What is the slope of the line represented by the equation y = -1/2X + 1/4?

Answer:

(f o g)(x) = 4x^4 - 24x^2 + 37

(g o f)(x) = 16x^4 + 8x^2 - 2

Step-by-step explanation:

f(x) = 4x^2 + 1

g(x) = x^2 - 3

(f o g)(x) = f(g(x)) = f(x^2 - 3) = 4(x^2 - 3)^2 + 1 =

= 4(x^4 - 6x^2 + 9) + 1

= 4x^4 - 24x^2 + 37

(g o f)(x) = g(f(x)) = g(4x^2 + 1) = (4x^2 + 1)^2 - 3 =

= 16x^4 + 8x^2 - 2

Answer:

|x - 4| ≤ 0.3

Step-by-step explanation:

The actual width = 4

Maximum variation, x = 0.3

Hence, the lowest width position based on actual width and possible variation is :

4 - 0.3 ≤ x ≤ 4 + 0.3

3.7 ≤ x ≤ 4.3

Answer:

Step-by-step explanation:

The matched statement to its corresponding reason for the given alternate interior angles as:

Given: Let points A, B, and C form a triangle.

definition: Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Congruent angles: m∠1=m∠4, m∠3 = m∠5

Linear pair theorem: m∠4+m∠2+m∠5 = 180°

As per the shown figure,

Given:

Let points A, B, and C form a triangle.

Defining a parallel line and labeling angles:

Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Alternate Interior Angles Theorem:

∠1=∠4

∠3 = ∠5

Congruent angles have equal measures:

m∠1=m∠4

m∠3 = m∠5

Definition of a straight angle and angle addition:

m∠4+m∠2+m∠5 = 180°

Substitution:

m∠1 + m∠2 +m ∠3 = 180°

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Answer:

Step-by-step explanation:

3mn (m+y)

= 3[tex]m^{2}[/tex]n + 3mny

Answer:

512

Step-by-step explanation:

Answer:

The x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.

Step-by-step explanation:

We have the function:

[tex]\displaystyle y=\frac{x^2 -1}{x}[/tex]

And we want to find the x-coordinates for which the gradient (or slope) at the point is 5.

The gradients of a curve at a point is given by its derivative. Find the derivative:

[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\frac{x^2-1}{x}\right][/tex]

Use the quotient rule:

[tex]\displaystyle \frac{dy}{dx}=\frac{(x^2-1)'(x)-(x^2-1)(x)'}{(x)^2}[/tex]

Simplify:

[tex]\displaystyle \frac{dy}{dx}=\frac{(2x)(x)-(x^2-1)(1)}{x^2}[/tex]

Simplify:

[tex]\displaystyle \frac{dy}{dx}=\frac{x^2+1}{x^2}[/tex]

Since the gradient is 5, substitute 5 for dy/dx and solve for x:

Multiply both sides by x² (x ≠ 0):

[tex]5x^2=x^2+1[/tex]

Subtract x² from boths sides:

[tex]4x^2=1[/tex]

Solve for x:

[tex]\displaystyle x=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}\text{ or } -\frac{1}{2}[/tex]

So, the x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.

Answer:

x could be 0 or it could be 5/2

Step-by-step explanation:

Answer:

x= 5/2

Step-by-step explanation:

4x^2 + 4x - 14x = 0

subtract 4x from 14x because they are like terms

4x^2 - 10x=0

4x^2 = 0 + 10x

4x^2 = 10x

x^2/x = 10/4

x=10/4

x=5/2

Answer:

C 35:15

Step-by-step explanation:

because 35:15 =5:3 so it is not equal to a ratio of 5 is to 2

Answer:

C

Step-by-step explanation:

If you simplify all the ratios, then you get the following:

A. 25/5 : 10/5 = 5:2

B. 35/7 : 14/7 = 5:2

C. 35/5 : 15/5 = 7:3

D. 40/8 : 16/8 = 5:2

Answer:

Step-by-step explanation:

perimeter of rectangle = 1100

let breadth be x

length = 300 + x

perimeter of rectangle = 2(l + b)

1100 = 2(300 + x + x)

1100 = 2(300 + 2x)

1100 = 600 + 4x

1100 - 600 = 4x

500 = 4x

500/4 = x

125 = x

therefore breadth is 125 feet

length = 300 + 125

=425 feet

Answer:

The rectangular field is 425 feet by 125 feet.

Step-by-step explanation:

Let w represent the width of the rectangular field.

Since the length is 300 feet more than the width, the length can be modeled by the expression (w + 300).

The perimeter of a rectangle is given by the formula:

[tex]P=2(w+\ell)[/tex]

Where P is the perimeter and w and l are the width and length, respectively.

We are given that the perimeter is 1,100 feet. Substitute:

[tex]1100=2(w+\ell)[/tex]

Divide both sides by two:

[tex]550=w+\ell[/tex]

We know that l = (w + 300). So:

[tex]550=w+(w+300)[/tex]

Simplify:

[tex]2w=250[/tex]

Divide both sides by two. So, the width is:

[tex]w=125\text{ feet}[/tex]

Since the length is 300 feet more than the width, that means the length is 425 feet.

The rectangular field is 425 feet by 125 feet.

Answer:

45.60

Step-by-step explanation:

12 × 51.60 = 619.20

1804.80 - 619.20 = 1185.60

1185.60 ÷ 26 = 45.60

The cost of a ticket for a child will be 45.60 dollars

Answer: See explanation

Step-by-step explanation:

1. 5x-7+3x and 3x-7+5x

5x - 7 + 3x

Collect like terms

5x + 3x - 7 = 8x - 7

3x-7+5x

Collect like terms

3x + 5x - 7 = 8x - 7

They're equivalent

2. 4y+9+3y and 3y+9+4y

4y + 9 + 3y

Collect like terms

4y + 3y + 9 = 7y + 9

3y + 9 + 4y

Collect like terms

3y + 4y + 9 = 7y + 9

They're equivalent

3. 6z-2z+4 and 4+2z-6z

6z - 2z + 4 = 4z + 4

4 + 2z - 6z = 4 - 4z

They're not equivalent

Answer: (c)

Step-by-step explanation:

Given

The function is [tex]y=-x^2+6x-4[/tex]

Range of a function describes the values y can take

from the graph it is clear that the maximum value of y is 5

[tex]\therefore y\leq5[/tex]

Hence. option (c) is correct.

Step-by-step explanation:

Domain: possible value of x

Range: possible values of y

Domain:

Given in the question

-1smaller or equal to x smaller or equal to 1

Range:

y is greater than 1, smaller than 3

[tex] \sqrt{ \frac{y - 1}{2} } = x \\ [/tex]

y cannot be smaller than 1

when substitute velue of x= 1 or negative 1

we get y=3 and any values between 1 and negative 1 when substitute in x, will give values of y in between 3 and 1.

first list all elements of x and y..

x= -1,0,1

y=2x^2+1

whenx=-1 y=2×-1^2+1=5

similarly, when x=0,y=1

x=1, y=5

therefore, domain=x={-1,0,1}

range=y={1,5}

Answer:

8038.65

Step-by-step explanation:

[tex]4000(1+\frac{.07}{12})^{12*10}=8038.65[/tex]

Answer:

33.6 seconds

Step-by-step explanation:

if he begins at 136 feet and wants to go to 42 feet, the distance is 94 feet

d = 94

r = 2.8

d = rt; solving this formula for 't':

t = d/r

t = 94/2.8

t = 33.6 seconds

36:60

= 18:30

= 9:15

= 3:5

Answer:

19/3

Step-by-step explanation:

1 2/3 = (1*3 + 2)/3 = 5/3

3 4/5 = (5*3 + 4)/5 = (15 + 4)/5 = 19/5

5/3 * 19/5 = 19/3    The 5s cancel.

The simplest form is not obvious to me. I think the answer above is in simplest form, and I will put that below the answer above. But 6 1/3 is also possible.

Answer:

4 1/3

Step-by-step explanation:

1 [tex]\frac{2}{3}[/tex] × 3 [tex]\frac{4}{5}[/tex] =

[tex]\frac{5}{3}[/tex] × [tex]\frac{19}{5}[/tex] =

[tex]\frac{95}{15}[/tex] = 4 [tex]\frac{5}{15}[/tex] = 4 1/3

Answer:

Equation of the circle :  

                      [tex](x+ 1)^2 + (y+4)^2 = 9[/tex]

Step-by-step explanation:

Equation of a circle with centre (a, b) and radius ,r :

[tex](x - a)^2 + (y-b)^2 = r^2[/tex] ------(1)

Here a = -1, b = -4

find radius:

Since the circle passes through (-1, -1) , the radius is the distance between the centre and the point.

[tex]distance, r = \sqrt{(-1 -(-1))^2 +(-4 -(-1))^2 }[/tex]

               [tex]= \sqrt{9} = 3[/tex]

Substitute the values in (1) :

             [tex](x - (-1))^2 + (y-(-4))^2 = 3^2\\\\(x+ 1)^2 + (y+4)^2 = 9[/tex]

Answer:

a) 2.5 pounds of candy

b) 2.5 pounds of candy

    [tex]\frac{0.5}{1} :\frac{y}{5}[/tex]

    y × 1 = 0.5 × 5

    y = 2.5

Step-by-step explanation:

1 = 5

1/2 = y or 0.5 = y

[tex]\frac{0.5}{1} :\frac{y}{5}[/tex]

y × 1 = 0.5 × 5

y = 2.5

straightAnswer:

Step-by-step explanation:

The strategy would be to look for the equations of  lines that passes for the points. it can be done but it's a hard work. I prefer to use a calc sheet . You can se that house 2 has a perfect fit to data because it has a [tex]R^2=1[/tex], however house 1 does not have a perfect fit, [tex]r^2=0.99..[/tex] altough it is a very good fit, in the image you can see the corresponding equations

The value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

We have:

y varies directly with x and inversely with z.

y ∝ x/z

Removing the proportional sign.

y = kx/z

k is the constant of proportionality.

Plug y = 27, x = 21, and z = 7 to get the value of k

27 = 21k/7

k = 9

y = 9x/z

Plug x = 25, and z = 5

y = 9(25)/5

y = 45

Thus, the value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

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Answer:

yes I can help you but ???

Answer:

Step-by-step explanation:

the equation you write to solve this should be:

x = 900 (1 + 0.055)^7

x = 900 (1.055)^7

x = 900 (1.454679131133794609375)

x = 1,309.21

*** Note that the answer was rounded to the nearest hundredths digit. ********

Answer:

158 m^2

Step-by-step explanation:

l = 5 m, w = 3 m, h = 8 m

S.A. = [tex]2(lw+wh+lh)[/tex]

S.A. = 2{(5)(3) + (3)(8) + (5)(8)}

S.A. = 2(15 + 24 + 40)

S.A. = 2(79)

S.A. = 158 m^2

Hope this help!!!

Have a nice day!!!

9514 1404 393

Answer:

  no

Step-by-step explanation:

The first step is to understand that the question is asking about the future value of series of payments. An appropriate formula is ...

  P = A(n/r)((1 +r/n)^(nt) -1)

where P is the future value, A is the periodic payment made n times per year for t years. r is the annual interest rate.

The next step is to substitute the given values and do the arithmetic. Using the given values, we have ...

  P = 250(12/0.056)((1 +0.056/12)^(12×2.5) -1) ≈ 8030.32

Shen will have accumulated about $8,030.32, which is not enough to meet his goal.

Answer:

I think you meant to add a list of answers but didn't so here's the characteristics of a plane: Flat, two dimensional, extends infinitely, and is assembled about multiple points and lines.

Step-by-step explanation:

Answer:

If you are taking the FLVS test it is "Two endpoints"

Step-by-step explanation:

Just took the test

hope it helps :)

Answer:

6 1/4 simplified 25/4 decimal 6.25

Step-by-step explanation:

if the rope is 8 3/4 and you took away a piece that is equal to 2 1/2 which means you subtract them from each other to get your final answer of 6 1/4

Answer:

y = –1 + 3x

Step-by-step explanation:

To know which option is correct, we shall use the equation given in each option to see which will validate the table. This is illustrated below:

Option 1

y = –1x + 3

x = –2

y = –1(–2) + 3

y = 2 + 3

y = 5

This did not give the required value of y (i.e –7) in the table.

Option 2

y = 1 + 3x

x = –2

y = 1 + 3(–2)

y = 1 – 6

y = –5

This did not give the required value of y (i.e –7) in the table.

Option 3

y = –3 + 1x

x = –2

y = –3 + 1(–2)

y = –3 – 2

y = –5

This did not give the required value of y (i.e –7) in the table.

Option 4

y = –1 + 3x

x = –2

y = –1 + 3(–2)

y = –1 – 6

y = –7

This gives the required value of y (i.e –7) in the table.

Thus, the equation that matches the table is:

y = –1 + 3x