A rectangular piece of wood is 12 centimeters longer than it is wide. A strip 1 centimeter wide is cut off all around. This decreases the area by 120 square centimeters. What were the original dimensions?

Answer:

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

The height of the blimp above the ground is h = 153.884 yard

No,  the fans will not be able to read the advertisement.

The exact angle if the blimp is at 150 feet is 45.74°

Step-by-step explanation:

From the summary of the information given :

The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line.

That statement above being illustrated in the attached diagram below for better understanding.

a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?

The trigonometric ratio that can be used to calculate how high the blimp will be above the 50 yard line is :

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

b. How high above the ground is the blimp?

Using the above derived trigonometric ratio,

tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]

[tex]tan \ 72^0 = \dfrac{h}{50}[/tex]

[tex]h =tan \ 72^0 \times {50}[/tex]

[tex]h =3.07768 \times {50}[/tex]

h = 153.884 yard

The height of the blimp above the ground is h = 153.884 yard

c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet.

Will the fans be able to read the advertisement?

No,  the fans will not be able to read the advertisement.

This is  because, 153.884 yard to feet

=  153.884 × 3

= 461.652 feet which is more than the maximum given 150 feet.

If not, what possible angle of elevation could we use?

The possible angle of elevation can be determined by taking the tangent of the trigonometric ratio.

SO

tan θ = [tex]\dfrac{h}{150}[/tex]

tan θ = [tex]\dfrac{153.884}{150 \ feet}[/tex]

tan θ =  1.026

θ = tan ⁻¹ (1.026)

θ = 45.74°

d. What is the exact angle if the blimp is at 150 feet?

The exact angle if the blimp is at 150 feet is 45.74°

Answer:

1)D 2)C 3)A 4)B 5) A

Step-by-step explanation:

1) The area rectangle is 36x^2 -1

We know ,

A= l*b

=36x^2 -1

=(6x)^2 -1

=(6x+1) (6x-2)

This the value of l,b respectively.

So, Perimeter of rectangle is 2(l+b)

P=2(6x+1) + 2(6x-1)

=24x

2)The area of square is 4(x+5)^2

We know,

A=l^2

=4(x+5)^2

=4(x^2 + 10x + 25)

=(2x+10)^2

This is the value of l=2x+10.

So, Perimeter of square is 4l

P=4(2x+10)

=8x+40

3)The fully factorized form is

= -2x^2 + 10x +12

= -2x^2 + 12x -2x +12

= -2x(x-6) -2(x-6)

= -2(x-6) (x+1)

4)The fully factorized form is

=x^4 -81

=(x^2)^2 -9^2

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

=(x^2 + 9) (x^2 - 3^2)

=(x^2 + 9) (x + 3) (x - 3)

5)The fully factorized form is

= 5x^4 - 320

= 5(x^4 - 64)

= 5((x^2)^2 - 8^2)

= 5(x^2 + 8) (x^2-8)

Answer:

27

Step-by-step explanation:

3 cubed=3✖️3✖️3=27

Answer:

3³ = 3 × 3 × 3 = 9 × 3 = 27

Hope this helps you

Answer:

The number of houses built in Town B is 56.

Step-by-step explanation:

We are given that in 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B.

Also, 70 houses were built in Town A during 210.

Let the number of houses built in Town B be 'x'.

So, according to the question;

Number of houses built in Town A = Number of houses built in Town B + 25% of the houses built in Town B

[tex]70 = x + (25\% \times x)[/tex]

[tex]70 = x(1+0.25)[/tex]

[tex]x=\frac{70}{1.25}[/tex]

x = 56

Hence, the number of houses built in Town B is 56.

Answer:

c. (3x^2-1)(x-7)

Step-by-step explanation:

=(3x^3-21x^2)+(-x+7)

=-(x-7)+3x^2(x-7)

=(3x^2-1)(x-7)

Answer:

x=0    x=3

Step-by-step explanation:

F(x)=3x(2x-6)

Set equal to zero

0 =3x(2x-6)

Using the zero product property

3x =0   2x-6 =0

x =0     2x = 6

             x = 6/2

             x = 3

Answer:

x = 0 or x = 3

Step-by-step explanation:

Set the output to 0

0 = 3x(2x-6)

Set factors equal to 0.

3x = 0

x = 0

2x - 6 = 0

2x = 6

x = 3

Answer:

AB = DE

BC = EF

AC = DF

∠ABC = ∠ DEF

∠BAC = ∠EDF

∠BCA = ∠EFD

Step-by-step explanation:

As its congruent all the corresponding parts will be equal

Answer:

C. 2(3x + 16)

Step-by-step explanation:

If we replace x by 1 in the expression, we get:

4(1+ 1 + 7) - 2(1) + 8 - 4 = 4(9) - 2 + 8 - 4 = 38

If we replace x by 2 in the expression, we get:

4(2+ 2 + 7) - 2(2) + 8 - 4 = 4(11) - 4 + 8 - 4 = 44

Then, if we replace x=1 and x=2 on expression A, we get:

6x+11 = 6(1) + 11 = 17

6x + 11 = 6(2) + 11 =23

if we replace x=1 and x=2 on expression B, we get:

3(x + 7) = 3(1 + 7) = 24

3(x + 7) = 3(2 + 7) = 27

if we replace x=1 and x=2 on expression C, we get:

2(3x + 16) = 2(3(1) + 16) = 38

2(3x + 16) = 2(3(2) + 16) = 44

if we replace x=1 and x=2 on expression D, we get:

3x + 16 = 3(1) + 16 = 19

3x + 16 = 3(2) + 16 = 22

Finally, the answer is C, because we get the same answers as in the initial equation

Answer:

335

Step-by-step explanation:

Factor the given binomial:

x - y = 5

xy = 14

x = y + 5

(y + 5)y = 14

y^2 + 5y - 14 = 0

(y + 7)(y - 2) = 0

y = -7 or y = 2

y = -7

xy = 14

-7x = 14

x = -2

y = 2

2x = 14

x = 7

Solutions:

x = -2, y = -7

x = 7, y = 2

For x = -2, y = 7

x^3 - y^3 =

= (-2)^3 - (-7)^3

= -8 - (-343)

= 335

For x = 7, y = 2

x^3 - y^3 =

= 7^3 - 2^3

= 343 - 8

= 335

Answer:

315.1° (1 d.p.)

Step-by-step explanation:

Please see the attached picture for the full solution.

Complete Question:

The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)^7 B. 5(7)(0.06) C. 5(1.06)^7 D. 5(7)(1.06)

Answer:

C. 5(1.06)^7

Step-by-step explanation:

The volume of a tree increases by 7% every year

The formula we would be using is

V(t) = Vo (1 + r)t

Where V(t) = Volume after t years

Vo = Present of initial volume

r = rate of increase

t = time

From the question,

V(t) = Volume after t years = unknown

Vo = Present of initial volume = 5m³

r = rate of increase = 6% = 0.06

t = time = 7 in years

V(t) = 5 × ( 1 + 0.06)^ 7

V(t) =(5)(1.06)^7

Therefore, its volume be after 7 years if its volume is 5 cubic meters now is

Option C: (5)(1.06)^7

Answer:

C

Step-by-step explanation:

The slope formula is y^2 - y^1 over x^2 - x^1    

hope this helps!

also the answer is just the inverse of that answer

Answer:

6/13

Step-by-step explanation:

Of the 13 students who do not own a graphing calculator, 6 are girls.  The probability is 6/13.

Step-by-step explanation:

Let the other endpoint be (x,y)

Since, (1,6) is the midpoint between (9,1) and (x,y)

Therefore,

1=(9+x)/2

=> 2=9+x

=> x= -7

and,

6=(1+y)/2

=>12= 1+y

=> y=11

So, the other endpoint is ( -7, 11)

Answer:

Step-by-step explanation:

Let the coordinates of Endpoint 2 be

(x ,y)

The midpoint of the endpoints is given by

[tex](1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )[/tex]

Where x and y are coordinates of Endpoint 2

Comparing with the midpoint we have

[tex]1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7[/tex]

[tex]6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11[/tex]

Therefore x = - 7 and y = 11

The coordinates of Endpoint 2 are

Hope this helps you

Answer:

-10=661.5

-1=6.7

0=4.0

1=2.4

2=1.4

8=0.1

(0,4)

Step-by-step explanation:

The y intercept is (0,4)

A function is a law that relates a dependent and an independent variable.

The function is g(x) = 4 (0.6)ˣ

The table shows the value of x

The value of g(x) at different value of x is

At x = -10

g(x) = 661.5

At x = -1

g(x) = 6.7

At x = 0

g(x) = 4

At x = 1

g(x) = 2.4

At x = 2

g(x) = 1.4

At x = 8

g(x) = 0.1

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Answer:

The correct option is;

[tex]h(x) = \sqrt[3]{x + 2}[/tex]

Step-by-step explanation:

Given that h(x) is a translation of f(x) = ∛x

From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;

When x = -1, h(x) = 1

When x = -3, h(x) = -1

h''(x) = (-2, 0)

Which gives  

d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)

When h(x) = 0, x = -2 which gives;

[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]

Therefore, a = (0/(-2/9))^(-3/5) + 2

a = 2

The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]

We check, that when, x = -1, y = 1 which gives;

h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)

For the point (-3, -1), we have;

h(x) = [tex]\sqrt[3]{-3 + 2} = \sqrt[3]{-1} = -1[/tex]

Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).

Answer: B

Step-by-step explanation:

Answer:

The 4 packages of 15 tops for $18 is a better deal

Step-by-step explanation:

We can see which set of tops have the lowest unit price.

4 packages of 15 tops for $18:

4*15=60

There is a total of 60 tops for $18, which means each top costs 18/60 dollars, or $0.30.

5 packages of 10 tops for $16

5*10=50

There is a total of 50 tops for $16, which means that each top costs 16/50 dollars, or $0.32.

0.32>0.3

The 4 packages of 15 tops for $18 is a better deal :)

Have a great day

Answer:

Step-by-step explanation:

9x + 8 = 7.5x + 17

1.5x = 9

x = 6 hours

Answer:

If I'm not mistaken your graph is supposed to be like this

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

25 children

So , each child will get 25 pens and 7 pencils

You have to find the highest common factor of 125 and 175 which is 25 and then you have to multiply it by those two numbers to find how may pens and pencils will be given to 1 child

Hope this helps and pls mark as brianliest :)

Answer:

The hundredths place.

Step-by-step explanation:

48 is the whole number, and .061 is the decimals. As you probably know, this is the whole numbers place value.

ones, tens, hundreds, thousand, 10 thousand, 100 thousand, million...ect.

The decimal places are different

in this case the 0 is the tenths

the 6 is the hundredths

and the 1 is the thousandths.

Mostly, the decimal points are just with added ths to the end.

Hope this helped :D

As per the given number, the place value of 6 is that it is at hundredths place.

Place value is the value assigned to each digit in a number. Depending on its location, each digit in such a number has a unique value. Because a digit's value relies on where it appears in an integer, it is possible for an amount to have two equivalent digits with different values.

The decimal equivalent of 48 is .061. The entire number is 48. This is the entire integer's place value, as you are surely aware.

The decimal places are different

In the given question, the 0 is at tenths place ,6 is the hundredths place and 1 is the thousandths place.

The decimal points are typically only inserted at the end.

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Answer:

₹711,674.04

Step-by-step explanation:

1.firstly we need to solve for the total area of Bella's back garden deck.

2. Then we need to estimate mate the total cost of the garden given that a square metre cost ₹5,391.47 to build.

Given

length of garden = 12 metres

width of garden = 11 metres

Hence the area of the garden is given as

[tex]Area= length* width[/tex]

[tex]Area = 12*11= 132m^2[/tex]

if a square metre cost ₹5,391.47 to build.

132 square metre will cost= ₹5,391.47*132= ₹711,674.04

Answer:

Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]

Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]

Step-by-step explanation:

Given

Height of Burj Khalifa = 828 m

Height of CN Tower in Toronto = 553 m

Base of rectangular prism is a square with sides 10 cm [tex]\times[/tex] 10 cm.

Height of Burj Khalifa prism = 40 cm

828 m is represented as 40 cm

[tex]\Rightarrow 553 m[/tex] is represented as [tex]\frac{40}{828 } \times 553 = 26.71\ cm[/tex]

So, height of rectangular prism of CN Tower = 26.71 cm

Volume of a Prism is given by the Formula:

[tex]V=Area\ of\ Base \times Height[/tex]

Base is a square, so Area of base = [tex]Side^2[/tex]

Volume of Burj Khalifa Prism:

[tex]V_B=10^2 \times 40 = 4000\ cm^2[/tex]

Volume of CN Tower Prism:

[tex]V_C=10^2 \times 26.71 = 2671\ cm^2[/tex]

So, the answer is:

Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]

Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]

a+b+c=68

b-3=a

c-5=b

now just solve the system of equations, substitue so that there are only b's in the equation:

a+b+c=68

(b-3) + b + (b+5) = 68

3b=66

b=22

Therefore Barbara is 22

The required age of barbar is 22 years.

Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old.  How old is Barbara to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Alice, Barbara and Carol are a, b and c.

Age Alice is 3 years younger than Barbara,

a = b - 3     - - - -(1)

Age Barbara is 5 years younger than Carol

b = c - 5

c = b + 5     - - - -(2)

Together the sisters are 68 years old i.e.

a + b +c =68

From equation 1 and 2

b - 3 + b + b +5 = 68

3b + 2 = 68

3b = 66

b  = 33

Thus, the required age of barbar is 22 years.

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Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

[tex]|u|=\sqrt{14^2+9^2}[/tex] which is [tex]\sqrt{277}[/tex]

[tex]|v|=\sqrt{3^2+6^2}[/tex] which is [tex]\sqrt{45}[/tex]

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

[tex]cos\theta=\frac{uv}{|u||v|}[/tex] where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

[tex]cos^{-1}\theta=\frac{96}{111.64676}[/tex] which returns an angle measure of 30.7. Plugging that all into the dot product formula:

[tex]u*v=\sqrt{277}*\sqrt{45}cos(30.7)[/tex] gives you a dot product of 96

Answer:

Option D. 9

Step-by-step explanation:

There are two ways to obtain the answer to the question.

Method 1:

Let 2x + 1 = 0

Making x the subject, we have

2x + 1 = 0

Collect like terms

2x = –1

Divide both side by 2

x = –1/2

Now, put the value of x into the expression 4x³ – 6x² – 8x + 7, we have:

4x³ – 6x² – 8x + 7

x = –1/2

4(–1/2)³ – 6(–1/2)² – 8(–1/2) + 7

4(–1/8) – 6(1/4) – 8(–1/2) + 7

–1/2 – 3/2 + 4 +7

– 4/2 + 4 + 7

– 2 + 4 + 7

= 9

Method 2:

Divide 4x³ – 6x² – 8x + 7 by 2x + 1

Please see attached photo for explanation.

Answer: 7

Step-by-step explanation:

The smaller number is 7.75.

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, quadratic equations.

The system of equations are used to solve complex problems.

Let the smaller number is x.

The larger number is 2 less than three times the smaller number

Then the larger number is 3x -2

The sum of the two numbers is 29

The sum is the output of the mathematical operation, Addition.

The equation formed is :

3x -2 + x = 29

Grouping the variables and the constants

4x = 31

Dividing both side of the equation by 4

x = 7.75

The value of the smaller number is obtained.

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Answer:

0.73

Step-by-step explanation:

Data obtained from the question include the following:

Length (L) of square = x

Base (b) of triangle = (3x – 2)

Height (h) of triangle = (2x + 4)

Area of square = L²

Area of square = x²

Area of triangle = ½bh

Area of triangle = ½(3x – 2) (2x + 4)

Expand

½ [3x(2x + 4) –2(2x + 4)]

½[6x² + 12x – 4x – 8]

½[6x² + 8x – 8]

3x² + 4x – 4

Area of triangle = 3x² + 4x – 4

Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:

Area of triangle = area of square

Area of triangle = 3x² + 4x – 4

Area of square = x²

Area of triangle = area of square

3x² + 4x – 4 = x²

Rearrange

3x² – x² + 4x – 4 = 0

2x² + 4x – 4 = 0

Solving by formula method

a = 2, b = 4, c = –4

x = – b ± √(b² – 4ac) / 2a

x = – 4 ± √(4² – 4×2×–4) / 2×2

x = – 4 ± √(16 + 32) / 4

x = – 4 ± √(48) / 4

x = (– 4 ± 6.93)4

x = (– 4 + 6.93)4 or (– 4 – 6.93)4

x = 0.73 or –2.73

Since the measurement can not be negative, the value of x is 0.73.

Answer:

The length is 20 ft, and the width is 10 ft.

Step-by-step explanation:

area = length * width

Let the width = w

length = 2w

A = LW

A = 2w * w = 200

2w^2 = 200

w^2 = 100

w = 10

L = 2w = 20

The length is 20 ft, and the width is 10 ft.

Answer:

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Step-by-step explanation: