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2 years ago

Please help!!! I will mark best answer!!! Show some kind of work I don’t want to get it wrong!!!

Mathematics

1 answer:

umka2103 [35]2 years ago

6 0

Answer:

Step-by-step explanation:

Vertex is (1,6)

Axis of symmetry is x=1

Min/Max value is (1,6)

The graph is the parabola opening downward.

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Solve the equation x+3/x-4 = x-5/x+4

Serga [27]

Answer:

$\large\boxed{x=\dfrac{1}{2}}$

Step-by-step explanation:

$\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\\\\\text{Domain:}\ x-4\neq0\ \wedge\ x+4\neq0\\\\x\neq4\ \wedge\ x\neq-4\\\\D:x\in\mathbb{R}-\{-4,\ 4\}$

$\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\qquad\text{cross multiply}\\\\(x+3)(x+4)=(x-4)(x-5)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(4)+(3)(x)+(3)(4)=(x)(x)+(x)(-5)+(-4)(x)+(-4)(-5)\\\\x^2+4x+3x+12=x^2-5x-4x+20\qquad\text{combine like terms}\\\\x^2+(4x+3x)+12=x^2+(-5x-4x)+20\\\\x^2+7x+12=x^2-9x+20\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\7x+12=-9x+20\qquad\text{subtract 12 from both sides}\\\\7x=-9x+8\qquad\text{add}\ 9x\ \text{to both sides}\\\\16x=8\qquad\text{divide both sides by 16}\\\\x=\dfrac{8}{16}\\\\x=\dfrac{8:8}{16:8}\\\\x=\dfrac{1}{2}\in D$

7 0

2 years ago

If $10,000 is invested at an annual rate of 11%, compounded quarterly, find the value of the investment after the given number o

lana [24]

Answer:

$a) A\simeq17204.28$

$b) A\simeq29598.74$

$c)A\simeq50922.51$

Step-by-step explanation:

The amount formula in compound interest is:

$A=P(1+\frac{r}{n} )^{nt}$

where:

P = principal amount

r = annual interest

n = number of compounding periods

t = number of years

We already know that:

P = $10000

$r = 11\% = \frac{11\%}{100\%}=0.11$

n = 4 (quarterly in a year)

a ) t = 5 years

$A=10000(1+\frac{0.11}{4} )^{(4)(5)}\\\\A=10000(1+\frac{0.11}{4} )^{20}\\\\A=17204.28431\\\\A\simeq17204.28$

b) t = 10 years

$A=10000(1+\frac{0.11}{4} )^{(4)(10)}\\\\A=10000(1+\frac{0.11}{4} )^{40}\\\\A=29598.73987\\\\A\simeq29598.74$

c) t = 15 years

$A=10000(1+\frac{0.11}{4} )^{(4)(15)}\\\\A=10000(1+\frac{0.11}{4} )^{60}\\\\A=50922.51361\\\\A\simeq50922.51$

5 0

2 years ago

Read 2 more answers

Mariah owed her grandfather $2.25 but was recently able to pay him back $1.50. How much does mariah currently owe her grandfathe

andrey2020 [161]

She owes her grandpa $0.75

5 0

2 years ago

Read 2 more answers

If the given expression is multiplied by 3^6, which expression is not equivalent?

nordsb [41]

Answer:

Step-by-step explanation:

I can't see the pic.

7 0

2 years ago

The triangles below are similar. Find DE. If necessary, round 2 decimal places.

Law Incorporation [45]

We know that the 2 triangles are proportional and are similar so that means there must be a scale factor between the sides of the triangles. To find the D, we need to use the scale factor and multiply it by CD to find DE. The scale factor can be found by dividing 2 similar sides so: EF divided by DG is 5/1.25 which is 4. We can then multiply the scale factor which is 4 by CD so: 3.25 * 4 is 13. DE = 13

7 0

3 years ago