Pls answer only 16 and 19

Pls Answer Only 16 And 19

Answers

Answer 1

Question 16:

[tex]\alpha[/tex] and [tex]\beta[/tex] are the roots of the equation.

That means [tex](x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0\\[/tex]

[tex](x-\alpha )(x-\beta ) = 2x^{2} -6x+5 = 0[/tex]

          [tex]2x^{2} -6x+5 = 0\\x^{2} -3x+\frac{5}{2} =0[/tex]

          [tex](x-\alpha )(x-\beta ) =x^{2} - (\alpha +\beta )x +\alpha \beta[/tex]

So,

[tex]x^{2} - (\alpha +\beta )x +\alpha \beta = x^{2} -3x+\frac{5}{2}[/tex]

Compare coefficient

[tex]\alpha +\beta = 3\\\alpha \beta = \frac{5}{2}[/tex]

Consider [tex]\frac{\beta }{\alpha } + \frac{\alpha }{\beta }[/tex]

[tex]\frac{\beta }{\alpha } + \frac{\alpha }{\beta } =\frac{ \alpha ^{2} +\beta ^{2}}{\alpha \beta }[/tex]

[tex]= \frac{(\alpha +\beta )^{2} -2\alpha \beta }{\alpha \beta } \\= \frac{3^{2} -2*\frac{5}{2} }{\frac{5}{2} } \\= 4*\frac{2}{5} \\=\frac{8}{5}[/tex]

Ans: 8/5

Question 19:

[tex]f(x+2) = 2x^{2} +5x-3\\[/tex]

Substitute x with -1

So,

[tex]f(1) = 2(-1)^{2} +5(-1)-3\\=2-5-3\\=-6[/tex]

Ans: -6


Related Questions

Please answer circle theorem question.
Many thx.

Answers

Answer:

x = 125

Step-by-step explanation:

Tangents from an external point to a circle are congruent , that is

CA = CB

Then Δ ABC is isosceles with base angles being congruent

∠ BAC = ∠ ABC = [tex]\frac{180-70}{2}[/tex] = [tex]\frac{110}{2}[/tex] = 55°

∠ ABC and x are adjacent angles on a straight line and sum to 180° , so

x = 180° - 55° = 125°

Then x = 125

Which graph best represents the solution to this system of inequalities?

A.
B.
C.
D.

Answers

Answer:

letter A po

Step-by-step explanation:

thanks for brain less

Please answer!!!!!!!!!!!!!! 25 PTS!

Answers

Answer:

b

Step-by-step explanation:

b

It’s b I hope it helps

Blake gives piano lessons in the evenings. He earns $20 for each piano lesson and has between 0 and 6 lessons each evening. The amount he earns in an evening depends on the number of lessons he gives. What is the range of this relation?.

Answers

The range of the relation will be expressed as 0 ≤ g(x) ≤ 120

Let the number of lessons he gives be x

If he earns $20 for each piano lesson, the amount he will earn on x lessons will be $20x

Writing this as a function will give:

g(x) = 20x

where g(x) is the range of the relation.

If he has between 0 and 6 lessons each evening, the corresponding range at x = 0 and x = 6 is given as;

g(0) = 20(0) = 0g(6) = 20(6) = 120

Therefore the range of the relation will be expressed as 0 ≤ g(x) ≤ 120

Learn more on range of a function here: https://brainly.com/question/10878781

Answer: {0, 20, 40, 60, 80, 100, 120}

Step-by-step explanation: Remember we only use inequality signs for continuous relations with an infinite amount of values or data points or values or points. When we're given a set finite amount of data points we use brackets for this data because it is a discrete relation.

And for this problem we're looking for the range of the relation and recall the range is the dependent values or variables that depend on the domain or independent variables. The amount of money he earns depends on the amount of hours he works. Hence, the range is {0, 20, 40, 60, 80, 100, 120} the amount of possible money he can earn.

Help please, 9th grade math.

Answers

Answer:

table k

Step-by-step explanation:

4:3 ratio

Sorry I did this in 6th grade, I’ll help tho!

READ THIS, it helps!

24 and 18 (divide each by 3 and you get your 8 and 6)

48 and 36 ( divide both by 6 and you get 8 and 6)

64 and 48 ( you divide 64 by 8 and get 8 and divide 48 by 6 and you get 8)

Answer: Table K
Hope this helps!!

Sketch the graph of each linear inequality

Answers

Answer:

hope you can see these, the red graph is problem 3 and the blue graph is problem 5 :)

Sally saved 65% of her pay check. If she made $500, how much did she save?

Answers

Answer: 325 dollars

Step-by-step explanation:

In order to find out a percentage of somethin, you can simply multiply and divide

[tex]500*65=32500[/tex]

32500÷100= 325

Use the factorial operation to evaluate 4!
4×3×2×1
4+3+2+1
4.321
4-3-2-1​

Answers

Answer:

4x3x2x1=25

Step-by-step explanation:

hope this helps :)

y³ written in expanded form is

Answers

y x y x y

hope this helps

In this diagram shown,
PQRS is a rectangle

Answers

Ok that’s ok got re

Answer:

In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm,...In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm, find h

EXPLANATION

From the diagram, PQRS is a rectangle

Area of shaded part = 72sq.cm

But 72 = 3h - 4 + 6h - 4 + 4h

= 72 - 16h - 8

= 16h - 72 + 8

=16h = 80

h = 80/16

= 5cm

5 What rate of interest is paid on a deposit of $2000 which earns $400
interest in 5 years?

Answers

Answer:

4%

Step-by-step explanation:

Given

I = 400P = 2000R = ?T = 5 years

Formula

I = PRT

Solving.

I = PRT400 = 2,000 × R × 5400 = 10,000 × R400 / 10,000 = R0.04 = R

Change 0.04 to percent

0.04 × 100 = 4%

Answer:

4%

Every eight minutes the river raft can load 88 passengers what is the loading rate for passengers per minute

Answers

Answer:

11 passengers per minute.

Step-by-step explanation:

To find how many passengers board the boat in a minute, you'd have to divide 88 with 8.

88/8 = 11

To check:

11 passengers per min x 8 mins = 88 passengers.

A car travels 220 miles in 3 hours 20 minutes. What is its average speed?

Answers

I believe the answer is 68.75…

Answer:

66 miles per hour

Step-by-step explanation:

average speed = distance / time

distance : 220 miles

time : 3 hours 20 minutes or 3.33 hours

220 miles / 3.33 hours = 66 miles per hour

What is the area of a rectangle with the following measurements:

Answers

Answer:

24x^5

Step-by-step explanation:

3 x 8 = 24

x multiplied by x^4 = x^5

(the exponents add to each other when multiplied)

y=1.5x+8 which represents the equation when solved for x?

Answers

[tex]y=1.5x+8\\\\\implies 1.5x = y-8\\\\\implies x = \dfrac{y-8}{1.5}\\\\\implies x = \dfrac{y-8}{\tfrac 32}}\\\\\implies x = \dfrac{2(y-8)}{3}\\\\\implies x = \dfrac 23 y- \dfrac{16}3[/tex]

Pls help plss

Right answer = Brainliest
Wrong answer = Reported​

Answers

Answer:

Step-by-step explanation:

1. 15/50 = 3/10

2. 8/24 = 1/3

3. 14/49 = 2/7

4. 6/63 = 2/21

5. 18/81 = 2/9

Ok done. Thank to me :>

hi pls help me solve this​

Answers

Answer:

-23.33

Step-by-step explanation:

C = 5/9 (F - 32)

C = 5/9 (-10 - 32)

C = 5/9 (-42)

C = -23.33

what is the solution to the equation 4(x - 3) - 8 = 16?

Answers

Step-by-step explanation:

4(x-3)-8=16

4x-12-8=16

4x-20=16

4x-20+20=16+20

add

4x=36

divide both

4x/4  36/4

Simplify

x = 9

Find sum of arithmetic series where a1 = 7, n=31, nth a =127

Answers

Answer:

Sum of arithmetic series is [tex]2077[/tex]

Step-by-step explanation:

We have [tex]n[/tex]th term of arithmetic sequence

[tex]a+(n-1)d[/tex]

Here

[tex]a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4[/tex]

Sum of arithmetic sequence [tex]=\frac{n}{2} (2a+(n-1)d)[/tex]

[tex]=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077[/tex]

Answer:

The sum of arithmetic series is 2077.

Step-by-step explanation:

Solution :

Here we have provided that :

»» [tex]\rm{a_1}[/tex] = 1»» [tex]\rm{n}[/tex] = 31»» [tex]\rm{a_n}[/tex] = 127

We need to find :

»» The sum of arithmetic series.

Here's the required formula to find the sum of arithmetic series :

[tex]\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

Substituting all the given values in the formula to find the sum of arithmetic series :

[tex]{\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}[/tex]

[tex]{\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}[/tex]

[tex]{\longrightarrow{\sf S = 31 \times 67}}[/tex]

[tex]{\longrightarrow{\sf S = 2077}}[/tex]

[tex]\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}[/tex]

Hence, the sum of arithmetic series is 2077.

[tex]\rule{300}{1.5}[/tex]

2(1+a) * 5(1+a)
help u u want to help or else continue helping

Answers

Step-by-step explanation:

We simply multiply what there is to multiply:

10(1+a)^2 = 10a^2 + 20a + 10

= (2+2a)*(5+5a)
=10+10a+10a+10a^2
=10+20a+10a^2

A store owner bought 15001500 pencils at \$0.10$0.10 each. If he sells them for \$0.25$0.25 each, how many of them must he sell to make a profit of exactly \$100.00$100.00

Answers

Based on the information given, the number of pencils that should be sold will be 1000 pencils.

Let the number that should be sold be x.

A store owner bought 1500 pencils at $0.10 each. Therefore, the cost price will be:

= 1500 × $0.10 = $150

Profit = Selling price - Cost price

100 = 0.25x - 150

0.25x = 100 + 150

0.25x = 250

x = 250/0.25

x = 1000

Therefore, 1000 pencils should be sold.

Learn more about equations on:

https://brainly.com/question/13802812

mr farmer rectangular land measures 2000 meters by 3000 meters. if he walks around the perimeter of his land, how far does he walk

Answers

Answer:

10000 meters

Step-by-step explanation

To find perimeter you add the length of each side of the shape. Since the land is a rectangle there are two pairs that are parrallel, being 2000 and 3000. Making the distance 2000 + 2000 + 3000+ 3000 = 10000

Hope this helps!

Are quantity and amount are same thing, if no so tell the difference ?

no spam ​

Answers

Answer:

No

Amount should be used when you're talking about a singular noun that CAN'T be measured. ... –Quantity should be used for an inanimate, single or plural noun that CAN be counted or measured.

Step-by-step explanation:

Hope this helps you !!!

The sum of a number and six is 22. What is the number?

Answers

Answer:

16

Step-by-step explanation:

22-6=16 16+6=22

hope this helps! :)

16 because if you add 16 you should get your answer

Rita’s earnings are based on how many hours she works. Rita worked 22 hours and earned $379.50. What would Rita earn for working 52 hours?


Answers

Rita will earn $897 for working 52 hours.

Word problems in mathematics are mathematical operations that are applied to solve real life cases.

From the information given:

Rita's earnings are dependent on the hours she works

If Rita worked for 22 hours, she earns $379.50

Now, if Rita worked for 52 hours, the amount Rita will earn can be expressed by using the relation:

[tex]\mathbf{= \dfrac{52 \ hours \times \$379.50}{22 \ hours} }[/tex]

= $897

Learn more about word problems in mathematics here:

https://brainly.com/question/21405634

How to rationalize the denominator that is a radical.

Answers

Answer:

Option B is the correct answer, 3√2

Need help please if anyone one can help me now I will like that. Thanks

Answers

The answer is the last on

Help please
Simplify the difference quotient (f(x + h) − f(x) )/h if h ≠ 0.
f(x) = x2 + 38

Answers

Answer:

2x + h

Step-by-step explanation:

[tex]\frac{f(x+h)-f(x)}{h}[/tex]

= [tex]\frac{(x+h)^2+38-(x^2+38)}{h}[/tex]

= [tex]\frac{x^2+2hx+h^2+38-x^2-38}{h}[/tex]

= [tex]\frac{2hx+h^2}{h}[/tex]

= [tex]\frac{h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator

= 2x + h

A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 feet per second. Use the formula b(t)= -16t^2 + 5t + 15 to find the time it takes for the ball to reach the maximum height of the ball. Round to the nearest tenth

A. 0.2 seconds

B. 0.1 seconds

C. 0.3 seconds

D. 0.9 seconds​​

Answers

Answer:

0.2 seconds

Step-by-step explanation:

The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward.  The maximum value of b(t) occurs at the vertex.  The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.  

Answer:

A) 0.2 seconds

Step-by-step explanation:

[tex]b(t)=-16t^2+5t+15[/tex]

[tex]v(t)=-32t+5[/tex] <-- Take the derivative

[tex]0=-32t+5[/tex] <-- Set equal to 0

[tex]-5=-32t[/tex]

[tex]\frac{5}{32}=t[/tex]

[tex]t=\frac{5}{32}[/tex]

[tex]t\approx0.2[/tex]

Therefore, it will take the ball about 0.2 seconds to reach its maximum height (which happens to be about 15.4 feet BTW).

Alternatively, another non-calculus approach is the fact that the parabola opens downward, and as such, the maximum of [tex]b(t)[/tex] occurs at the vertex where [tex]t=-\frac{b}{2a}[/tex], therefore [tex]t=-\frac{5}{2(-16)}=\frac{-5}{-32}=\frac{5}{32}\approx0.2[/tex]

6x+3y=-3 how to graph it need answers quick

Answers

Answer:

Equation in slope intercept form: y = -2x -1

Step-by-step explanation:

First you must convert this equation from standard form to slope intercept form (y=mx+b).

Subtract 6x on both sides to get 3y = -6x - 3. Then divide by 3 on both sides to get y = -2x - 1.

Now to graph:

First we will plot the y-intercept, which will be (0,-1). The point will be on the y-axis, since that's the point in which the line will cross.

Next we will go down 2 units and over to the right 1 unit, until we get to the next point.

(Picture is attached above for your convenience⤴⤴⤴)

Hope this helps you :)

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