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3 years ago

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A polynomial function has -5+√3t as a root. Which of the following must also be a root of the function? a) -5-√3t b) -5+√3t c) 5

-√3t d) 5+√3t

1 answer:

juin [17]3 years ago

4 0

Answer:

a

Step-by-step explanation:

Radical roots occur as conjugate pairs

Given - 5 + $\sqrt{3}$ t is a root , then

- 5 - $\sqrt{3}$ t is also a root → a

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Complete this proof.<br><br> Given: EC AC, DB AC, ∠A = ∠F<br> Prove: ΔMDF ∼ ΔNCA

Gelneren [198K]

Answer:

Proved

Step-by-step explanation:

Given: EC || AC, DB || AC, ∠A = ∠F

Prove: ΔMDF ∼ ΔNCA

Solution

See diagram attached to the solution to better understand the following workings.

Redrawing ΔMDF or rotating to be facing the same direction.

EC is parallel to AC

DB parallel to AC

Using similar triangle theorem:

If ΔMDF ∼ ΔNCA

Ratio of Corresponding sides would be equal

(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)

DF/ CA = MD/NC = FM/AN

∠A = ∠F

∠M = ∠N

∠D = ∠C

Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.

ΔMDF ∼ ΔNCA

6 0

3 years ago

Read 2 more answers

A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-ra

S_A_V [24]

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

Compounds money quarterly

Double your money in 10 years

Step:1

Formula to calculate future investment with compounded quarterly,

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

Where, A - Future amount

P - Initial investment\

r - Rate of interest

n - No. of compounding in a year

t - No. of years

Step:2

Let, P = X

A = 2X ( Double your money )

From given, n - 4 ( for compounding quarterly )

t - 10 years

From equation (1)

$2X =X(1+\frac{r}{4} )^{(4)(10)}$

$\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}$

$2 =(1+\frac{r}{4} )^{40}$

Take root $40^{th}$ root on both side,

$\sqrt[40]{2} = (1+\frac{r}{4} )$

$1.017479692 = (\frac{4+r}{4} )$

$(1.017479692)(4) = (r+4)$

$4.06992=(r+4)$

$r = 4.06992 -4$

$r =( 0.06992)(100)$

r = 6.992 %

Result:

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

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3 years ago

Whats 1 added up to 1?

Finger [1]

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2 years ago

A ja ja ja ibsnisbisnobs

deff fn [24]

Answer:

20

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Data consistent with summary quantities in the article "Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among

Olegator [25]

Answer:

a) X[bar]₁= 1839.20 cal

b) X[bar]₂= 1779.07 cal

c) S₁= 386.35 cal

Step-by-step explanation:

Hello!

You have two independent samples,

Sample 1: n₁= 15 children that did not eat fast food.

Sample 2: n₂= 15 children that ate fast food.

The study variables are:

X₁: Calorie consumption of a kid that does not eat fast food in one day.

X₂: Calorie consumprion of a kid that eats fast food in one day.

a)

The point estimate of the population mean is the sample mean

X[bar]₁= (∑X₁/n₁) = (27588/15)= 1839.20 cal

b)

X[bar]₂= (∑X₂/n₂)= (26686/15)= 1779.07 cal

c)

To calculate the sample standard deiation, you have to calculate the sample variance first:

S₁²= $\frac{1}{n_1-1}$ [∑X₁² - (( ∑X₁)²/n₁)]= $\frac{1}{14} + [52829538 - (\frac{27588^{2} }{15})$ = 149263.4571 cal²

S₁= 386.35 cal

I hope it helps!

7 0

3 years ago