=x^2
16+36=x^2
52=x^2
sqrt both sides
7.2111=x
7.2=x

5.c=20
a=x
b=14

x^2+14^2=20^2
x^2+196=400
minus 196 both sides
x^2=204
sqrt both sides
x=14.2829
x=14.3

1. D
2. C
3. A
4. 7.2
5. 14.3

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What is n? If 3 to the power of n equals 27

Answers

3^n=27

Solve Exponent.

3^n=27

log(3n)=log(27)(Take log of both sides)

n*(log(3))=log(27)

n=log(27) / log(3)

n=3

3 to the third power equals 3*3*3= 27

Y = 4x+1 y=x^2 + 2x - 2 A.6,2 B. 2,6 C. -6,2 D. -6,-2

Answers

Answer:

The solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Step-by-step explanation:

Given that

$y = 4x + 1 (i)$

$y = x^2 + 2x -2 (ii)$

Now, by susbstituting the value of 'y' from equation i to equation ii, we get

$4x+1=x^2 + 2x -2$

$0=x^2 + 2x -2-4x-1$

$0=x^2 + (2x -4x) +(-2-1)$

$0=x^2 + (-2x) +(-3)$

$0=x^2 -2x -3$

$x^2 -2x -3 = 0 (iii)$

Now by factorization, equation iii can be written as

$x^2 -3x +x -3 = 0$

$x(x -3) + 1(x -3) = 0$

$(x -3)(x +1) = 0$

x = 3 and x = -1

By putting the values of x in equation i, we get

y = 4(3) + 1

y = 12 +1

y = 13

and

y = 4(-1) + 1

y = -4 +1

y = -3

Therefore, the solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Given a mean of 100, and a standard deviation of 5.3, what is the Z-score for 130?

Answers

Answer:

5.66038

Step-by-step explanation:

Given

Mean= μ=100

SD= σ=5.3

Z-score of 130= ?

The z-score of any value tells us that how many standard deviations that value is from the average or mean.

The Z-score of any data value is found by subtracting the mean from it and then dividing by the standard deviation.

z-score= (x- μ)/σ

z-score of 130= (130-100)/5.3

=30/5.3

=5.66038

Is it possible for a number to be a rational number that is not an integer but is a whole number? Explain.

Answers

A rational number is a fraction pretty much or a decimal. An integer is a counting number including zero and the negatives. A whole number is a counting number not including the negatives and is not a fraction or decimal. So no i don't think you can get that combination.

Which expressions are equivalent to -3-(7.5+4)

Answers

-3-(7.5+4)
PEMDAS
P for Parenthesis
E for Exponents
M/D for Multiplication/Division
A/S for Addition/Subtraction
We should first clear the ones in parenthesis: (Oder Of Operations)
= -3-(11.5)
= -3-11.5
= -14.5
Basically -3-(11.5)

Which compound inequality could this graph be the solution of?

Answers

Answer:

B. 2x + 3 ≥ 11 or 4x - 7 ≤ 1

Step-by-step explanation:

Given compound inequality,

In option A,

2x + 3 ≥ 11 and 4x - 7 ≤ 1

⇒ 2x ≥ 8 and 4x ≤ 8

⇒ x ≥ 4 and x ≤ 2

$\implies [4,\infty)\cap (-\infty, 2]$

$=\phi$

2x + 3 ≥ 11 and 4x - 7 ≤ 1 can not be the correct inequality,

In option B,

2x + 3 ≥ 11 or 4x - 7 ≤ 1

⇒ 2x ≥ 8 or 4x ≤ 8

⇒ x ≥ 4 or x ≤ 2

$\implies [4,\infty)\cup (-\infty, 2]$

Which is shown in the given graph,

Thus, 2x + 3 ≥ 11 or 4x - 7 ≤ 1 is the correct compound inequality,

In option C,

2x + 3 > 11 or 4x - 7 < 1

⇒ 2x > 8 or 4x < 8

⇒ x > 4 or x < 2

$\implies (4,\infty)\cup (-\infty, 2)$

So, which is not shown in the graph,

2x + 3 > 11 or 4x - 7 < 1 can not be the correct compound inequality,

In option D,

2x + 3 ≥ 11 or 4x - 7 ≥ 1

⇒ 2x ≥ 8 or 4x ≥ 8

⇒ x ≥ 4 or x ≥ 2

$\implies [4,\infty)$

Which is not shown in the graph,

2x + 3 ≥ 11 or 4x - 7 ≥ 1 is not the correct compound inequality.

B.. 4 is less than or equal to x, 2 is greater or equal to x