Solve the following quadratic equation for complex solutions 3x^2- 7x + 11 = 0

Answer:

x = 1/6 or x = 3

Step-by-step explanation:

Given :

Solving :

Answer:

$6,722.63

Step-by-step explanation:

Now: $10,200

In 1 year: 0.92 × $10,200 = $9,384

In 2 years: 0.92 × $9,384 = $8,633.28

In 3 years: 0.92 × $8,633.28 = $7,942.6176

In 4 years: 0.92 × $7,942.6176 = $7,307.208192

In 5 years: 0.92 × $7,307.208192 = $6,722.63

Answer: $6,722.63

Answer:

$6,722.63

Step-by-step explanation:

Using this formula A=P(1-d/100)^n where

A = Amount

P = Principal

d = percent

n = number of year

A=P(1-d/100)^n

A = 10,200(1-8/100)⁵

A = 10,200(1-0.08)⁵

A = 10,200(0.92)⁵

A = 10,200(0.6591)

A= $6,722.63

Answer:

(a) BC = 91 cm

(b) ∠C = 33.4° (nearest tenth)

(c) AD = 79.5 cm (nearest tenth)

Step-by-step explanation:

(a) Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

⇒ 60² + BC² = 109²

⇒ 3600 + BC² = 11881

⇒ BC² = 11881 - 3600

⇒ BC² = 8281

⇒ BC = √(8281)

⇒ BC = 91 cm

(b) Sine rule to find an angle:

   \(\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles, and a, b and c are the sides opposite the angles)

Given:

\(\implies \dfrac{\sin (90)}{109}=\dfrac{\sin C}{60}\)

\(\implies \sin C=60 \cdot\dfrac{\sin (90)}{109}\)

\(\implies \sin C=\dfrac{60}{109}\)

\(\implies C=33.39848847...\textdegree\)

\(\implies C=33.4\textdegree \ \sf(nearest \ tenth)\)

(c) Sine rule to find a side length:

   \(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

(where A, B and C are the angles, and a, b and c are the sides opposite the angles)

Sum of interior angles of a triangle = 180°

Given:

\(\implies \dfrac{AD}{\sin (90)}=\dfrac{60}{\sin (49)}\)

\(\implies AD=\sin (90) \cdot \dfrac{60}{\sin (49)}\)

\(\implies AD=79.5007796...\)

\(\implies AD=79.5 \ \sf cm \ (nearest \ tenth)\)

Answer:

Step-by-step explanation:

Similar triangles have the same shape but different sizes.

A is incorrect. We don't know the length of the sides, or if it is equilateral so we can't say that fg/lm=fh/ln

B is correct. FH and LN may be different sizes but they are similar

C is correct. Since the triangles are similar the angles are similar.

D is incorrect. The triangle is the same shape, not neccesarily the same size

E is correct. See C for explanation.

Step-by-step explanation:

see the above attachment.

hence your answer is A.

hope this helps you .

Answer:

y = 8

Step-by-step explanation:

RT = RS+ST

13y – 23 = ( 6y+2) + (3y+7)

13y – 23 = 9y +9

13y – 9y = 9+23

4y = 32

y = 32/ 4

y = 8

I hope I helped you^_^

Answer:

y = 8

Step-by-step explanation:

I. When RS = 6y + 2, ST = 3y + 7 and RT = 13y - 23

  That makes RT = RS + ST

                   13y - 23 = 6y + 2 + 3y + 7

                    13y - 23 = 9y + 9

                   13y - 9y = 9 + 23

                         4y = 32

                           y = 8

II. Prove by replace y.value

                13y - 23 = 6y + 2 + 3y + 7

                13(8) - 23 = 6(8) + 2 + 3(8) + 7

                104 - 23 = 48 + 2 + 24 + 7

                          81 = 81 true

So 81 is total length of RT.

Good luck.

The number of ways if the order of the choices is taken into consideration is 24 and the number of ways if the order of the choices is not taken into consideration is 4

The given parameters are:

Letters, n = 4

Letters to select, r = 3

The order of the choices is taken into consideration.

This means permutation.

So, we have:

nPr = n!/(n -r)!

This gives

4P3 = 4!/1!

Evaluate the quotient

4P3 = 4!

Expand

4P3 = 4* 3 * 2 * 1

Evaluate

4P3 = 24

Hence, the number of ways if the order of the choices is taken into consideration is 24

The given parameters are:

Letters, n = 4

Letters to select, r = 3

The order of the choices is not taken into consideration.

This means combination.

So, we have:

nCr = n!/r!(n -r)!

This gives

4C3 = 4!/(3! * 1!)

Expand

4C3 = 4 * 3!/(3! * 1!)

Evaluate the quotient

4C3 = 4

Hence, the number of ways if the order of the choices is not taken into consideration is 4

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Answer:

Step-by-step explanation

Here ya go.

The slope of the graph of this linear function is -1/2 in decimal form.

What is slope?

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (6, 1) and (x2, y2) = (-6, -5)

slope = (-5 - 1) / (-6 - 6)

slope = -6/12

slope = -1/2

Therefore, the slope of the graph of this linear function is -1/2 in decimal form.

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Answer:

Can you import the progress report picture please

Step-by-step explanation:

So we can solve it

Answer:

Ms. Rangtonsmith will get $30 after raise

Step-by-step explanation:

Current salary = $25

raise = 1/5 of current salary

substituting current salary with $25

raise in dollar value = 1/5 of $25 = 1/5 *$25 = $5

Thus, raise is $5

total salary after raise will be sum of current salary and raise

total salary after raise = $25 + $5 = $30

Thus, Ms. Rangtonsmith will get $30 after raise

Step-by-step explanation:

the scale factor is 1

1/1

both triangles are similar and the scale factor is 1/1

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

Answer:

1. q = p - mn

2. c = -6

3. 10

Step-by-step explanation:

1.

\(mn=p-q\\\textsf{add q to both sides}\implies mn + q = p\\\textsf{subtract mn from both sides}\implies q = p-mn\)

2.

\(5c+23=c-1\\\textsf{subtract 23 from both sides}\implies5c=c-24\\\textsf{subtract c from both sides}\implies4c=-24\\\textsf{divide both sides by 4}\implies c=-6\)

3.

\(4f^2-g\\\implies 4(2)^2-3=13\\\\3f^2-3g\\\implies 3(2)^2-(3 \times3)=3\\\\13-3=10\)

Answer:

87

Step-by-step explanation:

Believe it or not, this "math" question actually requires no math whatsoever. If you flip the image upside down, you'll see that what you're dealing with is a simple number sequence.

Answer:

87

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

because since AC is 24 units long, and BC is half of AC, then that would be 12 units, and since DC is half of BC, then that would be six units.

The polynomial function is: y = f(x) = -3(x^2 - x - 2)(x^2 +2)

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has an exponent equal to 1.

f(x) = k(x+1)(x-2) (x - sqrt(2)*i)(x + sqrt(2)*i)

f(x) = k(x^2 - 2x + 1x - 2)( x^2 - 2*(-1))

f(x) = k(x^2 -x - 2)(x^2 + 2)

f(1) = 18

k*(1 - 1 - 2)(1 + 2) = 18

k*(-2)(3) = 18

k*(-6) = 18

k = -3

The polynomial function is:

                        y = f(x) = -3(x^2 - x - 2)(x^2 +2)

You can finish multiplying them together if you must.

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Answer:

C. 1-x

Step-by-step explanation:

Negatives are alwys less than positives meaning a&b are out and 1-100 is -99 and 10-100 is -90 meaning that C is your answer

The first plane is farther from the airstrip after the second leg

The first plane

Initial distance = 150 miles west

Additional distance = 220 miles 30 degrees SW

This means that

Additional distance = 220 * cos(30) miles SW

Additional distance = 190.53 miles

Total distance = 150 + 190.53 = 340.53

The second plane

Initial distance = 220 miles east

Additional distance = 150 miles x degrees SE

This means that

Additional distance = 150 * cos(x) miles SW

Total distance = 220 + 150 cos(x)

Given that

x < 30

We have

Second plane < First plane

220 + 150 cos(x) < 340.53

Evaluate

cos(x) < 0.8035

Take the arc cos of both sides

x < 36

x < 36 is not the same as x < 30

Hence, the first plane is farther

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Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

\(v=5\)

Explanation:

The equation is asking for multiplication (13 * v), and the opposite of multiplication is division. So if we divide 65 by 13, we find 5.

13 * 5 = 65

Answer:

v = -5

Step-by-step explanation:

1. Pull out like factors :

  -13v - 65  =   -13 • (v + 5)

2. Solve :    -13   =  0

This equation has no solution.

A a non-zero constant never equals zero.

3. Solve  :    v+5 = 0

Subtract  5  from both sides of the equation :

                     v = -5

Answer:

For #17:

This is a 45-45-90 triangle. Therefore, the missing side length (x) is equal to the other leg of the triangle, which is 6.

For #18:

This is a 30-60-90 triangle. Therefore, the missing side length (m) is equal to the hypotenuse (18) divided by 2, or 9.

For #19:

This is a 30-60-90 triangle. Therefore, the missing side length (y) is equal to the hypotenuse (12) multiplied by the square root of 3, or 12√3.

For #20:

This is a 30-60-90 triangle. Therefore, the missing side length (u) is equal to the short leg (5√3) multiplied by 2, or 10√3.

For #21:

This is not a right triangle because the angles do not add up to 180 degrees.

For #22:

This is a right triangle because the angles add up to 180 degrees and one of the angles is 90 degrees.

Step-by-step explanation:

A defective stamp is likely to be chosen at random 1.4% of the time, or about 0.014 times. The observed percentage probability  faulty stamps is below the 3.5% maximum permitted rate,

Name an event from one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favorable outcomes from the total number of possibilities that are feasible.

P(faulty) = quantity of defective stamps divided by total quantity of stamps

P(defective) = 10/700.

0.014 P(defective)

Consequently, there is a 1.4% chance (or about 0.014) that a randomly chosen stamp will be flawed.

B-The observed percentage of flawed stamps is:

10 / 700 0.5 – 0.014

Divide this rate by 100 to get the percentage:

0.014 x 100 approximately 1.4%

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1) If the 10 kg sugar is Rs. 880 . Find the cost of 15 kg sugar.....

Solution,

let the required cost be Rs x

Here , the quantities of sugar and their cost are direct proportion

So, 10 : 15 = 8: x

\( \: \frac{10}{15} = \frac{880}{x} \\ x = \frac{880 \times 15}{10} \\ x = Rs1320\)

Hence , the cost of sugar is Rs.1320

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2) 50 students in a hostel have provisions for 21 days . How long would it last for 75 students?

Solution,

Let the required number of a day = x

Here , the number of student and the number of days are in inverse proportion.

•°• 50 : 75. = x : 21

\( \frac{50}{75} = \frac{x}{21} \\ x = \frac{50 \times 21}{75} \\ x = 14 \: days \\ \)

Hence, the provisions last for 14 days for75 students

~nightmare 5474~

1) The cost of 15 kg sugar is; Rs. 1320

2) The number of days that it would take the provisions to last for 75 students is; 14 days

1) Cost of 10 kg = Rs. 880

Thus, by proportion the cost of 15 kg sugar will be;

(15 × 880)/10

>> 13200/10

>> Rs. 1320

2) We are told that;

50 students = provisions for 21 days

Thus for 75 students the number of days the provisions would last them is gotten by proportion;

(50 × 21)/75

>> 1050/75

>> 14 days

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Answer:

y=1-5x

Step-by-step explanation:

10x+2y=2

add subtract 10 from both sides

10x+2y=2

-10x. -10x

so now the equation should look like

2y=2-10x

then after that you have to get the Y variable alone so you have to divide everything by 2

2y÷2 = 2÷2 - 10x÷2

After you divide every term by 2 you slope intercept should be

y= 1-5x

please correct me if I am wrong

9514 1404 393

Answer:

  x = 16

Step-by-step explanation:

"Solve algebraically" means "solve it using the rules of algebra." You could also solve it by guessing, or by graphing, or by submitting the equation to a machine solver (calculator, app, or web site).

__

To solve for x, undo what has been done to x. The expression on the right shows that x has 2 added, and the sum is divided by 3. We "undo" these operations in reverse order.

undo divide by 3

Multiplication is the inverse operation for division, so we want to multiply both sides of the equation by 3:

  3(6) = 3(x +2)/3

  18 = x +2

undo add 2

Subtraction is the inverse operation for addition, so we want to subtract 2 from both sides of the equation:

  18 -2 = x +2 -2

  16 = x

The value of x that makes this equation true is x = 16.

Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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Answer: B = 15 kph or 15 kph

step by step

(b-5)*10=(b+5)*5

10b-50=5b+25

5b=75

b=15 kph in still water

my name is jeff   Step-by-step explanation: