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4 years ago

Find the length of a leg

Mathematics

2 answers:

N76 [4]4 years ago

8 0

The answer to your question is b.

KatRina [158]4 years ago

4 0

The triangle has two angles of 45°, so the straight legs a are equal. Pythagoras says that

a² + a² = 16², so 2a² = 256, a = √128 = √64·√2 = 8√2

You might be interested in

A manufacturer of metal fasteners expects to ship an average of 1197.00 boxes of fasteners per day. A random sample of 24 days p

lana66690 [7]

Answer:

The p-value obtained is less than the significance level at which the test was performed, hence, we reject the null hypothesis, accept the alternative hypothesis & conclude that there is evidence showing that the average number of boxes shipped per day is different from 1197.00

Step-by-step explanation:

For hypothesis testing, we first clearly state our null and alternative hypothesis.

The null hypothesis is that there is no evidence showing that the average number of boxes shipped per day is different from 1197.00. That is, there is no significant difference between the number of boxes shipped per day and 1197.00

And the alternative hypothesis is that there is evidence showing that the average number of boxes shipped per day is different from 1197.00

Mathematically, the null hypothesis is

H₀: μ₀ = 1197.00

The alternative hypothesis is

Hₐ: μ₀ ≠ 1197.00

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = 1193.69 boxes per day

μ₀ = standard that we're comparing the sample mean with = 1197.00

σₓ = standard error of the sample mean

= (σ/√n)

where n = Sample size = 24 days

σ = standard deviation of the sample = 3.3166 boxes per day

σₓ = (3.3166/√24) = 0.677

t = (1193.69 - 1197) ÷ 0.677

t = -4.89

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 24 - 1 = 23

Significance level = 0.05

p-value (for t = -4.89, at 0.05 significance level, with a two tailed condition) = 0.000061

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 5% = 0.05

p-value = 0.000061

0.000061 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & conclude that there is evidence showing that the average number of boxes shipped per day is different from 1197.00

Hope this Helps!!!

6 0

3 years ago

A basket ball team played six games. In those games, the team won by 8 points, lost by 10, won by 7, won by 10, lost by 3, and w

sergiy2304 [10]

Answer: 3

Step-by-step explanation:

Mean simply means average. To calculate mean,we add together all the numbers given and divide them by the amount of numbers.

The Mean here will be:

= [8 +(-10) + 7 + 10 + (-3) + 6]/6

=18/6

= 3

The mean is 3

6 0

3 years ago

Shanice read a book that was 123 pages long. The first week, she read 67 pages. Then, she read the rest of the book over the nex

katrin2010 [14]

Answer:

She read 8 pages each day

Step-by-step explanation:

123 - 67 = 56

56/7 = 8

PLEASE GIVE BRAINLIEST THANK YOU

8 0

3 years ago

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 bx c, is shown.step 1: –c = ax2 bxwhich b

Ksju [112]

Answer:

option (b) is correct.

First step to solve for deriving the quadratic formula from the quadratic equation is completing the square.

Step-by-step explanation:

Given : the quadratic equation $ax^2+bx+c=0$

We have to find the first step for deriving the quadratic formula from the quadratic equation.

Quadratic formula is given by $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Consider the given quadratic equation $ax^2+bx+c=0$

Divide the equation by a, we get,

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

Take $\frac{c}{a}$ to other side, we get,

$x^2+\frac{b}{a}x=-\frac{c}{a}$

Add $(\frac{b}{2a})^2$ to both side, we get,

$x^2+\frac{b}{a}x+(\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac{c}{a}$

Thus, the left side is in the form of $(a+b)^2=a^2+b^2+2ab$

On solving, we get,

$(x+\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac{c}{a}$

Then solve for x , we get quadratic formula $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Thus, first step to solve for deriving the quadratic formula from the quadratic equation is completing the square.

Thus, option (b) is correct.

3 0

3 years ago

Read 2 more answers

Solve the equation for x by combining like terms first. <br> 3x-10+5x=2x-13

diamong [38]

Step-by-step explanation:

$\tt{3x - 10 + 5x = 2x - 13}$

Combine like terms on left hand side. Like terms are those which have the same base. Only coefficients of like terms can be added or subtracted.

⟼ $\tt{3x + 5x - 10 = 2x - 13}$

⟼ $\tt{8x - 10 = 2x - 13}$

Transpose 2x to left hand side and change it's sign.

Similarly , Transpose 10 to right hand side and change it's sign.

⟼ $\tt{8x - 2x = - 13 + 10}$

⟼ $\tt{6x = - 3}$

Divide both sides by 6

⟼ $\tt{ \frac{6x}{6} = - \frac{3}{6}}$

⟼ $\tt{x = - \frac{1}{2}}$

$\red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt {x = - \frac{1}{2}}}}}}} }$

Hope I helped ! ♡

Have a wonderful day / night ! ㋡

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8 0

3 years ago