Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?

Answer:

x=80

Step-by-step explanation:

the figure depicts a pentagon.

we can use linear pair method to find x

we should find interior angles

angle E= 180-90= 90

angle D=180-60= 120

angle C=180-x

angle A= 90 given

angle B= 180-40= 140

angle sum of a pentagon = 540

by formula (n-2)180. n is the number of sides

equation= 90+120+180-x+90+140= 540

620-x= 540

620-540=x

80=x

Answer:

20 centimeters

Step-by-step explanation:

A square has all sides equal.

6x - 1 = 4x + 6

6x - 4x = 6 + 1

2x = 7

x = 7/2

Plug in x as 7/2 in one of the side lengths.

6(7/2) - 1

42/2 - 1

21 - 1 = 20

Answer:

Step-by-step explanation:

Sides of a square are always equal.

6x - 1 = 4x + 6

Move the variable to L.H.S and change its sign

6x - 4x - 1 = 6

Move the constant to RHS and change its sign.

6x - 4x = 6 + 1

Simplify

2x = 7

Divide both sides by 2

2x/2 = 7/2

X = 7/2

Again,

6x - 1

plugging the value of X

= 6 * 7/2 - 1

= 3 * 7 - 1

= 21 - 1

= 20

Hope this helps...

Answer:

perimeter=[tex]2(l+b)[/tex]

2(3b+5+2b-1)=

2(5b+4)=0

5b+4=o

b=-4/5

but be can't be -ve

therefore,b=4/5 or 0.8

Answer:

6) The perimeter of the triangle is 3(3x - 1)

7) The perimeter of the rectangle is 2(5b + 4)

Step-by-step explanation:

The perimeter of a triangle and a rectangle is found by adding up all the sides.

6) Perimeter of triangle = 3x - 3 + 4x - 1 + 2x + 1 = 3x + 4x + 2x - 3 - 1 + 1 = 9x - 3 = 3(3x - 1)

7) Perimeter of rectangle = 2(L + B) = 2(3b +5 + 2b - 1) = 2(5b + 4)

Answer:

If x = 0, then the value of the polynomial = 0

Step-by-step explanation:

Given that ;

F(x ) = 5x - 4x^2

Substituting 0 for x we have;

F(0) = 5(0) -4(0)^2 = 0 + 0 = p

Answer:

y = -x - 1

Step-by-step explanation:

hello,

this is a line, right?

So the equation should be something like

y = ax+b and we need to find a and b

we can see that the points (-1,0) and (0,-1) are in the line so we can write

0 = a*(-1) + b <=> b - a = 0 <=> a = b

-1 = a*0 + b <=> b = -1

so the equation is

y = -x - 1

hope this helps

Answer:

y = - x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (0, - 1)

m = [tex]\frac{-1-1}{0+2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - x - 1 ← equation of line

Answer:

The 8ft tall pine tree will not affect the box plot here is why........

Outliers are important because they are numbers that are "outside" of the Box Plot's upper and lower fence, though they don't affect or change any other numbers in the Box Plot they are still important.

If you want to find your fences you will first take your IQR and multiply it by 1.5. I call this your "magic number".

Lower fence: Take your Q1 and subtract it from your magic number, that number your get is your lower fence.

Upper fence: Take your Q3 and add it to your magic number, that number you get is your upper fence.

Answer:

Step-by-step explanation:

Q1; 10 units

The dotted lines separate the figure into 3 shapes - 1 square, 2 triangles.

The area of a square is s^2, where s is the side length.

The side length of the square is 2. 2^2 =4

The area of the square is 4 units.

The area of a triangle is bh/2, where b is the base and h is the height.

The base of the triangle on the left is 2 and the height is also 2. 2(2)/2 =2

The area of the left triangle is 2 units.

The triangle on the right has a base of 2 and a height of 4. 4(2) =8 /2 = 4

The area of the right triangle is 4 units.

The area of the composite figure is the area of the 2 triangles and the square added together; 4+2+4 =10

The area of the figure is 10 units.

Q2: The area of the shaded area is 44.2654825 [tex]cm^2[/tex].

The area of a circle is π[tex]r^2[/tex]. The radius of this circle is 4cm.

Therefore, the area of the circle is 16π[tex]cm^2[/tex].  

The formula for area of a rectangle is length times width. The length of this rectangle is 3 and the width is 2.

Therefore, the area of the rectangle is 6 cm^2

We're looking for the area of the shaded region (area of circle- rectangle), so we subtract the area of the rectangle from the area of the circle.

16π simplifies to 50.2654825 cm^2.

50.2654825-6 = 44.2654825 cm^2

The area of the shaded area is 44.2654825 [tex]cm^2[/tex].

How many magazines are there?

12 magazine.

Step by step explanation:

The ratio of stories to magazines is 4 to 3, if there are 28 stories, how many magazines are there?

Story: c

Magazine: r

C / R

C = 4K

R = 3k

4K + 3k = 28

7k = 28

K = 7/28

K = 4

Substituting:

C = 4X4 = 16

R = 3x4 = 12

Ratio of stories to magazines: 4:3

There are 28 stories, so that would mean we would have to divide 28 by 4 to get the common rate.

28/4 = 7

So, now we can substitute it to solve the amount of magazines.

4 x 7 = 28

3 x 7 = 21

Thus, there are 21 magazine and the non-simplified ration of stories to magazines is 28:21.

Answer:

2.Ellipse

Step-by-step explanation:

The given equation represents an ellipse.

Standard form of ellipse is given as:

[tex] \frac{x^2}{a^2} +\frac{y^2}{b^2} = 1\\\\

\implies \frac{x^2}{16} - \frac{y^2}{4} = 1\\[/tex]

Answer:

When we use a graphing calc, we should see that we get A as our best choice.

Step-by-step explanation:

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

Explanation:

Parallel lines have equal slopes, but different y intercepts. The given line y = -2x+4 has a slope of -2. Any line parallel to this will also have a slope of -2.

So m = -2

The unknown line goes through the point (x,y) = (2,4). Which means x = 2 and y = 4 pair up together.

Plug m = -2, x = 2, y = 4 into y = mx+b and solve for b

y = mx+b

4 = -2(2)+b

4 = -4+b

4+4 = b ... adding 4 to both sides

8 = b

b = 8

Since m = -2 and b = 8, we go from y = mx+b to y = -2x+8

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

Side note: the y intercept of the original equation is 4 while the y intercept of the new equation is 8

Answer:

y=-2x+8

Step-by-step explanation:

y= -2x + 4 and passes through point A(2, 4)

if a line is parallel then the two lines have the same slope

since the line passes through A(2,4) then

y=-2x+b find b

4=-2(2)+b

b=4+4=8

b=8

y=-2x+8

Answer:

Step-by-step explanation:

If you plot those points on a coordinate plane, you'll see that the distance from the origin up the y-axis to the point is greater than is the distance from the origin down the x-axis to the other point. That means 3 things to us: 1. the greater distance is a and the shorter is b; 2. the point (0, 11) is the vertex while the point (4, 0) is the co-vertex; and 3. this is a vertically stretched ellipse. A vertically stretched ellipse has an equation

[tex]\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1[/tex] where h and k are the coordinates of the center, a is the greater distance (between the center and the vertex), and b is the smaller distance (between the center and the co-vertex).  Here's what we have then thus far:

h = 0

k = 0

a = 11

b = 4

Filling in our equation then looks like this:

[tex]\frac{(x-0)^2}{4^2} +\frac{(y-0)^2}{11^2} =1[/tex] and simplifying:

[tex]\frac{x^2}{16} +\frac{y^2}{121} =1[/tex]. It appears that the last answer is the one you want, although when I teach this to my precalc students, I do not encourage them to move the x and y terms around as that answer appears to have done. But addition is also commutative so I'm sure it's acceptable (I just think it looks strange that way).

The equation of ellipse is [tex]\dfrac{y^2}{121}+\dfrac{x^2}{16}=1[/tex] option D is correct.

Important information:

The standard form of an ellipse is:

[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]

Where, [tex](0,a)[/tex] is vertex and [tex](0,b)[/tex] is vertex.

Substitute [tex]a=11,b=4[/tex] in the above equation.

[tex]\dfrac{x^2}{(4)^2}+\dfrac{y^2}{(11)^2}=1[/tex]

[tex]\dfrac{x^2}{16}+\dfrac{y^2}{121}=1[/tex]

[tex]\dfrac{y^2}{121}+\dfrac{x^2}{16}=1[/tex]

Therefore, the correct option is D.

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Step-by-step explanation:

if each the bonus is shared equally each will get 420

if 40% is shared by managers each manager will get 560

if 7 sales persons share 60% each will get 360

therefore Peter salesperson will get 360

but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct

Answer:

I hope it will help you...

Answer:

Monday= -5°c

on Tuesday dropped 2 °c

question

what was temperature on Tuesday

answer

=-5 - 2= -7°c on tuesday

hope it helps you

#passionforlearning

Answer:

9 cm

Step-by-step explanation:

c^2=81

Take the square root of both sides.

The square root of c^2 is c.

The square root of 81 is 9.

c=9

Answer:

C = 9 centimeters

Step-by-step explanation:

First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 *  9 = 81. Thus the answer is 9 centimeters.

Answer:

D) n(c) = c/15 - 2.

Step-by-step explanation:

c(n) = 15n + 30

c = 15n + 30

15n + 30 = c

15n = c - 30

n = c/15 - 2

D) n(c) = c/15 - 2

Hope this helps!

The correct answer is option D which is n(c) = c/15 - 2.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The inverse function of the given expression will be calculated as follows:-

c(n) = 15n + 30

c  = 15n + 30

15n + 30 = c

15n = c - 30

n = c/15 - 2

Therefore the correct answer is option D which is n(c) = c/15 - 2.

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Answer:

16

Step-by-step explanation:

64 = 4x

64/4 = 4x/4

16 = x

Answer:

48 miles per hour.

Step-by-step explanation:

The definition of a sample statistic is "any function of observed data, such as the sample mean, sample variance, etc.".

We are given both the sample mean and the sample variance. But samples exist to be compared to the population.

Since we are given the data that "the mean speed of vehicles is greater than 45 miles per hour", we are told what is happening to the mean, not the standard deviation. So, we will use the mean of the sample of 25 vehicles to state the sample statistic: mean speed of 48 miles per hour.

Hope this helps!

Answer:

D

Step-by-step explanation:

Given

[tex]R_{y-axis}[/tex] ￮ [tex]R_{y=x}[/tex] : (2, 3 )

Then the order of reflections is from right to left, that is

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(2, 3 ) → (3, 2 )

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , thus

(3, 2 ) → (- 3, 2 ) → D

Answer:

Probability of blue or red = 3/10

Step-by-step explanation:

4 are black 10 are blue, 3 are red, 6 are green , 6 are blue and red and 1 .

Total = 30

Probability of having a blue = 6/30

Probability of having a blue= 1/5

Probability of a red = 3/30

Probability of a red= 1/10

Probability of a blue or a red=

Probability of blue + probability of red

= 6/30 + 3/30

= 9/30

= 3/10

Answer:

730 trains would be needed  to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required

Step-by-step explanation:

Number of carriages in 1 train = 15

Number of seats in 1 carriage = 32

Number of seats in 15 carriages =[tex]32 \times 15 =480[/tex]

So, Number of seats in 1 train = 480

Number of trains needed  to seat 350,000 passengers=[tex]\frac{350000}{480}=730[/tex]

Number of carriage in 1 train = 15

Number of carriage in 730 trains = [tex]15 \times 730=10950[/tex]

Number of seats in 1 carriage = 32

Number of seats in 10950 carriage =[tex]32 \times 10950=350400[/tex]

Hence 730 trains would be needed  to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required

Answer:

The correct answer will be "0.756596 m²".

Step-by-step explanation:

The given values are:

The radius of an umbrella,

r = 0.4 m

The height of an umbrella,

h = 0.45 m

As we know,

The lateral surface of an umbrella will be:

⇒  [tex]\pi r\sqrt{r^2+h^2}[/tex]

On substituting the values, we get

⇒  [tex]\pi \times 0.4\sqrt{(0.4)^2=(0.45)^2}[/tex]

⇒  [tex]0.756596 \ m^2[/tex]

So that the amount of fabric needed will be "0.756596 m²".

Answer:

64

Step-by-step explanation:

Answer:

y ≤ -1/5x +1

Step-by-step explanation:

The line had an incline of -1/5 and the intersect with the y-axis is 1, so the line is given by

y = -1/5x +1

The indicated area in graph is below the line, so now you have enough to get the right inequality:

y ≤ -1/5x +1

Answer:

x=6

Step-by-step explanation:

Suppose x is 36÷6

x=36÷6

x=6

Answer:

36 / 6 = 6

36 = 6 * 6

36 = 36

Hope this somewhat helps!

Answer:

A) f(x)

Step-by-step explanation:

f(x) has 4 x-intercepts, becoz it "cross" the x axis 4 times.

g(x) would have an infinite number of intercepts coz it is a cos function, but it gave a limit to the domain which is 0 to 2[tex]\pi[/tex], so it only has 2 x-intercepts.

h(x) is the degree of x^3, so in theory, it has 3 x-intercepts.

The function that has the most x-intercept is given by: Option A: f(x)

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 becuase at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

Suppose that we've got a polynomial function as y = p(x),

where p(x) is of degree n (the highest power its variable pertains in any of its composing terms).

Then, the maximum number of roots it can possess for p(x) = c (c is a constant), or p(x) - c = 0 is n

So, the number of roots of p(x) - c = 0 cannot exceed the degree of p(x).

From the graph, we see that:

f(x) intersects x-axis at 4 places, so it has 4 x-intercepts.

g(x) intersects the x-axis at 2 places as in the graph, and therefore, it has 2 x-intercepts.

h(x) is a polynomial of degree 3. The maximum number of intercepts it can have is the maximum number of roots h(x) = 0 can have which is 3(the degree of h(x) ). So it cannot be bigger than 3.

Thus, the function that has the most x-intercept is given by: Option A: f(x)

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Answer:

(a)Exponential

(b)[tex]P(t)=4.70(1.0136)^t[/tex]

(c)The price of milk next year will be: $4.76

(d)5 years

Step-by-step explanation:

The price of a gallon of milk has been rising about 1.36% per year since 2000.

(a)Since the price grows by a percentage (or constant factor) each year, an exponential function would be best to model the scenario.

(b)The exponential growth model is given as:

[tex]P(t)=P_0(1+r)^t$ where:\\P_0$=Initial Price\\r=Growth factor\\t=time (in years, for this case)[/tex]

The independent variable in the function is t. This represents the number of years since 2000.

(c)

[tex]I$nitial Price, P_0=\$4.70\\r=1.36\%=0.0136\\P(t)=4.70(1+0.0136)^t\\\\P(t)=4.70(1.0136)^t[/tex]

Therefore, the price of milk next year will be:

[tex]P(1)=4.70(1.0136)^1=\$4.76[/tex]

(d)We want to determine how long it will take for the price to top $5.

P(t)=$5

[tex]5=4.70(1.0136)^t\\$Divide both sides by 4.7$\\(1.0136)^t=\frac{5}{4.7} \\$Change to logarithm form\\t=Log_{1.0136}\frac{5}{4.7}\\t=4.58[/tex]

Therefore, in exactly 4.58 years, the milk price would be $5. Therefore, by the 5th year, the milk price would top $5.

Answer:

No there is a remainder of -512

Step-by-step explanation:

Divide (x+7) into (x^3 - 3x^2 + 2x - 8)

x^2-10x+72 R -512/(x+7)

According to the Factor theorem,  (x+7)  is not a factor of f(x) = x^3 − 3x^2 + 2x − 8.

The theorem is as follows: A polynomial f(x) has a factor (x−p) if and only if f(p)=0.  

Consider, f(x) = x^3 − 3x^2 + 2x − 8

Here, the expression we have is (x + 7), so we have to find f(-7) in order to check if (x+7) is a factor of f(x) or not

Here,  p = −7  

Now, lets check

f(−7)=(−343)−3(49)−14−8  

f(−7)=−343−147−14−8  

f(−7)=−512, which is not equal to 0  .

So, According to the Factor theorem,

(x+7)  is not a factor of f(x) = x^3 − 3x^2 + 2x − 8.

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Answer:

c, d, g, k

Step-by-step explanation:

in that order