On a recent test, Shawna was given the following problem:

Shawna's work is shown below:
1. a2+72=252
2. a2+14=50
3. a2=36
4. a=6 m

In which step did Shawna make an error?
Step 1. She incorrectly applied the Pythagorean theorem.
Step 2. She incorrectly squared the numbers.
Step 3. She incorrectly isolated a2
Step 4. She incorrectly solved for a.

Final answer:

To evaluate (f ∘ g)(4), we substitute the value of g(4) into f(x) which gives us 22.

Explanation:

To find (f ∘ g)(4), we need to first evaluate g(4) and then plug that value into f(x). Given that g(4) = 8 and f(8) = 22, we can substitute 8 into f(x) as follows:

(f ∘ g)(4) = f(g(4))

(f ∘ g)(4) = f(8)

(f ∘ g)(4) = 22

[tex] a^2+16^2=20^2[/tex]

[tex] a^2+256=400[/tex]

Subtracting 256 from both sides

[tex] a^2=144[/tex]

Taking squareroot both sides

[tex] a= \sqrt144[/tex]

[tex] a = \sqrt2.2.3.2.2.3[/tex]

[tex] a=12[/tex]

Therefore length of missing leg is

[tex] a = 12 units[/tex]

a^2+16^2=20^2

a^2+256=400

Subtracting 256 from both sides

a^2=144

Taking squareroot both sides

a= \sqrt144

a = \sqrt2.2.3.2.2.3

 a=12

Therefore length of missing leg is  

a = 12 units

15.0 ( to the nearest tenth )

calculate the distance (d) using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (7, - 4 ) and (x₂, y₂ ) = (- 8, - 5 )

d = √(-8 - 7 )² + (- 5 + 4 )² = √(225 + 1 ) = √226 ≈ 15.0

Try this option:

1) to difine the equations of the lines given in the picture. They are: y= -0.5x+2 (for the left line, see the attached picture) and y=2x-3 (for the right line).

2) according to the condition (dark area and type of the line) the 1st inequation is y≥ -0.5x+2, the 2d inequation is y>2x-3.

3) the required system is

[tex]\left \{ {{y>2x-3} \atop {y\geq -0.5x+2}} \right.[/tex]

See this solution/explanation (answer is '7 meters'):

1. According to the condition 'y' means the height, and 'x' - the length from the start of the lift hill.

2. The phrase 'height of 343 meters' means y=343.

3. From the another side y=x³. If to substitute 343 instead of 'y': 343=x³, - it is possible to find the value of 'x'.

x=7 [m] - how far from the start of the lift hill...

Total of fees: 1,000 + 4,900 = 5,900

You are told the APR is the total fees divided by the amount financed, so divide the total fees by the amount financed:

5,900 / 83,098.59 = 0.71

0.71 x 100 = 7.1% APR.

The answer is B.

I will interpret and evaluate your expression following order of operations rules strictly.  6*5 (multiplication) and 3*3*3 / 3 (division) must be done first, before subtraction.  Then we have 30 - 9, or 21.  If you truly meant 3*3*3, why not write that as 3^3?

You seem to generally have the right idea, and you seem to be able to solve the equations you write. However, your choice of equations for the problem sometimes needs a little work.

∠DBC = ∠DBE + ∠EBC

(12x -3) = (5x +12) + (3x +13) . . . . . substitute given values

12x -3 = 8x +25 . . . . . . . . . collect terms

4x = 28 . . . . . . . . . . . . . . . add 3-8x

x = 7 . . . . . . . . . . . . . . . . . . divide by 4

3x +13 = 3·7 +13 = 34

∠EBC = 34°

__________

∠FBC = ∠CBE

10x -9 = 4x +15 . . . . . substitute given values

6x = 24 . . . . . . . . . . . .add 9-4x

x = 4 . . . . . . . . . . . . . . divide by 4

∠FBC = (10·4 -9)° = 31°

∠FBE = 2·∠FBC = 2·31°

∠FBE = 62°

__________

∠1 +∠2 = 90°

(7x -19) +(x +5) = 90 . . . . . . substitute the given values

8x -14 = 90 . . . . . . . . . . . . . collect terms

8x = 104 . . . . . . . . . . . . . . . add 14

x = 13 . . . . . . . . . . . . . . . . . . divide by 8

∠2 = (13 +5)°

∠2 = 18°

__________

∠1 = ∠4

6x +25 = 10x -11 . . . . substitute the given values

36 = 4x . . . . . . . . . . . add 11-6x

9 = x . . . . . . . . . . . . . .divide by 4

∠1 = (6·9 +25)°

∠1 = 79° . . . . . . matches your answer

Answer: about 0.0432 or 4.32%

Step-by-step explanation:

Given : A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles.

Total marbles = 7+5+4+2=18

Let R : Event of getting first marble as red .

Y= Event of getting second marble as yellow.

Jon selects a marble, replaces it, then selects another marble.

⇒Both events are independent .

Probability of getting first marble as red = [tex]P(R)=\dfrac{\text{Number of red marbles}}{\text{Total marbles}}[/tex]

[tex]\\\\=\dfrac{7}{18}[/tex]

Probability of getting second marble as yellow = [tex]P(Y)=\dfrac{\text{Number of yellow marbles}}{\text{Total marbles}}[/tex]

[tex]\\\\=\dfrac{2}{18}[/tex]

Now, the probability that Jon selects a red marble and then a yellow marble :

[tex]P(R)\times P(Y)=\dfrac{7}{18}\times\dfrac{2}{18}\approx0.0432=4.32\%[/tex]  [ ∵ Event R and Y are independent .]

Hence, the probability that Jon selects a red marble and then a yellow marble is about 0.0432 or 4.32%.

Try this option (this is not the only way!):

1. the rule: if 'number_1' - 'number_2' > 0, then number_1>number_2. If 'number_1'-'number_2'<0, then number_2>number_1.

2. according to the rule above: 9.36-9.359=0.001. 0.001>0, it means, 9.36>9.359.

Functions can't have multiple y values have the same x value.

[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)] ** No repeating x-values.

[(-2, 1), (-4, 2), (0,3), (4, 1), (-2,5)]

[(-1, 5), (-1,4), (-1, 3), (-1, 2) (-1, 1)]

[(-6, -4), (-4, -2), (0, 0), (-4, 2) (-6, 4)]

Answer:

[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)]

B

A(6) = 2500 × [tex]e^{(0.05(6))}[/tex] = 2500 × [tex]e^{0.3}[/tex] = $3, 374.65

My investment amount will be 3374.65 rupees after 6 years.

So, option B is the correct answer.

What is Euler's number ?

A(t) [tex] = p {e}^{rt} [/tex] is known as Euler's number.

A is the desired amount per account/price/population/etc. equal

P is the principal or amount you start with.

e is a particular irrational number that is approximately 2.718. Just as pi is a concrete irrational number, so is e. The Euler number is often used as a title for e. Just as pi is an infinite non-repeating decimal, so is e. And just as many people use 3.14 to approximate pi, some use 2.718 for e. However, using the special π button on the calculator gives a more accurate answer than 3.14, and using the e button on the calculator is more accurate than using 2.718.

r is a rate written as a decimal, not a percentage.

t is time.

Let's say you have a population of bacteria that is constantly growing at a rate of 15% per hour. If there were 40 bacteria at the beginning of the experiment, how many bacteria will there be after 8 hours?

A is the amount after 8 hours, it's unknown, so I'll just use the variable A.

P initially has 40 bacteria.

e I use the “e” button on my calculator.

r is the hourly rate of 15%, I write it as 0.15

t is time, in this case 8 hours.

A = 40•e^(0.15•8)

A = 132.8, you need to round down because you haven't reached the next whole number of bacteria.

132 bacteria after 8 hours.

Here given,invest amount is $2,500 and rate of interest is 5% and total time period is 6 years.

Here we need to use continuous function A(t)[tex] = p {e}^{rt} [/tex]

Where P is principal,r rate of interest is interest and t is time.

Now,

[tex]p = 2500 \\ r = 5\% = 0.05\\ t = 6 \: years[/tex]

So,after 6 years the amount become ,A(6)

= [tex]2500 \times {e}^{0.05 \times 6} \\ = 2500 \times {e}^{0.3} [/tex]

[tex] = 2500 \times 1.34986 \\ = 3374.65[/tex]

Therefore,my investment amount will be 3374.65 rupees after 6 years.

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Answer:

1 unit right and 1 unit down

Step-by-step explanation:

When you replace x with x - h, you translate the graph h units horizontally.

When you replace y with y - k, you translate the graph k units vertically.

y = |x - 1| - 1

y + 1 = |x - 1|

y - (-1) = |x - 1|

Compare the last equation above with y = |x|. x was replaced by x - 1, so h = 1, and the translation is 1 unit horizontally. Since 1 is positive, it is a 1 unit translation to the right. y was replaced by y - (-1), so k = -1, and the vertical translation is 1 unit down.

Answer:

1 unit right and one unit down

Step-by-step explanation:

Answer:

a = 4.762203156

Step-by-step explanation:

Given:

ab^4 = 12 and a^5b^5 = 7776

Making the equations a subject of a;

a = 12/b^4 and a^5 = 7776/b^5

Finding fifth root on both sides of equation two;

a = [tex]\sqrt[5]{7776}[/tex]/b

You will get a = 6/b

Equating the two equations;

12/b^4 = 6/b

Multiplying both sides by b^4 gives:

b = [tex]\sqrt[3]{2}[/tex] = 1.25992105

We had that a = 12/b^4 so;

a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156

2x + 16 = 5

2x = -11

x = -5.5

y = 5

(-5.5,5)

Final answer:

The solution to the system of equations y=5 and y=2x+16 is found using substitution, yielding the solution (-5.5, 5).

Explanation:

To solve the system of equations y=5 and y=2x+16, we can use the method of substitution. Since the first equation directly gives us the value of y, we can substitute y = 5 into the second equation to find the corresponding value of x. Doing so, we have 5 = 2x + 16. To solve for x, we subtract 16 from both sides to get -11 = 2x, and then divide both sides by 2 to find that x = -5.5. Thus, the solution to the system is (-5.5, 5).

Answer:

I'd say you need to be more specific.

Step-by-step explanation:

"Different" doesn't tell you much.

Consider the equations ...

These equations are "different", but they are dependent.

_____

I'd mentally (or actually) put the equations in the same form and compare the coefficients of x and y. If they have different ratios, the system is independent and consistent.

If they have the same ratio, the system will not have a single solution. Whether there is no solution or an infinite number of solutions depends on the constant, which I would examine next.

The system above can be put in the form

In both cases, the ratio of the x coefficient to the y coefficient is 2/-1 = 4/-2 = -2. This means the lines are at least parallel, if not identical. The numbers in the second equation are all 2 times the numbers in the first equation, so the equations are dependent, and there are an infinite number of solutions. (Both describe the same line.)

If the second equation were 4x -2y = 1, then the two equations would be describing parallel lines, so they would be called inconsistent.

To have equal numbers of bowls and cups, Randy should buy 4 packs of bowls and 3 packs of cups, as the least common multiple of 6 (number of bowls per pack) and 8 (number of cups per pack) is 24.

If Randy needs an equal number of bowls and cups for his picnic and one pack consists of 6 bowls and another pack consists of 8 cups, the least common multiple (LCM) of 6 and 8 must be found to ensure an equal number of both items. The LCM of 6 and 8 is 24, because 24 is the smallest number that both 6 and 8 can divide evenly into. Therefore, Randy will need to buy 4 packs of bowls (4 packs × 6 bowls per pack = 24 bowls) and 3 packs of cups (3 packs × 8 cups per pack = 24 cups) to have an equal number of each for his picnic.

x | - 8 - 4 0 4 8

y | 28 16 4 - 8 - 20

to calculate the values of y, substitute the given values of x into the equation

x = - 8 : y = (- 3 × - 8 ) + 4 = 24 + 4 = 28

x = - 4 : y = (- 3 × - 4 )+ 4 = 12 + 4 = 16

x = 0 : y = (- 3 × 0 ) + 4

0 + 4 = 4

x = 4 : y = (- 3 × 4 ) + 4 = - 12 + 4 = - 8

x = 8 : y = (- 3 × 8 ) + 4 = - 24 + 4 = - 20

-110 = 13 + 3(4h -6) . . . . . . given

-110 = 13 + 12h -18 . . . . . . . eliminate parentheses using the distributive property

-110 = 12h -5 . . . . . . . . . . . . collect terms

-105 = 12h . . . . . . . . . . . . . . add 5 to both sides of the equation

-105/12 = h = -8.75

______

There are many ways you can solve this. Another is to undo the operations done to h. The variable h is ...

When you undo these, you do it in reverse order:

-110 -13 = 3(4h -6) . . . . subtract 13

-123/3 = 4h -6 . . . . . . . divide by 3

-41 +6 = 4h . . . . . . . . . .add 6

-35/4 = h . . . . . . . . . . . divide by 4

h = -8.75

the mode of the data is 4.

mode is the number repeats in the data set the most.

Answer:

6782

Step-by-step explanation:

Answer:

She would have to work for 33 hours.

Step-by-step explanation:

239.25/7.25=33. Since we are going with hours, this would be 33.

The open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.

To graph [tex]\(x < \frac{17}{5} + \frac{7}{20}\)[/tex] on a number line, we'll first simplify the expression:

[tex]\(\frac{17}{5} + \frac{7}{20}\)[/tex]

To add these fractions, find a common denominator, which in this case is 20:

[tex]\(\frac{17}{5} = \frac{17 \times 4}{5 \times 4} = \frac{68}{20}\)[/tex]

Now, add the fractions:

[tex]\(\frac{68}{20} + \frac{7}{20} = \frac{75}{20}\)[/tex]

So, the expression simplifies to [tex]\(x < \frac{75}{20}\)[/tex].

To simplify [tex]\(\frac{75}{20}\)[/tex]:

[tex]\(75 \div 20 = 3.75\)[/tex]

This means the inequality is [tex]\(x < 3.75\)[/tex].

Now, to graph this on a number line, mark a point at 3.75, but as it is "less than" <, make sure to have an open circle at 3.75, indicating that it does not include the value itself. Then, draw an arrow to the left, signifying all values less than 3.75.

```

0-------------------o-------------------3.75------------------->

```

Here, the open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.

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(1)

substitute y = 3 into the other equation

3 = 2x + 3 ( subtract 3 from both sides )

0 = 2x → x = 0

solution : (x, y) → (0, 3 )

(2)

substitute y = x into the other equation

x = 2x - 5 ( subtract x and add 5 to both sides )

5 = x then y = x so y = 5

solution : (x, y) → (5, 5 )

(3)

substitute y = - 6 into the other equation

- 6 = 4x + 10 ( subtract 10 from both sides )

- 16 = 4x ( divide both sides by 4 )

x = - 4

solution : (x, y) = (- 4, - 6 )

Answer:

8 2/35 miles per hour

Step-by-step explanation:

We are given distance traveled and the time required. We can use those directly in the relation that gives speed:

speed = distance / time

... = (18 4/5 miles)/(2 1/3 hours)

... = (94/5 miles)/(7/3 hours) . . . . . . converte mixed numbers to improper fractions

... = (94/5×3/7) miles/hour . . . . . . . "invert and multiply"

.. = 282/35 miles/hour . . . . . . . . . . improper fraction result

... = 8 2/35 miles/hour . . . . . . . . . . as a mixed number

I believe that the answer is C, I don't know if it is addition or multiplication, but if is is addition, it would be 146, C

The student’s total percent of all successful quizzes for the entire year is 72%.

To determine the percent of all successful quizzes for the entire year, we need to follow these steps:

Calculate the number of quizzes passed so far: The student has passed 60% of 20 quizzes. This is calculated as follows:

0.60 x 20 = 12 quizzes passed.

Determine the number of quizzes remaining: The student needs to write 50 quizzes in total, so the remaining quizzes are 50 - 20 = 30 quizzes.

Calculate the number of additional quizzes passed: The student is expected to pass 80% of the remaining quizzes.

0.80 x 30 = 24 quizzes passed.

Calculate the total number of quizzes passed: Add the quizzes passed so far to the additional quizzes passed.

12 + 24 = 36 quizzes passed in total.

Determine the percentage of successful quizzes for the entire year: Divide the total number of successful quizzes by the total number of quizzes.

(36 / 50) x 100 = 72% successful quizzes.

Thus, the student’s total percent of all successful quizzes for the entire year is 72%.

There is no way to factor this so i would assume the answer is no solution.

Step-by-step explanation:

A triangle can be of many types like right angled triangle, isosceles triangle, scalene triangle, obtuse, acute etc.

A right angle can be defined as the triangle in which one of the angle is 90 degrees.

An obtuse angle is that type of triangle in which the the angle is more than 90 degrees and less than 180 degrees.

An isosceles triangle is one in which two sides are equal.

An acute angle is the triangle in which the angle is less than 90 degrees.

The attached triangle is :

1. Right angle triangle

2. Isosceles triangle

Answer:

216

Step-by-step explanation:

9 * 6 = 54

54 * 8 = 432

432/2 = 216 is the answer

The volume of a triangular prism is the area of the base multiplied by the height. This can be represented as volume = base × height

Let's first identify our values:

9 m = height of the prism

6 m = base of the triangle

8 m = height of the triangle

First, we need to calculate the area of the triangle. To calculate the area of a triangle, the formula is base × height ÷ 2.

The base of the triangle is 6 and the height of the triangle is 8 so 6 multiplied by 8 will give us a product of 48. Next, we need to divide 48 by 2 and we will get a quotient of 24.

Finally, we need to multiply the area of the triangle by the height of the prism.

24 × 9 = 216

Therefore, the volume of the triangular prism is 216[tex]m^{3}[/tex]