Two rectangles are joined together to form a single large area. The rectangles do not overlap. The first rectangle has side lengths of 333 meters and 555 meters. The second rectangle has side lengths of 777 meters and 444 meters. What is the combined area?

Answer:

a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

   (ii) [tex]k=2[/tex]

Step-by-step explanation:

It is given that,

[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

a)

We need to find the value of a+b+c.

[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b)

(i) We need to find the value of a+2c.

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.

[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]

[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]

On comparing both sides, we get

[tex]k=2[/tex]

Answer:

28

Step-by-step explanation:

[tex]4 {x}^{2} + - - x + 49 \\ this \: is \: the \: expanded \: form \: of \\ {(2x + 7)}^{2} = 4 {x}^{2} + 28x + 49[/tex]

Answer:

[tex]\huge \boxed{28}[/tex]

Step-by-step explanation:

The trinomial is a perfect square.

Take the square root of the first term and the last term.

[tex](\sqrt{4x^2}+\sqrt{49})^2[/tex]

[tex]\sqrt{4x^2}=2x\\ \sqrt{49} =7[/tex]

[tex](2x+7)^2[/tex]

Expand to find the second term of the trinomial.

[tex](2x+7)(2x+7)\\2x(2x+7)+7(2x+7)\\4x^2 +14x+14x+49\\4x^2 +28x+49[/tex]

The second term of the trinomial is 28x.

Answer:

[tex]\Large \boxed{-10x-50}[/tex]

Step-by-step explanation:

[tex]-10(x+5)[/tex]

Distribute -10 to the terms in the brackets.

[tex]-10(x)-10(5)[/tex]

[tex]-10x-50[/tex]

Answer: -10x - 50

Step-by-step explanation:

Distribute -10 to both terms.

-10 * x = -10x

-10 * 5 = -50

The equation now looks like this:

-10x - 50

You have nothing to simplify, so you're finished.

Hope this helps!

Answer: 6/7

Step-by-step explanation: Since the Greatest common factor of 84 and 98 is 14, you divide both sides of 84/98 by 14 to get 6/7

Answer:6/7

Step-by-step explanation:The greatest common factor of both numerator and denominator is 14.So if you divide 84 by 14 you will get 6 and if you divide 98 by 14 you get 7.

Answer:

Step-by-step explanation:

Given the equation solved by Ernesto expressed as [tex]\sqrt{\dfrac{1}{2}w+8}=-2[/tex], the extraneous solution obtained by Ernesto is shown below;

[tex]\sqrt{\dfrac{1}{2}w+8}=-2\\\\square\ both \ sides \ of \ the \ equation\\(\sqrt{\dfrac{1}{2}w+8})^2=(-2)^2\\\\\dfrac{1}{2}w+8 = 4\\\\Subtract \ 8 \ from \ both \ sides\\\\\dfrac{1}{2}w+8 - 8= 4- 8\\\\\dfrac{1}{2}w= -4\\\\multiply \ both \ sides \ by \ 2\\\\\dfrac{1}{2}w*2= -4*2\\\\w = -8[/tex]

Hence, the extraneous solution that Ernesto obtained is w = -8

Answer:

$0.20

Step-by-step explanation:

4 x 1.45 = $5.80

6.00 - 5.80 = 0.20

Answer: $0.20

Step-by-step explanation:

Do 4 *$1.45 = $5.80

This is how much her total was.

She gave $6 in cash.

Subtract.

6-5.80=$.20

Answer:

  f(x) and h(x) have the same maximum value: 3

Step-by-step explanation:

The maximum value of f(x) is 3 at (π, 3).

The maximum value of g(x) is -2 at (-3, -2).

The maximum value of h(x) is 3 at (0, 3).

Both f(x) and h(x) have the same (greatest) maximum value.

Answer:

No it's not.

Step-by-step explanation:

[tex]1 \frac{1}{3} = \frac{4}{3} = 1.333333[/tex]

Integers are set of numbers consisting

It doesn't consist

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{\sf No}[/tex]

Step-by-step explanation:

[tex]\displaystyle 1 \frac{1}{3} =1.3333333...[/tex]

Integers are whole numbers that can be positive or negative. Integers do not include fractions and decimals.

Answer:

120c

Step-by-step explanation:

7c(-5c)*(-4+6)

7c+5c*4+6

12c*10

120c

Answer:

the answer can be step by step explanation will be found in the answer was Matilda by 776 7 x 6 then the answer you will you - with the answer dancer used you New divide the answer that answer the simple your answer if we multiply you can contact me and say me in which is correct or wrong and I am a teacher

Answer:

Z - score = 2.83

Step-by-step explanation:

Given the following :

Number of samples (N) = 60

Sample mean (x) = 41.9mg

Population mean (μ) = 40mg

Population standard deviation (sd) = 5.2

Using the relation :

Z = (x - μ) / (sd / √N)

Z = (41.9 - 40) / (5.2 / √60)

Z = 1.9 / (5.2 / 7.7459666)

Z = 1.9 / 0.6713171

Z = 2.8302570

Therefore, the z-score = 2.83

Answer: 3.50 Per hour

Step-by-step explanation:

Divide 84 by 24

Answer:

the answer is $27.90

Step-by-step explanation:

if you do 15 times 2.79 you will get $41.85

then do 25 times 2.79 and you will get $69.75

then subtract 69.75 from 41.85 and your answer will be $27.90

i hope this helps this is the only way i could find the answer!

$29.4864 money will you save by driving your friend's car.

Given that, your car gets 15 miles per gallon and your friend's car averages 25 mpg.

You decide to go on a road trip to St. George Island, which is 361 miles away.

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters exactly.

Gallons needed for your car =361/15=24.06 gallons

Cost of 24.06 gallons of gas=24.06×2.79=$69.774

Gallons needed for friends car =361/25=14.44 gallons

Cost of 4.44 gallons of gas=14.44×2.79=$40.2876

Hence, while driving a friend's car you will save 69.774-40.2876=$29.4864

Therefore, $29.4864 money will you save by driving your friend's car.

To learn more about the gallons visit:

https://brainly.com/question/9917229.

#SPJ5

Answer:

1. (x+9)^2 = 89

2. (Choice D) D x = − 9 ± 89 x=−9± 89 ​ x, equals, minus, 9, plus minus, square root of, 89, end square root

Step-by-step explanation:

x^2 - 6 = 2 - 18x

1) rewrite the equation by completing the square

x^2 - 6 = 2 - 18x

x^2 + 18x = 2+6

x^2 + 18x = 8

Find the half of the coefficient of x and square it

18x

Half=9

Square half=(9)^2

=81

Add 81 to both sides

x^2 + 18x = 8

x^2 + 18x + 81 = 8 + 81

x^2 + 18x + 81 = 89

(x+9)^2 = 89

Check:

(x+9)(x+9)=89

x^2 + 9x + 9x + 81=89

x^2 + 18x +81 =89

2) (x+9)^2 = 89

√(x+9)^2 = √89

x+9=√89

x=√89 - 9

It can be rewritten as

x= -9 ± √89

(Choice D) D x = − 9 ± 89 x=−9± 89 ​ x, equals, minus, 9, plus minus, square root of, 89, end square root

Answer:

12

Step-by-step explanation:

Hello, as the coefficient of the leading term is negative we know that the vertex of the parabola is a maximum. So we need to find the vertex.

This expression is maximum for

[tex]t=-\dfrac{b}{2a} \text{ where the parabola equation is}\\\\ax^2+bx+c=0[/tex]

So, here, it gives t = 8/2=4, and then, the maximum is

[tex]-4^2+8*4-4=-16+32-4=32-20=12[/tex]

So the answer is 12.

Thanks

Answer:

The answer is below

Step-by-step explanation:

Given that:

The radius of the circle (r) = 5 units

The central angle (θ) = 25π

A sector of a circle is the portion of a circle made up of two of its radii and an arc. The area of a sector that subtends with a central angle (θ) and a radius (r) is given by the formula:

[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2[/tex]

Substituting the radius of the circle and the central angle:

[tex]Area\ of\ sector=\frac{\theta}{360} *\pi r^2\\\\Area\ of\ sector=\frac{25\pi}{360} *\pi (5)^2\\\\Area\ of\ sector=\frac{125\pi^2}{72}[/tex]

Answer:

Step-by-step explanation:

Angle 1 and angle 4 are Alternative angles:

Alternative angles are pair of angles on the inner side of each of those two lines but on opposite sides.

∠2-∠2=180  ,∠2=180-62=118

∠4+118=180  ⇒∠4=180-118 ⇒∠4=62 degrees

  ∠1=∠4                  alternative angles        

Answer: 1/2 is correct.

Step-by-step explanation:

There are 8 total parts, and 4 of them are shaded. 4 is half of 8, therefore, your answer is 1/2.

Hope this helps!

Answer:

The answer is A

Step-by-step explanation:

because there are 4 shaded parts and 8 parts in total.

4/8=1/2

It's A

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = the amount spent on daily transportation

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312

           [tex]\sigma[/tex] = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

                      P(X < $1,000) = 0.05

                      P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

                      P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

                           [tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]                

                            [tex]\sigma=\frac{-\$5312}{-1.645}[/tex]  = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

      P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)

 P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)

                                                            = 1 - 0.5359 = 0.4641

 P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)

                                                            = 1 - 0.7642 = 0.2358  

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

                    P(X > x) = 0.03   {where x is the required range}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

                    P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

                           [tex]\frac{x-\$6312}{3229.18}=1.88[/tex]                

                         [tex]{x-\$6312}=1.88\times 3229.18[/tex]  

                          x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Answer:

1) [tex]DIAGRAM \mapsto B[/tex]  

2) DEFINITION [tex]\mapsto A[/tex]

3) THEOREM [tex]\mapsto C[/tex]

4) POSTULATE [tex]\mapsto D[/tex]

Step-by-step explanation:

1) DIAGRAM  B) A visual tool representing mathematical ideas to be interpreted

A diagram is the depiction or representation of information using symbols

2) DEFINITION A) A formal statement declaring the meaning of a word

A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign

3) THEOREM C) A mathematical statement proven using postulates and definitions

A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates

4) POSTULATE D) A mathematical statement taken as a fact

An assumed truth taken as the foundation for further reasoning

Answer:

Step-by-step explanation:

Hello, please consider the following.

Option A. First week we got $200.

Week 2, we got $200+$50=$250

Week 3, we got $250+$50=$300

Week 4, we got $300+$50=$350

Week 5, we got $350+$50=$400

Week 6, we got $400+$50=$450

[tex]\begin{array}{c |c |c |c |c |c |c|}Week & 1 & 2 & 3 & 4 & 5 & 6\\----&---&---&---&---&---&---\\Amount &200 &250 &300 &350 & 400 &450\end{array}[/tex]

Option B. First week we got $200.

Week 2, we got $200+$200*10%=$200+$20=$220

Week 3, we got $220(1+10%)=$220(1.10)=$242

Week 4, we got $242(1.10)=$266.2

Week 5, we got $266.2(1.10)=$292.82

Week 6, we got $292.82(1.10)=$322.102

[tex]\begin{array}{c |c |c |c |c |c |c|}Week & 1 & 2 & 3 & 4 & 5 & 6\\----&---&---&---&---&---&---\\Amount &200 &220 &242 &266.2 & 292.82 &322.102\end{array}[/tex]

Thank you.

Answer:

2 in

Step-by-step explanation:

18/3=6 , 6 is the scale factor

12/6=2

Answer:

width= 2

Step-by-step explanation:

18 inches is the original height and we are now reducing that to 3 inches.

In order to do that, we have to divide 18 by 3 which equals 6.

Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which  equals 2.

Your final answers should be: width= 2

Answer:

1. tan A = 1/(tan B)

Step-by-step explanation:

By definition,

tangent A = opposite / adjacent = a / b

and

tangent B = opposite / adjacent = b / a

Therefore tangent A = a/b = 1/tan(B)

Answer: Tan a=tan b

I belive

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

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

The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.

--------

tan(angle) = opposite/adjacent

tan(theta) = AC/BC

tan(theta) = 12.3/8.4

theta = arctan(12.3/8.4)

theta = 55.6697828044967

theta = 55.7 degrees approximately

--------

arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]

make sure your calculator is in degree mode

Answer:

D

Step-by-step explanation:

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

Answer:

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:

[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]

According to the statement of the problem, these variables are known:

[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]

Hence, the x coordinate of P is found by direct substitution:

[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]

[tex]4 = 12\cdot x -12[/tex]

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

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Answer:

The pairs are;

t,         v

2,       96

4,       32

5,       0

6,      -32

7,      -64

9,     -128

Step-by-step explanation:

The given equation is f(t) = -16·t² + 160·t

We have, the velocity, v = d(f(t))/dt = d(-16·t² + 160·t)/dt = -32·t + 160

Which gives;

t,                                 v  

0,    -32×(0) + 160 =   160

1,     -32×(1) + 160 =    128

2,    -32×(2) + 160 =    96

3,    -32×(3) + 160 =    64

4,    -32×(4) + 160 =     32

5,    -32×(5) + 160 =     0

6,    -32×(6) + 160 =   -32

7,    -32×(7) + 160 =    -64

8,    -32×(8) + 160 =    -96

9,    -32×(9) + 160 =   -128

The given velocity values are;

96, -64, 32, 0, -128, -32  which correspond to 2, 7, 4, 5, 9, 6

The pairs are;

t,         v

2,       96

4,       32

5,       0

6,      -32

7,      -64

9,     -128

Answer: (-6,8)

Step-by-step explanation:

Translation rules are

Left c units : [tex](x,y)\to(x-c,y)[/tex]

Down c units : [tex](x,y)\to(x,y-c)[/tex]

The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:

[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]

Hence, the image point is (-6,8).

Answer:

xyz

Step-by-step explanation:

[tex](-6x)(\frac{1}{2}y)(-\frac{1}{3}z) = (-6)*\frac{1}{2}*(-\frac{1}{3}) * xyz = \frac{6}{6} xyz = xyz[/tex]

Answer:

Step-by-step explanation:

|x-a|≤b

-b≤x-a≤b

add a

a-b≤x≤a+b

put a-b=-8

a+b=-4

add

2a=-12

a=-12/2=-6

-6+b=-4

b=-4+6=2

so |x+6|≤2