Write 7,250,000,000 in scientific notation.

Answer:

[tex]x=\dfrac{1 +\sqrt{673}}{24}, \quad x=\dfrac{1 -\sqrt{673}}{24}[/tex]

Step-by-step explanation:

Given equation:

[tex]3x( 4x +7 ) + 3( 8 + 2 ) = 11( 2x + 3 ) + 11[/tex]

Distribute the parentheses:

[tex]\implies 12x^2+21x+24+6=22x+33+11[/tex]

[tex]\implies 12x^2+21x+30=22x+44[/tex]

Subtract 22x from both sides:

[tex]\implies 12x^2+21x+30-22x=22x+44-22x[/tex]

[tex]\implies 12x^2-x+30=44[/tex]

Subtract 44 from both sides:

[tex]\implies 12x^2-x+30-44=44-44[/tex]

[tex]\implies 12x^2-x-14=0[/tex]

Use the quadratic formula to solve for x.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies a=12, \quad b=-1, \quad c=-14[/tex]

Therefore:

[tex]\implies x=\dfrac{-(-1) \pm \sqrt{(-1)^2-4(12)(-14)}}{2(12)}[/tex]

[tex]\implies x=\dfrac{1 \pm \sqrt{1+673}}{24}[/tex]

[tex]\implies x=\dfrac{1 \pm \sqrt{673}}{24}[/tex]

Question number 4

Given:

One side of a right-angled triangle 6 and the hypotenuse of the triangle 10

Required:

Another side of the triangle

Explanation:

For the right-angled triangle, Pythagorean theorem is applied which is

where

a=side of the right triangle

b=side of the right triangle

c=hypotenuse

so hypotenuse =

Final Answer:

8

Outcomes are the possible pairings of crust and pizza that Heather can choose. Based on the tree diagram, we see that there are 12 possible pairings starting from (thin, onions) to (pan mushrooms). Hence, there are 12 outcomes.

Based on the list of outcomes, there is only 1 outcome in which both the regular crust and sausage are chosen.

Lastly, for pepperoni OR mushroom being chosen, let's take a look and count.

There are 6 outcomes in which pepperoni or mushrooms were chosen.

Answer:

-8

Step-by-step explanation:

So first off, x is 2-4. So that's the default. It would be -2. If you multiply -2 by 2, it is -4.

Solution

The area of a circle with diameter d is

Therefore, the exact area is 4π centimeters square.

Given:

The difference between two numbers is 22.

The sum of twice the smaller number and 3 times the greater number is 246.

Required:

To find the two numbers.

Explanation:

Let the two numbers be x and y.

Let y be the smaller number.

The difference between two numbers is 22.

The sum of twice the smaller number and 3 times the greater number is 246.

Now

Now x is,

Final Answer:

The two numbers are 58 and 36.

Net Income tax payable $41,516.75 (f + g)

As per the data are given in the above question it is given that,

Henrich has $195,000 of taxable income,

i.e. Taxable Income (a) $195,000  

Which includes $50,000 of long-term capital gain that is taxed at preferential rates.

i.e. Preferentially taxed income (b) $50,000

Assume his modified AGI is $210,000.

Therefore Income taxed at ordinary rates ( c) $145,000

Tax on c above (d) $33,636.75 = $18,558.75 + [($145,000 - $91,150) x 28%]

Tax on b above ( e) $7,500.00 = $50,000 x 15%

Total Income tax (f) $41,136.75 (d + e)

Investment Income, if any (g) $380 Only $10,000 is taxed at 3.8%, only ($210,000 - $200,000) i.e. $10,000

Net Income tax payable $41,516.75 (f + g)

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the given UPC bar code digit is

2- 91273 - 05213 - d

for determining d we will follow the rule

first, we sum up all the odd place numbers

like

2 + 1 + 7 + 0 +2 + 3 = 15

then multiply with 3

15 * 3 = 45

then

we sum up all the even place numbers,

9 + 2 + 9 +5 + 1 = 26

now we will add these two results

26 + 45 = 71

now we can see that 71 is 9 less than the next multiple of 10 that is 80 in this case'

80 - 71 = 9

so the answer is

d = 9 .

the set consist totally 10 numbers,p(s)=numbers divided by 12/total number

The remainder, R(3) = 18

The given function is:

According to the remainder theorem, the remainder when the function f(x) is divided x-3 is gotten by substituting x = 3 into f(x)

The remainder = 18

SOLUTION:

The graph presented is a quadratic graph with the expression f(x)

It forms a n-curve indicating a negative quadratic curve.

the vertical axis is the y-axis or f(x)-axis AND

the horizontal axis is the x-axis

f(1)

We are required to find by tracing the value of y when x=1

Final answer:

The value of y when x=1 is -3

f(1) OR y= -3

Let x be the regular price, then we can set the following equation:

Solving for x we get:

Answer

Perimeter = 22 units

Explanation

To answer this, we need to note that two tangents to a circle that start from the same point usually have the same lengths.

So,

AD = AE = 6

CD = CF = 4

Since,

AB = 7 and AB = AE + EB

AE = 6

So,

AB = AE + EB

7 = 6 + EB

EB = 7 - 6

EB = 1

FB = EB = 1

So,

AC = AD + DC = 6 + 4 = 10

AB = 7

CB = CF + FB = 4 + 1 = 5

So, the perimeter of the triangle is given as the sum of all its exterior sides

Perimeter = AB + AC + CB

Perimeter = 7 + 10 + 5 = 22 units

Hope this Helps!!!

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

ladder = 16 feet

base = 5 feet

height = ?

Step 02:

Pythagoras Theorem Formula

c ² = a² + b²

16 = c

5 = b

height = a

16² = a ² + 5²

16² - 5² = a²

15.2 = a

The answer is:

The distance to the top of the ladder is 15.2 feet

Angle 4 and angle 6 are supplementary to each other.

Given : the two line r and s are parallel to each other and there are two transversals

And thus angle 6 and angle 4 are equal because angles corresponding angles are equal. This is because of a theorem which states that angles on the same side of the two parallel lines are equal .

And this further implies that the angle adjacent to angle 4 and angle form will form an angle whose sum would be equal to 180 degree. That is they will form a supplementary angle .

And this angle and angle 1 are equal because these two angles are corresponding angles and as mentioned above because of that theorem they are equal.

Thus from these two above mentioned arguments it is clear that angle 4 and angle 6 are supplementary angles .

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We are given the following expression:

We can apply the distributive property to get:

Since there are no like terms this expression can't be simplified any further.

Answer

y = -1/4

Step-by-step explanation:

Let the unknown variable be y

5 more than the product of a number and 8 equals to 3 can be expressed mathematically as

Recall, that the unknown variable is y

5 + (8 * y) = 3

Open the parenthesis

5 + 8y = 3

Substract 5 from both sides

5 - 5 + 8y = 3 - 5

8y = -2

y = -2/8

y = -1/4

[tex]f^{ - 1} (x)[/tex]

IS THE INVERSE OF f(x) .TO OBTAIN THE INVERSE OF A GRAPH WE SWAP POINTS. MEANING WHAT WAS THE X COORDINATE BECOMES THE Y COORDINATE AND WHAT WAS THE Y COORDINATE BECOME THE X COORDINATE.

DOING WHAT I EXPLAINED (-2,3)IS THE POINT OF THE INVERSE GRAPH .

GOODLUCK

x ≤ -5

This can be written in interval notation as :

( - ∞ , -5]

The correct option is option A

Solution

For this case we can do the following procedure:

then the answer is: 44.4%

Generally when a coordinate (x , y) is rotated 180 degrees about the origin, it becomes (-x , -y).

Now, the coordinates of the vertices of the triangle will follow a similar transformation when the triangle is rotated 180 degrees about the origin, as follows:

See the figure below which shows the transformation

Answer:

  m∠E = 52°

Step-by-step explanation:

You seem to want a step-by-step explanation of the logic to find the measure of angle E.

There are a number of approaches you might take to this. Here is one.

  [tex]\begin{array}{ccc}\text{Step}&\text{Angle}&\text{Reason}\\1&m\angle C=64^\circ&\text{Given}\\2&m\angle ADE=64^\circ&\textsf{Corresponding angles}\\3&m\angle DAB=64^\circ&\textsf{Alternate interior angles}\\4& m\angle DAE=64^\circ& \textsf{Angle bisector de}\textsf{finition}\\5& m\angle E=52^\circ&\textsf{Sum of angles in a triangle}\end{array}[/tex]

The measure of angle E is 52°.

Answer:

11/15 < 4/5

Step-by-step explanation:

this is because:

3/4 < 4/6 is the same as 9/12 < 8/12 which is incorrect

5/6 > 10/12 is the same as 10/12 > 10/12 which is incorrect

8/16 = 1/4 is the same as 8/16 = 4/16 which is incorrect

therefore the only possible answer is 11/15 < 4/15 because:

it is the same as 11/15 < 12/15 which is CORRECT

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

(y + 3)(y² + 8y – 2). (y + 3)(y² + 8y – 2)

simplify

Step 02:

We must apply the algebraic rules to find the solution.

(y + 3)(y² + 8y – 2). (y + 3)(y² + 8y – 2)

Part 1:

(y + 3)(y² + 8y – 2) = y³ + 8y² - 2y + 3y² + 24y - 6

= y³ + 11y² + 22y - 6

Part 2:

(y³ + 11y² + 22y - 6) * (y³ + 11y² + 22y - 6) =

That is the full solution.

Answer: [tex]1\frac{16}{25}[/tex]

Step-by-step explanation:

1.64 is 1 64/100. Now to get the simplest form find a number you can divide both the numerator and the denominator by, like 4. Now you have 1 16/25. 16 and 25 do not have a common number you can divide both by so it is the simplest form.

The angle relationship of the diagram is as follows:

13. ∠AGH and ∠DHG are alternate interior angles

14. ∠FGB and ∠CHE are  alternate exterior angles.

15. ∠CHG and ∠DHE are vertically opposite angles.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.

The parallel lines are line AB and CD.

The transversal line is FE.

Therefore,

∠AGH is congruent to ∠DHG because they are alternate interior angles.

Alternate interior angles are congruent.

∠FGB is congruent to ∠CHE because they are  alternate exterior angles.

Alternate exterior angles are congruent.

∠CHG is congruent to ∠DHE because they are vertically opposite angles.

Vertically opposite angles are congruent.

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Given the equation of the circle:

We will complete the squares for x and y to write the equation of the circle as:

Where (h,k) is the coordinates of the circle and r is the radius of the circle

so, the equation will be:

So, the radius of the circle = 4

And the center of the circle = ( -2, 6 )

Now, we will make the transformation for the circle:

Shift 1 unit up, the center will be = ( -2, 7 )

shift 2 units right, the center will be = ( 0, 7 )

Reflection across the x-axis, the center will be = ( 0, -7)

So, the equation of the circle after transformation will be:

So, the answer will be:

ANSWER:

The value of x is 2

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solve as follows: