Which expression is equivalent to −4.6+(−0.4)+(−7.2) ?

−(4.6−0.4)+(−7.2)

(4.6+0.4+7.2)

−4.6−(0.4+7.2)

(4.6+0.4)+(−7.2)

Answer:

The answer is [tex]4x^3-29x^2+10x-21[/tex]

Step-by-step explanation:

In order to determine the answer, we have to know what it means (t*s)(x).

When we need to multiply two functions, where y(x) and z(x) are the functions, we can describe the process with the notation (y*z) (x). This notation means that the function y(x) is being multiplying by the function z(x).

So, in this case, we have two functions:

[tex]s(x)=x-7\\t(x)=4x^2-x+3[/tex]

Multiplying both functions (t*s) (x):

[tex](t*s)(x)=t(x)*s(x)\\(4x^2-x+3)(x-7)\\4x^3-28x^2-x^2+7x+3x-21\\4x^3-29x^2+10x-21[/tex]

Finally, the expression is:

[tex]4x^3-29x^2+10x-21[/tex]

the answer is log3x=2!

hope this helps :D. just took a test online and this was one of the questions. got it right btw.

To find the median, sort the numbers in ascending order and average the two middle values. The median of the given numbers is 29.5.

To find the median of the numbers 26, 30, 24, 32, 32, 31, 27, and 29, follow these steps:

Thus, the median of the given set of numbers is 29.5.

Final answer:

To find the height of the Statue of Liberty, we set up an equation considering the total height of the pedestal and the height difference between the statue and the pedestal. Solving the system of linear equations, we determine that the height of the Statue of Liberty itself is 46.05 meters.

Explanation:

To find how tall the Statue of Liberty is, excluding its pedestal, we can set up an equation based on the information given. Let's denote the height of the Statue of Liberty as S, and the height of the pedestal as P.

We know that the total height of the Statue of Liberty and its pedestal is 92.99 meters, and we can express that as:

S + P = 92.99

Additionally, it is given that the pedestal is 0.89 meters taller than the Statue of Liberty, so we have:

P = S + 0.89

Using substitution, we can replace P in the first equation with S + 0.89:

S + (S + 0.89) = 92.99

This simplifies to:

2S + 0.89 = 92.99

To find the height of the Statue of Liberty (S), we subtract 0.89 from both sides of the equation:

2S = 92.99 - 0.89

2S = 92.10

And then we divide both sides by 2 to solve for S:

S = ​92.10 / 2

S = 46.05

So, the height of the Statue of Liberty itself is 46.05 meters.

Answer:

7%(plzzzz brainlist thiss!!!)

Step-by-step explanation:

The answer is 16 mins

The solution of given system of equations is [tex]\boxed{(10,-1)}[/tex].

Further explanation

The system of equations is given  as follows:

[tex]\begin{aligned}x+3y&=7\\2x-4y&=24\end{aligned}[/tex]

The equations are the form of linear equation in two variables.

The general form of linear equation in two variables is [tex]ax+by+c=0[/tex] where [tex]a,b,c[/tex]are real numbers.

Here, the system of equations is as follows:

[tex]x+3y=7[/tex]      .....(1)

[tex]2x-4y=24[/tex]  ......(2)

Now, we can rewrite the equation (1) as follows:

[tex]x=7-3y[/tex]  

Substitute the value of [tex]x=7-3y[/tex] in equation (2) as follows:

[tex]2(7-3y)-4y=24[/tex]  

Solve the above expression to find the value of [tex]y[/tex].

[tex]\begin{aligned}14-6y-4y&=24\\14-10y&=24\\-10y&=24-14\\-10y&=10\\y&=-1\end{aligned}[/tex]  

Therefore, the value of [tex]y[/tex] is [tex]-1[/tex].

Now, Substitute the value of [tex]y=-1[/tex] in equation (1) to get the value of [tex]x[/tex].

[tex]\begin{aligned}x+(3\times(-1))&=7\\x-3&=7\\x&=7+3\\x&=10\end{aligned}[/tex]  

Therefore, the value of [tex]x[/tex] is [tex]10[/tex].

The solution of given system of equations is [tex](10,-1)[/tex].

Option (a)

In option (a) it is given that the solution is [tex](2,-6)[/tex].

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (a) is incorrect.

Option (b)

In option (b) it is given that the solution is [tex](10,-1)[/tex].

As per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (b) is correct.

Option (c)

In option (c) it is given that the solution is [tex](-2,8)[/tex].

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (c) is incorrect.

Option (d)

In option (d) it is given that there are infinte solution.

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex] which is a unique solution.

Therefore, option (d) is incorrect.

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3. Problem on the general form of the equation of the circle https://brainly.com/question/1506955

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations in two variables

Keywords: Linear equations in one variable, linear equations in two variables, function, sets, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open interval.

Final answer:

Dots sold 192 T-shirts and 64 shorts in April. We found this by setting up a system of equations with the given information and solving for the number of T-shirts (T) and shorts (S) sold.

Explanation:

To solve the problem of how many T-shirts and shorts Dots sold, we use a system of equations. Let's denote the number of T-shirts as T and the number of shorts as S. Given that T-shirts cost $2 each and shorts cost $3 each, and the total sales were $576, we can write our equations as follows:

2T + 3S = $576

We are also told that the store sold 3 times as many T-shirts as shorts, which gives us the second equation:

T = 3S

Substituting the second equation into the first, we get:

2(3S) + 3S = $576

6S + 3S = $576

9S = $576

Now, dividing both sides by 9 to isolate S, we get:

S = $576 / 9

S = 64

Since T is three times S:

T = 3 × 64

T = 192

Therefore, Dots sold 192 T-shirts and 64 shorts in April.

Answer:

TRUE.

Step-by-step explanation:

It's in an assignment I'm doing.

Also, THERE ARE WAYS TO FIND THE AREA UNDER A NORMAL CURVE is also TRUE

The expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i) which correct option(B).

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

(B) (9 + 4i) + (–1 – 7i)

⇒ (9 + 4i) + (–1 – 7i)

⇒ 9 + 4i –1 – 7i

Rearrange the terms like wise and apply arithmetic operations

⇒ 9 - 1 + 4i - 7i

⇒ 8 – 3i

Hence, the expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i).

Learn more about complex number here:

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Answer: the first part is option B

the second part is option C

Step-by-step explanation:

The amount of Honey produced by 1000 hives is the multiplication of 1000 to 85 thus 85000 pounds will be produced.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

As per the given question,

Larson's Honey Farm usually produces 85 pounds of honey per year.

If one family is producing 85 pounds of honey per year then,

1000 hives will produce ⇒ 85 × 1000 = 85000 pounds.

Hence "The amount of Honey produced by 1000 hives is the multiplication of 1000 to 85 thus 85000 pounds will be produced".

For more information about multiplication,

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The ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \), where \( r_A \) and \( r_B \)[/tex] are the radii of disks A and B, respectively.

Linear acceleration ( a ) of a point on the rim of a rotating disk is given by [tex]\( a = r \alpha \)[/tex], where ( r ) is the radius of the disk and [tex]\( \alpha \)[/tex] is the angular acceleration.

Since both disks are rotating with constant angular acceleration, the linear acceleration of a point on the rim of each disk is directly proportional to the radius of the disk.

Therefore, to find the ratio of the linear accelerations, we only need to compare the radii of the two disks.

Let [tex]\( r_A \) and \( r_B \)[/tex] be the radii of disks A and B, respectively.

The ratio of linear accelerations is given by [tex]\( \frac{a_A}{a_B} = \frac{r_A \alpha}{r_B \alpha} \)[/tex].

Notice that the angular accelerations cancel out since both disks have the same angular acceleration.

Thus, the ratio simplifies to [tex]\( \frac{r_A}{r_B} \)[/tex].

This ratio represents how many times larger the radius of disk A is compared to the radius of disk B.

For example, if [tex]\( r_A = 2r_B \)[/tex], then the linear acceleration of a point on the rim of disk A is twice that of disk B.

Therefore, the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \)[/tex].

Complete Question:

For the two disks in problem 3, what is the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B? Please show detailed calculation.

The 95% confidence interval for the mean number of hours Americans spend relaxing or engaging in enjoyable activities post-work is between 1.38 and 1.92 hours per day, which signifies the statistical range where the true mean likely falls. This statistic is crucial for understanding leisure's role in health and well-being.

The 95% confidence interval given in the General Social Survey of (1.38, 1.92) hours for the mean number of hours spent relaxing or pursuing activities after an average workday suggests that we can be 95% confident that the actual mean number of hours all Americans have for such activities falls within this range. This is an important statistic considering that leisure and recovery are essential for well-being, mental health, and stress prevention, as pointed out by researchers like Sonnentag & Zijlstra and Juliet Schor. Juliet Schor also highlighted that Americans have significantly declined in leisure time. The comparison of leisure time across different countries, such as Americans working more hours compared to Europeans, adds context to the importance of this interval in reflecting Americans' potential lack of leisure that could impact health.

The derivative of y = (x³ + 2)²(x⁴ + 4)⁴ using logarithmic differentiation is;

y' =  {[6x²In(x³ + 2)]/(x³ + 2)} + {[16x³In(x⁴ + 4)⁴]/(x⁴ + 4)} × [(x³ + 2)²(x⁴ + 4)⁴]

We are given the function;

y = (x³ + 2)²(x⁴ + 4)⁴

We want to find the derivative using logarithmic differentiation;

Step 1; Take the natural log of both sides;

In y = In[(x³ + 2)²(x⁴ + 4)⁴]

Step 2;

Using log of a product property on this, we have;

In y = In(x³ + 2)² + In(x⁴ + 4)⁴

Step 3; We will now differentiate both sides with chain rule to get;.

y'/y = [6x²In(x³ + 2)]/(x³ + 2) + [16x³In(x⁴ + 4)⁴]/(x⁴ + 4)

Step 4; Using multiplication property of equality, multiply both sides by y to get;

y' =  {[6x²In(x³ + 2)]/(x³ + 2) + [16x³In(x⁴ + 4)⁴]/(x⁴ + 4)} × y

Step 5; Plug in the value of y = (x³ + 2)²(x⁴ + 4)⁴ to get;

y' =  {[6x²In(x³ + 2)]/(x³ + 2)} + {[16x³In(x⁴ + 4)⁴]/(x⁴ + 4)} × [(x³ + 2)²(x⁴ + 4)⁴]

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Final answer:

To find the dimensions and volume of a square-based box with the greatest volume under the given conditions, we need to maximize the volume. The dimensions of the box should be 54 inches by 54 inches by 54 inches, and the volume is 157,464 cubic inches.

Explanation:

The airline policy states that the sum of the length, width, and height of the baggage must not exceed 162 inches. To find the dimensions and volume of a square-based box with the greatest volume under these conditions, we need to maximize the volume of the box.

Let's assume the length, width, and height of the box are all equal to a. Therefore, the sum of the three dimensions is 3a.

According to the policy, 3a must not exceed 162 inches, so we have:

3a ≤ 162

a ≤ 54

Since the length, width, and height of a square-based box are all equal, a is the side length of the square base. Therefore, the dimensions of the box should be 54 inches by 54 inches by 54 inches, and the volume can be calculated as:

Volume = a³ = 54³ = 157,464 cubic inches.

Answer:

23.06

Step-by-step explanation: