Two complementary angles are in the ratio 7:8. What is the measure of the larger angle?

Answer:

Step-by-step explanation:

If the first floor of the Willis Tower is 21 feet high. and each additional floor is 12 feet high, then the floor heights as we move from one floor to another we keep increasing by 12feets and forms an arithmetic progression as shown;

21, (21+12), (21+12+12), ...

21, 33, 45...

a) To write an equation for the nth floor of the tower, we will have to find the nth term of the sequence using the formula for finding the nth term of an arithmetic sequence.

The nth term of an arithmetic sequence is expressed as [tex]T_n = a + (n-1)d[/tex]

a is the first term = 21

d is the common difference = 33-21 = 45-33 = 12

n is the number of terms

Substituting the given parameters into the formula;

[tex]T_n = 21+(n-1)*12\\T_n = 21+12n-12\\T_n = 21-12+12n\\T_n = 9+12n[/tex]

Hence the equation for the nth floor of the tower is expressed as [tex]T_n = 9+12n[/tex]

b) To get the height of the 65th floor, we will substitute n = 65 into the formula arrived at in (a)

[tex]T_n = 9+12n\\T_{65} = 9 + 12(65)\\T_{65} = 9+780\\T_{65} = 789 ft[/tex]

Hence the height of the 65th floor is 789feets.

Answer:

[tex]\frac{-13}{5}[/tex] or -2.6

Step-by-step explanation:

To do this you would first have the equation [tex]5(x+4)=12[/tex] and then you could multiply the x+5 by 5 which is 5x+25 so then your equation would be [tex]5x+25=12[/tex] then you would subtract 25 from both sides to cancel out the 25 so then your equation would look like this [tex]5x=-13[/tex] then you would divide from both sides to just get x so you would get  [tex]x=\frac{-13}{5}[/tex] so you could leave it as is or you could turn it into a decimal which is -2.6

Answer:

Domain:  [tex]-3\leq x\leq 1[/tex]

Range:  [tex]-4\leq y\leq 0[/tex]

Step-by-step explanation:

If you find the coordinate of the graph you can get the domain and range

(-3,0), (-2,-4), (-1,-2), (0,0), (1, -4)

Now that we have that find the domain and range

Domain -  x coordinate

Range - y coordinate

Domain: (-3, -2, -1, 0, 1)

Range: (-4, -2, 0)

Since the domain ranges from -3 to 1 you can use the inequality [tex]-3\leq x\leq 1[/tex] to represent the domain and [tex]-4\leq y\leq 0[/tex] for the range

Answer:

Equation: x + 5 ≤ 26

Solved: x ≤ 21

Answer:

Yes, 6 is greater then 0.06 and 0.006

Step-by-step explanation:

6 = 6.00

and both 0.06 and 0.006 are not even a whole number

Answer: Yes it is

Step-by-step explanation:

6>0.06 and 6 >0.006

Answer:

Area of diamond=8192

Area of trapezoid =72 square unit

Step-by-step explanation:

Area of diamond:

find the distance between the points:

(0,64), (64,0), (0,-64),(-64,0)

d=√(x2-x1)²+(y2-y1)²

d=√64²+64²

d=64√2=90.51( rounded to the nearest hundredth)

since it is shape of square then all sides are equal

A=length*width

A=64√2*64√2

4- Area of trapezoid= ((base a +base b)/2) h

base a=3, base b=6 height=8 ( from graph count the tiles)

Area of trapezoid = ((3*6)/2 )* 8

Area=18/2*8

Area=9*8=72 square unit

The area of a diamond is 8192 square units and the area of a trapezoid is 72 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The area of the diamond will be calculated as below:-

find the distance between the points:

(0,64), (64,0), (0,-64),(-64,0)

d=√(x2-x1)²+(y2-y1)²

d=√64²+64²

d=64√2=90.51( rounded to the nearest hundredth)

Since it is the shape of a square then all sides are equal

A=length x width

A=64√2 x 64√2

A=8192 square unit

The area of the trapezoid will be calculated as below:-

Area of trapezoid= ((base a +base b)/2) h

base a=3, base b=6 height=8 ( from graph count the tiles)

Area of trapezoid = ((3*6)/2 )* 8

Area=( 18/2 ) x 8

Area=9 x 8=72 square unit

Therefore, the area of a diamond is 8192 square units and the area of a trapezoid is 72 square units.

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Answer:

72

Step-by-step explanation:

You would first change 25% to 0.25

Then divide 18 by 0.25 (18/0.25)

Which equals 72

Answer:

4.5 because its basically 18 divided by 4

Step-by-step explanation:

Answer:

JUSTICE LEAGUE

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

It is basically 7×6 when you replace the b with 7

Answer:

The answer is 13.

Step-by-step explanation:

Find the value of 6 + b:

Replacing b by 7 gives 6 + 7. (example)

Answer:

220

Step-by-step explanation:

55 percentage of x = 121

so X = 220

as simple as that

Step-by-step explanation:

y=2x-5 is in y=mx+b

Where m = slope

[tex]slope = m = 2[/tex]

To find y-intercept :

[tex]y = 2x - 5[/tex]

Let x =0

[tex]y = 2(0) - 5 \\ y = 0 - 5 \\ y = - 5[/tex]

Answer:

Step-by-step explanation:

[tex]A = \frac{1}{2} \times b \times h\\A = 32\\b = ?=x\\h = 4\\\\32 = \frac{1}{2} \times x \times 4\\\\32 = \frac{4x}{2} \\\\Cross \: Multiply\\\\64 =4x \\Divde \: both \: sides \: of \: the \:equation \:by \: 4\\\\\frac{4x}{4} = \frac{64}{4} \\\\x = 16[/tex]

Answer:

7 t-shirts

Step-by-step explanation:

Because you know the cost of shipping ($6) is constant no matter the quantity you order (fixed cost), you can subtract it from the total cost of the order to find the total variable cost. Next you divide the left over cost by the cost per t-shirt to get the quantity ordered.

$111 - 6 = $105

$105 / $15 per shirt = 7 t-shirts

Hope this helps!

-The Business Man

Answer:

(x-6)(x+1)

Step-by-step explanation:

Answer:

3)infinitely many solution

Step-by-step explanation:

-3 - 7t = -7t - 3

-7t + 7t = -3 + 3

0 = 0

if there is same number on both side it have infinitely many solution.

hope u like it ‍❤️‍❤️‍‍❤️‍

for any question comment me

Answer:

6(-3)*4(3)*3

-12 *12 *3

-144*3

-432

Answer: -432

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

f(x) = 3 – 5x

f(-8) + f(-10) = 96

f(-8) + f(-10) =  96

f(-8) = 3 - 5×(-8)

= 3 + 40

= 43

f(-10) = 3 - 5×(-10)

= 3 + 50

= 53

f(-8) + f(-10) = 43 + 53 = 96

Answer:

-30-45k

Step-by-step explanation:

-5*6=-30

-5*9k=-45k

Answer:

-30 -45k

Step-by-step explanation:

-5(6+9k)

Distribute

-5*6 -5*9k

-30 -45k

Answer:

C.

Step-by-step explanation:

pi(r)^2

pi(2x+1)^2

6x(4pix^2+4pix+1pi)

24pix^3+24pix^2+6pix

Answer:

C

Explanation:

Volume for a cylinder is V= (pi)(r^2)(h)

r being radius, h being height.

The radius is 2x+1, so square that

(2x+1)^2 = 4x^2 + 4x + 1

Then multiply by 6x, the height

(4x^2 + 4x + 1)(6x) = 24x^3 + 24x^2 + 6x

Then multiply each term pi, which would be answer C.

Answer:

El número de hombres = 8 hombres

El número de mujeres = 7 mujeres

El número de niños = 5 niños

Step-by-step explanation:

El número total de personas en la excursión = 20

La suma de los hombres y las mujeres = 3 veces el número de hijos

El número de mujeres = 1 menos el número de hombres

Sea el número de hijos = A

Sea el número de mujeres = B

Sea el número de hombres = C

Tenemos;

B + C = 3 × A .................... (1)

B = C - 1 .......................... (2)

A + B + C = 20 .............. (3)

Sustituyendo el valor de A + B en la ecuación (1) en la ecuación (3), tenemos;

A + B + C = 20

A + 3 × A = 20

4 × A = 20

A = 5

Sumando la ecuación (1) a la ecuación (2), obtenemos

B + C + B = 3 × A + C - 1

2 · B + C - C + 1 = 3 · A

2 · B + 1 = 3 · A = 3 × 5 = 15

2 · B + 1 = 15

B = (15 - 1) / 2 = 7

B = 7

De la ecuación (2),

B = C - 1

7 = C - 1

C = 7 + 1 = 8

El número de niños = 5

El número de mujeres = 7

El número de hombres = 8.

Answer: 6

Step-by-step explanation: 12x+3=75

                                                  -3    -3

                                             12x=72

                                              12    12

                                                x=6

Answer:

x=6

Step-by-step explanation:

12x+3=75

12x=75-3

12x=72

x=6

Answer:

4(4a+5) = 16 a + 20 = True

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠ADE =  74   {Vertically opposite angles are equal}

∠AED + 127 = 180  {Straight line }

∠AED = 180 - 127

∠AED = 53

In ΔADE,

∠DAE + ∠AED + ∠ADE = 180 {angle sum property of triangle}

∠DAE + 53 + 74 = 180

∠DAE + 127 = 180

∠DAE = 180 -127

∠DAE = 53

Answer:

The answer to this problem is 3

Step-by-step explanation:

Answer:

[tex]y=-4x+16[/tex].

Step-by-step explanation:

From the given graph it is clear that the y-intercept is 16.

The line passes through (-2,24) and (2,8). So, slope of line is

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]Slope=\dfrac{8-24}{2-(-2)}[/tex]

[tex]Slope=\dfrac{-16}{4}[/tex]

[tex]Slope=-4[/tex]

Slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

Substitute m=-4 and b=16 in the above equation.

[tex]y=(-4)x+(16)[/tex]

[tex]y=-4x+16[/tex]

Therefore, the required equation is [tex]y=-4x+16[/tex].

Answer: DJ receive 12 requests for hip-hop songs on Friday night.

Step-by-step explanation:

As per given , we have

[tex]\text{(Number of request country songs ) = }2+\dfrac{4}{3}\times (\text{Number of request for hip-hop songs})[/tex]

Let X represents the number of request for hip-hop songs which equation represents the situation .

If  they're 18 request for country songs, then

[tex]18=2+\dfrac{4}{3}X\\\\\Rightarrow\ 18-2 =\dfrac{4}{3}X\\\\\Rightarrow\ 16 =\dfrac{4}{3}X\\\\\Rightarrow\ X=\dfrac{3}{4}\times16= 3\times4=12\\\\\Rightarrow\ X=12[/tex]

Hence, DJ receive 12 requests for hip-hop songs on Friday night.

Answer: Priscilla can make 8 bracelets in 48 minutes.

Step-by-step explanation:

So the givens are that:

2 bracelets in 12 minutes, how many in 48 minutes

So find the ratio of bracelets to minutes:

2/12 simplified is 1/6

So Priscilla can make 1 bracelet per 6 minutes. We just need to find how many in 48 minutes.

1/6 * 8 = 8/48

So Priscilla can make 8 bracelets in 48 minutes.

Hence your answer.

I'm confused as to why there's a random "10" but the answer is actually pretty simple. Insert (11-210) into the problems.

Basically substitute (11-210) into the numbers with the x variable.

Answer:

addition property of equality

Step-by-step explanation:

−18+p=18

Add 18 to each side using the addition property of equality

−18+18+p=18+18

p = 36