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3 years ago

What is the measure of ∠E? Enter the correct value. Do not enter the degree symbol.

Mathematics

2 answers:

zmey [24]3 years ago

6 0

Answer:

45 degrees

Step-by-step explanation:

Since this triangle is isosceles, we know that the other angles, D and E, are both 45 degrees because of the sum of interior angles of a triangle always equaling 180 degrees.

HACTEHA [7]3 years ago

3 0

Answer:

To find < E we use tan

tan E = opposite / adjacent

DF is the opposite

EF is the adjacent

DF = 11

EF = 11

tan E = 11/11

tan E = 1

E = 45

Hope this helps

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A circle's circumference is approximately 76 cm what is the diameter of the circle rounded to nearest whole number

SSSSS [86.1K]

The diameter is approximately 24 cm. The radius is approximately 12 cm. The area is approximately 144 cm2 or 452 cm2.

8 0

3 years ago

Find all the zeros of the polynomial function P(x) x^4-4x^3 -5x^2+38x- 30

worty [1.4K]

Answer:

The zeros of the polynomial function are 1, -3, 3+i and 3-i.

Step-by-step explanation:

The given function is

$P(x)=x^4-4x^3-5x^2+38x-30$

We can find a zero of the given function by hit and trial method.

Substitute x=1 in the given function.

$P(1)=(1)^4-4(1)^3-5(1)^2+38(1)-30$

$P(1)=0$

The value of function is 0 at x=1 it means (x-1) is a factor of given function.

Substitute x=-3 in the given function.

$P(-3)=(-3)^4-4(-3)^3-5(-3)^2+38(-3)-30$

$P(-3)=0$

The value of function is 0 at x=-3 it means (x+3) is a factor of given function.

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

Divide the given function by $x^2 + 2 x - 3$ , to get remaining factors.

$\frac{x^4-4x^3-5x^2+38x-30}{x^2 + 2 x - 3}=x^2 - 6 x + 10$

So, the factor form of given function is

$P(x)=(x - 1) (x + 3) (x^2 - 6 x + 10)$

Quadratic formula: If a quadratic equation is $ax^2+bx+c=0$ , then

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using quadratic formula find the zeroes of $x^2 - 6 x + 10$ .

$x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(10)}}{2(1)}$

$x=\frac{6\pm \sqrt{-4}}{2}$

$x=\frac{6\pm 2i}{2}$ $[\because \sqrt{-1}=i]$

$x=3\pm i$

Therefore the zeros of the polynomial function are 1, -3, 3+i and 3-i.

3 0

3 years ago

The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than four and greater than 1.

Lyrx [107]

The compound inequality that gives the normal range for the pH values of lemon juice is given by:

$1.5 < pH < 4$

<h3>What is a compound inequality?</h3>

A compound inequality is modeled by:

$a < x < b$

Which means that x is greater than a and less than b. In this problem, the pH is greater than 1.5 and less than 4, hence the inequality is given by:

$1.5 < pH < 4$

More can be learned about compound inequalities at brainly.com/question/24528399

#SPJ1

5 0

2 years ago

Suppose that the volume of a right circular cylinder is 500 A cubic

Tanya [424]

The height of the right circular cylinder with volume of 500π cubic centimetre and radius of 5 centimetre is 20 cm.

<h3>Volume of a cylinder</h3>

volume = πr²h

where

r = radius
h = height

Therefore,

volume = 500π cm³

r = 5 cm

Therefore,

volume of the cylinder = πr²h

500π = 5²πh

500π = 25πh

divide both sides by 25π

500π / 25π = 25πh / 25π

h = 20 cm

learn more on cylinder here: brainly.com/question/11083770

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3 years ago

Find the distance between the points (13, 20) and (18, 8).

Jlenok [28]

Distance = sqrt (13-18)^2 + (20-8)^2 )

= sqrt ( 5^2 + 12^2)

= sqrt 169 = 13

7 0

3 years ago

Read 2 more answers