The student council needs to make a banner for the seventh-grade dance. The dance committee decides that the length of the banner will be 16 feet. What are the possible widths of the banner if the students can use no more than 40 square feet of material? Find the solution set of the inequality 16w ≤ 40 to solve the problem.

A rectangle with a length of 16 feet and width of w.

What are the possible widths of the banner if the students can use no more than 40 square feet of material?
at most 2.5 ft wide
less than 2.5 ft wide
at least 0.4 ft wide
no more than 0.4 ft wide

Answer:

19.1

Step-by-step explanation:

Answer:

x ≈ 19.1

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos33° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{x}[/tex] ( multiply both sides by x )

x × cos33° = 16 ( divide both sides by cos33° )

x = [tex]\frac{16}{cos33}[/tex] ≈ 19.1 ( to the nearest tenth )

Answer:

V = 24.28 in ^3

Step-by-step explanation:

The area of the base is

A =5/2 × s × a  where s is the side length and a is the apothem

A = 5/2 ( 2.13) * .87

A = 4.63275

The volume is

V = Bh  where B is the area of the base and h is the height

V = 4.63275 ( 5.24)

V =24.27561 in^3

Rounding to the  hundredth

V = 24.28 in ^3

Answer:

D

Step-by-step explanation:

graph it

Answer:

2(2)+7=11

2(3)+7=13

2(4)+7=15

2(5)+7=17

2(9)+7=25

Step-by-step explanation:

2(2)+7

4+7=11

2(3)+7

6+7=13

2(4)+7

8+7=15

2(5)+7

10+7=17

2(9)+7

18+7=25

Answer:

Step-by-step explanation:

Scale factor is 2. 6/3=2, 8/4=2. So it’s 1/2

Image of figure ABCD is missing and so i have attached it.

Answer:

D_new = (-1, - 12)

Step-by-step explanation:

From the figure attached, the current coordinates of D are; (-5, -2)

Now, we are told the figure undergoes a translation of (x,y) (x+6,y-10)

Thus, this means we add 6 to the x value and subtract 10 from the y-value.

Thus, new coordinate of D is;

> (-5 + 6, -2 - 10)

> (-1, - 12)

Answer:

1, -12

Step-by-step explanation:

D = -5, -2

|

-5 + 6 = 1

|

-10 and -2 is -12

1, -12

did it on edge, got it right.

Answer: No solution

Step-by-step explanation:

-6(x - 2) + 3x = -3(x + 3) + 21

-6x + 12 + 3x = -3x - 9 + 21

Collect like terms

-6x + 3x + 3x = -9 + 21 - 12

-6x + 6x = - 9 + 9

0 = 0

In this scenario, it can be deduced that there is no solution to Kenya's equation.

Answer:

infinitely many solutions

Step-by-step explanation:

i got it right

Step-by-step explanation:

C1:

The pattern for this: you add 1/2 every time.

C2:

3, 3 1/2, 4, 4 1/2

C3:

5 1/2

C4:

The 14th

C5:

10

D1:

You add twice as more than you did before, starting at 3.

D2:

48, 96, 192, 384

D3:

192

D4:

The 9th

D5:

384

Hope this all helps.

Answer:

C)

1) As the sequence progresses, each term in the sequence increases by 1/2.    2) 3 ; 3 1/2 ; 4 ; 4 1/2

3) The 10th term in the sequence is 5 1/2.

4) 7 1/2 is the 14th term in the sequence.

5) The 17th term is 9.

D)

1) As the sequence progresses, each term multiplies by 2.

2) 48 ; 98 ; 192 ; 384

3) The 7th term in the sequence is 192.

4) 768 is the 9th term in the sequence.

5) The 8th term in the sequence is 384.

Step-by-step explanation:

FOR C : 1 + 1/2 = 1 1/2, 1 1/2 + 1/2 = 2, 2 + 1/2 = 2 1/2, and so on. This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.

FOR D: 3 x 2 = 6, 6 x 2 = 12, 12 x 2 = 24, and so on.  This pattern tells me the rule of the sequence. Continue this sequence to answer 1, 2, 3, 4, and 5.

Answer:

a^2 + b^2 = c^2

4+16 = c^2

20 = c^2

c = [tex]\sqrt{20}[/tex] = [tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

we have 8 choises   8  its even number so

we can write 8= 2*4

X=4 ss the answear between the fiveth  and sixeth choise  72+92/2 AND YOU WILL FIND THE ANSWEAR

Answer:

k=8

Step-by-step explanation:

We can solve using the slope formula

m= (y2-y1)/(x2-x1)

3/5 = (k-2)/(4- -6)

3/5 = (k-2)/(4+6)

3/5 = (k-2)/10

Multiply each side by 10

10*3/5 = (k-2)/10 *10

6 = k-2

Add 2 to each side

6+2 = k-2+2

8 = k

y = x^2 - 2x - 3

Factored Form: y = (x - 3)(x + 1)

X-Intercepts: (3, 0) and (-1, 0)

Axis of Symmetry: x = 1

Vertex: (1, -4)

Domain: All Real Numbers (or negative infinity to infinity)

Range: y > -4

Hope this helps!

Answer: 441 pages

Step-by-step explanation:

[tex]\frac{1}{3}p-3=144\\\frac{1}{3}p=147\\3(\frac{1}{3})p=147(3)\\p=441[/tex]

This is because the two chords are the same length, so they are the same distance away from the center.

We can prove this by drawing the following red segments as shown below. These segments are radii of the circle. After forming the two right triangles, note how we can use the hypotenuse leg (HL) theorem to prove the triangles congruent. So this leads to x = 9 because the corresponding pieces of the triangles must be the same.

Answer: its going to be 3 dollars and 67 cents

Step-by-step explanation:

Answer:

see above there is the answer sorry for rough

Step-by-step explanation:

6a.

[tex] - 5 = - 3 + a[/tex]

[tex] - 2 = a[/tex]

6b.

[tex]3c + 2 = - 22[/tex]

[tex]3c = - 24[/tex]

[tex]c = - 8[/tex]

Answer:

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex]

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

[tex]x^2 + (y-yc)^2 = R^2[/tex] ,

where  

R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So,  is the trajectory path equation to the circle

Let [tex]x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)[/tex] be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t  

At t= 10s, y = 16 m so we have,

[tex]9 + 7 * sin(10* w + \phi) = 16[/tex] ---------------(1)

Also, at t= 25s, y =2 m so we have,

[tex]9 + 7* sin(25 * w +\phi) = 2[/tex]--------------(2)

Solving we have, [tex]10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2[/tex]

[tex]15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6[/tex]  

Therefore [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex] is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

[tex]y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)[/tex]

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)

Answer:

0.028x-6-0.48x-2+0.552x

(0.028-0.48+0.552)x-6-2

0.1x-8

The simplified expression, when evaluated for x=36, is -4.4, when following expression and evaluate for x=36 b= 0.02(1.4x - 300)-0.2(2.4x+10)+0.552x

To simplify the expression and evaluate it for x=36, let's break it down step by step:

0.02(1.4x - 300) - 0.2(2.4x + 10) + 0.552x

First, let's simplify the terms within each set of parentheses:

0.02 * (1.4 * 36 - 300) - 0.2 * (2.4 * 36 + 10) + 0.552 * 36

Next, perform the multiplications and additions/subtractions within each set of parentheses:

0.02 * (50.4 - 300) - 0.2 * (86.4 + 10) + 0.552 * 36

0.02 * (-249.6) - 0.2 * (96.4) + 19.872

Now, evaluate the remaining multiplications:

-4.992 - 19.28 + 19.872

Finally, perform the additions and subtractions:

-4.992 - 19.28 + 19.872 = -4.4

Therefore, the simplified expression, when evaluated for x=36, is -4.4.

To know more about  simplified , here

https://brainly.com/question/28595186

#SPJ2

Answer:

15

Step-by-step explanation:

The amplitude of y=sin(x) is 1 with a maximum of y=1 and a minimum of y=-1. It's amplitude is 1 because that is the distance the max( y=1 )is from the mid line (y=0) or the distance the min( y=-1 ) is from the mid line (y=0).

So we just need to find the distance the mid line, y=-12, and the max,y= 3, is from each other.

3--12=3+12=15

Answer:

42 and 43.

Step-by-step explanation:

This problem can be solved just by knowing the sum of the page numbers, as page numbers on the same face are always one digit apart. Thus we can take 85, subtract 1, divide by 2, and then get 42,42, and add 1 back to the second-page number.

To check our work we can multiply 42*43 to get 1806.

Answer:

A

Step-by-step explanation:

As the angles are equal, AB=BC, 16x-7=12x+1, 4x=8, x=2.

Answer:

12

Step-by-step explanation:

We are looking for the highest common factor

Breaking each term into primes

144 = 12*12 =  4*3 * 4*3 =  2*2*3*3

180 = 20 *9 = 4*5*3*3 = 2*2*3*3*5

240 = 24*10 = 4*6*2*5 = 2*2*2*3*2*5 = 2*2*2*2*3*5

300 = 30*10 = 5*6*2*5 = 5*2*3*2*5 = 2*2*3*5*5

Look for the common factor

2*2*3 = 12

The steps to create attached screenshot of the inscribed circle of triangle ΔABC using GeoGebra tools includes;

1) Clicking on the Geometry link, under Powerful Math Apps group

2) On the opened Geometry page click on the Polygon icon and follow the instructions that come up, which is Select all vertices and then the first vertex (selected) again (a second time)

3) Once the triangle is created, select the Angle Bisector icon, under the Construct group; A message will appear, asking to Select three points or two lines, select three vertex, of the triangle created with a mouse click, with the vertex A in the center, such as BAC, or CAB a straight line representing the angle bisector of angle ∠A is created

4) Repeat the above to create the angle bisector of angle ∠B

5) Click on the Point button under the Basic Tools group, then click on the intersection of the two angle bisectors created above, the point will be automatically labelled point D

6) Click on the Perpendicular Line, icon under the Construct group, then click on point D, and then the line AB to draw the perpendicular from D to AB

7) Click on the point Point icon and then the intersection point of the perpendicular from D and AB to label the point E

8) Click on the Circle with Center basic tool and then points D and E above, to create the inscribed circle of triangle ΔABC

9) Select the Segment tool, then select the center of the circle and a point

on the circumference. Click on the label, from the pop up options, select

the label option AA then change the label of the segment created to Radius

and select Show Label and Show Value. The inscribed circle of ΔABC created with GeoGebra tools is attached

Learn more about GeoGebra hear;

https://brainly.com/question/10400398

Answer:

Step-by-step explanation: from edmentum

Answer:

6

[tex] \sqrt{2} [/tex]

Answer:

Step-by-step explanation:

The series is missing from the question. I will answer this question with a general explanation by using the following similar series:

[tex]\sum\limits^6_{n=0} 7^n[/tex]

Required

The series

To do this, we simply replace n with the values

[tex]\sum\limits^6_{n=0}[/tex] means n starts from 0 and ends at 6

[tex]\sum[/tex] means the series is a summation series

So, we have:

[tex]\sum\limits^6_{n=0} 7^n = 7^0 + 7^1 + 7^2 + ...... + 7^6[/tex]

[tex]\sum\limits^6_{n=0} 7^n = 1 + 7 + 7^2 + ...... + 7^6[/tex]

Answer:

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.

Step-by-step explanation:

La probabilidad condicional :

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

En el cual:

P(B|A) es la probabilidad de que ocurra el evento B, dado que A sucedió.  

[tex]P(A \cap B)[/tex] es la probabilidad de que ocurran tanto A como B.  

P(A) es la probabilidad de que ocurra A.

En esta pregunta :

Evento A: Estudiante A aprueba.

Evento B: Estudiante B aprueba.

La probabilidad de que el estudiante A apruebe un examen de MM-100 es 0.6

Entonces [tex]P(A) = 0.6[/tex]

La probabilidad de que ambos estudiantes aprueben es 0.3

Entonces [tex]P(A \cap B) = 0.3[/tex]

¿Cual es la probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.6} = 0.5[/tex]

0.5 = 50% probabilidad de que apruebe el estudiante B dado que el estudiante A aprueba.