Solve the following quadratic equations using completing the square x2 – 8x – 34 = 0

Answer:

[tex]x-8[/tex],  smaller integer is 8.

Step-by-step explanation:

Given:

The product of two consecutive integers is 72.

The equation x(x+1)=72 represents the situation, where x represents the smaller integer.

Question asked:

Which equation can be factored and solved for the smaller integer ?

Solution:

[tex]x(x+1)=72\\\\ x^{2} +x=72\\ \\ By\ subtracting\ both\ sides\ by\ 72\\ \\ x^{2} +x-72=72-72\\ \\ x^{2} +x-72=0\\ \\ x^{2} +9x-8x-72=0\\ \\ Taking\ x+9\ as\ common \\ \\ x(x+9)-8(x+9)=0\\ \\ x+9=0,x-8=0\\ \\ x=-9,x=8[/tex]

[tex]x-8[/tex]  can be factored and solved for the smaller integer, and that is 8.

Two consecutive integers are 8 and  9 and their product is 8 [tex]\times[/tex] 9 = 72

Answer:

Straight line joining (0,6) and (24,0)

Step-by-step explanation:

y = (-1/4)x + 6

Make a straight line passing through:

y = 0 + 6 = 6

(0,6)

And

0 = (-1/4)X + 6

-6 = -x/4

x = 24

(24,0)

sorry honey but i dot have a graph to you how but

all you do is  start at 6 positive and then mark a point one down and 4 to left and mark other point and then draw a line through it

Answer:

star a; 5.7 units

Step-by-step explanation:

the average of wieght od the kittens in the slether?

[tex]x_0=\dfrac{-b}{2a} =\dfrac{-4}{2\times(-2)}=1\\y_0=-2\times1^2+4\times1+1=-2+4+1=3\\Answer: The\: vertex\: is \:(1;3). It's\:maximum\:point \:because \:a=-2<0[/tex]

Answer:

Step-by-step explanation:

The alternate hypothesis use the sumbol for the population value

Let p be the proportion , Mean be [tex]\mu[/tex] and stadard deviation be [tex]\sigma[/tex]

The null hypothesis states that population value is equal to the value mentioned in the given claim.

[tex]H_0:\mu=18[/tex] (by given).

The alternate hypothesis for the significance test states that the opposite of the null hypothesis(based on the claim )

∴ [tex]H_a:\mu<18[/tex]

The symbol "<" because we want to test if the maze is completed faster and thus if the time has decreased.

Given:

The time required for a box to slide down an inclined plane is

[tex]T = \sqrt{\frac{2a}{g(sin\theta cos\theta)} }[/tex]

where,

g be the,acceleration due to gravity.

[tex]\theta[/tex] be the inclined plane.

To find the value of [tex]\theta[/tex] for which the given expression is undefined.

Now,

T will be undefined if the denominator is 0.

⇒ [tex]g(sin \theta cos \theta) = 0[/tex]

or, [tex]sin\theta cos\theta = 0[/tex] [ g ≠ 0 it is a constant]

either [tex]sin\theta = 0[/tex] or [tex]cos\theta = 0[/tex]

For, [tex]sin\theta = 0[/tex] ⇒ [tex]\theta = 0^\circ[/tex]

Again,

For, [tex]cos\theta = 0[/tex] ⇒ [tex]\theta = 90^\circ[/tex]

Hence,

The expression will be undefined for the value of 0° and 90° of θ.

Option C.

Option(C). In the formula √(2a/g•sin(theta)•cos(theta)), the expression is undefined when theta=0° or 90°, since in these cases, sin(theta) or cos(theta) equal to zero respectively.

Consider the formula √(2a/g•sin(theta)•cos(theta)).

The expression in the root (√) is undefined when we divide by zero. Looking at the formula, we divide by the product of sin(theta) and cos(theta). For the expression to be undefined, one or both must be zero.

The values of theta that would cause this to happen are when theta=0°, sin(theta)=0 and when theta=90°, cos(theta)=0.

Therefore, the expression is undefined when theta is either 0° or 90°.

So, the answer is C. Both A and B.

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Answer:

<1 : 36 degrees

<2 : 90 degrees

<3 : 36 degrees

<4 : 54 degrees

Step-by-step explanation:

First off, rhombus's have right angles formed at the middle, meaning that <2 is 90 degrees. Then, it's given that angle is 54 degrees, and its alternate interior angle is the one that is adjacent to <3. To find <1, add 90 and 54, and subtract that from 180. So <1 is 36 degrees. So that automatically makes < 3, 36 degrees and < 4, 54 degrees.

The equation [tex]\( K = C + 237.15 \)[/tex]) provides a way to convert temperatures from degrees Celsius to Kelvin. It reflects the fact that the Kelvin scale starts from absolute zero and is offset from the Celsius scale by 273.15 degrees.

K as the temperature in Kelvin,

C as the temperature in Celsius.

We're given that a temperature in Kelvin is 237.15 greater than the temperature in degrees Celsius. So, we can express this relationship as an equation:

[tex]\[ K = C + 237.15 \][/tex]

This equation shows that to convert from Celsius to Kelvin, you add 237.15 to the Celsius temperature. Similarly, to convert from Kelvin to Celsius, you subtract 237.15.

Here's the equation:

[tex]\[ K = C + 237.15 \][/tex]

1. **Definition of Kelvin and Celsius Scales**:

  - Kelvin (K): Kelvin is an absolute temperature scale where 0 Kelvin represents absolute zero, the lowest possible temperature where particles cease to move. One Kelvin is equal in magnitude to one degree Celsius.

  - Celsius (C): Celsius is a temperature scale based on the freezing and boiling points of water, where 0 degrees Celsius represents the freezing point of water and 100 degrees Celsius represents the boiling point of water at standard atmospheric pressure

2. **Relationship between Kelvin and Celsius**:

  - To convert from Celsius to Kelvin, you add 273.15 to the Celsius temperature. This adjustment is made because the Kelvin scale starts from absolute zero, which is -273.15 degrees Celsius.

3. **Given Relationship**:

  - The given information states that a temperature in Kelvin is 237.15 greater than the temperature in degrees Celsius. This means that to convert from Celsius to Kelvin, you add 237.15 to the Celsius temperature.

  - We can express this relationship mathematically as [tex]\( K = C + 237.15 \).[/tex]

    - Here, [tex]\( K \)[/tex] represents the temperature in Kelvin, and  [tex]\( C \)[/tex]represents the temperature in degrees Celsius.

    - Adding 237.15 to the Celsius temperature converts it to Kelvin.

  - The equation [tex]\( K = C + 237.15 \)[/tex]) provides a way to convert temperatures from degrees Celsius to Kelvin. It reflects the fact that the Kelvin scale starts from absolute zero and is offset from the Celsius scale by 273.15 degrees.

For part A, the student has 13 colleges to choose from that are not expensive and near home. For part B, the total possible selections of two colleges is 156, considering the student won't attend the same college before and after the transfer.

The subject of this question pertains to probability and set theory, a branch of mathematics. We use the principle of inclusion and exclusion to solve the problem.

For part A. there are total 24 colleges, 8 are expensive which means 24 - 8 = 16 are not expensive. Among 24 colleges, 8 are far from home which means 24 - 8 = 16 are near. But remember, there are 5 colleges that are both expensive and far, hence these 5 colleges got subtracted twice. So, we need to add them back. The number of colleges that are not expensive and near home are 16 + 16 + 5 = 37. However, this goes beyond the total number of colleges, so we subtract 24 from it to get the correct count of 13.

For part B, the number of ways before transferring are the same as in part A, 13. The number of ways after transferring, there are total 24 colleges, 8 are expensive which means 24 - 8 = 16 are not expensive. Among 24 colleges, 8 are near which means 24 - 8 = 16 are far. Adding the count of not expensive and far gets us 16 + 16 = 32. Subtract the total number of colleges to get the correct figure 32 - 24 = 8. Nothing the student can't attend the same college before and after the transfer, so the count of total selections is 13 choices for the first selection multiplied by 12 choices for the second selection, getting us a total of 156 possible selections.

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Answer:

64, 81, 100, 121 there are 4

Step-by-step explanation:

Answer:

heyyy there

Step-by-step explanation:64, 81, 100, 121, are the perfect square numbers between 50 and 140..

64=8*8

81=9*9

100=10*10

121=11*11

................12 *12 bcoms 144 so its not between 144

hope it helps

Answer:

Since h(max) is less than 30 ft, it will never reach a height of 30ft

The maximum height it can reach is 11.25ft.

Step-by-step explanation:

Given;

The height equation of the rock;

h = -16t^2 +20t +5

To determine whether it would reach 30 ft, we need to find its maximum height. Which is at;

dh/dt = 0

dh/dt = -32t +20 = 0

At Maximum height.

t = 20/32

We then substitute into the height equation.

h(max) = -16(20/32)^2 + 20(20/32) +5

h(max) = 11.25 ft

Since h(max) is less than 30 ft, it will never reach a height of 30ft

The maximum height it can reach is 11.25ft.

Answer:

There are no real solution to the equation [tex]h = -16t^2 +20t +5[/tex] when h = 35 ft.

Step-by-step explanation:

Here we have the equation for the height of the rock in ft given as

[tex]h = -16t^2 +20t +5[/tex]

For the rock to reach 30 ft we must have

[tex]30 = -16t^2 +20t +5[/tex]

That is [tex]0 = -16t^2 +20t +5 - 30 = -16t^2 +20t -25[/tex]

[tex]0 = -16t^2 +20t -25[/tex] or

[tex]16t^2 -20t +25 = 0[/tex]

From which it is observed that since the root of the equation is given by the quadratic formula

b² should be greater than 4·a·c  however

(-20)²[tex]\ngeqslant[/tex] (4×16×25)

Hence the equation has only imaginary roots.

Answer:

149,730 strawberries

Step-by-step explanation:

Answer:

149,730 strawberries

Step-by-step explanation:

Answer:

x=7

y=8

Step-by-step explanation:

-Given that the mean and median is the same.

-Let b=mean =median

#Given that the set is arranged in order and is even:

[tex]median=\frac{n+1}{2}\\\\Median=3^{rd} \ term\\\\=x[/tex]

Hence:

[tex]b=median=mean\\\\b=x\\\\\therefore mean=median=x[/tex]

-Applying the mean formula:

[tex]\bar x=\frac{1}{n}\sum{x_i}\\\\\therefore 5x=4+6+x+y+10\\\\4x=20+y\\\\x=5+0.25y[/tex]

#Since the number are in order:

[tex]6<x<y<10\\\\\#let\ x=7,y=8\\\#Substitute\\\\7=5+0.25(8)\\7=7\\\\[/tex]

Hence, x=7 and y=8

Answer: x = -1

Step-by-step explanation:

1) x - 5 = 36 -7x -49

2) x - 5 = -13 -7x

3) x + 7x =- 13 +5

4) 8x =- 8

5) x = -1

Please mark this as the brainliest answer! :) I hope this helped! <3

Answer:

the equation would be

28÷(11.50+5.50)

hope this helps :)

Answer:

28=5.50h+11.50

Step-by-step explanation:

Answer:

B. $0.72

Step-by-step explanation:

Here is the stock listing for Enam Telecom

52 wk high is 122.86

52 wk low is 64.77

Div. is 3.45

Close is 99.14

Net change is 4.74

From the question the lowest price which was 64.77 was 48 days ago.

therefore net change in value is:

Close - lowest price:

99.14 - 64.77 = 34.37

Since change is in 48 days,

the average change per day is:

Total change / number of days = 34.37/48 = 0.716

This answer is approximately 0.72

Therefore average change per day is 0.72

Answer:

B

Step-by-step explanation:

Answer:

p= 8

Step-by-step explanation:

1/2 p = 4

p = 2(4)

Answer:

p=8

Step-by-step explanation:

This will ake the problem 8/2 which is the same as 4.  

Thus, 8 is your answer.

Leave 5 stars if this helped.

Answer:

35 People

Step-by-step explanation:

From the given information

Let the number of people attending the banquet=x

Therefore:

Cost of Hall Rental + Total Meal Cost = Total Bill

125+12x=545

12x=545-125

12x=420

x=420/12=35

Since x=35, we conclude that 35 People attended the banquet.

Answer:

D. 21,386

Step-by-step explanation:

The question is incomplete. Here is the complete question.

"The number of trees in a forest follows the logistic growth function,

f(t) = 32000/1+12.8e^-0.065t where t is the time in years. According to the growth model, how many trees will there be after 50 years?"

Given the logistics growth function,

f(t) = 32000/1+12.8e^-0.065t

To calculate the number of trees that will be there after 50years, we will substitute the value of t = 50 into the function

f(50) = 32000/1+12.8e^-0.065(50)

f(50) = 32000/1+0.496

f(50) = 32000/1.496

f(50) = 21,385.94

f(50) = 21,386

Number of trees that will be there after 50years is 21,386years

Answer:

it will take 20hrs to fill the pool

Answer:

It would take 20 hours to fill the pool.

Step-by-step explanation:

We are give the Dimensions of the Pool. Recall that Volume of a Rectangular Prism is V = l*w*h which will return 800[tex]m^{3}[/tex]. Using Dimensional Analysis and recalling that the rate is being pumped at a rate of [tex]\frac{40m^{3}}{h}[/tex],   [tex]\frac{m^{3} }{\frac{m^{3}}{h} } = h[/tex] so, just divide the Volume by the Rate given since they are under the same units: [tex]\frac{16*10*5}{40} = \frac{800}{40} = 20 hours[/tex].

Step-by-step explanation:

Your mistake is here: cos(-45°) = +½√2, not -½√2.

±√((1 + ½√2) / 2)

= ±√((2 + √2) / 4)

Answer is: 16x8 = 128

Answer:

the the scale of the drawing is 1/4

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

As we know that, the formula to find the are of a triangle is:

A = 1/2 b*h where:

From the photo, we can see that, the height is 3 units and the base is 6 units. So the area of the shaded triangle is:

A = 1/2 6*3 = 9 square units

Given that the triangle depicted by the drawing has an actual area of 36 square units. So the the scale of the drawing is:

area of the shaded triangle / the actual area

9 /36 = 1/4

Hope it will find you well.

Final answer:

The amplitude of a wave is its maximum displacement from equilibrium and can be directly read from the equation as A, while the period is the time for one complete cycle, inversely related to frequency as T = 1/f. Given a frequency of 2.0 MHz, the period is 5.0 x 10⁻⁷ seconds, with the amplitude being 30 V/m.

Explanation:

The period and amplitude of a sinusoidal function can be determined from its formula or graph. For example, in the given context, if we are presented with a wave with an amplitude of 30 V/m and a frequency of 2.0 MHz, we can calculate the period. We know that the period (T) of a wave is the inverse of the frequency (f), so T = 1/f. Given the frequency of 2.0 MHz, or 2.0 x 106 Hz, the period T is 5.0 x 10-7 seconds (since 1 Hz = 1/s). The amplitude is the maximum displacement from the equilibrium position, in this case, 30 V/m. The amplitude is typically denoted by A in the wave equation y(x, t) = A sin(kx - wt + p), and the period can be derived from the angular frequency with T = 2π/ω.

For a physical representation, observing a wave plotted on a graph such as in Figure 24.8(b) or a given wave function, the amplitude is seen as the distance from the equilibrium position (center line) to the peak, and the period is the time it takes for one complete cycle of the wave. Understanding these concepts is crucial for analyzing waves whether in physics or mathematics.

Answer:

C ( 6 units

Step-by-step explanation:

just took the quiz

Answer:

$18.90

Step-by-step explanation:

Lets break this question down into smaller sections to make it easier:

There are 3 bottles

Each bottle can hold 0.75 liters

For every 25 milliliters she pays $0.21

With that information in mind, we notice that we need to convert liters to milliliters in order to get an accurate answer.

For every 1 liter = 1000 milliliters

So, we need to take 0.75 * 1000 = 750 milliliters per bottle

Next, we take 750 milliliters / 25 milliliters to find how many times we have to fill one bottle

Each bottle will take 30 times of 25 milliliters to fill the whole bottle

Now take 30 * $0.21 to find the cost of one bottle

One bottle = $6.30 to fill

Take $6.30 * 3 to find the total cost to fill ALL the bottles.

For a final result, we get $18.90 to fill all three bottles completely

Hope this Helps!

Answer:

it's 18.90

Step-by-step explanation

my friend told me it was 5.67 and for some reason i believed her but no i took the test and it's 18.90

Answer:

False

Step-by-step explanation:

Correct statement would be:

A tangent line is a line that insersects a circle at exactly one point.