which graph represents the function f(x)=4[x]?

Answer:

Choice D is correct

Step-by-step explanation:

We have been given the expression;

[tex]21\leq-3(x-4)<30[/tex]

The first step is to open the brackets using the distributive property;

-3(x-4) = -3x + 12

Now we have;

[tex]21\leq-3x+12<30\\\\21-12\leq-3x+12-12<30-12\\ \\9\leq-3x<18\\\\\frac{9}{-3}\geq x>\frac{18}{-3}\\\\-6<x\leq-3[/tex]

Answer:

32

Step-by-step explanation:

f(x)=1/3x^2+5

Let x = -9

f(-9) = 1/3* (-9)^ 2 +5

       = 1/3 * 81 +5

       = 27+5

       =32

Answer:

vertex form:  [tex]y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}[/tex]

B correct

Step-by-step explanation:

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

[tex]y=x^2+9+6x+x^2+16+8x[/tex]

[tex]y=2x^2+14x+25[/tex]

[tex]y=2(x^2+7x)+25[/tex]

[tex]y=2(x^2+7x+\dfrac{49}{4}-\dfrac{49}{4})+25[/tex]

[tex]y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}[/tex]

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = (x + 3)² + (x + 4)² ← expand and simplify

  = x² + 6x + 9 + x² + 8x + 16

  = 2x² + 14x + 25

To obtain vertex form use the method of completing the square

The coefficient of the x² term must be 1

Factor out 2 from 2x² + 14x

y = 2(x² + 7x) + 25

add/ subtract ( half the coefficient of the x- term )² to x² + 7x

y = 2(x² + 2([tex]\frac{7}{2}[/tex]) x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] ) + 25

y = 2(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{2}[/tex] + [tex]\frac{50}{2}[/tex]

y = 2(x + [tex]\frac{7}{2}[/tex] )² + [tex]\frac{1}{2}[/tex]

Answer:

[tex]2\frac{1}{2}[/tex]

Step-by-step explanation:

we have

[tex]10x^{2} y^{-2}[/tex]

we know that

[tex]10x^{2} y^{-2}=10\frac{x^{2}}{y^{2}}[/tex]

Substitute the value of x=-1 and y=-2 in the expression

[tex]10\frac{(-1)^{2}}{(-2)^{2}}[/tex]

[tex]10\frac{1}{4}[/tex]

[tex]\frac{10}{4}[/tex]

Simplify

[tex]\frac{5}{2}=2\frac{1}{2}[/tex]

Answer:

f(5) = 6(5 - 2) = 6(3) = 18

Step-by-step explanation:

You're asked to "evaluate" f(x)=6(x-2) when x = 5.

To do this, replace both instances of x with 5:  f(5) = 6(5 - 2) = 6(3) = 18

Answer:

Hence, the value of the function for f(5) is 18..

Step-by-step explanation:

Consider the provided function.

[tex]f(x)=6(x-2)[/tex]

We need to find the value of function at x = 5.

Substitute x = 5 in above function and simplify.

[tex]f(5)=6(5-2)[/tex]

[tex]f(5)=6(3)[/tex]

[tex]f(5)=18[/tex]

Hence, the value of the function for f(5) is 18.

The solutions of:

[tex]x^2-2x-4=-3x+9[/tex] are:

The x-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9

Solution to a system of equation--

A solution to a system of equation are the possible values of x that satisfy both the equation.

These are obtained by finding the x-coordinate of the point of intersection of the equations i.e. the point where the y-values is equal.

Hence, the given can be solved by finding the points of intersection of the graph:

[tex]y=x^2-2x-4[/tex] and [tex]y=-3x+9[/tex] and then taking the x-coordinate of the point.

Answer:

y = 4[2]^x

Step-by-step explanation:

One possible model for this function is the exponential y = a(b)^(kx).  Notice that if x = 0, y = a, and so, from the graph, we see that a = 4.

Then we have the exponential y = 4(b)^(kx).  Substitute 8 for y and 1 for x:

8 = 4(b)^(k), or 2 = b^k.

Then y = a(b)^(kx) becomes y = 4(b)^(kx) = 4[b^k]^x = 4[2]^x = y

The desired function is y = 4[2]^x.

Check this out.  Does the point (0, 4) satisfy this function?

Is 4 = 4[2]^0 true?  YES, it is.

Is 8 = 4[2]^1 true?  Is 8 = 4(2) true?  YES, it is

Answer:

Pairs (0, 14) and (10, 0)

Answer:

Step-by-step explanation:

In this question we have to find the two points that can be joined to best draw the line in best fit.

From the given graph we can see if we join (0, 13) and (10, 0) then other ordered pairs given will be equal in numbers on both the sides of the line.

Therefore, by definition of these are the points which can be joined to draw a line which best fit the scatter plot.

Answer:

-3/4

Step-by-step explanation:

To find the slope, we use the formula

m = (y2-y1)/(x2-x1)

    = (-1-2)/(4-0)

    = -3/4

Answer:

b.

Step-by-step explanation:

expand (x-2)(x+4)

(x-2)(x+4)=0

x²+2x-8=0

a=1,b=2,c=-8

From this equation we know that ,

a>0, the shape of the graph is a minimum graph.

c is the y-intercept ,the graph will intercept -8 at y-axis .

By solving this (x-2)(x+4)=0 we know the x-intercept of the graph .

(x-2)(x+4)=0

x=2 ,x=-4

Hello!

The first step you would want to do here is distribute the -3 to inside the parentheses. This can be done by multiplying -3 by what's inside the parentheses. This would make the original equation become:

y + 1 = -3(x - 5)

y + 1 = (-3 * x) - (5 * -3)

Then, complete the multiplication inside the parentheses to get:

y + 1 = -3x + 15

Now, subtract both sides by 1 to isolate the y on the left side.

y + 1 - 1 = -3x + 15 - 1

Therefore, your final answer is:

y = -3x + 14

(it can also be f(x) = -3x + 14, y and f(x) are the same thing in this case)

Hope this helped!

The equation in point - slope form can be written in the form of linear function as y = -3x + 14.

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is that the equation in point - slope form as -

y + 1 = - 3(x - 5)

We can write the equation as the linear function as -

y + 1 = -3(x - 5)

y + 1 = -3x + 15

y = -3x + 15 - 1

y = -3x + 14

Therefore, the equation in point - slope form can be written in the form of linear function as y = -3x + 14.

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Area is in square units.

Square the scale factor: 4^2 = 16

The area is 16 times the original area.

Answer:

cubic

Step-by-step explanation:

Answer:

cubic

Step-by-step explanation:

What units are used for volume;

cubic

Answer:

The slope is 4 and the y-intercept is 12.

Answer:

The slope is 4, and the y-intercept is 12.

Step-by-step explanation:

In the given graph consider to coordinates of line:

(-3,0), (-2,4)

Slope of the of line can be calculated by using formula:

[tex](x_1,y_1) , (x_2,y_2)[/tex]

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

[tex]m=\frac{4-0}{-2-(-3)}=\frac{4}{1}=4[/tex]

And the equation of the line can be given as:

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

m = slope of the line

[tex](y-0)=4\times (x-(-3)[/tex]

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

Slope intercept form of line:

[tex]y=mx+c[/tex]...

c = intercept on y axis

On comparing equation line with slope intercept form

y=4x+12

y=mx+c

m = 4, c = 12

The slope is 4, and the y-intercept is 12.

Answer:

750 households

Step-by-step explanation:

45+57+18=120

45/120=3/8

(3/8)*2120= 750 households would support.

Hope I helped.

Answer:

The slope is -1

Step-by-step explanation:

(-5 - 3)/(2 - [-6]) = -8/8 = -1

Answer:

= 48 ways to order a 2-course meal.

Step-by-step explanation:

Number of appetizer choices = 8

Number of main course choices = 6

Number of possible combinations of appetizer and main course

= 6 x 8

= 48 ways to order a 2-course meal.

The number of ways is an illustration of selections and arrangements

There are 48 ways to order a two-course meal

The given parameters are:

[tex]\mathbf{Appetizer = 8}[/tex]

[tex]\mathbf{Main = 6}[/tex]

A person can choose 1 a-piece from each menu.

This means that:

There are 8 ways of selecting appetizers, and 6 ways of selecting the main courses.

So, the number of ways (n) is:

[tex]\mathbf{n = Appetizer \times Main}[/tex]

This gives

[tex]\mathbf{n = 8 \times 6}[/tex]

[tex]\mathbf{n = 48}[/tex]

Hence, there are 48 ways to order a two-course meal

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Answer:

A Is the correct answer ( y = 2x - 4 )

Step-by-step explanation:

The answers listed are provided in Y= Mx + B. What this means is M = Slope and B = Y Intercept.  The Y-Intercept is where the imaginary line crosses the Y axis of the graph or where x = 0. In this case the Y-Int is -4 and the slope of the graph is 2 over 1 ( A rise of two and a run of one ) in other terms it's just 2, but once you put this into the equation y = Mx + B it becomes 2x. Your final product would be y = 2x - 4

Answer:

6m

Step-by-step explanation:

for every one meter there's 100 cm so 600cm = 6m

There are 100 cm in 1 m this means that to find how many meters are in cm you would divide 600 by 100

600 / 100

6 m

There are 6 meters in 600 centimeters

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]\large\boxed{y=\dfrac{2}{3}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 (0, b)

The formula of a slope:

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

We have the points:

(0, 4) → y-intercept (b = 4)

(3, 6)

Substitute:

[tex]m=\dfrac{6-4}{3-0}=\dfrac{2}{3}[/tex]

Finally we have the equation:

[tex]y=\dfrac{2}{3}x+4[/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 )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-2}{0+3}[/tex] = [tex]\frac{2}{3}[/tex]

note the line crosses the y- axis at (0, 4) ⇒ c = 4, hence

y = [tex]\frac{2}{3}[/tex] x + 4 ← in slope- intercept form

OR

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{2}{3}[/tex] and (a, b) = (3, 6), hence

y - 6 = [tex]\frac{2}{3}[/tex](x - 3) ← in point- slope form

Answer:

81 degrees

Step-by-step explanation:

A quadrilateral has four interior angles which sum up to 360 degrees.

As we are given that two angles are right angles which means the sum of two angles will be 180 degrees and the third angle is 99 degrees.

As we know that the four angles sum up to 360 degrees.

Let A,B,C and D denote the four angles,

Then

Sum of angles = 360

A+B+C+D=360

90+90+99+D=360

279+D=360

D=360-279

D= 81 degrees

So the fourth angle is 81 degrees ..

Answer:

Step-by-step explanation:

Trick question. Good to know.

0 is the closest 100.

33 will round to 0

For this case we have that by definition, a quadratic equation is of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Where the roots are given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have the following equation:

[tex]x ^ 2-3x-2 = 0[/tex]

Then, according to the definition, the values are:

[tex]a = 1\\b = -3\\c = -2[/tex]

Answer:

[tex]a = 1\\b = -3\\c = -2[/tex]

Answer:

The values of a, b, and c in the quadratic equation are:

[tex]a=1\\b=-3\\c=-2[/tex]

Step-by-step explanation:

The general form of a quadratic equation is as follows

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

Where a, b and c are real numbers that represent the coefficients of the quadratic equation and [tex]a \neq 0[/tex]

In this case we have the following quadratic equation

[tex]x^2 - 3x - 2[/tex]

Therefore, notice that:

[tex]a=1\\b=-3\\c=-2[/tex]

Answer:

B

Step-by-step explanation:

10(10m+6)<=12        

100m+60<=12       Distributive Property

100m     <=12-60

100m    <=-48

     m    <=-48/100

     m    <=-.48

This says values for m that are less than or equal to -.48

-.48 is between -1 and 0 so the answer is B

Graph the solution set on a number line 10(10m+6)<12

10(10m+6)<=12        

100m+60<=12       Distributive Property

100m     <=12-60

100m    <=-48

m    < =-48/100

m    < =- 48

This says values for m that are less than or equal to -.48

Option B. M≤ -48

Four popular derivative notations include: The Leibniz notation, which has a d/dx format. The Lagrange notation, characterized by prime notation. The Euler notation, where a capital D is used.

It's just a different notation to express the same thing. On the other hand, if you want to represent the set with interval notation, you need to know the upper and lower bound of the set, or possibly the upper and lower bound of all the intervals that compose the set.

An equation involving x and y, which is also a function, can be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” and means that y is a function of x.

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Answer:

Chromosome is made up of DNA tightly coiled many times around proteins.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

A

Step-by-step explanation:

17 / 12

(12 + 5) / 12

12/12 + 5/12

1 5/12

Answer:line a would have a y intercept of three and a slope of 1/2. Line b would have a y intercept of negative one and a slope of 3/2

Step-by-step explanation:line a would start at 3 on the y axis and move up one to the right two. Line b would start at -1 on The y axis and move up three to the right two

The system of equations y=1/2x + 3 and y= 3/2x -1 can be represented as two lines on a graph, the intersection of which indicates any common solution.

The system y=1/2x + 3 and y= 3/2x -1 represents two linear equations. These two equations can be graphed out onto the x and y-axis. The first equation y=1/2x + 3 will have a slope of 1/2 and y-intercept of 3, and the second equation y= 3/2x -1 will have a slope of 3/2 and y-intercept of -1.

To graph the first equation, start at the point (0,3) on the y-axis. From there, as the slope is 1/2, for every 2 units you move to the right on the x-axis, you will move 1 unit up on the y-axis.

To graph the second equation, start at the point (0,-1) on the y-axis. As the slope is 3/2, for every 2 units you move to the right on the x-axis, you will move 3 units up on the y-axis.

These lines intersect at their solution, if one exists, that is a common point on both lines.

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The measure of angle A in the right triangle with sides a=76.4 ft and b=39.3 ft can be found using the tangent function and is approximately 62 degrees when rounded to the nearest degree.

To find the measure of angle A in a right triangle with given sides a=76.4 ft and b=39.3 ft, we can use trigonometric functions. Since side a is opposite to angle A and side b is adjacent to angle A, we will use the tangent function, which is the ratio of the opposite side to the adjacent side. The formula to find the angle is angle A = tan∑(a/b).

Plugging in the values, we get:

angle A = tan∑(76.4/39.3)

By using a calculator, we find:

angle A = tan∑(1.9435) ≈ 62 degrees

Rounded to the nearest degree, the measure of angle A is approximately 62 degrees.

Evelyn can serve nine friends with her three apples if she gives each friend 1/3 of an apple by performing a simple multiplication of the number of apples, which is 3, by the reciprocal of 1/3.

Evelyn has three apples and wants to serve each friend 1/3 of a whole apple. To find out how many friends she can serve, we must divide the total number of apples (which is 3) by the fraction each friend receives (which is 1/3).

We perform the division by multiplying the total number of apples by the reciprocal of 1/3, which is 3. So, 3 apples x3 gives us 9. Therefore, Evelyn can serve nine friends.

Understanding fractions can be made easier by relating them to everyday examples. Say, if you have a whole pie, then one-third of this pie represents a slice that is one out of three equal parts of the pie. Knowing that four quarters make one dollar can also make it easy to grasp that four quarters (or four 1/4s) make a whole, just like four 1/4s of a pie would make a full pie.

Answer:

4 times smaller

Step-by-step explanation: