If f(x) = 3x^2 and g(x) = 4x^3 + 1, what is the degree of (fg)(x)?

Answer:

see explanation

Step-by-step explanation:

Since the denominators of both fractions are common

Add the numerators leaving the denominator

= [tex]\frac{8g^2+8-4g^2-2}{h^2-3}[/tex]

= [tex]\frac{4g^2+6}{h^2-3}[/tex]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{5}[/tex], hence

y = [tex]\frac{2}{5}[/tex] x + c ← is the partial equation

To find c substitute (- 3, - 1) into the partial equation

- 1 = - [tex]\frac{6}{5}[/tex] + c ⇒ c = - 1 + [tex]\frac{6}{5}[/tex] = [tex]\frac{1}{5}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{5}[/tex] ← in slope- intercept form

Answer:

[tex](-\frac{7}{6} )[/tex]

Step-by-step explanation:

From the question the emerald was located at a depth which is between -1/2 and -1 2/3 meters

This statement can be written as

[tex](-1\frac{2}{3}) -(-\frac{1}{2} )[/tex]

To get the depth, you find the depth of the emerald location, you find difference between the two mentioned depths

[tex]-(1\frac{2}{3} )-(-\frac{1}{2} )\\\\[/tex]

Change first term to improper fraction

[tex]=-(\frac{5}{3} )-(-\frac{1}{2} )\\\\[/tex]

Find the LCM to solve the operation the involves the fractions.The Least common multiple here is 6 i.e 3*2

[tex]=(-\frac{5}{3} )-(-\frac{1}{2})\\[/tex]

[tex]=\frac{-5}{3} +\frac{1}{2} =\frac{-10+3}{6} =\frac{-7}{6}[/tex]

The number that could represent the depth at which the emerald was located is

[tex]=\frac{-7}{6}[/tex]

Answer:

Reflection across the x-axis, followed by reflection across y-axis and Reflection across the x-axis, followed by translation 10 units rights

Answer:

Reflection across the x-axis, followed by translation 10 units right.

Step-by-step explanation:

I'm sorry, I know the question asks for two transformations, but let's look a the math before tackling the figure (see attachment).

When you are asked to do a reflection on the x-axis, they are asking you to invert the sign on the y coordinate of every point, and when you are asked to do a reflection on the y-axis, just invert the sign of the x coordinate, always following the convention of (x, y).

Translation to the right means to add the amount of units given to all the x coordinates, to the left means to subtract said number of units.

Translation down is to subtract those units to the y coordinate and translation up, is to add to that y coordinate.

So in this exercise:

Fig 1 coordinates are:

(-5, 2)  (-3, 4)  (-4, 7)  (-6, 5)

Fig 2 coordinates are:

(5, -2)  (7, -4)  (6, -7)  (4, -5)

So let's test the options given:

a. Reflection across the y-axis, followed by reflection across x-axis

Reflection across the y-axis:

Fig 1.1: (5, 2)  (3, 4)  (4, 7)  (6, 5) <- Every x coordinate with inverted sign

Then reflection across x-axis:

Fig 1.2: (5, -2)  (3, -4)  (4, -7)  (6, -5) <- Every y coordinate with inverted sign

if we compare this new Fig 1.2 with Fig 2:

(5, -2)  (3, -4)  (4, -7)  (6, -5)  ≠  (5, -2)  (7, -4)  (6, -7)  (4, -5)   Wrong

b. Reflection across the x-axis, followed by reflection across y-axis

Reflection across the x-axis:

Fig 1.1: (-5, -2)  (-3, -4)  (-4, -7)  (-6, -5) <- Every y coordinate with inverted sign

Then reflection across y-axis:

Fig 1.2: (5, -2)  (3, -4)  (4, -7)  (6, -5) <- Every x coordinate with inverted sign

if we compare this new Fig 1.2 with Fig 2:

(5, -2)  (3, -4)  (4, -7)  (6, -5)  ≠  (5, -2)  (7, -4)  (6, -7)  (4, -5)   Wrong

c. Reflection across the x-axis, followed by translation 10 units right

Reflection across the x-axis:

Fig 1.1: (-5, -2)  (-3, -4)  (-4, -7)  (-6, -5) <- Every y coordinate with inverted sign

Then translation 10 units right:

Fig 1.2: (5, -2)  (7, -4)  (6, -7)  (4, -5) <- Every x coordinate +10

if we compare this new Fig 1.2 with Fig 2:

(5, -2)  (7, -4)  (6, -7)  (4, -5)  =  (5, -2)  (7, -4)  (6, -7)  (4, -5)   Correct!

d. Reflection across the y-axis, followed by translation 5 units down

Reflection across the y-axis:

Fig 1.1: (5, 2)  (3, 4)  (4, 7)  (6, 5) <- Every x coordinate with inverted sign

Then translation 5 units down:

Fig 1.2: (5, -3)  (3, -1)  (4, 2)  (6, 0) <- Every y coordinate -5

if we compare this new Fig 1.2 with Fig 2:

(5, -3)  (3, -1)  (4, 2)  (6, 0)  ≠  (5, -2)  (7, -4)  (6, -7)  (4, -5)     Wrong

So from all options only c. works

Answer:

120

Step-by-step explanation:

Slope = rise / run

1/20 = 6 / run

run = 120

a. Practically speaking, you compute the differential in much the same way you compute a derivative via implicit differentiation, but you omit the variable with respect to which you are differentiating.

[tex]y=\cos x\implies\boxed{\mathrm dy=-\sin x\,\mathrm dx}[/tex]

Aside: Compare this to what happens when you differentiate both sides with respect to some other independent parameter, say [tex]t[/tex]:

[tex]\dfrac{\mathrm dy}{\mathrm dt}=-\sin x\dfrac{\mathrm dx}{\mathrm dt}[/tex]

b. This is just a matter of plugging in [tex]x=\dfrac\pi3[/tex] and [tex]\mathrm dx=0.1[/tex].

[tex]\boxed{\mathrm dy\approx-0.087}[/tex]

The differential dy for y = cos(x) is evaluated by finding the derivative of y which is -sin(x), then multiplying by dx. For x = π/3 and dx = 0.1, the calculated differential dy is approximately -0.0866 when rounded to three decimal places.

The differential dy of a function y with respect to x is given by the derivative of y with respect to x, multiplied by dx. For the function, y = cos(x), the derivative of y is -sin(x), hence dy = -sin(x)dx.

To evaluate dy for x = π/3 and dx = 0.1, we substitute x into -sin(x) and multiply by dx. This results in dy = -sin(π/3) × 0.1, which simplifies to dy = -0.1 √3/2. Rounding to three decimal places, dy ≈ -0.0866.

Answer: D. 61.2 cm

Step-by-step explanation:

The formula to calculate the circumference of a circle is given by :-

[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.

In the given picture.,  we have the diameter of circle = 19.5 cm

Then , the circumference of the circle is given by :-

[tex]C=(3.14) (19.5)=61.23\approx61.2\ cm[/tex]

Hence, the circumference of the circle = 61.2 cm

Answer:

61.2

Step-by-step explanation:

Answer:

-80, -110

Step-by-step explanation:

Answer:

8x2-4x+72. good luck.

Answer:

P (over 6 feet tall or good aim) = 5/9

Step-by-step explanation:

We are given that there are a total of 27 players who are trying out for the school basketball team.

8 of them are more than 6 feet tall while 7 of them have good aim.

We are to find the probability that the coach would randomly pick a player over 6 feet tall or a player with a good aim, considering that no players over 6 feet tall have good aim.

P (more than 6 feet tall) = [tex]\frac{8}{27}[/tex]

P (good aim) = [tex]\frac{7}{27}[/tex]

P (over 6 feet tall or good aim) = [tex]\frac{8}{27} + [/tex] [tex]\frac{7}{27}[/tex] = 5/9

Answer:

5/9

Step-by-step explanation:

just did test

Answer:

y = -3 + 6ˣ

Step-by-step explanation:

-3 is the lowest it goes, and the more you increase the base, the more it its stretch will become. Now, although it passes through -2, we are not dealing with y-intercept here because this is NOT a linear function. This is called a horizontal asymptote. This is an exponential function, from the parent function of y = abˣ, if I can recall correctly. Anyway, you understand?

ANSWER

-2 shift the graph of the basic function down by 2 units.

EXPLANATION

The given cosine function is:

[tex]y = - 2 - 3 \cos(x + \pi) [/tex]

This equation can be rewritten as:

[tex]y = - 3 \cos(x + \pi) + - 2[/tex]

We compare this to

[tex]y = a \cos(bx + c) + d[/tex]

The effect d has on the graph is that, it shifts the graph up by d units.

If d is negative the graph shifts down by d units.

Since d=-2, the graph will shift down by 2 units.

Answer:

Vertical Shift Down 2 Units

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Given

[tex]x^2-x[/tex]

We know that the formula is:

[tex]a^2-2ab-b^2[/tex]

The middle term is:

x which should be equal to 2ab. So,

[tex]x = 2ab\\x = 2*x*b\\x/2x = b\\1/2 = b[/tex]

So we know now that we will add (1/2)^2 = 1/4 in the given expression to complete the square as the last term is square in the formula.

The expression will become:

[tex]x^2-x+1/4[/tex]

Option A is correct ..

Answer:

3/4

Step-by-step explanation:

Line up points

(3  , 7)

(-1,   4)

subtract vertically

4      3

2nd diff/1st diff=3/4

Answer:

A

Step-by-step explanation:

it would equal 34 nd on the bottom would be 32 so AAAA

(3,7) ordered pair is the solution to the system.

A finite collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.

Given

2x+4y = 34

6x +2y = 32

x = 3

[tex]2*3[/tex] + 4y = 34

[tex]6*3[/tex] + 2y = 32

18 + 2y = 32

y = 7

(3,7) ordered pair is the solution to the system.

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Answer:

[tex]\large\boxed{36x^3a+45xa=9xa(4x^2+5)}[/tex]

Step-by-step explanation:

[tex]36x^3a=(9xa)(4x^2)\\\\45xa=(9xa)(5)\\\\36x^3a+45xa=(9xa)(4x^2)+(9xa)(5)=9xa(4x^2+5)[/tex]

Answer:

∠3 = 60°

Step-by-step explanation:

Since g and h are parallel lines then

∠1 and ∠2 are same side interior angles and are supplementary, hence

4x + 36 +3x - 3 = 180

7x + 33 = 180 ( subtract 33 from both sides )

7x = 147 ( divide both sides by 7 )

x = 21

Thus ∠2 = (3 × 21) - 3 = 63 - 3 = 60°

∠ 2 and ∠3 are alternate angles and congruent, hence

∠3 = 60°

The measure of angle 3 is 60 degrees, the correct option is B.

Given

In the diagram, g is parallel to h.

The measurement of angle 1 is (4x +36).

The measurement of angle 2 is (3x-3).

Interior angles;

The angles that lie in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles.

∠1 and ∠2 are the same side interior angles and are supplementary then the sum of both angles is equal to 180 degrees.

[tex]\rm 4x+36+3x-3=180\\\\7x+33=180\\\\7x=180-33\\\\7x=147\\\\x=\dfrac{147}{7}\\\\x=21[/tex]

The measure of the angle 2 is = 3(21)- 3= 63 - 6 = 60 degrees.

Hence, Angle 2 and ∠3 are alternate angles and congruent then the measure of angle  3 is 60 degrees.

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Answer:

The answer is 7/17

Step-by-step explanation:

Answer:

C. [tex](x-3)^2+(y-1)^2=2^2[/tex]

Step-by-step explanation:

The standard equation of a circle, given the radius r units and center (h,k) is given by:

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

From the question, we have the center of the circle to be (3,1) and the radius is 2 units.

We substitute the center and radius of the circle into the equation to get:

[tex](x-3)^2+(y-1)^2=2^2[/tex]

The correct answer is C

Step-by-step explanation:

12. BAE+DAE=90 (angle in a right angle) BAE=48

90=48+DAE

DAE=90-48=42

14. CE=5X+8 BD=13-2

AC=2*CE

=2*(5X+8)

=10X+16

13. BE=22

AE=22(ISSOCELES TRIANGLE)

Answer:

[tex]f(x)=(x-3)^{2}(x-2)(x-1)[/tex]

Step-by-step explanation:

we know that

The roots (or x-intercepts) of the equation are

x=1 -----> with multiplicity 1

x=2 -----> with multiplicity 1

x=3 -----> with multiplicity 2 (because is a turning point)

so

The factors are

[tex](x-1), (x-2), (x-3),(x-3)[/tex]

The equation is equal to

[tex]f(x)=(x-3)(x-3)(x-2)(x-1)\\ \\f(x)=(x-3)^{2}(x-2)(x-1)[/tex]

To write a quadratic equation in factored form, find two binomials that when multiplied together yield the original quadratic. Factoring is essential in understanding the roots and the shape of a parabolic graph. For more complex quadratics, techniques like completing the square might be required.

When we are looking to write the equation of a graph in factored form, we are typically dealing with a polynomial function, and specifically when the graph is of a parabola, we are working with a quadratic equation. Factoring a quadratic equation involves finding two binomials that when multiplied together give us the original quadratic. For example, if we have a graph of a quadratic with its roots at x = p and x = q, the factored form would be y = a(x - p)(x - q), where a represents the leading coefficient.

If given an equation like 6x² + xy - y² - 17x - y + 12 = 0, it can be factored into two linear terms, which represents the intersection of two lines. In cases where completing the square is needed, such as x² - ( ) x = -() y, we add to each side (half the coefficient of x)² to form a perfect square on the left-hand side, leading us to an equation of the form (x − A)² = -4a(y − B).

Learning about graphing polynomials provides insights into how the constants in an equation affect the shape of the curve. By adjusting coefficients and analyzing the individual terms, we can understand how these terms combine to produce the overall graph of the polynomial.

Answer:

16.7%.

Step-by-step explanation:

There are initially [tex]24 + 15 + 8 = 47[/tex] pencils in the bag.

Take a pencil out of this bag of 47 pencils. 15 out of the 47 pencils blue. Let [tex]A[/tex] represent the event of getting a blue pencil on the first pick. The probability of getting a blue pencil is:

[tex]\displaystyle P(A) = \frac{15}{47}[/tex].

There are now [tex]47 - 1 = 46[/tex] pencils left in the bag. However, given that the first pencil removed from the bag is blue, the number of red pencils in the bag will still be 24. Take another pencil out of this bag of 46 pencils. Let [tex]B[/tex] represent the event of getting a red pencil on the second pick. The possibility that the second pencil is red given that the first pencil is blue will be:

[tex]\displaystyle P(B|A) = \frac{24}{46}[/tex].

The question is asking for the possibility that the first pencil is blue and the second pencil is red. That is:

[tex]\displaystyle P(A\cap B) = P(A) \cdot P(B|A) = \frac{15}{47}\times \frac{24}{46} = 0.166512 \approx 16.7\%[/tex].

Answer:

LR is 12

Step-by-step explanation:

LP is hypotenuse and PR is base so LR is perpendicular

formula to calculate perpendicular is

p^2=H^2 -b^2

p^2=15^2-9^2

p^2=225-81

p^2=144

p=12(root of 144 is 12)

Answer:

it would be 24 cuz 15 + 9 = 24

Answer:

fog(x)=[tex]x^2+8[/tex]

Step-by-step explanation:

Here we are given two functions

f(x) = x+2

g(x)=[tex]x^2+6[/tex]

We are required to find fog(x)

fog(x) is a composite function.

fog(x) = f(g(x))

g(x) = [tex]x^2+6[/tex]

f(g(x)) = f( [tex]x^2+6[/tex] )

f(x)= x+2

Hence we replace x in f(x) with [tex]x^2+6[/tex]

f(g(x))=([tex]x^2+6[/tex])+2

f(g(x))=[tex]x^2+8[/tex]

Hence

fog(x) = [tex]x^2+8[/tex])

Answer:

The volume is 113.04 cubic inches

Step-by-step explanation:

We are given:

Radius = r = 3 inches

As we know the formula for finding the volume of sphere is:

[tex]V=\frac{4}{3} \pi r^{3} \\Putting\ values\ of\ \pi \ and\ r\\V = \frac{4}{3} * 3.14 * (3)^3\\= \frac{12.56}{3} * 27\\= \frac{339.12}{3}\\ =113.04\ cubic\ inches[/tex]

The volume is 113.04 cubic inches ..

The required solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.

Simplification involves using rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

We can solve the equation (x - 2)(x + 10) = 13 using the following steps:

Therefore, the solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.

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Answer:

171 tons of plastic and 835 tons of aluminium was recycled

Step-by-step explanation:

So with the amount they recycle, it is a ratio of 5:1

Add those two together gives the number in which you divide 1026. 5 + 1 = 6

Now divide 1026 by 6.

1026 : 6 = 171

As there is five time more aluminium recycled than plastic, times 171 by 5. 171 * 5 = 835

Aluminium is easy. 171 tons of it.

Answer:

171 tons of plastic and 835 tons of aluminium was recycled

Step-by-step explanation:

Step-by-step explanation:

Answer is B but what kind of question is this? You don't even have to find the equation just find which one is different from the others.

A) y+2 = 4x-4

y = 4x-6

B)y-2 = 4x+4

y= 4x+6

C)y = 4x-6 (same with A )

D)y-6 = 4x-12

y= 4x-6 (Same with A and C)

So b is the different one.

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

m = -5

b = -8

so...

y = -5x - 8

Hope this helped!

Answer:

B

Step-by-step explanation:

Slope-intercept form of a line:

y = mx + b

m = slope

b = y-intercept

The question asks for a line w/ a slope of -5 and y-int of -8.

B would be the correct choice as in y = -5x - 8,

m (slope) = -5 and

b (y-int) = -8.

Answer:

t = [tex]\frac{d}{r}[/tex]

Step-by-step explanation:

Given

d = rt , or

rt = d ( solve for t by dividing both sides by r )

t = [tex]\frac{d}{r}[/tex]

Answer:

Can confirm that the correct answer is t=d/r

Step-by-step explanation:

hope u have a nice day