Find the surface area of the figure shown.

134 ft 2
166 ft2
184 ft2
208 ft2

Answer:

= 135 m²

Step-by-step explanation:

First we divide the kite into 2  isosceles triangles

The bigger triangle has base angles = 45°

We can use these angle as follows to find the common base of the two triangles.

Cos 45=adjacent/9√2

Adj=9√2×cos 45

=9

common base =9×2=18

We can use the angle 45° above to find the height of the bigger triangle.

Tan 45°=opposite/adjacent

Opposite = adjacent×Tan 45

=9 tan 45=9

Area =1/2BH+1/2Bh where B is the common base H is the height of the big triangle, h represents the height of the smaller triangle.

A=1//2× 18 × 9 +1/2× 18 × 6

= 135 m²

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

Look at the picture.

We have

center at (3, 5) → h = 3 anf k = 5

radius r = 8

Substitute:

[tex](x-3)^2+(y-5)^2=8^2\\\\(x-3)^2+(y-5)^2=64[/tex]

Answer:

A) 32y³ + 24y² - 12y - 9

Step-by-step explanation:

(-8y² + 3)(-4y - 3) = (-8y² x -4y) + (-8y² x -3) + (3 x -4y) + (3 x -3)

                           = 32y³ + 24y² - 12y - 9

The product of [tex]-8y^2+3[/tex] and [tex]-4y-3[/tex] is:

               [tex]32y^3+24y^2-12y-9[/tex]

We are asked to find the product of the two expressions which are given by:

[tex]-8y^2+3[/tex] and [tex]-4y-3[/tex]

i.e.

we are asked to find the product of a quadratic and a linear polynomial.

We are asked to find the result of:

[tex](-8y^2+3)\cdot (-4y-3)[/tex]

Hence, on using the distributive property we have:

[tex]-8y^2(-4y-3)+3(-4y-3)\\\\=-8y^2\times -4y-8y^2\times (-3)+3\times (-4y)+3\times (-3)\\\\i.e.\\\\=32y^3+24y^2-12y-9[/tex]

The correct answer is: Option: A

Answer:

United Kingdom , France,  Soviet Union , and China  

Step-by-step explanation:

United Kingdom , France,  Soviet Union , and China  was an ally of the United States durning World War II.

If you look at the graph, the line crosses the y axis at (0,3).

That means you can eliminate the inequality that shows the y intercept as -3 (which is the 3rd option)

Also the inequality has to have y ≤ ....     so that the correct part of the graph is shaded. This elimates all of the inequalities that has y ≥ ... ( which is the 2nd and 4th option)

This leaves you with only the first inequality left:

y ≤ 2x² - 8x + 3

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

Answer

y ≤ 2x² - 8x + 3

Answer:

Yes,a similar formula is used to find all the products

Step-by-step explanation:

The formula applied in this case is;

(a+b)²=   (a+b) (a+b)= a(a+b)+b(a+b) = a²+ab+ab+b²= a²+2ab+b²

In the first one;

[tex](x+3)^2= (x+3) (x+3) = x(x+3)+3(x+3) = x^2 +3x+3x+9  = x^2 +6x +9[/tex]

In the second one;

[tex](x+4)^2 = (x+4) (x+4) = x(x+4)+ 4(x+4) = x^2 +4x+4x+16 = x^2 +8x+16[/tex]

⇒This is the same for the third and fourth product.

Answer:

3rd option is right

Step-by-step explanation:

Answer:

Option 1 is correct

Step-by-step explanation:

Given expression is:

[tex](3x^3y^{-2})^2\\[/tex]

Putting the values

[tex]= [3 (-2)^3 (5)^{-2}]^2\\We\ have\ to\ make\ the\ powers\ positive\\= [{\frac{3(-2)^3}{5^{2}} }]^2\\= \frac{[{3(-2)^3}]^2}{(5^2)^2} \\Applying\ outer\ power\\= \frac{3^2(-2)^6}{5^4} \\[/tex]

Hence option one is correct ..

[tex]77500[/tex]

In this case, the digit in the hundredths place is a [tex]5[/tex].  We need to take a look at the next digit to the right, which is a [tex]4[/tex].

Since it is [tex]4[/tex] or less, we can simply replace the [tex]4[/tex] and the rest of the digits to the right with [tex]0[/tex]s to round it.

If the [tex]4[/tex] was [tex]5[/tex] or more, we would round the [tex]5[/tex] up to [tex]6[/tex] and replace the remaining digits to the right with [tex]0[/tex]s.

Answer:

77500

Step-by-step explanation:

To round something to the nearest hundred, we first look to the 10s digit. It is 4. Since 4 is less than 5, then we keep the same hundreds place. So we get 77500.

hypotenuse = 8

unknown leg = b

known leg = 4

Pythagorean theorem:

[tex]c=\sqrt{{a}^{2}+{b}^{2}}[/tex]

The answer is

[tex]8=\sqrt{{b}^{2}+{4}^{2}} [/tex]

The value of x that is not in the domain is x = 7.

which of the following values of X is not in the domain of f(x)?

Remember that in math we can't divide by zero, so any value that makes the denominator equal to zero can't be in the domain.

Here the rational function is:

f(x) = (x + 3)/(x - 7)

When x = 7, the denominator becomes zero, so x = 7 is not in the domain.

Answer:

∠2 = 18°

Step-by-step explanation:

∠WXZ = ∠1 + ∠2 ← substitute ∠1 = 3∠2

∠WXZ = 3∠2 + ∠2, that is

72 = 4∠2 ( divide both sides by 4 )

18 = ∠2, that is

∠2 = 18°

Answer:

subtract 3 from both sides

Step-by-step explanation:

Given

2x + 3 = 11 ( subtract 3 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

$3.80

Step-by-step explanation:

We are given a graph showing the location of 3 houses where you had to do lawn work today, with the distances from your house.

Given that one truck gets 8 miles per gallon of gasoline and gas costs $1.52 per gallon, we are to find the total cost of the gas used.

Total distance = 7 + 3 + 4 + 6 = 20 miles

Gallons of gas used = 20 / 8 = 2.5

Total cost of gas used = 2.5 * 1.52 = $3.80

Answer:

see below

m = males = 50

e = females = 25

a = adults = 7

Step-by-step explanation:

Givens

Let the adults = a

let the males students = m

lef the female students = e

Equations

a + m + e = 82                                  

m = 7*a + 1

e = 1/2 * (7a + 1)

Solution

a + 7a + 1 + 1/2(7a + 1) = 82                 Remove the brackets on the left.

a + 7a + 1 + 3.5*a + 1/2 = 82                Combine the like terms on the left.

11.5a + 1.5 = 82                                    Subtract 1.5 from both sides.

11.5a + 1.5 - 1.5 = 82 - 1.5                     Combine

11.5a = 80.5                                          Divide by 11.5

a = 80.5/11.5

a = 7                  

The number of adults = 7

===============================

m = 7a + 1

m = 7*7 + 1

m = 50

===============================

e = 1/2 m

e = 1/2 * 50

e = 25

Answer:

[tex]20x^{11}[/tex]

Step-by-step explanation:

An expression in algebra that contains one term is called a monomial.

These include numbers, whole numbers and variables that are multiplied together.

Any number, a whole number without variables can also be monomial, like 32, 5236 etc.

So, here the monomial is [tex]20x^{11}[/tex].

Option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

As we know in the monomial there will be only one term.

Option (C) and Option (D) contains two terms so they are not monomial.

Option (B) contain fractional term.

Thus, option (A) represents a monomial which has only one term option (A) 20x¹¹ is correct.

Learn more about Polynomial here:

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Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Slope = change in y ÷ change in x

The line passes through (3,7) and (-1,4)

Slope = [tex]\frac{7 - 4}{3 - -1}[/tex] = [tex]\frac{3}{4}[/tex]

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

According to the data we have the following points:

[tex](x_ {1}, y_ {1}): (- 1,4)\\(x_ {2}, y_ {2}) :( 3,7)[/tex]

Substituting we have:

[tex]m = \frac {7-4} {3 - (- 1)} = \frac {3} {3 + 1} = \frac {3} {4}[/tex]

Thus, the slope of the line is [tex]\frac {3} {4}[/tex]

Answer:

[tex]\frac {3} {4}[/tex]

Answer:

Answer:

X

The given statement is true.

Step-by-step explanation:

An inverse function can be defined as  a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x.

Examples are x+2 and x-2

WE get f(x) = x+2

Apply g(x) = g(f(x))=g(x+2)

=x+2-2=x

Thus by applying composiiton g f or fg in any order we get the answer as x

THis is the property of any inverse function

Step-by-step explanation:

Answer:

X

Step-by-step explanation:

It was corrected on E2020.

Answer:

see explanation

Step-by-step explanation:

Given

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

let f(x) = y

y = [tex]e^{2x}[/tex] - 4

Switch x and y and solve for y, that is

x = [tex]e^{2y}[/tex] - 4 ( add 4 to both sides )

x + 4 = [tex]e^{2y}[/tex]

Take the ln of both sides

ln(x + 4) = ln [tex]e^{2y}[/tex] = 2y [tex]ln_{e}[/tex] = 2y

Divide both sides by 2

y = [tex]\frac{ln(x+4)}{2}[/tex], that is

[tex]f^{-1}[/tex] (x) = [tex]\frac{ln(x+4)}{2}[/tex]

Answer:

C. parallel lines

Explanation:

If two straight lines be at right angles to the same plane, the straight lines would be parallel.

Answer:

a) -5/2.

Step-by-step explanation:

Try substituting (-5/2) into f(x):

6(-5/2)^4 + 5(-5/2)^3 - 33(-5/2)^2 - 12(-5/2) + 20

= 234.375 + -78.125 - 206.25 + 30 + 20

= 0.

So it is -5/2.

Answer:

a) [tex]x= -5/2[/tex]

Step-by-step explanation:

We substitute in the function the values given in the options to confirm whether they are roots or not

a) [tex]x= -5/2[/tex]

the function will be:

[tex]f(-\frac{5}{2} )=6(-\frac{5}{2} )^4 + 5(-\frac{5}{2} )^3-33(-\frac{5}{2} )^2-12(-\frac{5}{2})+20[/tex]

simplifying:

[tex]f(-\frac{5}{2} )=6(\frac{625}{16} )-5(\frac{125}{8} )-33(\frac{25}{4} )+30+20[/tex]

[tex]f(-\frac{5}{2} )=234.375-78.125-206.25+50\\f(-\frac{5}{2} )=0\\\\[/tex]

since the function when [tex]x= -5/2[/tex] is equal to zero, this is an actual root of f(x).

Answer:

(a)(b²)√a

Step-by-step explanation:

√(a³b⁴)

Root both variables. Note that pairs of the same variables can be brought out of the root.

√(a³) = √(a * a * a) = a√a

√(b⁴) = √(b * b * b * b) = b²

(a)(b²)√a is your answer.

Answer:

its A :(

Step-by-step explanation:

Answer:

the ninth root of 3

Step-by-step explanation:

3 to the 2 over 3 power, to the 1 over 6 power rewritten as a radical expression is ''the ninth root of 3''.

Hope this helps!

Answer:

kk

Step-by-step explanation:

Answer:

-y(7+y) =0

Step-by-step explanation:

-7y - y^2 = 0

Factor out a -y

-y(7+y) =0

Using the zero product property

-y =0  and 7+y =0

y=0     7-7+y = 0-7

y=0    y = -7

Answer:

x = 8

Step-by-step explanation:

Step 1: Write an equation

2x - 9 = 7

Step 2: Use the Addition Property of Equality

2x = 16

Step 3: Use the Division Property of Equality

x = 8

Answer:

number = 8

Step-by-step explanation:

Let "number" = x. Set the equation.

"product of 2 and number" = 2(x)

"nine less" = -9

"equal to 7" = "= 7"

2x - 9 = 7

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 9 to both sides.

2x - 9 (+9) = 7 (+9)

2x = 7 (+9)

2x = 16

Divide 2 from both sides.

(2x)/2 = (16)/2

x = 16/2

x = 8

8 is your answer.

~

Answer:

29.74 degrees.

Step-by-step explanation:

Tan(theta) = opposite / adjcent.

opposite = 8

adjacent = 14

Tan(theta) = 8/14

Tan(theta) = 0.5714

theta = tan^-1(0.5714)

theta = 29.74 degrees

Answer:

√61

Step-by-step explanation:

Distance between 2 points (x1, y1) and (x2,y2) is given by

Distance = √ [ (x2-x1)² + (y2-y1)² ]

in our case, x1 = 0, y1 = 6, x2 = 5, y2 = 12

Distance

= √ [ (5-0)² + (12-6)² ]

= √ [ (5)² + (6)² ]

= √ 61

Answer:

√61

Step-by-step explanation:

The distance between two points is given by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (5-0)^2 + (12-6)^2)

  =sqrt( 5^2 + 6^2)

 = sqrt(25+36)

 = sqrt(61)

Answer:

  x = 1

Step-by-step explanation:

The graph is shown below. The solution is x = 1.

___

√x +2 = 3x . . . . given

√x = 3x -2 . . . . . subtract 2

x = 9x^2 -12x +4 . . . . square both sides

9x^2 -13x +4 = 0 . . . . subtract x to put in standard form

(x -1)(9x -4) = 0 . . . . . factor the quadratic

x = 1 . . . or . . . x = 4/9 . . . . values of x that make the factors zero

The "solution" x = 4/9 is extraneous, in that it does not satisfy the equation. It would correspond to the intersection of the line with the negative branch of the square root function. That is, it does satisfy -√x +2 = 3x.

The solution is x=1.

Answer:

The answer is B.

e^a=55

Taking log on both sides,

lne^a = ln 55

a lne= ln55

a= ln55.

The value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).

A log function is a way to find how much a number must be raised in order to get the desired number.

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

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

We solve the value of this expression using the basic logarithm,

[tex]\rm{log_ab=c[/tex]

Similarly,

[tex]\rm{log_e55=a[/tex]

we know that the log base of exponent is natural log, therefore,

[tex]\rm ln\ 55=a[/tex]

Therefore, the value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).

Learn more about Logarithm:

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Answer:

The solutions are x=0, x=1

Step-by-step explanation:

we know that

The solution of the equation f(x)=g(x)

are the values of x when the value of f(x) is equal to the value of g(x)

Observing the table

For x=0

f(0)=1  and g(0)=1

so

For x=0 ------> f(x)=g(x)

For x=1

f(1)=1/2  and g(1)=1/2

so

For x=1 ------> f(x)=g(x)

therefore

The solutions are x=0, x=1