1. Factor each of the following completely. Look carefully at the structure of each quadratic function and consider the best way to factor. Is there a GCF? Is it an example of a special case? SHOW YOUR WORK

The answer is " D. Graph D"

Answer: It is a polynomial function of degree 2 and whose graph is a parabola.

Step-by-step explanation:

By definition a quadratic function is a polynomial function of degree 2 and whose graph is a parabola.

The Standard form of a quadratic function is:

[tex]y= ax^2 + bx + c[/tex]

Where "a", "b" and "c" are real numbers ([tex]a\neq0[/tex])

The Vertex form of a quadratic function is:

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

Where the point (h,k) is the vertex of the parabola.

The Intercept form of a quadratic function is:

[tex]y=a(x-p)(x-q)[/tex]

Where "p" and "q" are the x-intercepts.

Final answer:

A quadratic function is a second-order polynomial of the form f(x) = ax² + bx + c, whose graph is a parabola. The solutions of quadratic equations are found by various methods to determine the roots or zeros of the function.

Explanation:

A quadratic function is a type of mathematical function that can be represented in the form f(x) = ax² + bx + c, where a, b, and c are constants, and a ≠ 0. This form is a second-order polynomial, as its highest exponent is 2. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the a coefficient.

The solution of quadratic equations refers to finding the values of x that make the equation equal to zero. These solutions are also known as roots or zeros of the function.

To solve a quadratic equation, one can use different methods such as factoring, completing the square, using the quadratic formula, or graphing. Each of these methods provides a way to find the roots of the quadratic function.

Answer:

2

Step-by-step explanation:

1) Take the natural log of both sides, obtaining:

   -0.20x + ln 3.80 = ln 2

2)  Group the ln terms on the right side:  -0.20x = ln 2 - ln 3.80

3)  Find the natural logs of 2 and 3.80 and combine them:  -0.408, so that we have 0.20x = 0.408.

4) Solving for x, we get 2.03, or approx 2 (Answer C)

Answer:

a. 3 is the closest choice.

Step-by-step explanation:

2 = 3.80 e^-0.20x

e^-0.20x = 2/3.8

Taking logs:

-0.20x = ln(2/3.8) = -0.64185

x =  3.2.

Answer:210

Step-by-step explanation:

3 x 280 = 840

840 ÷ 4 = 210

Answer:

The distance from the midpoint of the interval to  either endpoint is 6 units

Step-by-step explanation:

step 1

Find the midpoint of the interval

The formula to calculate the midpoint between two numbers is equal to

[tex]M=(\frac{x1+x2}{2})[/tex]

substitute

[tex]M=(\frac{2+14}{2})[/tex]

[tex]M=8[/tex]

step 2

Find the distance from the midpoint of the interval to  either endpoint.

14-8=6 units

or

8-2=6 units

therefore

The distance from the midpoint of the interval to  either endpoint is 6 units

To find the distance from the midpoint of the interval (2,14) to either endpoint, first find the midpoint, which is 8, then calculate the distance to either endpoint by subtracting the lower endpoint from the midpoint, resulting in a distance of 6 units.

The question asks to find the distance from the midpoint of the interval (2,14) to either endpoint. To start, we find the midpoint of the interval by adding the two endpoints together and dividing by 2:

Midpoint = \((2 + 14) / 2\) = \(16 / 2\) = 8

Next, we calculate the distance from the midpoint to one of the endpoints. The distance can be found by subtracting the lower endpoint from the midpoint:

Distance = \(8 - 2\) = 6

Therefore, the distance from the midpoint of the interval to either endpoint is 6 units.

Answer:

reciprocal

Step-by-step explanation:

Final answer:

To divide two fractions, rewrite the operation as the first fraction multiplied by the reciprocal of the second. Multiplication of fractions involves simply multiplying the numerators and denominators, then simplifying by any common factors.

Explanation:

To divide two fractions, first rewrite the problem as the dividend times the reciprocal of the divisor. When dividing by a fraction, it is equivalent to multiplying by the reciprocal of that fraction. For example, dividing by ⅓ is the same as multiplying by 3 (the reciprocal of ⅓). Similarly, multiplying by ½ is the same as dividing by 2 because ½ is the reciprocal of 2. To multiply fractions, simply multiply the numerators together and the denominators together, simplifying by any common factors as necessary.

Demonstrating this concept through an example, let’s consider the division of 4 by ⅓. First, we find the reciprocal of ⅓, which is 3, and then we multiply 4 by 3 to get 12. Through the multiplication of fractions, if we have ⅛ multiplied by ⅓, we would multiply the numerators (2 and 1) and the denominators (8 and 3), and then simplify the resulting fraction by canceling out any common factors.

9.3 points. Look at the tenths place, whatever number is between 2 and 4 (3) is your answer.

Answer:

Yes. In between both of those would be 9.3. Best of luck to you! :)

-mark as brainliest please!- XD

Answer:

9

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

13-4 =9

Lets check:

Take the third term and subtract the second term

22-13 =9

The common difference is 9

Answer:

9

Step-by-step explanation:

9 is the common difference between the numbers in this sequence

4 +9 = 13

13 +9 = 22

22 +9 = 31

31 +9 = 40

Therefore the common difference is 9

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Answer:

11/15

Step-by-step explanation:

First, get a common denominator of 30. 2/5 becomes 12/30. 4/6 becomes 20/30. 1/3 becomes 10/30.

Now we can add and subtract accordingly.

12/30 + 20/30 = 32/30.

32/30 - 10/30 = 22/30.

Finally, simplify the fraction.

22/30 becomes 11/15 when each number is divided by 2.

Answer: [tex]\frac{11}{15}[/tex]

Step-by-step explanation:

The first step is to find the Least Common Denominator of  the fractions. Descompose each denominator into its prime factors and muliply the commons and non-commons with the least exponent. Then:

[tex]5=5\\6=2*3\\3=3\\\\LCD=2*5*3=30[/tex]

Divide each denominator by the LCD and multiply this quotient by the corresponding numerator, add the products and then reduce the fraction.

Therefore you get:

[tex]=\frac{(2*6)+(4*5)-(1*10)}{30}=\frac{12+20-10}{30}=\frac{22}{30}=\frac{11}{15}[/tex]

Answer:

it's A

Step-by-step explanation:

The domain is all the input values which is x|x=-5,-3,1,2,6

Step-by-step explanation:

If x is the amount the eldest receives, y is the amount the middle receives, and z is the amount the youngest receives, then:

x + y + z = 656000

x = 6z

y = z + 15000

Substituting the last two equations into the first:

(6z) + (z + 15000) + z = 656000

8z + 15000 = 656000

8z = 641000

z = 80125

Solving for the remaining variables:

x = 6z = 480750

y = z + 15000 = 95125

The eldest receives $480,750, the middle receives $95,125 and the youngest receives $80,125.

The youngest sibling receives $80,125, the middle sibling gets $95,125, and the eldest receives $480,750 from the $656,000 estate. The distribution complies with the stipulation that the eldest receives 6 times what the youngest does, and the middle sibling receives $15,000 more than the youngest.

The distribution of an estate of $656,000 among three siblings with specific conditions. Let's designate the amount the youngest sibling receives as y. According to the provided information, the eldest sibling receives 6 times as much as the youngest, meaning they receive 6y. The middle sibling receives y + $15,000. To find out how much each sibling receives, we need to solve the equation: y + 6y + (y + $15,000) = $656,000.

Add up the terms containing y: 8y + $15,000 = $656,000. Subtract $15,000 from both sides: 8y = $641,000. Divide both sides by 8 to find y:
y = $80,125.

Now, calculate each sibling's share:

The youngest receives y, which is $80,125.

The middle sibling receives y + $15,000, which is $95,125.

The eldest receives 6y, which is $480,750.

These calculations ensure that the total is $656,000, distributed according to the stipulated conditions.

Answer:

F 4 ^ -2

Step-by-step explanation:

4 ^ -5

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

4^-3

We know that a^b/ a^c = a^ (b-c)

4 ^ (-5 -  -3)

4 ^ (-5 +3)

4 ^ (-2)

Answer: [tex]0.96\ m^2[/tex]

Step-by-step explanation:

We can make the conversion from milimeters to meters (Remember that [tex]1m=1,000\ mm[/tex]). Then:

[tex]1,200\ mm[/tex] to [tex]m[/tex]:

[tex](1,200\ mm)(\frac{1\ m}{1,000\ mm})=1.2\ m[/tex]

[tex]800\ mm[/tex] to [tex]m[/tex]:

[tex](800\ mm)(\frac{1\ m}{1,000\ mm})=0.8\ m[/tex]

Now, we need to use this formula for calculate the area of a rectangle:

[tex]A=lw[/tex]

Where "l" is the lenght and "w" is the width.

Knowing that:

[tex]l=1.2\ m\\w=0.8\ m[/tex]

We can substitute values into the formula. Then we get:

[tex]A=(1.2\ m)(0.8\ m)\\\\A=0.96\ m^2[/tex]

Final answer:

The area of the rectangular shape is 0.96 square meters.

Explanation:

To find the area of a rectangle, we multiply its length by its width. Given that the length is 1200 mm and the width is 800 mm, we can convert these measurements to meters by dividing each measurement by 1000. So, the length in meters is 1.2 m and the width in meters is 0.8 m. To find the area in square meters, we multiply the length and width in meters: Area = 1.2 m × 0.8 m = 0.96 m².

Answer:

$240

Step-by-step explanation:

If x is the missing number and 25% equals to 1/4 then 1/4 times x equals 60.

Then once you multiply x on both sides you get $240.

Answer:

option a

Step-by-step explanation:

To find the slope 'm' we use 2 points from the line, those are given in the statement:

[tex]x_{1} =3\\y_{1} =6\\\\x_{2} =5\\y_{2} =3\\m=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}\\m=\frac{3 -6 }{5-3}}\\m=\frac{-3 }{2}}[/tex]

Hi !

625 - (625 ÷ 25) - 25 = 575

Answer:

575

Step-by-step explanation:

Following the order of operations, division is performed before subtraction

Given

625 - 625 ÷ 25 - 25 ← perform the division

= 625 - 25 - 25 ← now perform the subtraction

= 600 - 25

= 575

Answer:

[tex]\large\boxed{h(x)=x^3}[/tex]

Step-by-step explanation:

[tex]f(x)=(6x^3-7)^3\\\\(h\circ g)(x)=h\bigg(g(x)\bigg)\to\text{exchange x to}\ g(x)=6x^3-7\\\\f(x)=(\underbrace{6x^3-7}_{g(x)})^3=\bigg(g(x)\bigg)^3=h\bigg(g(x)\bigg)\\\\\text{Therefore}\ h(x)=x^3[/tex]

Answer:

D

Step-by-step explanation:

Matrices are equal when they are of the same order and their corresponding entries are equal.

This is the case with the given matrix and matrix D

Answer:

27

Step-by-step explanation:

3^-9/ 3^-12

Simply change the division into multiplication. The denominator will become numerator. We are doing so because the base are same.

3^-9 * 3^12

Negative sign of power 12 become positive

Add the powers because the base is same.

3^-9+12

3^3

3^3 means multiply 3 three times

3*3*3

=27....

Answer:

3^3 In scientific notation terms

Step-by-step explanation:

First let's look at this in a little more simple way

[tex]\frac{3^{-9}}{3^{-12}}[/tex]

there so know we can start,

First since the main number is 3, put that away to the side for now:

3<----------     [tex]\frac{-9}{-12}[/tex]

Then, we need to replace the / symbol or the fraction with a subtraction equation:

[tex]^{-9-(-12)}[/tex]

Next, we need to simplify:

[tex]^{-9 + 12}[/tex]

Then, simplify some more and you should get:

[tex]^{3}[/tex]

Finally, get back the original 3 and combine it with the smaller 3:

[tex]3^{3}[/tex]

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Answer:

[tex]-2y^{b-1}[/tex]

Step-by-step explanation:

[tex]\frac{12x^ay^b}{-6x^ay}[/tex]

In multiplication of fractions you can do this:

[tex]\frac{a}{c} \cdot \frac{b}{d}=\frac{a \cdot b}{c \dot d} \text{ or the other way around } \frac{a \cdot b}{c \dot d}=\frac{a}{c} \cdot \frac{b}{d}[/tex].

So that is exactly what we are going to do here:

[tex]\frac{12x^ay^b}{-6x^ay}[/tex]

[tex]\frac{12}{-6} \cdot \frac{x^a}{x^a} \cdot \frac{y^b}{y}[/tex]

We know that 12 divided by -6=12/-6 =-2.

We also know assuming x isn't 0 that x^a/x^a=1.

On the last fraction, the only thing you can do there to simplify is use the following law of exponents: [tex]\frac{v^m}{v^n}=v^{m-n}[/tex].

So we have

[tex]\frac{12x^ay^b}{-6x^ay}[/tex]

[tex]\frac{12}{-6} \cdot \frac{x^a}{x^a} \cdot \frac{y^b}{y}[/tex]

[tex](-2) \cdot (1) \cdot (y^{b-1})[/tex]

Simplifying a bit and leaving out the ( ).

[tex]-2y^{b-1}[/tex]

[tex]\bf \underset{\textit{same denominator}}{\cfrac{4x+2}{x+5}+\cfrac{3x-1}{x+5}}\implies \cfrac{(4x+2)+(3x-1)}{x+5}\implies \cfrac{7x+1}{x+5}[/tex]

Answer:

(7x+1)/(x+5)

Step-by-step explanation:

4x+2       3x-1

--------  +  ----------

x+5           x+5

Since the denominator is the same, we can add the numerators

4x+2   +    3x-1

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

x+5    

Combine like terms

7x+1  

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

x+5      

Answer:

So you will want to graph the following 3 points:

(0,2)

(3,3)

(-3,1)

Then connect the points.

Step-by-step explanation:

So we have the equation x-3y=-6.

I'm going to solve for y once so I don't have to do it 3 times when choosing a value for x.

x-3y=-6

Subtract x on both sides:

 -3y=-x-6

Divide both sides by -3:

   [tex]y=\frac{-x}{-3}+\frac{-6}{-3}[/tex]

Simplify where you can:

  [tex]y=\frac{1}{3}x+2[/tex]

So since this in the slope-intercept form, y=mx+b where slope is m and b is y-intercept we have that (0,2) is on our line.  If you plug in 0, you will get 2 like this y=1/3 (0)+2=0+2=2.  

Now I'm going to choose easy values to plug in, ones that are divisible by 3 since x is being multiplied by 1/3.

So if x=3, then [tex]y=\frac{1}{3}(3)+2=1+2=3[/tex], so (3,3) is on the line.

So if x=-3, then [tex]y=\frac{1}{3}(-3)+2=-1+2=1[/tex]. so (-3,1) is on the line.

So you will want to graph the following 3 points:

(0,2)

(3,3)

(-3,1)

Answer:

f(x) = (-4/5)*x + 4

Step-by-step explanation:

The line which passes through these points will decrease y by 12 for every x increase of 15. This is the same as decreasing y by 4 for every x increase of 5. This means the slope (rise over run) is -4/5. If this is applied to the first point to find what y is at 0, then the point (0, 4) is on the line.

This means that f(x) = (-4/5)*x + 4

Answer:

[tex]\large\boxed{y=-\dfrac{4}{5}x+4}[/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 formula of a slope:

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

We have the points (-5, 8) and (10, -4). Substitute:

[tex]m=\dfrac{-4-8}{10-(-5)}=\dfrac{-12}{15}=-\dfrac{12:3}{15:3}=-\dfrac{4}{5}[/tex]

Put it to the equation of a line:

[tex]y=-\dfrac{4}{5}x+b[/tex]

Put the coordinates of the point (-5, 8) to the equation, and solveit for b:

[tex]8=-\dfrac{4}{5\!\!\!\!\diagup_1}(-5\!\!\!\!\diagup^1)+b[/tex]

[tex]8=4+b[/tex]           subtract 4 from both sides

[tex]4=b\to b=4[/tex]

Finally we have:

[tex]y=-\dfrac{4}{5}x+4[/tex]

Answer:

B) 4

Step-by-step explanation:

Tan is opposite/adjacent. That means that 3 is the opposite side while 4 is the adjacent side.

[tex]\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ e^{\ln(1)}=e^{\ln(5x)}\implies e^{\log_e(1)}=e^{\log_e(5x)}\implies 1=5x\implies \cfrac{1}{5}=x[/tex]

Answer: it’s 1 and 5x on edg

Step-by-step explanation:

Answer:

d= 2

Step-by-step explanation:

To find the common difference, take the second term and subtract the first

-2 - (-4)

-2+4 = 2

We add 2 each time

Lets check

Take the third term and subtract the second

0- -2

0+2 =2

The common difference is 2

Step-by-step explanation:

Cavalieri's Principle. A method, with formula given below, of finding the volume of any solid for which cross-sections by parallel planes have equal areas. This includes, but is not limited to, cylinders and prisms.

Answer:

30/3x

Step-by-step explanation:

Let

x ----> a number

we know that

The algebraic expression of the phrase" thirty" is equal to the number 30

The algebraic expression of the phrase"three times a number" is equal to multiply the number by 3 ----> 3x

therefore

"The quotient of thirty and three times a number" is equal to divide the number 30 by 3x

30/3x

Answer:  The correct option is (B) [tex]\dfrac{30}{3x}.[/tex]

Step-by-step explanation:  We are given to translate the following phrase into an algebraic expression :

"the quotient of thirty and three times a number."

Let the unknown number be represented by x.

Then, according to the given phrase, the algebraic expression can be written as :

[tex]E=\dfrac{30}{3\times x}\\\\\\\Rightarrow E=\dfrac{30}{3x}.[/tex]

Thus, the required algebraic expression is [tex]\dfrac{30}{3x}.[/tex]

Option (B) is CORRECT.

Answer:

B

Step-by-step explanation:

Matrices are equal when they are of the same order and their corresponding entries are equal.

This is the case for the given matrix and matrix B

Answer:

The second option.

Step-by-step explanation:

It is the one that is marked.

The elements are the same and in the same location.