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3 years ago

Someone help me with quadratics? will give points

Mathematics

1 answer:

goldenfox [79]3 years ago

8 0

The answer is Option 1: $\frac{1\±i\sqrt{31}}{2}$

Step-by-step explanation:

Given equation is;

x²-x+8=0

Here,

a=1 , b= -1 , c=8

Quadratic formula is;

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

Putting values in equation;

$x=\frac{-(-1)\±\sqrt{(-1)^2-4(1)(8)}}{2(1)}\\\\x=\frac{1\±\sqrt{1-32}}{2}\\\\x=\frac{1\±\sqrt-31}{2}\\\\x=\frac{1\±i\sqrt{31}}{2}$

The answer is Option 1: $\frac{1\±i\sqrt{31}}{2}$

Keywords: quadratic formula, equation

Learn more about quadratic formula at:

#LearnwithBrainly

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John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^{t}$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{2}=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0

4 years ago

Please write the equation and solve:

Olegator [25]

A nonmember would have to go skating 11 times a year and a member would have to go skating 12 times a year.

They each paid $110.

I hope this is correct!

Good luck:)

3 0

3 years ago

66.

Naddik [55]

Answer: 530.66 units²

<u>Step-by-step explanation:</u>

$Area_{(circle)}=\pi r^2\qquad and\qquad r=\dfrac{diameter}{2}\\\\\\\implies Area_{(circle)}=\pi \bigg(\dfrac{diameter}{2}\bigg)^2\\\\\\\text{It is given that the diameter = 26:}\\A=\pi\bigg(\dfrac{26}{2}\bigg)^2\\\\\\.\quad =\pi \cdot 13^2\\\\\\.\quad =169\pi\\\\\\.\quad =\large\boxed{530.66}$

3 0

4 years ago

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

jolli1 [7]

Answer:

y = 5cos(πx/4) +11

Step-by-step explanation:

The radius is 5 ft, so that will be the multiplier of the trig function.

The car starts at the top of the wheel, so the appropriate trig function is cosine, which is 1 (its maximum value) when its argument is zero.

The period is 8 seconds, so the argument of the cosine function will be 2π(x/8) = πx/4. This changes by 2π when x changes by 8.

The centerline of the wheel is the sum of the minimum and the radius, so is 6+5 = 11 ft. This is the offset of the scaled cosine function.

Putting that all together, you get

... y = 5cos(π/4x) + 11

_____

The answer selections don't seem to consistently identify the argument of the trig function properly. We assume that π/4(x) means (πx/4), where this product is the argument of the trig function.