What is the standard form

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:

[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:

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:

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:

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.

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:

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:

1200 cm²

Step-by-step explanation:

width = x cm

length = 3x  cm

perimeter = 160 cm

2(x + 3x) = 160

4x = 160/2

4x = 80

x = 80/4

x = 20  cm  - width

length = 3x = 3 · 20 = 60 cm

Area = length · width = 60 · 20 = 1200 cm²

The rectangle's width is 20 cm and its length is 60 cm. Thus, the area of the rectangle is 1200 square centimeters.

We are given that the length of a rectangle is three times its width. Let's denote the width as 'w'. Consequently, the length would be '3w'.

The perimeter of a rectangle is given by the formula: 2*(length + width). Given that the perimeter is 160 cm, we can substitute our variables into the formula: 2*(w + 3w) = 160. This simplifies to 8w = 160. Therefore, the width (w) equals 20 cm, and the length is 60 cm (3w).

The area of a rectangle is calculated by multiplying its length and width. Hence, the area of our rectangle is: 60 cm * 20 cm = 1200 square centimeters.

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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:

0.40625

Step-by-step explanation:

Answer:

The answer is 13/2

Step-by-step explanation:

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:

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:

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:

51/x

The first number/ variable always goes on top

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.

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Answer:

2nd , 3rd, & 4th

Step-by-step explanation:

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:

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]

See the attached picture:

Answer:

Step-by-step explanation:

y-intercept: (0, y)

x-intercept: (x, 0)

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

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:

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: 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:

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:

the answer will be verticle angles

Step-by-step explanation:

∠4 and ∠5 form vertical angles.

When two lines intersect each other, then non-adjacent opposite angles are called vertical angles.

Vertical angles are always equal in measurement.

If line AB and CD intersect each other at point O, ∠AOC and ∠BOD are vertical angles, similarly, ∠AOD and ∠BOC are also vertical angles.

Here lines 1 and 2 intersect each other.

So ∠4 and ∠5 are formed which are non-adjacent and opposite also.

Therefore ∠4 and ∠5 form vertical angles.

Learn more about vertical angles

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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

Answer:

241,389.613

Step-by-step explanation:

The first 1 is in the hundred millons place​.

Answer:

3

Step-by-step explanation:

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:

-7

Step-by-step explanation:

Mischa's equation is   -x² + 4x - 7 = 0

The standard form is ax² + bx + c = 0

c is the constant term in the quadratic equation.

If we compare terms, we find that c = -7.