this graph shows the outside temperature (in degrees celsius) over the course of 12 hours, starting at midnight (x=0)

The answer choice which correctly draws a comparison between the end behaviors of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.

As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).

It therefore follows that as; x reduces (approaches -∞), the y value increases.

And, as x -increases (approaches +∞), the y-value decreases.

For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).

Consequently, as x reduces (approaches -∞), the y- values decrease.

And, as x increases (approaches +∞), the y-values decrease.

Ultimately, the two functions in discuss can be concluded to have; Choice C.

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Answer:

In a mathequation when needed

Step-by-step explanation:

Answer:

-3 + sqrt 42

-3 - sqrt42

Step-by-step explanation:

assuming you want me to factor it and then find the roots:

2x^2 +12x-66

2(x^2 + 6x-33)

Answer:

26.92%

Answer choice “A”

Explanation:

14 cards of hearts in a deck out of 52.

14/52 = 26.92%

The probability of drawing a heart card from a full deck of cards is 26.92%

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

As, we know there we have 14 cards of hearts in a deck out of 52.

So,

probability of drawing a heart card from a full deck of cards

=14/52

= 26.92%

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Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.

Step-by-step explanation:

Hope this helps :)

triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B

Answer:

area of the rectangle =

\( {93.75cm}^{2} \)

Step-by-step explanation:

width = x cm

length = x + 5 cm

Perimeter = 2(length + width)

\(p = 2(x + (x + 5)) \\ 40 = 2(x + x + 5) \\ 40 = 2(2x + 5) \\ 40 = 4x + 10 \\ 40 - 10 = 4x \\ 30 = 4x \\ \frac{30}{4} = x \\ 7.5 = x\)

width = 7.5cm

length = 7.5 + 5 = 12.5cm

Area of the rectangle = length × width

\(a = 12.5cm \times 7.5 cm\\ a = 93.75 {cm}^{2} \)

y=-1/3x-2. Hope this helped! :)

Answer:

Step-by-step explanation:

Given line:

Parallel line has the same slope:

Use the given point to find the y-intercept:

The line is:

Answer:

Interest charged over two years: $20

Total amount: $220

Step-by-step explanation:

The formula for simple interest is A = P ( 1 + rt ).

A = 200 ( 1 + (0.05 * 2))

A is the total amount ( interest + principle )

A = 220

P is the principle ( initial amount deposited )

P = 200

R refers to rate (in percent)

R = 0.05

T = time period (in years)

T = 2

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

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We can compute Amy's monthly budget for each question using division operations, as follows:

1. Amy's monthly budget for textbooks and course supplies is $100.

2. Amy's monthly budget for rent, utilities, and food is $1,422.

3. Amy's monthly budget for personal and miscellaneous costs is $251.

4. Amy's total monthly budget is $1,825.

The total monthly budget is the total budget divided by the period (nine months).

Division operations can be used to determine the individual monthly budgets for each expense class by dividing the total cost by 9.

Textbooks and Course Supplies =         $900      $100

Rent, Utilities, and Food =                   $12,798   $1,422

Personal & Miscellaneous Expense = $2,259     $251

Transportation =                                      $468       $52

Total non-tuition expenses =             $16,425  $1,825 ($16,425/9)

The number of months for the year = 9 months

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Step-by-step explanation:

According to the diagram:

The area is:

Answer:

20.5 cm

Step-by-step explanation:

The perimeter of a shape is the lengths of all the sides.

Add up all the given sides in the picture and you get 93.1

Subtract 113.6 - 93.1 and you get 20.5

Answer:

-36

-3y

Step-by-step explanation:

F

Answer:

(4,-7)

Step-by-step explanation:

y=4x-9

y+3=x

y=4(y+3)-9

y=4y+12+9

y=4y+21

y-4y=21

-3y=21

y=-7

Now use y to find x

y+3=x

-7+3=4

x=4

Answer: no, you cannot because you would get an undefined line which isn't a true function. You always substitute 1 for x to get a basic function which site and teachers will want you to use unless you've been told to do difrently. :)

I hope this is what your looking for

Answer:

p = 8/25

Step-by-step explanation:

500 - 340 = 160 girls

p = 160/500

p = 8/25

Answer:

7*(5)^0,5

:D hope it helps

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

The true statement about the system of equations is the fourth one:

"(8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

The system of equations is:

x - 3y = 2

y = x + 6

We want to see which statement is true, all of them refer to the point (8, 2), so let's see if it is a solution of the system.

Replacing the values in the first equation we will get:

8 - 3*2 = 2

8 - 6  =2

2 = 2

For the second equation:

2 =8 + 6

2 = 14

This is false, so (8, 2) is not a solution of the second equation.

Then the true statement is:

" (8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

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Answer:

-2

Step-by-step explanation:

When you fill it in you get 4(2)+3(-3)-1 then multiply and add

Answer:

5^2×5

=25×5

=125

hope this will help you

Answer:

125

Step-by-step explanation:

hope this helps you

=25×5

=125

Answer:

The area after 6 years is \(1519.49km^2\)

Step-by-step explanation:

Given

\(a = 2100\) --- Initial Value

\(r = 5.25\%\) --- Rate

Required

Determine the area after 6 years

Because the area reduces,, the following formula will be used to solve the question.

\(y = a*(1 - r)^t\)

Here

\(t = 6\)

So, we have:

\(y = 2100*(1 - 5.25\%)^6\)

Convert percentage to decimal

\(y = 2100*(1 - 0.0525)^6\)

\(y = 2100*(0.9475)^6\)

\(y = 1519.47866516\)

\(y = 1519.49\) -- approximated

The area after 6 years is \(1519.49km^2\)

Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

Answer:

\(pg\int\limits^7_7(10-y)2\sqrt{7^2-y^2} \, dy\)

*The last bound is negative 7

Then it equals 15085928 or 1.5E7

Step-by-step explanation:

\(x^2+y^2=7^2\)

area = 2xdy

depth = (7+3)-y -> (10-y)

total force = \(pg\int\limits^7_7 {(10-y)2x} \, dy\)

Substitute 2x from the first equation as x=\(\sqrt{7^2-y^2}\)

total force = \(pg\int\limits^7_7 {(10-y)2\sqrt{49-y^2} } \, dy\)

=pg1539.38

=(1,000)(9.8)(1539.38)=1.5E7 N

*Lower bound is -7, can't get the program to allow me to put it as a negative

The hydrostatic force against one side of the plate is an integral 1.5E7 N.

The general equation of a circle is \((x-h)^{2} +(y-k)^{2} = r^{2}\). The coordinate is (0, 0) at the origin, so the equation will become \((x)^{2} +(y)^{2} = r^{2}\).

\((x)^{2} +(y)^{2} = 7^{2}\)

area of circular plate = 2xdy

depth = (7+3)-y =  (10-y)

The total force = \(pg\int\limits^7_7[ {10-y} ]2xdy\)

Substitute 2x from the first equation as x = \(\sqrt{7^{2} -y^{2} }\)\(pg\int\limits^7_7[ {10-y} ]\sqrt{49 -y^{2} }dy\)            

= pg 1539.38

= (1,000)(9.8)(1539.38)

= 1.5E7 N

Thus, The hydrostatic force against one side of the plate is an integral 1.5E7 N.

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The Integral \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

Given integral;

\(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt\)

By solving the above integral, we have;

⇒ \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt\)

By applying the sum rule,

⇒ \(\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\)

\(=\int \sec ^2\left(t\right)idt+\int \:t\left(t^2+1\right)^4jdt+\int \:t^6\ln \left(t\right)kdt\)

\(\int \sec ^2\left(t\right)idt=i\tan \left(t\right)\)

\(\int \:t\left(t^2+1\right)^4jdt = \frac{j\left(t^2+1\right)^5}{10}\)

\(\int \:t^6\ln \left(t\right)kdt = k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

⇒ \(i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

Therefore, the integral \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

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Answer:

error in Step 2

Step-by-step explanation:

2(x - 3) + 3x = 19

Step 1 : 2x - 6 + 3x = 19 ← simplify left side by collecting like terms

Step 2 : 5x - 6 = 19 ← add 6 to both sides

Step 3 : 5x - 6 + 6 = 19 + 6

Step 4 : 5x = 25 ← divide both sides by 5

Step 5 : x = 5

Error was made by student in Step 2 who should have added 2x and 3x, not multiplied 2 × 3

Answer:

\(x=3\\y=-10\)

Step-by-step explanation:

\(13x=-21-6y\\-8x=36+6y\)

Let's take one of the equations and solve for x. I'll take the first one.

\(13x=-21-6y\)

Divide by 13.

\(x=\frac{-21-6y}{13}\)

Now replace x in the second equation.

\(-8x=36+6y\\-8(\frac{-21-6y}{13} )=36+6y\)

Distribute -8

\(\frac{168+48y}{13}=36+6y\)

Break down the fraction.

\(\frac{168}{13}+\frac{48}{13}y=36+6y\)

Subtract \(\frac{168}{13}\)

\(\frac{48}{13}y=36+6y-\frac{168}{13}\)

Subtract 6y

\(\frac{48}{13}y-6y=36-\frac{168}{13}\)

Combine like terms;

\(\frac{48-13*6}{13}y=\frac{36*13-168}{13}\)

Solve;

\(\frac{48-78}{13}y=\frac{468-168}{13}\)

Keep solving;

\(\frac{-30}{13}y=\frac{300}{13}\)

Multiply by the negative reciprocal of the fraction next to y.

\((-\frac{13}{30} )\frac{-30}{13}y=\frac{300}{13}(-\frac{13}{30} )\)

On the right side; 13 and 13 become 1. 300/30 = 30/3 = 10

\(y=-10\)

After having found y, replace it in any of the equations to find x.

\(13x=-21-6y\\13x=-21-6(-10)\\13x=-21+60\\13x=39\\x=\frac{39}{13}\\ x=3\)

Answer:

x=3

y=-10

Step-by-step explanation:

13x=-21-6y...............(1)

-8x=36+6y................(11)

Add (11) to (1)

5x=15-6y+6y

5x=15

Divide both sides by 5

5x/5=15/5

x=3

Substitute x=3 in 13x=-21-6y

13(3)=-21-6y

39=-21-6y

Collect like terms

39+21=-6y

60=-6y

Divide both sides by -6

60/-6=-6y/-6

-10=y

y=-10

Step-by-step explanation:

divide 62 by 100 and then multiply that number by 66. I don't have a calculator on me rn sorry

Answer:

Fraction:

\(\frac{1023}{25}\)

Decimal:

40.92

Mixed Number:

\(40\frac{23}{25}\)

Step-by-step explanation:

66% is the same this as \(\frac{66}{100}\). You can simplify \(\frac{66}{100}\) to \(\frac{33}{50}\). Then, find \(\frac{33}{50}\) of 62, which is the same thing as \(\frac{33}{50}\) x 62. You’ll get either of the three options, a fraction, decimal, or a mixed number, but all three are the same thing (you get to choose which one).

Hope this helps! :)

Answer:

x = 6, y = -2, z = 0

Step-by-step explanation:

To find x, we have to plug 0 into f(x). Therefore, x = f(0) = 2 * 0² - 8 * 0 + 6 = 6. Similarly, to find y, we have to plug 2 into f(x) so y = f(2) = 2 * 2² - 8 * 2 + 6 = -2. Finally, z = f(3) = 2 * 3² - 8 * 3 + 6 = 0.

Answer:

6, -2, 0

Step-by-step explanation: