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4 years ago

Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29)

Mathematics

1 answer:

vichka [17]4 years ago

5 0

Answer:

x=-4,1,2+5i,2-5i

Step-by-step explanation:

Given is an algebraic expression g(x) as product of two functions.

Hence solutions will be the combined solutions of two quadratic products

$g(x) = (x^2 + 3x - 4)(x^2 - 4x + 29)\\$

I expression can be factorised as

$(x+4)(x-1)$

Hence one set of solutions are

x=-4,1

Next quadratic we cannot factorize

and hence use formulae

$x=\frac{4+/-\sqrt{16-116} }{2} =2+5i, 2-5i$

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If anyone can help me I will really appreciate!!

astraxan [27]

Answer:

The decimal form of the equation is y = 2.5x + 10

The equivalent fraction form is y = (5/2)x + 10 because 5/2 = 2.5

===========================================================

Explanation:

We can pick any two columns from the table to form the two points needed.

I'll pick the first two columns

(1, 12.5)

(2, 15)

Then apply the slope formula to those points

m = (y2-y1)/(x2-x1)

m = (15-12.5)/(2-1)

m = (2.5)/(1)

m = 2.5

Now use that slope with either point mentioned to find the y intercept b.

y = mx+b

12.5 = 2.5*1 + b

12.5 = 2.5 + b

12.5 - 2.5 = b

10 = b

b = 10

y = mx+b

15 = 2.5*2+b

15 = 5+b

15-5 = b

10 = b

b = 10

We end up with the same b value.

We found that m = 2.5 is the slope and b = 10 is the y intercept

Therefore we go from y = mx+b to y = 2.5x + 10

This is the same as saying y = (5/2)x + 10 since 2.5 = 5/2

3 0

3 years ago

Will mark brainliest please help

Kruka [31]

Option A

Opposite angles in a cyclic quadrilateral add up to 180°

her

x and 133 are opposite angles

x+133=180
x=180-133
x=47°

Part A is done after part B

3 0

2 years ago

Read 2 more answers

Simplify using the vertical method. (3k + 4)(3k^2 – 5k – 3)

liubo4ka [24]

Answer:

$9k^{3} -3k^{2}-29k-12$

Step-by-step explanation:

Step 1: Expand by distributing sum groups.

$3k(3k^{2} -5k-3)+4(3k^{2} -5k-3)$

Step 2: Expand by distributing terms.

$9k^{3} -15k^{2} -9k+4(3k^{2} -5k-3)$

Step 3: Expand by distributing terms.

$9k^{3}-15k^{2} -9k+12k^{2} -20k-12$

Step 4: Collect like terms.

$9k^{3}+(-15k^{2} +12k^{2} )+(-9k-20k)-12$

Step 5: Simplify.

$9k^{3} -3k^{2}-29k-12$

3 0

3 years ago

Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of def

boyakko [2]

Answer:

$z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17$

The p value for this case would be given by:

$p_v =P(z>3.17)=0.00076$

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

$\hat p=\frac{59}{400}=0.1475$ estimated proportion of defectives from the company B

$p_o=0.1$ is the value to verify

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:

Null hypothesis: $p \leq 0.1$

Alternative hypothesis: $p > 0.1$

The statistic would be given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17$

The p value for this case would be given by:

$p_v =P(z>3.17)=0.00076$

8 0

4 years ago

Abi invests £500 for 4 years in a bank account.

lora16 [44]

Total interest= principal*interest rate*time
I=500×0.023×4
I=46

7 0

3 years ago