WhWhat are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

(6, 31)
(−6, 31)
(6, −31)
(−6, −31)

Train A's unit rate is 68 km per hour.

Train B's unit rate is 75 km per hour.

The faster train is Train B.

The unit rate of the trains is equal to the average speed of the trains. The unit rate is the total distance travelled by the train per time.

The unit rate can be determined by dividing the total distance travelled by the total time travelled. The train that is faster would have a higher unit rate per time.

Unit rate = total distance / total time

The unit rate for Train A is 68 kilometers per hour. This is because this is the total distance covered in 1 hour.

d = (68 x 1) = 68 km / hr

The unit rate for Train B = 150 / 2 = 75km / hr

Train B is faster because it covers more kilometers in one hour when compared with Train A.

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Answer:

the euro is 75 € ok......

75 euros increase

Step-by-step explanation:

25% 300 is 85

Answer:

94

Step-by-step explanation:

Let the score she needs be x. Then,

[tex]\frac{81+58+95+x}{4}=82 \\ \\ 234+x=328 \\ \\ x=94[/tex]

Answer:

140°

Step-by-step explanation:

Angles ABC and CBD form a linear pair, and thus add to 180°.

Answer:-11

Step-by-step explanation:

5x+2-2=4x-9-2

5x-+2-2=4x-9-2

5x=4x-9-2

5x=4x-9-2

5x=4x-11

5x=4x-11

5x-4x=4x-11-4x

5x-4x=4x-11-4x

1x=4x-11-4x

1x=4x=11-4x

x=4x-11=4x

x=4x-11-4x

x=-11

Answer:

-11

Step-by-step explanation:

Group

[tex]5x+2-4x=4x-9-4x\\5x-4x+2=4x-9-4x\\[/tex]

Simplify

[tex]1x+2=4x-9-4x\\x+2=4x-9-4x[/tex]

Group(Again)

[tex]x+2=4x-4x-9[/tex]

Simplify it

[tex]x+2=-9[/tex]

Group(Yet again)

[tex]x+2-2=-9-2[/tex]

Simplify(Final)

[tex]x=-9-2\\x=-11[/tex]

No

Since ratios are simply proportions, they may be represented in multiple ways as long as the relationship remains equal.

Simplifying Ratios

There are 2 ways to check if these ratios are equivalent. The first is to simplify both ratios and see if they match each other. Firstly, find the greatest common factor (GCF) between the 2 numbers.

Then, divide each ratio by its GCF

Since 7:10 is not equal to 3:5, we know that these ratios are not equal. It is important to note that this method only works when both ratios have been completely simplified.

Find the Relationship as a Decimal

Another to see if 2 ratios are equivalent is to see if their relationships are equal as decimals. To find the relationship of a ratio as a decimal, simply divide the 2 numbers within a ratio.

Clearly, the ratios do not have equal relationships. Thus, the ratios are also not equivalent.

The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

What is Quadratic equation?

An algebraic equation of the second degree is called a quadratic equation.

Given that;

A quadratic equation is;

3x² = -12x - 15

Now, The equation is written as;

3x² + 12x + 15 = 0

Take 3 common, we get;

3 (x² + 4x + 5) = 0

x² + 4x + 5 = 0

Factorize the equation by using Sridharacharya Formula;

x = - 4 ± √4² - 4*1*5 / 2*1

x = -4 ± √16 - 20 / 2

x = - 4 ± √-4 / 2

Since, √-1 = i

x = -4 ± 2i / 2                            

x = - 2 ± i

It gives two values of x as;

x = - 2 + i

And, x = - 2 - i

Hence, The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

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Answer:

a

Step-by-step explanation:

A wave is a disturbance that moves along a medium from one end to the other. If one watches an ocean wave moving along the medium (the ocean water), one can observe that the crest of the wave is moving from one location to another over a given interval of time. The crest is observed to cover distance. The speed of an object refers to how fast an object is moving and is usually expressed as the distance travelled per time of travel. In the case of a wave, the speed is the distance travelled by a given point on the wave (such as a crest) in a given interval of time. In equation form,

If the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2.0 m/s. On the other hand, if the crest of an ocean wave moves a distance of 25 meters in 10 seconds (the same amount of time), then the speed of this ocean wave is 2.5 m/s. The faster wave travels a greater distance in the same amount of time.

Reflection phenomena are commonly observed with sound waves. When you let out a holler within a canyon, you often hear the echo of the holler. The sound wave travels through the medium (air in this case), reflects off the canyon wall and returns to its origin (you). The result is that you hear the echo (the reflected sound wave) of your holler.

Noah stands 170 meters away from a steep canyon wall. He shouts and hears the echo of his voice one second later. What is the speed of the wave?

In this instance, the sound wave travels 340 meters in 1 second, so the speed of the wave is 340 m/s. Remember, when there is a reflection, the wave doubles its distance. In other words, the distance travelled by the sound wave in 1 second is equivalent to the 170 meters down to the canyon wall plus the 170 meters back from the canyon wall.

Speed of a Wave Lab - Sample Data

Trial    Tension(N)   Frequency(Hz)   Wavelength(m)    Speed(m/s)

1               2.0               4.0                     54.00                16.2

2               2.0               8.03                    2.00                16.1

3               2.0              12.30                   1.33                16.4

4               2.0              16.2                     1.00                 16.2

5               2.0               20.2                    0.800               16.2

6               5.0               12.8                    2.00                 25.6

7               5.0               19.3                    1.33                 25.7

8               5.0               25.5                    1.00                 25.5

In the first five trials, the tension of the rope was held constant and the frequency was systematically changed. The data in rows 1-5 of the table above demonstrate that a change in the frequency of a wave does not affect the speed of the wave. The speed remained a near constant value of approximately 16.2 m/s. The small variations in the values for the speed were the result of experimental error, rather than a demonstration of some physical law. The data convincingly show that wave frequency does not affect wave speed. An increase in wave frequency caused a decrease in wavelength while the wave speed remained constant.

The last three trials involved the same procedure with a different rope tension. Observe that the speed of the waves in rows 6-8 is distinctly different than the speed of the wave in rows 1-5. The obvious cause of this difference is the alteration of the tension of the rope. The speed of the waves was significantly higher at higher tensions. Waves travel through tighter ropes at higher speeds. So while the frequency did not affect the speed of the wave, the tension in the medium (the rope) did. In fact, the speed of a wave is not dependent upon (causally affected by) properties of the wave itself. Rather, the speed of the wave is dependent upon the properties of the medium such as the tension of the rope.

Variables Affecting Wave Speed

What variables affect the speed at which a wave travels through a medium? Does the frequency or wavelength of the wave affect its speed? Does the amplitude of the wave affect its speed? Or are other variables such as the mass density of the medium or the elasticity of the medium responsible for affecting the speed of the wave? These questions are often investigated in the form of a lab in a physics classroom.

Suppose a wave generator is used to produce several waves within a rope of a measurable tension. The wavelength, frequency and speed are determined. Then the frequency of vibration of the generator is changed to investigate the effect of frequency upon wave speed. Finally, the tension of the rope is altered to investigate the effect of tension upon wave speed. Sample data for the experiment are shown below.

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The length of the base and height of the triangle as described in the task content are; 6cm and 3cm respectively.

It follows from the task content that the Area of the triangle is; 9 cm².

Since, Area = (1/2)b × h. where h = (b-3).

Therefore we have;

9 = (1/2)b × (b-3)

18 = b² -3b

b² -3b -18 = 0.

On this note, by solving quadratically; we have; b = 6 or b = -3.

The base of the triangle is therefore 6 as it cannot be a negative measure.

Consequently, the height, h = (b-3) = 6-3 = 3.

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Answer:

[tex]y=700x+48000[/tex]

[tex]52,200[/tex]

Step-by-step explanation:

Generally for a linear equation you use the slope-intercept form: [tex]y=mx+b[/tex]

In this form, [tex]m=\text{slope},\ b=\text{y-intercept}[/tex]

The y-intercept is just when x=0, so it can be seen as a "starting point". in this case the initial population was 48,000 so we know that: [tex]b=48000[/tex]

The slope is just how much y-changes as x increases by one, and in this case our "x" will represent how many years it's been since 2003. So the slope will represent how much the population increases each year, and this is given in the word problem as 700 people each year.

So now we have the equation: [tex]y=700x+48000[/tex]

From 2003 to 2009, 6 years have passed meaning the population is the y-value when x=6: [tex]y=700(6)+48000\\y=52,200[/tex]

The terms and coefficients of the expressions are found by taking the connectors as additions using the '+' symbol as follows;

A. 1. Terms; 12•x, 13•y, (-4•z), 2

2. Coefficients; 12, 13, -4, 2

B. The error is in not expressing the addition connecting the constant term.

C. The coefficient is 1

A term in an expression are the parts of the expression that are connected together using addition or subtraction

A coefficient is the number multiplying a variable within a term of the expression

Therefore;

A. The expression 12•x + 13•y - 4•z + 2, can be written as follows;

12•x + 13•y - 4•z + 2 = 12•x + 13•y + (-4•z) + 2

The terms of the given expression 12•x + 13•y - 4•z + 2, which is the same as 12•x + 13•y + (-4•z) + 2, are therefore;

1. Terms; 12•x, 13•y, (-4•z), 2

The coefficients are;

2. Coefficients; 12, 13, -4, 2

B. The given expression is 9•a + 4•b - 18

Writing the subtractions as additions, to indicate the signs of the coefficient gives;

9•a + 4•b - 18 = 9•a + 4•b + (-18)

The terms are therefore; 9•a, 4•b, and (-18)

C. The expression, b + 10, has only one variable, which is b, the coefficient of the expression is therefore the coefficient of b, which is 1.

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Answer:

Step-by-step explanation:

                                       Functions used:

[tex]\displaystyle\\\boxed {(\frac{u}{v})'=\frac{u'v-v'u}{v^2} }\ \ \ \ \ \boxed {(u+v)'=u'+v'}\ \ \ \ \ \boxed {(x^n)'=n*x^{n-1}}[/tex]

[tex]\displaystyle\\f(x)=\frac{x}{x^4-5} \\\\f'(x)=(\frac{x}{x^4-5})'\\ f'(x)=\frac{x'(x^4-5)-(x^4-5)'x}{(x^4-5)^2} \\\\f'(x)=\frac{1(x^4-5)-((x^4)'-5')x}{(x^4-5)^2}\\\\f'(x)=\frac{x^4-5-(4x^3-0)x}{(x^4-5)^2} \\\\f'(x)=\frac{x^4-5-(4x^3)x}{(x^4-5)^2}\\\\f'(x)=\frac{x^4-5-4x^4}{(x^4-5)^2} \\\\f'({x)=\frac{-3x^4-5}{(x^4-5)^2} \\\\[/tex]

[tex]\displaystyle\\f'(x)=\frac{-(3x^4+5)}{(x^4-5)^2} \\\\f'(x)=-\frac{3x^4+5}{(x^4-5)^2}[/tex]

The value of

x = 1/9

y = 1/63

We have given two equations :

   1/x - 1/3y = -12   ... eq. (1)

- 4/5x + 7y = -1/5    ... eq. (2)

First we will multiply the 1st equation by 4/5,

We get, 4/5x - 4/15y = -48/5   ... eq. (3)

Now, we will add the equation 3 and equation 2

     4/5x - 4/15y = -48/5

   - 4/5x + 7y     = -1/5

____________________

          7y - 4/15y = -49/5

     (105y - 4)/15y = -49/5

              105y - 4 = (-49/5) × 15y

              105y - 4 = -49 × 3y = -147y

        105y + 147y = 4

                         y = 4/252

                        y = 1/63

We get the value of  y which is 1/63,

Now, we will solve the eq. 1 by putting  is equal to 1/63.

                      1/x - 1/3y = -12

        1/x - (1 × 63/3 × 1) = -12

                          1/x -21 = -12

                                1/x = 21 - 12 = 9

                                 x = 1/9

Hence, we get the value of x and y as 1/9 and 1/63 respectively.

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The football team's total payroll is B. 2.5753 x [tex]10^{11}[/tex] dollars more than the baseball team's total payroll.

Option B is the correct answer.

We have,

To find how many more dollars the football team's total payroll is than the baseball team's total payroll, we need to subtract the baseball team's total payroll from the football team's total payroll.

Football team's total payroll = 2.6 x 10^11 dollars

Baseball team's total payroll = 2.47 x 10^9 dollars

Difference = Football team's total payroll - Baseball team's total payroll

Difference = [tex](2.6 \times 10^{11}) - (2.47 \times 10^9)[/tex]

To subtract these numbers, we need to make sure they have the same exponent:

2.47 x [tex]10^9[/tex] dollars = 0.247 x [tex]10^{10}[/tex] dollars

(move the decimal one place to the right)

Now, subtract:

Difference = (2.6 x  [tex]10^{11}[/tex]) - (0.247 x [tex]10^{10}[/tex])

Difference = 2.5753 x [tex]10^{11}[/tex] dollars

Thus,

The football team's total payroll is B. 2.5753 x [tex]10^{11}[/tex] dollars more than the baseball team's total payroll.

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The equation of the parabola is : y = -6x² + 13x + 2

The general equation for parabola is -

y = ax² + bx + c. We will keep the values of x and y in this equation, to find the coefficients. Once we get the coefficients, again this equation will be used to find the equation of parabola based on given points.

For the point (1, 9)

9 = a(1)² + b(1) + c

9 = a + b + c : equation 1

For the point (2, 4)

4 = a(2)² + b(2) + c

4 = 4a + 2b + c : equation 2

For the point (4, -30)

-30 = a(4)² + b(4) + c

-30 = 16a + 4b + c : equation 3

Subtract equation 2 from equation 1

9 = a + b + c

-4 = 4a + 2b + c

We get: 5 = -3a -b

Rearranging the equation: 3a + b = -5 : equation 4

Subtraction equation 2 from equation 3

-30 = 16a + 4b + c

-4 = 4a + 2b + c

We get: -34 = 12a + 2b : equation 5

Multiplying equation with 2

6a + 2b = -10 : equation 6

Subtract equation 6 from equation 5

12a + 2b = -34

-6a + 2b = -10

6a = -24

a = -6

Keep value a in equation 6 to find the value of b

6(-6) + 2b = -10

-36 + 2b = -10

2b = 36 - 10

2b = 26

b = 13

Keep the value of a and b in equation 1 to find the value of c

-6 + 13 + c = 9

c = 9 - 7

c = 2

Keeping all the coefficients in general equation to find the equation of parabola -

y = -6x² + 13x + 2

Hence, the equation of parabola is : y = -6x² + 13x + 2

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The inverse of the given function f(x) = 3x + 1 is f⁻¹(x) = x/3 - 1/3.

Given the function in the question;

f(x) = 3x + 1

To determine the inverse of the function, write f(x) as y.

f(x) = 3x + 1

y = 3x + 1

Now, interchange the variable

x = 3y + 1

Solve for y by subtracting 1 from both sides

x = 3y + 1

x - 1 = 3y + 1 - 1

x - 1 = 3y

Reorder

3y = x - 1

Divide both term in the equation by 3

3y/3 = x/3 - 1/3

y = x/3 - 1/3

f⁻¹(x) = x/3 - 1/3

Therefore the inverse of the given function f(x) = 3x + 1 is f⁻¹(x) = x/3 - 1/3.

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42 cans each 1.5 litres in capacity can be filled from a tank containing 63 litres of water.

Given, the capacity of each can is 1.5 litres and the tank holding 63 litres of water. We have to find the number of cans that can be filled from the tank containing 63 litres of water.

Let x number of cans can be filled from the tank containing 63 litres of water having each 1.5 litres in capacity, we have

x = 63/1.5

x = 630/15

x = 42

∴ The required answer is 42.

Hence, 42 cans each 1.5 litres in capacity can be filled from a tank containing 63 litres of water.

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They have to carry 15.5 kg.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Piloncillo   14 kg

Tejocote    1½ kg-

Apple         2¾ kg

oldestq         3

Guava         0.75 kg

Plum            1.75 kg

Cane           2.40 kg

Cinnamon      ½ kg

So, if they take piloncillo and the tejocote

they carry,

=14 + 1 1/2

=14 + 3/2

=14 + 1.5

=15.5 Kg

Hence, they have to carry 15.5 kg.

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The complete and translated question is

My mom and I, yesterday we went to the supermarket and

we bought

punch

following items:

everything you need to make the

Christmas, and we bought the

Piloncillo 14 kg

Tejocote 1½ kg-

Apple 2¾ kg

oldestqx3

Guava 0.75 kg

Plum 1.75 kg

Cane 2.40 kg

Cinnamon ½ kg

If my mom took the piloncillo and the tejocote,

How many kilos did I carry in total?

13

Answer:

Step-by-step explanation:

its e223r252t23t22t.2t23t'23.t'2.t'2.t'2.t2't.23't.2't.32'.t2'.trfff i think

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]\cfrac{3x+2y}{5}=1\implies 3x+2y=5\implies 2y=-3x+5 \\\\\\ y=\cfrac{-3x+5}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}} x+\cfrac{5}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so then, a perpendicular line to that will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3}\implies \cfrac{2}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is 2/3 and it passes through (-9 , -9)

[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-9)}) \implies y +9= \cfrac{2}{3} (x +9) \\\\\\ y+9=\cfrac{2}{3}x+6\implies y=\cfrac{2}{3}x-3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( \cfrac{2}{3}x-3 \right)}[/tex]

[tex]3y=2x-9\implies -2x+3y=-9\implies 2x-3y=9 \\\\\\ 2x-3y=(9)(1)\implies {\LARGE \begin{array}{llll} \cfrac{2x-3y}{9}=1 \end{array}}[/tex]

Answer:

76.83

Step-by-step explanation:

its like 1 plus 1 equals 2 you add the amount of salt present beforehand in the bowl and the one you've added together the sum would equate to 76.73

Answer:

Third choice
x < -2; y ≤ -x -2

Step-by-step explanation:

The dotted vertical line passing through x = 2 shows it is a < inequality corresponding to x < -2. If it were a ≤ inequality, then it would be a solid vertical line

That eliminates the first two choices. Second choice is x < -3 which is not correct because we can see that the shaded region includes everything below x = -2 not below x = -3. For example, x = -2.5 is in the shaded region

So we have to choose between the third and fourth choices. Note that the line equation for choice 3 is y = -x -2 and for choice 4 it is y = -x +2

Choose (x, y) = (-3, 0)

choice 3
y ≤ -x -2
Substitute x with -3 in -x + 2 giving
-(-3) -2 = 3 - 2 = 1

Point(-3,1) lies on the line and therefore does satisfy the second inequality

choice 4
y ≤ -x + 2
Substitute x with -3 giving

-x + 2 = -(-3) + 2 = 3 + 2 =5
But (-3, 5) is not on the line. In fact, it is outside the shaded region so it does not satisfy the second inequality

So the correct choice is the third choice
x < -2, y ≤ -x -2

Answer:

See below

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

Answer: 6

2 x3 =6

Step-4by-step explanation:

Answer:

m = 15

Step-by-step explanation:

Given equation,

→ 3m = 45

Solving for the value of m,

→ 3m = 45

→ m = 45/3

→ [ m = 15 ]

Hence, the value of m is 15.

Answer:

15

Step-by-step explanation:

3m=45 divide both sides by 3 and 45 by 3 is 15 thats the answer

Answer:

12

Step-by-step explanation:

If the perimeter is 56, then 2(W+L) = 56.

If the length is 4 more than the width, then we can write the length as

Width+4 = L or W+4=L

Now, we can plug this back into the equation of 2(W+L)= 56

2(W+(W+4)) = 56

2(2w+4) = 56

4w+8=56

Minus 8 on both sides of the equation

4w = 48

divide both sides by 4

w = 12

Answer: 160 L

Step-by-step explanation:

There is 24 weeks in 6 months. 6x4= 24

24 weeks divided by 3 (the amount of weeks Danny’s family consumes 20L of milk). You end up with 8 weeks.

Then multiple 8 weeks time the 20 L.