Rounding the given value to the nearest tenth would be 1020.5
How to round to the nearest tenthThe tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .
Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.
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A wooden block in the shape of a rectangular pyramid is shown below:
A shaded right rectangular pyramid is shown.
If a cross section of the block is cut in a plane parallel to the base of the pyramid, which of the following shapes describes the cross section? (5 points)
Triangle
Rectangle
Trapezoid
Hexagon
Answer:
Triangle????????????????? ¿
What does 13 round to the nearest thousandth
Your total monthly bill (T
) from the Electric and Gas Company depends on how much electricity and how much gas you use each month. For every kilowatt hour of electricity (k
) you use, you are charged $0.25
and for each therm (t
) of gas used you are charged $0.97
.
Which of the following equations represents the relationship between electricity and gas used and your bill?
The equation representing the relationship between Electricity and Gas used, and your Bill is:
T = 0.25 * k + 0.97 * t
Step-by-step explanation:
Make a plan:
We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).
T = 0.25 * k + 0.97 * t
Solve the problem:
1 - Write the Equation for the cost of Electricity:
0.25 * k
2 - Write the Equation for the Cost of Gas:
0.97 * t
3 - Combine the Equations to Represent the total Monthly Bill (T):
T = 0.25 * k + 0.97 * t
Draw the Conclusion:Hence, The equation representing the relationship between Electricity and Gas used, and your Bill is:
T = 0.25 * k + 0.97 * t
I hope that helps!
A rectangle Is removed from a right triangle to create the shaded region shown below.if
Answer:
[tex]9\frac{1}{2} cm^2[/tex]
Step-by-step explanation:
The area of the shaded region = area of triangle - area of the rectangle
Base, b of the triangle = 3 + 4 = 7 cm
Ar of triangle = base*height/2
= 7*5/2
= 35/2
[tex]=17\frac{1}{2} cm^2[/tex]
ar of rectangle = length *breadth
= 4*2
= 8 cm²
The area of the shaded region = area of triangle - area of the rectangle
[tex]=17\frac{1}{2} - 8\\\\=9\frac{1}{2} cm^2[/tex]
Answer:
16.5 cm²
Step-by-step explanation:
The shaded area is the area of the triangle minus the area of the rectangle.
A = bh/2 - LW
For the triangle,
b = 3 cm + 4 cm = 7 cm
h = 2 cm + 5 cm = 7 cm
For the rectangle,
L = 4 cm
W = 2 cm
A = bh/2 - LW
A = (7 cm)(7 cm)/2 - (4 cm)(2 cm)
A = 24.5 cm² - 8 cm²
A = 16.5 cm²
Need help please help if you can with answers
a. The probability of spending less than 10 minutes is approximately 0.6255.
b. The probability of spending longer than 5 minutes is 0.9741.
c. The probability of spending between 8 and 15 minutes is 0.7181.
How to calculate the probability(a) We'll use the z-score formula:
z = (x - μ) / σ
Plugging in the values:
z = (10 - 9.3) / 2.2 ≈ 0.3182
Now, we'll look up the cumulative probability corresponding to the z-score of 0.3182 in the standard normal distribution table or use a calculator. The cumulative probability is approximately 0.6255.
(b) To find the probability of spending longer than 5 minutes, we'll again use the z-score formula:
z = (x - μ) / σ
z = (5 - 9.3) / 2.2 ≈ -1.9545
Therefore, the probability of spending longer than 5 minutes is approximately 1 - 0.0259
= 0.9741.
(c) For 8 minutes:
z1 = (8 - 9.3) / 2.2 ≈ -0.5909
For 15 minutes:
z2 = (15 - 9.3) / 2.2 ≈ 2.5909
Next, we find the cumulative probabilities for these z-scores using a standard normal distribution table or a calculator. The cumulative probability for z1 ≈ 0.2776, and for z2 ≈ 0.9957.
Finally, we subtract the cumulative probability for 8 minutes from the cumulative probability for 15 minutes to get the probability between these two values:
0.9957 - 0.2776
≈ 0.7181
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I need help figuring out this question. Please help
The area of the figure WXYZ which can be calculated as the sum of the area of the composite triangles ΔXYZ and ΔXWZ is 12 square units
What are composite figures?Composite figures are figures comprising of two or more regular figures.
The slope of the side WZ = 2/5
The slope of YZ = -2/1 = -2
The slope of WZ is not the negative inverse of the slope of YZ, therefore, the figure WZ is not perpendicular to YZ and the figure is not a rectangle.
Considering the two triangles formed by the diagonal XZ, we get;
The figure XYZW is a quadrilateral, which is a composite figure comprising of two triangles, triangle ΔXYZ and ΔXWZ
Area of triangle ΔXYZ = (1/2) × 6 × 2 = 6 square units
Area of triangle ΔXWZ = (1/2) × 6 × 2 = 6 square units
The area of the figure = Area of triangle ΔXYZ + Area of triangle ΔXWZ
Area of triangle ΔXYZ + Area of triangle ΔXWZ = 6 + 6 = 12 square units
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Find the slope of the line graphed below.
Answer:
7/4
Step-by-step explanation:
You can think of slope as rise over run, or the change in y / the change in x.
In the image, we can view the two points that are marked on the coordinate system.
We can see how many spaces up we need to go and how many spaces to the right we need to go to find the slope. We can count that we go 7 spaces up and 4 spaces to the right giving us a slope of 7/4. We can also do the change in y over the change in x.
Change in Y: 3 - (-4) = 7
Change in X: (-1) - (-5) = 4
Slope: = Change in Y / Change in X = 7/4
a sphere with radius r and a cylinder with radius r and a height of r are shown below. how do the surface areas of these solid figures compare?
which statements are correct? check all that apply
A: the surface area of the sphere in terms of r is 4(pi)r^2 square units
B: the surface area of the cylinder in terms of r is 4(pi)r^2 square units
C: the surface area of the cylinder in terms of r is 6(pi)d^2 square units
D: the surface area of the cylinder and sphere are the same
E: the surface area of the cylinder and sphere are NOT the same
The correct statements are A and B, while C, D, and E are incorrect.
The correct statements are:
A: The surface area of the sphere in terms of r is 4(pi)r^2 square units. This is true. The formula for the surface area of a sphere is given by A = 4(pi)r^2, where r is the radius.
B: The surface area of the cylinder in terms of r is 4(pi)r^2 square units. This is true. The formula for the lateral surface area of a cylinder is given by A = 2(pi)rh, where r is the radius and h is the height. Since the height of the cylinder is also r, the formula simplifies to A = 2(pi)rh = 2(pi)r(r) = 2(pi)r^2. Additionally, the two circular bases of the cylinder also contribute to the surface area, each with an area of (pi)r^2. Therefore, the total surface area of the cylinder is A = 2(pi)r^2 + 2(pi)r^2 = 4(pi)r^2.
C: The surface area of the cylinder in terms of r is 6(pi)d^2 square units. This statement is incorrect. The formula provided is incorrect. The correct formula for the surface area of a cylinder is A = 2(pi)rh, not 6(pi)d^2.
D: The surface area of the cylinder and sphere are the same. This statement is incorrect. The surface areas of a cylinder and a sphere are different. The surface area of a sphere is given by A = 4(pi)r^2, while the surface area of a cylinder is given by A = 2(pi)r^2 + 2(pi)rh. The presence of the curved surface in the cylinder makes its surface area different from that of a sphere.
E: The surface area of the cylinder and sphere are NOT the same. This statement is correct. As mentioned above, the surface areas of a cylinder and a sphere are different, so they are not the same.
In summary, the correct statements are A and B, while C, D, and E are incorrect.
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What formula(s) below represents the frequency of
that E? Check all that apply.
The expression that What formula(s) below represents the frequency of
that E are Option A, C and E.
What are the correct expressions?A stored expression that can be invoked from other expressions is known as an expression rule. You can use rule inputs in your expression rules to allow you to dynamically alter the data your expression returns.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is called an expression or a mathematical expression.
From the option A, we have [tex]440. 2^{\frac{7}{12} } \\\\[/tex]
Then this can be written as ; [tex]440 ^{\sqrt[12]{2} }[/tex]
which can be written as [tex]440 .10597^7}[/tex]
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Useful chatting ~ ChatGPT is an open-access online chatbot that allows users to ask questions and request content. In 2023, researchers surveyed US adults who have used ChatGPT for entertainment, education, or work and collected their opinion on the usefulness of ChatGPT.
Chun-Yi would like to determine if adults living in Taiwan have similar opinions to those living in the US. She takes a random sample of 405 Taiwanese adults who have used ChatGPT and records their opinions.
The results from both surveys are summarized in the table below.
Opinion of usefulness 2023 U.S. Adults Observed counts in Taiwan
Extremely useful 15.5% 62
Very useful 21.6% 84
Somewhat useful 40% 186
Not too useful 16.6% 52
Not at all useful 6.3% 21
Round all calculated answers to 4 decimal places.
QUESTION: 7. The observed test statistic for this problem is 7.9527. Calculate the p-value.
p-value =
The calculation of a p-value generally requires knowing the statistical test used and the degrees of freedom involved, as well as the direction of the test (one-sided or two-sided). This question doesn't specify which statistical test was used or whether the test was one- or two-sided.
One potential scenario is that a chi-square goodness-of-fit test was used, which is common for comparing observed frequencies with expected frequencies. If this is the case, the observed test statistic value of 7.9527 represents the chi-square statistic. The degrees of freedom would be the number of categories minus 1, which is 5-1 = 4 in this case.
To find the p-value, we would look up the chi-square statistic of 7.9527 in a chi-square distribution table with 4 degrees of freedom or use software that can calculate it.
This question doesn't provide enough information to calculate the exact p-value and normally this would be done using a statistical software package or an online chi-square calculator. However, a typical rule of thumb is that a chi-square statistic greater than about 10 with 4 degrees of freedom would suggest a statistically significant result at the 0.05 level, so it's likely that the p-value here is greater than 0.05 (i.e., the result is not statistically significant at the 0.05 level).
Please note this is an approximation and the actual p-value should be calculated using appropriate statistical software or a chi-square calculator.
Blue Spruce Corp, was organized on January 1, 2025. It is authorized to issue 20,700 shares of 5%, $50 par value preferred stock
and 473,000 shares of no-par common stock with a stated value of $3 per share. The following stock transactions were completed
during the first year.
Jan. 10 Issued 66,100 shares of common stock for cash at $6 per share.
Mar. 1 Issued 14,700 shares of preferred stock for cash at $52 per share.
May 1 Issued 121,500 shares of common stock for cash at $8 per share.
Sept. 1 Issued 6,300 shares of common stock for cash at $7 per share.
Nov. 1 Issued 4,300 shares of preferred stock for cash at $55 per share.
(A) Journalize the transactions
(B) post to the stockholders equity accounts
(C) Prepare the paid-in capital portion of the stockholders equity section at December 31, 2025
If Blue Spruce Corp, was organized on January 1, 2025. The entry on June 10 is:Debit Cash 396,600, Debit Common Stock 198,300,Credit Additional Paid-in Capital 198,300.
What is the journal entry?(A) Journalize the transactions:
Jan. 10:
Debit Cash 396,600
(66,100 shares x $6)
Debit Common Stock 198,300
(66,100 shares x $3)
Credit Additional Paid-in Capital 198,300
Mar. 1:
Debit Cash 764,400
(14,700 shares x $52)
Credit Preferred Stock 764,400
(14,700 shares x $52)
May 1:
Debit Cash 972,000
(121,500 shares x $8)
Credit Common Stock 364,50
(121,500 shares x $3)
Credit Additional Paid-in Capital 607,500
Sept. 1:
Debit Cash 44,100
(6,300 shares x $7)
Credit Common Stock 18,900
(6,300 shares x $3)
Credit Additional Paid-in Capital 25,200
Nov. 1:
Debit Cash 236,500
(4,300 shares x $55)
Credit Preferred Stock 236,500
(4,300 shares x $55)
(B) Post to the stockholders equity accounts:
Preferred Stock:
Date | Explanation | Debit | Credit
Mar. 1 | Issuance | | $764,400
Nov. 1 | Issuance | | $236,500
Common Stock:
Date | Explanation | Debit | Credit
Jan. 10 | Issuance | | $198,300
May 1 | Issuance | | $364,500
Sept. 1 | Issuance | | $18,900
Additional Paid-in Capital:
Date | Explanation | Debit | Credit
Jan. 10 | Issuance | | $198,300
May 1 | Issuance | | $607,500
Sept. 1 | Issuance | | $25,200
(C) Prepare the paid-in capital portion of the stockholders equity section at December 31, 2025:
Paid-in Capital:
Preferred Stock: $1,000,900 ($764,400 + $236,500)
Common Stock: $581,700 ($198,300 + $364,500 + $18,900)
Additional Paid-in Capital: $831,000 ($198,300 + $607,500 + $25,200)
Total Paid-in Capital = ($1,000,900 + $581,700 + $831,000)
=$2,413,600
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Find y" by implicit differentiation.
cos(y) + sin(x) = 1
y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.
To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.
Equation: cos(y) + sin(x) = 1
Differentiating once with respect to x using the chain rule:
-sin(y) * dy/dx + cos(x) = 0
Now, differentiating again with respect to x:
Differentiating the first term:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2
Differentiating the second term:
-d/dx(cos(x)) = -(-sin(x)) = sin(x)
The equation becomes:
-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0
Now, let's isolate the second derivative, d^2y/dx^2:
-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)
Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):
-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)
Thus, the second derivative (y") by the equation:
y" = cos(y) * dy/dx - sin(x) + sin(y)
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1/-12 plus 2/-15 pls answers fast
Answer:
-13/60
Step-by-step explanation:
trust me
Can someone help me please ?
The table represents a linear relationship.
x −2 0 4
y 4 3 1
Which equation represents the table?
y equals one half times x plus 5
y equals negative one-half times x plus 3
y = 2x − 3
y = −4x + 2
Answer:
You have selected the correct answer.
Step-by-step explanation:
y = mx + b
the slope is the m or the change in y over the change in x.
b is the y value at (0,b) In this case (0,3).
Which of the following z-scores is NOT outside the middle 68% of the data for a normal distribution?
a.) -0.8
b.) -2.8
c.) 1.8
d.) 3.8
Answer:
Step-by-step explanation:
A, use three_digite rounding arithmetic to compute 13- 6 and determine the absolute,relative ,and percentage errors.
tepeat part (b) using three – digit chopping arithmetic.
Does this table represent a function? Why or why not?
A. No, because one x-value corresponds to two different y-values.
OB. Yes, because there are two x-values that are the same.
OC. No, because two of the y-values are the same.
D. Yes, because every x-value corresponds to exactly one y-value.
The table is not a function because (a) No, because one x-value corresponds to two different y-values
Determining if the table is a functionFrom the question, we have the following parameters that can be used in our computation:
The table
The table can be represented as
x y
2 1
2 4
3 4
4 2
5 5
The above table of values is not a function
This is so because some output values have the same input values.
i.e. it would fail the vertical line test when represented on a graph
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Question 1 of 10
Which of the following steps were applied to ABC obtain SA'EC?
Ä
OA Shifted 4 units left and 4 units up
B. Shifted 2 units left and 2 units up
OC. Shifted 2 units left and 4 units up
OD. Shifted 4 units left and 2 units up
Answer:
C
Step-by-step explanation:
just look at point A and the difference to A'.
A was moved 2 units to the left and 4 units up to get A'.
and the same happened, of course, to all other points of the triangle.
so, C is correct.
Which statement best describes the growth rates of the functions below?
The quadratic function grows faster than the exponential function over the entire interval; 0
The exponential function grows faster than the quadratic function over the entire interval; 0
The exponential function grows faster than the quadratic function over only one interval; 2
The exponential function grows faster than the quadratic function over two intervals; 2
"The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
There are three commonly-used forms of quadratics:
Standard Form: y = a x 2 + b x + c y= [tex]ax^2+bx+c y=ax2+bx+c.[/tex]
Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y= a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)
Vertex Form: y = a ( x − h ) 2 + k y= [tex]a(x-h)^2+k y=a(x−h)2+k.[/tex]
Quadratic functions can be represented symbolically by the equation, y(x) = ax2 + bx + c, where a, b, and c are constants, and a ≠ 0. This form is referred to as standard form.
The statement "The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.
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Which describes the transformations applied in the figure above?
A. a counterclockwise rotation of 180 degrees and move 5 units to the left
B. 7 units right and a clockwise rotation of 90 degrees
C. 7 units left and a reflection about the x-axis
D. 7 units left and 2 units up
The statement that describes the transformations applied in the figure above include the following: C. 7 units left and a reflection about the x-axis.
How to reflect the quadrilateral based on the transformation rule?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
Based on the graph, the coordinates of point A are located at (-6, 1) in quadrant II.
By applying a translation to the A horizontally right by 7 units, the new coordinate A1 of quadrilateral ABCD include the following:
(x, y) → (x + 7, y)
A (-6, 1) → (-6 + 7, 1) = A1 (1, 1)
By applying a reflection over the x-axis to the coordinates of point A1, we have the following coordinates of the image A';
(x, y) → (x, -y)
Point A1 (1, 1) → A' (1, -(1)) = G' (1, -1)
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You have a whole life policy with the face value of $100,000. Your annual premium is $2,000. The cash value of the policy is expected to be $15,000 in 10 years. If you could invest your money elsewhere for a 5% annual yield, what is the net cost of insurance?
The net cost of insurance, considering the alternative investment with a 5% annual yield, is $5,000.
The net cost of insurance can be calculated by considering the opportunity cost of investing the annual premium in an alternative investment that yields a 5% annual return.
Let's break down the calculation step by step:
Calculate the future value of the annual premium after 10 years:
Using the compound interest formula, the future value (FV) of the $2,000 premium invested at a 5% annual yield for 10 years can be calculated as:
FV = PV * (1 + r)^n,
where PV is the present value (annual premium), r is the interest rate (5% or 0.05), and n is the number of periods (10 years).
FV = $2,000 * (1 + 0.05)^10
FV = $2,000 * (1.05)^10
FV ≈ $3,263.18
Calculate the net cost of insurance:
The net cost of insurance is the difference between the total premiums paid over 10 years and the cash value of the policy after 10 years.
Total premiums paid over 10 years = Annual premium * Number of years = $2,000 * 10 = $20,000
Net cost of insurance = Total premiums paid - Cash value of the policy after 10 years
Net cost of insurance = $20,000 - $15,000 = $5,000
Therefore, the net cost of insurance, considering the alternative investment with a 5% annual yield, is $5,000.
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Please help me solve these questions attached below
Answer:
6
Step-by-step explanation:
Jabez was solving the math problem 54 x 0.06. Before solving, he estimates that his answer will be less than 54 but greater than 5.4. His classmate, Christina, disagrees and thinks the answer will be less than 5.4. Who is correct, Jabez or Christina? Explain how you know who is correct without calculating the product of 54 x 0.06.
Jabez is correct without calculating the product of 54 x 0.06 correctly because his estimation aligns with the mathematical principle that multiplying a number by a decimal less than 1 will result in a smaller product.
To determine who is correct without calculating the product of 54 x 0.06, we can use estimation.
Jabez estimated that the answer will be less than 54 but greater than 5.4. Let's analyze his estimation. When multiplying a number by a decimal less than 1, the product will always be smaller than the original number. In this case, 54 is the original number. Since 0.06 is less than 1, the product of 54 x 0.06 will definitely be smaller than 54.
On the other hand, Christina thinks the answer will be less than 5.4. Let's analyze her estimation. The original number, 54, is already greater than 5.4. When multiplying it by a decimal less than 1, the product will be even smaller. Therefore, Jabez's estimation is incorrect.
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I need help asap please!!!
The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and
What is sine of angles?he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle. It is defined as the length of the opposite side divided by the length of the hypotenuse
The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360
2∅ 2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720
sin 2∅ = sin0 = 0; Sin90=1; sin180=0; sin240= -0.8660; sin270 = -1;
Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397
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Select all the statements that are true for the following systems of equations.
System A
2x-3y = 4
4x - y = 18
00
System B
3x - 4y = 5
y = 5x +3
All three systems have different solutions.
Systems B and C have the same solution.
System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
Systems A and B have different solutions.
Systems A and C have the same solution.
Reset
System C
2x-3y=4
12x-3y = 54
Next
The statements that are true about the system of equations are: Options C, D, and E.
How to Find the Solution to a Systems of Equations?Let's analyze each statement and determine whether it is true or false for the given systems of equations:
System A
2x - 3y = 4
4x - y = 18
System B
3x - 4y = 5
y = 5x + 3
System C
2x - 3y = 4
12x - 3y = 54
A. All three systems have different solutions.
To determine if the systems have different solutions, we need to solve them. Solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems A and C have the same solution.
B. Systems B and C have the same solution.
As mentioned above, solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems B and C have different solutions.
C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
To simplify system C, we can divide the second equation by 3, resulting in:
2x - 3y = 4
4x - y = 18
This is exactly the same as system A. Therefore, this statement is true.
D. Systems A and B have different solutions.
As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Therefore, this statement is true.
E. Systems A and C have the same solution.
As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is true.
In summary:
A. False
B. False
C. True
D. True
E. True
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Complete Question:
Select all the statements that are true for the following systems of equations.
System A
2x - 3y = 4
4x - y = 18
System B
3x - 4y = 5
y = 5x +3
System C
2x - 3y = 4
12x - 3y = 54
A. All three systems have different solutions.
B. Systems B and C have the same solution.
C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.
D. Systems A and B have different solutions.
E. Systems A and C have the same solution.
What is 22x22 and 4x4
Answer:
22x22=484
4x4=16
Step-by-step explanation:
4x4
4+4+4+4
4+4=8
4+4=8
8+8=16
I NEED YOUR HELP!! I'LL. GIVE YOU BRAINLIEST
Answer: ∠16 and ∠11
Step-by-step explanation:
All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.
The correct corresponding angles are ∠16 and ∠11.
find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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Find the perimeter of the triangle whose vertices are (−8,−8)
, (1,4)
, and (6,−8)
. Write the exact answer. Do not round.
Answer:
answer is 42
Step-by-step explanation:
use the distance formula and it's simple afterwards. I am pretty sure the answer is correct but let me know if you need more help
If 250 MG of a radioactive element decays 2 a 190 mg in 48 hours find the half-life of the element round your Answer to the nearest whole number
Answer:
61 hours
Explanation:
In this question we will use radioactive decay model
m0= 250 mg
h is the hlf life of element
m(t) is the mass left after t time
so,solving this equation for h
re aranging and taking ln on both the sides we get
solving further we get
h= 60.62 hours ≅61 hour
the half life of element is 61 hours
Step-by-step explanation:
Enter the number that belongs in the green box
The angle C in the triangle is 34.05 degrees.
How to use cosine law to find angles in a triangle?
The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:
Therefore, let's find the unknown angle in the triangle as follows;
c² = a² + b² - 2ab cos C
Hence,
4² = 5² + 7² - 2 × 7 × 5 cos X
16 = 25 + 49 - 70 cos X
16 = 74 - 70 cos X
16 - 74 = -70 cos X
-58 = -70 cos X
cos X = 58 / 70
X = cos⁻¹ 0.82857142857
X = 34.0478785629
X = 34.05 degrees
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