4. Given the function f(x) = x2 + 4x – 7. Bonus 2: What transformations are applied on f(x) in Question 4? (1pt)

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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If its half-life is 93 minutes, then the amount left after 279 minutes will be equal to 164 grams.

In radioactivity, the half-life is the amount of time needed for half of a radioactive sample's atomic nuclei to spontaneously decay (convert into different nuclear species by emitter particles and energy) or, alternatively, the amount of time needed for the radioactive material's disintegration rate to drop by half.

As per the given information given in the question,

Initial amount, N₀ = 1312 grams

Time elapsed, t = 279 min

Half-life, \(t^1^/^2\) = 93

Then, use the formula of half-life:

N(t) = N₀\((\frac{1}{2})^t^/^(^t^)^1^/^2\)

Substitute the values in above equation,

N(t) = 1312\((\frac{1}{2})^2^7^9^/^9^3\)

N(t) = 1312(1/2)³

= 1312 × 0.125

N(t) = 164 grams.

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Answer: 164 grams

Step-by-step explanation: I got the answer right on my ixl

Answer:

There is no integer or rational solution to the equation 4 = x^5 + x^4. This can be verified by trying integer and rational values of x and seeing that none of them satisfy the equation. Therefore, the solution is "no solution".

Answer:

The answer is 4/9

Step-by-step explanation:

All you have to do is break down the numbers to their greatest common factor and cross out everything that the top and bottom have in common than whatever you all left with you will multiply across and that is how you would get your answer

Answer:

8/21

Step-by-step explanation:

1- 2/7 - 1/3 = 21/21 - 6/21 - 7/21 = 8/21

Answer:4.12

Step-by-step explanation: I need brainliest for next rank I’d appreciate it

Answer

Statements B, C and E are correct.

Statements A and D are not correct.

Explanation

To pick the correct statements, we will have to examine each of the statements given to pick the correct ones.

The Cost of peanuts is presented on the y-axis while the weight of the corresponding peanuts is on the x-axis.

First, we have to calculate the slope of the graph given to establish the cost of 1 pound of peanuts.

For this graph, it passes through (0, 0) and (7, 17.5)

Hence, we have established that the cost of 1 pound of peanuts is $2.5

So, taking the options one at a time

A.) 2.5 pounds of peanuts costs $1

We have already established that 1 pound of peanuts costs $2.5

1 pound = $2.5

2.5 pounds = 2.5 × $2.5 = $6.25

Hence, this statement isn't correct.

B.) 1 pound of peanuts costs $2.50

This is correct because we already established this from calculating the slope of the graph.

C.) 5 pounds of peanuts costs $12.50

1 pound = $2.5

5 pounds = 5 × $2.5 = $12.50

Hence, this statement is correct.

D.) 9 pounds of peanuts costs $19.50

1 pound = $2.5

9 pounds = 9 × $2.5 = $22.50

Hence, this statement isn't correct.

E.) The point (4, 10) is on the graph of the proportional relationship.

The point (4, 10) means 4 pounds of peanuts costs $10.

1 pound = $2.5

4 pounds = 4 × $2.5 = $10

Hence, this statement too is true.

Hope this Helps!!!

Answer:

1. {y,x} = {20/3,-68/3} (not sure)

2. x=45

3. x=−9

4.  y=1

5. y=14

Step-by-step explanation:

Answer:

tan 25° = b / 8 m

Step-by-step explanation:

You need to know what the ratios are.

sin X = opp/hyp

cos X = adj/opp

tan X = opp/adj

For angle B, the opposite leg is b, ad the adjacent leg is 8 m.

The hypotenuse is AB.

sin B = sin 25° = opp/hyp = b/AB

tan B = tan 25° = opp/adj = b / 8 m

Since the interest rate is 5%. She needs to express the percentage as a decimal.

In order to do it, she needs to divide 5 by 100, so:

Answer:

r = 0.05

Answer:

-2

Step-by-step explaniaton

Answer:

find the squares of both numbers

5²= 25

13²=169

minus the squares

169-25=144

find the square root of the answer above

✓144=12

the possibility of the third side is 12

Answer: Okay so do 3x7.5 then 3x11.5 then 7.5x11.5 then add it up and you should get  143.25

There is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

In the posed query,

We must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

Option A is the proper response, so.

The complete question is:-

What is the probability that a standard normal random variable will be between .3 and 3.2?

A. .3814

B. .3808

C. .9993

D. .6179

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Answer:

4:10

24:60

48:120

As long as you multiply or divide both sides of the ratio by the same number, you will have an equivalent ratio.

Answer:

C. .45

Step-by-step explanation:

Think of it like this: that is 45 hundredths and you are trying to find what 45% is and it is like 45/100 so .45 is your answer.

answer c=0.45

0.45 is equal to 45%.

The chance of seeing a plate with the first digit being strictly less than the second one depends on the number of possible digits. Assuming the digits range from 0-9, there are 10 possible digits.

For the first digit, it can be any number from 0-8 (as it must be strictly less than the second digit). For each of these 9 options, there are different numbers of possibilities for the second digit:

- If the first digit is 0, there are 9 options for the second digit (1-9).
- If the first digit is 1, there are 8 options for the second digit (2-9).
- If the first digit is 2, there are 7 options for the second digit (3-9).
- And so on, until the first digit is 8, with only 1 option for the second digit (9).

To calculate the total number of possibilities with the first digit being strictly less than the second, you add up the options for the second digit: 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45. There are 100 total possibilities (10 digits for the first spot multiplied by 10 digits for the second spot). Therefore, the chance of seeing a plate with the first digit being strictly less than the second one is: 45/100 = 0.45 or 45%., So, there is a 45% chance of seeing a plate with the first digit being strictly less than the second one.

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Answer:

frfr

Step-by-step explanation:

redfcefce

The  value of x is 94.5.

We are given that a basketball player averages 13.5 points per game.

x=Number of points scored in 7 games

We have to find the value of x

In order to find the points scored in 7 games we will multiply 7 by 13.5.

Number of games=7

Number of point scored in one game=13.5

Number of points scored in 7 games=

Number of points scored in 7 games=94.5

Hence, value of x=94.5

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Answer: 15 dimes 12 nickels 12 pennies 7 quarters?

Step-by-step explanation:

Answer:

Infinite solutions or the solution is all real numbers

Step-by-step explanation:

5(r+9) = 5r + 45 when simplified

This is identical to the RHS with the exception that there is an x instead of r.

What it means that if you were to graph those 2 lines in the coordinate plane they would be right on top of each other. 2 identical straight lines intersecting forever with infinite solutions.

The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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A residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

The residual plot is a graphical tool used to assess the appropriateness of the line of best fit or the regression model for the data. It helps to examine the distribution and patterns of the residuals, which are the differences between the observed data points and the predicted values from the regression model.

In a residual plot, the horizontal axis typically represents the independent variable or the predicted values, while the vertical axis represents the residuals. The residuals are plotted as points or dots, and their pattern can provide insights into the line of best fit.

To determine if the line of best fit is appropriate, you would generally look for the following characteristics in the residual plot:

Randomness: The residuals should appear randomly scattered around the horizontal axis. If there is a clear pattern or structure in the residuals, it suggests that the line of best fit is not capturing all the important information in the data.

Constant variance: The spread of the residuals should remain relatively constant across the range of predicted values. If the spread of the residuals systematically increases or decreases as the predicted values change, it indicates heteroscedasticity, which means the variability of the errors is not constant. This suggests that the line of best fit may not be appropriate for the data.

Zero mean: The residuals should have a mean value close to zero. If the residuals consistently deviate above or below zero, it suggests a systematic bias in the line of best fit.

It's important to note that a residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

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I'm sorry this isn't the answer, but I just want you to know that you are incredible and that I love you for you! You are special to everyone you meet, and should not change who you are. I know your life may be tough, but you are strong and can get through it!

Answer:

yes it is

Step-by-step explanation:

The period of the function is 30 seconds.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

The period of a function is the length of one complete cycle or oscillation. In this case, the function represents the height of a weight on a spring as a function of time. To determine the period, we need to identify the time it takes for the function to repeat.

Looking at the given table, we can observe that the values of t repeat after 30 seconds. From t = 0 to t = 30, the function completes one full cycle.

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The conversions for (a) Octal: 674, Hexadecimal:  DE0, for (b) Octal: 1161 Hexadecimal:  9C1. and for (c) Octal: 11140.
Hexadecimal: 930

(a) To convert from binary to octal, we group the binary digits into groups of three starting from the right and then convert each group to its octal equivalent. So, we have:

110 111 100

Converting each group to octal, we get:

6 7 4

Therefore, the octal equivalent of 110111100 is 674.

To convert from binary to hexadecimal, we group the binary digits into groups of four starting from the right and then convert each group to its hexadecimal equivalent. So, we have:

1101 1110 0

Converting each group to hexadecimal, we get:

D E 0

Therefore, the hexadecimal equivalent of 110111100 is DE0.

(b) To convert from binary to octal, we group the binary digits into groups of three starting from the right and then convert each group to its octal equivalent. So, we have:

001 001 110 001

Converting each group to octal, we get:

1 1 6 1

Therefore, the octal equivalent of 1001110001 is 1161.

To convert from binary to hexadecimal, we group the binary digits into groups of four starting from the right and then convert each group to its hexadecimal equivalent. So, we have:

1001 1100 01

Converting each group to hexadecimal, we get:

9 C 1

Therefore, the hexadecimal equivalent of 1001110001 is 9C1.

(c) To convert from binary to octal, we group the binary digits into groups of three starting from the right and then convert each group to its octal equivalent. So, we have:

001 001 001 100 0

Converting each group to octal, we get:

1 1 1 4 0

Therefore, the octal equivalent of 10010011000 is 11140.

To convert from binary to hexadecimal, we group the binary digits into groups of four starting from the right and then convert each group to its hexadecimal equivalent. So, we have:

1001 0011 0000

Converting each group to hexadecimal, we get:

9 3 0

Therefore, the hexadecimal equivalent of 10010011000 is 930.

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Answer:

Adult: $ 4

Student: $ 7

Step-by-step explanation:

Adult: x

Students: y

a) 3x + 9y = 75

b) 8x + 5y = 67

Substitution:

a) 3x = -9y + 75

x = (-9y + 75)/3

x = -3y + 25

Substitute:

b) 8(-3y+25) + 5y = 67

-24y + 209 + 5y = 67

-19y = -209 +67

y = -133/-19

y = 7

Substitute:

x = = 3(7) + 25

x = -21+25

x = 4

Answer:

I THINK I GOT IT!!! I think by 19 weeks (rounding) she will have to run 1 extra mile or 95 percent more!!!!!!!

Step-by-step explanation:Please do not blame me if its wrong i only thought about for like 1 min!