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sweet-ann [11.9K]
3 years ago
13

Determine if the statement is always, sometimes, or never true:

Mathematics
2 answers:
andrezito [222]3 years ago
7 0
The answer is:  "never".
_____________________________

MissTica3 years ago
6 0

Answer:

never

Step-by-step explanation:

To Find :An equilateral triangle is a right triangle.

              1. always

              2.sometimes

              3.never

Solution :

Definition of equilateral triangles: a triangle having all sides equal in length

Since all sides are equal so by property of triangle (angle opposite to equal sides are equal ) so, all angles are equal .

If equilateral triangle is right angle then one of its angle is of 90°

And in equilatera triangle all angles are equal so all angles must be of 90°

We know that triangle sum property is : Sum of all angles of triangle is equal to 180°

So, 90°+90°+ 90° =180°

⇒270°≠180°

since this violates the angle sum property of triangle .

Thus an equilateral triangle can never be a right triangle

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In a 2008 survey, people were asked their opinions on astrology— whether it was very scientific, somewhat scientific, or not at
crimeas [40]

Answer:

95% Confidence interval:  (0.0415,0.0647)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1430

Number of people who responded that astrology was very scientific, x = 76

\hat{p} = \dfrac{x}{n} = \dfrac{76}{1430} = 0.0531

95% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

Putting the values, we get:

0.0531\pm 1.96(\sqrt{\dfrac{0.0531(1-0.0531)}{1430}})\\\\ = 0.0531\pm 0.0116\\=(0.0415,0.0647)

95% confidence interval for the population portion with this belief: (0.0415,0.0647)

7 0
3 years ago
How do u do mean median range
liq [111]
Mean: Add up all of the values then divide by the number of values
Ex.  3+5+2 = 10 divided by three

3 0
4 years ago
Read 2 more answers
When using substitution method to solve the following system of equations, what is the result of the first step ? x +2y=5 y=6x+3
steposvetlana [31]

Answer:

x=3

Step-by-step explanation:

Sub y=x-1 into 2x+y=8.

You will get 2x+x-1=8.

Simplify 3x-1=8

Solve 3x=9

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6 0
3 years ago
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What is the vertex of the function x2 - 6x + 8 = 0?
RUDIKE [14]

<u>Answer: </u>

The vertex of the function \bold{x^{2} -6 x + 8 = 0}is (h,k) = (3 , -1)

<u>Solution: </u>

The vertex form of quadratic equation is generally given as,

f(x) = a(x - h)^{2} + k

Where h,k is the vertex of the parabola.

From question, given that x^{2}-6 x+8=0 .

we have to find the vertex of the function.

Let us first convert the given quadratic equation to vertex form (eqn 1)

x^{2}-6 x+8=0

x^{2}-6 x=-8

By adding “9” on both sides of equation, we get

x^{2}-6 x+9=-8+9

x^{2}-6 x+9=1

By using the identity (a-b)^{2}=a^{2}-2 a b+b^{2} ,the right hand side of above equation becomes,

(x-3)^{2}=1

(x-3)^{2}-1=0

Now,the equation (x-3)^{2}-1=0 is of the vertex form.

By comparing (x-3)^{2}-1=0 with a(x-h)^{2}+k

we get the values of (h,k)

a = 1; h = 3; k = -1

hence the vertex of the function x^{2}-6 x+8=0 is (h,k) = (3 , -1)

5 0
3 years ago
Perform the indicated operation and express the result as a simplified complex number. I need help with 35
skelet666 [1.2K]

Given:-

\frac{3+4i}{2-i}

To find:-

The simplified form.

At first we take conjucate and multiply below and above.

The conjucate is,

2+i

So now we multiply. we get,

\frac{3+4i}{2-i}\times\frac{2+i}{2+i}

Now we simplify. so we get,

\frac{3+4i}{2-i}\times\frac{2+i}{2+i}=\frac{6+3i+8i+4(i)^2}{2^2-i^2}

We know the value of,

i^2=-1

Substituting the value -1. we get,

\begin{gathered} \frac{6+3i+8i+4(i)^2}{2^2-i^2}=\frac{6+3i+8i+4(-1)_{}^{}}{2^2-(-1)^{}} \\ \text{                               =}\frac{6-4+11i}{2+1} \\ \text{                              =}\frac{2+11i}{3} \end{gathered}

So now we split the term to bring it into the form a+ib. so we get,

\frac{2+11i}{3}=\frac{2}{3}+i\frac{11}{3}

So the required solution is,

\frac{2}{3}+i\frac{11}{3}

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