A portion of the Quadratic Formula proof is shown. Fill in the missing statement

Answer:

Option B is correct.

Explanation:

Remove the denominators:

[tex]\sf \rightarrow \dfrac{1}{2}x - \dfrac{1}{5} y = 2[/tex]

make the denominator's same

[tex]\sf \rightarrow \dfrac{5}{10}x - \dfrac{2}{10} y = 2[/tex]

Join the fraction's:

[tex]\sf \rightarrow \dfrac{5x-2y}{10} = 2[/tex]

Multiply both sides by 10

[tex]\sf \rightarrow {5x-2y} = 20[/tex]

Remove the denominators:

[tex]\rightarrow \sf x + \dfrac{2}{3}y =5[/tex]

make the denominator's same

[tex]\rightarrow \sf \dfrac{3x}{3} + \dfrac{2}{3}y =5[/tex]

Join the fraction's:

[tex]\rightarrow \sf \dfrac{3x+2y}{3} =5[/tex]

Multiply both sides by 3

[tex]\rightarrow \sf 3x+2y} =15[/tex]

Answer:

B)  5x - 2y = 20  and  3x + 2y = 15

Step-by-step explanation:

Rewrite both equations in standard form:

Equation 1

[tex]\dfrac{1}{2}x-\dfrac{1}{5}y=2[/tex]

Multiply both sides by 10:

[tex]\implies \dfrac{1 \cdot 10}{2}x-\dfrac{1 \cdot 10}{5}y=2 \cdot 10[/tex]

[tex]\implies \dfrac{10}{2}x-\dfrac{10}{5}y=20[/tex]

[tex]\implies 5x-2y=20[/tex]

Equation 2

[tex]x+\dfrac{2}{3}y=5[/tex]

Multiply both sides by 3:

[tex]\implies x \cdot 3+\dfrac{2 \cdot 3}{3}y=5 \cdot 3[/tex]

[tex]\implies 3x+2y=15[/tex]

Therefore, the equivalent system is:

5x - 2y = 20  and  3x + 2y = 15

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\: Concept }}}[/tex]

[tex] \large\underline{ \boxed{ \sf{✛\: Assumptions\:✛ }}}[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\: let's\:solve }}}[/tex]

[tex] \rm\angle \: p + \angle \: q = 180 \degree \\ [/tex]

★ Substituting values

[tex] \rm { \pink➾ \:( 3x - 4) + (3x - 8) = 180} \\ \rm { \pink➾}arranging \: and \: solving \: like \: terms \\ \rm { \pink➾ \: 3x + 3x - 4 - 8 = 180} \\ \rm { \pink➾ \: 6x - 12 = 180} \\ \rm { \pink➾6x = 180 + 12}[/tex]

[tex] \qquad \qquad\rm { \pink➾6x = 192} \\ \qquad\qquad\rm { \pink➾ \: x = \frac{ \cancel{192}}{ \cancel6} } \\ \qquad\qquad\rm { \pink➾x = 32}[/tex]

★ Hence the value

[tex] \boxed{↪\underline{ \boxed{ \rm{\: x = 32\green✓}}}↩}[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

Hope it helps !

A circle is a curve sketched out by a point moving in a plane. The circumference of the ring of fire is 6.2831 meters.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The circumference of the ring if the radius is 1 meter is,

Circumference of the ring = 2πr = 2 × π × 1 = 6.2831 meters

Hence, the circumference of the ring of fire is 6.2831 meters.

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CALCULATE THE AREA

=LENGTH X BREADTH

=6M X 1M

[tex]6 {m}^{2} [/tex]

NOW CHANGE THE METRES TO MILLIMETRES

=1000MM=1M

SO,IF 1M=1000MM

THEN 6M=MORE

IF MORE LESS WILL DIVIDE

GIVING YOU

[tex] \frac{6}{1} \times 1000mm[/tex]

[tex]6000mm[/tex]

Answer: 1/200

Step-by-step explanation:

1/6 divided  by 6 is equal to 0.05555555555 Which is equal to about 1/200

The expression [tex]\frac{(-6.4)^8}{(-6.4)^6}[/tex] is an exponential expression and the value of the expression is 40.96

The expression is given as:

[tex]\frac{(-6.4)^8}{(-6.4)^6}[/tex]

Expand the expression by applying the law of indices

[tex]\frac{(-6.4)^8}{(-6.4)^6} = (-6.4)^{8-6}[/tex]

Evaluate the difference

[tex]\frac{(-6.4)^8}{(-6.4)^6} = (-6.4)^2[/tex]

Evaluate the exponent

[tex]\frac{(-6.4)^8}{(-6.4)^6} = 40.96[/tex]

Hence, the value of the expression is 40.96

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By dividing both sides by 3, we conclude that each person gets $6.25.

Here we want to solve the equation:

3n = 18.75

for n.

Remember that if we perform the same operation in both sides of the equality, then the equality remains true.

So here we can divide both sides of the equation by 3, so we get:

(3n)/3 = 18.75/3

n = 18.75/3 = 6.25

n = 6.25

So we can conclude that each one gets $6.25

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Answer: 8 units

Step-by-step explanation:

  We will use the distance formula.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]\displaystyle d=\sqrt{(-4-4)^2 +(7-7)^2}[/tex]

[tex]\displaystyle d=\sqrt{(-8)^2 +(0)^2}[/tex]

[tex]\displaystyle d=\sqrt{64[/tex]

d = 8

Answer:

8192

Step-by-step explanation:

The pattern is mulitply by 2 to get the next term

4*2=8

8*2=16

So: 4,8,16,32,64,128,256,512,1024,2048,4096,8192

The take-home pay of Tyson after deduction of his obligations from total income equals to $28,524.

This means the net income that an individual takes home.

Take-home pay = Annual Salary - Federal Income Tax - FICA - Disability Insurance - Life Insurance

Take-home pay = $42,500 - $8,500 - $3,251 - $2,125 - $$100

Take-home pay = $28,524

Thus, the take-home pay of Tyson after deduction of his obligations from total income equals to $28,524.

Therefore, the Option C is correct.

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Answer:

Let a two digit number be, 10x + y.

75% of the number is,

= 75 % of (10 x + y)

= 75/100 × (10x+y)

= 3/4 × ( 10x + y)

According to the question, When increased by 75%, The digits must be reversed.

So,

(10 x + y) + 3/4 ( 10x + y) = 10y + x

4 (10x + y) + 3 ( 10x + y) = 4 ( 10y + x)

7(10x + y) = 4(10y + x)

70x + 7y = 40y + 4x

70x - 4x = 40 y - 7y

66x = 33y

2x = y

So,

x = 1, y = 2, 10x + y = 12

x = 2, y = 4, 10x + y = 24

x = 3, y = 6, 10x + y = 36

x = 4 , y = 8 , 10x + y = 48

x can't be 5, as y will be 10 ( y should be a single digit).

Therefore, 4 two digit numbers are possible.

Answer:

230 tickets

Step-by-step explanation:

Create a proportion using the given information:

Let's set x equal to the number of tickets that need to be sold.

[tex]\frac{207}{90} =\frac{x}{100}[/tex]

Cross multiply and you get:

[tex]90x=20700\\[/tex]

Then divide both sides by 90 to get:

[tex]x = 230[/tex]

This means that 230 tickets need to be sold in order to fill all of the seats on the flight.

The measure of the angle MOP is 61° (Third option)

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Angle MON is a straight angle → ∠MON=180°

∠QON=58° (according to the graph)

OP bisects angle ∠MOQ, then OP divides angle ∠MOQ into two equal angles:

∠MOP=∠POQ=∠MOQ/2  (1)

∠MOQ+∠QON=∠MON

Replacing the known values in the equation above:

∠MOQ+58°=180°

Solving for ∠MOQ: Subtracting 58° on both sides of the equation

∠MOQ+58°-58°=180°-58°

∠MOQ=122°

Replacing ∠MOQ by 122° in the equation (1)

(1) ∠MOP=∠POQ=122°/2

∠MOP=∠POQ=61°

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Answer: 570 total calories

Step-by-step explanation:

450 calories in 50 grams of fat

120 calories in 30 grams of protein

120 + 450= 570

Answer:

Step-by-step explanation:

You need the Pythagorean Theorem to solve this question. There is no be part.

Equation

c^2 = a^2 + b^2

Givens

a = 32

b = 21

c = ?

Solution

c^2 = a^2 + b^2              Substitute the values

c^2 = 32^2 + 21^2          Expand

c^2 = 1024 + 441            Combine

c^2 = 1465                     Take the square root of both sides

√c^2 = √1465  

c = 38.275

Answer: 38.3 rounded

The given statement can be written as:

6+√-80

To solve √-80 re-write -80 as -1 * 80

Now √-80 =√-1 * 80

Now we can write it as:

6+ √-1 * √80

We know that √-1 = i

Thus it becomes:

6+ i√80

Now find the square root of 80

80 does not have a perfect square root

Its square root can be found as 80 = 4*4*5

Then,

6+i√4*4*5

Notice that 4 makes a pair.. So we will write it outside the square root

6+1*4√5

We will write it as:

6+4i√5

Thus the correct option is 6 plus 4 i times the square root of 5....

The area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We know the area in the polar coordinates is given by:

[tex]\rm A =\int\limits^a_b {\dfrac{1}{2}r^2} \, d\theta[/tex]

We have r = sin2θ

Here the quadrant is not given, so we are assuming we need to find the area in the first quadrant.

Put this value in the above integration and limit 0 to π/2

[tex]\rm A =\int\limits^{\dfrac{\pi}{2}}_0 {\dfrac{1}{2}(sin^22\theta)} \, d\theta[/tex]

After solving the above integration, we get:

[tex]\rm A = \dfrac{\pi}{8}[/tex]

Thus, the area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units

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Answer:

see the attachment!

i hope this can help you.

Answer:

Step 1-Write an equation, letting x represent Kareem’s age:

(x + 3) + x + 2 x = 33

Step 2-Solve the equation:

(x + 3) + x + 2 x = 33. 3 + 4 x = 33. 4 x = 30. x = 7 1/2.

Step 3-Sadie is 10 1/2, Kareem is 7 1/2, and Nadra is 3 3/4.

Which corrects the student’s first error?

1. In Step 1, the student should have used One-half x to represent Nadra’s age, and written the equation (x + 3) + x +1/2x = 33.

2. In Step 2, the student should have added 3 on both sides of the equation to find a solution of x = 9.

3. In Step 3, the solution represents Sadie’s age. Therefore, Sadie is 7 1/2, Kareem is 4 1/2, and Nadra is 2 1/4.

4. In Step 3, Nadra’s age is the difference between 33 and Sadie’s and Kareem’s ages, so Nadra is 15.

Answer:

1848 cm

Step-by-step explanation:

You would multiply 22 by 10.5 by 8 centimeters which would equal 1848 centimeters.

Answer:

Step-by-step explanation:

1440.

Answer:

234 students

Step-by-step explanation:

% Don't ride the bus = 100% - % Ride the bus

Number of students who don't ride the bus :

The total cost for the number of raffle tickets is given by y = 4x; while the cost of 6 tickets is $24

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the total cost of x tickets.

From the table:

1 ticket cost $4, hence:

y = 4x

The cost of 6 tickets is:

y = 4(6) = 24

The total cost for the number of raffle tickets is given by y = 4x; while the cost of 6 tickets is $24

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Answer:

Agree.

Step-by-step explanation:

1. (5^r)^t can be represented simply as 5^rt.

2. when r as negative integer, t as positive integer, rt is always a negative integer

3. when ever the indices rt is negative, the number 5^rt will be less than 1, thus cannot be a whole number for sure.

it's base× height (same as a rectangle:

4×5=20

the triangle, 3, and right angle are there just to confuse you :)

area: 37.74 yds

you get this by multiplying the length and width

perimeter: 25 yds

you get this by adding up the length of each side

Answer:

opposite meanings

Step-by-step explanation:

An antonym is a word that means the opposite of another word