-Exponential and Logarithmic functions- Write an exponential function of the form...

Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

Answer:

Do you need the answer or the factor??

Step-by-step explanation:

Answer: -(5a+16)

Step-by-step explanation:

The length of the pool would be 8.5 x 4.5 = 38.25 meters.

Using the Pythagorean theorem the diagonal is:

Diagonal = sqrt(38.25^2 + 8.5^2)

Diagonal = 39.183 meters

You swim it 6 times.

Total distance = 39.183 x 6 = 235.098 meters.

Round to 2 decimals = 235.10 meters

The probability that either event will occur is 0.33

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

Read more about probability at

brainly.com/question/251701

#SPJ1

Answer:1.5

Step-by-step explanation:

Y=1/2 of x

To calculate the average speed of the lap record, we need to know the distance covered and the time taken.

Distance = 5.303 km

Time = 1 minute and 24 seconds = 84 seconds

To convert seconds to hours, we divide by 3600 (the number of seconds in an hour):

\( \frac{84 \: seconds \:}{3600} = 0.02333 \: hours\)

Now we can calculate the average speed:

\(Average \: speed = \frac{d}{t} = \frac{5.303km}{0.02333} \)

Average speed = 227.59 km/h

Ellie needs 5050 grams extra fertilizer and total cost of fertilizer = 22.81-pound sterling.

Multiplication is the product of two or more numerical terms. Division is the process of dividing any numbers into equal parts.

Cost of 750 grams fertilizer = 2.95-pound sterling,

the area of the lawn = 145 square meters.

Ellie uses 40 grams fertilizer for every square meter of lawn.

So, fertilizer needed for the 145 square meters of land = (145 × 40)

                                                                                        = 5800 grams

it stated earlier that 750-gram fertilizer was bought but Ellie needs 5800 grams fertilizer.

the extra amount of fertilizer that Ellie needs = (5800 - 750) = 5050 grams.

cost of 750 gram fertilizer = 2.95-pound sterling

cost of 5050-gram fertilizer = (2.95 × 5050) / 750 = 19.86-pound sterling

cost of extra fertilizer = 19.86-pound sterling.

Total cost of fertilizer = (2.95 + 19.86) pound sterling

                                   = 22.81-pound sterling

To learn more about division and multiplication visit:

https://brainly.com/question/1292482

#SPJ1

Answer:

58 campers,

Step-by-step explanation:

you do 200 - 25 then 175 divided by 3

Answer: The mean difference is between 799586.3 and 803257.9.

Step-by-step explanation: To estimate the mean difference for confidence interval:

Find the statistic sample:

For the traffic count, mean = 1835.8 and s = 1382607.3

The confidence interval is 90%, so:

α = \(\frac{1-0.9}{2}\)

α = 0.05

The degrees of dreedom are:

df = n - 1

df = 10 - 1

df = 9

Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.

Error will be:

E = \(t.\frac{s}{\sqrt{n} }\)

E = 1.833.(\(\frac{1382607.3}{\sqrt{10} }\))

E = 801422.1

The interval is: mean - E < μ < E + mean

1835.8 - 801422.1 < μ < 1835.8+801422.1

-799586.3 < μ < 803257.9

The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.

Answer:

100

Step-by-step explanation:

30 rounds down

Generally, the equation representing the simple interest on a deposited amount is;

where ;

I is the simple interest

R is the rate

T is the time

We have other varaints of this formula, depending on the term missing

All we have to is to make the missing term the subject of the equation and input the other given values to get the missing term

We can have the variants of this formula as follows

a) Missing Principal

b) Missing Rate

c) Missing Time

Recall the inverse function theorem. If \(f\) is invertible and differentiable in all the right places, then

\(f^{-1}\bigg(f(x)\bigg) = x \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'\bigg(f(x)\bigg) f'(x) = 1 \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'\bigg(f(x)\bigg) = \dfrac1{f'(x)} \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'(x) = \dfrac1{f'\left(f^{-1}(x)\right)} \\\\ ~~~~~~~~ \implies \left(f^{-1}\right)'(-4) = \dfrac1{f'\left(f^{-1}(-4)\right)}\)

Solve for \(x\) such that \(f(x)=-4\).

\(x^3 + 2x - 1 = -4 \\\\ x^3 + 2x + 3 = 0 \\\\ (x + 1) (x^2 - x + 3) = 0\)

\(x^2-x+3=0\) has non-real solutions, so we're left with

\(x+1 = 0 \implies x = -1\)

Then we have

\(f(-1) = -4 \implies f^{-1}(-4) = -1 \implies \left(f^{-1}\right)' (-4) = \dfrac1{f'(-1)} = \boxed{\dfrac15}\)

since

\(f(x) = x^3 + 2x - 1 \implies f'(x) = 3x^2 + 2 \implies f'(-1)=5\)

The table with the absolute guessing errors should be completed as follows;

Guess                                  2    15   10   8    12   19   20   5    7    9

Absolute guessing error   12    1      4    6    2     5    6    9    7    5

A graph of the guess and absolute guessing error is shown in the image attached below.

Yes, the absolute guessing error is a function of the guess because every guess (input value) has one absolute guessing error (output value).

In Mathematics, the margin of error (MOE) is sometimes referred to as an absolute guessing error and it can be defined as a measure of the difference that exist between an observed value and a true value of the population parameter.

Mathematically, the absolute guessing error for the guesses made by these group of ten friends with respect to the actual number of 14 as follows;

Absolute guessing error = 14 - 2 = 12

Absolute guessing error = 14 - 15 = 1

Absolute guessing error = 14 - 10 = 4

Absolute guessing error = 14 - 8 = 6

Absolute guessing error = 14 - 12 = 2

Absolute guessing error = 14 - 19 = 5

Absolute guessing error = 14 - 20 = 6

Absolute guessing error = 14 - 5 = 9

Absolute guessing error = 14 - 7 = 7

Absolute guessing error = 14 - 9 = 5

Read more on absolute value function here: brainly.com/question/1616026

#SPJ1

Answer:

I think it would be: -10u - 6x 12

Step-by-step explanation:

(step 1) -2(5u - 3x-6) "First you need to times -2 by 5, 3 and -6"

that should give you -10u - 6x 12

Answer:

Below

Step-by-step explanation:

-4 1/4  +  5 3/8  

-17/4  + 43/8

-34/8 + 43/8 =  9/8 = 1  1/8

Answer:

Step-by-step explanation:

1 1/8

I converted the numbers into a mixed number

The first one was -17/4 and the other one was -43/8 but I had to find a common denominator so I multiplied the first one by 2 and the 2nd by one getting -34/8 and then for the 2nd one it stayed the same which is -43/8.

After I subtracted -34 and -43 and got 9/8 which is equal to 1 1/8

(Hope this is right...if wrong I'm sorry)

The way the numbers will be placed in the square box will be:

First row = 4 12 14

Second row = 2 10 18

Third row = 6 8 16

It should be noted that the question is simply about adding the numbers and getting 39 in each place.

This will be:

First row = 4 12 14 = 4 + 12 + 14 = 30

Second row = 2 10 18 = 2 + 10 + 18 = 30

Third row = 6 8 16 = 6 + 8 + 16 = 30

Learn more about squares on:

brainly.com/question/24673551

#SPJ1

False. If opposite angles of a quadrilateral are supplementary then the quadrilateral is not a parallelogram.

Two angles are said to be supplementary angles if their sum is equal to 180 degrees.

In a parallelogram the sum of adjacent angles is equal to 180 degrees which means that the adjacent angles are supplementary. Whereas, the opposite angles in a parallelogram are congruent (equal). Hence, the statement is false.

To learn more about supplementary angles visit the link below:

https://brainly.com/question/27624512

#SBJ4

Answer:

divide 90 and 30 to see what you got

Step-by-step explanation:

Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

Answer:

-32

Step-by-step explanation:

do you need me to explain?

Answer:

y = -32

Step-by-step explanation:

thanks for helping me

The algebraic values of x include:

Using the same reasoning as in the previous problem:

24² + 45² = x²

576 + 2025 = x²

2601 = x²

x = ±51

Since x represents a length, discard the negative solution. Therefore, the value of x is 51.

Using the Pythagorean Theorem:

30² + 40² = x²

900 + 1600 = x²

2500 = x²

x = ±50

Since x represents a length, discard the negative solution. Therefore, the value of x is 50.

Using the Pythagorean Theorem:

18² + 80² = x²

324 + 6400 = x²

6724 = x²

x = ±82

Since x represents a length, discard the negative solution. Therefore, the value of x is 82.

Using the Pythagorean Theorem:

18² + 4² = x²

324 + 16 = x²

340 = x²

x = √340 = 2√85

Therefore, the value of x is 2√85 in simplest radical form.

Using the Pythagorean Theorem:

8² + 5² = x²

64 + 25 = x²

89 = x²

x = √89

Therefore, the value of x is √89 in simplest radical form.

Using the Pythagorean Theorem:

20² + 18² = x²

400 + 324 = x²

724 = x²

x = √724 = 2√181

Therefore, the value of x is 2√181 in simplest radical form.

Using the Pythagorean Theorem:

25² + 3² = x²

625 + 9 = x²

634 = x²

x = √634

Therefore, the value of x is √634 in simplest radical form.

Using the Pythagorean Theorem:

3² + 6² = x²

9 + 36 = x²

45 = x²

x = √45 = 3√5

Therefore, the value of x is 3√5 in simplest radical form.

Using the Pythagorean Theorem:

22² + 4² = x²

484 + 16 = x²

500 = x²

x = √500 = 10√5

Therefore, the value of x is 10√5 in simplest radical form.

To determine if a triangle is a right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore:

a² + b² = c²

Substituting a = 8, b = 15, and c = 17:

8² + 15² = 17²

64 + 225 = 289

289 = 289

Since the equation is true, the triangle satisfies the Pythagorean Theorem and is therefore a right triangle.

Using the same method:

27² + 36² = 45²

729 + 1296 = 2025

2025 ≠ 2025

Since the equation is false, the triangle does not satisfy the Pythagorean Theorem and is therefore not a right triangle.

Using the same method:

9² + 11² = 4²

81 + 121 = 16

202 ≠ 16

Since the equation is false, the triangle does not satisfy the Pythagorean Theorem and is therefore not a right triangle.

To determine the classification of this triangle, compare the lengths of its sides. If all sides are less than the sum of the other two, then the triangle is acute; if one side is greater than or equal to the sum of the other two, then the triangle is obtuse; and if one side is equal to the sum of the other two, then the triangle is degenerate (a straight line).

Substituting a = 3, b = 4, and c = 6:

a + b = 3 + 4 = 7 < c

b + c = 4 + 6 = 10 > a

a + c = 3 + 6 = 9 > b

Since none of the sides are equal to or greater than the sum of the other two, the triangle is acute.

Substituting a = 9, b = 11, and c = 16:

a + b = 9 + 11 = 20 < c

b + c = 11 + 16 = 27 > a

a + c = 9 + 16 = 25 > b

Since none of the sides are equal to or greater than the sum of the other two, the triangle is acute.

Find out more on triangles here: https://brainly.com/question/1058720

#SPJ1

Image transcribed:

Algebra Find the value of x.

1. 12, 9, x

To start, use the Pythagorean Theorem. Then substitute 9 for a, 12 for b, and x for c.

2. 45 24 x

3. 30, 40, x

4. 80, 18, x

Algebra Find the value of x. Express your answer in simplest radical form.

8. 18, 4, x

9. 8, 5, x

10. 20, 18, x

11. 25, 3, x

12. 3, 6, x

13. 22, 4, x

Is each triangle a right triangle? Explain.

16. 15, 17, 8

17. 27, 45, 36

18. 9, 11, 4

The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.

19. 3,4,6

To start, compare to a+b. Substitute the greatest length for c.

20. 9, 11, 16

Answer:

Sure, I can help with that! Here are the steps to solve each problem:

a) Since sin A = 0.6018, we can use the inverse sine function (sin^-1) to find the measure of angle A. Taking the inverse sine of 0.6018 gives us 37.19 degrees rounded to the nearest degree.

b) Since cos B = 0.9205, we can use the inverse cosine function (cos^-1) to find the measure of angle B. Taking the inverse cosine of 0.9205 gives us 23.06 degrees rounded to the nearest degree.

c) Since tan C = 0.0349, we can use the inverse tangent function (tan^-1) to find the measure of angle C. Taking the inverse tangent of 0.0349 gives us 2.00 degrees rounded to the nearest degree.

I hope that helps! Let me know if you need any further assistance.

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

Learn more about truth table visit:

https://brainly.com/question/29155453

#SPJ1

Answer:

4 cm^2

Step-by-step explanation:

2 x 2 x 0.5 x 2 = 4 cm^2

Hi there!

\(\huge\boxed{4 \text{ cm}^{2}}\)

Find the area of the shaded area using the given dimensions:

The shaded area is divided up into two triangles, each with a base of 2 cm and a height of 2 cm. Use the following equation to solve for area:

A = 1/2(bh)

A = 1/2(2 · 2)

A = 1/2(4) = 2 cm²

There are two triangles, therefore:

2 × 2 = 4 cm²

Answer:

5years, 3months, 16 days

Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, \(\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}\).

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

\(f(x)=2x+100\)

This can be checked by using the values given in the problem:

\(f(30)=2(30)+120=180\\f(50)=2(50)+120=220\)

The base rate of $120 and $2 per person satisfies the given equation and established values.

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

For similar question on total interest.

https://brainly.com/question/29415701  

#SPJ8

Step-by-step explanation:

f(x) = 3x² - 2x + 8 , x = 3

f(3) = 3.3² - 2.3 + 8

= 27 - 6 + 8

= 29

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)