Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's Solve ~

[tex]\qquad \sf  \dashrightarrow \: 4 {x}^{2} + 20x + 25[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {x}^{2} + 10x + 10x + 25[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5) (2x + 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5) {}^{2} [/tex]

or

[tex] \sf{\qquad \sf  \dashrightarrow \: 4x² + 20x + 25 } [/tex]

[tex] \sf{\qquad \sf  \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²} [/tex]

[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]

so, let's use this identity here to factorise :

[tex] \sf{\qquad \sf  \dashrightarrow \: (2x + 5)²} [/tex]

I hope it was helpful ~

Answer:

56x² + 8x

(second option listed)

Step-by-step explanation:

area: length × width

length: 7x + 1

width: 8x

(8x)(7x + 1)

{distribute 8x}:

(8x)(7x):  8x × 7x = 8 · 7 · x · x = 56 · x · x = 56x²

(8x)(1) = 8x

area = 56x² + 8x

so, the area of this rectangle is 56x² + 8x

Answer:

56x² + 8x

[answer B]

Answer:

A 10m ladder is leaning against a wall. The ladder makes an angle of 78o with the ground. How high up the wall does the ladder reach? Please include a diagram in the answer.

Th function you need is the sine function. The sine of 78° is about 0.978. That is the ratio of the opposite side (wall) over the hypotenuse (ladder) of the right triangle in this problem.

10 m · sin 78° = 10 m · 0.978 = 9.78 meters.

The ladder reaches 9.78 meters up on the wall.

Step-by-step explanation:

Answer:

[tex]\boxed{\sf x = 1, \ x = -5}[/tex]

Explanation:

[tex]\rightarrow \sf 4x^2 + 16x - 20 = 0[/tex]

[tex]\rightarrow \sf 4(x^2 + 4x - 5) = 0[/tex]

[tex]\rightarrow \sf x^2 + 4x - 5 = 0[/tex]

[tex]\rightarrow \sf x^2 + 5x -x- 5 = 0[/tex]

[tex]\rightarrow \sf x(x + 5) -1(x+ 5) = 0[/tex]

[tex]\rightarrow \sf (x-1)(x+ 5) = 0[/tex]

[tex]\rightarrow \sf x = 1, \ x = -5[/tex]

Answer:

Step-by-step explanation:

Write the number as [tex]abc[/tex] and use the divisibility rules for 10 and 3. From the rule for 10, we know that the last digit of [tex]abc+cba[/tex] is [tex]o[/tex], hence [tex]a+c=10[/tex]. Thus the options are [tex]a=1[/tex] & [tex]c=9[/tex], [tex]a=2[/tex], & [tex]c=8[/tex], etc.

From the rule for 3, namely that the digit sum must be divisible by 3, we find that [tex]2a+2b+2c=20+2b[/tex]  is divisible by [tex]3[/tex]. By hand it's easy to check that [tex]b=2,5,8[/tex] are the only options that work.

So there are 9 choices for [tex]a[/tex] and [tex]c[/tex] and [tex]3[/tex] for [tex]b[/tex] , giving 27 total.

The associative property of real numbers is shown in the number expression 3 + ((-5) + 6) = (3 + (-5)) + 6

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a number expression:

= 3 + ((-5) + 6) = (3 + (-5)) + 6

As we know in the associative property:

a + (b + c) = (a + b) + c

= (3 + (-5)) + 6

Thus, the associative property of real numbers is shown in the number expression 3 + ((-5) + 6) = (3 + (-5)) + 6

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ1

Answer:

Step-by-step explanation:

Comment

An x intercept occurs when y = 0. So the table shows three of them.

Answer

There are 3 x values when y = 0. They are

Answer: A. [tex](-1, 0)[/tex]

Step-by-step explanation:

The x-intercept is every point where y=0. To see this, we should look at the table's f(x) section to find any zeroes.

According to the table and this knowledge, one x-intercept of this continuous function is [tex](-1, 0)[/tex].

I hope this helps! Pls mark brainliest!! :)

The probability of getting two correct answers will be 0.0625.

The probability of getting two correct answers will be:

Probability of getting the correct answer will be:

= 1/4 = 0.25

The probability of getting two correct answers will be:

= 0.25 × 0.25

= 0.0625

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:

[tex]7.98 \times 10^8[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we have that:

Hence, without considering the order, the number of playlists is given by:

[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:

[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1

Answer:

Step-by-step explanation:

By using the remainder theorem we found that ( x - 5 ) is the factor of function  f(x) = x³ – 5x² + 7x – 35.

Factorization is defined as splitting the polynomial into its most simplified form. This factor satisfies the polynomials from which it is extracted.

The factorization by using the Remainder theorem.

x - 5 )   x³ – 5x² + 7x – 35.( x ² + 7

             x³  -  5x²

             ______________

                00         7x - 35

                             7x - 35

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

                                     00

Here the function is completely divided by the factor x - 5 therefore

by using the remainder theorem we found that ( x - 5 ) is the factor of function  f(x) = x³ – 5x² + 7x – 35.

To know more about factorization follow

https://brainly.com/question/25829061

#SPJ1

Answer:

30.5 cm^2

Step-by-step explanation:

Recall the formula for the area of a circle: [tex]A_{circle}=\pi r^2[/tex] where [tex]\pi \approx 3.14[/tex], and "r" is the radius of the circle (distance from center to any point on the edge).

From the diagram, the radius is 5cm.

[tex]A_{circle}=\pi r^2[/tex]

[tex]A_{circle}=(3.14)(5[cm])^2[/tex]

[tex]A_{circle}=78.5[cm^2][/tex]

Recall the formula for the area of a rectangle: [tex]A_{rectangle}=bh[/tex] where "b" is the base of the rectangle (length of bottom or length of top), "h" is the height of the rectangle (distance from bottom to top).

From the diagram, the base is 8cm, and the height is 6cm.

[tex]A_{rectangle}=bh[/tex]

[tex]A_{rectangle}=(8[cm])(6[cm])[/tex]

[tex]A_{rectangle}=48[cm^2][/tex]

Having found the areas for each of the first parts, we can find the difference to find the shaded area:

[tex]A_{shaded}=A_{circle}-A_{rectangle}[/tex]

[tex]A_{shaded}=(78.5[cm^2])-(48[cm^2])[/tex]

[tex]A_{shaded}=30.5[cm^2][/tex]

Answer:

approximately $23,655.91 (rounded to the nearest hundredths place)

Step-by-step explanation:

[tex]22,000=0.93x\\x=23,655.91[/tex]

The value of e:g is 2:7.

A ratio indicates how many times one number contains another.

Given:

e:f=3:7

f:g=2:3

Now take LCM of 2 and 7 i.e., 14.

e/f= 3/7= 3*2/7*2= 6/14

and, f/g= 2/3= 2*7/3*7= 14/21

So,

e/g= e/f *f /g

     = 6/14*14/21

     = 6/21

e:g = 2:7

Hence, the value of e:g is 2:7.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ1

Answer:

15 degrees

Step-by-step explanation:

Answer:

The earth turns 15 degrees in one hour. Hope this helps!

Step-by-step explanation:

Answer:

Area of Floor = 21.6.m²

Area of tile = 288 cm² = 0.0288 m²

No. of tiles = Area of floor/ area of tile

= 21.6/0.0288

= 750

Answer:

1) 8x/2x = 4

2) 2y/4y = 1/2

3) (4 x 1/2 x 3) = 6

4) /2

solutions= 6/2=3

Answer:

Step-by-step explanation:

Givens

x intercept =

The vertex is at 3, 4

The vertex is upside down.

Solution

(x - 1) and (x - 5) produce the two roots.

There must be 1 minus somewhere so that the quadratic goes upside down.

Answer

y = - (x -1)(x - 5)

Answer:

0 and -6

(0,-6)

Step-by-step explanation:

Can't really explain, but this is a guess on the actual question.

Answer:

It makes sense for Phil to sell his products online.

Step-by-step explanation:

Answer:

x = -1/2 = -0.5

Step-by-step explanation:

4.5x + 9 -1/2x = -3.75 +5 1/2 + 5.25

⇔ (4 1/2 - 1/2)x + 9 = (5 1/2 + 5 1/4) - 3 3/4

⇔ 4x + 9 = 10 3/4  - 3 3/4

⇔ 4x + 9 = 10 - 3

⇔ 4x + 9 = 7

⇔ 4x = 7 - 9

⇔ 4x = -2

⇔ x = -2/4

⇔ x = -1/2

⇔ x = -0.5

Since [tex]x^2 + x + 1 = 0[/tex] means [tex]x^2+x = -1[/tex], we have for any [tex]n[/tex] the recursive relation

[tex]x^n (x^2 + x) = x^{n+2} + x^{n+1} = -x^n \implies x^{n+2} = -x^{n+1} - x^n[/tex]

Let [tex]f(x)=x^{2015}+x^{2013}+x[/tex]. Substitution using the recursive rule generates an alternating power-reduction pattern:

[tex]f(x) = \left(-x^{2014} - x^{2013}\right) + x^{2013} + x = -x^{2014} + x[/tex]

[tex]f(x) = -\left(-x^{2013} - x^{2012}\right) + x = x^{2013} + x^{2012} + x[/tex]

[tex]f(x) = \left(-x^{2012} - x^{2011}\right) + x^{2012} + x = -x^{2011} + x[/tex]

[tex]f(x) = -\left(-x^{2010} - x^{2009}\right) + x = x^{2010} + x^{2009} + x[/tex]

[tex]f(x) = \left(-x^{2009} - x^{2008}\right) + x^{2009} + x = -x^{2008} + x[/tex]

[tex]f(x) = -\left(-x^{2007} - x^{2006}\right) + x = x^{2007} + x^{2006} + x[/tex]

and so on.

Notice that in the equivalent forms of [tex]f(x)[/tex] involving 3 terms, the largest power of [tex]x[/tex] is a multiple of 3, and the next largest power is 1 less. This means after so many iterations of substitutions, we would end up with

[tex]f(x) = x^3 + x^2 + x[/tex]

Then by factorizing, the expression of interest reduces to

[tex]f(x) = x (x^2 + x + 1) = x \times 0 = \boxed{0}[/tex]

Answer:

[tex] f(-4) = \dfrac{1}{9} [/tex]

Step-by-step explanation:

[tex] f(x) = 9(3)^x [/tex]

[tex] f(-4) = 9(3)^{-4} [/tex]

[tex] f(-4) = 3^2 \cdot 3^{-4} [/tex]

[tex] f(-4) = 3^{-2} [/tex]

[tex] f(-4) = \dfrac{1}{9} [/tex]

Answer:

1/9

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

Answer:

jxdhjsssdddddsssssdd

Answer:

increasing

Step-by-step explanation:

look left to right, line goes up

The profit is the amount left from you net income after your fixed expenses have been paid.

The amount earned by an individual or corporation after costs, allowances, and taxes is referred to as net income. Net income in company is what remains after all costs, such as salaries and wages, the cost of goods or raw materials, and taxes, have been paid.

Profit is a financial gain, specifically the sum obtained over that which was used to acquire, maintain, or produce the good or service.

Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.

Hence the profit is the amount left from you net income after your fixed expenses have been paid.

Learn more about profit here:

https://brainly.com/question/23103804

#SPJ10

Answer: what is the question

Step-by-step explanation:

Based on the indices of the regular polygons, the number of sides that X has is 8. See the computation below.

Assuming that X has G number of sides; and

Y has H number of sides, this means that:

G-H = 3 ...........1

Recall that the formula for the exterior angles is:

360/n; where n is number of sides

X = 360/G

Y = 360/H

(360/G) + (360/H) = 117°.......2

Solving 1 and 2 simultaneously, we obtain:

G= 8 and

H = 5

Thus, X has 8 sides.

Learn more about Polygons at:
https://brainly.com/question/1592456
#SPJ1

The solution to the equation r(1 - 2cosФ) = 1 is given as x² + y² - 4x√(x² + y²)  + 4x² = 1

An equation is an expression that shows the relationship between two or more variables and numbers.

In polar form:

r = √(x² + y²) and cosФ = x / √(x² + y²)

Hence:

r(1 - 2cosФ) = 1

√(x² + y²) [1 - 2(x / √(x² + y²))] = 1

√(x² + y²) - 2x = 1

Take square of both sides:

x² + y² - 4x√(x² + y²)  + 4x² = 1

The solution to the equation r(1 - 2cosФ) = 1 is given as x² + y² - 4x√(x² + y²)  + 4x² = 1

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

5.9

Step-by-step explanation:

345√ is 18.6=3.14*r2 cuz formula

Is πr2