how many zeros does the function f(x)=4x3-x2+1 have​

The prism's base perimeter is 28 units, calculated by summing the lengths of its sides or using the rectangle perimeter formula.

Step 1: Identify the Prism and Its Base

Given a triangular prism, focus on the rectangular base formed by sides S1, S2, S3, and S4.

Step 2: Understand Perimeter Calculation

Recall that the perimeter of any shape is the sum of all its sides.

Step 3: Label the Sides of the Base

Define the sides of the rectangular base:

S1 = 4 + 5

S2 = 5

S3 = 4 + 5

S4 = 5

Step 4: Apply Perimeter Formula

Utilize the formula for the perimeter of a rectangle: P = 2 * (length + width).

For the rectangular base, length = S1 + S3 and width = S2.

Step 5: Calculate Perimeter

Substitute the values into the formula: P = 2 * (9 + 5) = 2 * 14 = 28 units.

Step 6: Verify Using Summation

Confirm the result by adding the individual sides: P = S1 + S2 + S3 + S4 = 9 + 5 + 9 + 5 = 28 units.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ D(\stackrel{x_1}{9}~,~\stackrel{y_1}{8})\qquad H(\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ DH=\sqrt{(1-9)^2+(3-8)^2}\implies DH=\sqrt{(-8)^2+(-5)^2} \\\\\\ DH=\sqrt{64+25}\implies DH=\sqrt{89}\implies DH\approx 9.4[/tex]

Answer:

D

Step-by-step explanation:

The system of equation will also have a solution of (2,0) are,

x + 4y = 2, 7x = 14.

Given that,

The solution to the system of equations shown is (2,0).

3x – 2y = 6 ,  x + 4y = 2

When the first equation is multiplied by 2, the sum of the two  equations is equivalent to 7x = 14.

We have to determine,

Which system of equations will also have a solution of (2,0).

According to the question,

To determine the system of the equation after applying all the given conditions in the steps, follow all the steps given below.

System of equations;  3x – 2y = 6 ,  x + 4y = 2.

                   [tex]2 \times (3x-2y) = 2 \times 6\\\\6x - 4y = 12[/tex]

                   [tex]6x - 4y + x + 4y = 12+ 2\\\\7x = 14\\\\x = \dfrac{14}{7}\\\\x = 2[/tex]

                      [tex]6(2) - 4y = 6\\\\12-4y = 6\\\\-4y = 6-12\\\\-4y == -6\\\\y = \dfrac{-6}{-4}\\\\y = \dfrac{3}{2}[/tex]

Hence, The required system of equation will also have a solution of (2,0) are, x + 4y = 2, 7x = 14.

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Answer:

HL

Step-by-step explanation:

You have a the two hypotenuses from the two triangles are congruent.

You also have a pair of of legs from each of the triangles that are congruent.

So HL means hypotenuse-leg which is what you have in the pic!

Final answer:

To prove two 'A's are equivalent, methods such as direct proof, disjunctive syllogism, conditional proof, and indirect proof can be applied. The selection of the method depends on the nature of the proof and the preference of the solver.

Explanation:

To establish that both 'A's are equivalent in a given proof, one might utilize several methods including direct proof, disjunctive syllogism, conditional proof, or indirect proof. For instance, a disjunctive syllogism can be employed when an argument has an either/or scenario, which allows for a conclusion to be drawn when one of the options is eliminated. Conversely, if you aim to reach a conclusion in the form of a conditional A → B, you might opt for a conditional proof method where you start a subproof by assuming A and then proceed to derive B within that subproof. In cases where a direct proof is challenging, you might resort to an indirect proof approach by assuming the negation of what you're attempting to prove and then showing this leads to a contradiction.

Direct proof and indirect proof are both formally legitimate, even though one might offer a more straightforward path to the solution or resonate more with the problem-solver's reasoning style. When planning an experiment or mapping out a mathematical proof, it is vital to consider the different methods and choose one that aligns with the nature of the problem and the proof you wish to establish.

Answer:

Step-by-step explanation:

Use Pythagorean theorem.

c^2 = a^2+b^2

c^2 = 4^2+6^2

c^2 = 16+36

c^2 = 52

c = √52 = 7.21

ANSWER

[tex]{r}^{2} = 4 \cos2\theta[/tex]

EXPLANATION

The Cartesian equation is

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

We substitute

[tex]x = r \cos( \theta) [/tex]

[tex]y = r \sin( \theta) [/tex]

and

[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]

This implies that

[tex] {( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )[/tex]

Let us evaluate the exponents to get:

[tex] {r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)[/tex]

Factor the RHS to get:

[tex] {r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)[/tex]

Divide through by r²

[tex]{r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)[/tex]

Apply the double angle identity

[tex]\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta) [/tex]

The polar equation then becomes:

[tex]{r}^{2} = 4 \cos2\theta[/tex]

To convert the Cartesian equation to polar form, we substitute x and y with polar coordinates r and theta. Simplifying the equation with trigonometric identities leads to a polar equation, r^2 = 4cos^2\theta, which is the correct option among those given.

To convert the Cartesian equation (x^2 + y^2)^2 = 4(x^2 - y^2) to a polar equation, we use the relationships x = r\cos\theta and y = r\sin\theta. Substituting these into the given equation, we get:

(r^2\cos^2\theta + r^2\sin^2\theta)^2 = 4(r^2\cos^2\theta - r^2\sin^2\theta)

This simplifies to:

r^4 = 4r^2(\cos^2\theta - \sin^2\theta)

Using the double angle identity for cosine, \cos(2\theta) = \cos^2\theta - \sin^2\theta, we can further simplify:

r^4 = 4r^2\cos(2\theta)

Dividing both sides by r^2, as long as r \neq 0, gives us:

r^2 = 4\cos(2\theta)

However, this is not one of the provided options, so we must go further and use another trigonometric identity:

\cos(2\theta) = 2\cos^2\theta - 1

The equation r^2 = 4\cos(2\theta) can then be rewritten as:

r^2 = 4(2\cos^2\theta - 1)

Since this is still not aligning with the provided options, it is important to check the original approach. There may have been a simplification error or a misinterpretation of the trigonometric identities. The correct polar equation that corresponds to the given choices should indeed be r^2 = 4\cos^2\theta, which is found by recognizing that \cos(2\theta) can also be written as 2\cos^2\theta - 1.

The answer you are looking for is 6y + 9.

In the equations (5y + 9) + y, you'd combine like terms to find the answer. You aren't distributing anything into the parenthesis, and 5y and 9 are not like terms (since the 9 doesn't have a "y" after it). That being said, you simply add "y" and 5y together to get 6y, and add the 9 to the end. Thus getting 6y + 9 as an answer.

I hope this helps!

Answer:

A. 6y+9

Step-by-step explanation:

Distributive property:

    ↓

[tex]A(B+C)=AB+AC[/tex]

First, you remove parenthesis.

5y+9+y

Group like terms:

   ↓

5y+y+9

Then,  you add by similar into elements.

5y+y=6y

6y+9 is the correct answer.

Answer: 2X+5Y≥ 90

Step-by-step explanation:

since you get two points per/ each (key word of multiplication) true & false question, this will be represented by 2X

since you get five points per/ each multiple choice question, this will be represented by 5Y

he needs at least 90 points in total to get an A in his class

Check the picture below.

so the pentagonal prism in the picture is been seen from the bottom, namely so we can see its base, however the base is at the bottom, what does that mean, it means that the pentagonal bases are the top and bottom of the prism, that matters, because the other sides are the lateral sides.

so, if we notice, the lateral sides are really just 5 rectangles, each one a 12x4, so if we simply get the area of all those rectangles.

5(12 * 4) = 240 in².

The lateral area of the given regular pentagonal prism is 240 square inches, calculated using the formula Lateral Area = Perimeter of Base * Lateral Edge.

The lateral area of a prism, particularly a regular pentagonal prism, can be calculated using the formula Lateral Area = Perimeter of Base * Lateral Edge. In this case, the base is a regular pentagon implying that all its sides are equal. Therefore, its perimeter would be 60 inches (12 inches * 5 sides).

The lateral edge is given as 4 inches. Applying the values to the formula, we get Lateral Area = 60 inches * 4 inches = 240 square inches.

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Answer:

B) -7m - 8 = m - 4

D) m - 4 = -7m - 8

E) -8 - 7m = -4 + m

Step-by-step explanation:

Solve all of the equations to see if they end up with the same result. Start with the original:

-2m - 5m - 8 = 3 + (-7) + m

-7m - 8 = -4 + m (now we know B and D and E are correct)

-7m - m - 8 = -4 + m - m

-8m - 8 = -4

-8m - 8 + 8= -4 + 8

-8m = 4

Answer:

-7m - 8 = m - 4

m - 4 = -7m - 8

-8 - 7m = -4 + m

Step-by-step explanation:

Given equation,

-2m - 5m - 8 = 3 + (-7) + m,

Combining like terms,

-7m - 8 =-4 + m

Subtract m from both sides,

-8m - 8 = -4

Add 8 on both sides,

-8m = 4

Divide both sides by -8,

m = [tex]-\frac{1}{2}[/tex]

(i)  -15m = -4m  ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0

(ii) -7m - 8 = m - 4  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(iii) -3m - 8 = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

(iv) m - 4 = -7m - 8  ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(v) -8 - 7m = -4 + m  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(vi) -8 - 3m = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

Answer:

The answer is B

Step-by-step explanation:

happy cheating

Answer:

The answer is B

Step-by-step explanation:

And it's not cheating just trying to make it through high school.

Answer:

B

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

solution = (0, - 4) → B

Answer:

B (0,-4)

Step-by-step explanation:

The solution to a system of equations is where the graphs intersect.

The two lines cross at x=0, y= -4

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

-y=x+1

Find the y-intercept

For x=0

-y=0+1

y=-1

The y-intercept is the point (0,-1)

Find the x-intercept

For y=0

-0=x+1

x=-1

The x-intercept is the point (-1,0)

Find a third point

For x=1

-y=1+1

-y=2

y=-2

The third point is (1,-2)

Plot the three points to graph the linear equation

see the attached figure

Note Remember that to graph the linear equation is sufficient with two points

Answer:

(2,1) (0,-1) (-6,7)

Step-by-step explanation:

Answer: [tex]g(x)=2x^4+3[/tex]

Step-by-step explanation:

These are some transformations for a function f(x):

If [tex]f(x)+k[/tex], then the function is shifted up "k" units.

If [tex]mf(x)[/tex], and [tex]k>1[/tex], then the function is stretched vertically  by a factor of "m".

Knowing this transformation and knowing that the function [tex]f(x)=x^4[/tex] is stretched vertically by 2 and shifted up 3 spaces, then we can conclude that new function, which we can call g(x), is:

[tex]g(x)=2(x^4)+3[/tex]

[tex]g(x)=2x^4+3[/tex]

Answer:

(x+2) (x+4)

Step-by-step explanation:

x^2+6x+8

What 2 numbers multiply together to give us 8 and add together to give us 6

(2*4) =8

(2+4) = 6

(x+2) (x+4)

Answer:

(x + 4)(x+2)

Step-by-step explanation:

We must multiply 8 and 1, and find two numbers which add to 6:

8 * x(suppose x is 1) = 8

Two numbers which add to 6, but also multiply to 8:

4 and 2

4 * 2 = 8

4 + 2 = 6

Hence, the answer would be (x + 4)(x+2)

Answer:

1/3 sin(3x)+C

Step-by-step explanation:

int (cos(3x) dx)

Let u=3x then du=3 dx so 1/3 du=dx

rewriting integral

int(1/3 cos(u) du)

now evaluating

1/3 sin(u)+C    since (sin(u))'=cos(u)

Replace u with 3x

Answer is 1/3 sin(3x)+C

Answer:

Step-by-step explanation:

Integral of cos3x = ⅓sin3x

So when integrating just simply multiply by reciprocal of the cooeffecient of the angle and the integral of that particular trig ratio, in this case it's the sinx.

Answer:

14

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) = 2x² + 3x + x - 2 = 2x² + 4x - 2

To evaluate (f + g)(2) substitute x = 2 into (f + g)(x)

(f + g)(2) = 2(2)² + 4(2) - 2 = 8 + 8 - 2 = 14

Answer:

14

Step-by-step explanation:

First find an algebraic formula for (f + g)(x).  To do this, combine like terms from f and g:  (f + g)(x) = 2x^2 + 4x -2

Next, substitute 2 for x:  (f + g)(2) = 2(2)^2 + 4(2) - 2 = 8 + 8 - 2 = 14

Answer:

[tex]\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Step-by-step explanation:

we know that

Te volume of the cone is equal to

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

we have

[tex]r=(r/2)\ units[/tex]

substitute

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

[tex]V=\frac{1}{12}\pi r^{2}h[/tex]

Te volume of the cylinder is equal to

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

we know that

To find the volume of the space remaining in the cylinder after the cone is placed inside it, subtract the volume of the cone from the volume of cylinder

so

[tex]\pi r^{2}h-\frac{1}{12}\pi r^{2}h=\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Answer: 33

if you add them all up,they are 33

Answer:

y= 4x + (-16)

Step-by-step explanation:

The slope of the given lime is m=4

x-intercept of the parallel line: (4,0)

plug that into the equation y= mx+b to find that b= -16

since the slope stays the same for parallel lines, and we just found b, we have the new line equation

The equation of parallel line with x intercept of 4 will be : y= 4x + (-16)

Given,

x intercept : 4

Slope = 4

Now,

x-intercept of the parallel line: (4,0)

As the equation of line to be obtained is parallel . Thus both lines will have same slope .

Slope of parallel line = 4

Substitute the value to find y intercept,

y = mx + b

0 = 4(4)  + b
b = -16

So,

Equation of parallel line: y = 4x + (-16)

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Which of the following lists the angles from smallest to largest?

Answer:

T, R, S

Answer:

A

Step-by-step explanation:

Given

- 3x + 1 + 10x = x + 4 ( simplify left side )

7x + 1 = x + 4 ( subtract x from both sides )

6x + 1 = 4 ( subtract 1 from both sides )

6x = 3 ( divide both sides by 6 )

x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

I just know its formula 2 pie r square

Step-by-step explanation:

Answer: A = 12.56 cm

Step-by-step explanation:

A = 3.14 x r^2

A = 3.14 x 2^2

A = 3.14 x 4

A = 12.56 cm

Answer:

(y-2) (x+5)

Step-by-step explanation:

x(y-2) + 5(y-2) =

We can factor out the expression (y-2), leaving us with x+5

(y-2) (x+5)

Answer: (x+5)(y-2)

Because the x and the 5 are being multiplied by the same factor you can change it to make the answer (x+5)(y-2)

Answer:

How many people are not allergic to any of the three choices? 22

How many people are allergic to all three choices? 1

How many people are allergic to both dogs and cats but not allergic to pollen? 7

How many people are allergic to cats only? 18

A survey of common allergies

The survey of the common allergies was made to see the percentage of people affected by the same sort of allergies and analysis the disease. The Venn diagrams are thus made in order to refer to the types of diseases that elate and people can be identified.

As per the answer, the Venn people allergic to cats are 18, not allergic are 22, and allergic to all three is one.

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Answer:

Part 1) The exact value of the arc length is [tex]\frac{25}{6}\pi \ in[/tex]

Part 2) The approximate value of the arc length is [tex]13.1\ in[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi\ in[/tex]

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

[tex]\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in[/tex]

step 3

Find the approximate value of the arc length

To find the approximate value, assume

[tex]\pi =3.14[/tex]

substitute

[tex]\frac{25}{6}(3.14)=13.1\ in[/tex]

Answer:

13.1 (rounded to tenths)

Step-by-step explanation:

150 ° into radian is 5/6.

150°/1 (π/180) =5π/6.

Then multiply the radian angle by the radius.

5π/6 (5) = 25π/6

25π/6 = 13.1 (rounded to tenths)

Answer:

I would say the third one ( 15x + 10 = 10 )

Step-by-step explanation:

I say this because, if we take 10 from both sides, 15x = 0. Even if you tried to divide by 15, x = 0. x also =0 if you try to do it the other way by finding what times 15 +10 = 10 it would be zero. The third one is your Answerr

Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.

Equation of functions With only one solution

Equations With just one solution are knoWn to have a leading degree of one and Without a modulus sign

Fro the linear function 15x + 10  = 10

Check:

Subtract 10 from both sides

15x + 10 - 10 = 10 - 10
15x = 10 - 10
15x = 0

Dividde both sides by 15 to have:

15x/15 = 0/15
x = 0
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.

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Answer:

x=a²+ab+b²/a+b , y=-ab/a+b

Step-by-step explanation:

The system of the given equation may b written as:

ax+by-a²=0

bx+ay-b²=0

Here,

a1=a,b1=b,c1= -a²

a2=b,b2=a and c2= -b²

By cross multiplication we get

x/b*(-b²)-(-a²)*a = -y/a*(-b²)-(-a²)*b = 1/a*a-b*b

x/-b³+a³ = -y/-ab²+a²b  = 1/a²-b²

Now

x/-b³+a³ = 1/a²-b²

x=a³-b³/a²-b²

x=(a-b)(a²+ab+b²)/(a-b)(a+b)

x=a²+ab+b²/a+b

And,

-y/-ab²+a²b = 1/a²-b²

-y=a²b -ab²/a²-b²

y=ab²-a²b/a²-b²

y=ab(b-a)/(a-b)(a+b)

y= -ab(a-b)/(a-b)(a+b)

y= -ab/a+b

Hence x=a²+ab+b²/a+b , y=-ab/a+b....

The incorrect step and with error is subtract 3 from both sides. Option 3

We have that the equation is;

-3/8 (-8-16d) + 2d= 24

multiply the values, we get;

-24 + 48d + 2d = 24

add the like terms

-24 + 50d = 24

50d = 48

d = 48/50

The other steps are;

Subtract 3 from both sides (However, the instruction mentions subtracting 3, but there is no number 3 in the equation.

Divide both sides by the equation by -14