Please help with 2 questions.

The addition of the two functions f(x) and g(x) is 8x² − x − 4. Then the correct option is C.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The functions are given below.

[tex]\rm f(x)=5x^2-2x \\\\g(x)=3x ^2+x-4[/tex]

The addition of the functions is given as

f(x) + g(x) = 5x² − 2x + 3x² + x − 4

f(x) + g(x) = 8x² − x − 4

More about the function link is given below.

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The correct answer for the equation of the circle with center (-1,4) and passes through point (3,-5) is   [tex](x+1)^2 + (y-4)^2 = 97[/tex].

Given Co-ordinates:

Centre:

(-1,4)

Point of intersection:

(3,-5)

The standard equation of circle with center (h, k) is:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

(h, k) are co-ordinates of center

Given in question:

h= -1

k = 4

Find radius of the circle:

distance between the center(-1,4) and the given point (3, -5).

[tex]r = [\sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2 }[/tex]

[tex]r = [\sqrt{((3- (-1))^2 + (-5-4)^2 }[/tex]

[tex]= \sqrt{(4)^2 + (-9)^2 }[/tex]

[tex]= \sqrt{16 + 81}[/tex]

[tex]= \sqrt{97}[/tex]

Now, Equation of circle:

[tex](x-(-1))^2 + (y-4)^2 = (\sqrt{97})^2[/tex]

[tex](x+1)^2 + (y-4)^2 = 97[/tex]

The equation of circle is [tex](x+1)^2 + (y-4)^2 = 97[/tex].

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The equation of the circle with center (-1, 4) and passing through the point (3, -5) is (x + 1)² + (y - 4)² = 97.

The subject of this question is geometry, specifically about the equations of circles. We start by noting that the general equation of a circle is (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the circle's center and r is the radius of the circle.

Here, the center of the circle is at (-1, 4). We don't know the radius yet, but we know that the circle passes through the point (3, -5). The radius is the distance from the center of the circle to any point on the circle. We can find this using the distance formula which is d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²].

Substituting the given points into the distance formula, we get: r = sqrt[(3 - (-1))² + (-5 - 4)²] which simplifies to r = sqrt[(4)² + (-9)²] = sqrt[16 + 81] = sqrt[97].

Now we can write the equation of the circle, substituting the center and radius values into the equation. This gives us: (x - (-1))² + (y - 4)² = sqrt[97]² which simplifies to (x + 1)² + (y - 4)² = 97.

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we have that

f(x)=3x-2

g(x)=4x-1

3x-2=4x-1-------------> 4x-3x=-2+1--- > x=-1

find the value of f(x) or g(x) for x=-1

f(x)=3x-2 ------->  f(-1)=3*(-1)-2 ------> f(-1)=-5

the solution is the point (-1,-5)

using a graph tool

see the attached figure

the answer is 

You have studied polynomials consisting of constants and/or variables combined by addition or subtraction. The variables may include exponents. The examples so far have been limited to expressions such as 5x4 + 3x3 – 6x2 + 2x containing one variable, but polynomials can also contain multiple variables. An example of a polynomial with two variables is 4x2y – 2xy2 + x – 7.

Many formulas are polynomials with more than one variable, such as the formula for the surface area of a rectangular prism: 2ab + 2bc + 2ac, where a, b, and c are the lengths of the three sides. By substituting in the values of the lengths, you can determine the value of the surface area. By applying the same principles for polynomials with one variable, you can evaluate or combine like terms in polynomials with more than one variable.

The product of (7x²y³) and (3x⁵y⁸) is obtained by multiplying the coefficients and adding the exponents of like terms, resulting in c) 21x⁷y¹¹.

To find the product of the two algebraic expressions (7x²y³) and (3x⁵y⁸), we simply multiply the coefficients and add the exponents of corresponding variables:

Multiply the coefficients: 7 * 3 = 21

Add the exponents of x: x² * x⁵ = x²⁺⁵ = x⁷

Add the exponents of y: y³ * y⁸ = y³⁺⁸ = y¹¹

Therefore, the product is 21x⁷y¹¹, which corresponds to option (c).

Answer:

b

Step-by-step explanation:

took the test got it right

Answer:

[tex]2[/tex]

Step-by-step explanation:

we have

[tex]\frac{\sqrt{120}}{\sqrt{30}}[/tex]

we know that

[tex]\frac{\sqrt{120}}{\sqrt{30}}=\sqrt{\frac{120}{30}}=\sqrt{4} =2[/tex]

Answer:

its D

Step-by-step explanation:

The Answer is 7(ab).

I did the quiz.

Answer: 7ab

Step-by-step explanation:

The given polynomial : [tex]14a^3b^4-7ab^7+21a^2b[/tex]

The terms of the above polynomial can be written as :

[tex]14a^3b^4=(7\times2)a^{2+1}b^{3+1}=(7\times2)a^2(a)b^3b\\\\-7ab^7=-7ab^{6+1}=-7ab^6(b)\\\\21a^2b=(7\times3)a^{1+1}b=(7\times3)a(a)b[/tex]

Now, we can see that the greatest common factor of the polynomial's terms= [tex]7ab[/tex]

Final answer:

When each score in a sample is multiplied by a constant, the mean of the new distribution will also be multiplied by that constant, resulting in a new mean value of 450.

Explanation:

The mean of a sample is a measure of the average value of the data points in that sample.

When each score in a sample is multiplied by a constant, like 5 in this case, the resulting mean of the new distribution will also be multiplied by that constant.

In this scenario, since each score is multiplied by 5, the mean of the new distribution will be 5 times the original mean, giving a new mean of 450.

Answer:

Rotation.

Step-by-step explanation:

There are three rigid motions (which do not change the shape and size of the figures): rotation, translation and reflection.

You make a rotation of a figure when you turn it about a fixed point (which can be inside, on an edge or outside the figure) and it is measured in degrees.  The rotation can be clockwise or counterclockwise.

Answer:

The answer is Reflection