Solve for x. 9x + 2 = 5x + 22

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Plug x = -5 into f(x)

f(x) = 2x-20

f(-5) = 2(-5) - 20

f(-5) = -10-20

f(-5) = -30

Then plug x = -5 into g(x)

g(x) = x-1

g(-5) = -5-1

g(-5) = -6

Divide the two results

(f/g)(-5) = f(-5)/g(-5)

(f/g)(-5) = (-30)/(-6)

(f/g)(-5) = -5

For this case we have the following functions:

[tex]f (x) = 2x-20\\g (x) = x-1[/tex]

We must find [tex]\frac {f (-5)} {g (-5)}[/tex], then:

We have in mind that:

[tex]+ * - = -[/tex]

Equal signs are added and the same sign is placed.

[tex]\frac {f (-5)} {g (-5)} = \frac {2 (-5) -20} {- 5-1} = \frac {-10-20} {- 6} = \frac {-30} {- 6} = 5[/tex]

Answer:

5

Answer:

A. A translation right 2 units:

We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation right 2 units would be:

g(x) = f(x-2).

B. A translation left 2 units:

We know that given f(x), the function g(x) = f(x+m), is the same function f(x) but shifted m units to the left. In that sense, a translation left 2 units would be:

g(x) = f(x+2).

C. A translation up 2 units:

We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation up 2 units would be:

g(x) = f(x) + 2

D. A translation down 2 units:

We know that given f(x), the function g(x) = f(x) + m, is the same function f(x) but shifted m units up. In that sense, a translation down 2 units would be:

g(x) = f(x) - 2

Final answer:

The function f(x) translated to g(x) via a translation right 2 units, which shifts the graph of the function 2 units to the right on the x-axis.

Explanation:

The transformation that transformed the parent function, f(x), to g(x) is a translation right 2 units. This is because when the argument of the function f(x) becomes f(x-2), the graph of f(x) is shifted to the right by 2 units along the x-axis. To understand this, let us consider the original function y = f(x).

The graph of the new function y = f(x-2) is the same as the original, but every point on the graph has been moved 2 units to the right. This can also be viewed as if the x-axis (and origin) has shifted 2 units to the left while the graph remains stationary.

The answer is:

She needs to buy 3 spindles of 60 CDS and 2 spindles of 25 CDs.

We know that the possibilities will depend always on how many CDs contain each type of spindles.

There is only one possible combination of spindles that can give the exact amount of CDs needed.

Let's try to find the combinations:

- First combination: With 1 spindle of 60 CDs:

[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-60}{25}=\frac{170}{25}=6.8Spindles[/tex]

Since the result is not a whole number, we know that the first combination does not work.

- Second combination: With 2 spindles of 60 CDs:

[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(2)*60}{25}=\frac{110}{25}=4.4Spindles[/tex]

Since the result is not a whole number, we know that the second combination does not work.

- Third combination: With 3 spindles of 60 CDs:

[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(3)*60}{25}=\frac{230-180}=\frac{50}{25}=2Spindles[/tex]

Since the result is a whole number, we know that the third combination works.

Hence, the combination will be:

[tex]TotalCDs=3Spindles_{60}+2Spindles_{25}=3*60+2*25=180+50=230[/tex]

She needs to buy 3 spindles of 60 CDs and 2 spindles of 25 CDs.

Have a nice day!

Answer:2 of 25 cds 3 of 60 cds

Step-by-step explanation:

1. 3x60=180

2.2×25=50

3. So for science class she needs quality 2 of 25

4. Quality of 3 of 60

So there u go

Answer:

Answer = 3.14 * 40 = 125.6m^2

Step-by-step explanation:

Let R be the greater radius and r be the smaller radius

A) Area of the sidewalk =  \pi R^2 -  \pi r^2   - This can be the expression

B)  pi  = 3.14  

= pi (R^2-r^2)

= pi (11^2-9^2)

= pi (121-81)

= pi *40

That was the simplified expression

Answer = 3.14 * 40 = 125.6m^2

To find the midpoint, add the two X values together and divide that by 2 and then add the two Y values together and divide by 2.

X = 8 +3 = 11 /2 = 5.5

Y = 5 +7 = 12 /2 = 6

Depending on how you need to answer the midpoint for X could stay the fraction 11/2, or you can divide it and get 5.5

The midpoint is (11/2,6) or (5.5,6)

Answer:

nope

Step-by-step explanation:

Answer:

The answer is both a and b

Answer:

both a and b is correct

Answer:

$420

Step-by-step explanation:

Principal = $7000

Rate = 8%

Time = 9 months

9 months = 3/4 or 0.75 of a year

Simple Interest = Principal * Rate * Time ÷ 100

= $7000 * 8% * 0.75 ÷ 100

= $420

Answer:

The answer to this is 0.25

Step-by-step explanation:

7/12= 0.58333 repeating, and 1/3 is 0.3333 repeating. When you subtract 7/12 from 1/3 you get 0.25

Hope it helps

Answer:

0.25

Step-by-step explanation:

I am going to assume that you mean:

x² < 49

To solve this you must do the opposite of squaring, which would be taking the square root. What you do to one side you must do to the other.

√x² < √49

x < 7

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

To solve the inequality x^2 < 49, we take the square root of both sides resulting in the solution -7 < x < 7, which means x can be any real number between -7 and 7.

Explanation:

The student's question is about solving an inequality involving a square of a variable, specifically x^2 < 49. To solve this inequality, we will first take the square root of both sides, keeping in mind that when we take the square root of a square inequality, we must consider both the positive and negative roots. Therefore, we can express the inequality as -7 < x < 7, since both positive and negative square roots of 49 are 7 and -7, respectively. This represents the range of values for x where the original inequality holds true.

The solution implies that x can take on any real value that is less than 7 and greater than -7. There's no need for tools like completing the square or the quadratic formula here, as the inequality is already in a solvable form.

Answer:

C. (-5,-4,-3,1,2,5) From the graph we can see the following points first come x-axis and Y-axis like (x, y). From graph we can see 6 points they are (-5,6),(-4,1),(-3,4),(2,4),(1,-2),(5,-3) Here the first no. is the domain like in (-5,6). -5 is domain and 6 is range so all the first no. of the points is in option C so it is the domain.

Note: The volume of a cylinder is:

radius² × π × height

First lets work out the volume of Cylinder A:

Volume = 1² × π × 4

             = 4π  m³

Now lets work out the volume of Cylinder B

Volume = 2² × π × 4

             = 16π  m³

__________________________________________

Now lets compare the volumes ( Cylinder A : Cylinder B)  :

4π : 16π

Lets simplify this by dividing both sides by 4π:

     4π : 16π            ( ÷ 4π)

----> 1 : 4        

_____________________________________________________

Answer:

Option b) 1 : 4

Answer:

1:4

Step-by-step explanation:

The number line represents the solution to the inequality -2x + 7 > 8, and the solution is x < -0.5.

The filled circle and the arrow pointing left on the number line indicate that the solution to the inequality is to the left of -2.

The inequality that represents this solution is -2x + 7 > 8.

To solve this inequality, we can subtract 7 from both sides to isolate the x variable.

This gives us -2x > 1. Finally, we divide both sides of the inequality by -2, remembering that when we divide by a negative number, the inequality sign flips.

So, the solution to the inequality is x < -0.5.

Thus, Correct option for the given number line is F. -2x + 7 > 8.

Final answer:

The number line indicates the solution to the inequality H. 6x - 9 < -21, where x < -2, including -2 (since the circle is filled). The solution matches the given number line plot.

Explanation:

The number line given indicates the solution to an inequality that includes all numbers to the left of – the filled circle on –2, which means –2 is included in the solution set. This represents an inequality that is of the form x ≤ a where a is –2 in this case. Now let's analyze each of the provided inequalities.

F. -2x + 7 > 8: Solving this we get –x > 1 or x < –1, which does not match the plot.

G. 7x + 11 < 4: Solving this inequality we get x < –1, which also is not a match.

H. 6x - 9 < -21: Resolving this inequality leads to x < –2, which matches the number line.

J. -3x - 15 < -27: Solving this we get x > 4, which is incorrect as per the number line plot.

Therefore, the correct inequality is H. 6x - 9 < -21.

For this case we have a quadratic equation given by:

[tex]4x ^ 2 + 2x-1 = 0[/tex]

The roots are found by means of the quadratic formula below:

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

Where:

[tex]a = 4\\b = 2\\c = -1[/tex]

So, we have:

[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]

Or in an equivalent way we have:

[tex]x = \frac {-2 \pm \sqrt {2 ^ 2 + 4 (4) (1)}} {2 (4)}[/tex]

Answer:

The correct option will be:

[tex]x = \frac {-2 \pm \sqrt {2 ^ 2-4 (4) (- 1)}} {2 (4)}[/tex]

Answer:

a = 4, b = 2 and c= -1

Step-by-step explanation:

Quadratic formula: x =√[-b ± v(b² - 4ac)]/2a

Here quadratic equation is  4x2 + 2x – 1

a = 4, b = 2 and c= -1

x =[-b ± √(b² - 4ac)]/2a

 = [-2 ± √(2² - 4*4*-1)]/2*4

 = [-2 ± √(4  + 16)]/8

 = [-2 ± √20)]/8

 = [-2 ± 2√5)]/8

 =  [-1 ± √5)]/4

x = [-1 ± √5)]/4

Answer:

horizontal line

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through.

Hence

y = - 1 is a horizontal line passing through all points with a y- coordinate - 1

Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

To obtain this form use the method of completing the square.

Given

x² + y² - 6x + 14y = 142

Collect the x and y terms together

x² - 6x + y² + 14y = 142

add (half the coefficient of both x and y terms )² to both sides

x² + 2(- 3)x + 9 + y² + 2(7)y + 49 = 142 + 9 + 49

(x - 3)² + (y + 7)² = 200 → A

Answer:

y = (5/6)x - 7

is with

y = - (6/5)x + 1

y = - (5/6)x - 8

is with

y = (6/5)x - 5

y = - (7/4)x - 1

is with

y = (4/7)x + 9

y = (7/4)x - 2

is with

y = - (4/7)x + 2

Step-by-step explanation:

You can double check by dividing -1 by the number before x. The answer from that calculation will be the number before the x of the perpendicular line's equation

pair with their perpendicular equations are

y = - (6/5)x + 1

y = (6/5)x - 5

y = (4/7)x + 9

y = - (4/7)x + 2

The given line is perpendicular to the required line under the condition of perpendicular lines m1×m2=–1.

As, m1*m2=-1

m1= -1/m2

For first equation

y = (5/6)x - 7

m1= 5/6

So, m2= -1/m2= -6/5

Hence, the equation of perpendicular line is y = - (6/5)x + 1.

Similarly,

y = (5/6)x - 7

m1= 5/6

So, m2= -1/m2= -6/5

Hence, the equation of perpendicular line is y = (6/5)x - 5.

again,

y = - (7/4)x - 1

m1=-7/4

So, m2= -1/m2= 7/4

Hence, the equation of perpendicular line is y = (4/7)x + 9

again,

y = (7/4)x - 2

m1= 7/4

So, m2= -1/m2= -4/7

Hence, the equation of perpendicular line is y = - (4/7)x + 2.

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Looking at the given points on the right side from (0,2) to (1,6) for 1 increase in X ( 1-0=1) the Y value increases by 3 ( 6/2 = 3)

This same increase happens for th other two points: 18/6 = 3

54 / 18 = 3

The rate of increase is 3.

[tex]\sqrt[3]{b^{27}}=\sqrt[3]{(b^9)^3}=b^9[/tex]

Answer:

Step-by-step explanation:

note :

the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :

Δ = b² -4ac

1 )  Δ > 0  the equation has two reals solutions : x =  (-b±√Δ)/2a

2 ) Δ = 0 : one solution : x = -b/2a

3 ) Δ < 0 : no reals solutions

in this exercice : 4x²-30x+45=0

a= 4    b= -30  c=45

Δ = (-30)² - 4(4)(45) = 900 - 720 = 180.......continu

Answer:

I'm pretty sure if you subtract 2 from eight you will find the answer of 6 i'm not sure if that question was implying this answer but I hope this helps

Step-by-step explanation:

Answer: 372in³

Step-by-step explanation:

All we have to do is find the volume of the two separate rectangular prisms and add them up.

First we will find the volume of the standing prism:

5in * 3in * 12in = 180in³

Now the other prism:

12in * 4in * 4in = 192in³

Now add them up:

180in³ + 192in³ = 372in³

Answer:

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

Step-by-step explanation:

Imagine the figures are each separate. The top figure's dimensions would be L=12 in, W=4 in, and H=4 in. The bottom figure's dimensions would be L=5 in, W=3 in, and H=12 in. So, do the volume formula for each: L x W x H and then add them together.

12 x 4 x 4 = 192 inches^3

5 x 3 x 12 = 180 inches^3

192 + 180 = 372 inches^3

Answer:

B

Step-by-step explanation:

For this case we must find the product of the following expression:

[tex](n ^ 3) ^ 2 * (n ^ 5) ^ 4[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Rewriting the expression we have:

[tex]n ^ 6 * n ^ {20} =[/tex]

By definition of multiplication of powers of the same base, we put the same base and add the exponents:

[tex]n^{6 + 20} =\\n^{26}[/tex]

Answer:

[tex]n^{26}[/tex]

Answer:

n^26

Step-by-step explanation:

To create a dot plot, you draw a number line from the smallest to the largest value in your dataset. Then, for each number in the dataset, mark a dot above the corresponding number on the line. If a number occurs more than once, stack the dots.

Creating a dot plot for a set of data on a number line involves the following steps:

Unfortunately, as this is a text-based platform, it's impossible to hover over the numbers and drag to create a dot plot interactively. This instruction seems to be meant for a specific interactive software or online tool.

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Answer:

B y=54 degrees

Step-by-step explanation:

Since a triangle's angles always add up to 180.

180-72=108

108/2=54

It must be divided by two because y is two angles not one.

Answer: FALSE

Step-by-step explanation:

The first step is to rewrite the equation in the form [tex]ax^2+bx+c=0[/tex], then:

[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]

Now, we need to calculate the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

We can identify in the given equation that:

[tex]a=3\\b=-6\\c=9[/tex]

Then, we only need to substitute these values into the formula:

 [tex]D=(-6)^2-4(3)(9)[/tex]

 [tex]D=-72[/tex]

Since [tex]D<0[/tex] then the equation has no real solutions.

Answer:

Infinitely many solutions.

Step-by-step explanation:

2 (n - 1) + 4n = 2 (3n - 1) Let's simplify this to solve it.

2n - 2 + 4n = 6n - 2 Distribute 2(n-1) and 2(3n-1)

2n + 4n - 2 = 6n - 2 Rearrange the left side of the equation.

6n - 2 = 6n - 2 Add 2n + 4n.

-6n        -6n Subtract 6n from both sides.

-2 = -2? Yes, -2 equals -2.

Therefore, the answer is infinitely many solutions, meaning that n can be any real number.

An equation can have no solution, one solution or infinitely many solutions.

The equation [tex]2(n -1) + 4n = 2(3n - 1)[/tex] has infinitely many solutions

Given that:

[tex]2(n -1) + 4n = 2(3n - 1)[/tex]

Open brackets

[tex]2n -2 + 4n = 6n - 2[/tex]

Collect like terms

[tex]2n + 4n - 6n= - 2+2[/tex]

[tex]0 = 0[/tex]

When the solution to an equation is 0 on both sides, the equation has infinitely many solutions

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Answer:

The total number of copy rooms in the building is 9.

Step-by-step explanation:

With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).

From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:

[tex]n = 6 \cdot r + 7[/tex]

From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:

[tex]n = 7 \cdot r - 2[/tex]

From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:

[tex]6 \cdot r + 7 = 7 \cdot r - 2[/tex]

Puting known and unknowns on opposite sides, we get:

[tex]7+2 = (7-6) \cdot r [/tex]

Solving we get:

[tex]9 = r[/tex]

Therefor the total number of rooms is 9.

Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.

As a reference, the following link is useful:

https://en.wikipedia.org/wiki/System_of_linear_equations

The number of boxes of paper exists at 61.

The whole number of copy rooms as r and the boxes of paper Reginald has to distribute among them (already named [tex]$\mathbf{n}$[/tex] ).

Reginald gives 6 boxes of paper to each room, he will always have 7 boxes. We can write this as:

[tex]$n=6 \cdot r+7$$[/tex]

Reginald shows 7 boxes of paper to each room, he would always require 2 boxes. We can write this as:

[tex]$n=7 \cdot r-2$$[/tex]

From the above equation, we have a [tex]$2 \times 2$[/tex] system of equations, which can be solved in any form. In this issue, we can utilize equalization to easily find the number of rooms.

From the 2 relations we can write:

[tex]$6 \cdot r+7=7 \cdot r-2$[/tex]

Putting known and unknowns on opposite sides, we get:

[tex]$7+2=(7-6) \cdot r$$[/tex]

Solving we get:

[tex]$9=r$$[/tex]

Thus the total number of rooms exists at 9.

Plugging this solution into any of the 2 equations, then we get

The number of boxes of paper exists at 61.

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Answer:

Vertical angles must have the same vertex and be congruent as well.

Step-by-step explanation:

Answer:

Correct answer is B and C.

Step-by-step explanation:

Vertical angles are those angles opposite each other when two lines intersect. So, they have the same vertex.

When two lines intercept form 4 angles. Those that are opposite to each other are vertical angles, these angles are always congruent.

Check the picture below.

notice the alternate interior angles in the picture.

[tex]\bf tan(68^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{x}}\implies x=\cfrac{1.5}{tan(68^o)}\implies x\approx 0.61 \\\\[-0.35em] ~\dotfill\\\\ tan(56^o)=\cfrac{\stackrel{opposite}{1.5}}{\stackrel{adjacent}{w}}\implies w=\cfrac{1.5}{tan(56^o)}\implies w\approx 1.01 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{width of the crater}}{x+w\implies 1.62}~\hfill[/tex]

The width of the crater is 1.61 km.

Plane is flying at altitude of  1.5 km

The angle of depressions to point A = 68 degrees/

The angle of depression to point B = 56 degrees.

In the given diagram below, we can see:

Angle XPD is right angle and thus we have:

[tex]\angle APD + \angle APX = 90\\\angle APD = 180 - \angle APX = 90 - 68 = 22^\circ[/tex]

Similarly, Angle  YPD is right angle and thus:

[tex]\angle DPB + \angle BPY = 90\\\angle DPB = 90 - \angle BPY = 90 - 56 = 34^\circ[/tex]

Since the triangle ADP and triangle  PDB  are right angled triangles, thus we have by trigonometric ratios:

[tex]tan(22) = \dfrac{AD}{PD}\\\\0.404 \times 1.5 = AD\\\\AD = 0.606\: \rm km[/tex]

Similarly,

[tex]tan(34) = \dfrac{BD}{PD}\\\\0.674 \times 1.5 = BD\\\\BD = 1.01 \: \rm km[/tex]

The width of the crater = AD + DB = 1.01 km + 0.606 km  = 1.61 km

Thus, width of the crater is 1.61 km.

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