Three students used factoring to solve a quadratic equation? The equation was solve correctly by ______.The solutions of the equation are__________.

Answer:

- 1

Step-by-step explanation:

Given

( [tex]\frac{1+i}{1-i}[/tex] )²

= [tex]\frac{(1+i)^2}{(1-i)^2}[/tex]

= [tex]\frac{(1+i)(1+i)}{(1-i)(1-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{1+2i+i^2}{1-2i+i^2}[/tex] ← simplify using i² = - 1

= [tex]\frac{1+2i-1}{1-2i-1}[/tex]

= [tex]\frac{2i}{-2i}[/tex]

= - 1

Answer:

Length of first leg = 1.4feet

Hypotenuse = 4.2feet

Explanation:

Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.

Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.

From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.

Also the other leg is four feet i.e c= 4

Substituting this values into the Pythagoras formula;

a²=b²+c²

(3b)² = b²+4²

9b² = b²+16

9b²-b² = 16

8b² = 16

b² = 16/8

b² = 2

b = √2

b = 1.4

Since a = 3b

a = 3(1.4)

a = 4.2

Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.

Answer:

A

Step-by-step explanation:

Put your information in the the point slope formula y-y1=m(x-x1)

This will give you y+5=3(x+3)

simplify

y+5=3x+9

Now subtract 5

y=3x+4

Answer:

The height of the statue is 217 m

Step-by-step explanation:

The hill is 25 ft above the ground,

you are standing 53 ft from the base of the hill,

angle of depression from the top of the angle to where you stand is 12.4°

Let us designate the total height from the base of the hill to the top of the statue as y.

This problem will then form a right angle triangle problem, with the base as the opposite side to the angle, and the total height of the statue and the hill as the adjacent side.

given the opposite as 53 ft,

and the adjacent as y,

and angle ∅ = 12.4°

we use tan ∅ = opp/adj

tan 12.4 = 53/y

0.219 = 53/y

y = 53/0.219 = 242 m

But this height y from base of the hill to the top of the statue is equal to the height of the hill from the base which is 25 ft, and the height of the statue from the top of the hill. This means

y = 242 = 25 + n

where n is the height of the statue.

242 = 25 + n

n = 242 - 25 = 217 m

Answer:

Length 1 - Width = 19, Area = 19

Length 2 - Width = 18, Area = 36

Length 3 - Width = 17, Area = 51

Length 4 - Width = 16, Area = 64

Length 5 - Width = 15, Area = 75

Step-by-step explanation:

Area Formula: A = lw

Since we only have a combined total of 20 m to use, we have to subtract the number of length in order to find length:

Length 1 = 20 - 1 = Width 19 m

Length 2 = 20 - 2 = Width 18 m

Length 3 = 20 - 3 = Width 17 m

Length 4 = 20 - 4 = Width 16 m

Length 5 = 20 - 5 = Width 15 m

Then we simply plug in our l values and w values into the area formula:

A = 1(19) = 19 m²

A = 2(18) = 36 m²

A = 3(17) = 51 m²

A = 4(16) = 64 m²

A = 5(15) = 75 m²

width from 1-5 =

when lem

length=1, width=19

length=2,width=18

length=3,width=17

length=4,width=16

length=5,width=15

length =1,Area=19

length=2,Area=36

length=3,area=51

length=4,area=64

length=5,area=75.

Step-by-step explanation:

to get our width, we minus each length from the given value which is 20m.

e.g.

when length =1 our width becomes 20-1=19.

and you do same for the rest.

the formula for the area was given to us in the question so we use that to find the area.

A=Length×Width.

e.g when length=1, width =19

so the area becomes 1×19=

[tex] {19m}^{2} [/tex]

please note that your area should be in

[tex] {m}^{2} [/tex]

Answer:

Step-by-step explanation:

f(x) = 2x

When x = 2

Substitute the value of x into f(x)

That's

f(2) = 2(2)

= 4

Hope this helps you

Answer:

f(2)= 4

Step-by-step explanation:

To find f(2) we will use y=2x since f(x)=y

●y=2*2= 4 wich is f(2)

Answer: Intercept (b) = - 2.2567

Step-by-step explanation:

(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6)

Using the online regression calculator :

ŷ = -0.60205X - 2.2567

y is the predictor variable

X - the independent variable

0.60205 = slope or gradient

- 2.2567 = intercept (b) where the line best fit cross the y-axis.

The linear regression line is made using the least-squares method. The value of b is -2.2567.

Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least-squares method.

Given the points of the data(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6).

Now, Since the question states about using the technology, therefore, if we use the online regression calculator:

ŷ = -0.60205X - 2.2567

y is the predictor variable

X - the independent variable

-0.60205 is the value of m which is the slope or gradient of the regression line, while -2.2567 is the value of the intercept of the regression line.

Hence, the value of b is -2.2567.

Learn more About Linear Regression Line:

https://brainly.com/question/14313391

#SPJ2

Hi,

[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]

Have a good day.

Answer:

72 inch²

Step-by-step explanation:

Rectangular classroom

Length=36ft

Width=32ft

scale drawing length = 9 inches

Scale drawing width=x

Ratio of the length to the scale drawing length = 36/9

Ratio of the width to the scale drawing width=32/x

To find x

36/9=32/x

Cross product

36x=32*9

x=288/36

=8

x=8

Area of a rectangle= length × width

Length=9 inches

Width=8 inches

Area of the rectangular classroom= 9 inches × 8 inches

=72 inch²

Answer:

50

Step-by-step explanation:

Answer:

The third one.

Step-by-step explanation:

The last bar graph is skewed to the right, since the values of its fourth and fifth bars are way smaller than the values of its first, second, and third graphs. The drastically smaller values pull down the mean of the last bar graph, making it be more different from the median.

Comparatively, bar graphs one and two have approximately symmetrical distributions of numbers on both sides of the central bar. This means that their mean is balanced out on both sides and that neither of them is significantly skewed left or right.

A bar graph. The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 38. The second bar is 43. The third bar is 21. The fourth bar is 5. The fifth bar is 1 is data distribution would most likely have a mean and median that are not close in value.

We have to determine, which data distribution would most likely have a mean and median that are not close in value.

According to the question,

The mean and the median both reflect the skewing, but the mean reflects it more.

The last bar graph is skewed to the right since the values of its fourth and fifth bars are way smaller than the values of its first, second, and third graphs.

The drastically smaller values pull down the mean of the last bar graph, making it be more different from the median.

The mean and the median are the same. This example has one mode (unimodal), and the mode is the same as the mean and median.

Bar graphs one and two have approximately symmetrical distributions on both sides of the central bar.

This means that their mean is balanced out on both sides and that neither of them is significantly skewed left or right.

Hence, The horizontal axis is unnumbered. The vertical axis is numbered 0 to 50. The first bar is 38. The second bar is 43. The third bar is 21. The fourth bar is 5. The fifth bar is 1.

To know more about Probability click the link given below.

https://brainly.com/question/23044118

Answer: 40x

First, let's find f(2x)

[tex]f(2x)=4(2x)=8x[/tex]

Using this, let's find g(f(2x)):

[tex]g(f(2x))=g(8x)=5(8x)=40x[/tex]

That's the answer. Let me know if you need any clarifications, thanks!

Answer:

80x²

Step-by-step explanation:

f(x) = 4x², g(x) = 5x

f(2x) = 4(2x)² = 16x²

g(f(2x)) = 5(16x²) = 80x²

Answer:

3x + 4y ≥ 82

Step-by-step explanation:

3x + 4y ≥ 82

we can read as: 3 time of right answers of true/false plus 4 times of right answers of multiple choice must be bigger or at least 82

Answer:

$6.8

Step-by-step explanation:

Let x be the amount of money in Molly's amount

according to question,

4x-25=2.20

4x=2.20+25

4x=27.20

x=27.20/4

x=6.8

So,the amount of money in Molly's amont is $6.8

Answer: $6.80

Step-by-step explanation:

We will represent the amount of money that Molly has with a m. So it tells us the relationship between Kevin's amount and Molly's amount. It is says Kevin has 2.20 less that 4 times Molly's amount so we could represent it by the equation.

25 = 4m -2.20   solve for m.

+2.20     +2.20

27.20 = 4m

m= 6.8

4(6.8) = 27.20 - 25 = 2.20

Answer:

3/4

Step-by-step explanation:

Since, angles θ and α are complementary.

Therefore,

θ + α = 90°

θ = 90° - α

Taking sin both sides.

sin θ = sin (90° - α)

sin θ = cos α (sin (90° - θ) = cos θ)

Since, sin θ = 3/4.....(given)

Hence, cos α = 3/4

Answer:

1/4

Step-by-step explanation:

The slope of a graph is always the rate of change for every value of x, in this case, days. Since she is adding 1/4 of a mile to her run each day, this means that the slope of this linear relationship is 1/4.

She increases a full mile in 4 days, just a little note.

Answer:

Step-by-step explanation:

Given,

x = 2

y = - 4

Now, let's solve:

[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]

plug the values

[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]

A negative base raised to an odd power equals a negative

[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]

Determine the sign of the fraction

[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]

Write the expression in exponential form with a base of 2

[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]

Calculate the product

[tex] - \frac{1}{ {2}^{5} } [/tex]

Evaluate the power

[tex] - \frac{1}{32} [/tex]

Hope this helps...

Best regards!!

Answer:

The cost is $.08 per ounce or 8 cents per ounce

Step-by-step explanation:

1 quart = 32 ounces

2 quarts = 64 pints

2 quarts costs 5.12

Take the cost and divide by the number of ounces

5.12 / 64

.08 per ounce

The cost is $.08 per ounce or 8 cents per ounce

=================================================

Explanation:

1 quart = 32 fluid ounces

2 quarts = 64 fluid ounces (multiply both sides by 2)

He paid 5.12 dollars for 64 fluid ounces, so the unit rate is 5.12/64 = 0.08 dollars per fluid ounce, or 8 cents per fluid ounce.

---------

We can think of it this way in terms of an equation

5.12 dollars = 64 fluid ounces

5.12/64 dollars = 64/64 fluid ounces ... divide both sides by 64

0.08 dollars = 1 fluid ounce

We divided both sides by 64 to turn "64 fluid ounces" into "1 fluid ounce", due to how the term "unit rate" is set up. The term "unit" means "one". Basically we're finding the cost per 1 unit, or per 1 fluid ounce.

Answer:

1) $10b

2) 20

3) $5a

Answer:

57°

Step-by-step explanation:

∠LOM and ∠MON are complementary angles, so they add up to 90.

This means that:

3x-15 + 5x-23 = 90 =>

8x - 38 = 90 =>

x = 128/8 = 16

So m∠MON = 5*16 - 23 = 57°

Answer:

Step-by-step explanation:

(3x-15)=90

find x

x=35

input it into the equation

42+23 =m<mon

x=45 degrees

Answer:

Option A is the correct option.

Step-by-step explanation:

As the graph of ( f + g ) ( x ) is a line. So, ( f + g ) ( x ) is linear which means x² of f ( x ) and x² of g ( x ) get cancelled on adding . They must be equal and opposite in sign.

So, Option A is correct.

Hope this helps..

Best regards!!

Answer:

Step-by-step explanation:

To find the slope first write the equation in the form

y = mx + c

where m is the slope

c is the y intercept

3x - 3y = -45

3y = 3x + 45

Divide both sides by 3

y = 3/3x + 45/3

y = x + 15

From the equation the slope = 1

Parallel lines have equal slope

So

The line parallel to the above line is also

1

Hope this helps you

Answer:

The equation is true

Step-by-step explanation:

The best way to check if this equate is true is to convert the pi in radians to degree and actually evaluate the trigonometric terms.

Mathematically we know that pi = 180 degrees

So pi/8 = 22.5

and pi/4 = 180/4 = 45

So let’s make our check.

Insert pi = 22.5 and pi = 45

So we have;

tan 22/5 = √(1-cos45)/(1+cos45)

Now let’s evaluate this using a calculator.

tan 22/5 = 0.414213562373

The term in the root; 0.171572875254

The square root of this number is 0.414213562373

This is exactly as what is obtained with the tan 22.5

So we conclude that what we have is true

Answer:

Step-by-step explanation:

Initial balance of Marta Fuentes  = $1200.50

Charge made by her bank;

Credit of $505 and Charge on new checks is $12.

Total charge incurred = $505+$12

Total charge incurred = $517

Since there will be no outstanding checks or deposit, her checkbook balance will be the difference between the initial balance and amount charged by the bank.

Checkbook balance = $1200.50 - $517

Checkbook balance = $683.50

Hence her checkbook balance should be $683.50

Answer:

[tex]n^6[/tex].

Step-by-step explanation:

[tex]n^4 * \frac{n^7}{n^5}[/tex]

= [tex]n^4 * n^{7 - 5}[/tex]

= [tex]n^4 * n^2[/tex]

= [tex]n^{4 + 2}[/tex]

= [tex]n^6[/tex].

Hope this helps!

Answer:

BCD

Step-by-step explanation:

Answer: B,C & D

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

(f - g)(x) = ( f(x) ) -  ( g(x) )

(f - g)(x) = (4x^2 - 6) - ( x^2 - 4x - 8)

(f - g)(x) = 4x^2 - 6 - x^2 + 4x + 8

(f - g)(x) = (4x^2-x^2) + 4x + (-6+8)

(f - g)(x) = 3x^2 + 4x + 2

Answer:

Option D. (8, – 4)

Step-by-step explanation:

3x + 4y = 8 ..... (1)

x – y = 12.... (2)

To solve the above equation by elimination method, do the following:

Step 1:

Multiply equation 1 by the coefficient of x in equation 2 i.e 1.

Multiply equation 2 by the coefficient of x in equation 1 i.e 3. This is illustrated below:

1 × Equation 1

1 × (3x + 4y = 8)

3x + 4y = 8 ...... (3)

3 × Equation 2

3 × ( x – y = 12)

3x – 3y = 36......(4)

Step 2:

Subtract equation 3 from equation 4. This is illustrated below:

. 3x – 3y = 36

– (3x + 4y = 8)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

– 7y = 28

Divide both side by the coefficient of y i.e –7

y = 28/–7

y = – 4

Step 3:

Substitute the value of y into any of the equation to obtain the value of x. In this case, we shall substitute the value of y into equation 2 as shown below:

x – y = 12

y = –4

x – (–4) = 12

x + 4 = 12

x = 12 – 4

x = 8

Therefore, the solution to the equation above is (8, – 4)

Answer:

(8, – 4)

Step-by-step explanation:

my math teacher told me