Add Decimals-Instruction - Level E
June makes slime using 1.5 liters of white glue and 0.72 liter of a starch and water mixture.
Find the total volume of the slime.
Are there enough hundredths to make a tenth?
➡ There are ? hundredths. That is
enough to make a tenth.
✓is
is not

The values of x and y are given as follows:

Similar polygons are polygons that share these two features presented as follows:

The proportional relationship for the side lengths in this problem is given as follows:

x/10.5 = 5/y = 5/7.5.

Hence the value of x is given as follows:

7.5x = 5 x 10.5

x = 5 x 10.5/7.5

x = 7.

The value of y is given as follows:

5/y = 5/7.5

y = 7.5.

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Answer:

x=6

Step-by-step explanation:

the two dashes show that the two lines are parallel, so 23=3x+5; subract 5 from both sides to get 18=3x, so x=6

The volume of the rectangular prism based on the assumed values will be 640 inches³.

It should be noted that to find the volume of a rectangular prism, we have to multiply the length of the prism by the width of the prism by the height of the prism.

Let's assume that the base length of a rectangular prism is 8 inches, the base width is 5 inches and the height of the prism is 16 inches, as we want to find the volume of the rectangular prism.

The volume of the rectangular prism formula, the volume of rectangular prism = length × width × height of the prism

= 8 × 5 × 16

= 640 cubic inches.

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The statistical measures relative to each definition are given as follows:

The sentences are completed using four statistical measures, and their definitions, as follows:

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Answer:

17.6 feet.

Step-by-step explanation:

The length of the I-beam can be calculated as follows:

Weight = Length * Weight per Foot

Rearranging this equation:

Length = Weight / Weight per Foot

Substituting the given values:

Length = 444.5 lb / 25.4 lb/ft = 17.6 ft

So, the length of the I-beam is 17.6 feet.

The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(3/5) (30x - 15) = 72

Solve the linear equation with a single variable for 'x', then we have

(3/5) (30x - 15) = 72

3(6x - 3) = 72

18x - 9 = 72

18x = 81

x = 4.5

The solution of the linear equation with a single variable (3/5) (30x - 15) = 72 will be 4.5. Then the correct options are C, D, and E.

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The weighted average price index is 171, which means that the average price of the components in Year 2 was 171% of their average price in Year 1.

To compute the weighted average of relatives, we need to find the weighted average of the ratio of the prices of each component in Year 2 to Year 1. Let's call this ratio the "relative price".

Relative price for component A = Po Year 2 / Po Year 1 = 6.00 / 3.00 = 2.00

Relative price for component B = Pn Year 2 / Pn Year 1 = 8.50 / 6.80 = 1.25

Relative price for component C = Pn Year 2 / Po Year 1 = 17.68 / 20.80 = 0.85

Next, we'll find the weighted average of the relatives by summing the product of each relative price and its corresponding standard weight, and dividing by the sum of the standard weights.

Weighted average of relatives = (2.00 * 16 + 1.25 * 6 + 0.85 * 2) / (16 + 6 + 2)

= (32 + 7.5 + 1.7) / 24

= 41.2 / 24

= 1.71

The weighted average of relatives is 1.71, which means that the average price of the components increased by 71% from Year 1 to Year 2.

To compute the weighted average price index, we'll use the weighted average of relatives as a reference point and multiply it by 100.

Weighted average price index = Weighted average of relatives * 100

= 1.71 * 100

= 171

Therefore the weighted average price index is 171, which means that the average price of the components in Year 2 was 171% of their average price in Year 1.

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Answer:

Step-by-step explanation:

Given the information that the polynomial function P(x) has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0, and a root of multiplicity 1 at x = -5, we can use this information to find a possible formula for P(x).

A polynomial function's roots are the values of x that make the function equal to zero. If a root has multiplicity n, it means that (x - root) is a factor of the polynomial function n times.

So, based on the given information, we know that P(x) must be divisible by the factors (x - 1)^2, (x - 0)^2, and (x + 5), and that the leading coefficient must be 1.

Putting it all together, a possible formula for P(x) is:

P(x) = (x - 1)^2 (x - 0)^2 (x + 5) = (x^2 - 2x + 1)(x^2)(x + 5) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5

So, the possible formula for P(x) is P(x) = x^6 - 7x^5 + 17x^4 - 22x^3 + 17x^2 - 7x + 5.

Answer:   [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Explanation:

If k is a root of P(x), then x-k is a factor. The multiplicity is the exponent for that factor.

For instance, the root x = 1 with multiplicity 2 leads to the factor [tex](\text{x}-1)^2[/tex]

The leading coefficient is the number out front. For example, if the leading coefficient was 8, then we'd have [tex]P(\text{x}) =8\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

However, we change that "8" to a "1" since the leading coefficient is 1 here.

That's how we get to

[tex]P(\text{x}) = 1\text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex] aka [tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5)[/tex]

Optionally if you were to expand everything out, combine like terms, and simplify then you'd get

[tex]P(\text{x}) = \text{x}^2(\text{x}-1)^2(\text{x}+5) = \text{x}^5 + 3\text{x}^4- 9\text{x}^3+5\text{x}^2[/tex]

I don't recommend doing this because you lose the information about the roots along with their corresponding multiplicities. It's better to keep things factored.

You can use a graphing tool like Desmos or GeoGebra to verify the answer.

The percentage of students who are doing their homework regularly is 75%.

A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.

To find the percentage of students who are doing their homework regularly,

We find the total students and this is 75 + 5 = 80 students

The percentage is 60/80 * 100

= 75%

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The missing value in the expression A = -2(x-9)² + ? is 162, which represents the maximum area of the storage bin.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

To complete the perfect square, we need to factor out the coefficient of the squared term (-2) from the expression:

A = -2x² + 36x

A = -2(x² - 18x)

Next, we need to add and subtract the square of half the coefficient of the x-term (-18/2 = -9) inside the parentheses:

A = -2(x² - 18x + (-9)² - (-9)²)

Simplifying the expression inside the parentheses, we get:

A = -2[(x - 9)² - 81]

Distributing the -2, we get:

A = -2(x - 9)² + 162

Therefore, the missing value in the expression is 162.

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Answer:

12 [tex]in^{3}[/tex]

Step-by-step explanation:

Volume is the length x  the width x the height

The rectangle of the bottom would be

(4)(2)(1) = 8

The rectangle on the top would be

(1)(2)(2) = 4

8 + 4 = 12 [tex]in^{3}[/tex]

Answer:

1. -7

2. -1

3. 5

Step-by-step explanation:

Substitute the value given into the equation

The area of the attached figure is 32 square mm

The similar question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

A square a triangle and a parallelogram

The shapes can be combined to

a triangle and a parallelogram

So, we have

Area = Sum of individual areas

Using the dimensions of the shapes as a guide, we have the following:

Area = 0.5 * 2 * 8 + 4 * 6

This gives

Area = 32

Hence, the area is 32 square mm

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Horizontal lines have a slope of zero, since the "rise" is; zero.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Since we know that Vertical lines have an undefined slope, since the "offset" is zero, and division by zero is not allowed.

If the slope has a value of zero, the line is horizontal, neither increases nor decreases.

Therefore,

Horizontal lines always have an equation of the form; y = a

Vertical lines always have an equation of the form; x = b

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Answer:

add wtwo numbers x by 3? I am sorry don't understand question

Step-by-step explanation:

The derivative of the composite function f(x) = (3 · x · cos x + √x) / [5 · x² · (sin x + 1)] is equal to f'(x) = [[3 · cos x - 3 · x · sin x + (1 / 2√x)] · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · [5 · x · (sin x + 1) + 5 · x² · cos x]] / [5 · x² · (sin x + 1)]².

In this problem we must determine the derivative of the composite function f(x) = (3 · x · cos x + √x) / [5 · x² · (sin x + 1)]. This can be done by using the following derivative rules:

Derivative of the addition of two functions

d [f(x) + g(x)] / dx = df(x) / dx + dg(x) / dx

Derivative of the product of two functions

d [f(x) · g(x)] / dx = [df(x) / dx] · g(x) + f(x) · [dg(x) / dx]

Derivative of the division of two functions

d[f(x) / g(x)] / dx = [[df(x) / dx] · g(x) - f(x) · [dg(x) / dx]] / [g(x)]²

Derivative of a function and a constant

d [c · f(x)] / dx = c · df(x) / dx

Derivative of a power function

d [xⁿ] / dx = n · xⁿ⁻¹

Derivative of cosine

d [cos x] / dx = - sin x

Derivative of sine

d [sin x] / dx = cos x

Now we proceed to determine the derivative of the function by derivative rules:

f'(x) = [d [3 · x · cos x + √x] / dx · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · d [5 · x² · (sin x + 1)] / dx] / [5 · x² · (sin x + 1)]²

f'(x) = [[3 · cos x - 3 · x · sin x + (1 / 2√x)] · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · [5 · x · (sin x + 1) + 5 · x² · cos x]] / [5 · x² · (sin x + 1)]²

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ΔXVZ and ΔXWY are similar by SAS property of similarity.

We have,

ΔXVZ and ΔXWY

XW/WV = XY/YZ

15/20 = 27/36

3/4 = 3/4

The ratio of two pairs of corresponding sides is equal. ______(1)

And,

m∠XWY = m∠XVZ = 90

The included angle of the two triangles is equal. ________(2)

Now,

From (1) and (2),

ΔXVZ and ΔXWY are similar.

By SAS property of similarity.

Thus,

ΔXVZ and ΔXWY are similar by SAS property of similarity.

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Bro Use SOH CAH TOA and you check through to now whether u use Cos, Sine or tan

Answer:

To convert from kilometers per hour to miles per hour, we use the conversion factor of 1 mile per hour = 1.609 kilometers per hour.

So, 50 km/h = 50 x 1.609 mph = 80.45 mph

Rounding to one decimal place, the answer is 80.5 mph.

The typical speed limit in Europe is,

⇒ 833.3 miles per hour.

We have to given that,

A typical speed limit in Europe is, 50 km/h (kilometers per hour).

We can change the speed limit from kilometers per hour in miles per hour.

⇒ 50 kilometers per hour

⇒ 50 × 1000 / 60 miles per hour.

⇒ 50000 / 60  miles per hour.

⇒ 833.3 miles per hour.

Therefore, The typical speed limit in Europe is,

⇒ 833.3 miles per hour.

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If the shortest leg of the small triangle is 4 in and the hypotenuse is 12 in and the shortest leg of the large triangle 8 in, then the length of the hypotenuse of the large triangle is 24 inches.

We know that two triangles are proportional if their corresponding sides are in proportion to each other. That is, the ratio of the lengths of the corresponding sides is the same for both triangles.

Let's denote the length of the hypotenuse of the large triangle by "h". We can set up a proportion using the given information:

shortest leg of small triangle / hypotenuse of small triangle = shortest leg of large triangle / hypotenuse of large triangle

Plugging in the values we get:

4/12 = 8/h

Simplifying the equation we get:

h = (12*8)/4 = 24

To explain the solution, we used the fact that similar triangles have proportional sides. We then used the given information about the lengths of the sides of the small and large triangles to set up a proportion and solve for the unknown length of the hypotenuse of the large triangle.

The key to this problem was recognizing the relationship between similar triangles and using that relationship to set up and solve a proportion.

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Answer:

2.64

Step-by-step explanation:

For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

What exactly is a linear inequality?

In mathematics, inequality denotes a mathematical statement with no equal sides. An inequality happens in mathematics when a connection results in a non-equal comparison of two expressions or two numbers. Any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters "< and >" denote severe inequalities, whereas ‘≤’ and ‘≥’  denote slack inequalities. A linear inequality looks to be a linear equation, however the formula is different.

Now,

As stated in Commutative property the order in addition does not matter and in addition property the value added on both sides does not affect the result.

In step 3 we can write this as 5x-x-5<11x+x-21

which will not change result and

in step 7, 21 is added both sides which will not change result.

Hence,

           For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

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The equation of the cubic function is 2( x-4) (x-3) x+3)

A cubic function is a polynomial function of degree 3 and is of the form f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0.

The equation of a cubic function is given as;

x³-(a+b+c) x² + ( ab+bc+ca) x + abc

where a,b,c are the root of the cubic function

a = 4, b = 3 and c= -3

a+b+c = 4+3-3 = 4

ab = 4×3 = 12

bc = -3×3 = -9

ca = -3×4 = -12

ab+bc+ca = 12-9-12 = -9

abc = 4×3×-3 = -36

therefore;

x³-( 4)x² + ( -9)x -36

x³-4x²-9x -36

therefore y = a( x-4) (x-3) x+3)

at point (2,20)

substitute x by2 and y by 20

20 = a( -2) (-1) (5)

20 = a10

a = 20/10

a= 2

therefore the equation of the cubic function is

2( x-4) (x-3) x+3)

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Given diagram drawn on the graph is parallelogram.

For find out 4th coordinate of parallelogram.

We must know the basics of graph.

Graph can defined as pictorial representation using data or point in the organized manner.

Graph having x-coordinate and y-coordinate.

For find out the location of point.

We must know how to locate coordinates.

For find X-point , parallel distance from y-axis.

For  find Y-point , parallel distance from x-axis.

Observe the given diagram.

Find out the parallel distances of x-axis and y-axis.

4th coordinate of parallelograms is c(2,-5).

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1/(x+1)(x-2) is the simplified form of the expression

Given the expression below

x+2/4x²+5x+1 · 4x+1/x²-4

Factorise the quadratic expressions

4x²+5x+1 = 4x²+4x + x+1

4x²+5x+1 = 4x(x+1)+1(x+1)

4x²+5x+1 = (4x+1)(x+1)

For the expression x²-4

x²-4 = (x+2)(x-2)

Substitute

x+2/4x²+5x+1 · 4x+1/x²-4 = x+2/(4x+1)(x+1) · 4x+1/(x+2)(x-2)

x+2/4x²+5x+1 · 4x+1/x²-4 = 1/x+1 · 1/x-2

x+2/4x²+5x+1 · 4x+1/x²-4  = 1/(x+1)(x-2)

Hence the simplified form of the expression is 1/(x+1)(x-2)

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The requried solution of the system of equations is (-1, -2). Option C is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Two intersecting lines will have exactly one solution (i.e., a unique point of intersection) if and only if they are not parallel.

In other words, if the slopes of the two lines are different, they will intersect at a single point. This is because the slopes of the lines determine how steep they are, and if they are not the same, they will eventually cross at a single point. So from the graph, both lines intersect at (-1, -2) implying that The solution is (-1, -2).

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