Plans for a new shopping center call for buildings directly across the sidewalk from each other to be congruent. This computer printout shows a clothing store.

If the vertices of a home improvement store are located at (−x1,y1), (−x2,y2), (−x3,y3), and (−x4,y4), will the home improvement store be congruent to the clothing store?

Answer:

[tex]\displaystyle z = 4\, \log_{10} \left(\frac{32}{5}\right)[/tex].

Step-by-step explanation:

Multiply both sides by [tex](1/5)[/tex] and simplify:

[tex]\displaystyle \frac{1}{5} \times 5\, (10)^{z/4} = \frac{1}{5} \times 32[/tex].

[tex]\displaystyle (10)^{z/4} = \frac{32}{5}[/tex].

Take the base-[tex]10[/tex] logarithm of both sides:

[tex]\displaystyle \log_{10}\left(10^{z/4}\right) = \log_{10} \left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle \frac{z}{4} = \log_{10}\left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle z = \log_{10}\left(\frac{32}{5}\right)[/tex].

Answer:

6y = -5x + 6

y = -5/6 x + 1

Step-by-step explanation:

y = -5/6 x + b

1 = b

Answer:

x=0       x=8          x = -1/10

Step-by-step explanation:

- 2x(x − 8)(10x + 1) = 0

Using the zero product property

-2x =0   x-8 = 0    10x+1= 0

x= 0    x= 8             10x = -1

x=0       x=8          x = -1/10

Answer:

Step-by-step explanation:

The general form of this equation is

[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

[tex]A=45000e^{-.02t[/tex]

Seena’s mother is 4 times as old as Seena. After 5 years her mother will be 3 times as old as she will be then .Find their present ages.

✧ Let us assume :

Seena's age be x

Her mother's age be 4x

✧ After 5 years :

Seena's age = x + 5

Her mother's age = 4x + 5

✧ Ratio of age after 5 years :

Seena's mother = 3

Seena's ratio = 1

Hence, the equation is :

[tex] \looparrowright\frak{ \frac{4x + 5}{x + 5} = \frac{3}{1} }[/tex]

By cross multiplying we get

[tex] \looparrowright \frak{3(x + 5) = 4x + 5}[/tex]

[tex] \looparrowright \frak{3x + 15 = 4x + 5}[/tex]

[tex] \looparrowright \frak{x = 10}[/tex]

Hence, the ages are

Seena's age = x = 10 yrs

Her mother's age = 4x = 4 × 10 = 40 years

∴ Seena's age is 10 and her mother's is 40 respectively

Answer:

X⁴–X²–2X –1=0

(X²+X+1)(X²–X–1)=0

[tex]x = - \frac{1 - i\sqrt{3} }{2} \\ x = - \frac{ 1 + i \sqrt{3} }{2} [/tex]

[tex]x = \frac{1 + \sqrt{5} }{2} \\ x = \frac{1 - \sqrt{5} }{2} [/tex]

I hope I helped you^_^

Answer:

Graph A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Mean of the data = sum of the data / number of frequencies:

Correct choice is d

Answer:

x = 1 and y =5

Step-by-step explanation:

[tex]8x -2y= -2\\Divide by -2\\-4x+y = 1\\add 4x\\y= 1+4x\\[/tex]

Substitute this value of y in the next equation.

[tex]9x+5(1+4x) = 34\\9x+5+20x=34\\29x+5=34\\29x=29\\x=1[/tex]

Solve for y using x.

[tex]y=4x+1\\y=4(1)+1\\y=5[/tex]

Answer:

y= [tex]\frac{c-2x}{3}[/tex]

Step-by-step explanation:

2x+3y=C

isolate y

3y=C-2x

y= [tex]\frac{c-2x}{3}[/tex]

Answer:

9

Step-by-step explanation:

r/3  +5 ≤ 8

Subtract 5 from each side

r/3  +5 -5≤ 8-5

r/3   ≤ 3

Multiply each side by 3

r/3  *3 ≤ 3*3

r   ≤ 9

The only value that is less than or equal to 9 is 9

Answer:

Step-by-step explanation:

[tex]tan \ 83.1 = \frac{opposite \ side}{adjacent \ side} = \frac{BC}{100}\\\\8.2635 = \frac{BC}{100}\\\\8.2635*100=BC\\\\826.35 = BC[/tex]

Height of tower = 826.35 m

Answer:

x=4

Step-by-step explanation:

f(x) = x^2 - 8x+16

Set equal to zero

0 = x^2 -8x +16

Factor

what 2 numbers multiply to 16 and add to -8

-4*-4 = 16

-4+-4 = -8

0= (x-4)(x-4)

Using the zero product property

x-4 = 0  x-4 =0

x=4  x=4

Answer:

x = -1 y = 3

Step-by-step explanation:

x = 2y-7

2x + 3y = 7

Substitute x =2y-7 in 2y + 3y = 7

2(2y-7) + 3y = 7

4y-14+3y = 7

7y - 14 = 7

7y = 7 + 14

7y = 21

7y/7 = 21/7

y = 3

Substitute 3 for y in x = 2y-7

x = 2(3) - 7

x = 6 -7

x = -1

Answered by Gauthmath

Answer:

x² - x - 12 = 0

Step-by-step explanation:

Given the x- intercepts are x = - 3 and x = 4 , then the factors are

(x + 3) and (x - 4)

Expressing as a zero product

(x + 3)(x - 4) = 0 ← expand using FOIL

x² - x - 12 = 0

Transformations are operators that can act on functions, modifying them in different ways. In this particular problem, we see the translations.

The correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x)=  1∕x left by 3 units and downward by 5 units.

Let's describe the transformations:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the shift is to the left.

If N is negative, the shift is to the right

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

Now that we know this, let's see the problem.

We have:

[tex]g(x) = \frac{1}{x + 3} - 5[/tex]

So, the original function is:

[tex]f(x) = \frac{1}{x}[/tex]

Now from f(x) we can apply translations to create g(x).

If first, we apply a translation of 3 units to the left, we get:

[tex]g(x) = f(x + 3) = \frac{1}{x + 3}[/tex]

If now we apply a translation of 5 units downwards, we get:

[tex]g(x) = f(x + 3) - 5 = \frac{1}{x + 3} - 5[/tex]

So we can conclude that the correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units.

If you want to learn more about translations, you can read:

https://brainly.com/question/12463306

Answer:

4

Step-by-step explanation:

The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.

Answer:

b. 8

Step-by-step explanation:

Simplify the left side by dividing the top and bottom by 5

35/5 = 7

40 /5 = 8

7/8

Hey there!

35/40 = 7/x

Cross Multiply the fraction

35(x) = (7)(40)

→ 35x = 280

DIVIDE 35 to BOTH SIDES

35x/35 = 280/35

CANCEL out: 35/35 because that gives you 1

KEEP: 280/35 because that helps solve for the x-value

→ x = 280/35

x = 8

Therefore, your answer is most likely: 8 (Option B)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

-2

Step-by-step explanation:

The output of the chart and graph drops by 2 for every input.

1. Electrical energy consumption is measured at kilowatt-hour (KWh). Thus the cost of energy consumed for the month is $31.104.

2. The amount of energy used in the house for the month is 731.634 KWh.

3. The length of the board equals the sum of each length of the pieces. The length of the board to buy is 8.70 feet.

1. The rate of consumption of energy is measured in kilowatt-hour.

In the given question,

12 cent is paid per kilowatt-hour.

60 watts of light for 1 hour = 0.06 KWh

3 light bulbs of 60 Watts each for 1 hour = 3 x  0.06

                                           = 0.18 KWh

But,

30 days = 30 x 24 hours

                        = 1440 hours

The total energy consumed for the month = 1440 x 0.18

                                      =  259.20 KWh

The total cost for the month = 0.12 x 259.20

                                               = $31.104

Thus, the total cost for the month is $31.104.

2. Charge per kilowatt-hour = $0.11

Total power bill = $80.48

So that,

Total cost on bill = amount charge per kilowatt x total energy consumed in KWh

Which implies;

$80.48 = $0.11 x total energy consumed in KWh

total energy consumed = [tex]\frac{80.48}{0.11}[/tex]

                               = 731.634 KWh

Therefore, the amount of energy used in the house for the month is 731.634 KWh.

3. Each length of the two end pieces = 2.6 feet each

Given that the remaining piece needs to be 0.86 times longer than each of the first two. Then;

the length of the remaining piece = 2.6 + 0.86

                                                         = 3.46

The length of the remaining piece = 3.46 feet

The length of the board to buy = 2.6 + 2.6 + 3.46

                                                   = 8.66

Thus, the length of the board to buy is 8.70 feet.

Related link: 1, 2. https://brainly.com/question/13988193

                     3. https://brainly.com/question/16046083

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]

Dimes: 3 times greater than nickels:

This means that:

[tex]y = 3x[/tex]

Quarters: One greater than double the number of nickels:

This means that:

[tex]z = 2x + 1[/tex]

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]

[tex]0.05x + 0.1(3x) + 0.25(2x+1) = 3.65[/tex]

[tex]0.05x + 0.3x + 0.5x + 0.25 = 3.65[/tex]

[tex]0.85x = 3.4[/tex]

[tex]x = \frac{3.4}{0.85}[/tex]

[tex]x = 4[/tex]

y and z:

[tex]y = 3x = 3(4) = 12[/tex]

[tex]z = 2x + 1 = 2(4) + 1 = 9[/tex]

There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at https://brainly.com/question/17096268

Step-by-step explanation:

Right now, we would solve everything within the parenthesis first.

(8 - 16) + (8 + 6)

(-8) + (14)

14 - 8

6

But if we remove the parenthesis, it doesn't matter what order we do things in.

8 - 16 + 8 + 6

8 + 8 - 16 + 6

16 - 16 + 6

6

The reason why both of these are the same, is because the only calculations we're doing are addition and subtraction, which don't care about parenthesis.

Answer:

A

Answer:  3

Step-by-step explanation:                                                                                                          

[tex]\displaystyle\ \Large \boldsymbol{} We \ have \ a \ square\ function \\\\ f(x)=ax^2+bx+c \\\\And \ we \ know \\\\ \left[\left \[ {{f(0)=a\cdot 0+b\cdot0+c=0} \atop {f(-4)=a(-4)^2+-4b+c=-24}} \right.=>[/tex]                                                [tex]\displaystyle\ \Large \boldsymbol{} \left[ \ {{c=0} \atop {16a-4b=-24}} \right. =>\boxed{4a-b=-6} \\\\\\ and \ x_0 =-\frac{b}{2a}=1 =>\boxed{ b=-2a} \\\\\\ \left \{ {{4a-b=-6} \atop {b=-2a}} \right. =>4a+2a=-6=> a=-1 \ ; \ b=2 \\\\\\then \ b-a=2-(-1)=\boxed{3}[/tex]                                                                                    

Answer:

a) 450 gravel   b)1250 sand

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

369 = x + (x+2) + (x+4)

369 = 3x + 6

363 = 3x

121 = x

now that we know that x = 121, we can solve the equation by plugging in the variable

369 = x + (x+2) + (x+4)

369 = 121 + 123 + 125

369 = 369

The smallest three integers are 121,123 and 125.

Let, the smallest odd integers be n

Then according to the given condition,

[tex]n+(n+2)+(n+4)=369\\3n+6=369\\3n=363\\n=121[/tex]

So, the numbers are,

[tex]n=121\\n+2=121+2=123\\n+4=121+4=125[/tex]

Learn More:https://brainly.com/question/2254193

Answer:

but what to do in do I have to find the area of the particular Region or a length of that

Answer:

64

Step-by-step explanation:

4^4*4^-1      

4^4*1/4

256*1/4

256/4

64