You go to the store and notice the people standing in line. 7 adults and 4 children. If this ratio stays the same and there 55 people in the store, how many would be children?

We are given the polynomial:

2x³ - 3x² + 4x - 1 = 0

We need to find the value of r² + s² + t² where r,s,t are the solutions.

Simplifying r² + s² + t²:

r² + s² + t² = (r + s + t)² - 2(rs + st + rt)

[since a²+b²+c² = (a+b+c)² - 2(ab + bc + ca)]

Using the Vieta's formulae:

Above, we can see that in order to find the value of r² + s² + t², we need to find the value of the sum of solutions and sum of solutions taken 2 at a time.

Sum of roots:

We know that the Vieta's formula to find the sum of roots is:

Sum of roots = [tex]-\frac{b}{a}[/tex]

Where b and a are the coefficients from the general form: ax³ + bx² + cx - d

We notice that for the given equation, b = -3 ;  a = 2

Sum of roots = [tex]-(\frac{-3}{2})[/tex]

Sum of roots = [tex]\frac{3}{2}[/tex]

Hence, the sum of roots (r + s + t) = 3/2

Sum of roots taken two at a time:

We know that the Vieta's formula to find the sum of roots taken 2 at a time is: Sum of roots taken 2 at a time = [tex]\frac{c}{a}[/tex]

Where c and a are the coefficients from the general form: ax³ + bx² + cx - d

for the given equation, c = 4 ; a = 2

Sum of roots taken 2 at a time = [tex]\frac{4}{2}[/tex]

Sum of roots taken 2 at a time = 2

Hence, the sum of roots taken 2 at a time (rs + st + rt) = 2

Finding the value of r² + s² + t²:

We proved before that:

r² + s² + t² = (r + s + t)² - 2(rs + st + rt)

now that we know the values of (r + s + t) and (rs + st + rt), we can plug those values to get our answer

r² + s² + t² = ([tex]\frac{3}{2}[/tex])² - 2(2)

r² + s² + t² = ([tex]\frac{9}{4\\}[/tex]) - 4

r² + s² + t² = [tex]\frac{9 - 16}{4\\}[/tex]

r² + s² + t² = [tex]\frac{-7}{4}[/tex] = -1.75

Hence, the value of r² + s² + t² is -1.75

Answer:

y = -2/7x + 4

Answer: 10 I think not sure

Step-by-step explanation: 1/2 base times height-> 1/2(6•10)

3(2x-5)+2x+3=1

6x-15+2x+3=1

8x-12=1

    +12 +12

8x=13

/8   /8

x=1.625

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sorry if this doesn't help

Answer:

X=8

Step-by-step explanation:

48+22=70

4×8=48

so X is 8

Answer:

f(2)=29

Step-by-step explanation:

just plug in 2 for x

12(2) +5

24+5

29

Answer:

f=54

Step-by-step explanation:

ma is m times a 3x18= 54

Answer:

F = -54

Step-by-step explanation:

You plug in the numbers that you can

so.. F = ma     -ma= m * a

M= 3

a = -18

F = 3* (-18)

because there is one (-) number and you are multiplying your answer is going to be (-)

F= -54

Answer:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Step-by-step explanation:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Answer: C

Step-by-step explanation: Because I said soooaiahi

Answer:-12[tex]x^{2}[/tex]-9x-4584671418

Step-by-step explanation:

Answer:

A. It is in standard form because the exponents are in order from highest to lowest

Step-by-step explanation:

On edg 2021

Answer:

can I please get brainliest

Step-by-step explanation:

Answer:

hope it helps...........

Answer:

[tex]x=-2/3, 2/3[/tex]

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

[tex]y = x -3[/tex]  

Step-by-step explanation:

1) First, find the slope by using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. We can see that the two points marked on the line are (0, -3) and (3,0). So, substitute the x and y values of those points into the formula and solve:

[tex]m = \frac{(0)-(-3)}{(3)-(0)} \\m = \frac{0+3}{3-0} \\m = \frac{3}{3} \\m=1[/tex]

So, the slope is 1.

2) Slope-intercept form is represented by the formula [tex]y = mx+b[/tex]. Substitute values for [tex]m[/tex] and [tex]b[/tex] in order to write an equation.

Substitute 1 for [tex]m[/tex] since it represents the slope. Substitute -3 for [tex]b[/tex] since it represents the y-intercept. (Remember that the y-intercept is the point at which the line intersects the y-axis. So, by looking at the graph provided, we can see that (0,-3) is the y-intercept without doing any calculations.) This gives the following answer:

[tex]y = x -3[/tex]

Answer:

if you have a calculator...

Step-by-step explanation:

take 85 to the 5th power and then divide that by 3.

Answer:

20

Step-by-step explanation:

correct on edge

Answer:

your answer is the third one

Step-by-step explanation:

Answer:

its  4

Step-by-step explanation:

Answer:

ordü use uuuuuv bûsh!!!!!!!!!!

Answer:

9x^3-5

Step-by-step explanation:

Answer:

a) QT = 8

b) QN = 24  

c) QP = 23

d) MP = 46

e) RT = 6

f) TP = 12

Step-by-step explanation:

Find the diagram attached

If T is the centroid of<MNP, then the following are true;

TN = 2QT

Given TN = 16

16 = 2QT

QT = 16/2

QT = 8

QN = QT + TN

QN = 8 + 16

QN = 24

MQ + QP = MP and MQ = QP

If MQ = 23

QP = 23

Recall that MP =  MQ + QP

MP = MQ + MQ

MP = 2MQ

MP = 2(23)

MP = 46

Similarly, TP = 2RT

RT = TP/2

Also RP = RT + TP

RP = RT + 2 RT

RP = 3RT

18 = 3RT

RT = 18/3

RT = 6

Recall that TP = 2RT

TP = 2(6)

TP = 12

Step-by-step explanation:

We would do multiplication first, because of order of operations.

2x3=6

Now we add.

6+4=10

hope it helps! :3

Answer:

C. x = -4, 5/2

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

I did the quadratic formula, so 2 is A, 3 is B, and -20 is C. I got -4 and 5/2 as my answers...

(hope this helps :P)

-3, -3

,........... .......

Answer:

48

Step-by-step explanation:

All the angles of a triangle add up to 180

180-45-87=48

Hope this helps! If it did, please mark it brainliest!

P.S. Make sure not to fall for the link scams ;)

Answer:

5y+4x

Step-by-step explanation:

Answer:

4x + 5y

Step-by-step explanation:

3y + 3x + 2y + x

4x + 5y

Answer:

There is sufficient statistical evidence to suggest that the US presidents are taller than the average American male

Step-by-step explanation:

The given parameters are;

The mean height of American Males, μ = 69.5 inches

The mean height of 43 male presidents, [tex]\overline x[/tex] = 70.78

The standard deviation, s = 2.77 inches

The number of male presidents = 43

The null hypothesis; H₀ μ = [tex]\overline x[/tex]

The alternative hypothesis; Hₐ μ ≠ [tex]\overline x[/tex]

The significance level, α = 0.05

The t test for the sample with unknown population standard deviation is given as follows;

[tex]t=\dfrac{\bar{x}-\mu }{\dfrac{s }{\sqrt{n}}}[/tex]

Therefore, we have;

[tex]t=\dfrac{70.78-69.5 }{\dfrac{2.77 }{\sqrt{43}}} \approx 3.0302[/tex]

The degrees of freedom, df = n - 1 = 43 - 1 = 42

The critical 't' value = 2.0181

Therefore, given that the t test value is larger than the critical-t, we reject the null hypothesis, therefore, there is sufficient statistical evidence to suggest that the US presidents are taller than the average American male

Answer: 453

Step-by-step explanation:

To solve the question, we have to calculate the margin of error which will be:

= (61.7% - 52.3%) / 2

= 9.4% / 2

= 4.7%

4.7% = 1 / ✓n

0.047 = 1 / ✓n

✓n = 1 / 0.047

✓n = 21.28

Square both sides to.gwt the value of n

n = 21.28²

n = 452.69

n = 453

453 residents were surveyed

Answer:

Commission rate is 20%.

Step-by-step explanation:

Joey's weekly salary is $325

Plus a commission on his total sales.

Let commission is x% on his total sales.

So, we can set up equation for the given information as

325+x%(2950)= 915

Solve this equation for x%.

Subtract both sides 325

x%(2950) =590

Divide both sides by 2950

x%=0.2

We know x% means it is [tex]\frac{x}{100}[/tex]

So, [tex]\frac{x}{100} =0.2[/tex]

Multiply both sides by 100

x=20%.

So, commission rate is 20%