Use completing the square to rewrite y=x^2+4x-13 in vertex form. Identify the maximum or minimum value.

Answer:

[tex]C =8t+16\\7\ hours[/tex]

Step-by-step explanation:

Given that, Fixed charge = $16

Per hour charge for renting the bike = $8/hour

To find:

If Matt paid $72 to rent a bike, for how many hours did he rent the bike?

Solution:

Let 't' be the time for which Matt rents the bike.

1 hour charge for the bike rent = $8

't' hour charge for the bike rent = $8 [tex]\times t[/tex]

Total Charge for the bike = Charge for renting the bike for t hours + fixed charge

Let 'C' be the total charge, so the equation becomes:

[tex]C = 8t + 16[/tex]

Given that C is $72, we need to find t:

[tex]72 = 8t+16\\\Rightarrow 8t=72-16\\\Rightarrow 8t=56\\\Rightarrow t = 7\ hours[/tex]

So, he rented the bike for 7 hours.

The equation is: [tex]C = 8t + 16[/tex]

50x30x9x70jssjgsvebdghxhdbgd

Answer:

Step-by-step explanation:

(5 * 10³) * (9*10⁷) = 5*9 * 10³⁺⁷

                          = 45 * 10¹⁰

                          = 4.5 * 10¹¹

(7*10⁵)÷ (2*10²) =

                         [tex]\frac{7}{2}*10^{5-2}\\\\=3.5*10^{3}[/tex]

Answer:

a = -1

b = 1

Step-by-step explanation:

Step 1: Isolate x's

x² + 2x = -2

Step 2: Complete the Square

x² + 2x + 1 = -2 + 1

(x + 1)² = -1

Step 3: Move everything to 1 side

(x + 1)² + 1 = 0

And we have our answer.

Answer:

A=1 and b=1

Step-by-step explanation:

Answer:

12 years

Step-by-step explanation:

Let's say the number of years we're looking for is x.

Nova's age: 33+x

Mia's age: 18+x

and of course: 33+x = 3/2 * (18+x)

This is an equation you can solve.

33+x = 3/2 x + 27

x - 3/2 x = 27-33

1/2 x = 6

x = 12

Answer:

No, This is not necessary

Step-by-step explanation:

She is not correct because there are some number which on square have a result smaller than the actual number.

Let me make you more clear by the following example:

=> The number 0.5 on squaring becomes 0.25

And 0.25 is less than the actual number 0.5.

Answer:

UV and VW

Step-by-step explanation:

Those are the points of the angles adjacent to the highlighted angle

Answer:

Comprobar explicación

Check Explanation

Step-by-step explanation:

Los números negativos son números menores que 0. Son muy importantes en la naturaleza y en cualquier trato con los números. Por lo general, se escriben con un signo menos delante de ellos.

Las situaciones en las que el uso de números negativos son absolutamente necesarios incluyen

1) En los negocios, los números negativos se utilizan para indicar la deuda y la salida de efectivo.

2) En los circuitos eléctricos, se usan números negativos para describir el voltaje nominal cuando se invierten las polaridades de la batería.

3) En mediciones de temperatura para indicar temperaturas inferiores al punto de congelación del agua, especialmente en la escala Celsius (0°C).

4) Para indicar profundidades debajo del nivel del mar. El nivel del mar generalmente se designa como nivel 0 en términos de elevación.

5) En la numeración de los pisos debajo de la planta baja para un edificio alto.

6) En el análisis económico general, se utilizan para indicar una disminución de la economía, el PIB del país o un déficit en el presupuesto.

- En el análisis matemático general, los cálculos y las manipulaciones, los números negativos se usan ampliamente y son muy importantes.

- En química, los números negativos se utilizan para indicar la carga en los aniones (iones negativos).

¡¡¡Espero que esto ayude!!!

English Translation

6 situations in which the use of negative numbers is necessary.

Solution

Negative numbers are numbers that are lesser than 0. They are very important in nature and in any dealings with numbers. They are usually written with a minus sign in front of them.

The situations in which the use of negative numbers are absolutely necessary include

1) In business, negative numbers are used to indicate debt and outflow of cash.

2) In electrical circuits, negative numbers are used to describe the rated voltage when the polarities of the battery are reversed.

3) In temperature measurements to indicate temperatures lesser than the freezing point of water especially on the Celsius scale (0°C).

4)To indicate depths below the sea level. The sea level is usually designated to be 0 level in terms of elevation.

5) In the numbering of the floors below the ground floor for a tall building.

6) In general economic analysis, they are used to indicate a decline in the economy, country's GDP or deficit in budget.

- In general mathematical analysis, calculations and manipulations, negative numbers are used very extensively and are very important.

- In chemistry, negative numbers are used to indicate the charge on anions (negative ions).

Hope this Helps!!!

Answer:

(-3, -3)

Step-by-step explanation:

1.) Rewrite the second equation so 3y is on one side of the equation:

3y=6+5x

2.) Substitute the given value of 3y (replacing 3y with 6+5x, since we know they equal each other) into the equation 17x=-60-3y

Should end up with this:

17x=-60-(6+5x)

3.) Solve 17x=-60-(6+5x)

Calculate Difference: 17x=-66-5x

Combine Like Terms: 22x = -66

Divided both sides by 22 to isolate and solve for x: -3

So We know x=-3, now we got to find the y value. We can use either the first or second equation to find y value, so lets use the second.

3y=6+5x

1.) We know that x=-3, so we can simply substitute x in the equation

3y=6+5x with -3

3y=6+5(-3)

2.) Solve 3y=6+5(-3)

Combine Like Term: 3y=6+-15

Combine Like Term Even More: 3y= -9

Divide by 3 on both sides to isolate and solve for y: y=-3

So now we know y=-3 and once again we know x=-3, so if we format that

(-3,-3)

^  ^

x  y

Answer:

D. Cost

Step-by-step explanation:

In a scatter diagram we have that the x axis corresponds to the explanatory variable or also called the independent variable, since it is the value that is entered in the equation and does not depend on another.

While the y-axis corresponds to the response variable or also called the dependent variable since it is the value of the result of the equation

In this case, the explanatory variable is weight, that is, on the x-axis the weight would go and the cost is the response variable and would go on the y-axis, therefore, the answer is D. Cost

Answer:

4(7+3)

Step-by-step explanation:

28 and 12 are both divisible by 4.

28 ÷ 4 = 7

12 ÷ 4 =  3

Answer:

4(7+3)

Step-by-step explanation:

4(7) = 28

4(3)= 12

28+12=28+12

Hope this helps!

Answer:

6

Step-by-step explanation:

Here, we are told to find the length of EB

Since the chords AB and CD are both 5 units(equidistant) away from the center of the circle, then we can conclude that they are both congruent and thus are equal in length

Now we use a circle theorem to solve for the length EB

The theorem is that a line that joins the center of a circle to a chord makes a perpendicular angle with the chord and splits the chord into 2 equal parts.

Now we can say that; AB = AE + EB so we split 12 into 2 which is 6 units and that is the length of EB

Answer:

A: 71,235,000

B: 71,235,00

C: 71,240

Step-by-step explanation: Round by thousands, hundreds and tens.

Answer:

on the dive boat deck

Step-by-step explanation:

Answer:

the above is right

Step-by-step explanation:

Answer:

...........................

Answer: 450 watches

Step-by-step explanation:

Given the following :

Let Initial number of watches = n

Total number sold in January and February = 342

Total sold in march = 25% of (n - 342) = 0.25(n - 342) = 0.25n - 85.5

Total watches left = 18% of n = 0.18n

Therefore,

Initial number of watches = (watches left + total watches sold)

n = 0.18n + (0.25n - 85.5) + 342

n = 0.18n + 0.25n - 85.5 + 342

n = 0.43n + 256.5

n - 0.43n = 256.5

0.57n = 256.5

n = 256.5 / 0.57

n = 450

n = Initial number of watches = 450

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.

If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:

AngleASZ Is-congruent-to AngleZSB

Answer:

AngleASZ Is-congruent-to AngleZSB

Step-by-step explanation:

D is the correct answer

Answer:

become more confident in his faith

Answer:

he will become confident in his faith

Explanation:

the Bible is very open to interpretation and does not always have definite answers. if you are able to form your own ideas and interpretation of the Bible then you'll have a stronger connection to it which will make you more confident in your faith.

Answer:

D. tan50° = 3/a

Step-by-step explanation:

We use tangent (tan∅) to find a. Remember tan is opposite over adjacent.

Really ? ?

Price per inch has the units of  "price/inch".  See that ?  It comes from dividing 'price' by 'inches'.

Price = $7.56

Inches = don't know;

... but we know it's 7 feet, and every foot has 12 inches in it

... so there are (7 x 12) = 84 inches of ribbon.

Price per inch = ($7.56) / (84 inches)

Prince per inch = (7.56/84) (dollars/inch)

Now, YOU go ahead and do the division to get the final answer.

Answer:

A

Step-by-step explanation:

the triangles share one angle and they have two equal sides

Answer:

The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).

Step-by-step explanation:

Each vertex can be represented as a vector with regard to origin.

[tex]\vec X = -4\cdot i + 7\cdot j[/tex], [tex]\vec Y = 6\cdot i + 2\cdot j[/tex] and [tex]\vec Z = 3\cdot i -8\cdot j[/tex].

The magnitudes and directions of each vector are, respectively:

X:

[tex]\|\vec X\| = \sqrt{(-4)^{2}+7^{2}}[/tex]

[tex]\|\vec X\| \approx 8.063[/tex]

[tex]\theta_{X} = \tan^{-1}\left(\frac{7}{-4} \right)[/tex]

[tex]\theta_{X} \approx 119.744^{\circ}[/tex]

Y:

[tex]\|\vec Y\| = \sqrt{6^{2}+2^{2}}[/tex]

[tex]\|\vec Y\| \approx 6.325[/tex]

[tex]\theta_{Y} = \tan^{-1}\left(\frac{2}{6} \right)[/tex]

[tex]\theta_{Y} \approx 18.435^{\circ}[/tex]

Z:

[tex]\|\vec Z\| = \sqrt{3^{2}+(-8)^{2}}[/tex]

[tex]\|\vec Z\| \approx 8.544[/tex]

[tex]\theta_{Z} = \tan^{-1}\left(\frac{-8}{3} \right)[/tex]

[tex]\theta_{Z} \approx 290.556^{\circ}[/tex]

Now, the rotation consist is changing the direction of each vector in [tex]\pm 90^{\circ}[/tex], which means the existence of two solutions. That is:

[tex]\vec p = r \cdot [\cos (\theta \pm 90^{\circ})\cdot i + \sin (\theta \pm 90^{\circ})\cdot j][/tex]

Where [tex]r[/tex] and [tex]\theta[/tex] are the magnitude and the original angle of the vector.

Solution I ([tex]+90^{\circ}[/tex])

[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}+90^{\circ})\cdot i + \sin (119.744^{\circ}+90^{\circ})\cdot j][/tex]

[tex]\vec p_{X} = -7\cdot i -4\cdot j[/tex]

[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}+90^{\circ})\cdot i+\sin(18.435^{\circ}+90^{\circ})\cdot j][/tex]

[tex]\vec p_{Y} = -2\cdot i +6\cdot j[/tex]

[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}+90^{\circ})\cdot i +\sin(290^{\circ}+90^{\circ})\cdot j][/tex]

[tex]\vec p_{Z} = 8.029\cdot i +2.922\cdot j[/tex]

Solution II ([tex]-90^{\circ}[/tex])

[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}-90^{\circ})\cdot i + \sin (119.744^{\circ}-90^{\circ})\cdot j][/tex]

[tex]\vec p_{X} = 7\cdot i +4\cdot j[/tex]

[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}-90^{\circ})\cdot i+\sin(18.435^{\circ}-90^{\circ})\cdot j][/tex]

[tex]\vec p_{Y} = 2\cdot i -6\cdot j[/tex]

[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}-90^{\circ})\cdot i +\sin(290^{\circ}-90^{\circ})\cdot j][/tex]

[tex]\vec p_{Z} = -8.029\cdot i -2.922\cdot j[/tex]

The rotated vertices are: i) X' = (-7,-4), Y' = (-2,6), Z'=(8.029, 2.922) or ii) X' = (7,4), Y' = (2,-6), Z' = (-8.029, -2.922). The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).

Answer:

16

Step-by-step explanation:

15x = 240 x stands for number of students at 1 table

To solve this we divide by 15 both sides for the "x" to remain alone on one side of the equality sign.

(15/15) x = 240/15

So, x = 16.

Answer:

18, 23

Step-by-step explanation:

a. We know that W = 5 and D = 3 so:

P = 3W + D = 3 * 5 + 3 = 18 points

b. We know that P = 50 and D = 14 and that we are solving for W so we get:

50 = 3W + 14

36 = 3W

W = 12 which means the losses are 35 - 12 = 23.

(a) Given:

number of wins = 5

and, number of draws = 3

To find :

Point of the team.

Solution:

P = 3*5 + 3

 = 18

Point of the team = 18

(b)  Given:

number of points = 50

and, number of draws = 14

To find :

Number of games lost by the team.

Solution:

50 = 3*win + 14

3*win = 36

win = 12

Number of games lost by the team = 35 -  12 =23

Answer:

[tex] \theta = 51.8^\circ [/tex]   or   [tex] \theta = 308.2^\circ [/tex]

Step-by-step explanation:

[tex] \cos^2 \theta + \cos \theta − 1 = 0 [/tex]

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] \cos \theta = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)} [/tex]

[tex] \cos \theta = \dfrac{-1 \pm \sqrt{1 + 4}}{2} [/tex]

[tex] \cos \theta = \dfrac{-1 \pm \sqrt{5}}{2} [/tex]

[tex] \cos \theta = 0.61803 [/tex]   or  [tex] \cos \theta = -1.61803 [/tex]

The range of the cos θ function excludes θ = -1.61803, so we discard that solution.

[tex] \theta = 51.8^\circ [/tex]   or   [tex] \theta = 308.2^\circ [/tex]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $120 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1.

State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.

At a 0.01 level of significance, what is your conclusion? What is the p-value?

Answer:

Null hypotheses = H₀ = σ₁² ≤ σ₂²

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic = 1.44

p-value = 0.1954

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

Step-by-step explanation:

Let σ₁² denotes the variance of 4 years old automobiles

Let σ₂² denotes the variance of 2 years old automobiles

State the null and alternative hypotheses:

The null hypothesis assumes that the variance in annual repair costs is smaller for older automobiles.

Null hypotheses = H₀ = σ₁² ≤ σ₂²

The alternate hypothesis assumes that the variance in annual repair costs is larger for older automobiles.

Alternative hypotheses = Ha = σ₁² > σ₂²

Test statistic:

The test statistic is given by

Test statistic = σ₁²/σ₂²

Test statistic = 120²/100²

Test statistic = 1.44

p-value:

The degree of freedom corresponding to 4 years old automobiles is given by

df₁ = n - 1  

df₁ = 26 - 1  

df₁ = 25

The degree of freedom corresponding to 2 years old automobiles is given by

df₂ = n - 1  

df₂ = 23 - 1  

df₂ = 22

Using Excel to find out the p-value,  

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.44, 25, 22)

p-value = 0.1954

Conclusion:

When the p-value is less than the significance level then we reject the Null hypotheses

p-value < α   (reject H₀)

But for the given case,

p-value > α

0.1954 > 0.01

Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.

We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.

The answer that line of best fit, how many toys were sold 13 days after the store opened is A.) 195

Answer: x=2

Step-by-step explanation:

7x+1=x+4

7x=x+3

6x=3

x=2

hope it correct :D

Answer:

A

Step-by-step explanation:

If you see - 12a3bc, - 12a divided by 3 will give you - 4a then just put the rest beside them. So the answer will be A.

Answer:

  18x +16y +4

Step-by-step explanation:

The area is the product of length and width, so the length is ...

  A = LW

  L = A/W = (72xy +18x)/(9x) = 8y +2

The perimeter is double the sum of length and width:

  P = 2(L +W) = 2(8y +2 +9x)

  P = 18x +16y +4 . . . . the perimeter of the sandbox

Answer:

Here,

The length of an arc of a sector with theta nag radius'r' is:

[tex] \frac{theta}{360} 2\pi \: r[/tex]

CD=?

Radius=7.9 cm

theta=66.4

Length of CD

[tex] \frac{66.4}{360} \times 2 \times \pi \times 7.9 \\ = \frac{66.4}{360} \times 2 \times 3.14 \times 7.9 \\ = 9.1506 \\ = 9.2 \: cm[/tex]

Hope this helps...

Good luck on your assignment..