the graph of the absolute value parent function is vertically stretched by a factor of three, then shifted two units left & five units down. Write the equation of the new function in vertex form.

Answer:

A right triangle and an isosceles

Step-by-step explanation:

Note: Consider we need to find the solution of given equation.

Given:

The equation is

[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]

To find:

The solution of the equation.

Solution:

We have,

[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]

[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]

By cross multiplication, we get

[tex]6(2+x^2)=11(2x)[/tex]

[tex]12+6x^2=22x[/tex]

[tex]6x^2-22x+12=0[/tex]

[tex]2(3x^2-11x+6)=0[/tex]

Divide both sides by 2.

[tex]3x^2-11x+6=0[/tex]

Splitting the middle term, we get

[tex]3x^2-9x-2x+6=0[/tex]

[tex]3x(x-3)-2(x-3)=0[/tex]

[tex](x-3)(3x-2)=0[/tex]

Using zero product property, we get

[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]

[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]

Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].

Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).

Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

We are given the algebraic equation:  1/x+x/2=11/6

Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.

LCD(x,2,6) = 6x

Multiply all through the fractions by 6x

(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)

6 + 3x² = 11x

Rewriting the equation:

3x² - 11x + 6 = 0

Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

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Answer:

11118 people voted

Step-by-step explanation:

Given

[tex]Eligible\ Voters = 21800[/tex]

[tex]Registered\ Voters = 85\%[/tex]

[tex]Voted\ Voters = 60\%[/tex]

Required

Determine the number of voters

First, we need to determine the number of registered voters.

[tex]Number = \%Registered\ Voters * Eligible\ Voters[/tex]

[tex]Number = 85\% * 21800[/tex]

[tex]Number = 18530[/tex]

Next, we determine the actual voters using

[tex]Voters = \%Voters * 18530[/tex]

[tex]Voters = 60\% * 18530[/tex]

[tex]Voters = 11118[/tex]

Hence, 11118 people voted

Answer:

it should be 30 gallons

Step-by-step explanation:

Answer:

there is none

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

Real number solutions only or real and complex solutions. A solution to the system:

y=-2x+2

y=x2-2x+4

is the value of x such that when you plug it into both equations, they both produce the same value of y, or the value of x such that

-2x+2=x2-2x+4

solving this equation----------> x2=-2, taking square root of both sides gives x= ±√2i, or the system has no real solutions but has 2 complex solutions. If you graph both functions in the xy-plane, where x, y are real numbers, you' ll see they do not intersect, which implies there is no real number solutions.

Answer:

The expected value of lateness [tex]\frac{7}{20}[/tex] hours.

Step-by-step explanation:

The probability distribution of lateness is as follows:

  Lateness             P (Lateness)

  On Time                     4/5

1 Hour Late                  1/10

2 Hours Late                1/20

3 Hours Late                1/20​

The formula of expected value of a random variable is:

[tex]E(X)=\sum x\cdot P(X=x)[/tex]

Compute the expected value of lateness as follows:

[tex]E(X)=\sum x\cdot P(X=x)[/tex]

         [tex]=(0\times \frac{4}{5})+(1\times \frac{1}{10})+(2\times \frac{1}{20})+(3\times \frac{1}{20})\\\\=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20}\\\\=\frac{2+2+3}{20}\\\\=\frac{7}{20}[/tex]

Thus, the expected value of lateness [tex]\frac{7}{20}[/tex] hours.

An expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment.

Expected value of lateness is  [tex]\frac{7}{20}[/tex] hours.

Let us consider, P(x) is represent that probability of lateness and x represent number of hours late.

So, below a table is formed.

         x       0             1            2           3

      P(x)      4/5         1/10      1/20       1/20

From formula of expected value,

        E(x) = ∑ x P(x)

[tex]E(x)=(0*\frac{4}{5} )+(1*\frac{1}{10} )+(2*\frac{1}{20} )+(3*\frac{1}{20} )\\\\E(x)=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20} \\\\E(x)=\frac{7}{20}[/tex]

So, expected value of lateness is 7/20 hours.

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Answer:

300g

Step-by-step explanation:

Given parameters:

Mass of carbohydrate in the cereal meal  = 18g

Unknown:

Grams of carbohydrate recommended each day = ?

Solution:

The 18grams of the carbohydrate is just 6% of the total carbohydrate need per day;

         6% x total carbohydrate recommendation  = 18

       [tex]\frac{6}{100}[/tex] x total carbohydrate  = 18

       Total carbohydrate = 18 x [tex]\frac{100}{6}[/tex]   = 300g

Answer:

The answer is 300 grams of carbs on a 2000-calorie diet!

Step-by-step explanation:

Mass = 18g

daily allowance: ???

6% x total carbohydrate recommendation  = 18

x total carbohydrate  = 18

Total carbohydrate = 18 x    = 300g on a 2000-calorie diet

Answer:

Slope= -1/2 ; y-inter = 0

Step-by-step explanation:

Answer:The anwers is  5/6 in decimal it is 0.83repeating

Step-by-step explanation:

Answer:

The second option

Step-by-step explanation:

Answer:

7 weeks

Step-by-step explanation:

49 divided by 7 is 7

Answer:

Ace is the next level after expert.

Answer:

Amelie drove 3/4 mile.She then drove another 8/9 mile. How many miles did she drive in all?

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

ez any thing else just hit me up of so

Answer:

What is this about?

Step-by-step explanation:

What topic?

Answer:

i believe its C

Step-by-step explanation:

Answer:

52 degree angle

Answer:

False

Step-by-step explanation:

Cause the graphs show false instead of being true

Answer:

1:2

Step-by-step 1:2explanation:

it doesnt say anything about colors. so how many dots? how many stripes? 2 and 4. Ratio: 2:4. Ratios can be fractions: 2/4. What does 2/4 simplify to? 1/2 That means for every 1 dot rectangle there are 2 stripe rectangle. Ratio : 1:2 or 1 to 2 or 1/2

Step-by-step explanation:

4x^2+2x-5

4(-1)^2+2(-1)-5

4-2-5

2-5= -3

The discriminant is greater than zero, the equation has 2 solutions

Given the quadratic expression as shown:

-x^4 + 4x + 1 + 3 = 0

x^4 - 4x - 4 = 0

The discriminant is given as b^2 - 4ac

where;

a = 1

b = -4

c = -4

Substitute

D =(-4)^2 - 4(1)(-4)

D = 16 + 16
D = 32

Since the discriminant is greater than zero, the equation has 2 solutions

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Answer: 2

Step-by-step explanation: got it right

Answer: in the long run, 76.47% will have Cable TV

Step-by-step explanation:

Given the data in the question;

the matrix of transition from having cable TV to not having cable TV is

P = [ 0.92    0.08

       0.26    0.74  ]

Now if [ 0.564   0.436 ] is the distribution in 1990,

then in 1995 we have;

[ 0.564   0.436 ]  [ 0.92    0.08          = [ 0.6322    0.3678 ]

                              0.26    0.74  ]

so 63.22% will have cable TV in 1995

[ 0.6322    0.3678 ]  [ 0.92    0.08         = [ 0.6773    0.3227 ]

                                    0.26    0.74  ]

also 67.73% will have cable TV in 2000

let V = [ V1  V2 ] be the long run vector then

V1 + V2 = 1 ------lets say equ1    and  VP = V

⇒[ V1  V2 ]    [ 0.92    0.08        =  [V1  V2 ]

                       0.26    0.74  ]

⇒0.92V1 + 0.26V2 = V1

  0.08V1 + 0.74V2 = V2

OR 0.26V2 = 0.08V1

from equ 1, V1 = (1 - V2)

SO

0.26V2 = 0.08 (1 - V2)

0.26V2 = 0.08 - 0.08V2

0.34V2 = 0.08

V2 = 0.08 / 0.34

V2 = 0.2353

THUS

0.26V2 = 0.08V1

0.26(0.2353) = 0.08V1

0.061178 = 0.08V1

V1 = 0.061178 / 0.08

V1 = 0.7647

Therefore in the long run, 76.47% will have Cable TV

Answer:

n/4 + 1 =5

n/4 = 5-1

n/4 = 4

n = 4*4

n = 16

Answer:

So do this,

Step-by-step explanation:

stand up and go ask your mom!

Answer:

Distribute the 5 to get 10a-15=20+a and solve

Answer:

I think 2hours

Step-by-step explanation:

but I'm not sure

Answer:

A.Reject Upper H0 because the​ P-value is less than or equal to to α.

B.There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is more than 51​%.

Step-by-step explanation:

Given the claim :

Less than 51% will erase their personal information :

We take this as the null ;

H0 < 0.51 ;

Alternative hypothesis which is the opposite of the Null

H1 > 0.51

P value = 0.0148

α = 0.05

At α = 0.05 ; if p value is less than α ; reject the the Null

If p value is greater than Null ; then we fail to reject the Null

Pvalue < α

The P value is less than 0.05; then we reject the Null

B.) There is significance evidence to support the Alternative hypothesis claim, that the percentage of adult that would erase all their personal information online if they could is more Than 51%

Answer: Focus, Vertex, Axis, and Directrix.

Step-by-step explanation:

Answer:

X=-3

Step-by-step explanation:

2x+15=-3x

15=-5x

x=15/-5

x=-3

Answer:

x = -3

Step-by-step explanation:

2x + 15 = -3x

15 = -5x

x = -3

Answer:

A.

Step-by-step explanation:

Bc if you multiply every side by 3 you get the answer choices in answer A.

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Side lengths form a triangle that is similar to triangle ABC are 30, 21, 45 and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the side lengths form a triangle that is similar to triangle ABC:

Step 1 - First determine the ratio of the length of AB and AC.

[tex]\rm \dfrac{AB }{AC} = \dfrac{10}{15}[/tex]    --- (1)

Step 2 - Now, determine the ratio of the length of AC and BC.

[tex]\rm \dfrac{AC }{BC} = \dfrac{15}{7}[/tex]  --- (2)

Step 3 - Determine the ratio of the length of BC and AB.

[tex]\rm \dfrac{AB }{BC} = \dfrac{10}{7}[/tex]   --- (3)

Step 4 - Now, check the ratio of the side lengths given in option A).

[tex]\dfrac{30}{21}=\dfrac{10}{7}[/tex]           (Similar to expression 3)

[tex]\dfrac{45}{21}=\dfrac{15}{7}[/tex]           (Similar to expression 2)

[tex]\dfrac{30}{45}=\dfrac{10}{15}[/tex]           (Similar to expression 1)

Therefore, the correct option is A).

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