21x^3 - 2x^2 + 20x +11 / 7x+4

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the glacier is moving at a rate of 0.3 inches every hour. It means the average rate of change is 0.3.

Let d is the total moved distance of glacier and t is number of hours. Then the total moved distance of glacier after t hours is defined as

[tex]d=0.3t[/tex]

At t=1,

[tex]d=0.3(1)=0.3[/tex]

At t=2,

[tex]d=0.3(2)=0.6[/tex]

At t=3,

[tex]d=0.3(3)=0.9[/tex]

At t=4,

[tex]d=0.3(4)=1.2[/tex]

Total moved distance of glacier after 4 hours is 1.2 inches.

The value of x is 1.2. Therefore the correct option is 1.

The solution of the two expressions for x = 20 will be equivalent.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two expressions are 8(12x + 4) and 96x + 32. The expressions will be solved as,

8(12x + 4) = 8[12(20) + 4 ] = 1952

96x + 32 = 96 (20) + 32 = 1952

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what he said hope it helped      

Step-by-step explanation:

Answer:  The required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]

Step-by-step explanation:  We are given to find measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}.[/tex]

Let x and y represents the positive and negative co-terminal angles respectively.

We know that

the measures of any two co-terminal angles differ from each other by a multiple of [tex]2\pi.[/tex]

So, the values of x and y can be found as follows :

[tex]x=\dfrac{\pi}{2}-2\pi=-\dfrac{3\pi}{4},\\\\\\y=\dfrac{\pi}{2}+2\pi=\dfrac{5\pi}{2}.[/tex]

Thus, the required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]

Final answer:

The positive coterminal angle with π/2 is 5π/2, and the negative coterminal angle is -3π/2; both angles are found by adding and subtracting 2π radians from the original angle.

Explanation:

To find the measures of two angles, one positive and one negative, that are coterminal with π/2, we need to add and subtract 2π (360 degrees) to the original angle since the angles are coterminal when they share the same initial and terminal sides and differ by a full circle (360 degrees) or a multiple thereof. The angle π/2 radians is equivalent to 90 degrees, so adding 2π radians (360 degrees) gives us a positive coterminal angle, and subtracting 2π radians (360 degrees) gives us a negative coterminal angle.

Positive coterminal angle: π/2 + 2π = 5π/2.

Negative coterminal angle: π/2 - 2π = -3π/2.

When using a Venn diagram to determine how many people like either funnel cake or fried Oreos out of a survey of 50, after subtracting the 20-person overlap from each individual preference to avoid double counting, the total number liking either is found to be 35 people.

To determine how many people like either funnel cake or fried Oreos, we need to use the concept of set union from Venn diagrams. First, we draw two overlapping circles, one for people who like funnel cake and another for those who like fried Oreos.

The overlapping area represents people who like both. Given that 30 people like funnel cake and 25 like fried Oreos, with a 20-person overlap liking both, we add the individual preferences and subtract the overlap to avoid double counting.

The representation is:

Number liking funnel cake only: 30 - 20 = 10

Number liking fried Oreos only: 25 - 20 = 5

Number liking both: 20

Adding these, the total number liking either funnel cake or fried Oreos is 10 + 5 + 20 = 35 people.

Answer:

Step-by-step explanation: False.

Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.

To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.

First, let's use the Law of Sines which states that:

sin(A)/a = sin(B)/b = sin(C)/c

Given:

We can calculate angle B using:

sin(B) = (b × sin(A)) / a

sin(B) = (382 × sin(38°)) / 432 ≈ 0.556

Finding the arc sine of 0.556, we get:

B ≈ 33.8°

Now, we find angle C:

C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°

Using the Law of Sines again to find side c:

c = (a × sin(C)) / sin(A)

c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85

Thus, it's possible to form one such triangle with the given conditions.

I think its b

Hope this helps

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Answer:

  The sides of the rectangle are 4 and 8 meters long.

Explanation:

Please consider the attached figure. Both the rectangle and the square are symmetrical about the x- and y-axes, so we only need to consider the corner of the rectangle in one quadrant.

If the rectangle is twice as long as wide, then the distance of the corner to one axis (we chose y) will be twice the distance to the other axis. The locus of points for which that is true is the line with slope 1/2. The corner of the rectangle will be on that line.

If the corner of the rectangle is also on the square, then it will be located at the point of intersection of the line with slope 1/2 and the line representing the edge of the square. That point of intersection is the point (4, 2) on this graph. That is, half the length of the rectangle is 4 m, and half the width is 2 m. This indicates the sides of the rectangle are 8 m and 4 m in length.

__

The diagonals of the square are 12 m long, so orienting the square the way we have makes the x- and y-intercepts 6 units from the origin in each quadrant.

Answer:

Step-by-step explanation:

four and eight, use soh cah toa

Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is [tex]21^{\circ}[/tex].

Given,

The inscribed angle [tex]\angle ABC[/tex] is [tex]3x-1.5[/tex].

And the Intercepted arc AC is [tex]3x+9[/tex].

We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

[tex]3x-1.5=\frac{1}{2} (3x+9)[/tex]

[tex]2 (3x-1.5)=3x+9[/tex]

[tex]6x-3.0=3x+9[/tex]

[tex]6x-3x=9+3[/tex]

[tex]3x=12\\x=4[/tex]

Since the intercepted arc AC is [tex]3x+9[/tex], putting the value of [tex]x=4[/tex] we get,

intercepted arc AC is [tex]21^{\circ}[/tex].

Hence the intercepted arc AC is [tex]21^{\circ}[/tex].

For more details on the Inscribed Angle theorem follow the link:

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The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.

So the deduction will be given as

[tex]\rm Deduction = \dfrac{4}{100} *1305.6\\\\Deduction = 0.04 * 1305.6\\\\Deduction = 52.224 \approx 52.22[/tex]

The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.

More about the percentage link is given below.

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Answer:

The correct answer is B

Step-by-step explanation:

Answer: A-$300 is correct