The width of a vegetable garden is į times its length.
If the length of the garden is 7 feet, what is the width
in simplest form?

The table of values for the functions f(x) = x^2 + 1, g(x) = f(x - 5) and h(x) = f(x+3) is:

[tex]\left[\begin{array}{cccccc}x&f(x)&x&g(x)&x&h(x)\\-2&5&-2&50&-2&2\\-1&2&-1&37&-1&5&0&1&0&26&0&10&1&2&1&17&1&17&2&5&2&10&2&26\end{array}\right][/tex]

The equations of the functions are given as:

[tex]f(x) = x^2 + 1[/tex]

[tex]g(x) = f(x - 5)[/tex]

[tex]h(x) = f(x+3)[/tex]

For function f(x), we have:

f(-2) = (-2)^2 + 1 = 5

f(-1) = (-1)^2 + 1 = 2

f(0) = (0)^2 + 1 = 1

f(1) = (1)^2 + 1 = 2

f(2) = (2)^2 + 1 = 5

For function g(x), we have:

g(-2) = f(-2 - 5) = f(-7) =  (-7)^2 + 1 = 50

g(-1) = f(-1 - 5) = f(-6) =  (-6)^2 + 1 = 37

g(0) = f(0 - 5) = f(-5) =  (-5)^2 + 1 = 26

g(1) = f(1 - 5) = f(-4) =  (-4)^2 + 1 = 17

g(2) = f(2 - 5) = f(-3) =  (-3)^2 + 1 = 10

For function h(x), we have:

h(-2) = f(-2 + 3) = f(1) =  (1)^2 + 1 = 2

h(-1) = f(-1 + 3) = f(2) =  (2)^2 + 1 = 5

h(0) = f(0 + 3) = f(3) =  (3)^2 + 1 = 10

h(1) = f(1 + 3) = f(4) =  (4)^2 + 1 = 17

h(2) = f(2 + 3) = f(5) =  (5)^2 + 1 = 26

Substitute the above values in the blank table.

So, we have:

[tex]\left[\begin{array}{cccccc}x&f(x)&x&g(x)&x&h(x)\\-2&5&-2&50&-2&2\\-1&2&-1&37&-1&5&0&1&0&26&0&10&1&2&1&17&1&17&2&5&2&10&2&26\end{array}\right][/tex]

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Answer:

20

Step-by-step explanation:

He only can put 12 boxes in 1 crate to ship 230 boxes of oatmeal the least number of crates he can use is 20 because 20 crates would= up to 240 boxes.

He can't do 19 boxes because he is short he would then only have 228 boxes and that is 2 short.

But if he does 20 crates he would be good for what needs and just have 10 more extra.

My calculations.

2 0

1  2

____

      4    0

 2    0  0

+

_________

2  4 0

This is saying he had 20 crates and use x as number of boxes for example each 1 crate could ship x amount of boxes and x is representing 12 boxes per crate and since he has 20 crates what is 20 x 12= x( the number of boxes total(240 boxes)

I hope this helps have a awesome day:)

Answer:

20 crates

Step-by-step explanation:

Since he has 230 boxes and each crate can have up to 12 boxes, we can divide 230 by 12 to see how many crates will be needed:

[tex]\boxed{\frac{230}{12} }[/tex]

Let's do long division to solve this:

we have the equation 230 ÷ 12

  __________

12  |    2    3    0



     __0_______

12  |    2    3    0

        -0

         2    3



     __0__1____

12  |    2    3    0

        -0

         2    3

        -1     2

         1     1     0



     __0__1__9_

12  |    2    3    0

        -0

         2    3

        -1     2

         1     1     0

        -1    0     8

         0    0    2

So, as we can see, the quotient is 19 but we have a remainder of 2, which means that, from the 230 boxes, 228 fits into 19 crates and 2 boxes are left. This means that we will need one extra crate to put these 2 boxes.

So, in total, he will need 20 crates.



[tex]Solved~by~-InLoveWithNature-[/tex]

If you have any queries please ask.



Answer: 124

Step-by-step explanation:

First, subtract 6 on both sides to get:

[tex]\sqrt[5]{249-2x} =1[/tex]

Take both sides to the 5th power. The radical will cancel, and the right side will be unchanged:

[tex]249-2x=1[/tex]

Subtract 249 on both sides:

[tex]-2x=-248[/tex]

[tex]2x=248[/tex]

[tex]x=124[/tex]

Answer:

x=124

Step-by-step explanation:

[tex]6+\sqrt[5]{249-2x} =7\\\sqrt[5]{249-2x} =7-6=1\\249-2x=1^5=1\\249-1=2x\\2x=248\\x=\frac{248}{2} =124[/tex]

Answer:

x = y the answer is this...

Step-by-step explanation:

[tex] \frac{x + 3}{3} = \frac{y + 2}{2} [/tex]

[tex]2(x + 3) = 3(y + 2)[/tex]

[tex]2x + 6 = 3y + 6[/tex]

[tex]2x = 3y[/tex]

[tex] \frac{x}{3} = \frac{y}{2} [/tex]

Answer:

Any value of "x" makes the equation true

Step-by-step explanation:

(-∞,∞)

All real numbers

i hope this work for you

Answer:

17÷86×100%

=0.19×100%

=19%

Answer:

d~~12.65

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

By order of operations, in this case, we first have to solve exponents and THEN multiply by 3.

Therefore, this equation is false.

Answer:

False

Step-by-step explanation:

4^2=16

4^2=163x16=48

4^2=163x16=4848=144

4^2=163x16=4848=144The numbers dont match.

4^2=163x16=4848=144The numbers dont match.Hence the equation is false.

The volume of the cylinder is between 5 and 6 gallons.

A cylinder is a three-dimensional shape that is made up of a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

22/7 x 28 x (15^2) = 19,800 cubic centimeters

First convert the volume to liters = 19,800 / 1000 = 19.8

Now convert to gallons =  19.8 / 3.785 = 5.23 gallons

Please find attached the complete question. To learn more about to determine the volume of a cylinder, check: https://brainly.com/question/9624219

Answer:

Step-by-step explanation:

If each lap is 1/8 of a mile, then we have to do 3x8 to get our answer.

8x3=24

So hence, Rex has to go 24 times around his block to ride his bike for 3 miles.

Thanks!

Answer:

See below

Step-by-step explanation:

Radius (r) = 8 inches

Chord = 8 inches

Since, length of radii and chord are equal. Thus the Triangle so formed by radii and chord will be an equilateral triangle.

[tex]\implies [/tex] angle subtended at the centre of the circle [tex](\theta)=60\degree [/tex]

Formula for area of segment of a circle is given as:

[tex]A = \frac{ {r}^{2} \theta }{36 0 \degree} \pi - \frac{1}{2} {r}^{2} \sin \theta \\ \\ \implies \: A = \frac{ {(8)}^{2} ( \cancel{60 \degree)}}{ \cancel{360 \degree}} \pi - \frac{1}{2} {(8)}^{2} \sin 60\degree \\ \\ \implies \: A = \frac {64 }{6} \pi - \frac{1}{2} \times 64 \times \frac{ \sqrt{3} }{2} \\ \\ \implies \: \huge \purple{ \boxed{A = \bigg( \frac {32 }{3} \pi - 16 \sqrt{3}\bigg) }\: sq\:in}[/tex]

Answer:

D) I, III, and V

Step-by-step explanation:

Edge

area of circle:

π * radius²

π * 2²

4π in²

area of rectangle:

length * width

20 * 4

80 in²

total area:

4π in² + 80 in²

93 in²

area of triangular prism:

( base length * perpendicular height * length ) ÷ 2

( 12.6 * 1.6 * 10.75 ) ÷ 2

216.72 ÷ 2

108.36 mm³

Answer:

Absolute Value Inequality entered :      |2x-6|<10 

Step by step solution :STEP 1:Rearrange this Absolute Value InequalityAbsolute value inequalitiy entered      |2x-6| < 10 STEP 2:Clear the

Absolute Value BarsClear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-6| For the Negative case we'll use -(2x-6) For the Positive case we'll use (2x-6) STEP 3:Solve the Negative Case      -(2x-6) < 10      Multiply      -2x+6 < 10      Rearrange and Add up      -2x < 4      Divide both sides by 2       -x < 2      Multiply both sides by (-1)      Remember to flip the inequality sign       x > -2    
  Which is the solution for the Negative Case

STEP 4:Solve the Positive Case      (2x-6) < 10      Rearrange and Add up      2x < 16      Divide both sides by 2       x < 8      Which is the solution for the Positive Case

STEP 5:Wrap up the solution    -2 < x < 8 Solution in Interval Notation    (-2,8) Solution on the Number Line

One solution was found :    -2 < x < 8

Step-by-step explanation:

mark me brainliest!!

Answer:

No, they do not

explanation: "The sum of the lengths of any two sides of a triangle must be greater than the length of the third side."

Explanation:

Think of the vertical lines as train tracks (the metal rails).

Stuff between the rails are interior angles.

Angles 3 and 6 are one pair of alternate interior angles because they are on alternating sides of the transversal line. The other pair of alternate interior angles are angles 4 and 5.

Alternate interior angles are congruent when we have parallel lines like this.

The answer is x=-4

I’ve attached my work explaining why below :)

x≤-4 is the inequality represents all the solutions of -2(3x + 6) = 4(x + 7)

Two or more expressions with an Equal sign is called as Equation.

The given equation is -2(3x + 6) = 4(x + 7

We need to find the inequality which represents the solutions of the equation.

Let us solve for x

-2(3x + 6) = 4(x + 7)

Apply distributive property

-6x-12=4x+28

Take the variable terms on one side.

-6x-4x=28+12

-10x=40

Divide both sides by 10

x=-4

Hence, x≤-4 is the inequality represents all the solutions of -2(3x + 6) = 4(x + 7)

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Answer:

Jenna is right

Step-by-step explanation:

Jenna is right because what makes up a square is its four sides. When calculating the area of a rectangle you use the same formula as you would for a square. A rectangle is just an elongated square.

Answer: 144 square centimeters

Step-by-step explanation:

An area of a triangle is determined by this formula: Area = Length * Height/2. Since 12 x 24 = 288, divide 288 by 2 and you will have 144

Conclusion:

it's 144 square centimeters

Answer:

The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean. To determine the sum of squares, the distance between each data point and the line of best fit is squared and then summed up. The line of best fit will minimize this value.

Answer:

28

Step-by-step explanation:

because it's value increases by 28 every month

Answer:

Write two expressions (with at least two terms each) that when added together have a sum of -4 n + 6.

100 POINTS AND BRAINLIEST

Answer:

9in³

Step-by-step explanation:

Hope this answers helps you

Answer:

Jace is correct they can use their loaves of bread to show 1/2 is less than 1/3. Because they have 2 loaves of bread

We have the given indefinite integral ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{x+1}{x(xe^{x}+2)}dx}[/tex]

We will use substitution hence to solving this integral

Now , put ;

[tex]{:\implies \quad \sf e^{x}=u}[/tex]

So that :

[tex]{:\implies \quad \sf dx=\dfrac{du}{u}\quad and\quad log(u)=x}[/tex]

Now , putting the values in the integral , it can be written as ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{log(u)+1}{log(u)\{ulog(u)+2\}}\times \dfrac{du}{u}}[/tex]

Now , we will again use substitution method for making the integral easy. So put ;

[tex]{:\implies \quad \displaystyle \sf ulog(u)+2=v}[/tex]

So that ;

[tex]{:\implies \quad \displaystyle \sf du=\dfrac{dv}{log(u)+1}\quad and\quad ulog(u)=v-2}[/tex]

Now , we have ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\cancel{\{log(u)+1\}}}{log(u)v}\times \dfrac{dv}{\cancel{\{log(u)+1\}}u}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dv}{v\{ulog(u)\}}}[/tex]

Now , putting the value of ulog(u) = v - 2

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dv}{v(v-2)}}[/tex]

Now , using partial fraction decomposition , ths given integral can be further written as ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int \left(\dfrac{1}{v-2}-\dfrac{1}{v}\right)dv}[/tex]

Now ,as integrals follow distributive property. So ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\left(\int \dfrac{1}{v-2}dv-\int \dfrac{1}{v}dv\right)}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}(log|v-2|-log|v|)+C}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{v-2}{v}\bigg| +C}[/tex]

Putting value of v ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{ulog(u)+2-2}{ulog(u)+2}\bigg| +C}[/tex]

Now, putting value of u ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{e^{x}log(e^{x})}{e^{x}log(e^{x})+2}\bigg| +C}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{xe^{x}}{xe^{x}+2}\bigg| +C}[/tex]

[tex]{:\implies \quad \therefore \displaystyle \underline{\underline{\int \bf \dfrac{x+1}{x(xe^{x}+2)}dx=\dfrac{1}{2}log\bigg|\dfrac{xe^{x}}{xe^{x}+2}\bigg| +C}}}[/tex]

By using what we know about circles and distance between points, we will see that:

BD = 18 units

BC = 16.97 units

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

The distance from B to D, will be equal to the distance from B to A, minus the radius of the circle.

Because we know that the center of the circle is at (8, 10), and the edge of the circle is 4 units above the x-axis, we can assume that the closest point on the circle to the x-axis is:

(8, 4)

Then the radius of the circle is given by the distance between these two points:

[tex]r = \sqrt{(8 - 8)^2 + (10 - 4)^2} = 6[/tex]

Now we need to find the distance between A and B.

A = (8, 10)

B = (0, 10 - 16*√2)

The distance between these points is:

[tex]d = \sqrt{(8 - 0)^2 + (10 - 10 + 16*\sqrt{2})^2 } \\\\d = \sqrt{(8)^2 + (16*\sqrt{2})^2 } = 24[/tex]

And the distance from B to D is the distance from B to A, minus the radius of the circle, so we have:

BD = BA - r = 24 - 6 = 18

The distance from B to D is 18 units.

To get the value of BC, we use the fact that this is a cathetus of a right triangle with a hypotenuse of 18 units, and where the other side AC measures 6 units, then we have:

BC^2 + 6^2 = 18^2

BC = √(18^2 - 6^2) = 16.97 units.

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Answer:

1 and 2/8 yards of material used

Step-by-step explanation: