I’ll give u 10 points 5 for answer 5 for explanation

2/3

Step-by-step explanation:

the anwser would be either 2/3 or 1/3

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: c. When a > 0 and b > 1, the function models exponential growth.

You have exponential decay when a > 0 and 0 < b < 1.

Step-by-step explanation:

Answer:

2

2

+

1

2

−

5

4

2

(

2

+

6

−

2

7

)

Step-by-step explanation:

Step-by-step explanation:

angle ABC is a parallel to angle DEF

Answer:

If you give me options and a picture I can help.

Step-by-step explanation:

If not the question makes no sense

Answer:

Step-by-step explanation:

1). Geometric mean of a and b = [tex]\sqrt{a\times b}[/tex]

   Therefore, geometric mean of 2 and 50 = [tex]\sqrt{2\times 50}[/tex]

                                                                       = 10

2). By geometric mean theorem,

   [tex]\frac{JM}{KM}=\frac{KM}{ML}[/tex]

   [tex]\frac{6}{e}=\frac{e}{24}[/tex]

   e² = 6 × 24

   e = √144

   e = 12

  Similarly, [tex]\frac{JL}{KJ}=\frac{KJ}{JM}[/tex]

   [tex]\frac{6+24}{d}=\frac{d}{6}[/tex]

   d² = 6 × 30

   d = √180

   d = 6√5

   And [tex]\frac{JL}{KL}=\frac{KL}{ML}[/tex]

   [tex]\frac{6+24}{c}=\frac{c}{24}[/tex]

   c² = 30 × 24

   c = √720

   c = 12√5

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: 10 I think not sure

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

Answer:

y = -2/7x + 4

Answer:

44°

Step-by-step explanation:

cos B = 0.7193  =  44°

Answer:

m<v' is 133 m<x' is 102 m<y' is 136

Step-by-step explanation:

when reflecting the shape doesn't change shape or size so the angle measure will stay the same

Answer:

9;7

Step-by-step explanation:

Answer: C

Step-by-step explanation: Because I said soooaiahi

Answer:

60 points is the right answer

Step-by-step explanation:

Answer:

ya

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

-2.5 x 3 = 7.5

Answer:-7.5

Step-by-step explanation:

(−2.5)(3)

=−7.5

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:

Diego is moving quickly.

Step-by-step explanation:

Noah and Diego are moving with the constant speed.

But their speeds are different which will be decided by the slope of the lines given in the graph.

Slope of the line representing Noah speed = [tex]\frac{\text{Distance covered}}{\text{Time elapsed}}[/tex]

Since, line for Noah has less slope than line for Diego, speed of Diego will be more.

Therefore, Diego is moving quickly.

Answer:

sen 30; cos 60

Step-by-step explanation:

Answer:

There are 220 ways by which the medals can be awarded to three of the 15 gymnast, if exactly one of the Americans wins a medal

Step-by-step explanation:

From the question, we have;

The number of gymnast in the Olympic women's competition = 15

The number of the gymnast who are Americans = 4

The number of medals awarded = 3 medals

The number of ways hat the medals can be awarded to the three of the gymnast if exactly one of the Americans wins a medal is given as follows;

The number of ways one of the medals can be won by one of the four Americans = ₄C₁ = 4 ways

The number of ways the other two medals can be won by the remaining 11 gymnast = ₁₁C₂ = 55 ways

Therefore, the total number of ways, 'N', the medals can be awarded to three of the 15 gymnast, if exactly one of the Americans wins a medal is given as follows;

N = ₄C₁ × ₁₁C₂

∴ N = 4 × 55 = 220

Answer:

1. 302.1 ÷ 5 can be rewritten as 181.26 ÷ 3

2. 12.15 ÷ 0.02 can be rewritten as 2430 ÷ 4

3. 1.375 ÷ 0.11 can be rewritten as 75 ÷ 6

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\text{The area of a circle is }\pi r^2\text{ so the area of half a circle is }\frac{\pi r^2}{2}\\ \\ A=\frac{\pi 11^2}{2}\\ \\ A=\frac{3.14(121)}{2}\\ \\ A\approx 189.97cm^2[/tex]

Answer:

760.25

Step-by-step explanation:

The formula for the surface area of a sphere is A=4πr².

r=the radius, or half of the diameter, of the circle.

when you plug in the radius and answer the formula, you should get 1520.5.

You should then divide it by 2 since we are trying to find half of the circle.

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

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

-3, -3

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

Answer:

The answer is 22.

Step-by-step explanation:

6x+2x+4=180

8x+4=180

8x=176

x=22

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%

Answer:

A. The shape has three sides

Step-by-step explanation:

Hope this helps, have a great day

The solution is Option A.

The shape of the clock is having three sides and it represents a triangle

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the shape of the clock be represented as A

Now , let the coordinates of the clock be

The first coordinate point of clock P = P ( -8 , 6 )

The second coordinate point of clock Q = Q ( 8 , 0 )

The third coordinate point of clock R = R ( 8 , 6 )

So , there are three sides to the clock with three coordinate points

The figure represents a triangle with 3 sides

Therefore , the value of A is a triangle

Hence , the figure represents a triangle

To learn more about triangles click :

https://brainly.com/question/16739377

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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