Solve the quadratic equation 12x^2 - 288 = 0 using the square root method.

Solve The Quadratic Equation 12x^2 - 288 = 0 Using The Square Root Method.

Answers

Answer 1

Answer:

C) x = ± 4

Step-by-step explanation:

12x² - 288 = 0

Add 288 on both sides. Anything plus zero gives itself.

12x ² = 288

Divide both side by 12

[tex] \small \sf \: x {}^{2} = \frac{288}{12} \\ [/tex]

Divide 288 by 12 to get 24

[tex]\small \sf x {}^{2} = \frac{ \cancel{288 }}{ \cancel{12}} \\ [/tex]

x² = 24

Taking square root of each side and remember to use positive and negative roots

[tex] \small \sf \: \sqrt{x {}^{2} } = ± \sqrt{ 24} [/tex]

[tex] \small \sf \: x_1, _2 = ± \sqrt{ 24} [/tex]

[tex] \small \sf \: x_1, _2 = ± 4.899 [/tex]


Related Questions

What is the range of g?
y
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9
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6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
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7
7

Answers

Answer:

y 9 5 473648

Step-by-step explanation:

A study is done to determine the average salary for all Santa Clara County teachers. If we were to randomly pick 15 schools in Santa Clara County and average together the salaries of all teachers, would this be a good sampling technique or a bad sampling technique

Answers

Answer:

Good sampling technique

Step-by-step explanation:

In other to determine the mean value for a population, it may be necessary to make inference from the a small subset of the population, called the sample, if it is impossible, difficult or inefficient to get all population data. Hence, in other to select a subset of the population, then the sample must be selected at random, such that all elements of the population have equal chances of being selected and hence, be representative of the population. Since, the sampling technique adopted above is done at random, hence, it is a good sampling technique.

the Barnes family drove 140 miles the first day and 220 miles on the second day. If they drove about 60 miles per hour, approximately how many hours did they drive? ​

Answers

140+220=360
60x6=360
therefore your answer is 6 hours

Congruent sides???????????

Answers

Answer:

the second option : ST and WX

Step-by-step explanation:

congruent means they would completely cover each other when oriented in the same direction and positioned at the same location.

after dying the two mirroring actions we get

VS correlates to ZW

ST correlates to WX

TU correlates to XY

UV correlates to ZY

A chemical engineer must report the average volume of a certain pollutant produced by the plants under her supervision. Here are the data she has been given by each plant:plantvolume of pollutantPittCross CreekSusquehannaWhat average volume should the chemical engineer report

Answers

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Total quantities of plant-produced pollutants:

[tex]=(10.88+15.82+0.92) \ L\\\\=27.62\ L[/tex]

We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be

[tex]\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L[/tex]

Badluckville had been expecting a $50 million investment for a new golf resort, but the contract was cancelled.
Badluckville's mayor estimates that this will cost the city $300 million in total economic activity. What is the mayor's
estimate of the multiplier and marginal propensity to consume?

Answers

Answer:

multiplier = 6

marginal propensity to consume = .83

Step-by-step explanation:

/ means divided by

1 .

300,000,000 / 50,000,000 =

multiplier =

6

2.

300,000,000 - 50,000,000 =

250,000,000

250,000,000/300,000,000 =

marginal propensity to consume =

0.83333333333

or

.83

quizlet

marginal propensity to consume is equal to ΔC / ΔY, where ΔC is the change in consumption, and ΔY is the change in income

investopedia

Find the probability of selecting 3 cards from a standard deck without
replacing them and all 3 are hearts.

Answers

Answer:

B

Step-by-step explanation:

THere are 52/4= 13 hearts we can draw

The number of ways to draw 3 hearts from 13 is

13C3= 286

The number of ways to draw 3 cards from 52 is

52C3= 22100

divide these

286/22100= 11/850

This is answer B

Which of the following statements must be true about this diagram? Check all
that apply.
4 3
1
1
N
A. The degree measure of 23 equals the sum of the degree
measures of 21 and 22.
B. m23 is greater than m 2
C. The degree measure of 24 equals the sum of the degree
measures of 22 and 23.
D. m 4 is greater than m_2.
E. m24 is greater than m 1.
F. The degree measure of 24 equals the sum of the degree measures
of 21 and 22.

Answers

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Use Cramer's Rule to solve (if possible) the system of linear equations.

x1 + 2x2 =8
- x1 + x2 = 1

Required:
Find the coefficient matrix.

Answers

Answer:

x1 = 2

x2 = 3

Step-by-step explanation:

[tex]x_1=\frac{D_{x1}}{D}\\\\x_2=\frac{D_{x2}}{D}[/tex]

Here D is the coefficient matrix.

Hence

[tex]x_1=\frac{6}{3}\\x_1=2[/tex]

&

[tex]x_2=\frac{9}{3}\\x_2=3[/tex]

If 6 playes cost 54$ how much do 30 plates cost

Answers

Answer:

270 plates

Step-by-step explanation:

First, you need to find how much one plate costs.

6x = 54

----    ----

6       6

x = 9

Now, multiply 30 plates with x, which is 9.

30(9) = 270

The answer is 270.

Answer:

270

Step-by-step explanation:

54($)÷6= 9 then 9×30=270

Please help me out with these questions :

Answers

Answer:

Step-by-step explanation:

1. 3/7 x = 12

  3x = 84

    x = 28

2. 3x+ 6 = 39

   3x = 33

    x = 11

3. 1/3 x - 3/4 x = 15

    9x  - 4x  = 180

       x =  36

4.   1/4 x = x -21

      3/4 x = 21

      3x = 84

        x=28

5.    86-36 = 50

      50/2

       25

Get brainly if right!! Plsss help

The 8t h term in the arithmetic sequence is 17, and 12t h term is 25. Find the first
term, and the sum of the first 20 terms.

Answers

Step-by-step explanation:

t8 = a1 + (n - 1)*d

t8 = 17

17 = a1 + 7*d

t12 = 25

25 = a1 + 11d

17 = a1 + 7d Subtract

8 = 4d Divide by 4

8/4 = 4d/4

2 = d

17 = a1 + 7d

17 = a1 + 7*2

17 = a1 + 14 Subtract 14

3 = a1

Sum 20 terms

The 20 term = a1 + 19*2

The 20 term = 3 + 38

= 41

Sum = (a1 + a20) * 20 / 2

Sum = (3 + 41)* 20/2

Sum = 44 * 10

Sum = 440

The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force vs. the number of juvenile violent crime arrests for each of the 50 states. The least-squares regression line has been drawn in on the plot. We would like to predict what the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force. This is called

Answers

Answer:

Extrapolation

Step-by-step explanation:

From the linear regression plot created in the picture given, se could see that Tha percentage of student covered by the the plot is just above 16%. Therefore, to predict the percentage of the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force will require us to assume that the current trend continues into the future. Hence, we use the information and indications we have at present to make prediction into the future based on the assumption that we the current trend will remain relevant and applicable. This assumption into the future based on current trend is called EXTRAPOLATION.

Why is the number of operators per shift multiplied by approximately 4.5 to obtain the total number of operators required to run the plant

Answers

I believe you meant "why is the number of shifts multiplied by approximately 4.5 to obtain the total number of operators required to run the plant"

Answer and Explanation:

There are 3 shifts per day, 49 weeks per year and 5 shifts per operator per week

To get total number of operators required to run the plant, we multiply number of shifts in a year by number if operators per shift.

49 weeks×5 shifts= 245 shifts per operator per year

365×3 shifts= 1095 shifts per year

1095/245=4.5 operators per shift

total number of operators required to run the plant(per day) = 4.5×3= 13.5 approximately 14

total number of operators required to run the plant(per year) =4.5×1095=4927.5 approximately 4928

An RLC series circuit has an applied voltage of 240 volts. R = 48 ohm, XL = 100 ohm, and XC = 36 ohm. What is the circuit impedance (Z)?

Answers

9514 1404 393

Answer:

  48 +j64 ohms

Step-by-step explanation:

The impedance of a series circuit is the sum ...

  R + jXl -jXc

  = 48 +j100 -j36

  = 48 +j64 . . . . ohms

_____

Additional comment

"j" is the electrical engineer's name for √-1, because "i" is used to represent current.

Kaitlin is riding her bike. The number of revolutions (turns) her wheels make varies directly with the distance she travels. See the graph below.



How far does Kaitlin travel per revolution?

What is the slope of the graph?

Answers

Answer:

m = Δy/Δx = 4/32 = 1/8

8 ft/rev.

Step-by-step explanation:

Answer:

[tex]\frac{1}{8}[/tex] for both

Step-by-step explanation:

1. Distance per revolution

We see that the distance travelled at 2 revolutions is 16

This means that she travels [tex]\frac{1}{8}[/tex] of a mile per revolution

2. Slope

The slope formula is rise/run, or ([tex]y[/tex]₂[tex]-y[/tex]₁)/([tex]x[/tex]₂[tex]-x[/tex]₁)

We can take two points, (16,2) and (32,4)

[tex]\frac{4-2}{32-16}=\frac{2}{16}=\frac{1}{8}[/tex]

The slope is [tex]\frac{1}{8}[/tex]

Hope this helps! Please mark brainliest :)

Long division: 2/ 2769

Answers

Answer:

1384.5

Step-by-step explanation

Diviseion is just the oppisite of multiplication so you can think to yourself that what times two equals 2769. If you multiply 1384.5 on a calculater you get 2769.

1384.7 I think I’m not sure tho

The of the matrix whose columns are vectors which define the sides of a parallelogram one another is the area of the parallelogram?

Answers

Answer:

absolute value of the determinant, adjacent to, equal to

Step-by-step explanation:

The absolute value of a determinant  of the [tex]\text{matrix whose}[/tex] columns are the vectors and they define the [tex]\text{sides}[/tex] of a [tex]\text{parallelogram}[/tex] which is adjacent to  one another and is equal to the [tex]\text{area}[/tex] of the [tex]\text{parallelogram}[/tex].

The determinant is a real number. They are like matrices, but we use absolute value bars to show determinants whereas to represent a matric, we use square brackets.

Multiply the polynomial 4x(2x+3) (show work pls)

Answers

Answer:

8^2+12x

Step-by-step explanation:

4x(2x+3)

=4x times 2x+4x times 3

=4 times 2xx+4 times 3x

Answer:

8x^2 +12x

Step-by-step explanation:

Step 1) Multiply each term in the parentheses by 4x

4xx2x+4xx3

Step 2) Calcuate the product

8x^2 +12x

Sofia bought a clothes iron that was discounted 15% off of the original price of $35. What was the sale price of the clothes iron?

Answers

Answer:

35 - 0.15 * 35 so it is $29.75

Step-by-step explanation:

I got u

Answer:

$29.75

Step-by-step explanation:

15% = .15

.15 x 35 = 5.25

35 - 5.25 = 29.75


11 Emilio makes metal fences.
He is making a fence using this design.
1.44 m
DO NOT WRITE IN THIS AREA
1.8 m
.
The fence will need
3 horizontal metal pieces of length 1.8m
2 tall metal pieces of length 1.44 m
5 medium metal pieces
6 short metal pieces as shown on the diagram.
The heights of the tall, medium and short metal pieces are in the ratio 9:8:7
.
How many metres of metal in total does Emilio need to make the fence?

Answers

Answer:

Step-by-step explanation:   7  3  13  31

3 × 1.8      long pieces                                  Calculate the ratios

2 × 1.44    9  tall vertical piece                     1.44 / 9  = x / 9      x = 1.44

5 × ___    8  medium vertical pieces          1.44 / 9  = x / 8      x = 1.28

6 × ___    7  short vertical pieces                1.44 / 9  = x / 7       x = 1.12

3 × 1.8      long pieces

2 × 1.44    9  tall vertical piece                     1.44 / 9  = x / 9      x = 1.44

5 × 1.28    8  medium vertical pieces          1.44 / 9  = x / 8      x = 1.28

6 × 1.12    7  short vertical pieces                1.44 / 9  = x / 7       x = 1.12

3 × 1.8      long pieces                                 =  5.4 m

2 × 1.44    9  tall vertical piece                   =  2.88  m

5 × 1.28    8  medium vertical pieces        =  6.4 m

6 × 1.12    7  short vertical pieces              =   6.72 m                  

                                                Total           =  21.4  m

Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month.
Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month.

Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? (1 point)

Select one:
a. Zach's method is linear because the number of minutes increased by an equal factor every month.
b. Victoria's method is linear because the number of minutes increased by an equal number every month.
c. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month.
d. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.

Answers

9514 1404 393

Answer:

  b. Victoria's method is linear because the number of minutes increased by an equal number every month

Step-by-step explanation:

Zach's reading doubled each month, a characteristic of an exponential function.

Victoria's reading increased by 15 minutes each month, characteristic of a linear function.

The only reasonable description among those offered is the one shown above: choice B.

A family eats out at a restaurant and the total for their meals is $73.89. They also pay sales tax of 5.8% and leave a tip for their server. If the family leaves a total of $93, which of the following might be a description of the service they received?
a.
They left a 10% tip, so the service was probably below average.
b.
They left a 15% tip, so the service was probably average.
c.
They left a 20% tip, so the service was probably above average.
d.
They left a 25% tip, so the service was probably outstanding.

Answers

C. 20%

$73.89 • 5.8% = 4.29
73.89 + 4.29 = 78.18
78.18 • 20% = 15.636 so 15.64
78.18 + 15.64 = 93.82
Hope it helps

The answer is They left a 20% tip, so the service was probably above average.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

First step is to the amount of the sales tax.

If 100% is $73.89,

5.8% will be x (tax):

100% : $73.89 = 5.8% : x.

x = $73.89 * 5.8% : 100%.

x = $4.28.

Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:

$93.00 - $73.89 - $4.28 = $14.83.

So, the tip is $14.83.

Let represent it as percent.

If $73.89 is 100%, $14.83 will be x.

$73.89 : 100% = $14.83 : x.

x = $14.83 * 100% : $73.89.

x = 20%.

So, they left a 20% tip, so the service was probably above average.

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You return from a trip with 480 Canadian dollars. How much are your Canadian dollars worth in U.S. dollars? Use the exchange rate shown below. Currency U.S. dollars per Canadian dollar Canadian dollars per U.S. dollar Canadian dollar 0.5823 1.717 The 480 Canadian dollars are equivalent to about $ (Round to the nearest cent as needed.)​

Answers

591 Dollars 42 Cents (591 Dollars when rounded)

I WILL MARK THE ANSWER AS BRAINLIEST IF RIGHT

PLEASE HELP ME BE CORRECT BEFORE ANSWERING PLEASE

Answers

9514 1404 393

Answer:

  D  neither

Step-by-step explanation:

Reflection across a vertical line is required to change the figure left-to-right without changing it top-to-bottom. Translation along a directed line segment must then map corresponding points.

Sequence A involves reflection over a horizontal line, so can be rejected immediately. Sequence B does the translation so that point N gets moved to the location of point B. However, point N corresponds to point D (see the similarity statement), so that translation is inappropriate.

Neither sequence will map KLMN to ABCD.

Need help with this math

Answers

Answer:

Step-by-step explanation:

office at point A =(-7,-5)   ........................in the form (x1,y1)

supermarket and point B = (-2,-6)........in the form (x2,y2)

home Home at point C = (4,-6).............in the from (x3,y3)

find the total distance from A to B + B to C

ABdist= sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

ABdist = sqrt[ (-2-(-7))^2 + (-6-(-5))^2 ]

ABdist = sqrt[ (-2 + 7)^2 + (-6 +5)^2]

ABdist = sqrt[ [tex]5^{2}[/tex] + [tex](-1)^{2}[/tex]]

ABdist = sqrt[ 25 + 1 }

ABdist = [tex]\sqrt{26}[/tex]

BCdist= sqrt[ (x3-x2)^2 + (y3-y2)^2 ]

BCdist = sqrt[ (4-(-2))^2 + (-6-(-6))^2]

BCdist = sqrt[ 4+2)^2  + -6+6)^2 ]

BCdist = sqrt [ [tex]6^{2}[/tex] + [tex]0^{2}[/tex] ]

BCdist = [tex]\sqrt{36}[/tex]

BCdist = 6

total distance = [tex]\sqrt{26}[/tex] +6

The first answer looks good

If a+bi, where b is not equal to 0, is a complex zero of a polynomial with real coefficients, then so is its _____ , a-bi.

a.) linear factorization
b.) irreducible factor
c.) reducible factor
d.) complex factor
e.) fundamental theorem
f.) conjugate​

Answers

Hello,

answer f: conjugate

if all coefficients are real and a+ib a zero, its conjgate a-ib is also a zero.

Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation

Answers

Answer:

Yes it is an equivalence relation

Explanation:

An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.

Example, given set {x, y, z} where ~ means equivalence:

x ~ y if y ~ z means symmetric

since x ~ y and y ~ z, then x ~ z means transitive

x ~ x means reflexive

Equivalence relations share a common attribute or attributes(example, a satisfying condition)

The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.

Jessica purchases a kayak in Florida, where the state sales taxes are 6%. She paid $72 in sales tax. What was the retail price of the kayak?

Answers

Answer:

72 is 6% of 1200.

Step-by-step explanation:

Multiply 72 by 100.

72*100

Then divide the number by 6

(72*100)/6

You should get 1200.

Find the domain and range of the function graphed below, in interval notation.

Answers

Answer:

Domain: [-2,1)

Range: [0,4]

Step-by-step explanation:

The required domain and range of the function graphed are -2 ≤ x < 1 and 0 ≤ y ≤ 4.

Given that,
To determine the domain and range of the function graphed below, in interval notation.

What is the range?

Range, it is the set of the values that come out to an outcome for a certain mathematical operations.

Here,
The projected line of the curve on the horizontal axis is from greater and equal to -2 to less than 1,
Domain = -2 ≤ x < 1
The projected line of the curve on  the vertical axis is from greater or equal to 0 to less than or equal to 4,
Range = 0 ≤ y ≤ 4.

Thus, the required domain and range of the function graphed are -2 ≤ x < 1 and 0 ≤ y ≤ 4.

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