Decide if the function is an exponential function. If it is state the initial value and the base y=x^2

Answer:

Part 3)

[tex]x=6\ units[/tex]

[tex]y=3\ units[/tex]

Part 4) [tex]x=18\sqrt{2}\ units[/tex]

Step-by-step explanation:

Part 3)

step 1

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

so

[tex]cos(30\°)=\frac{3\sqrt{3}}{x}[/tex]

and remember that

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}[/tex]

Simplify

[tex]x=(2*3)=6\ units[/tex]

step 2

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

so

[tex]sin(30\°)=\frac{y}{x}[/tex]

and remember that

[tex]sin(30\°)=\frac{1}{2}[/tex]

substitute

[tex]\frac{1}{2}=\frac{y}{6}[/tex]

[tex]y=6/2=3\ units[/tex]

Part 4) Find the value of x

Applying the Pythagoras Theorem

[tex]x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units[/tex]

Simplify

[tex]x=18\sqrt{2}\ units[/tex]

Answer:

The correct answer is "Study of tree rings and associated geology shows that the Earth is more than 12,429 years old"

Step-by-step explanation:

While tress have been growing long enough to prove the earth is more than 12,000 years old, it is not able to prove much longer than that. Luckily geology is able to show is that Earth is over 4.6 billions years old. As a result, the above is the only true statement.

The age of the Earth is approximately 4.5 billion years, as determined by radioactive dating methods and supported by other geological evidence. Although not directly determining the Earth's age, the study of tree rings provides valuable information about climate conditions in specific periods.

The scientific study of tree rings, known as dendrochronology, can provide valuable information about the Earth's climate in different periods. However, it doesn't directly determine the overall age of the Earth.

Conversely, radioactive dating methods, like uranium-238 dating or rubidium-strontium dating, have been used to determine the Earth's age by dating the oldest rocks and minerals on Earth's crust. For example, the Jack Hills zircons from Australia were found by uranium-lead dating to be nearly 4.4 billion years old.

Using these dating methods in connection with the study of tree rings and other geological evidence, scientists have estimated that the age of the Earth is approximately 4.5 billion years.

This age is significantly older than what could be derived from tree rings alone, as the oldest living trees, like the Methuselah tree, are estimated to be just over 4,800 years old.

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Answer:

[tex]5\sqrt{3}[/tex] OR [tex]8.69[/tex]

Step-by-step explanation:

Let's first simplify [tex]\sqrt{75}[/tex].

5 and 15 multiply to get 75. 5 and 3 multiply to get 15. Since we have a pair of fives and a three leftover, we can write [tex]\sqrt{75}[/tex] as:

[tex]5\sqrt{3}[/tex]

Now, let's find the answer in decimal form. We know that:

[tex]8^2=64[/tex] and [tex]9^2=81[/tex]

With that information, we know that the answer has to be between 8 and 9.

Divide 75 by 8: [tex]\frac{75}{8}=9.375[/tex]

Take the average of that answer and 8: [tex]\frac{9.375+8}{2}=\frac{17.375}{2}=8.6875[/tex]

This answer we got is extremely close to the exact answer of [tex]\sqrt{75}[/tex], which is [tex]8.66025403...[/tex]. Since we are estimating, the answer above will do just fine.

Answer:

W = 16 in

Step-by-step explanation:

P = 2L + 2W

56 = 2(12) + 2W

56 = 24 + 2W

56-24 = 2W

32 = 2W

W = 32/2

W = 16 in

Best regards

Answer:

C. -2

Step-by-step explanation:

Since the leading coefficient is 1 and rational roots are of the form ...

±(divisor of the constant)/(divisor of the leading coefficient)

all of the possible rational roots must be whole number diviors of 12. The only one on the list is -2.

The Rational Root Theorem allows us to determine that -2 is a possible rational root for the polynomial p(x)=x2+3x+12.

According to the Rational Root Theorem, the possible rational roots of a polynomial equation can be found by taking all the factors of the constant term (in this case, 12) and dividing them by all the factors of the leading coefficient (in this case, 1 as the coefficient for x2 is 1). The factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12. As our leading coefficient is 1, our possible roots can include ±1, ±2, ±3, ±4, ±6, ±12.

Looking at the list of options provided: A. 24, B. -1/2, C. -2, D. 1/6, E. 1/2, we see that only -2 is a possible rational root for the polynomial p(x)=x2+3x+12 based on the Rational Root Theorem.

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Answer:

whew chiile

Step-by-step explanation:

Answer:

k > 3

Option D

For any value of k greater than 3

Step-by-step explanation:

We ara dealing with an inequality

(k/3)*12 > 12

Dividing by 12 each side

(k/3)*12/12 > 12/12

(k/3) > 1

Multiplying by three

3*(k/3) > 3*1

k > 3

Answer:

k > 3

Option D

For any value of k greater than 3

Step-by-step explanation:

Answer:

1.91° and -1.91°.

Step-by-step explanation:

2.8% of the thermometers are rejected on either end of the curve.  The bottom end, where the readings are too far below the mean, will have an area from this point to the left tail of the curve of 0.028.

The top end, where the readings are too far above the mean, will have an area from this point to the left tail of the curve of 1-0.028 = 0.972.

We look in a z table for these values.  We look within the cells of the table; the closest value to 0.028 is 0.0281, which corresponds with a z score of -1.91.  The closest value to 0.972 is 0.9719, which corresponds with a z score of 1.91.

We substitute these values into the z score formula, along with our values for the mean (0) and the standard deviation (1):

[tex]-1.91=\frac{X-0}{1}[/tex]

Simplifying the right hand side, X-0 = X; X/1 = X.  This means X = -1.91.

For the second value,

[tex]1.91=\frac{X-0}{1}[/tex]

Simplifying the right hand side, X-0 = X; X/1 = X.  This means X = 1.91.

This means the two values are 1.91° and -1.91°.

The cutoff values separating the rejected thermometers in a normally distributed thermometer reading with a mean of 0 and a standard deviation of 1°C are -1.88°C and +1.88°C. These values are determined using the z-scores that corresponds to the tail probabilities (2.8%) of the normal distribution.

The question involves determining the cutoff values that separate the rejected thermometers based on a normally distributed thermometer reading. We know that 2.8% of the thermometers are rejected for being too high, and another 2.8% for being too low. Here, this involves using the concept of the normal distribution and z-scores.

First, since each tail contains 2.8% of the data, the cumulative probability up to the cutoff point will be 100% - 2.8% = 97.2% for the higher cutoff and 2.8% for the lower cutoff. To find the z-scores that correspond to these areas, you can consult a standard normal distribution table or use an online tool. Typically, z-scores around ±1.88 correspond to a cumulative probability closest to 97.2% and -1.88 for 2.8%.

Since the mean (μ) is 0 and the standard deviation (σ) is 1°C, the thermometer readings the cutoff values or z-scores represent are given by z = (X - μ)/σ. Therefore, the thermometer readings for these z-scores are -1.88°C and +1.88°C. These are the cutoff values which separate the rejected thermometers.

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Answer:

Option B. [tex](x-4)^{2}=44[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-8x-10=18[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-8x=18+10[/tex]

[tex]x^{2}-8x=28[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]x^{2}-8x+16=28+16[/tex]

[tex]x^{2}-8x+16=44[/tex]

Rewrite as perfect squares

[tex](x-4)^{2}=44[/tex]

Answer:

b

Step-by-step explanation:

Answer:

[tex](x-4)^{2}=44[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-8x-10=18[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-8x=18+10[/tex]

[tex]x^{2}-8x=28[/tex]

Complete the square . Remember to balance the equation by adding the same constants to each side

[tex]x^{2}-8x+16=28+16[/tex]

[tex]x^{2}-8x+16=44[/tex]

Rewrite as perfect squares

[tex](x-4)^{2}=44[/tex]

Answer:

8

Step-by-step explanation:

So a square is equal on all sides if I'm correct so. The area is pretty much the length x width. So 8 times 8 equals 64.

Hope this helps, have a good day

s = 8cm (Answer A)

Step-by-step explanation:

The area of a square, A, is the square of the length of any one side:

A = s².

If A = 64 cm², then 64 cm² = s².

Taking the square root of both sides yields s = 8cm (Answer A)

Answer:

Shifted horizontally to the right 3 units, and shifted vertically down 2 units

Step-by-step explanation:

The parent graph of this equation is y = |x|

There are 2 translations to this graph for the equation y = |x - 3| - 2

The "x - 3" part shifts the graph to the right 3 units

The -2 shifts the graph vertically down 2 units

See below for the parent graph, and the graph of the equation we are working with

The graph of function y = |x - 3| - 2 is shown in figure.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The equation is,

⇒ y = |x - 3| - 2

Now,

Since, The equation is,

⇒ y = |x - 3| - 2

Clearly, The equation y = |x - 3| - 2 is the translation of y = |x| with 3 units right and 2 units up.

Thus, The graph of function y = |x - 3| - 2 is shown in figure with 3 units right and 2 units up translation of y = |x|.

Learn more about the translation visit:

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Answer:

Step-by-step explanation:

Question 1:

For this case we must find the derivative of the following function:

[tex]f (x) = \frac {7} {x}[/tex] evaluated at [tex]x = 1[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

So:

[tex]\frac {df (x)} {dx} = - 1 * 7 * x ^ {- 1-1} = - 7x ^ {- 2} = - \frac {7} {x ^ 2}[/tex]

We evaluate in [tex]x = 1[/tex]

[tex]- \frac {7} {x ^ 2} = - \frac {7} {1 ^ 2} = - 7[/tex]

ANswer:

Option A

Question 2:

For this we must find the derivative of the following function:

[tex]f (x) = 4x + 7\ evaluated\ at\ x = 5[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

The derivative of a constant is 0

So:

[tex]\frac {df (x)} {dx} = 1 * 4 * x ^ {1-1} + 0 = 4 * x ^ 0 = 4[/tex]

Thus, the value of the derivative is 4.

Answer:

Option A

Question 3:

For this we must find the derivative of the following function:

[tex]f (x) = 12x ^ 2 + 8x\ evaluated\ at\ x = 9[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

So:

[tex]\frac {df (x)} {dx} = 2 * 12 * x ^ {2-1} + 1 * 8 * x ^ {1-1} = 24x + 8 * x ^ 0 = 24x + 8[/tex]

We evaluate for [tex]x = 9[/tex]we have:

[tex]24 (9) + 8 = 224[/tex]

Answer:

Option D

Question 4:

For this we must find the derivative of the following function:

[tex]f (x) = - \frac {11} {x}\ evaluated\ at\ x = 9[/tex]

We have by definition:

[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]

So:

[tex]\frac {df (x)} {dx} = - (- 1 * 11 * x ^ {- 1-1}) = 11x ^ {- 2} = \frac {11} {x ^ 2}[/tex]

We evaluate for [tex]x = 9[/tex] and we have:

[tex]\frac {11} {9 ^ 2} = \frac {11} {81}[/tex]

ANswer:

Option D

Question 5:

For this case we have by definition, that the derivative of the position is the velocity. That is to say:

[tex]\frac {d (s (t))} {dt} = v (t)[/tex]

Where:

s: It's the position

v: It's the velocity

t: It's time

We have the position is:

[tex]s (t) = 1-10t[/tex]

We derive:

[tex]\frac {d (s (t))} {dt} = 0- (1 * 10 * t ^ {1-1}) = - 10 * t ^ 0 = -10[/tex]

So, the instantaneous velocity is -10

Answer:

-10

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=6^x\qquad \boxed{x=-3}\qquad \implies f(-3)=6^{-3}\implies f(-3)=\cfrac{1}{6^3} \\\\\\ f(-3)=\cfrac{1}{6\cdot 6\cdot 6}\implies f(-3)=\cfrac{1}{36\cdot 6}\implies f(-3)=\cfrac{1}{216}[/tex]

Answer: B on Edg

Step-by-step explanation:

Answer:    14  15-pound weights

Step-by-step explanation:

15 × 14= 210

Julio should put 14 fifteen-pound weights on the bar to achieve a total weight of 210 pounds.

Julio wants to have a total of 210 pounds on the barbell. Since each weight he will add is 15 pounds, we simply need to divide the total desired weight by the weight of one plate to determine the number of plates required.

Here is the calculation:

Therefore, Julio should put 14 fifteen-pound weights on the bar to reach a total of 210 pounds.

If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:

7, 714/24 = 321.4167

This answer estimated can be 321. So yuh might need 321 panels.

ANSWER = 321 PANELS

Answer:300

Step-by-step explanation:

If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:

7, 714/24 = 321.4167

This answer estimated can be 321. So yuh might need 321 panels.

ANSWER = 321 PANELS

But the best estimate is 300 pannels

Answer:

176

Step-by-step explanation:

We see that it is an arithmetic sequence since we are subtracting the same number to a term to get the next term. So 876 - 7 = 869  &  869 - 7 = 862.

So the common difference d is -7

and the first term, a is 876

The nth term of an arithmetic sequence is given by  a + (n-1)d

where n would be 101, since we want to figure 101st term.

So:

[tex]a+(n-1)d\\876+(101-1)(-7)\\876+(100)(-7)\\=176[/tex]

Correct answer is the 2nd choice, 176

The 101st term in the sequence 876, 869, 862, ... is 176, found by using the formula for the nth term of an arithmetic sequence with a common difference of -7.

To find the 101st term in the sequence 876, 869, 862, ..., we first need to determine the common difference of the arithmetic sequence. Each term decreases by 7 (869 - 876 = -7 and 862 - 869 = -7), so the common difference is -7.

Now, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

The 101st term is calculated as follows:

Thus, the 101st term is 176.

Answer:

(-7 , 3)

Step-by-step explanation:

3x^2 + 12x = 63 //Subtract 63 on both sides.

3x^2 + 12x - 63 = 0 //Common factor 3.

3(x^2 + 4x - 21) = 0 //Divide both sides by 3.

(x^2 + 7x - 3x - 21) = 0

x(x + 7) - 3(x + 7) = 0

(x + 7) (x - 3) = 0

x = -7 and 3

Solution: (-7, 3)

Answer:

96sqrt(3)

Step-by-step explanation:

Simplest and most intuitive way is to find area of 1 triangles and multiply it by 6.

Area of one triangle:

base = 8 and a = 4sqrt(3)

Area of 1 trangle = ba/2

Area of base of hexagon = 6 times that.

[tex]\huge\boxed{\text{The $5$ needs to be negative.}}[/tex]

Since the first binomial is [tex](x-5)[/tex], the [tex]5[/tex] is negative and must be that way when using the table.

Here's the corrected table:

[tex]\begin{array}{c|c|c|}\multicolumn{1}{c}{}&\multicolumn{1}{c}{3x}&\multicolumn{1}{c}{1}\\\cline{2-3}x&3x^2&x\\\cline{2-3}-5&-15x&-5\\\cline{2-3}\end{array}\\\\\\3x^2+x-15x-5\\3x^2-14x-5[/tex]

Answer:

If those are supposed to be exponents the answers are:

1.  1/36

2.  - 1/6

3.     1

4.  -6

5.  36

Step-by-step explanation:

The student is provided with the correct evaluations of five expressions given the value x = -6. Each expression is computed, and the correct numerical matches are presented.

The student is attempting to solve expressions given the value of x = -6. To find the correct matches, each expression must be computed separately. Let's start by calculating the given expressions:

x - 2: When x is -6, the expression becomes (-6) - 2 = -8.

x - 1: When x is -6, the expression becomes (-6) - 1 = -7.

x + 0: When x is -6, the expression is simply -6.

x + 1: When x is -6, the expression becomes (-6) + 1 = -5.

x + 2: When x is -6, the expression becomes (-6) + 2 = -4.

With these computations, the matches would be:

x - 2 matches with -8

x - 1 matches with -7

x + 0 matches with -6

x + 1 matches with -5

x + 2 matches with -4

Answer:

The measure of the greatest angle is about 81° ⇒ answer (b)

Step-by-step explanation:

* Let the given triangle is ΔABC where,

- a = 18 inches ⇒ opposite to angle A

- b = 21 inches ⇒ opposite to angle B

- c = 14 inches ⇒ opposite to angle C

∵ The greatest angle is opposite to the largest side

∴ The greatest angle will be angle B because b is the largest side

* By using cos Rule:

∵ b² = a² + c² - 2ac cos(B)

* Lets re-arrange the terms to find the measure of angle B

∴ 2ac cos(B) = a² + c² - b²

∴ cos(B) = (a² + c² - b²)/2ac

∴ cos(B) = (18² + 14² - 21²)/2(18)(14) = 79/504

∴ m∠B = 80.98 ≅ 81°

∴ The measure of the greatest angle is about 81°

Answer:

The required expression is 24 - 4x

Step-by-step explanation:

Given,

Initial number of stickers she has = 24,

Also, the number of stickers she used for a card = 4,

⇒ the number of stickers she used for x cards = 4x,

So, the number of stickers she left after decorating x cards = Initial number of stickers - the number of stickers used for x cards,

= 24 - 4x

Which is the required expression.

Answer:

210

Step-by-step explanation:

As there is one circle in first row, 2 circles in 2nd row and three in third row, which clearly implies that the number of circles in each row is equal to the row number. So, we have to calculate sum of first 20 numbers to calculate the total number of circles.

n=20

Total Circles=(n(n+1))/2

=(20 (20+1))/2

=(20(21))/2

=  420/2

=210

So the total number of circles will be 210.  

Answer:

The radius is increased by 1.2599 times the original size.

Step-by-step explanation:

The volume is 3 dimensional whereas the radius is one dimensional.

Therefore the factor for the  radius will be the cube root of the factor for the volume.

So the radius is increased by 1.2599.

Answer:

17 hours

Step-by-step explanation:

As we know altogether means how many in all or in an easier saying the total.The total is 17.Hope that help you!

Answer:

P(6 times in 9 selection) = 0.116

Step-by-step explanation:

There are 11 red checkers and 5 black checkers in a bag so

P(red) = no. of red checkers / total no. of checkers = 11/(11+5) = 11/16

Checkers are selected one at a time, with replacement. So P(red) is the same for every selection at 11/16.

Use binomial distribution to find the probability of selecting a red checker exactly 6 times in 9 selections.

In this case, n = 9 and k = 6, P(red)=11/16 so

P(6 times in 9 selection) = nCk * P(red)^k * (1-P(red))^(n-k)

where 9C7 = 9! / [7!*(9-7)!] = 9! / 7!*2! = 9*8 / 2 =36

so  P(6 times in 9 selection)

= 36 * (11/16)^6 * (5/16)^3

= 0.116

The context is a binomial distribution where success is defined as drawing a red checker from the bag. With replacement, each draw is independent. Therefore, the formula for binomial probability can be used to calculate the probability of drawing a red checker exactly 6 times in 9 draws.

This is a problem of the binomial distribution. For a binomial distribution, each trial is independent, meaning the result of the previous trial does not affect the result of the next trial. This is satisfied since the question states that the checkers are selected with replacement.

'Success' in this context is defined as selecting a red checker which occurs with a probability of 11/16 (since there are 11 red checkers out of a total of 16). Failure is defined as selecting a black checker which occurs with a success probability of 5/16.

To find the probability of selecting a red checker exactly 6 times in 9 selections, we use the formula for binomial probability: P(k; n, p) = C(n, k) * (p^k) * (1 - p)^(n-k). Here, n=9 (number of trials), k=6 (desired 'successes') and p=11/16. When you substitute these values into the formula, you get the desired probability.

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Answer:

Option A. [tex]0.42[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]BA^{2}=(1/2)^{2}+(1/3)^{2} -2(1/2)(1/3))cos(100)[/tex]

[tex]BA^{2}=0.1756[/tex]

[tex]BA=0.42[/tex]

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=28\pi \end{cases}\implies 28\pi =2\pi r\implies \cfrac{28\pi }{2\pi }=r\implies 14=r[/tex]