AABC has been translated 5 units to the right, as shown in the diagram. What
is the length of AB?

A. 10
B. 6
C. 31
D. 15

Check the picture below.

so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so

[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]

now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena

[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]

Answer:

3 feet

Step-by-step explanation:

Let x be the width of the grass strip.

So the length of the grass strip=18+2x

Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2

But the available grass seed is enough for 234 ft squared

4x^2+66x=234

4x^2+66x-234=0

x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)

x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8

x={-66+-(90)}/8

Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)

So the width of the strip is 3 feet.

Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet

Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet

Therefore the strip is 3 feet wide

Ans : the measure of WX = 8

Answer:

Population = e. all shark attacks.

Sample = f. the 1000 records of shark attacks that were examined.

Variable = d. the set of groups to which the victims of shark attacks belong.

Step-by-step explanation:

The population in a particular study refers to the entire set of people to which the research study encompasses, that is all those who are eligible to be a part of the study or those who the study relates to and the outcome of the study Cann be applied to them. In the research study described above, the population of the study is all events of shark attacks.

The sample is a subset of the larger population ; the subset selected in the scenario above is the 1000 records examined out of all the events of shark attacks.

The variable in the study may refer to a set of independent variables which is according to the scenario is the set of groups to which victims of shark attack belong.

Answer:

30,000

Step-by-step explanation:

Given:

In the given circle, the measure of major arc TV is 220 degrees.

To find:

The measure of angle TUV.

Solution:

In a circle, the measure central angle of arc is equal to its corresponding arc measure and according to central angle theorem, the measure of subtended angle on an arc is half of the measure of central angle of that arc.

So, the measure of subtended angle is half of the measure of its corresponding arc.

[tex]m\angle TUV=\dfrac{1}{2}\times \text{Measure of major arc TV}[/tex]

[tex]m\angle TUV=\dfrac{1}{2}\times 220^\circ[/tex]

[tex]m\angle TUV=110^\circ[/tex]

Therefore, the measure of angle TUV is 110 degrees.

Answer:A

Step-by-step explanation: The formula for finding volume is LxWxH. 21x 11 is 231, and since one side is 11 so will the other side be, and then you get 2,541 m cubed.

Answer:

U just have to make her feel comfortable to trust u that she can tell u that she actually likes u....dont push anything just make her feel appreciated ok?

Step-by-step explanation:

that's all

Answer:

2/10ths?

Step-by-step explanation:

then it would be 1/5th

Answer:

x  =  76    y  =  112     z (max)  =  2104 $

Step-by-step explanation:

                               legs    rockers    short dowels     long dowels  Profit $

Model His (x)           4           2                   4                          8                10

Model Her (y)           4          2                    8                          4                12

Availability             900      400              1200                    1056

From the table above we find z

Objective Function z :

z  =  10*x  +  12*y    to maximize

Subject to

Constraint  1  quantity of legs available: 900

4*x +4*y ≤ 900

Constraint  2  quantity of rockers available:  400

2*x +  2*y  ≤ 400

Constraint  3  quantity of short dowels available: 1200

4*x  8*y  ≤  1200

Constraint  4  quantity of long dowels available: 1056

8*x  +  4*y  ≤ 1056

Constraint 5 condition between  x  and y

x  ≥  0.5*y

The model:

z  =  10*x  +  12*y    to maximize

Subject to:

4*x +4*y ≤ 900

2*x +  2*y  ≤ 400

4*x  8*y  ≤  1200

8*x  +  4*y  ≤ 1056

x  ≥  0.5*y        or    x  - 0.5*y ≥ 0

General constraints:

x  ≥ 0   y  ≥ 0  both integers

After 6 iterations with AtomZmath on-line solver optimal solution is:

x  =  76    y  =  112     z (max)  =  2104 $

Answer:

I think the second one is the answer ; 2√b

Answer:

103/28

Step-by-step explanation:

Let the number be 'x'

Equation:-

7x - 3/4 = 25

7x = 25 + 3/4

7x = 100/4 + 3/4

7x = 103/4

x = 103/(4 x 7)

x = 103/28

Answer:

if we make this a algebraic equation it will look like this

7x-3/4x=25

6.25x=25

25 divided by 6.25=4

x=4

to check

28-3=25

Hope This Helps!!!

Answer:

A and B are exhaustive.

Step-by-step explanation:

Given

[tex]A = \{1,2,4\}[/tex]

[tex]B = \{2,3,4,5,6\}[/tex]

[tex]C =\{3,4\}[/tex]

[tex]D = \{2,4,5\}[/tex]

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

[tex]S = P(X\ n\ Y)[/tex]

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]

and the sample space is:

[tex]S = \{1,2,3,4,5,6\}[/tex]

By comparison;

[tex]A\ n\ B = S[/tex]

Hence, A and B are exhaustive.

Answer:  there are 22 observations that are more than 116.

Step-by-step explanation:

Let x be the random variable.

Given: Sample size = 950

Mean = 78

Standard deviation = 19

The probability that the observations are more than 116 is given by :-

[tex]P(X>116)=P(\dfrac{X-mean}{standard \ deviation}>\dfrac{116-78}{19})\\\\=P(Z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ \ [\text{Using p-value calculator}]\\\\=0.0228[/tex]

Number of observations are more than 116 = [tex]0.0228\times950[/tex]

[tex]=21.66\approx22[/tex]

Hence, there are 22 observations that are more than 116.

Answer:

-14/2 , 1/3 and 0.325 are the rational numbers

Answer:

27 Nickels

Step-by-step explanation:

Divide 1.35 by 0.05

= 27

Answer:

[tex]P(E|A)= \frac{10}{11}[/tex]

Step-by-step explanation:

Given

Two rolls of die

[tex]E \to[/tex] one of the outcomes is 6

[tex]A \to[/tex] atleast one is 6

Required

P(E|A)

First, list out the outcome of each

[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]

So:

[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]

Where:

[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]n(E\ n\ A) = 10[/tex]

[tex]n(A) = 11[/tex]

So:

[tex]P(E|A)= \frac{10}{11}[/tex]

Answer:

C) 6

Step-by-step explanation:

Alternate interior angles are congruent meaning that they are equal to each other sp 18x+2=110 is simplified to 18x=108. Then divide by 18 to get x equal to 6. Hope this helped and post more :)

Answer:

11,500

Step-by-step explanation:

cost price of a book (CP) = 10000

profit percent = 15%

selling price of a book (SP) = ?

SP = CP + profit% of CP

=10000 + 15 / 100 * 10000

=1000000 + 150000/100

=1150000/100

=11500

Therefore, the book will cost 11,500

Answer:

B

Step-by-step explanation:

I'm not really shure tho

Answer:

D. -0.5

Step-by-step explanation:

AB dilated by scale factor -0.5 to produce AB'.

the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5

Answer:

area = 40.5 cm^2

Step-by-step explanation:

A quick calculation tells me it is none of them

Area = 6*(9 + 4.5) / 2

Area = 3*13.5

Area = 40.5

Answer:

half of 60 is 30

13 more than that is

13+30=43

so the answer is 43

Step-by-step explanation:

hope it helps you

Answer:

[tex]{ \tt{g(x) = - 3x}} \\ { \tt{g(x + h) = - 3(x + h)}} \\ \\ { \bf{ \binom{ \frac{ \delta \: y}{ \delta \: x} }{lim \: h→0} = \frac{g(x + h) - g(x)}{h} }} \\ \\ { \tt{ = \frac{ - 3(x + h) - ( - 3x)}{h} }} \\ \\ { \tt{ = \frac{ - 3x - 3h + 3x}{h} }} \\ \\ { \tt{ = \frac{ - 3h}{h} }} \\ \\ { \tt{ = - 3}} \\ { \bf{h→0, \: \frac{ \delta \: y}{ \delta \: x} = \frac{dy}{dx} }} \\ \\ { \tt{ \frac{dy}{dx} = - 3 }}[/tex]

Answer:

D.lines that lie in the same plane but will never intersect

Step-by-step explanation:

parallel lie in the same plane but never meet

Answer:

[tex]a_n = 8(-5)^{n-1}[/tex]

The fifth term of the sequence is 5000.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio. The nth term of a geometric sequence is:

[tex]a_n = a_1(r)^{n-1}[/tex]

a = 8; r = -5

Thus:

[tex]a_n = a_1(r)^{n-1}[/tex]

[tex]a_n = 8(-5)^{n-1}[/tex]

Fifth term:

This is [tex]a_5[/tex]. So

[tex]a_5 = 8(-5)^{5-1} = 5000[/tex]

The fifth term of the sequence is 5000.

Answer:

(-4) ^6

Step-by-step explanation:

(-4)*(-4)*(-4)*(-4)*(-4)*(-4)

There are six (-4)'s multiplied together

(-4) is the base and 6 is the exponent

(-4) ^6

Answer:

A.(-4)^6

Step-by-step explanation:

-4 is being multiplied by itself 6 times

So you would get rid of all but one negative for and add ^-6

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]

Given that 9x – 6y= 19

Find y when x=-6

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)}[/tex]

[tex] \tiny\pink{SO \: PUTTING \: VALUE} \: \orange{OF \: x \: FOR \: \: VALUE \: OF \: y}[/tex]

[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ {9( - 6) – 6y= 19} \\ - 54 - 6y = 19 \\ 6y = - 54 - 19 \\ - 73 = 6y \\ \green{ \frac{ - 73}{6} = y}[/tex]

[tex] \red{VARIFICATION - > }[/tex]

PUTTING VALUES IN EQUATION TO VARIFY THE ANSWER:-

[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)} \\ \green{y = \frac{ - 73}{6}} [/tex]

PUTTING VALUE

[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ 9( - 6) - 6( \frac{ - 73}{6} ) = 19 \\ - 54 \cancel{-}^{ \tiny{+} } \cancel{6} \frac{ \cancel{- }73}{ \cancel{6}} = 19 \\ - 54 + 73 = 19 \\ 19 = 19 \\ \orange{L.H.S} \purple{=} \green{ R.H.S}[/tex]

Answer:

y = 73 / -6

Step-by-step explanation:

Given ;

9x - 6y = 19

Where, x = - 6

Solve for y

9x - 6y = 19

plug the value of x

9 ( -6 ) - 6y = 19

- 54 - 6y = 19

Add 54 to both sides

- 54 + 54 - 6y = 19 + 54

-6y = 73

divide both side by -6

-6y / -6 = 73 / -6

y = 73 / -6