Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

Step-by-step explanation:

i) An intersecting system of linear equations

A system of linear equations comprises of two or more linear equations. Linear equations are simply straight line equations with a given slope and a unique y-intercept .

Solutions to systems of linear equations can be determined using a number of techniques among them being;

Elimination method

Substitution method

Graphical method

The graphs of a system of linear equations will intersect at a unique single point if the lines are not parallel.

An example of intersecting system of linear equations;

y = 2x -5 and y =5x + 4

The two lines will intersect at a particular single point since the slopes are not identical. The attachment below demonstrates this aspect.

ii) A parallel system of linear equations

Two lines are said to be parallel if they have an identical slope but unique y-intercepts. Parallel lines never intersect at any given point since the perpendicular distance between them is always constant.

Thus a parallel system of linear equations has no solution. An example of parallel system of linear equations;

y = 3x - 4 and y = 3x + 8

The attachment below demonstrates this aspect.

iii) A coincident system of linear equations

A system of linear equations is said to be coincident if the two straight lines are identical. That is the lines have an identical slope and y-intercept. Basically, we are just looking at the same line. Two parallel lines can also intersect if they are coincident, which means they are the same line and they intersect at every point.

Therefore, this system of linear equations will have an infinite number of solutions.

Answer: 25

Form a proportion. Let x be the missing term.

[tex]\frac{60}{144} = \frac{x}{60}[/tex]

Solve for x by cross-multiplying.

[tex]144x = 60(60)\\144x = 3600\\x = 25[/tex]

Answer:

Step-by-step explanation:

38. b. the mode would decrease

39. 4 since it is the middle point by count of x

Answer:

1)   the mean would basically decrease so its B

2) the balanced point would be 4 as the two numbers 4 and 4 come in the middle.

~batmans wife dun dun dun....

Answer:

0.22

Step-by-step explanation:

If 58% of the students play neither tennis nor baseball, then;

100 - 58 = 42% play tennis, baseball or both sports. Now,

Pr ( tennis ∪ baseball) = Pr ( tennis) + Pr ( baseball) - Pr ( tennis ∩ baseball)

42% = 40% + 24% -  Pr ( tennis ∩ baseball)

Pr ( tennis ∩ baseball) = 40 + 24 - 42

Pr ( tennis ∩ baseball) = 22%

Therefore, If you pick a student at random the probability that the student plays both tennis and baseball is 0.22

Answer:

A. he held the tube iver the flame too long

Final answer:

The cracking of the test tube could have been caused by thermal shock due to overheating one side of the test tube by holding it over the flame for too long, or by heating an empty test tube meant for containing liquids.

Explanation:

When heating substances in a test tube, such as in a chemistry lab, it's important to take certain precautions to prevent accidents, such as the cracking of the test tube. One potential cause for a test tube to crack is thermal shock, which can occur if the test tube is heated too quickly or unevenly. This brings us to option A: 'He held the test tube directly over the flame for too long'. Holding a test tube directly in the flame can cause one side to expand more rapidly than the other due to the heat, leading to stress and cracking, particularly if the glass isn't designed to withstand rapid temperature changes. To avoid this, the test tube should be moved in and out of the flame to heat it gently and evenly, and a boiling chip can be used to prevent superheating and ensure smooth boiling.

Option B suggests another possibility: 'He did not add water to the test tube'. While not adding water to a test tube might not directly cause it to crack, if the test tube was meant to contain a liquid and was instead heated while empty, the glass could become too hot and weaken, increasing the chance of breaking. It's always important to follow specific instructions for each experiment, including whether or not to add substances to the test tube.

Both scenarios emphasize the importance of careful temperature control when heating glassware to avoid breakage from thermal stress.

To solve the equation (x - 3)(x + 9) = -27, we simplified and set the quadratic equation to zero, which leads to solutions x = 0 or x = -6. We need to cross-verify this with the original equation as the student suggested different solutions.

To find a solution to the equation (x - 3)(x + 9) = -27, we can start by simplifying the left side of the equation. We'll distribute the terms:

x² + 9x - 3x - 27 = -27

Then we combine like terms:

x² + 6x - 27 = -27

To make it easier to solve, we want to set the equation to zero:

x² + 6x - 27 + 27 = 0

x² + 6x = 0

We factor out an x:

x(x + 6) = 0

Now, we can use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero:

x = 0 or x + 6 = 0

Which gives us the solutions:

x = 0 or x = -6

But the student has mentioned that the solutions are x = 3 or x = -7. To double-check, we substitute these values back into the original equation:

(3 - 3)(3 + 9) and (-7 - 3)(-7 + 9)

Both expressions simplify to an identity. Thus, there may be a mistake in our initial simplification, and we should review it to ensure accuracy.

Answer:

(-15)/3 = -5  

Step-by-step explanation:

(-15)/3

Assume that your positive tiles are yellow, and your negative tiles are red.

The question is asking, "if you take 15 red tiles and split them into three equal groups, how many will you have in each group?"

How can you model the first value of -15?  With 15 red tiles.

Let’s model how to divide the tiles into three equal groups by moving one tile at a time into three separate groups until all 15 tiles have been moved.

Step 1.

Start with 15 red tiles, as in the first picture.

Step 2.

Start by moving tiles one at a time to begin creating three new groups.

The middle picture shows the situation after you have moved the first three tiles.

Step 3.  

Continue moving tiles one at a time from the original group and stacking them evenly in the three new groups until you have no more tiles to move.  

The third picture shows the situation when you have finished.

How many red tiles are in each group?  There are five.

Is the answer positive or negative?  The answer is negative, because there are five red negative tiles in each group.

Conclusion? (-15)/3 = -5

Integers are expressions without decimals.

The result of the quotient of -15 and 3 is: -5

The expression is given as:

[tex]\mathbf{\frac{-15}{3}}[/tex]

To do this using integer tiles, we start by isolating the negative sign

[tex]\mathbf{\frac{-15}{3} = (-)\frac{15}{3}}[/tex]

Then divide 15 by 3 (see attachment for illustration of the division)

From the attached figure, we have:

[tex]\mathbf{\frac{15}{3} = 5}[/tex]

Substitute 5 for 15/3 in [tex]\mathbf{\frac{-15}{3} = (-)\frac{15}{3}}[/tex]

So, we have:

[tex]\mathbf{\frac{-15}{3} = (-)5}[/tex]

Remove bracket

[tex]\mathbf{\frac{-15}{3} = -5}[/tex]

Hence, the result of the expression is: -5

Read more about integer quotients at:

https://brainly.com/question/13733829

Answer:

B.

Step-by-step explanation:

I plugged it into a graphing calculator which got me this.

The equation that this graph represents is B. x²/3² + y²/2² = 1.

It should be noted that a graph simply means a diagram that represents the variation of variables

In this case, it's important to look at the points through which the graph passes. The y-intercept and the slope is also important.

The slope is the change in y over the change in x. By looking at the points, the equation that this graph represents is x²/3² + y²/2² = 1. This satisfies the given relation.

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ2

The formula for area of a sector is...

A = [tex]\frac{1}{2} r^{2}[/tex]θ

NOTE θ is converted from degree to radian

θ = 167 × [tex]\frac{\pi }{180}[/tex]

θ = [tex]\frac{167\pi }{180}[/tex]

so...

A = [tex]\frac{1}{2}(17.8)^{2} (\frac{167\pi }{180})[/tex]

A = (1/2)(316.84)(2.9146)

A = 158.42 * 2.9146

A = 461.7

Hope this helped!

The area of the shaded sector is A = 461.7

The formula for area of a sector is...

[tex]A = (1)/(2) r^(2)θ[/tex]

θ is converted from degree to radian

[tex]θ = 167 × (\pi )/(180)[/tex]

[tex]θ = (167\pi )/(180)[/tex]

so...

[tex]A = (1)/(2)(17.8)^(2) ((167\pi )/(180))[/tex]

A = (1/2)(316.84)(2.9146)

A = 158.42 x  2.9146

A = 461.7

Answer:

C.

Step-by-step explanation:

(m^2-m-3) + (m-4)

there is no like terms for m^2 so it stays the stay.

next you add -m to m because the first m is negative they cancel out leaving nothing. lastly we add -4+-3 these added together give you -7.

so you are left with m^2 +0 -7

which simplifies to m^2 - 7

Answer:

I need some more information

Step-by-step explanation:

..........

Answer:

Can you provide a picture/

Step-by-step explanation:

1 degree is [tex]\dfrac\pi{180}[/tex] radians. So 14 degrees is [tex]\dfrac{14\pi}{180}=\dfrac{7\pi}{90}[/tex] rad.

Easy way to remember this: one complete revolution in a circle is 360 degrees. But it's also [tex]2\pi[/tex] radians. So the conversion rate is

[tex]\dfrac{2\pi\,\rm rad}{360^\circ}=\dfrac{\pi\,\rm rad}{180^\circ}[/tex]

i.e. for every [tex]\pi[/tex] radians there are 180º.

Answer:

[tex]\large\boxed{14^o=\dfrac{7\pi}{90}\ radians}[/tex]

Step-by-step explanation:

[tex]\text{The formula for conversion of degrees to radians:}\\\\1^o=\dfrac{\pi}{180^o}\ radians\\\\x^o=\dfrac{x\pi}{180}\ radians\\\\\text{We have}\ x=14^o.\ \text{Substitute:}\\\\14^o=\dfrac{14\pi}{180}=\dfrac{7\pi}{90}[/tex]

Answer:

b I think

Step-by-step explanation:

hope that's helped

Answer:

Step-by-step explanation:

its A

Answer:

The rational function that is graphed is B

The rational function which is graphed below is:

                                Option: B

           B.   [tex]F(x)=\dfrac{x}{(x-1)(x+1)}[/tex]

From the graph of the function we see that the graph has vertical asymptote at x=1 and x= -1

The function in which above two property hold true is:

         B.   [tex]F(x)=\dfrac{x}{(x-1)(x+1)}[/tex]

( since in option: A

If denominator equal to 0 then x=0 and -1

This means that the vertical asymptotes are 0 and -1 .

In option: C

If denominator is equal to zero.

Then x=0 and 1

This means that the vertical asymptotes are 0 and 1

In option: D

When denominator=0

then x=0

This means that the vertical asymptote is at x=0

which is false )

Area of a triangle= base • height/2;

A=17•4/2= 17•2=34 ft^2

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

[tex](3+i)(4+2i)\\\\=(3)(4)+(3)(2i)+(i)(4)+(i)(2i)\\\\=12+6i+4i+2i^2\qquad\text{combine like terms}\\\\=(12-2)+(6i+4i)\\\\=10+10i[/tex]

Answer:

11 + 10i

Step-by-step explanation:

Note that we're multiplying two binomials here, and thus may use the FOIL method.  This requires four multiplications, as follows:

3*4 + 3*2i + 4i - 1               (The last term is 1 because i(i) = i^2 = -1.)

Simplifying, we get:

12 + 6i + 4i -1, or:

11 + 10i

Answer:

[tex]\large\boxed{x=\dfrac{-9\pm\sqrt{41}}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula of}[/tex]

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

[tex]\text{If}\ b^2-4a<0,\ \text{then the equation has no solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\=========================================[/tex]

[tex]\text{We have}\ x^2+9x+10=0\\\\a=1,\ b=9,\ c=10\\\\\text{substitute:}\\\\b^2-4ac=9^2-4(1)(10)=81-40=41>0\qquad _{\text{two solutions}}\\\\\sqrt{b^2-4ac}=\sqrt{41}\\\\x=\dfrac{-9\pm\sqrt{41}}{2(1)}=\dfrac{-9\pm\sqrt{41}}{2}[/tex]

Answer:

Step-by-step explanation:

Points to remember

solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given that, x² + 9x + 10 = 0.

To find the solution

Here a = 1, b= 9 and c = 10

x = [-b ± √(b² - 4ac)]/2a

 = [-9 ± √(9² - 4*1*10)]/2*1

 = [-9 ± √(81 - 40)]/2

 =  [-9 ± √(41)]/2

 = [-9 ± √41]/2

Therefore the solution of given quadratic equation  =  [-9 ± √41]/2

A. -3/8

B. -2/5, -1/2

Answer: im not even joking im trying to answer the same question rn because i have a math test tomorrow and havent done any of the unit yet

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

4x-7(x+3)=-36

Distribute

4x-7x-21=-36

Combine like terms

-3x-21 = -36

Add 21 to each side

-3x+21 = -36+21

-3x = -15

Divide by -3

-3x/-3 = -15/-3

x = 5

Answer: use photomath

Step-by-step explanation:

Answer:

This is the exact answer

Sample response: A triangular prism has a 3-sided base and 3 lateral faces. A rectangular prism has a 4-sided base and 4 lateral faces. The number of sides of the base of a prism is equal to the number of lateral faces of the prism.

Step-by-step explanation:

Answer:

A triangular prism has a 3-sided base and 3 lateral faces. A rectangular prism has a 4-sided base and 4 lateral faces. The number of sides of the base of a prism is equal to the number of lateral faces of the prism.

Step-by-step explanation:

creds to the other person

Answer:

1:3

Step-by-step explanation:

if a + b = 4a then b has to be 3a

(1) + (3) = 4(1)

(2) + (6) = 4(2)

it works no matter what you plug in for a

To find the ratio a:b given that a+b=4a, we rearrange the equation to find b=3a, and then simplify the ratio to get 1:3.

To find the ratio a:b, given that a+b=4a, we first need to express b in terms of a. This can be done by subtracting a from both sides of the equation:

a + b - a = 4a - a

b = 3a

Now that we have b expressed as 3a, we can find the ratio of a to b:

a : b = a : 3a

As we can simplify the ratio by dividing both terms by a (assuming a is not zero):

a : b = 1 : 3

Therefore, the ratio of a to b is 1:3.

Answer:

13.6

Step-by-step explanation:

I gave the same explanation on your previous question.

Answer:

The value of c is 10.9 ⇒ 3rd answer

Step-by-step explanation:

* Lets study the problem

* In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A  ⇒ BC

# b is opposite to angle B  ⇒ AC

# c is opposite to angle C  ⇒ AB

- m∠C = 68°  

- a = 8 ⇒ side BC

- b = 11 ⇒ side AC

- Find the value of c ⇒ side AB

* We have the length of two sides and the measure of the

  including angle between them and we want to find the

  length of the side opposite to this angle then the cosine

  rule is the perfect way

∵ c² = a² + b² - 2ab cos(C)

∵ a = 8 , b = 11 and m∠C = 68°

∴ c² = (8)² + (11)² -2(8)(11) cos(68°)

∴ c² = 119.069 ⇒ take √ for both sides

∴ c = 10.9 units

* The value of c is 10.9

Answer:

the range is 77.

Step-by-step explanation:

the range is 77. you calculate range by subtracting the smallest number from the biggest number.

This is your  answer feel free do double check

Answer:

[tex]y=256e^{-0.288x}[/tex]

where y is in thousands

Step-by-step explanation:

The equation in two variables that can be used to represent the situation given can be determined using computer software such Stat-Crunch or Ms. Excel or advanced calculators.

I shall use Ms. Excel for this question.

In Ms. Excel, enter the data into any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.

Excel returns a scatter-plot chart as shown in the attachment below.

After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical equation that best fits the scenario given.

Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.

Select the exponential option, since we were informed that he number of flip cell phones is in exponential decline,ensuring you check the box; Display Equation on chart.

Find the attached.

The equation in two variables is thus;

[tex]y=256e^{-0.288x}[/tex]

Answer:

the solution is (5, 6)

Step-by-step explanation:

Please reserve " × " for representing multiplication, and " x " as a variable name.

Starting with the system

6x-5y= 0  

4×-5y = -10​

multiply the 2nd equation by -1.  This results in the system

6x - 5y  = 0  

-4x + 5y = 10

and combining these two equations results in

​ 6x - 5y  = 0  

-4x + 5y = 10

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

2x         = 10, or x = 5.

Substituting 5 for x in the first equation, we get

6(5) - 5y = 0, or 5y = 30.  Then y = 6, and the solution is (5, 6).

Answer:

Step-by-step explanation:

4,3

Answer:

Step-by-step explanation:

Put z = 5 to the expression (10 + 25) ÷ z:

(10 + 25) ÷ 5 = 35 ÷ 5 = 7

Answer:

x=35

Step-by-step explanation:

These are alternate interior angles.  Since a and b are parallel, they are equal

5x - 54 = 3x+16

Subtract 3x from each side

5x-3x -54 = 3x -3x +16

2x -54 = 16

Add 54 to each side

2x-54+54 = 16+54

2x = 70

Divide each side by 2

2x/2 = 70/2

x = 35