A hat is marked down 45% and its new price is $69. What was the original price rounded to the nearest cent?

Answer:

a = -4

b = 3

c = 6

Step-by-step explanation:

x^2 + 8x = 38

We take the coefficient of the x term

Divide by 2 and then square it

8/2 =4

4^2 = 16

Add 16 to both sides

x^2 +8x + 16 = 38 + 16

x^2 +8x +16 = 54

Take b/2 and use it in the the (x+b/2)^2

(x+4)^2 = 54

Take the square root of each side

sqrt((x+4)^2) = ± sqrt(54)

x+4 =  ± sqrt(54)

Subtract 4 from each side

x+4-4 = -4  ± sqrt(54)

x = -4  ± sqrt(54)

Simplify the square root

x = -4  ± sqrt(9*6)

x = -4 ± sqrt(9) sqrt(6)

x = -4 ± 3 sqrt(6)

Answer:

The interest is: $1575

The total is: $8575

Step-by-step explanation:

7000*5*0.045 gets you the interest

Then you add the original amount, 7000, to the total

1575+7000=$8575

By using the Simple Interest formula (Principal * Rate * Time), we find that Jill will earn $1575 in interest over 5 years. Therefore, she will have $8575 in her account after 5 years.

To calculate how much Jill will have in her account after 5 years, we can use the simple interest formula, which is Principal * Rate * Time.

In Jill's case, the principal is the amount she initially deposited which is $7000. The rate is the simple interest rate offered by the bank annually, expressed as a decimal, so 4.5% becomes 0.045. The time is the number of years that the money remains in the account, which is 5 years.

By substituting these values into the formula, we have: $7000 * 0.045 * 5 = $1575.

This means the total interest Jill would earn over 5 years is $1575. The total amount in the account after 5 years would be the initial amount plus the interest, so $7000 + $1575 = $8575.

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Answer:

x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74

Step-by-step explanation:

Solve for x:

(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = 0

Simplify and substitute y = 4 - x.

(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = -434 + 257 (4 - x) - 37 (4 - x)^2

= -37 y^2 + 257 y - 434:

-37 y^2 + 257 y - 434 = 0

Divide both sides by -37:

y^2 - (257 y)/37 + 434/37 = 0

Subtract 434/37 from both sides:

y^2 - (257 y)/37 = -434/37

Add 66049/5476 to both sides:

y^2 - (257 y)/37 + 66049/5476 = 1817/5476

Write the left hand side as a square:

(y - 257/74)^2 = 1817/5476

Take the square root of both sides:

y - 257/74 = sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Add 257/74 to both sides:

y = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Substitute back for y = 4 - x:

4 - x = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Subtract 4 from both sides:

-x = sqrt(1817)/74 - 39/74 or y - 257/74 = -sqrt(1817)/74

Multiply both sides by -1:

x = 39/74 - sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74

Add 257/74 to both sides:

x = 39/74 - sqrt(1817)/74 or y = 257/74 - sqrt(1817)/74

Substitute back for y = 4 - x:

x = 39/74 - sqrt(1817)/74 or 4 - x = 257/74 - sqrt(1817)/74

Subtract 4 from both sides:

x = 39/74 - sqrt(1817)/74 or -x = -39/74 - sqrt(1817)/74

Multiply both sides by -1:

Answer:  x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74

The angle that subtends a chord is half the measure of the arc, so we have an arc QS of 2(84)=168 degrees.

Answer: 168 degrees

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

so...

y = -3x + 5

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be -3

y = -3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(0, 2)

2 = -3(0) + b

2 = 0 + b

2 = b

y = -3x + 2

Hope this helped!

~Just a girl in love with Shawn Mendes

In the equation y = mx + b, where m represents the slope and b represents the y-intercept, we can determine the slope of the line to be -3. When two lines are parallel, they have the same slope (m).

To find the value of b, we need to substitute the coordinates of a point the line passes through into the equation. In this case, the point is (0, 2).

By plugging in the values, we get:

2 = -3(0) + b

2 = 0 + b

2 = b

Answer:

1. august price = c + 0.25c

2. august price = 1.25c

Step-by-step explanation:

The problem statement tells us that the price of gas in August is 25% more than in July. Thus, 25% of the July price (0.25c) is added to the July price (c) to get the August price.

  c + 0.25c

The sum in the first part can be simplified by combining the coefficients of c.

  1.25c

Answer:

  A.  2x² +12x

Step-by-step explanation:

If the mobile is balanced, the weights at each level are the same. Each of those in the lowest tier will be equivalent to 3x, for a total of ...

  4×3x = 12x

Each of those in the top tier shown will be equivalent to x², for a total of ...

  2×x² = 2x²

Then the sum of all parts will be ...

  top tier + bottom tier = 2x² +12x

Answer:

  1/4 of the credit

Step-by-step explanation:

The problem statement tells you n=5. Putting that into the expression for lost credit, you get ...

  1/(5-1) = 1/4

of the credit is lost for a question with 1 wrong answer.

You will lose 1/4 of the credit.

Answer:

The credit will you lose for the part of question is 1/4 or 25%.

Step-by-step explanation:

Consider the provided information.

It is given that, if you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n−1) of the credit for that question.

Suppose the given multiple choice question has 5 answer. So for one wrong answer the loss will be:

Substitute the value of n=5 in above formula.

[tex]\frac{1}{n-1} \\\frac{1}{5-1} \\\frac{1}{4}=0.25[/tex]

That means you will lose 1/4 or 0.25credit.

Now convert it into %.

[tex]\frac{1}{4}\times 100=25\%[/tex]

Hence, the credit will you lose for the part of question is 1/4 or 25%.

Answer:

Step-by-step explanation:

  = x²(-3 +5) +y²(2 -3) +5xy -2y

  = 2x² -y² +5xy -2y

a) there are 4 terms in the simplified expression

b) 2 terms have negative coefficients (-y² and -2y)

Answer: [tex](-2,1)[/tex]

Step-by-step explanation:

It is important to remember that a rotation is a transformation in which the shapes and sizes do not change, but the object can be turned in different directions.

By definition, the rule for 180° counterclockwise rotation is this:

[tex](x,y)[/tex]→ [tex](-x,-y)[/tex]

Therefore, we know that the image of the point [tex]P=(2,-1)[/tex] under a 180° counterclockwise rotation is:

 [tex](2,-1)[/tex]→ [tex](-2,1)[/tex]

Answer:

expected value

Step-by-step explanation:

Answer:

Expected value

Step-by-step explanation:

Expected value- Any discrete variable's expected value is probability-weighted average of all of its possible values.

In simple words, any possible value that can be inferred by the any given variable is compounded by its probability of occurrence and the resulting products are added up to deliver the expected value.

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\pi \theta r^2 }{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=6\\ \theta =55 \end{cases}\implies A=\cfrac{\pi (55)(6)^2}{360}\implies A=\cfrac{11\pi }{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 17.28~\hfill[/tex]

Answer:

D 9 1/2

Step-by-step explanation:

5/(a+3) = 3/(a-2)

We can use cross products to solve

5 * (a-2) = 3 * (a+3)

Distribute

5a - 10 = 3a +9

Subtract 3a from each side

5a -3a -10 = 3a -3a +9

2a -10 =9

Add 10 to each side

2a -10+10 = 9+10

2a = 19

Divide each side by 2

2a/2 = 19/2

a = 19/2

a = 9 1/2

Answer:

Option D

Step-by-step explanation:

Please see attached picture for a detailed answer.

Answer:

  D.  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...

  Sin = Opposite/Hypotenuse

  sin(M) = ON/OM = 4(√3)/8 = (√3)/2

  M = sin⁻¹((√3)/2) = 60°

Answer:

  a.  18 units, 18 units, 13 units

Step-by-step explanation:

P = 49 means the sum of side lengths is 49. Only answer choice A has numbers that sum to 49.

___

As here, you often do not need to work a multiple-choice problem. You only need to check to see which answers make sense.

__

If you want to actually compute the side lengths, you know the two sides with a hash mark are the same length, so the perimeter is ...

  P = 49 = (2n+2) + (2n+2) + (2n-3) = 6n +1

  48 = 6n . . . . . subtract 1

  8 = n . . . . . . . divide by 6

Then ...

  2n +2 = 2·8 +2 = 18 . . . . . . . matches only the first answer choice.

Answer:

  C.)  f(x) = −4x + 200

Step-by-step explanation:

Since the number is decreasing, you know the slope will be negative, eliminating the first two choices. The equation in the last choice does not match the given data, so it can be eliminated.

In other words, the easiest way to solve this problem is to check the answers against the given data.

_____

If you want to write the equation from scratch, you need to find the slope. That is ...

  (change in number of cars)/(change in weeks) = (184 -192)/(4 -2) = -8/2 = -4

This matches only one answer, but you can go on to finish the equation by starting with point-slope form:

  y -192 = -4(x -2)

  y = -4x +8 +192 . . . . add 192, eliminate parentheses

  y = -4x + 200 . . . . matches choice C.)

Answer:

c.f(x)= -4x+200

Step-by-step explanation:

i took the test

Volume = 9in • 9in • 9in

Volume = 729 in^3

Now multiply the volume by 6 grams.

Let H = total weight of the cube in terms of grams.

H = V • 6

H = 729 • 6

H = 4,374 grams

Answer:

x = 4 or x = 1

Step-by-step explanation:

Solving absolute value equations can be a bit tricky.  Absolute values are actually distance measurements.  A very simple example is I x - 3 I = 2 says that "x is 2 units away from 3 on a number line".  2 units from 3 going to the right is 5, 2 units from 3 going to the left is 1.  So in other words, absolute value equations will have 2 answers, in this case 2 units to the right (+2) and 2 units to the left (-2).  That means that x - 3 = 2 OR x - 3 = -2.  Let's start to solve this one:

5I 2x - 5 I - 3 = 12

Start by adding 3 to both sides:

5I2x-5I = 15

Now divide both sides by 5:

I2x-5I = 3

We will set the left side equal to both +3 and -3 to get our 2 solutions:

2x - 5 = 3  and  2x - 5 = -3

Solving the first one for x:

2x = 8 and x = 4

Solving the second one:

2x = 2 and x = 1.

Fit these into the original absoute value statement and see if they are both true:

5I2(4)-5I-3=12 --> 5I3I - 3 = 12 and 15 - 3 = 12

5I2(1)-5I-3 = 12 --> 5I-3I - 3 = 12.  The absolute value of -3 is 3, so 15 - 3 = 12.  They both check out@

The probability of drawing a blue marble will be 1/3.

Blue marbles = 3

Red marbles = 2

Yellow marbles = 4

Total marbles = 3 + 2 + 4 = 9

The probability of drawing a blue marble will be:

= 3/9

= 1/3

The probability of drawing a marble that isn't red will be:

= 3/9 + 4/9

= 7/9

The probability of drawing a red and yellow marbles will be:

= 2/9 + 4/9

= 2/3

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Answer:

  (2, 5)

Step-by-step explanation:

Rotation clockwise 90° can be accomplished by the transformation ...

  (x, y) ⇒ (y, -x)

so

  (-5, 2) ⇒ (2, 5)

Answer: i'm pretty sure the only answer that applies is the last one.

Good luck!

Answer:

b) The yellow rectangle was translated right 5 units and reflected over the x-axis.

d) The yellow rectangle was translated right 5 units and up 3 units.

Step-by-step explanation:

Translation in geometry describes a function that moves an object a certain distance without altering it. The object is not rotated, reflected or re-sized after translation. Every point of the object is moved in the same direction through the same distance.

Reflection is a rigid transformation in which the given object is flipped across a line to create its image. Each point of the image maintains their distance from the line as in the object. In reflection, every point of the object changes initial location.

The options that describe the transformation are: The yellow rectangle was translated right 5 units and reflected over the x-axis, and the yellow rectangle was translated right 5 units and up 3 units.

The volume of the solid is 8/3 cubic units.

Visualization:

Imagine a right triangle with one leg on the x-axis and the other on the y-axis. The hypotenuse of the triangle intersects the line x + y = 2 at a point (x, y). The solid is formed by stacking square cross-sections perpendicular to the base triangle, with each square having a side length equal to the distance between the line x + y = 2 and the triangle's hypotenuse at that point.

Volume Calculation:

Let x be the distance from the origin to the point where the hypotenuse intersects the line x + y = 2. Then, the length of the side of each square cross-section is (2 - x). The area of each cross-section is therefore (2 - x)^2.

As we move from the origin to the vertex of the triangle where the hypotenuse intersects the line, the distance x increases from 0 to 2. Thus, the volume of the solid can be calculated by integrating the area of the cross-sections over the range of x:

Volume = ∫(2 - x)^2 dx from x = 0 to x = 2

Integration:

Solving the integral using the power rule, we get:

Volume = [4/3 * x^3 - 2x^2 + x] from x = 0 to x = 2

Evaluating the expression at the limits of integration:

Volume = (32/3 - 8 + 2) - (0 - 0 + 0) = 32/3 - 6 = 8/3 cubic units

Therefore, the volume of the solid is 8/3 cubic units.

Answer:

1. C. 8000 - 24x; 2 A. x + 2x + 2 = 40; 3. C. Step 3

Step-by-step explanation

1. Desmond  

[tex]\begin{array}{rcl}\text{Value of car two years ago} & = & 8000\\\\\text{Less depreciation = 24 mo} \times\dfrac{x}{\text{1 mo}} & = & -24 x\\\\\text{Current value} & = & \mathbf{8000 - 24x}\\\end{array}[/tex]

2. Avi and Sergi  

[tex]\begin{array}{rcl}\text{Sergi's money} & = & x\\\text{Double Sergi's money} & = & 2x\\\text{Avi's money} & = & 2x + 2\\\text{Avi's money + Sergi's money} & = & x + 2x + 2\\\text{Avi's money + Sergi's money} & = & 40\\x + 2x + 2 & = & 40\\\end{array}[/tex]

3. Isabella  

[tex]\begin{array}{crl} \textbf{Step} & \textbf{Work} & \textbf{Justification} \\ & 4x - 2x + 8 = 6(x + 4) & \\ 1 & 4x - 2x + 8 = 6x + 24 & \text{Distributive Property} \\ 2 & 2x + 8 = 6x + 24 & \text{Combine like terms} \\ 3 & -4x + 8 = 24 & \textbf{Subtraction Property of Equality}\\ 4 & -4x = 16 & \text{Subtraction Property of Equality} \\ 5 & x = -4 & \text{Division Property of Equality} \\ \end{array}[/tex]

Step 3 has the incorrect justification. Isabella subtracted 6x from each side, so she should have used the Subtraction Property of Equality

Answer:

  32°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the trig function relating angles to the opposite and adjacent sides of the triangle is ...

  Tan = Opposite/Adjacent

The side opposite the angle x is shown as having measure 5; the side adjacent has measure 8. Putting all this in the above equation gives ...

  tan(x) = 5/8

To find the angle from the value of the tangent, you use the inverse of the tangent function. The name of that is the arctangent function. It is often written as tan⁻¹(x) and often accessible on your calculator using a "second function" key. Some calculators, like the one shown in the attachment, recognize the arctan function name.

  x = arctan(5/8) ≈ 32°

The value of x rounded to the nearest whole degree is 32°.

Answer:

  arc ADB = 270°

Step-by-step explanation:

Arc ADB is the remainder of the circle after subtracting 90° arc AB. Its measure is ...

  ADB = 360° -90° = 270°

Answer:

A

Step-by-step explanation:

She can type 3.75 words per second.

There are 60 seconds in a minute

Therefore she can type 3.75 * 60 = 225 words per minute.

If 1 page contains 675 words, it will take 675 // 225 words /min = 3 minutes

Therefore 25 pages will take 75 minutes (3 * 25 = 75)

75 minutes = 1 hour with 15 minutes left over.

Final answer:

The court reporter, typing at a minimum rate of 3.75 words per second, would have spent 1 hour and 15 minutes actively typing a 25-page trial transcript with an average of 675 words per page.

Explanation:

The question asks us to calculate the time a court reporter would have spent actively typing a transcript. To find this duration, we first determine the total number of words the trial transcript contains by multiplying the number of pages by the average number of words per page. Then, we divide the total number of words by the court reporter's typing speed in words per second to find the total time in seconds. Finally, we convert the total time from seconds into minutes and hours to get the answer in a more understandable format.

First, calculate the total number of words:

25 pages × 675 words per page = 16,875 words

Next, convert the court reporter's minimum typing speed into words per second:

3.75 words per second

Now, calculate the time spent typing:

Total time (in seconds) = Total number of words ÷ Words per second

Total time (in seconds) = 16,875 words ÷ 3.75 words/second = 4,500 seconds

Convert seconds to minutes: 4,500 seconds ÷ 60 = 75 minutes

Convert minutes to hours: 75 minutes ÷ 60 = 1.25 hours

Therefore, the court reporter was actively typing for 1 hour, 15 minutes, which corresponds to option A.

Answer:

4.86 × 10^7

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

For example, 650,000,000 can be written in scientific notation as 6.5 × 10^8

So;

48,600,000 = 4.86 × 10^7

count backward to the last number.

Answer:

4.86 × 10^7

Your welcome!

Answer:

270 degrees

Step-by-step explanation:

180 would be diagonal from original, 360 would be where the original is and 90 would be in the second quadrant so therefore its 270

Answer:

B) 270°

Step-by-step explanation:

it was correct for me

Answer:

A. X>50 and X<150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.

Step-by-step explanation:

1. 110<2x+10

First, switch sides.

2x+10>110

Then, subtract by 10 both sides of equation.

2x+10-10>110-10

Simplify.

110-10=100

2x>100

Divide by 2 both sides of equation.

2x/2>100/2

Simplify, to find the answer.

100/2=50

x>50

x>50 is the correct answer.

__________________________

2. 2x+10<310

First, you subtract by 10 from both sides of equation.

2x+10-10<310-10

Then, simplify.

310-10=300

2x<300

Divide by 2 from both sides of equation.

2x/2<300/2

Simplify, to find the answer.

300/2=150

x<150

x<150 is the correct answer.

A. the first option is the correct answer.

Option A -  x > 50 and x < 150 Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates is the correct answer.

We have amount of carbs consumed in grams between the levels shown in the following compound inequality :

110 < 2x + 10

2x + 10 < 310

We have to solve for x in this inequality, and explain what the answer represents.

We can write the inequality as follows -

α < x < β (Since α is less then 0, it will be less then β)

According to question, we have -

110 < 2x + 10

110 - 10 < 2x + 10 - 10

100 < 2x

x > 50

2x + 10 < 310

2x + 10 - 10 < 310 - 10

2x < 300

x < 150

Hence, x > 50 and x < 150 : Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.

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