What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic function?

[tex]\bf 8n^2-4n+2=5n\implies 8n^2-4n-5n+2=0\implies 8n^2-9n+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{8}n^2\stackrel{\stackrel{b}{\downarrow }}{-9}n\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{\underline{two solutions}}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-9)^2-4(8)(2)\implies 81-64\implies 17[/tex]

Answer:

2 real distinct roots.

Step-by-step explanation:

8n^2 - 4n + 2 = 5n

Rearranging to standard form:

8n^2 - 9n + 2 = 0

The discriminant = b^2 - 4ac

= (-9)^2 - 4 * 8 * 2

= 17.

So there will be 2 real distinct roots.

We know that because it forms a right angle, BOF is 90 degrees. We also know that FAO and AOB combine to make 90 degrees.

We already know the value of FOA, so subtract that from 90.

90-35=55.

The measure of AOB is C. 55.

Hope this helps!

Answer:

5/6

Step-by-step explanation:

Dividing fractions:

Step 1: Rewrite the first fraction as it is.

Step 2: Replace the division sign with a multiplication sign.

Step 3: Flip the second fraction.

Step 4: Multiply the fractions and reduce the product if necessary.

Let's use the rule of dividing fractions on your problem.

Step 1: Rewrite the first fraction as it is.

[tex] \dfrac{5}{8} [/tex]

Step 2: Replace the division sign with a multiplication sign.

[tex] \dfrac{5}{8} \times [/tex]

Step 3: Flip the second fraction.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} [/tex]

Step 4: Multiply the fractions and reduce the product if necessary.

To multiply fractions, multiply the numerators together, and multiply the denominators together.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} = \dfrac{5 \times 4}{8 \times 3} = \dfrac{20}{24} [/tex]

We notice that the greatest common factor of 20 and 24 is 4, so we divide both the numerator and denominator by 4 to reduce the fraction.

[tex] = \dfrac{4 \times 5}{4 \times 6} = \dfrac{5}{6} [/tex]

Answer:

Number One

Step-by-step explanation:

This is because a natural number is a positive integer so it can't be 2,3,or 4 so the only other option is 1!!

Answer: Bottom Graph

Step-by-step explanation: An easy way to eliminate answers is to plug in 0 for x and see if the y-intercept is accurate. If we plug in 0 for x we get -1, which is the y-int for the bottom graph, but not the top graph, therefore the bottom graph is correct.

The graph of (x + 1)^(1/3) - 2 is option B.

A function is a mathematical expression, rule, or law that specifies the relationship between one variable (the dependent variable) and another variable (the independent variable).

Function given in the question = (x + 1)^(1/3) - 2

Initial function for this is f(x) = x^(1/3)

The changes done in the question is f(x + 1) - 2

Hence the graph of  x^(1/3) will go one unit to the left on the X-axis and two units down on the Y-axis.

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The given function F(x) = x^2-8x+7 has a minimum point of (4, -9). This is found by using the formula for the vertex of a quadratic function.

This question seems to be incomplete as only one function, F(x) = x^2-8x+7, is provided. However, I can still help you find the minimum of this function. A quadratic function, such as this one, has a minimum or maximum at its vertex. The x-coordinate of the vertex (h) can be found using the formula h = -b/2a.

In this function, a = 1 and b = -8, so h = 8/2 = 4. So the minimum point of the function is at x = 4. To find the corresponding y value, we substitute x = 4 in our function. F(4) = 4^2-8*4+7 = -9. So the minimum point of F(x) = x^2-8x+7 is (4, -9).

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Answer:

Option A is correct i.e 2R2+R3 -> R3

Step-by-step explanation:

The given matrix is:

[tex]\left[\begin{array}{ccc}-4&1&2&4\\0&-1&3&1\\3&2&4&5\end{array}\right][/tex]

If we perform the operation 2R2 + R3 we get the result given i.e

[tex]\left[\begin{array}{cccc}-4&1&2&4\\0&-1&3&1\\3&0&10&7\end{array}\right][/tex]

The operations performed are:

2R2 i.e. we multiply the row 2 with 2

we get 0  -2  6  2

now add it with row 3

0  -2   6   2

3   2   4   5

___________

3  0   10    7

So, Option A is correct i.e 2R2+R3 -> R3

Answer:

3.55 as a percentage is around an 80%

Step-by-step explanation:

1. Divide the number by 20.

2. Subtract 1 from that number.

Answer:

Somewhere around 80%

Step-by-step explanation:

Answer:

The volume of the cylinder is 150.72 cm³ ⇒ last answer

The volume of the cone is 314 cm³ ⇒ 1st answer

The volume of the pyramid is 160 cm³ ⇒ 2nd answer

The volume of the pyramid is 48 cm³ ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the volumes of some shapes

- The volume of the cylinder of radius r and height h is:

 V = π r² h

- The volume of the cone of radius r and height h is:

 V = 1/3 π r² h

- The volume of the pyramid is:

 V = 1/3 × its base area × its height

* Lets solve the problem

# A cylinder with radius 4 cm and height 3 cm

∵ V = π r² h

∵ π = 3.14

∵ r = 4 cm , h = 3 cm

∴ v = 3.14 (4)² (3) = 150.72 cm³

* The volume of the cylinder is 150.72 cm³

# A cone with radius 5 cm and height 12 cm

∵ V = 1/3 π r² h

∵ π = 3.14

∵ r = 5 cm , h = 12 cm

∴ V = 1/3 (3.14) (5)² (12) = 314 cm³

* The volume of the cone is 314 cm³

# A pyramid with base area 16 cm² and height 30 cm

∵  V = 1/3 × its base area × its height

∵ The area of the base is 16 cm²

∵ The height = 30 cm

∴ V = 1/3 (16) (30) = 160 cm³

* The volume of the pyramid is 160 cm³

# A pyramid with square base of length 3 cm and height 16 cm

∵  V = 1/3 × its base area × its height

∵ The area of the square = s²

∵ The area of the base = 3² = 9 cm²

∵ The height = 16 cm

∴ V = 1/3 (9) (16) = 48 cm³

* The volume of the pyramid is 48 cm³

a right cylinder with radius 4 cm

and height 3 cm = 150.72 cu cm

a pyramid with base area

16 sq cm and height 30 cm = 160 cu cm

a pyramid with a square base of

length 3 cm and height 16 cm  = 48 cu cm

a cone with radius 5 cm and

height 12 cm = 314 cu cm

5 sqrt 3i is the correct answer

Answer: b) √108

c√18.√6

e)√3.√36

Step-by-step explanation:

We know that, for example, √4 = √2² = 2

As the index of the number inside the root maches the index of the root, we can remove it from the root.

And the inverse process is also correct, so 2 can be written as

√2² = √4, this way:

6√3 = √3.√6² = √3.√36 = √108

a) √54 ≠ √108

b) √108 = √108 ok

c) √18.√6 = √108 ok

d) √3.√6 = √18 ≠ √108

e) √3.√36 = √108 ok

f) 108 ≠ √108

Answer:

The answer to this problem is 22.

Step-by-step explanation:

To solve this problem, we simply need to plug in the values given for a and b into the expression given and simplify.

We are given that a=3 and b=4, thus, these are the numbers we will plug in before we simplify.

2a^2 + b =

2(3)^2 + 4

Next, we should follow the rules of PEMDAS.  This tells us that we should solve the parentheses first, but since there are no parentheses, we can move onto exponents.

If we simplify, we get:

2(9) + 4

Next, we should perform the multiplication.

18 + 4

Finally, we can add together the remaining terms.

18 + 4 = 22

Therefore, your answer is 22.

Hope this helps!

2[tex]a^{2} + b[/tex]

First you must substitute a and b for the corresponding values:

a = 3

b = 4

so...

2*[tex]3^{2}[/tex] + 4

Now you must evaluate using the rules of PEMDAS (Parentheses, Exponent, Multiply, Divide, Add, Subtract)

There are no parentheses so skip that step and go on to the next one, exponent, which is [tex]3^{2}[/tex]

[tex]3^{2}[/tex] = 3*3

9

^^^Replace [tex]3^{2}[/tex] with 9

2 * 9 + 4

The next step is multiply 2 and 9

2*9 = 18

^^^Replace 2*9 with 18

18 + 4

Now add 18 and 4 together

22

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

1q = 2p

Step-by-step explanation:

One quart of liquid is the equivalent of 2 pints... one of the rare easy measures in the American measure system.

So, the equation needs to have 1 quart on one side, and 2 pints on the other side.  It's an equation because both values are equal, just expressed in different units.

1 quart = 2 pints, then rewritten to match the variables given in the question:

1q = 2p

Answer:

Proved,

P(A∪B)=0.72

Step-by-step explanation:

Sue travels by bus or walks when she visits the shops.

Probability( catch the bus to the shop ), P(A) = 0.4

Probability( catch the bus from the shop ), P(B) = 0.7

Both A and B are independent events.

Therefore,

P(A∩B) = 0.4×0.7

           = 0.28

Probability Sue walks one way = 1 - P(A∩B)

                                                   = 1 - 0.28

                                                   = 0.72

Hence, the probability that Sue walks at one way is 0.72

The probability that Sue walks one way is 0.18, derived by subtracting the probability that Sue takes a bus one way (0.82) from 1.

The question refers to the probability involving Sue's mode of transport to and from the shops. To show the probability that Sue walks one way, we need to first determine the probability that she takes a bus either to or from the shops, since taking a bus one way implies she walked the other way.

The probability that Sue takes a bus to the shops OR from the shops, but not both, can be calculated using the formula: P(A U B) = P(A) + P(B) - P(A ∩ B). In this case, A represents the probability Sue takes a bus to the shop (0.4) and B represents the probability she takes a bus from the shop (0.7). P(A ∩ B) is the probability she takes a bus both ways, which is 0.4 * 0.7 = 0.28.

Therefore, the probability she takes the bus one way is P(A U B) = 0.4 + 0.7 - 0.28 = 0.82.

Since Sue either takes a bus or walks, the sum of these two probabilities should be 1. Therefore, the probability Sue walks one way is 1 - the probability she takes the bus one way = 1 - 0.82 = 0.18, not 0.72 as suggested in the question.

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Answer:

D

Step-by-step explanation:

Answer:

5 (Answer B)

Step-by-step explanation:

As we move from A to B, x increases by 3 and y decreases by 4.  Apply the Pythagorean Theorem:

(length of AB) = √(3² + [-4]²) = 5 (Answer B)

Substitution.

Here is an example.

Let x be equal to 3 and y equal to 3.

[tex]x=3, y=3[/tex]

From this we can conclude that the values of both x and y are equal to three therefore x and y have the same value and are equal.

[tex]x\wedge y=3\Longrightarrow x=y[/tex]

Here in your case we have:

[tex]

AB=1, BC=1 \\

AB\wedge BC=1\Longrightarrow AB=BC[/tex]

Hope this helps.

r3t40

Answer:

the values of x, y and z are: x=8, y = -5 and z = -7

Step-by-step explanation:

2x+6y+4z=−42       eq(1)

4x+3y+8z=−39       eq(2)

4x+3y+2z=3          eq(3)

We would solve the above equations using elimination method.

Subtracting eq(3) from eq(2)

4x+3y+8z=−39      

4x+3y+2z=3

-   -     -       -

_____________

0+0+6z = -42

z = -42/6

z = -7

Multiplying eq(1) with 2 and subtracting with eq(2)

4x + 12y +8z = -84

4x +3y +8z = -39

-    -      -        +

_______________

0+9y+0=-45

9y = -45

y = -45/9

y = -5

Putting value of y and z in eq(1)

2x + 6y +4z = -42

2x + 6(-5) +4(-7) = -42

2x -30 -28 = -42

2x -58 = -42

2x = -42 +58

2x = 16

x = 16/2

x= 8

So, the values of x, y and z are: x=8, y = -5 and z = -7

Answer:

The answer is 6

Step-by-step explanation:

Answer: The answer is b, 2x=14

Step-by-step explanation:

You add the equations...

2x-14=0

Move -14 over...

2x=14

Answer:  The correct option is

(B) 2x = 14.

Step-by-step explanation:  We are given to solve the following system of equations by the method of Elimination :

[tex]x+y-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Also, to select the resulting equation when we eliminate y.

Adding equations (i) and (ii), we get

[tex](x+y-6)+(x-y-8)=0+0\\\\\Rightarrow 2x-14=0\\\\\Rightarrow 2x=14~~~~~~~~~~[\textup{this is the resulting equation}]\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]

From equation (i), we get

[tex]7+y-8=0\\\\\Rightarrow y-1=0\\\\\Rightarrow y=1.[/tex]

Thus, the required solution is (x, y) = (-1, 7) and the resulting equation while eliminating y is 2x = 14.

Option (B) is CORRECT.

The answer can be stated as "The solution to a system of two linear equations in two variables corresponds to the intersection of straight lines represented by them."

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

A system of linear equation in two variables can be written as,

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂= 0

In order to find their solution these equations are solved either by substitution or elimination.

A linear equation in two variable represents a straight line.

Thus, the solution to these equations are the coordinates of the intersection point of these two lines.

Hence, the solution to a system of linear equation in two variables indicate the coordinate of their intersection.

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Answer:

BD=AD-AB=6-4=2

Step-by-step explanation:

You have a line segment AD that measures 6 units

AB is part of it and it is 4 units

There is only one part left of AD and it is BD so you just find what's left of 6 if 4 is already spoken for.

For this case we have that the radius of the large circle is given by AD = 6, while the radius of the small circle is given by AB = 4. We want to know the length BD, that is, the difference of the radius of the big circle and the small one.

[tex]BD = AD-AB = 6-4 = 2[/tex]

So, [tex]BD = 2[/tex]

Answer:

[tex]BD = 2[/tex]

Answer:

The dimensions of the garden are

Length [tex]25.5\ ft[/tex]  and Width [tex]16.5\ ft[/tex]

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y ---> the width of the rectangular garden

Aw ----> the area of the walkway

we know that

[tex]x=y+9[/tex] ----> equation A

[tex]Aw=(x+8)(y+8)-xy[/tex]

[tex]Aw=400\ ft^{2}[/tex]

so

[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex]

[tex]400=8x+8y+64[/tex] ----> equation B

Substitute equation A in equation B

[tex]400=8(y+9)+8y+64[/tex]

[tex]400=8y+72+8y+64[/tex]

[tex]400=16y+136[/tex]

[tex]16y=400-136[/tex]

[tex]y=16.5\ ft[/tex]

Find the value of x

[tex]x=16.5+9=25.5\ ft[/tex]

therefore

The dimensions of the garden are

Length [tex]25.5\ ft[/tex]

Width [tex]16.5\ ft[/tex]

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 2x + 3 + x² - 8 ← collect like terms

               = x² + 2x - 5 ← in standard form → C

Answer:

Here's what I get.

Step-by-step explanation:

[tex]x = 7\frac{1}{2} \div \frac{3}{4}[/tex]

1. Convert the mixed number to an improper fraction

[tex]x = \dfrac{15}{2} \div \dfrac{3}{4}[/tex]

2. Invert the proper fraction and change division to multiplication

[tex]x = \dfrac{15}{2} \times \dfrac{4}{3}[/tex]

3. Multiply numerators and denominators

[tex]x = \dfrac{60}{6}[/tex]

4. Divide the numerator and the denominator

[tex]x = 10[/tex]

The quotient is what you get after you invert the denominator in Step 2 and then multiply the two fractions in Step 3.

Here I'm assuming 7 1/2 / 3/4 is  [tex]7\frac{1}{2} / \frac{3}{4}[/tex]

So let's solve, this first convert the mixed fraction into an improper fraction that is its ideal form to solve an equation

[tex]7\frac{1}{2} = \frac{15}{2}[/tex]

therefore,

= [tex]\frac{15}{2} /\frac{3}{4}[/tex]

= [tex]\frac{15}{2} * \frac{4}{3}[/tex]

= 5 * 2

= 10

A mixed fraction is a combination of a whole number and proper fraction.

Improper fractions and proper fractions are the types of fraction numbers (A fraction number which is written in the form of a/b i.e., " [tex]\frac{a}{b}[/tex] " in which a is called as numerator and b is denominator). A fraction is called improper fraction when its numerator is greater than its denominator and for proper fraction, it's vice versa.

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Answer:

f^-1 (x) = 2x+20

Step-by-step explanation:

f(x) = 1/2x – 10

To find the inverse, replace f(x) with y

y = 1/2 x -10

Exchange x and y

x = 1/2 y- 10

Solve for y

Add 10 to each side

x+10 = 1/2 y-10+10

x+10 = 1/2 y

Multiply by 2

2(x+10) = 1/2y *2

2x+20 = y

The inverse is

f^-1 (x) = 2x+20

Final answer:

To find the sum of one gross, a quarter of a dozen, and two scores, you add 144 (one gross), 3 (a quarter of a dozen), and 40 (two scores) to get a total of 187.

Explanation:

The sum of one gross, a quarter of a dozen, and two scores can be calculated as follows:

One gross = 144

A quarter of a dozen = 3

Two scores = 40

Therefore, the sum = 144 + 3 + 40 = 187

Answer: 187

Step-by-step explanation:

First, we need to define what these words mean numerically.

      One gross = 144

      A quarter of a dozen = 12/4 = 3

      Two scores = 2 * 20 = 40

Now, we can find the sum of one gross, a quarter of a dozen, and two scores. Sum means addition.

      144 + 3 + 40 = 187

Answer:

Dist = 45 m/h * x h

Step-by-step explanation:

We know a speed is a measure of distance over time:  speed = dist / time

In this case, we are looking for a distance expressed in terms of time.

So, we only need to modify the formula a bit: dist = speed * time

We don't know the time (which will be a variable), but we know their speed.  So, the formula becomes:

Dist = 45 m/h * x h

Enter the number of hours in the formula and that will give you an approximation of the distance traveled within that time (approximation since our result will be rely on an average).

Answer:

The line will be going 'uphill' from left to right

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where m is the slope

b is the y-intercept

If the coefficient of the x-term is positive

then

the slope is positive

therefore

If the values of x increases, the values of y increases

If the values of x decreases, the values of y decreases

The line will be going 'uphill' from left to right

Answer: the line slants up

Step-by-step explanation:

X being positive will cause a “ rise “ in the positive x,y plane.

Answer:

m<5 = 45 deg

Step-by-step explanation:

Since lines g and h are parallel, you have a transversal cutting parallel lines. Then, corresponding angles are congruent.

Angles 1 and 5 are corresponding angles, so they are congruent, and their measures are equal.

m<5 = m<1 = 45 deg.

Angles 5 and 8 are vertical angles, so they are congruent, and their measures are equal.

m<8 = m<5 = 45 deg

Answer: m<5 = 45 deg

Answer:

Third option

Step-by-step explanation:

By observing the diagram we can see that the diameter of circular base is 6 inches. The diameter will be sued to find the radius.

r = 6/2 = 3 inches

We can also see from the diagram that lateral height denoted by l is 5 in.

We know that the formula for surface area of a cone is given by:

[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\ of\ r\ and \l\\SA = \pi (3)(5)+\pi (3)^2[/tex]

Comparing it with the options we get that the third option is correct ..

Answer:

The correct answer is third option

 π(3)(5) + π3²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the radius of the cone and l is the slant height of cone

To find the correct answer

Here r = 6/2 = 3 in

l = 5 in

Surface area =  πrl + πr²

 =  π(3)(5) + π3²

The correct answer is third option

 π(3)(5) + π3²

[tex]m^{24}n^{18}[/tex]

We can distribute the terms using the distributive property first. [tex](m^4)^6 * (n^3)^6[/tex]

Then, use the power of a power property to multiply the powers. [tex]m^{4*6} * n^{3*6} = m^{24}n^{18}[/tex]