In ΔDEF, the measure of ∠F=90°, DE = 90 feet, and FD = 23 feet. Find the measure of ∠E to the nearest degree.

Answer:

[tex]\displaystyle x^\circ \approx 29.3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = x

Opposite Leg = 45

Hypotenuse = 92

Step 2: Solve for x

Answer:what’s the question?

Step-by-step explanation:

Answer:

The third option (9+[tex]3\sqrt{7}[/tex]-[tex]3\sqrt{7}[/tex]-[tex]\sqrt{49}[/tex])

Step-by-step explanation:

With FOIL, this can be expanded. (a+b)(a-b) is equal to a²+ab-ab-b² or a²-b².

In this case, all the answers have 4 terms, so we want the first option. This makes the equation 3²+(3×[tex]\sqrt{7}[/tex])-(3×[tex]\sqrt{7}[/tex])-([tex]\sqrt{7}[/tex])².

Solving these gives 9+[tex]3\sqrt{7}[/tex]-[tex]3\sqrt{7}[/tex]-7. This is the same as  9+[tex]3\sqrt{7}[/tex]-[tex]3\sqrt{7}[/tex]-[tex]\sqrt{49}[/tex].

**This content involves multiplying with surds and expanding perfect squares, which you may wish to revise. I'm always happy to help!

The equivalent expression is (c) [tex]9 - 3\sqrt 7 + 3\sqrt 7 - \sqrt {49}[/tex]

The difference of squares equation is given as:

[tex](a + b)(a - b) = a^2 -b^2[/tex]

And the radical expression is given as:

[tex] (3+ \sqrt 7)(3- \sqrt7)[/tex]

By comparing the above expression to [tex](a + b)(a - b) = a^2 -b^2[/tex], we have:

[tex]a =3[/tex]

[tex]b = \sqrt 7[/tex]

Substitute these values in [tex](a + b)(a - b) = a^2 -b^2[/tex]

[tex] (3+ \sqrt 7)(3- \sqrt7) = 3^2 - (\sqrt 7)^2[/tex]

This gives

[tex] (3+ \sqrt 7)(3- \sqrt7) = 9 - \sqrt {49}[/tex]

By complete expansion, we have:

[tex] (3+ \sqrt 7)(3- \sqrt7) = 9 - 3\sqrt 7 + 3\sqrt 7 - \sqrt {49}[/tex]

Hence, the equivalent expression is (c)

Read more about difference of two squares at:

https://brainly.com/question/3189867

Answer:

15x5−x4−2x3+21x2+7x

Step-by-step explanation:

=(3x2+x)(5x3+−2x2+7)

=(3x2)(5x3)+(3x2)(−2x2)+(3x2)(7)+(x)(5x3)+(x)(−2x2)+(x)(7)

=15x5−6x4+21x2+5x4−2x3+7x

=15x5−x4−2x3+21x2+7x

Answer:

904.78

Step-by-step explanation:

Answer:

355

Step-by-step explanation:

185+140= 325

325+20= 355

Answer:

30/185×100=

Step-by-step explanation:

30/140×100=

Answer:

Zoom in more and I can help

Step-by-step explanation:

Answer:

20 %

Step-by-step explanation:

If she saved 15 dollars and paid 60, the original price was 60+15 = 75

The percent discount is  (original - new) / original = ( 75-60)/75 = 15/75 = .2

Change to percent form = .2 * 100 =20%

Answer:

B.) 20 %

The percentage discount on the shoes is 20 % .

Step-by-step explanation:

She pays 60 dollers and saved 15 dollers on the regular price.

original price of pair of shoes = 60 + 15 = 75

Percentage discount is = original price - new price / original price

= 75 - 60 / 75 = 15 / 75 = 0.2

Percentage discount = 0.2

Change into percentage =0.2× 100 = 20%

Therefore, the percentage discount on the shoes is 20 % .

Answer

80 m^2

Step-by-step explanation:

basically 10 x 8 plus the value

Answer:

Part 1)

The height of the diving board is 19 feet.

Part 2)

Five seconds.

Part 3)

44 feet.

Step-by-step explanation:

Joyce's dive is represented by the equation:

[tex]h=-t^2+10t+19[/tex]

Where h represents her height (in feet) after t seconds.

Part 1)

Joyce is on the diving board right before she jumps. Therefore, to find the height of the diving board, we can let t = 0, since this is before she had jumped. Hence:

[tex]h(0)=-(0)^2+10(0)+19=19\text{ feet}[/tex]

The height of the diving board is 19 feet.

Part 2)

Since this is a quadratic, the maximum height will occur at its vertex point.

So, we need to find the vertex. We can use the following formulas:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -1, b = 10, and c = 19.

So, the t-coordinate of the vertex is:

[tex]\displaystyle t=-\frac{(10)}{2(-1)}=5\text{ seconds}[/tex]

Joyce will reach her maximum height after five seconds.

Part 3)

To find the maximum height, simply substitute this value back into the equation. Hence:

[tex]h(5)=-(5)^2+10(5)+19=44\text{ feet}[/tex]

So, her maximum height is 44 feet in the air.

Answer:

h = -34/3

Step-by-step explanation:

7h +8 = 4h - 26

Subtract 4h from each side

7h-4h +8 = 4h-4h - 26

3h+8 = -26

Subtract 8 from each side

3h+8-8 = -26-8

3h = -34

Divide by 3

3h/3 = -34/3

h = -34/3

Answer:

h = - [tex]\frac{34}{3}[/tex]

Step-by-step explanation:

Given

7h + 8 = 4h - 26 ( subtract 4h from both sides )

3h + 8 = - 26 ( subtract 8 from both sides )

3h = - 34 ( divide both sides by 3 )

h = - [tex]\frac{34}{3}[/tex]

Answer:

for the music blue the median would be in the middle

for the physics the upper quartile would be the farthest right

for the sports the lower quartile would be the farthest left

for the history the line  would go the farthest right

Answer:

To complete the square, we need to have the equation set up like this:

x^2 +4x =9

To do that, we'd need to move the 4x to the left side producing

4x + x^2 = 9

And that can be rewritten as

x^2 +4x =9

So the term that needs to be moved is -4x

https://www.1728.org/quadr2.htm

Step-by-step explanation:

Answer:

(a) Set of rational numbers

(b) [tex]\pi + (-\pi) = 0[/tex]

Step-by-step explanation:

Solving (a): Set that is closed under subtraction

The solution to this is rational numbers.

For a set of number to be closed under subtraction, the following condition must be true

[tex]a -b = c[/tex]

Where

a, b, c are of the same set.

The above is only true for rational numbers.

e.g.

[tex]1 - 2 = -1[/tex]

[tex]5 - 5 = 0[/tex]

[tex]\frac{1}{2} - \frac{1}{4} = \frac{1}{2}[/tex]

[tex]4 - 2 = 2[/tex]

The operations and the result in the above samples are rational numbers.

Solving (b): Choice not close under addition[See attachment for options]

As stated in (a)

For a set of number to be closed under subtraction, the following condition must be true

[tex]a -b = c[/tex]

Where

a, b, c are of the same set.

In the given options (a) to (d), only

[tex]\pi + (-\pi) = 0[/tex] is not close under addition because:

[tex]\pi[/tex] is irrational while [tex]0[/tex] is rational

In other words, they belong to different set

Answer:

the too left graph us the abswer,

Because

f(x) = (x + 3)(x - 2) has positive cieff of the x^2 term, and also it has roots of -3 and 2

The graph of the function  f(x) = (x + 3)(x - 2) is first graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To graph the function f(x) = (x + 3)(x - 2), we can start by finding its x-intercepts, y-intercept, and any vertical or horizontal asymptotes.

First, to find the x-intercepts, we set y = 0 and solve for x:

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

This equation is true when x = -3 or x = 2. Therefore, the x-intercepts of the graph are -3 and 2.

Next, to find the y-intercept, we set x = 0 and evaluate:

f(0) = (0 + 3)(0 - 2) = -6

Therefore, the y-intercept of the graph is -6.

The graph of f(x) = (x + 3)(x - 2) is a parabola that opens up because the sign of the two factors, (x + 3) and (x - 2), are both positive.

This means that the graph of f(x) will be a parabola that opens up with its vertex located at the point where the two factors are equal to each other

Hence, the graph of the function  f(x) = (x + 3)(x - 2) is first graph.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ7

Answer:

2x^2-9x+15

It is prime/unfactorable

Step-by-step explanation:

Answer:

Base - 7 yards

Height - 10 yards

Area - 35 square yards

Step-by-step explanation:

By definition, the base and height must be perpendicular. Technically, they are interchangeable, but base usually refers to the relative bottom of a figure.

The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is equal to [tex]A=\frac{1}{2}bh[/tex].

Therefore, we have:

[tex]A=\frac{1}{2}\cdot 7\cdot 10=\boxed{35\:\text{square yards}}[/tex]

Answer:

Step-by-step explanation:

according to the Pythagoras theorem ,

SohCahToa

Soh - sine is opposite , hypotenuse

Cah -cos is adjacent , hypotenuse

Toa - tan is opposite, adjacent

from the diagram above , the tan is 8/15.

Hope this is helpful ,

have a nice day :-)

Answer:

13 quarters and 24 dimes

Step-by-step explanation:

13*.25=3.25

24*.1=2.4

3.25+2.4=5.65

Answer:

The smallest integer is 11.

Step-by-step explanation:

Let the first integer be x.

Then the second will be (x + 1) and the third will be (x + 2).

The sum is 36. Hence:

[tex]x+(x+1)+(x+2)=36[/tex]

Solve for x:

[tex]3x+3=36[/tex]

So:

[tex]3x=33[/tex]

Hence:

[tex]x=11[/tex]

Our sequence is 11, 12, 13.

So, the smallest integer is 11.

Answer:

log (25 x^5)

Step-by-step explanation:

2 log 5 + 5 log x

We know alog b = log b^a

log 5^2 + log x^5

We know log a + log b = log (a*b)

log ( 5^2 * x^5)

5^2 = 25

log (25 x^5)

Answer:

log ( 25x⁵)

Step-by-step explanation:

use a×log × b = log b^a to transform the expression.

use log x + log y = log ( x×y ) to simplify the expression

Evaluate the power

Answer:

$375

Step-by-step explanation:

Method I

25% = .25

500 * .25 = 125

500 - 125 = 375

-----------------------

Method II

1 - .25 = .75

500 * .75 = 375

Answer:

The second statement is the

of the first.

X = у

y = x

A. contradiction

B. inverse contrapositive

C. inverse

D. converse

Step-by-step explanation:

imverse

The second statement is the contrapositive of the first.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that x → y is a conditional statement read as 'if x then q'.

And, The converse EXCHANGES the hypothesis and conclusion such as:

⇒ y → x

And, The 'contrapositive' statement basically NEGATES the converse of the conditional such as:

⇒ ¬y → ¬x

Coming back towards the question,

Given that;

x ⇒ y

¬y ⇒ ¬x

Therefore, The second statement is the contrapositive of the first.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ5

Answer:

255

Step-by-step explanation:

total cost paid = fixed cost + total variable cost

total variable cost = distance travelled x variable cost per unit

two equations can be derived from the question

a + 10b = 105  equation 1

a + 15b = 155   equation 2

a = fixed cost

b =  variable cost per unit

Subtract equation 1 from 2

5b = 50

b = 10

Substitute for b in equation 1

a + 10(10) = 105

a = 105 - 100 = 5

a = 5

cost of travelling a distance of 25km

5 + 10(25) = 255

Answer:

the answers  is =-0

Step-by-step explanation:

is -0

Answer:

answer for this solution is 10 degrees

Step-by-step explanation:

sin x + cos x = 90

5x + 3x +10 = 90

x = 10

Answer:

What grade math is this??

Step-by-step explanation:

Answer:92.1

Step-by-step explanation:

A=78+4.5

A=92.137166941154

A=92.1