A frame of width a surrounds a 5 by 7 inch photograph. Find the expression that represents the area of the frame in terms of a. HELP ASAP

A. a 2 − 35
B.a 2 + 12a + 35
C. None of these
D. 4a 2 + 24a
E. a 2 + 12a

Answer:

[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]

Step-by-step explanation:

The given expression is [tex](2x+y)(3x^2+y)[/tex].

We expand the parenthesis using the distributive property to obtain;

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

We expand further to get;

[tex](2x+y)(3x^2+y)=6x^3+2xy+3x^2y+y^2)[/tex]

This gives us;

[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]

Answer:

The mass of Jupiter is about 389.7331 times the mass of Venus.

Step-by-step explanation:

The question is asking for how much the two masses vary from one another. Since the mass of Jupiter is greater than that of Venus, what value is to be multiplied by the mass of Venus that would give the mass of Jupiter?

Thus, to determine this, we divide the mass of Jupiter by the mass of Venus;

     = [tex]\frac{1898*10^{24} }{4.87*10^{24} }[/tex]

    =  [tex]\frac{1898}{4.87}[/tex]

    = 389.7331

 Therefore, the mass of Jupiter is about 389.7331 times the mass of Venus.

Answer:

The correct option is C. The height of the cylinder is 9 cm.

Step-by-step explanation:

The radius of cone is 12 cm and the height of cone is 12 cm.

The volume of cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

[tex]V_1=\frac{1}{3}\pi (12)^2(12)[/tex]

[tex]V_1=576\pi[/tex]

The radius of cylinder is 8 cm. The volume of cylinder is

[tex]V=\pi r^2h[/tex]

[tex]V_2=\pi (8)^2h[/tex]

[tex]V_2=64\pi h[/tex]

It is given that the volume of cone and cylinder is same.

[tex]V_1=V_2[/tex]

[tex]576\pi=64\pi h[/tex]

[tex]\frac{576\pi}{64\pi}=h[/tex]

[tex]9=h[/tex]

Therefore the height of the cylinder is 9 cm and option C is correct.

To find the height of the cylinder that has the same volume as a cone, we can compare their volumes. By setting the volumes equal to each other and simplifying the equation, we find that the height of the cylinder is 9 cm.

To find the height of the cylinder, we need to compare the volumes of the cone and the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. The volume of the cone with radius 12 cm and height 12 cm is (1/3)π(12^2)(12) = 576π cm³. Now, let's calculate the volume of the cylinder using the formula V = πr^2h, with radius 8 cm. We know that the volumes of the cone and the cylinder are equal, so 576π = π(8^2)h. Simplifying this equation, we get 576π = 64πh. Dividing both sides of the equation by 64π, we find h = 9 cm. Therefore, the height of the cylinder is 9 cm.

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4.738 rounded to the nearest thousandth remains 4.738, as it is already at the required decimal precision.

To round to the nearest thousandth, you look at the digit in the thousandth place, which in this case is an 8. You do not need to alter the number since it is already at the thousandth decimal place. Therefore, 4.738 rounded to the nearest thousandth is simply 4.738.

To find the total number of college students, we solve a proportion equation using the given 36% for part-time students and 6.2 million part-time students to find a total of approximately 17 million students.

This problem can be addressed with a simple proportion equation. We know that 36% (or 0.36 in decimal form) of all enrolled college students equals 6.2 million. So, if we let X be the total number of college students, the equation becomes 0.36X = 6.2 million.

To solve for X, we divide both sides of the equation by 0.36 and hence, X=6.2 million / 0.36. After doing the calculation, we get approximately 17.22 million. Since the question asks us to round to the nearest million, our final answer is approximately 17 million total college students.

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Answer:

50

Step-by-step explanation:

First we have to find the height. Since we know the area we can use it to find the height. The area of a triangle is A=bh1/2 or half of the base times the height. So if we plug in what we know and solve, we can find the height. 336=48 x h x 1/2. The height is 14. Now we can solve for the hypotenuse using the Pythagorean Theorem. a^2 + b^2 = c^2 plug in what we know... 14^2 + 48^2 = c^2 simplify to get 196+2304= c^2 and further 2500= c^2 so find the square root of 2500. You will get 50.

The answer is B. It is an acute triangle because of 22^2 + 51^2 > 54^2. To identify the type of triangle referred to the problem, we use the Pythagorean Theorem which involves squaring the lengths of all sides of the triangle. If the hypotenuse’s square is less than the two smallest sides' squares added together, than it is an acute triangle. However, if the hypotenuse’s square is larger, then it is an obtuse triangle.

54 is the hypotenuse since it is the longest side.

Following the Pythagorean Theorem, a^2 + b^2 = c^2:

54^2=2916

51^2=2601

22^2=484

It becomes 2601+484 = 2916.

When the two shorter sides are added, the sum is greater than the square of the hypotenuse which is 2916. Thus, the formed triangle is acute. 

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation: I did the usa test prep

The required number is 10.

Given that,
When the sum of 7 and three times a positive number is subtracted from the square of the​ number, 0 results. That number is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the number be x,
The sum of 7 and three times a positive number is subtracted from the square of the​ number 0.
x²-x(3 + 7) = 0
x² = x(10)
x = 10

Thus, the required number is 10.

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