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3 years ago

DEFG is an isosceles trapezoid. Find the measure of E.

Mathematics

2 answers:

abruzzese [7]3 years ago

4 0

If it is isosceles angle E must be equal to F, in this case 75°

Scilla [17]3 years ago

4 0

Answer: The measure of ∠E is 75°.

Step-by-step explanation: Given that DEFG is an isosceles trapezoid, where m∠D = 105° and m∠F = 75°.

We are to find the measure of ∠E.

ISOSCELES TRAPEZOID is a trapezoid in which the base angles are equal and so the left and right side lengths are also equal.

Therefore, in the isosceles trapezoid DEFG, we have

m∠D = m∠G, m∠E = m∠F and DE = FG.

Since, m∠D = 105°, so m∠G = 105°.

The sum of all the four angles of a quadrilateral is 360° and a trapezoid is a quadrilateral with a set of opposite parallel sides, so in the trapezoid DEFG, we have

$m\angle D+m\angle E+m\angle F+m\ange G=360^\circ\\\\\Rightarrow 105^\circ+m\angle E+75^\circ+105^\circ=360^\circ\\\\\Rightarrow m\angle E+285^\circ=360^\circ\\\\\Rightarrow m\angle E=360^\circ-285^\circ\\\\\Rightarrow m\angle E=75^\circ.$

Thus, the measure of ∠E is 75°.

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Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

2 years ago

Ray BD bisects ∠ABC so that m∠DBC = (x + 7) and m∠ABD = (2x − 11). What is x? A. 6 B. 18 C. 29 D. 54

nata0808 [166]

Answer:

Step-by-step explanation:

Here, we want to the find the value of the x.

By bisecting the angle, the ray in question divides it into two other angles which are equal.

We proceed as follows;

x + 7 = 2x -11

Collect like

terms

2x -x = 7 + 11

x = 18

6 0

3 years ago

In the inequality 6a+4b>10, what could be the possible value of a if b=2?

Arlecino [84]

We are given the following inequality:

$6a+4b>10$

If we replace b = 2, we get:

$\begin{gathered} 6a+4(2)>10 \\ 6a+8>10 \end{gathered}$

Now we solve for "a" first by subtracting 8 on both sides:

$\begin{gathered} 6a+8-8>10-8 \\ 6a>2 \end{gathered}$

Now we divide both sides by 6

$\frac{6a}{6}>\frac{2}{6}$

Simplifying:

$a>\frac{1}{3}$

Therefore, for b = 2, the possible values of "a" are those that are greater than 1/3

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1 year ago

N is a whole number such that 6< 3n < 15 List all the possible values of n.

Sav [38]

Answer:

3, 4

Step-by-step explanation:

6 < 3n < 15

Divide the three "sides" by 3.

2 < n < 5

n must be between 2 and 5,a nd it must be a whole number.

n can be 3 or 4

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2 years ago

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the graph to the right represents mario’s mile time in minutes, y, based on the number of hours he spends training in hours , x

sveta [45]

Answer: it is 13+13=26

Step-by-step explanation:

I don’t care.

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2 years ago