Find area of the region under the curve y=9−3x^2 and above the x-axis.

Answer:

x + 2 y = -20

Step-by-step explanation:

The standard form of a linear is Ax+By=C

Multiply both sides by 2

simplify the right side

rewrite the equation

The standard form of the equation is x + 2y = -20.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = (-1/2)x - 10

This is in the slope-intercept form.

Now,

The standard form of an equation.

ax + by = c

So,

y = (-1/2)x - 10

y = (-x - 20)/2

2y = -x - 20

x + 2y = -20

Thus,

The standard form of the equation is x + 2y = -20.

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The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Step-by-step explanation:

u fyfucyfcr t xd tvycyfctc

Answer:

\(x∈( - ∞;8]\)

Step-by-step explanation:

\(x + 9 - 3 \leqslant 14\)

Collect like-terms:

\(x \leqslant 14 - 9 + 3\)

\(x \leqslant 8\)

\(x∈( - ∞;8]\)

\(-1~~,~~\stackrel{-1+4}{3}~~,~~\stackrel{3+4}{7}~~,~~\stackrel{7+4}{11}~~,~~\stackrel{11+4}{15}\qquad \qquad \stackrel{\textit{common difference}}{d = 4} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\stackrel{\textit{first term}}{-1}\\ d=\stackrel{\textit{common difference}}{4} \end{cases}\implies a_n=-1+(n-1)4 \\\\\\ a_n=-1+4n-4\implies a_n=4n-5\)

Answer:

x= -2

y= 3

Now,

5x-y = 12

5*(-2) - 3 = 12

-10 - 3 = 12

-13 = 12

So, this equation doesnot pass through (-2,3).

Answer:

-√26, 5.15, 5.2, 16/3

Step-by-step explanation:

-√26 = -5.09

16/3 = 5.33

Answer:

\(x(5x+1)\)

Step-by-step explanation:

To find the GCF, first you must list all factors of each term.

\(5x^{2}\): 1, 5, x, x

\(x\): 1, x

We find that 1 and \(x\) are the only common factors between the terms. Therefore, we can only factor out \(x\).

\(x(5x+1)\)

Answer:

$16.80

Step-by-step explanation:

1) Find 5% of $16

To find 5% of $16 we have to multiply the numbers together then divide the result by 100

2) Add it onto $16

As there is 5% tax onto the shirt you need to add $0.80 onto $16 to get the final price

Hope this helps, have a great day!

Answer:

3

Step-by-step explanation:

\(\frac{2a}{3b-c} \\=\frac{2(6)}{3(4) - 8} \\=\frac{12}{12-8} \\=\frac{12}{4} \\=3\)

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The value(s) of x that make it true. (a) x= -23 (b) x= -2 (c) x= 0.22  (d) x= -1.125 respectively.

This involves the simplify the equation to make x the subject

a. 10 = 1+7x/7+x

= 10(7+x) = 1+7x

Opening the brackets

10x-7x = 1-70

= 10x -7x = -69

3x=-69

x=-23

b. 0.2 =6+2x/12+\x

= 2.4+0.2x=6+2x

2.4-6 = 2x-0.2x

-3.6=1.8x

making x the subject

x=-2

c. 0.8= x/0.5+x

0.4-0.x=x

2.4=x+0.8x

0.4=1.8x

x=0.22

d. 3.5 =4+2x/0.5-x

1.75=4+2x

-2.25=2x

x=-1.125

In conclusion the values of x are -23, -2, 0.22, -1.125

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Answer:

10p

Step-by-step explanation:

p + 2p + 3p + 4p

= 10p

Answer:

10p

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

p + 2p + 3p + 4p

Step 2: Simplify

The value of n, considering the intersecting chords in the circle, is given as follows:

n = 6m.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Considering the two intersecting chords for the circle in this problem, the value of n is obtained as follows:

5n = 15 x 2

5n = 30

n = 30/6

n = 6m.

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The divisibility rule for 3 on any integer number  is proven in the detailed explanation of the solution.

Given a non-decimal number, n.

Suppose n may be divided by 3.

n should be thought of in terms of its digits as

n = d × 1 × 10⁽ⁿ⁻¹⁾⁽ⁿ⁻¹⁾ + d  × 2 × 10⁽ⁿ⁻²⁾ + ... + d × m × 10⁰

where d 1, d 2,..., d m are its digits and m is the number of digits in n.

The result of the preceding equation with n = 3k is

3k = d  × 1 × 10(m-1) + d × 2 × 10(m-2) +... + d × m × 10(m-0)

3000 is subtracted from both sides of the equation, giving us

0 = d × 1 × 10⁽ⁿ⁻¹⁾⁽ⁿ⁻¹⁾ + d  × 2 × 10⁽ⁿ⁻²⁾ + ... + d × m × 10⁰

We obtain by adding 3k to both sides of the equation.

3k = d × 1 × 10⁽ⁿ⁻¹⁾+ d

The divisibility rule is a heuristic for determining if two positive integers can be divided evenly (i.e. there is no remainder left over). For instance, determining if a number's last digit is 2, 4, 6, 8, or 0 makes it simple to determine whether it is even.

By examining the digits of the number, a divisibility rule provides a simple shorthand for determining if an integer is divisible by a particular set of factors without actually doing the division. This page only offers recommendations and examples for decimal, or base 10, numbers despite the fact that there are distinct divisibility tests for numbers in each radix or basis.

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The area of the composite figure here is 6m².

A collection of straightforward polygonal forms combined with circles make up the area of the composite shapes. We can add the areas of all the fundamental shapes to determine the area of the composite shapes. Simply add the area of each individual shape to get the area of composite shapes.

Since we are told that there are two congruent trapezoids, it means that they will have same base of 1m.

This Means the total base of the entire triangle will be:

Base = 1 + 1¾ + 1 + 1¾ = 5.5 m

Height of main triangle = 2 m

Thus,

Area = ½ × 5.5 × 2 = 5.5 m²

We are looking for best estimate, so let's approximate to the nearest whole number to get 6 m².

Therefore, the area of the composite figure is 6m².

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Answer:

Step-by-step explanation:

To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.

The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:

x-coordinate of C' = 1111 * 8 = 8888

y-coordinate of C' = 1111 * 8 = 8888

Therefore, the coordinates of point C' are (8888, 8888).

9514 1404 393

Answer:

  2

Step-by-step explanation:

Fill in the argument value and look up the function value on the graph.

  \((f\circ f)(-2) = f(f(-2)) = f(2) = \boxed{2}\)

Answer:

Step-by-step explanation:

The triangles are similar.

x/(x+4) = 7.2/12

x/(x+4) = 0.6

x = 0.6(x+4)

0.4x + 2.4

x = 6

Answer:

200 (12+3)

Step-by-step explanation:

They sold 200 tickets at a price of (12+3)

200 (12+3)

Answer:

B

Step-by-step explanation:

When a number is in front of the parethese, it is multiplying all the terms inside of it.

Looking at the first answer, the 2 multiplies 2/5x and 2, getting 4/5x + 4. This is not equivllent to 2 2/5x +1.

In the next one 2 is multiplying the same values, and results in 4/5x + 4. This is indeed equivelent to 4/5x + 4.

So this is your answer.

Hope this helps!

If the data were transformed and points with the coordinates

(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.

To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.

Let's calculate the logarithms for the given data:

x     y            log(y)

1     12          log(12) = 1.079

2     83        log(83) = 1.919

3     580      log(580) = 2.763

Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)

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Answer:

I am not sure if I understand the question correctly, but I believe it would be 1 hundred in each group.

Step-by-step explanation:

400 divided by 4 = 100

Answer:

The volume of the sphere is 3053. 63 inches.

Step-by-step explanation:

Formula for volume of a sphere is : V = 4 /3 · π · r³

V = 4/3 · π · 9³

V ≈ 3053. 63

The volume of the sphere is 3053. 63 inches.

Answer:

4 and 10/2 so actually 9

Step-by-step explanation:

Answer:

The answer is 9.

Step-by-step explanation:

You just need to substitute the variables, so:

10/2+4

= 9

I hope this helps!

Answer:

7x+8

Step-by-step explanation:

12x-5x    +       6 + 8

Answer:

10% of 100=10

20%of 100=20

5% of 100=5

50%=50

125