Which expression is equivalent to -2 1/4÷ (-2/3)​

Answer:

a=1, b=-6, c=2, d=1

Step-by-step explanation:

You are given the function

[tex]y=x^4+ax^3+bx^2+cx+d[/tex]

Find the derivative:

[tex]y'=4x^3+3ax^2+2bx+c[/tex]

The curve has a tangent line when x = 0 with equation y = 2x + 1, so

[tex]y'(0)=2\\ \\y(0)=1[/tex]

Hence,

[tex]y'(0)=4\cdot 0^3+3a\cdot 0^2+2b\cdot 0+c=2\Rightarrow c=2\\ \\y(0)=0^4+a\cdot 0^3+b\cdot 0^2+2\cdot 0+d=1\Rightarrow d=1[/tex]

The curve has a tangent line when x = 1 with equation y = -3x + 2, so

[tex]y'(1)=-3\\ \\y(1)=-3+2=-1[/tex]

So,

[tex]y'(1)=4\cdot 1^3+3a\cdot 1^2+2b\cdot 1+c=4+3a+2b+2=-3\Rightarrow 3a+2b=-9\\ \\y(1)=1^4+a\cdot 1^3+b\cdot 1^2+2\cdot 1+d=1+a+b+2+1=-1\Rightarrow a+b=-5[/tex]

From the second equation, a=-5-b, substitute it into the first one:

[tex]3(-5-b)+2b=-9\\ \\-15-3b+2b=-9\\ \\-b=-9+15\\ \\-b=6\\ \\b=-6\\ \\a=-5-b=-5-(-6)=-5+6=1[/tex]

Answer:

d = 6

Step-by-step explanation:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2 )

Givens

x2 = -12

x1   = -6

y2 = 4

y1 = 4

Solution

d = sqrt (-12 - - 6)^2 + (4 - 4)^2 )

d = sqrt ( ( - 6)^2 + 0)

d = sqrt(36)

d = 6

Answer:

6

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 6, 4) and (x₂, y₂ ) = (- 12, 4)

d = [tex]\sqrt{(-12+6)^2+(4-4)^2}[/tex]

  = [tex]\sqrt{(-6)^2+0^2}[/tex] = [tex]\sqrt{36}[/tex] = 6

Answer:2

Step-by-step explanation:

the bars make the integers absolute value so it would be 10-8 when you drop the bars making the answer 2

Answer:

y=4x+48

Step-by-step explanation:

Hey there! :)

3[-x + (2x + 1)] = x - 1

Simplify the parenthesis!

3[-x + 2x + 1]  =x - 1

Add like terms.

3[x + 1] = x - 1

Simplify!

3x + 3 = x - 1

Subtract 1x from both sides.

3x + 3 - 1x = x - 1 - 1x

Simplify.

2x + 3 = -1

Subtract 3 from both sides.

2x = -4

Divide both sides by 2.

2x ÷ 2 = -4 ÷ 2

Simplify.

x = -2

~Hope I helped! :)

Answer:

[tex]\large\boxed{g(1)=2}[/tex]

Step-by-step explanation:

[tex]g(x)=x^2+1\\\\g(1)-\text{put x = 1 to the equation of the function}\\\\g(1)=1^1+1=1+1=2[/tex]

Answer:

The equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n

Step-by-step explanation:

Points to remember

Identities

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

(xᵃ)ᵇ = xᵃᵇ

x⁻ᵃ = 1/xᵃ

To find the equivalent ratio of (3m⁻²n)⁻³/6mn⁻²

By using identities,

(3m⁻²n)⁻³ = 3m⁶n⁻³

(3m⁻²n)⁻³/6mn⁻² = 3m⁶n⁻³/6mn⁻²

 =  3m⁽⁶⁻¹⁾n⁽⁻³ ⁻ ⁻²⁾/6

 = m⁵n⁻¹/2

 = m⁵/2n

Therefore the equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n

Answer:

C) $9.00

Step-by-step explanation:

For this case we have that the cost of a ticket is given by the variable "x". We have the following equation:

[tex]4x + 12 = 48[/tex]

By clearing "x" we have:

We subtract 12 on both sides of the equation:

[tex]4x = 48-12\\4x = 36[/tex]

Dividing between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

Then, a ticket costs $ 9.00

Answer:

Option C

Answer:

Remote Interior Angle

Step-by-step explanation:

The name of an interior angle of a triangle that is not adjacent to a given exterior angle of the triangle is Remote Interior Angle.

If you take a look at the picture attached, you will find three angles: ∠A, ∠C and ∠D. In this case, we have that ∠A comes to be the exterior angle while ∠C and ∠D are the remote interior angle given that they are not adjacent to ∠A

Answer:

8 inches

Step-by-step explanation:

The problem gives us a basic formula, the volume formula for a rectangular prism. All we have to do is use this formula, plug in all the values that are given, and solve for the unknown value.

[tex]V = lwh[/tex]

[tex]192 = l(12)(2)[/tex]

[tex]192 = 24l[/tex]

From here, all we need to do is divide 24 from both sides of the equation, since what you do to one side of the equation you must do to the other!

[tex]8 = l[/tex]

The length of the box will thus be 8 inches.

it is going to be 8 inches                                                                                                    Hope it helps !!!!!

The solution of the system of equations is a = 4 and b = 5.

A system of equations is a set of two or more equations that you deal with at one time.

The given system of equations are;

8a + 12b = 92

6a – 4b = 4

From equation 1

[tex]\rm 8a + 12b = 92\\\\ 8a=92-12b\\\\a=\dfrac{92-12b}{8}[/tex]

Substitute the value of a in the equation 2

[tex]\rm 6a-4b=4\\\\6\times \dfrac{92-12b}{8}-4b=4\\\\3\times \dfrac{92-12b}{4}-4b=4\\\\ 276-36b-16b=16\\\\-52b=16-276\\\\-52b=-260\\\\b=\dfrac{-260}{-52}\\\\b=5[/tex]

Substitute the value of b in the equation 2

[tex]\rm 6a – 4b = 4\\\\6a-4\times 5=4\\\\6a-20=4\\\\6a=4+20\\\\6a=24\\\\a=\dfrac{24}{6}\\\\a=4[/tex]

Hence, the solution of the system of equations is a = 4 and b = 5.

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ANSWER

Option C is correct.

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x - 1} + 3[/tex]

The base function is

[tex]y = \sqrt[3]{x} [/tex]

The given function has the same domain as its base function which is all real numbers.

Any real number you plug into this function is defined.

Since the function has no restriction, the domain is all real numbers.

[tex]x | x \: is \: real \: number[/tex]

Answer:

bru thats not the answer^

Step-by-step explanation:

Answer:

Marcus practiced for 4 hours and Donnell practiced for 7 hours

Step-by-step explanation:

We can set up this problem as a system of linear functions

We'll use d to represent Donnell and m to represent Marcus

Since Donnell practiced 3 hours more than Marcus, we can represent this as an equation:

d=m+3

And since they both practiced for a combined total of 11 hours, we can represent this an an equation:

d+m=11

We can substitute d=m+3 into d+m=11 and we get:

m+3+m=11

2m+3=11

2m=8

m=4

Now we can substitute m=4 into d+m=11

d+4=11

d=7

Therefore, Donnell practiced for 7 hours and Marcus practiced for 4 hours

Answer:

y=8

Step-by-step explanation:

[tex]y = - \frac{1}{3} ( - 6) + 6 \\ y = 8[/tex]

Answer:

w+7<26

Step-by-step explanation:

number w increased by 7 means w+7

ls less than 25 means <25

So we have w+7<26

Answer:

[tex]\text{The slope:}\ m=-\dfrac{7}{8}\\\\\text{The point-slope form:}\ y+4=-\dfrac{7}{8}(x-7)\\\\\text{The slope-intercept form:}\ y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (7, -4) amd (-1, 3).

Calculate the slope:

[tex]m=\dfrac{3-(-4)}{-1-7}=\dfrac{7}{-8}=-\dfrac{7}{8}[/tex]

The point-slope form of an equation of a line:

[tex]y-(-4)=-\dfrac{7}{8}(x-7)\\\\y+4=-\dfrac{7}{8}(x-7)[/tex]

Convert to the slope-intercept form:

[tex]y+4=-\dfrac{7}{8}(x-7)[/tex]        use the distributive property

[tex]y+4=-\dfrac{7}{8}x+\dfrac{49}{8}[/tex]     subtract 4 = 32/8 from both sides

[tex]y=-\dfrac{7}{8}x+\dfrac{17}{8}[/tex]

The equation of the line passing through (7,-4) and (-1,3) has a slope of -7/8, the point-slope form is y + 4 = -7/8(x - 7), and the slope-intercept form is y = -7/8x + 17/8.

To write the equation of the line that passes through the points (7,-4) and (-1,3), we first need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1).

Applying this to our points, we get m = (3 - (-4)) / (-1 - 7), which simplifies to m = 7 / -8 = -7/8. Now, using the point-slope form y - y1 = m(x - x1), and the point (7, -4), we can write the equation as y - (-4) = -7/8(x - 7).

Next, to convert this to slope-intercept form, we simplify the point-slope equation to solve for y: y + 4 = -7/8x + 49/8, and then subtract 4 (or 32/8) from both sides to get y = -7/8x + 17/8. This is our slope-intercept form, where -7/8 is the slope, and 17/8 is the y-intercept.

Answer:

Step-by-step explanation:

[tex]\text{If}\ A(n)\ \text{represents a geometric sequence, then}\ \dfrac{A(n)}{A(n-1)}=\bold{constant}.\\\\A.\\\\A(n)=P(1+i)^{n-1}\\\\A(n-1)=P(1+i)^{n-1-1}=P(1+i)^{n-2}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{P(1+i)^{n-1}}{P(1+i)^{n-2}}\\\\=(1+i)^{(n-1)-(n-2)}=(1+i)^{n-1-n+2}=(1+i)^1=1+i=\bold{constant}[/tex]

[tex]B.\\\\A(n)=(n-1)(P+i)^n\\\\A(n-1)=(n-1-1)(P+i)^{n-1}=(n-2)(P+i)^{n-1}\\\\\dfrac{A(n)}{A(n-1)}=\dfrac{(n-1)(P+i)^n}{(n-2)(P+i)^{n-1}}=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-(n-1)}\\\\=\left(\dfrac{n-1}{n-2}\right)(P+i)^{n-n+1}=\left(\dfrac{n-1}{n-2}\right)(P+i)^1\neq\bold{constant}[/tex]

others the same

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant. This is different from a quadratic function which does not represent a geometric sequence.

In mathematics, a function represents a geometric sequence when each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The general form of a geometric sequence can be written as a, ar, ar^2, ar^3, ... where 'a' is the first term, and 'r' is the common ratio.

The important factor in a geometric sequence is the multiplication by a constant. For example, let's say we have a sequence 2, 4, 8, 16. This is a geometric sequence because each term is multiplied by 2 to get the next term.

In contrast, a quadratic function, for instance, does not represent a geometric sequence as it's formed by the equation ax^2 + bx + c where a, b, and c are constants.

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Answer:

[tex]17x[/tex]

Step-by-step explanation:

[tex]8x + 9x = 17x[/tex]

To simplify the expression 8x + 9x, you combine the like terms by adding the coefficients. The result is 17x.

The process involved in simplifying an equation like this is known as combining like terms. In this example, the terms are 8x and 9x. Because they both contain the same variable, x, you can combine them.

To perform this operation, you add the coefficients (the numbers in front of the variable). In this case, the coefficients are 8 and 9. So, 8x + 9x simplifies to 17x.

Therefore, the simplified form of the equation 8x + 9x is 17x.

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Answer:

5

Step-by-step explanation:

By trial and error, we see that we can multiply by 3/2 every time to continue the sequence! So multiplying 10/3 by 3/2, we get 5. So 5 is the next term of the geometric sequence.

Answer:

4/13

Step-by-step explanation:

6+3+4 =13

4/13

Answer:

4/13

Step-by-step explanation:

P( blackbeans) = number of cans of black beans

                           ----------------------------------------------

                           total cans

                   =   4

                      -------

                       ( 4+6+3)

              = 4

                 -----

                 13

Answer:

The statement is true.

Step-by-step explanation:

The statement is true.

This is true. Since they could be considered similar even when they are congruent, since in similar triangles, the measurements are proportional. In congruent triangles, this proportion is just one. or 1/1

Hope this helps!

Answer:

Step-by-step explanation:

y=-x+3

x+y=-1

y=-x+3

y=-x-1

-x+3=-x-1

add x to both sides

3=-1

no solutions

Answer: 64 °

64-1=63.

The parallel lines make the angles equal so they have the same measurement.

Answer:

[tex]\large\boxed{(3a+2)(4a^2-2a+9)=12a^3+2a^2+23a+18}[/tex]

Step-by-step explanation:

[tex](3a+2)(4a^2-2a+9)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(3a)(4a^2)+(3a)(-2a)+(3a)(9)+(2)(4a^2)+(2)(-2a)+(2)(9)\\\\=12a^3-6a^2+27a+8a^2-4a+18\qquad\text{combine like terms}\\\\=12a^3+(-6a^2+8a^2)+(27a-4a)+18\\\\=12a^3+2a^2+23a+18[/tex]

Answer:

2x² - 16x + 30

Step-by-step explanation:

To evaluate (p ￮ q)(x)

Substitute x = q(x) into p(x)

2(x - 3)² - 4(x - 3)

= 2(x² - 6x + 9) - 4x + 12

= 2x² - 12x + 18 - 4x + 12

= 2x² - 16x + 30

Answer: C. 30 degrees

Step-by-step explanation:

By definition, an hexagon is a polygon with six sides.

The sum of the interior angles of an hexagon is 720 degrees.

Based on this, the measure of eac interior angle is:

[tex]interior\ angle=\frac{720\°}{6}=120\°[/tex]

Therefore, the measure of ∠1 is:

 [tex]\angle 1=\frac{120\°}{2}\\\\ \angle 1=60\°[/tex]

So, to find the angle ∠2, you can divide ∠1 by 2:

[tex]\angle 2=\frac{60\°}{2}\\\\ \angle 2=30\°[/tex]

Answer:

0

Step-by-step explanation:

Final answer:

To find the output y for an input x of 6, assuming a linear relationship based on a derivative example provided, we use the equation y = 3x + 6. Substituting x with 6 gives us y = 24.

Explanation:

The question requires us to find the output y when the input x is 6. The equation provided in the excerpts can be interpreted in many ways due to lack of clarity in the given information. However, a linear function example is given by dy/dx = 6+3x, where the derivative suggests an initial value of 6 increasing by 3 with each unit increase in x. If we assume a linear relationship y = mx + b, we can use the pattern in the derivative example and set the slope m as 3 and the y-intercept b as 6. This yields the equation y = 3x + 6. When x is 6, the output y is calculated as y = 3(6) + 6 = 18 + 6 = 24.

Remember, the equation provided in the tutorial only applies if we assume a linear relationship based on the derivative example mentioned. It is important to have the exact equation or context to provide the precise output y.