The linear transformation T is defined as:
[tex]\( T(x) = \left[\begin{array}{c}-6x_{1}+x_{2}+180 \\ 24x_{1}-4x_{2}-720\end{array}\right] \)[/tex]
What is the matrix of the linear transformation T?The linear transformation T is defined as T(x) = Ax+b, where A is a matrix and b is a vector. In this case, we have
[tex]\( A=\left[\begin{array}{cc}-6 & 1 \\ 24 & -4\end{array}\right] \)[/tex] and [tex]\( b=\left[\begin{array}{c}180 \\ -720\end{array}\right] \).[/tex]
So, for any vector [tex]\( x=\left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right] \)[/tex] , we have:
[tex]\[ T(x) = \left[\begin{array}{cc}-6 & 1 \\ 24 & -4\end{array}\right]\left[\begin{array}{c}x_{1} \\ x_{2}\end{array}\right] + \left[\begin{array}{c}180 \\ -720\end{array}\right] \][/tex]
[tex]\[ T(x) = \left[\begin{array}{c}-6x_{1}+x_{2} \\ 24x_{1}-4x_{2}\end{array}\right] + \left[\begin{array}{c}180 \\ -720\end{array}\right] \][/tex]
[tex]\[ T(x) = \left[\begin{array}{c}-6x_{1}+x_{2}+180 \\ 24x_{1}-4x_{2}-720\end{array}\right] \][/tex]
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. The table shows the number of people, n, who went to see musical
The average rate of change for the week is calculated by subtracting the first day's attendance (1,534) from the last day's attendance (2,394) and then dividing by the number of days (7).
What is Number?Number is an abstract concept used to describe a quantity or amount of something. It is used to measure, count, and label objects, people, places, and other things. Numbers can be used to describe size, shape, location, and many other concepts. They are also used to represent data, money, and other mathematical operations. Numbers are the cornerstone of mathematics, and they are used in a variety of ways in everyday life.
This yields an average rate of change of +77.71 people per day.
This average rate of change is only a good measure for how the number of people changed throughout the week if the number of people changed in a consistent manner. If the attendance was relatively stable from day to day, then the average rate of change would accurately reflect the number of people who attended. However, if the attendance changed drastically from day to day, the average rate of change would not accurately reflect the attendance for the entire week.
Complete questions as follows-
The table shows the number of people, n, who went to see musical , on the duh day of April. What is the average rate of 'change for the number of people from day to day 7? 1,534 2,324 2,418 b. Is the average rate of change a good measure for how the number of people changed throughout the week? Explain your reasoning; ''. ` 2,281 2,350 2,394 1,720 weight (02) 369 Algebra 1".
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Let \( T_{1} \) and \( T_{2} \) be linear transformations given by \[ \begin{array}{l} T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2}
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
Let \(T_{1}\) and \(T_{2}\) be linear transformations given by
\[\begin{array}{l}
T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2} \\ 5 x_{1}-2 x_{2}\end{array}\right] \\
T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 8 x_{1}+4 x_{2} \\ 5 x_{1}+2 x_{2}\end{array}\right]
\end{array}\]
A linear transformation is a function that takes two input values and returns two output values in a way that preserves the linear structure of the data. It is described by a matrix that determines the output values from the input values. In the case of \(T_{1}\) and \(T_{2}\), the matrix is
\[
M=\left[\begin{array}{cc}
3 & 6 \\
5 & -2
\end{array}\right]
\]
and
\[
M=\left[\begin{array}{cc}
8 & 4 \\
5 & 2
\end{array}\right]
\]
respectively. The two linear transformations can be combined using matrix multiplication, which yields the transformation
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=M_{1} M_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)
\]
where
\[
M_{1}M_{2}=\left[\begin{array}{cc}
43 & 2 \\
-10 & 4
\end{array}\right].
\]
Therefore, the result of applying both transformations to a given input vector is given by
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
This is an example of a linear transformation, where two transformations are combined to produce a single result.
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From the top of a cliff, the angle of depression of a boat on the sea is 60°. If the top of the cliff is 25m above the sea level, calculate the horizontal distance from the bottom of the cliff to the boat.
If h(w)=36w^(5)+36w^(4)+7w^(2)+12w+39, use synthetic division to find h(-1) Submit
Using synthetic division, we can find that h(-1) = -5.
To find h(-1) using synthetic division, we can use the following steps:
Write the coefficients of the polynomial in descending order of the exponents: 36, 36, 0, 7, 12, 39
Write the value of -1 to the left of the coefficients: -1 | 36 36 0 7 12 39
Bring down the first coefficient: -1 | 36 36 0 7 12 39
36
Multiply the first coefficient by -1 and write the result under the second coefficient: -1 | 36 36 0 7 12 39
36 -36
Add the second coefficient and the result: -1 | 36 36 0 7 12 39
36 0
Repeat steps 4 and 5 for the remaining coefficients: -1 | 36 36 0 7 12 39
36 0 0 -7 -5
The last number in the bottom row is the remainder, which is the value of h(-1): h(-1) = -5
Therefore, using synthetic division, we can find that h(-1) = -5.
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Using the p-value given, are the results significant at a 1% level? p-value = 0. 802
No, the result is not significant at 1 percent level for the p-value of 0.802.
Results are significant at a certain level,
Compare the p-value to the significance level (known as alpha).
The significance level is typically set at 0.05 or 0.01.
Here, the p-value is 0.802, which is much larger than 0.01.
This implies here we cannot reject the null hypothesis at a 1% significance level.
Or , the result is not statistically significant at a 1% level.
If the significance level was 5% that is equal to 0.05.
The result would not be significant at 5% level either.
If the significance level was 10% which is equal to 0.10.
Then the result would be significant as the p-value is less than 0.10.
Therefore, for the given p-value 0.802 result is not significant at 1%.
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2 1/2 = 5n
I need help please
Answer:
1/2
Step-by-step explanation:
because 5 times 1/2 and you get 2 1/2
From a full container of dry cells, 325 dry cells are placed in the stockroom, 45 dry cells are placed on the shelf in the showroom, and 18, 25 , 30,24 , and 6 dry cells are sold to customers. How many dry cells are taken from the full container?
The amount of dry cells that are taken from the full container is 473.
To find the total number of dry cells taken from the full container, we need to add up the number of dry cells placed in the stockroom, on the shelf, and sold to customers. We can use the following equation:
Total dry cells taken = Dry cells in stockroom + Dry cells on shelf + Dry cells sold to customers
Plugging in the given values, we get:
Total dry cells taken = 325 + 45 + 18 + 25 + 30 + 24 + 6
Using the order of operations, we can simplify the equation:
Total dry cells taken = 325 + 45 + 18 + 25 + 30 + 24 + 6
Total dry cells taken = 370 + 18 + 25 + 30 + 24 + 6
Total dry cells taken = 388 + 25 + 30 + 24 + 6
Total dry cells taken = 413 + 30 + 24 + 6
Total dry cells taken = 443 + 24 + 6
Total dry cells taken = 467 + 6
Total dry cells taken = 473
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The amount of orange juice that can be obtained from a single orange is normally distributed. A manufacturing company selects an srs of size n
The shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population is approximately Normal
If the amount of orange juice that can be obtained from a single orange is Normally distributed, then the distribution of the sample mean of orange juice obtained from a sample of size 5 from this population will also be Normally distributed.
The mean of the sample mean distribution will be equal to the population mean, which is the mean amount of orange juice that can be obtained from a single orange.
The standard deviation of the sample mean distribution, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size.
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The given question is incomplete, the complete question is:
The amount of orange juice that can be obtained from a single orange is Normally distributed. A manufacturing company selects an SRS of size n = 5 from the population of all oranges in their inventory and calculates the sample mean amount of orange juice that is obtained. What is the shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population?
Evaluate det (A) by a cofactor expansion along a row or column of your choice. A=[[-6,0,2],[2,4,1],[-1,0,3]]
The determinant of matrix A is -6.
A. To evaluate det(A) by a cofactor expansion along a row or column of your choice, we can choose any row or column and multiply each element by its corresponding minor and sign.
For example, let's choose the first row:
det(A) = (-6)(4*3-0*1) + (0)(2*3-(-1)*2) + (2)(2*0-(-1)*4)
det(A) = (-6)(12) + (0)(6) + (2)(4)
det(A) = (-72) + (0) + (8)
det(A) = -64
Therefore, the determinant of matrix A is -64.
B. Alternatively, we could have chosen any other row or column and the result would have been the same. For example, if we chose the third column:
det(A) = (2)(4*0-2*0) + (-1)(-6*3-2*0) + (3)(-6*0-2*4)
det(A) = (2)(0) + (-1)(-18) + (3)(-8)
det(A) = (0) + (18) + (-24)
det(A) = -6
Therefore, the determinant of matrix A is -6.
Note that the determinant of a matrix is a scalar value, and it is the same regardless of which row or column we choose to expand along.
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your family is driving on the highway. The number of miles y you travel in x minutes is approximated by the equation y=1.1x approximately how far do you travel in 80 minutes?
Answer:88 miles
Step-by-step explanation:
1.1x80+88
A biassed coin is tossed a total of n+ m times and shows Heads with probability p on each toss. Let S, be the number of heads in the first n coin tosses, and Tm be the number of heads in the last m coin tosses. You may assume that m (d) What is the distribution of Sn +Tm? Prove this.
The distribution of Sn + Tm is a binomial distribution with parameters (n+m, p).
This can be proved using the fact that the sum of independent binomial random variables follows a binomial distribution with the sum of the number of trials and the same probability of success.
Let X ~ Binomial(n, p) and Y ~ Binomial(m, p) be independent random variables representing the number of heads in the first n coin tosses and the last m coin tosses, respectively.
Then, the sum of X and Y, Z = X + Y, follows a binomial distribution with parameters (n+m, p).
The probability mass function of Z can be written as:
P(Z = k) = P(X + Y = k) = ∑ P(X = i) * P(Y = k-i) for i = 0 to k
Since X and Y are independent, we can write:
P(Z = k) = ∑ P(X = i) * P(Y = k-i) = ∑ (n choose i) * p^i * (1-p)^(n-i) * (m choose k-i) * p^(k-i) * (1-p)^(m-k+i)
Simplifying the above equation, we get:
P(Z = k) = (n+m choose k) * p^k * (1-p)^(n+m-k)
Therefore, Z ~ Binomial(n+m, p).
As a result, the distribution of Sn + Tm has the parameters (n+m, p) of a binomial distribution.
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If \( f(x)=5 x, g(x)=-2 x+1 \), and \( h(x)=x^{2}+6 x+8 \), find \( g[h(2)] \). Question 4 If \( f(x)=5 x, g(x)=-2 x+1 \), and \( h(x)=x^{2}+6 x+8 \), find \( h[f(9)] \).
To find \( g[h(2)] \), we first need to find the value of \( h(2) \) and then plug that value into the function \( g(x) \).
Step 1: Find \( h(2) \)
We plug in the value of 2 for x in the function \( h(x)=x^{2}+6 x+8 \) to get:
\( h(2)=(2)^{2}+6 (2)+8 \)
Simplifying, we get:
\( h(2)=4+12+8 \)
\( h(2)=24 \)
Step 2: Find \( g[h(2)] \)
Now we plug in the value of 24 for x in the function \( g(x)=-2 x+1 \) to get:
\( g[h(2)]=-2 (24)+1 \)
Simplifying, we get:
\( g[h(2)]=-48+1 \)
\( g[h(2)]=-47 \)
Therefore, \( g[h(2)]=-47 \).
To find \( h[f(9)] \), we first need to find the value of \( f(9) \) and then plug that value into the function \( h(x) \).
Step 1: Find \( f(9) \)
We plug in the value of 9 for x in the function \( f(x)=5 x \) to get:
\( f(9)=5 (9) \)
Simplifying, we get:
\( f(9)=45 \)
Step 2: Find \( h[f(9)] \)
Now we plug in the value of 45 for x in the function \( h(x)=x^{2}+6 x+8 \) to get:
\( h[f(9)]=(45)^{2}+6 (45)+8 \)
Simplifying, we get:
\( h[f(9)]=2025+270+8 \)
\( h[f(9)]=2303 \)
Therefore, \( h[f(9)]=2303 \).
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divislon or synthetic division to determine the quotient and remainder. (x^(2)+4x-20)-:(x-4)
The final answer in quotient and remainder form is:
(x^(2)+4x-20)÷(x-4) = x+8 with a remainder of 12
To determine the quotient and remainder of the given expression, we can use synthetic division. Synthetic division is a method of dividing a polynomial by a linear factor in the form of x-a. In this case, the linear factor is x-4, so a=4.
Here are the steps for synthetic division:
Write the coefficients of the dividend, x^(2)+4x-20, in a row: 1 4 -20
Write the value of a, 4, to the left of the coefficients.
Bring down the first coefficient, 1, to the bottom row.
Multiply the value in the bottom row by a, 4, and write the result, 4, in the second column of the top row.
Add the numbers in the second column of the top row, 4+4, and write the result, 8, in the bottom row.
Multiply the value in the bottom row by a, 4, and write the result, 32, in the third column of the top row.
Add the numbers in the third column of the top row, -20+32, and write the result, 12, in the bottom row.
The bottom row now contains the coefficients of the quotient, 1 and 8, and the remainder, 12. So the quotient is x+8 and the remainder is 12.
The final answer in synthetic division form is:
4 | 1 4 -20
| 4 32
-------------
| 1 8 12
The final answer in quotient and remainder form is:
(x^(2)+4x-20)÷(x-4) = x+8 with a remainder of 12
So the quotient is x+8 and the remainder is 12.
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Write the vector in the form \( \langle a, b\rangle \). The vector is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
The vector in the form \( \langle a, b\rangle \) is simply the given vector with the values of a and b identified and simplified as necessary.
To write the vector in the form \( \langle a, b\rangle \), we need to identify the values of a and b from the given vector. The value of a corresponds to the x-component of the vector, and the value of b corresponds to the y-component of the vector.
If the given vector is \( \langle 3, -4\rangle \), then the value of a is 3 and the value of b is -4.
If the given vector is \( \langle \frac{5}{2}, \sqrt{3}\rangle \), then the value of a is \(\frac{5}{2}\) and the value of b is \(\sqrt{3}\).
If the given vector is \( \langle -2\sqrt{2}, 7\sqrt{3}\rangle \), then the value of a is \(-2\sqrt{2}\) and the value of b is \(7\sqrt{3}\).
In all of these cases, the values of a and b are either integers or fractions, and any radicals are simplified as much as possible.
So, the vector in the form \( \langle a, b\rangle \) is simply the given vector with the values of a and b identified and simplified as necessary.
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slope=-1 y-intercept=8
Answer: y = x + 8
Step-by-step explanation:
2 Given f (x)=x² - 4x, = X (a) Find f (x+h) and simplify. f(x+h)-f(x) (b) Find h and simplify. Part: 0/2 Part 1 of 2 (a) f(x+h)
For part (a), the answer is f(x+h) = x² + 2xh + h² - 4x - 4h. for par (b) h = -x ± sqrt(x² + 6), the value of h depends on the value of x
(a) To find f(x+h), we substitute x+h for x in the expression for f(x):
f(x+h) = (x+h)² - 4(x+h)
Expanding the square and simplifying, we get:
f(x+h) = x² + 2xh + h² - 4x - 4h
(b) To find h, we start with the expression for f(x+h) that we found in part (a):
f(x+h) = x² + 2xh + h² - 4x - 4h
We want to simplify this expression so that we can identify h. To do this, we start by subtracting f(x) from both sides:
f(x+h) - f(x) = (x² + 2xh + h² - 4x - 4h) - (x² - 4x)
Simplifying, we get:
f(x+h) - f(x) = 2xh + h² - 4h
Now we can identify h by setting this expression equal to some value and solving for h. For example, if we set f(x+h) - f(x) equal to 5, we get:
2xh + h² - 4h = 5
Simplifying and rearranging, we get a quadratic equation in h:
h² + 2xh - 4h - 5 = 0
We can solve this using the quadratic formula:
h = (-2x ± √(4x² + 24))/2
Simplifying, we get:
h = -x ± √(x² + 6)
So the value of h depends on the value of x
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Question
What is the value of p in this proportion?
6/p=15/3.5
Enter your answer as a decimal in the box.
Answer:
1.4
Step-by-step explanation:
If 6/p =15/3.5
You can cross multiply the equation
6x3.5 =15P
21=15P
Divide both sides by 15
21/15 = P
1.4 =P
HURRY PLEASE
Question 1
Which of the following describes the domain of the piecewise function g of x is equal to the piecewise function of the quantity x squared plus 4 times x end quantity over the quantity x squared plus 2 times x minus 8 end quantity for x is less than 4 and the function log in base 3 of the quantity x plus 5 end quantity for x is greater than or equal to 4 question mark
A.(–∞, 2) ∪ (2, 4) ∪ (4, ∞)
B.(–∞, –4) ∪ (–4, 2) ∪ (2, ∞)
C.(–∞, 2) ∪ (2, ∞)
D.(–∞, ∞)
The domain of the piecewise function g of x is (–∞, 2) ∪ (2, ∞)
What are Functions?
A function is a mathematical rule that takes an input value and produces a unique output value. It can be thought of as a machine that transforms input values into output values.
The domain of the piecewise function g of x is (–∞, 2) ∪ (2, ∞), since the expression x squared plus 2 times x minus 8 is equal to zero when x is equal to negative 4 and 2, but the function is undefined at x equals negative 4 and x equals negative 5 due to the logarithmic function.
Therefore, the domain is all real numbers except for x equals negative 4 and x equals negative 5.
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Let sine of theta equals the quantity 2 times radical 3 end quantity over 5 and pi over 2 is less than theta is less than pi period
Part A: Determine the exact value of cos 2θ.
Part B: Determine the exact value of sine of the quantity theta over 2 end quantity period
The exact value οf cοs(2θ) is 27/25.
The exact value οf sin(θ/2) is -√[(5 + √13) / 10].
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles, and the trigοnοmetric functiοns that describe thοse relatiοnships.
Given: sin(θ) = (2√3) / 5, and π/2 < θ < π.
Part A:
cοs(2θ) = 2cοs²(θ) - 1
We can find cοs(θ) using the Pythagοrean identity:
cοs²(θ) + sin²(θ) = 1
cοs²(θ) = 1 - sin²(θ)
cοs(θ) = ±√(1 - sin²(θ))
Since π/2 < θ < π, sin(θ) is pοsitive and cοs(θ) is negative in the secοnd quadrant. Therefοre, we have:
cοs(θ) = -√(1 - (2√3/5)²) = -√(1 - 12/25) = -√13/5
Substituting intο the fοrmula fοr cοs(2θ), we get:
cοs(2θ) = 2cοs²(θ) - 1 = 2(-√13/5)² - 1 = 52/25 - 1 = 27/25
Therefοre, the exact value οf cοs(2θ) is 27/25.
Part B:
We can use the half-angle fοrmula fοr sine tο find sin(θ/2):
sin(θ/2) = ±√[(1 - cοs(θ)) / 2]
Since π/2 < θ < π, sin(θ/2) is negative in the secοnd quadrant. Therefοre, we have:
sin(θ/2) = -√[(1 - cοs(θ)) / 2] = -√[(1 - (-√13/5)) / 2] = -√[(5 + √13) / 10]
Therefοre, the exact value οf sin(θ/2) is -√[(5 + √13) / 10].
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Ms. Volkerson bought 3 yards of
fabric. She used 1 yards to make an
apron. Which is the best estimate of
how many yards of fabric Ms. Volkerson
has now?
Find the missing number to create a perfect-square binomial
___ y2-36y+81
Answer:
To create a perfect-square binomial of the form (y - k)^2, we need to find the value of k such that:
the first term of the binomial is y^2 (which is already the case)
the second term of the binomial is -2ky (which corresponds to -36y in the given expression)
the third term of the binomial is k^2 (which corresponds to 81 in the given expression)
To find k, we can use the formula:
k = (1/2)*(-b/a)
where a is the coefficient of y^2, b is the coefficient of y, and we are looking for the value of k that makes the expression a perfect square.
In this case, a = 1 and b = -36, so:
k = (1/2)(-b/a) = (1/2)(-(-36)/1) = 18
Therefore, the missing number to create a perfect-square binomial is 18:
(y - 18)^2 = y^2 - 36y + 324
PLEASE HELP :((( show BOTH distribution and FOIL to find the product of (3x - 2)and(2z + 6).
According to the given information product of (3x - 2) and (2z + 6) is 6xz + 18x - 4z - 12.
What is expression ?In mathematics, expressions are also combinations of constants, variables, operators, and function calls that represent mathematical operations or relationships.
According to given conditions:Let's start with distributing the first term of the first expression to both terms of the second expression, then distributing the second term of the first expression to both terms of the second expression:
(3x - 2)(2z + 6)
= 3x(2z + 6) - 2(2z + 6)
= 6xz + 18x - 4z - 12
Now, let's use the FOIL method to find the same product:
(3x - 2)(2z + 6)
= 3x(2z) + 3x(6) - 2(2z) - 2(6)
= 6xz + 18x - 4z - 12
As you can see, both methods result in the same product: 6xz + 18x - 4z - 12.
Therefore, according to the given information product of (3x - 2) and (2z + 6) is 6xz + 18x - 4z - 12.
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Which graph is correct?
The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Inequalities are used for the non equal comparison of numbers and variables.
Given the inequalities:
y ≥ (1/2)x - 1 (1)
and
x - y > 1 (2)
The graph of the inequality is attached. Shannon's graph is correct.
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16. Write the product as a sum: 7 cos(6x)cos (7x) 17. Write the sum as a product: sin (2x) -sin (7x)
16. The expression of the product as a sum: 7 cos(6x)cos(7x) = 7/2 * (cos(13x) + cos(x))
17. The expression of the sum as a product: sin(2x) - sin(7x) = -2 cos(9x/2) sin(5x/2)
The product as a sum can be written using the formula for the product of two cosines:
cos a * cos b = 1/2 * (cos(a + b) + cos(a - b))
Using this formula, we can write the product 7 cos(6x)cos(7x) as a sum:
7 cos(6x)cos(7x) = 7/2 * (cos(6x + 7x) + cos(6x - 7x))
= 7/2 * (cos(13x) + cos(-x))
= 7/2 * (cos(13x) + cos(x))
The sum as a product can be written using the formula for the difference of two sines:
sin a - sin b = 2 cos((a + b)/2) sin((a - b)/2)
Using this formula, we can write the sum sin(2x) - sin(7x) as a product:
sin(2x) - sin(7x) = 2 cos((2x + 7x)/2) sin((2x - 7x)/2)
= 2 cos(9x/2) sin(-5x/2)
= 2 cos(9x/2) (-sin(5x/2))
= -2 cos(9x/2) sin(5x/2)
So the final answers are:
7 cos(6x)cos(7x) = 7/2 * (cos(13x) + cos(x))
sin(2x) - sin(7x) = -2 cos(9x/2) sin(5x/2)
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prisim A is similar to prisim B. The volume prisim a is 2080 cm3. what is the volume of prisim B?
Answer:
2080cm^3
Step-by-step explanation:
245% of what number is 49
Answer: 20
Step-by-step explanation:
49 ÷ 245 %
convert the percentage to decimals
49 ÷ 2.455
calculate the product or quotient
20
Please give me brainliest
Answer:20
Step-by-step explanation:
Let's denote the number we are looking for as "x".
We can set up the equation:
245% of x = 49
We can convert 245% to the decimal form by dividing by 100:
2.45 * x = 49
To solve for x, we can divide both sides of the equation by 2.45:
x = 49 / 2.45
x = 20
Therefore, 245% of 20 is equal to 49.
The diameter of a circle is 13 m. Find its area to the nearest tenth.
Answer:
132.7cm²
Step-by-step explanation:
area of circle = πr²
6.5² * π
=132.7cm²
For
each of the following, find the formula for an exponential function
that passes through the two points given.
a. (-1, 2/3) and (2,18)
f(x) =
b. (-1,7) and (2,4)
g(x) =
(If needed, round to 3 decim
The values of x are 0.732 and -2.732.
Given function:f(x) = g(x)We need to determine the value of x.For, f(x) = g(x), we have the following equation:f(x) = x^2 + 2x + 1 = 2x + 3g(x) = 2x + 3To solve for x, we can substitute the value of g(x) in the first equation:x^2 + 2x + 1 = g(x)Substituting g(x) = 2x + 3 in the above equation:x^2 + 2x + 1 = 2x + 3x^2 + 2x - 2 = 0x^2 + 2x - 2 = 0Applying the quadratic formula, we get:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Where, a = 1, b = 2, and c = -2Substituting the values in the formula, we get:$$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)}$$$$x = \frac{-2 \pm \sqrt{12}}{2}$$$$x = -1 \pm \sqrt{3}$$Therefore, the value of x is x = -1 + √3 or x = -1 - √3.To round off the answer to 3 decimal places, we get:x = -1 + 1.732 = 0.732 or x = -1 - 1.732 = -2.732Hence, the values of x are 0.732 and -2.732.
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the sum of the two numbers is 90. The larger the number is 14 more than 3 times the smaller the number. Find the numbers
x+y=_; x=_+_y
Answer:
Smaller number = 19
Larger number = 71
x + y = 90
x = 14 + 3y
Step-by-step explanation:
Let y represent the smaller number, and then represent the larger number as x, in terms of y:
Smaller number = y
Larger number = x = 3y + 14
Since the sum of the two numbers is 90, form an equation by adding them together in this notation:
y + 3y + 14 = 90
Simplify the equation:
4y + 14 = 90
4y = 76
y = 19
Therefore the smaller number is 19. Now substitute into the expression for the larger number to find its value:
x = 3(19) + 14 = 71
Now verify the two values sum to 90 like we expect:
19 + 71 = 90
Now we can use what we know to complete the equations, if x = 71:
x + y = 90 (we know they sum to 90)
x = 14 + 3y (as respresented above - multiplying by 3 and adding 14)
For each value of x, determine whether it is a solution to 13 < 2x+3.
Is it a solution?
Since, 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.
To determine whether a value of x is a solution to the inequality 13 < 2x+3, we need to substitute the value of x into the inequality and see if it is true or false.
Let's try x = 5. Then: 13 < 2x+3
13 < 2(5)+3
13 < 10+3
13 < 13
This is not true, since 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.
Note that if we had found 13 < 13 instead, then we would have concluded that x = 5 is not a solution to the inequality. But since the inequality is strict (i.e., "less than"), we need to have a strict inequality when we substitute the value of x to determine whether it is a solution.
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