Given f (x). find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely x.
f(x)=
[tex] \sqrt{ - 2 {x}^{2} + 3 } - 5[/tex]
find g(x) and h(x)​

Answer:

The answer is (5*2x) - (5*3)

Step-by-step explanation:

You just have to multiply the coefficient by the individual numbers and variables inside the parentheses. :)

Answer: You can use a graphing calculator in the future

(2,3)

A

Answer:  A(2,3)

Step-by-step explanation:

To solve the system of equations;

y=-1/2x+4 and y = 2x – 1

y=-1/2x+4   ----------(1)

y = 2x – 1 -----------(2)

Lets substitute equation 2 in equation 1

2x - 1 =  -1/2x+4

Collect like term

(We move the x variables from the right -hand side of the equation to the right-hand side of the equation to the right-hand-side of the equation and then move the constants to the right-hand side of the equation)

2x  + 1/2x  =   4  + 1

5x/2  =  5

To get the value of x, we will multiply both-side of the equation by 2/5

5x/2  ×   2/5       =  5   ×   2/5

(On the left-hand side of the equation, the 5/2 will cancel out the 2/5 leaving us with x  and on the right-hand side of the equation 5 will cancel out 5 leaving us with 2)

x   =  2

Substitute x =2 in equation (2)

y =  2x  -  1

y =  2(2)  - 1

y =   4  -1

y =3

The solution to the system of the equations is x=2 and y=3

Therefore the answer is A(2,3)

Answer:

Option C (207.5 feet)

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle is formed by the intersection of the lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

x^2 = y^2 + z^2 - 2*y*z*cos(X).

Let x be the distance covered by the outfielder's throw, let y be the distance between the pitcher's mound and the home plate, let z be the distance covered by the batter's shot, and let X be the mentioned angle.

The question specifies that y=60.5 feet, X=31°, and z=257 feet. Plugging in the values:

x^2 = 60.5^2 + 257^2 - 2(60.5)(257)*cos(31°).

Simplifying gives:

x^2 = 43053.9184501 feet.

Taking square root on the both sides gives x = 207.5 feet (rounded to the one decimal place).

This means that the Option C is the correct choice!!!

Answer:

51/x

The first number/ variable always goes on top

The first step of solving this inequality is subtracting 3 to both sides. This will cancel 3 from the left side to start isolating x.

2x + 3 - 3 ≥ 17 - 3

2x ≥ 14

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x≥7

Step-by-step explanatio

To solve this problem, subtract 3 from both sides and divide by 2 from both sides.

2x+3-3≥17-3

17-3=14

2x≥14

2x/2≥14/2

14/2=7

x≥7 is the correct answer.

Answer:

a CANNOT be even ⇒ answer A

Step-by-step explanation:

* Lets revise the rules of even and odd numbers

- Even numbers any number its unit digit is (0 , 2 , 4 , 6 , 8)

- Odd numbers any number its unit digit is (1 , 3 , 5 , 7 , 9)

# even + even = even ⇒ 2 + 4 = 6  

# odd + odd = even ⇒ 1 + 3 = 4  

# odd + even = odd ⇒ 1 + 2 = 3  

# even × even = even ⇒ 2 × 4 = 8

# odd × odd = odd  

⇒ 3 × 5 = 15

# odd × even = even  ⇒ 5 × 6 = 30

∵ a[b(c + d) + e] = odd

∵ odd × odd = odd  

∴ a must be odd and [b(c + d) + e] must be odd

∵ odd + even = odd

∵ odd × even = even

# Case 1

∴ b(c + d) must be odd  if e even

∵ b(c + d) is odd

∴ b must be odd and (c + d) must be odd

∵ c + d must be odd

∵ odd + even = odd

∴ c or d can be even

- We now now that e , c and d can be even

# case 2

∴ b(c + d) must be even  if e odd

∵ b(c + d) is even

∵ even × even = even

∴ b and (c + d) both can be even

∵ c + d can be even

∴ c or d can be even or odd

- We now now that e , c , d and b can be even

∴ Only a can not be even

* a CANNOT be even

Answer:

Step-by-step explanation:

f(x) = 1/4 x²+bx+10

the derivate is : f'(x) = 1/2 x +b

you have : f'(6)=0

1/2 (6)+b=0

3+b =0

b = -3

so f(x) = 1/4 x²-3x+10.......f(6) =1/4(6)² -3(6)+10 =9-18+10 =1

f(x) = 1/4(x-6)²+1... the vertex form

Value of 'b' from the quadratic function will be (-3).

If the quadratic equation for the parabolic path has been given as,

Axis of symmetry of the parabola will be given by,

Axis of symmetry = [tex]-\frac{b}{2a}[/tex]

  Quadratic function given in the question → [tex]f(x)=\frac{1}{4}x^2+bx+10[/tex]

Compare this equation by [tex]f(x)=ax^2+bx+c[/tex]

[tex]a=\frac{1}{4},b=b,c=10[/tex]

Axis of symmetry of the parabola will be,

Axis of symmetry = [tex]-\frac{b}{2(0.25)}[/tex]

                             = [tex]-2b[/tex]

Axis of symmetry has been given as x = 6,

[tex]6=-2b[/tex]

[tex]b=-3[/tex]

    Therefore, value of b will be (-3).

Learn more about the quadratic function here,

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Answer:

The answer is $0.32.

Step-by-step explanation:

You achieve this answer by taking the total price ($7.68) divided by the number of units for that price (24 cans).  Therefore:

[tex]\frac{7.68}{24} = 0.32[/tex]

Answer:

None of then, the slope is 1

Step-by-step explanation:

We have to use the general equation for lines, that is:

[tex]y=mx+b[/tex]

where 'm' is the slope (by comparison)

So, we only need to compare your equation ([tex]y=x-3[/tex]) with the general one.

We can see that m=1, b=-3

So our slope turns out to be equals to 1

Answer:

When studying a random sample of the population, you are studying one of many (generally the same) flying squirrels that live. This small selection represents the whole population, (because as said before, they are generally the same). In this way, you can assume that the small section that you picked is going to represent the entire flying squirrel population.

Intersecting chord rule:

DK x KB = AK x CK

12 x 4x+1 = 14 x 3+3x

Simplify:

48x +12 = 42x +42

Subtract 12 from each side:

48x = 42x + 30

Subtract 42x from each side:

6x = 30

Divide both sides by 6:

x = 5

Now find the length of KB: 4x +1 = 4(5) +1 = 20 +1 = 21

Now add KB and AK:

21 + 14 = 35

The answer is D. 35

The required length of KB(21) + AK(14) is 35. Option D is correct.

The figure is given,
where AK = 14. DK = 12, KB = 4x+1 and  KC =3+3x.
KB + AK to be determined.

The ratio can be defined as the relativeness of the fraction of one quantity towards others.

Here,
The ratio of AK: DK = KB:KC

[tex]14/12= 4x+1/3+3x\\14*(3+3x) = 12*(4x+1)\\2+42x = 48x+12\\42-12=48x-42x\\6x= 30\\x = 5[/tex]

Now,
= KA + KB
= 14 + 4x+1
= 14+ 4(5)+1
= 35

Thus, the required length of KB + AK is 35.

Learn more about ratios here:

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Answer:

is there an option for no solution? because when I solved there were no possible rational solutions

Step-by-step explanation:

Answer:

This was the correct answer choice in my case.

Step-by-step explanation:

Hope this helps!

Answer:

C. Left-handed: 48, Right-handed: 504

D. Left-handed: 30, Right-handed: 315

Step-by-step explanation:

We are given that there are 58 left-handed students and 609 right-handed students at East Middle School and these numbers of students are proportional to the number of left and right handed students at East Middle School.

Given the above information, we are are to determine which two options could be the the numbers of left-handed and right-handed students at West Junior High.

Ratio of right handed to left handed students at East Middle School = [tex]\frac{609}{58} = 10.5[/tex]

Checking for ratios of the given options:

A. [tex]\frac{483}{42} =11.5[/tex]

B. [tex]\frac{378}{28} =13.5[/tex]

C. [tex]\frac{504}{48} =10.5[/tex]

D. [tex]\frac{560}{56} =10[/tex]

E. [tex]\frac{315}{30} =10.5[/tex]

Therefore, the possible numbers of left-handed and right-handed students at West Junior High could be C. Left-handed: 48, Right-handed: 504 and D. Left-handed: 30, Right-handed: 315.

Answer:

OPTION C.

OPTION E.

Step-by-step explanation:

A relationship is proportional if the ratio between the variables is always the same.

In this case we know that the numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School and there are 58 left-handed students and 609 right-handed students at  East Middle School. Therefore, the ratio is:

[tex]ratio=\frac{58}{609}=\frac{2}{21}[/tex]

So, we can check the ratio in each option to know which has ratio [tex]\frac{2}{21}[/tex]:

OPTION A:

[tex]\frac{42}{483}=\frac{2}{23}[/tex]

OPTION B:

[tex]\frac{28}{378}=\frac{2}{27}[/tex]

OPTION C:

[tex]\frac{48}{504}=\frac{2}{21}[/tex]

OPTION D:

[tex]\frac{56}{560}=\frac{1}{10}[/tex]

OPTION E:

[tex]\frac{30}{315}=\frac{2}{21}[/tex]

Therefore, you can observe that the numbers of left-handed and right-handed students at West Junior High could be:

[tex]Left-handed: 48\\Right-handed: 504\\\\\\Left-handed: 30\\Right-handed: 315[/tex]

Answer:

987.

Step-by-step explanation:

The terms in a Fibonacci series are obtained form the sum of the previous 2 terms. So the next number F(16) = 377 + 610 = 987.

APEX ANSWER: 987

Step-by-step explanation:

377 + 610 = 987

Answer:

The middle term, once simplified is -x

Step-by-step explanation:

( x+3) (x-4)

FOIL

first

x*x = x^2

outer: -4*x = -4x

inner: 3*x = 3x

last: -4*3 = -12

Add them together  x^2 -4x+3x-12

                                 x^2 -x +12

Answer:

[tex]y = - \frac{1}{3}x[/tex]

Step-by-step explanation:

The equation of a direct variation is generally written as:

[tex]y = mx[/tex]

Where m is the slope of the equation of the direct variation line.

We want a direct variation equation that contains (6,-2).

We substitute the x=6 and y=-2 to find m.

[tex] - 2 = 6m[/tex]

Divide both sides by 6.

[tex] \frac{ - 2}{ 6} = \frac{6m}{ 6} [/tex]

[tex] - \frac{1}{3} = m[/tex]

The required equation is

[tex]y = - \frac{1}{3}x[/tex]

The equation of the direct variation that includes the point (6,-2) is y = -1/3x, calculated by substituting the point into the formula y = kx and solving for the constant of variation k.

The subject of this question is mathematical, focusing on direct variation - a specific type of relationship between two variables where one variable is a constant multiple of the other. In this case, the student is given the point (6,-2) on the graph of this relationship. With direct variation, the formula is typically written as y = kx, where k is the constant of variation.

For this particular question, we use the point (6,-2) and substitute x = 6 and y = -2 into the formula to find the constant of variation, i.e. -2 = k * 6. Solving for k, we get k = -2/6 = -1/3. Plugging this k back into y = kx gives us our equation of the direct variation: y = -1/3x.

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Answer:

29/5 or 5.8

Step-by-step explanation:

6+5(a−1)=30

first it would be good to distribute:

6+5(a-1)=30 -> 6+(5)(a)+(5)(−1)=30 which simplifies to 6+5a+−5=30

at this point it is best to rearrange:

(5a)+(6+−5)=30 which simplifies to 5a+1=30

from then on its a matter of doing opposite operation. at my school we would call this the "equality" method. what you do to one side you do the other.

Observe:

5a+1=30

    -1   -1

5a=29

5a/5=29/5

a=29/5 (in decimal it would be like 5.8)

I hope this is helpful!

Answer:

2nd , 3rd, & 4th

Step-by-step explanation:

Answer:

(Choice A)

-4(3e + 4)

Step-by-step explanation:

This is the only answer that makes sense:

-7 - 12e - 9 [Distribute the 3 amongst all the other terms in parentheses]

Then you combine like-terms:

-16 - 12e

Finally, you factor out the Greatest Common Factor [GCF]:

-4[4 + 3e]

12e is NOT an option, so you are left with (Choice A).

I am joyous to assist you anytime.

Answer:

Facing Right

Step-by-step explanation:

Given inequalities are:

4-x≤-1

Subtracting 4 from both sides

4-x-4≤-1-4

-x≤-5

Multiplying both sides with -1. Multiplying with a negative number changes the sign of the inequality

So,

x≥5

Second Inequality:

2+3x≥17

Subtracting 2 from both sides

2+3x-2≥17-2

3x≥15

Dividing both sides by 3

x≥5

Union of both solutions:

x≥5 ∩ x≥5

=> x≥5

Hence the solution will be facing right on the number line towards all numbers greater than or equals to 5 ..

Answer:

( 6x + 11 ) ( x - 5 )

Step-by-step explanation:

Let

6x2 - 19x - 55 = 0

6x2 - (30-11)x - 55 = 0

6x2 - 30x + 11x - 55 = 0

6x ( x - 5 ) + 11 ( x - 5 ) = 0

( 6x + 11 ) ( x - 5 ) = 0

Therefore, ( 6x + 11 ) ( x - 5 ) = 6x2 - 19x - 55

Answer:

Step-by-step explanation:

y-intercept: (0, y)

x-intercept: (x, 0)

Therefore the y-intercept is only (0, 1).

Answer:

241,389.613

Step-by-step explanation:

The first 1 is in the hundred millons place​.

Answer:

3

Step-by-step explanation:

Answer:

30 laps per hour

Step-by-step explanation:

The first thing you do is calculate the amount of hours he swam for. Since he swam 2 hours each day, 5 days each week, for 5 weeks we use the equation 2*5*5. The answer is 50. After that what we do is take the amount of laps and divide it by 50. We do 1500 divided by 50 and we get a total of 30 laps per hour.

Answer:

I don't know what your choices are but they are alternate interior angles.  Alternate interior angles are congruent.

Step-by-step explanation:

Alternate interior angles are the angles at the different intersection along the transversal that are on opposite sides of the transversal and inside the parallel lines.

This is exactly what you have here, alternate interior angles are congruent when the the lines are parallel.

There are also alternate exterior.  These are at the different intersections along the trasversal that are opposite sides of the transversal but outside the parallel lines.

There is also corresponding angles.  I like to call these the copy and paste angles because when you copy one intersection and paste it over the other, the corresponding angles will be the ones that lay on top of each other.

There are also same-side interior angles. There are inside and on the same side of the transveral at the different intersections. These angles add up to be 180 degrees when the transversal cuts through parallel lines.

Answer:

The answer is ---> x = y

Step-by-step explanation:

Here are the answer choices.

I got it correct, so this was the answer

Answer:

4/27

Step-by-step explanation:

x^-3y^-3

Let  x=2 and y=3

2^ (2) (3)^-3

2^2 * 1/3^3

4/27

Answer:

[tex]h(x)=\frac{1}{4}x[/tex].

Step-by-step explanation:

The inverse is basically you just swapping x and y.  People want to solve it for y to make it a function of x.

[tex]y=4x[/tex]

Swap x and y:

[tex]x=4y[/tex]

Now solve for y by dividing y on both sides:

[tex]\frac{x}{4}=y[/tex]

[tex]\frac{1}{4}x=y[/tex]

[tex]y=\frac{1}{4}x[/tex].

Answer:

0.40625

Step-by-step explanation:

Answer:

The answer is 13/2

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Answer:

X=4

Step-by-step explanation:

(x-4)(x-4)=0

if x=4 then 4-4=0

0^(x-4)=

x-4=0

0^0=0