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Daniel [21]
3 years ago
7

If the point (x, -2) is a solution to the equation y = 2x – 4, find the value of x.

Mathematics
2 answers:
kozerog [31]3 years ago
8 0

Answer:

(1,-2)

Step-by-step explanation:

(x,-2)

= -2 = 2x - 4

-2x     -2x

-2x -2 = -4

+2   +2

-2x = -2

/-2    /-2

x = 1

guapka [62]3 years ago
7 0
This should your answer:

X = 4

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For the following amount at the given interest rate compounded​ continuously, find​ (a) the future value after 9 ​years, (b) the
Stella [2.4K]

Answer:

(a) The future value after 9 ​years is $7142.49.

(b) The effective rate is r_E=4.759 \:{\%}.

(c) The time to reach ​$13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of P dollars is invested at a rate of interest r compounded continuously for t years, the compound amount is

A=Pe^{rt}

(a) From the information given

P=4700

r=4.65\%=\frac{4.65}{100} =0.0465

t=9 \:years

Applying the above formula we get that

A=4700e^{0.0465\cdot 9}\\A=7142.49

The future value after 9 ​years is $7142.49.

(b) The effective rate is given by

r_E=e^r-1

Therefore,

r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}

(c) To find the time to reach ​$13,000, we must solve the equation

13000=4700e^{0.0465\cdot t}

4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88

3 0
3 years ago
Find the lateral and total surface area of the prism.
tia_tia [17]

Lateral surface area of the prism = 920 in²

Total surface area of the prism  = 1180 in²

Solution:

Length of the prism = 13 in

Width of the prism = 10 in

Height of the prism = 20 in

Lateral surface area of the prism = 2(l + w)h

                                                       = 2(13 + 10) × 20

                                                       = 2(23) × 20

                                                       = 920 in²

Lateral surface area of the prism = 920 in²

Total surface area of the prism  = Lateral area + 2lw

                                                     = 920 + 2 × 13 × 10

                                                     = 920 + 260

Total surface area of the prism  = 1180 in²

Hence Lateral surface area of the prism = 920 in²

Total surface area of the prism  = 1180 in²

7 0
3 years ago
A team surveys 1,000 fans to find out their preference for the team’s new uniform color. The bar graph here shows the results. W
melamori03 [73]
Since, we don't have the actual graph, I cannot give you a final answer. However, I can explain how to find the answer.

If you are looking for the color that the fans like the least, just pick the bar that is the smallest. This will be the correct answer.
4 0
3 years ago
Define f(0,0) in a way that extends f to be continuous at the origin. f(x, y) = ln ( 19x^2 - x^2y^2 + 19 y^2/ x^2 + y^2) Let f (
kirill115 [55]

Answer:

f(0,0)=ln19

Step-by-step explanation:

f(x,y)=ln(\frac{19x^2-x^2y^2+19y^2}{x^2+y^2}) is given as continuous function, so there exist lim_{(x,y)\rightarrow(0,0)}f(x,y) and it is equal to f(0,0).

Put x=rcosA annd y=rsinA

f(r,A)=ln(\frac{19r^2cos^2A-r^2cos^2A*r^2sin^2A+19r^2sin^2A}{r^cos^2A+r^2sin^2A})=ln(\frac{19r^2(cos^2A+sin^2A)-r^4cos^2Asin^a}{r^2(cos^2A+sin^2A)})

we know that cos^2A+sin^2A=1, so we have that

f(r,A))=ln(\frac{19r^2-r^4cos^2Asin^a}{r^2})=ln(19-r^2cos^2Asin^2A)

lim_{(x,y)\rightarrow(0,0)}f(x,y)=lim_{r\rightarrow0}f(r,A)=ln19

So f(0,0)=ln19.

8 0
3 years ago
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Thepotemich [5.8K]

Answer:

Step-by-step explanation:

4y - 2(5 - y + 4) = 4y - 2(9 - y)

                         = 4y + 9*(-2) - y *(-2)

                         = 4y  - 18 + 2y      {Combine like terms 4y and 2y}

                         = 6y - 18

6y - 18 = 6*y - 6*3

           = 6(y - 3)

6y- 18 =  2 *3y - 2*9

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2(3y - 9) and 6(y- 3 ) are equivalent to 4y - 2(5- y +4)

Others are not equivalent

3 0
3 years ago
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