Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. After about how many years will the value of Cate’s stock be about $2000?

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.

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:

The solution of the inequality is a < 0.2870

Step-by-step explanation:

* Lets talk about the exponential function

- the exponential function is f(x) = ab^x , where b is a constant and x

 is a variable

- To solve this equation use ㏒ or ㏑

- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)

* Lets solve the problem

∵ 13^4a < 19

- To solve this inequality insert ㏑ in both sides of inequality

∴ ㏑(13^4a) < ㏑(19)

∵ ㏑(a^n) = n ㏑(a)

∴ 4a ㏑(13) < ㏑(19)

- Divide both sides by ㏑(13)

∴ 4a < ㏑(19)/㏑(13)

- To find the value of a divide both sides by 4

∴ a < [㏑(19)/㏑(13)] ÷ 4

∴ a < 0.2870

* The solution of the inequality is a < 0.2870

Answer:

a < 0.2870

Step-by-step explanation:

We are given the following inequality which we are to solve, rounding it to four decimal places:

[tex] 1 3 ^ { 4 a } < 1 9 [/tex]

To solve this, we will apply the following exponent rule:

[tex] a = b ^ { l o g _ b ( a ) } [/tex]

[tex]19=13^{log_{13}(19)}[/tex]

Changing it back to an inequality:

[tex]13^{4a}<13^{log_{13}(19)}[/tex]

If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].

Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].

[tex]4a<log_{13}(19)[/tex]

[tex]a<\frac{log_{13}(19)}{4}[/tex]

a < 0.2870

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:

4 times smaller

Step-by-step explanation:

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:

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.

To learn more about Notation, refer

https://brainly.com/question/2147364

#SPJ2

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:

Slope is 1

Step-by-step explanation:

Rise over Run.  Delta y over Delta x.  -8-2/-5-5 = -10/-10 = 1

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 radius is 4

EXPLANATION

The given equation is:

[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]

We complete the square to get the expression in standard form:

[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]

[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]

We factor using perfect squares to get:

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]

This implies that,

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]

Comparing to

[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The radius is r=4

Answer:

A

Step-by-step explanation:

17 / 12

(12 + 5) / 12

12/12 + 5/12

1 5/12

Answer:

i think the answer is undefined

Step-by-step explanation:

Answer: 1. inconsistent, 2. infinite, 3. (4, -1), 4. exactly two solutions.

Step-by-step explanation: HOPE THIS HELPS. ;))))

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:

Out of the four, the only statement true about the parent and the transformed function is:

"The domain of the transformed function and the parent function are all real numbers."

Step-by-step explanation:

Parent function:

f(x) = |x|

Applying transformations:

1. Stretched by a factor of 0.3:

f(x) = 3|x|

2. Translated down 4 units:

f(x) = 3|x| - 4

Transformed function:

f(x) = 3|x| - 4

We can see that:

Range of the parent function = All real numbers greater than or equal to 0.

Range of the transformed function = All real numbers greater than or equal to -4.

Domain of the parent and the transformed function is same and equal to all real numbers.

Hence, the first three statements are wrong and the fourth one is true.

Answer:

The domain of the transformed function and the parent function are both all real numbers.

Step-by-step explanation:

Stretching a function by any factor doesn't change either its domain nor its range.

Translating up or down a function changes its range. In this case, the lowest value the parent function can take is 0 when x=0; after translation, for x = 0 then f(x) = -4. Therefore,

f(x) = |x|  

domain = all real numbers

range = [0, infinity)

f(x) = 0.3*|x| - 4

domain = all real numbers

range = [-4, infinity)

Answer:

They would be perpendicular because the lines intersect at a ninety degree angle. Hope this helps! Please mark brainliest!

Step-by-step explanation:

Follow below steps:

The term that describes lines that intersect at 90-degree angles is perpendicular. Lines that are perpendicular to each other form four angles at the point of intersection. Each of these angles is a right angle, which measures 90 degrees. This is a fundamental concept in geometry, which is a branch of mathematics dealing with properties and relations of points, lines, surfaces, solids, and higher dimensional analogues.

For example, in the context of a coordinate plane, the x-axis and y-axis are perpendicular to each other. Moreover, theorems in geometry further explain the properties of perpendicular lines, such as the fact that if a line segment is drawn joining the extremities of two equal lines which are perpendicular to a given line, the joining segment is bisected at right angles by a third perpendicular line.

Answer:

[tex]\large\boxed{\dfrac{50}{3}}[/tex]

Step-by-step explanation:

If the polygons are similar, then the corresponding sides are in proportion:

[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex]        cross multiply

[tex]12z=(10)(20)[/tex]

[tex]12z=200[/tex]         divide both sides by 12

[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]

9 x 5 = 45 -> total $ on Friday

99 - 45 = 54 -> total $ on Saturday

54 ÷ 9 = 6 hours

Answer:

A, B.

Step-by-step explanation:

If Matt charges $9 an hour, and he worked for 5hrs on Friday night, then that means we have to do multiplication.

So, $9x5=$45.

And then it says he babysat again on Saturday, and in TOTAL, he earned $99.

So, if he already made $45, and he has a total of $99, then we need to work backwards to figure out how much he made on Saturday.

$99-$45=$54

So, he made $45 on Friday and $54 on Saturday.

Now, we continue to work backwards and divide how much he made on Saturday ($54), by how much he charges per hour.

$54/9=6

So, Matt worked a total of 6hrs on Saturday.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]

You are on the right tracks.

Since angle ABC is a right angle, that means lines AB and BC are perpendicular.

Therefore the gradient of BC = the negative reciprocal of the gradient of AB. We can use this to form an equation to find what K is.

You have already worked out the gradient of AB ( 1/2)  (note it's easier to leave it as a fraction)

Now lets get the gradient of BC:

[tex]\frac{5-k}{6-4}= \frac{5-k}{2}[/tex]

Remember: The gradient of BC = the negative reciprocal of the gradient of AB. So:

[tex]\frac{5-k}{2} =negative..reciprocal..of..\frac{1}{2}[/tex]

So:

[tex]\frac{5-k}{2}=-2[/tex]           (Now just solve for k)

[tex]5-k=-4[/tex]

[tex]-k=-9[/tex]                          (now just multiply both sides by -1)

[tex]k = 9[/tex]

That means the coordinates of C are: (4, 9)

We can now use this to work out the gradient of line AC, and thus the equation:

Gradient of AC:

[tex]\frac{1-9}{-2-4} =\frac{-8}{-6} = \frac{4}{3}[/tex]

Now to get the equation of the line, we use the equation:

y - y₁ = m( x - x₁)                            

Let's use the coordinates for A (-2, 1), and substitute them for y₁  and x₁  and lets substitute the gradient in for m:

y - y₁ = m( x - x₁)    

[tex]y - 1=\frac{4}{3}(x +2)[/tex]           (note: x - - 2 = x + 2)

Now lets multiply both sides by 3, to get rid of the fraction:

[tex]3y - 3 = 4(x+2)[/tex]             (now expand the brackets)

[tex]3y - 3 = 4x+8)[/tex]              

Finally, we just rearrange this to get the format: ay + bx = c

[tex]3y - 3 = 4x+8[/tex]              

[tex]3y = 4x+11[/tex]

[tex]3y - 4x = 11[/tex]          

And done!:

________________________________

Answer:

The equation of a line that passes through point A and C is:

[tex]3y - 4x = 11[/tex]        

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

Area is in square units.

Square the scale factor: 4^2 = 16

The area is 16 times the original area.

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:

cubic

Step-by-step explanation:

Answer:

cubic

Step-by-step explanation:

What units are used for volume;

cubic

Answer:

a = sqrt(33)

Step-by-step explanation:

a^2 + 4^2 = 7^2

a^2 + 16 = 49

a^2 = 33

a = sqrt(33)

Answer:

7/2

Step-by-step explanation:

Round 6 3/4 to 7

Round 1 1/2 to 2

7 divided by 2

=7/2

Answer:

15 ounces

Step-by-step explanation:

If there is 165 ounces in 11 boxes then divide the ounces by the boxes to get the amount of ounces in one box.

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trick question. Good to know.

0 is the closest 100.

33 will round to 0

[tex]x^2-5\leq0\\x^2\leq5\\x\leq \sqrt5 \wedge x\geq-\sqrt5\\x\in\left\langle-\sqrt5,\sqrt5\right\rangle[/tex]

For this case we must indicate the solution of the following inequality:

[tex]x ^ 2-5 \leq0[/tex]

Adding 5 to both sides of the inequality:

[tex]x ^ 2\leq5[/tex]

We apply square root on both sides of the inequality to eliminate the exponent:

[tex]x \leq\pm \sqrt {5}[/tex]

So, we have two solutions:

[tex]x\leq \sqrt {5}[/tex]

Since it is an inequality, the sign for the negative portion is changed:

[tex]x\geq- \sqrt {5}[/tex]

Answer:

[tex]x\leq \sqrt {5}\\x\geq-\sqrt {5}[/tex]

Answer:

subtraction property of equality

Step-by-step explanation:

The equation in the question is incomplete, the complete equation is:

5 + x = 2

To solve this equation we have to use the subtraction property of equality, that is, if you subtract some number at both sides of the equal sign, the equation doesn't change. So:

5 + x - 5 = 2 - 5 (You must select a number which isolate x)

x = -3

And the answer is gotten.

d

ur welcome its right