What is the solution to the following equation? 3(7x – 12) + 26 = 3x – 10

Answer:

  2x^2 -x +1 = 0

Step-by-step explanation:

For roots α and β, the original equation can be factored as ...

  f(x) = 2(x -α)(x -β)

If we add 1 to each of those roots, the factors become ...

  g(x) = 2(x -(α+1))(x -(β+1))

This can be rearranged to be ...

  g(x) = 2((x -1) -α)((x -1) -β)

That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.

  2(x -1)² +3(x -1) +2 = 0

  2x^2 -x +1 = 0

Answer:

picture is attached

Step-by-step explanation:

there are many options but this is one

Answer:

y = 3/2x + 3.

Step-by-step explanation:

With these two points, we can find the equation of line L.

y = mx + b

Slope: (5 --1) / (4 - 0) = 5 + 1 / 4 = 6 // 4 = 3/2

Intercept: [stated by the first pair of coordinates] (0, -1)

y = 3/2x - 1

Since the line is parallel to L, the slope is the same as line L.

y = 3/2x + b

The line passes through (-2, 0), so we can substitute the points into the equation and solve for b.

0 = 3/2 * -2 + b

b - 3 = 0

b = 3

So, the equation of the line which is parallel to L and passes through the point (-2, 0), is y = 3/2x + 3.

Hope this helps!

Answer:

C

Step-by-step explanation:

A = [tex]\pi[/tex]r^2 h/3

A= 235.62

B = [tex]\pi[/tex]r^2 h

B = 235.62

They are equal

I think the answer is D.

Step-by-step explanation:

(-4) x (-4) (-4)= the answer is -1

Answer:

b

Step-by-step explanation:

-141 is larger than -143 and -145

Answer:

(4x+1)(x²-2)

Step-by-step explanation:

one way to determine the factors of 4x^3 + x^2 - 8x - 2 by grouping:

x²(4x+1)-2(4x+1)

(4x+1)(x²-2)

Answer:

(x^2-2)(4x+1)

Step-by-step explanation:

4x^3 + x^2 - 8x - 2

Group:

(4x^3 + x^2)+( - 8x - 2)

Factor out as much as possible: (The GCF)

x^2(4x+1)-2(4x+1)

Regroup:

(x^2-2)(4x+1)

Answer:

3^x + 12x -4

Step-by-step explanation:

f(x) = 3^x + 10x

g(x) = 2x - 4,

(f + g)(x) = 3^x + 10x +  2x - 4

Combine like terms

             = 3^x + 12x -4

Answer:

(f + g)(x)= 3^x +12x -4

Step-by-step explanation:

To find (f+g)(x), we must add f(x) and g(x).

(f + g)(x)= f(x) + g(x)

We know that f(x)= 3^x + 10x and g(x)= 2x-4

Therefore, we can substitute these into the equation.

(f + g)(x)= (3^x+10x) + (2x-4)

Combine like terms. Add all the terms with an x.

(f + g)(x)= 3^x + (10x+2x) -4

(f + g)(x)= 3^x +12x -4

(f + g)(x) is 3^x +12x -4

Answer:

347

Step-by-step explanation:

2(3) + 210 = 216

2(3) + 125 = 131

216+131 = 347

Answer:

The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising. The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the. number of hours spent exercising.

Answer:

5 and 29

Step-by-step explanation:

If k= -2, l = 3, m = 4.

Then to solve

k + l + m and K^2 + l^2 + m^2 , we have to substitute the value of k, l and m with the respective values.

So for k + l + m :

k + l + m = -2 + 3 + 4 = -2 + 7 = 5

And for K^2 + l^2 + m^2:

K^2 + l^2 + m^2 = -2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29

Hope this helps

Answer:

93.7%  of the lifetimes  are within 3.8  standard deviations of the mean  

Step-by-step explanation:

   Generally Chebyshev's Theorem, can be mathematically represented as  

   [tex]1 - \frac{1}{k^2}[/tex]%

The percentage  of these lifetimes that are within k=3.8 standard deviations of the mean is mathematically  evaluated using Chebyshev's Theorem as follows      

        [tex]1 - \frac{1}{k^2}[/tex]%  [tex]= (1 - \frac{1}{3.8^2} )[/tex]% =  [tex]= 93.07[/tex]%

So from the above calculation we see that 93.7%  of the lifetimes  are within 3.8  standard deviations of the mean  

Answer:

3x= 2x+18

3x-2×=2×-2×+18

×=18

Answer:

18

Step-by-step explanation:

3x = 2x + 18

3x - 2x = 18

x = 18

Answer:

0.08

Step-by-step explanation:

The probability that the bus is late on any day is 0.2

The probability that it rains tomorrow is 0.4

The probability that it will rain tomorrow and the bus is late is the product of both individuals probabilities.

Therefore:

P(late & rains) = 0.2 * 0.4 = 0.08

Answer:

The probability that it rains and the bus is late is 1/7

Step-by-step explanation:

Practically, we can apply the Bayes’ theorem to solve this.

Mathematically, we use the Bayes’ problem as follows;

P( rain| late) = P(rain ^ late)/P(late) = P( late|rain) • P(rain)/[P(late|rain)P(rain) + P(not late|no rain)P(no rain)]

Where P(no rain) = 1-P(rain) = 1-0.4 = 0.6

P(on time) = 1-P(late) = 1-0.2 = 0.8

Kindly recall that P of raining = 0.4 and the probability that the bus is late is 0.2

Substituting these values into the Bayes’ equation above, we have;

P( rain| late) = (0.2)(0.4)/(0.2)(0.4) + (0.8)(0.6)

= 0.08/(0.08 + 0.48) = 0.08/0.56 = 1/7

Answer:

B - 13 and 15

Step-by-step explanation:

MARK AS YK... Pweeeez

Answer:

B

Step-by-step explanation:

To solve this, we just need to keep in mind the following:

Vertical angles are always congruent.

Vertical angles are formed by a pair of intersecting lines. The angles across from each other are what we call vertical angles.

So, to find the congruent pair of angles, we just need to find a pair of vertical angles.

In the options given, the only option with a pair of vertical angles would be <13 and <15.

There are a few options that would be congruent if the line segments were parallel, but that is not a given.

Answer:

Step-by-step explanation:

At maximum height, the velocity of the flare will be zero.

If the flare height above the ground is modeled by the equation

h = -16t²+64t+4

Velocity = dh/dt = 0

-32t + 64 = 0

-32t = -64

t = -64/-32

t = 2secs

This shows that the flare reaches its maximum height after 2secs.

To get the maximum height of the flare, we will substitute t = 2s into the equation h = -16t²+64t+4

h = -16(2)² + 64(2)+4

h = -64+128+4

h = 64+4

h = 68 feet

The maximum height of the flare is 64 feet.

Answer:

6

Step-by-step explanation:

Answer:2835

Step-by-step explanation:

Answer:

1) x = 71°, 2) x = 27°, 3) x= 32°

Step-by-step explanation:

1) Rectangle ABCD.

∠D = 90°

From ΔABE.

∠EAB +∠ABE + ∠BEA = 180°

45 + 90 +∠BEA = 180

∠BEA = 45

∠BEA + ∠AED +∠DEC = 180 °, because ∠BEC is a straight angle

45 + x + 64 = 180

x = 71°

2) Δ XYZ  is equilateral, all angles = 60°.

∠YZX = 60°.

∠YZW = 180°, because it is a straight angle.

∠YZX + ∠XZW= 180

60 +  ∠XZW= 180

∠XZW = 120.

From ΔXZW

∠ZXW + ∠XWZ + WZX = 180

x + 33 + 120 = 180

x = 27°

3) In ΔPQR,

PQ =  PR, so ∠PQR = ∠PRQ = 69°

∠PRQ + ∠PRS = 180, because ∠QRS = 180° as straight angle.

∠PRQ + ∠PRS = 180

69 + ∠PRS = 180

∠PRS  = 111°.

From ΔPRS

∠PRS  + ∠RSP + ∠SPR = 180

111 + 37 + ∠SPR = 180

111 + 37 + x= 180

x = 32

Answer:

Step-by-step explanation:

Lets assume that x (First city) and x-500 (Second City)

[tex]x.\frac{3}{100} +(x-500)\frac{7.5}{100} =487.5\\\\\frac{3x+7.5x-3750}{100}=487.5\\ 10.5x=48750+3750\\10.5x=52500\\x=5000 (first city)\\5000-500(second city)\\[/tex]

You can ask me ıf you don't understand

Answer:

by game 3(at 1:00 p.m.)

temperature increases to 5 degrees at 1:00 p.m

Answer:

The correct answer is A. [tex](-11, -9)[/tex].

Step-by-step explanation:

Given that the point is (8,6)

Let this point be A(8,6).

The composition is T3,30 RO,-180º

First translate the point by 3,3.

Let this point becomes A'.

A' is formed by translation of point A by 3,3

i.e.

x coordinate of A' = x coordinate of A + 3 and

y coordinate of A' = y coordinate of A + 3

So, A' (8+3, 6+3)

So, A'(11,9)

Now, a rotation of -180º is applied to point A'.

Let it becomes A''.

By a rotation of -180º,  the coordinate gets changed by 2 quadrants.

A is in 1st quadrant because both x and y coordinates are positive.

A'' will be in 3rd quadrant where both x and y coordinates are negative.

Please refer to the attached image for the graphical representation of A, A' and A''.

So, the answer will be option A. [tex](-11, -9)[/tex].

Answer:

9/4

Step-by-step explanation:

Using the slope formula

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

    = (1--8)/( 4-0)

    = (1+8)/4

    = 9/4

Answer:

ssa

Step-by-step explanation:

Answer: SSA

SSA typically applies when there are two triangles

Hey there! :)

Answer:

arc AB = 2.5π in (in terms of pi) or ≈7.85 in. (pi = 3.14)

Step-by-step explanation:

Begin by finding the circumference of the circle. Use the formula:

C = 2rπ

C = 2(9)π

C = 18π.

Since ∠AQB equals 50°, set up a ratio to find the length of arc AB:

[tex]\frac{50}{360} = \frac{x}{18\pi }[/tex]

Cross multiply:

50 · 18π = 360x

900π = 360x

Divide both sides by 360:

x = 2.5π in, or ≈7.85 in.

Answer:  0π

Step-by-step explanation:

[tex]sin\bigg(\dfrac{3\pi}{2}+x\bigg)+sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-2\\\\\\2sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-2\\\\\\sin\bigg(\dfrac{3\pi}{2}+x\bigg)=-1\\\\\\\dfrac{3\pi}{2}+x\bigg=sin^{-1}(-1)\\\\\\\dfrac{3\pi}{2}+x=\dfrac{3\pi}{2}\\\\\\\large\boxed{x=0}[/tex]

Answer:

1.25 : 1

0.25 : 1

Step-by-step explanation:

Ratios are basically fractions and proportions

10 : 8 is equal to 10/8 or 1.25/1, so 1.25 : 1

5 : 20 is equal to 5/20 or 0.25/1, so 0.25 : 1

Answer:

Clean price is $3,977.22

Dirty price = $4110.99

Step-by-step explanation:

We proceed as follows;

Semiannual coupon payments = $3000* 12%/2 = 6% * 3,000 = 6/100 * 3,000 = $180

Coupons are paid on 1st June and 1st December every year(semi-annually means twice a year, every 6 months)

No. of payments remaining = 11 (1 payment in 2020 on 1st December,2020 and 2 in each of the following 5 years)

Semiannual Yield = 6%/2 =3%

The clean price of the bond is given by

P = 180/1.03+ 180/1.03^2+.....+180/1.03^11+ 3200/1.03^11

=180/0.03*(1-1/1.03^11)+3200/1.03^11

=$3977.22

Dirty price = clean price +accrued interest

Accrued Interest = Interest from 1st June , 2020 to 1st December,2020

= no of days from 1st June to 15th October/no of days from 1st June to 1st December * $180

= 136/183*$180

=$133.77

So, Dirty price = $3977.22+$133.22 = $4110.99

Answer:

6.1 square units

Step-by-step explanation:

Since the triangle was translated from one position to another position, the dimensions of the triangle have not changed. The pre-image and image are congruent.

area = base * height/2

The two sides forming a right angle can be used as the base and the height in the area formula.

BC = base = 2

AB = A'B' = height = 6.1

area = 2 * 6.1/2

area = 6.1 square units

Answer:

The probability that he doesn’t win is 6/(n + 6)

Step-by-step explanation:

Mathematically, the probability that an event occur is 1 minus the probability that the event doe not occur.

Thus, what we are saying here is that the sum of the probabilities that Paul wins the raffle draw and he doesn’t win the raffle draw is 1

This can be mathematically expressed as;

probability that he doesn’t win = 1 - probability that he wins

Thus we have;

1- n/(n+ 6)

= [(n+ 6) -(n)]/(n+6) = 6/n+ 6