The sum of three numbers is 24. The third is 11 less than 3 times the second. 8 times the first is 4 less than 10 times the second. Find the numbers
Answers
Answer:
F + S + T = 24 F= 1st number, S = 2nd, T = 3rd
Step-by-step explanation:
T = 2S - 11
9F = 7 + 2S
divide by 9
F + (7+2S)/9
substitute for F and T
(7+2S)/9 + S + 2S -11 = 24
7+2S + 9S + 18S - 99 = 216
29S = 216 + 99 - 7 = 308
S = 308/29 = the 2nd number
T = 2S -11 = 616/29 -11 = 616/29 - 319/29 = 297/29 = 3rd number
F = (7+2S)/9 = (7 +616/29)/9 = 819/261 = 1st number
the 3 numbers are 819/261, 308/29 and 297/29
they sum to 819/261 + 308/29 + 297/29 = about 3.14 + 10.62 +10.24 = 24
F =( 7+2(10.62))/9 = (7+ 21.24)/9 = 28.24/9 = 314
S = 308/29 = 10.62
T = 2S-11 = 2(10.62) - 11 = 21.24-11 = 10.24
although odds are the problem may have been mis-copied or has a slight typo, with more integer type solutions in the corrected version. If the problem had an 8 instead of 9, (8F = 7+ 2S) then F=3.5, S=10.5, T = 10 as exact answers, not rounded off. 3.5+10.5+ 10 = 24
First number: [tex]\frac{167}{21}[/tex];
Second number: [tex]\frac{142}{21}[/tex];
Third number: [tex]\frac{130}{14}[/tex].
Step-by-step explanation:1. Assign variables to each number.First number: "x";
Second number: "y";
Third number: "z".
2. Form equations based on the problem's statement.Equation 1. "The sum of three numbers is 24", hence:
[tex](1)x+y+z=24[/tex]
Equation 2. "The third is 11 less than 3 times the second.", hence:
[tex](2)z=3y-11\\ \\(2)-3y+z=-11[/tex]
Equation 3. "8 times the first is 4 less than 10 times the second.", hence:
[tex](3)8x=10y-4\\\\(3)8x-10y=-4[/tex]
3. Group the 3 equations.[tex](1)x+y+z=24\\\\(2)-3y+z=-11\\\\(3)8x-10y=-4[/tex]
4. Expand the equations.As you may see, the 3 variables don't always appear on all 3 equations. Therefore, we'll have to introduce them even though they don't appear. For this, we write the variable with a coefficient of 0 next to it
[tex](1)x+y+z=24\\\\(2)0x-3y+z=-11\\\\(3)8x-10y+0z=-4[/tex]
5. Rewrite the equations as a 3x4 matrix.Using the coefficient of each variable in each equation, rewrite the system of equation into a matrix like this:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\8&-10&0&-4\end{array}\right][/tex]
6. Convert this matrix into the row-echelon form.Check the attached image to see the steps to making this convertion.
a) Getting the 1 on column 1.
Since there's already a 1 there, we skip this step.
b) Getting the 0 on column 1.
Since there's already a 0 there, we skip this step.
c) Getting the 0 on column 1.
Multiply row 1 values by "-8" and add them to row 3. The result of these operations should be:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&-3&1&-11\\0&-18&-8&-196\end{array}\right][/tex]
d) Getting the 1 on column 2.
Since we are working with column 2 and row 2, you may use the pivot value "-3" (the one that corresponds to the intersection of column 2 and row 2) and divide row 2 by itself to obtain a 1. Result is the following:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&-18&-8&-196\end{array}\right][/tex]
e) Getting the 0 on column 2.
Multiply row 2 by "18" and add it to row 3. Resulting table is:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&-14&-130\end{array}\right][/tex]
f) Getting the 1 on column 3.
We are working with column 3 and row 3, the intersection value is "-14" and we may use it as a pivot value. Hence, we may divide row 3 by "-14" in order to obtain the number 1 in column 3. Final table is:
[tex]\left[\begin{array}{cccc}1&1&1&24\\0&1&-\frac{1}{3} &\frac{-11}{-3} \\0&0&1&\frac{-130}{-14}\end{array}\right][/tex]
7. Calculate the values.Starting from the bottom up, take the expression of the resulting matrix and calculate the values of each variable.
a) From row 3 we have:
[tex]0x+0y+z=\frac{-130}{-14} \\ \\z=\frac{130}{14}\\ \\[/tex]
b) From row 2 we have:
[tex]0x+y-\frac{1}{3} z=\frac{-11}{-3} \\ \\y-\frac{1}{3} z=\frac{11}{3}\\ \\y-\frac{1}{3} (\frac{130}{14} )=\frac{11}{3}\\ \\y-\frac{130}{42} =\frac{11}{3} \\ \\y=\frac{11}{3}+\frac{130}{42}\\\\y=\frac{11*14}{3*14}+\frac{130}{42}\\ \\y=\frac{154}{42}+\frac{130}{42}\\ \\y=\frac{284}{42} \\\\y=\frac{142}{21}[/tex]
c) From row 1 we have:
[tex]x+y+z=24\\ \\x+\frac{142}{21}+\frac{130}{14} =24\\ \\x=24-\frac{142}{21}-\frac{130}{14}\\ \\x=\frac{1008}{42} -\frac{284}{42} -\frac{390}{42} \\ \\x=\frac{167}{21}[/tex]
8. Verify that the numbers work correctly in each of the equations.Equation 1: [tex]\frac{167}{21} +\frac{142}{21} +\frac{130}{14} =24[/tex] Correct.
Equation 2: [tex]-3(\frac{142}{21} )+\frac{130}{14} =-11[/tex] Correct.
Equation 3: [tex]8(\frac{167}{21} )-10(\frac{142}{21} )=-4[/tex] Correct.
9. Conclude.First number: [tex]\frac{167}{21}[/tex];
Second number: [tex]\frac{142}{21}[/tex];
Third number: [tex]\frac{130}{14}[/tex].
Important: Check the attached Excel sheet to see the changes made in the matrix.
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Related Questions
create a linear model that could be used to calculate the cost to mail a package, given its weight in ounces. let p represent the price to mail a package that weighs x ounces. enter the second linear model simplified in the from p
Answers
The linear model that could be used to calculate cost of mailing a large envelope is L(x) = 0.88 + 0.2(x – 1) and used to calculate cost of mailing a package is P(x) = 1.71 + 0.17(x – 3). The weight at which the cost a large envelope and a package will cost the same amount to mail is 17 ounces.
Linear models are used to describe a continuous response variable as a function of one or more predictor variables. Let x be the weight in ounces and L be the cost of mailing a large envelope. Based on the provided information, the cost of mailing a large envelope increases with increasing weight. The cost of mailing one ounce is $0.88 and increased by $0.2 for each additional weight. Hence,
L(x) = 0.88 + 0.2(x – 1)
Let x be the weight in ounces and P be the cost of mailing a package. Based on the provided information, the cost of mailing a package remains the same for weight of 1 to 3 ounces at the cost of $1.71, and then increases by $0.17 for each additional weight. Hence,
P(x) = 1.71 + 0.17(x – 3)
The weight at which a large envelope and a package will cost the same amount to mail is determined by equating the two models.
L(x) = P(x)
0.88 + 0.2(x – 1) = 1.71 + 0.17(x – 3)
0.88 + 0.2x – 0.2 = 1.71 + 0.17x – 0.51
0.68 + 0.2 x = 0.17 x + 1.2
0.2x – 0.17x = 1.2 – 0.68
0.03x = 0.52
x = 17.33 ≈ 17 ounces
Note: The question is incomplete. The complete question probably is: Provided table indicates the U.S. Postal Rates for large envelopes and packages of different weights. a) Create a linear model that could be used to calculate the cost to mail a large envelope, given its weight in ounces. Use L to represent the cost to mail a large envelope and x to represent the envelope weight in ounces. Create a linear model that could be used to calculate the cost to mail a package, given its weight in ounces. Use P to represent the cost to mail a package and x to represent the package weight in ounces. Find the weight at which a large envelope and a package will cost the same amount to mail, assuming your linear models still apply to higher weights.
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How many solutions will each system of linear equations have? Match the systems with the correct number of
solutions.
y=x+6 and 3x-3y = -18
y=-4x+11 and -6x + y = 11
y=-2x+5 and 2x + y = -7
infinitely many solutions
one solution
no solution
Answers
The correct answer is System 1: Infinitely many solutionsSystem 2: One solutionSystem 3: No solution
Let's analyze each system of linear equations and determine the number of solutions they have.
y = x + 6 and 3x - 3y = -18
In this system, the first equation is a linear equation in slope-intercept form, and the second equation is a linear equation in standard form. The two equations represent the same line. Since they are the same line, they intersect at infinitely many points. Therefore, this system has infinitely many solutions.
y = -4x + 11 and -6x + y = 11
Both equations in this system are in slope-intercept form. The slopes of the two lines are different (-4 and -6), indicating that the lines are not parallel. Since the lines are not parallel and have different slopes, they intersect at a single point. Therefore, this system has one solution.
y = -2x + 5 and 2x + y = -7
Both equations in this system are in slope-intercept form. The slopes of the two lines are equal (-2 and 2), but their y-intercepts are different. When the slopes are equal and the y-intercepts are different, the lines are parallel and do not intersect. Therefore, this system has no solution.
Matching the systems with the correct number of solutions:
System 1: Infinitely many solutions
System 2: One solution
System 3: No solution
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You are packing books into a box. The box can hold at most 10 books. The function y=5.2x represent the weight y (in pounds) of x books
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This question doesn't seem completed to me. Is there anything more after this?
(8k^3 - 19 k^2 + 2k + 10) /(k - 2) = ?
Answers
Answer: 8k^2 - 19k + 12
Step-by-step explanation: The way we found this answer was by simplifying the expression.
Step 1 : We want to get (x-2) in the numerator so we could cross it out with the x-2 at the bottom to get our simplified expression.
(8k^3-19k^2+2k+10)/(k-2) = (x-2)(8k^2-17k+5)/(x-2)
You would need to factor out the (x-2)
Step 2: When you cross the (x-2) above with the (x-2) below you end up with 8K^2-17k+5 as the answer.
Answer:
[tex]8k^2-3k-4+\frac{2}{k-2}[/tex]
Step-by-step explanation:
⭐ See the image I attached to my answer to see the working.
⭐ I recommend you look at the image while following along with the steps to understand the steps.
1. See what multiplies with the first term in the divisor to get the first term in the dividend. Then, put that answer in the quotient space.
2. Under the first term in the dividend, write a - sign and open parentheses. Put the first term inside the parentheses.
3. Multiply what you put in the quotient space from step #1 with the second term in the divisor.
4. Put the product from step #3 inside of the parentheses.
5. Subtract the first two terms in the parentheses from the first two terms in the dividend.
. . . . . . . . . . . . . note: in polynomial division, you will not always subtract two terms. we are subtracting two terms here because there are two terms in the divisor.
6. Write the answer from #5 under the parentheses, and bring down another term from the dividend.
7. See what multiplies with the first term in the dividend to get the answer from #5. Then, put that answer in the quotient space.
8. Under step #6, write a - sign and open parentheses. Put the answer from #5 inside the parentheses.
9. Multiply the answer from #7 with the second term in the divisor.
10. Next to the answer from step #8, write the product of step #9.
11. Subtract the terms from step #10 from step #6.
12. Repeat until you have "brought down" all of the terms from the dividend.
After you are done, your remainder will not be 0. Instead, it will be +2. When you have a remainder that isn't 0, you cannot use the quotient as your answer. Instead, you have to write your answer in this format:
[tex]q(x)+\frac{r(x)}{d(x)}[/tex], where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.
⇒ q(x) = [tex]8k^2-3k-4[/tex]
⇒ r(x) = +2
⇒ d(x) = k -2
⇒ [tex]8k^2-3k-4+\frac{2}{k-2}[/tex]
Can someone help me with this? Please and thank you
Answers
The measures in this problem are given as follows:
1. x = 14.
2. m < 1 = 58º.
3. m < 2 = 122º.
How to obtain the measures?Angles 1 and 2 are supplementary, as the angle 1 and the consecutive interior angle with angle 2 are corresponding angles, meaning that they are congruent, and then the angles are supplementary with their consecutive interior angles.
When two angles are supplementary, the sum of their measures is of 180º, hence the measure of x is obtained as follows:
m < 1 + m < 2 = 180
2x + 30 + 8x + 10 = 180
10x + 40 = 180
10x = 140
x = 140/10
x = 14.
Then the angle measures are obtained as follows:
m < 1 = 2(14) + 30 = 58º.m < 2 = 8(14) + 10 = 122º.More can be learned about parallel and transversal lines at https://brainly.com/question/24607467
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Match each expression on the left with its quotient. Use number sense and estimation to help.
5.85369.421.5
40.42 ÷ 4.3
15.48 ÷ 0.72
86.4 ÷ 2.4
50.31 ÷ 8.6
Answers
Answer:
5.85369.421.5 does not have a quotient because it is not a mathematical expression.
40.42 ÷ 4.3 = 9.4
15.48 ÷ 0.72 = 21.4
86.4 ÷ 2.4 = 36.0
50.31 ÷ 8.6 = 5.84
pls help me i will mark brainliest:)
Simplify −5g(3g + 4).
−15g + 4
−15g − 20g
−15g2 + 4
−15g2 − 20g
Answers
(-5g X +4)= -20g
Answer = -15g2-20g
Answer:
D = -15g² - 20g
-5g × 3g -5g×4
= -15g² -20g
# to put in ² when typing hold 2 for 5seconds...
#like please
Please help please and thank you
Answers
Answer:
11 inches
Step-by-step explanation:
If one inch represents 210 feet, then divide 2310 by 210 to get the number of inches in the scale drawing.
Answer:
11 inches
Step-by-step explanation:
2310/210 = 11
Solve this equation (Shown in the screenshot below)
Answers
Answer:
x = {-2, 0, 2}
Step-by-step explanation:
You want the solutions to √((√(x²) -1)²) = 1.
SolutionSquaring both sides gives ...
(√(x²) -1)² = 1² = 1
Taking the square root of both sides gives ...
√(x²) -1 = ±1
Adding 1, we have ...
√(x²) = 1 ± 1 = {0, 2}
We know that √(x²) = |x|, so this reduces to ...
|x| = {0, 2}
x = {±0, ±2}
x = {-2, 0, 2}
__
Additional comment
For finding the solutions graphically, we like to plot the equation in the form f(x) = 0. The graphing calculator readily identifies the x-intercepts, which are the solutions.
show that (2n-5)^2 - 13 is a multiple of 4 for all integers
Answers
Step-by-step explanation:
⭐ What does it mean for a number (x) to be a multiple of another number (y)?
If x is a multiple of y, then x is divisible by y.Thus, we have to show that [tex](2n-5)^2 - 13[/tex] is divisible by 4.
Let's compute [tex](2n-5)^2 - 13[/tex]:
[tex](2n-5)^2[/tex] is the polynomial identity [tex](a-b)^2[/tex][tex](a-b)^2 = a^2 -2ab + b^2[/tex][tex](2n-5) ^2 = 4n^2 -20n + 25[/tex]
[tex]4n^2 - 20n + 25 -13[/tex]
[tex]4n^2 - 20n + 12[/tex]
[tex]4n^2 - 20n + 12[/tex] is the expression we have.
To see if this expression is divisible by 4, we need to divide [tex]4n^2 - 20n + 12[/tex] by 4 and have a remainder of 0.
The given equation (2n-5)² - 13 equals 4² - 20n + 12. Because each term in the simplified equation can be divided evenly by 4, it proves that the equation is indeed a multiple of 4, assuming n is an integer.
Explanation:The problem is asking to show that the expression (2n-5)² - 13 is a multiple of 4 for all integers. To prove this, we need to expand and simplify the expression and then check whether it can be divided evenly by 4.
Let's start by expanding the expression:
(2n-5)² - 13 = 4n² - 20n + 25 - 13 = 4n² - 20n + 12
Now we can observe that all terms in the equation are divisible by 4:
4n²/4 = n², -20n/4 = -5n, and 12/4 = 3
Because all terms in the equation can be divided evenly by 4, we can say that the entire equation (2n-5)² - 13 is a multiple of 4, assuming n is an integer.
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I need help with my math homework
Answers
Brainly pls
help multipy
look at the picture
Answers
The answer is -2x² + 8x + 54 = 0.
What is multiplication?This refers to a method used to easily solve the task of repeated addition of the same number. It is used when we need to combine groups of equal sizes.
Given in the question:
[tex]\frac{2x +3 }{x^{2}-x}[/tex] *[tex]\frac{4x^{2 } +8x }{10x +30}[/tex]
Multiply the numerators and denominators and equate the two:
(2x + 3) * (4x² + 8x)= ( x² - x) * (10x + 30)
expanding further we have:
(2x + 3) * 4x² + (2x + 3) *8x = ( x² - x) * 10x + ( x² - x) * 30
8x³+12x² +16x² +24x= 10x³ -10x² + 30x² -30x
Resolving the left-hand side of the equation and the right-hand side and equating to zero we have:
8x³- 10x³ + 12x² +16x² +10x² -30x² +24x +30x
2x³ + 8x² + 54x = 0.
Divide through by x, we have:
[tex]\frac{-2x^{3} }{x}[/tex] + [tex]\frac{8x^{2} }{x}[/tex] + [tex]\frac{54x}{x}[/tex] = 0
-2x² + 8x + 54 = 0.
Hence the answer is-2x² + 8x + 54 = 0.
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Which of the following statements assigns a random integer between 1 and 10, inclusive, to rn ?
A int rn = (int) (Math.random()) * 10;
B int rn = (int) (Math.random()) * 10 + 1;
C int rn = (int) (Math.random() * 10);
D int rn = (int) (Math.random() * 10) + 1;
E int rn = (int) (Math.random() + 1) * 10;
Answers
The correct statement that assigns a random integer between 1 and 10, inclusive, to rn is (D).
int rn = (int) (Math.random() * 10) + 1.
The method Math.random() generates a random number between 0 and 1, inclusive. If we multiply this number by 10, we will get a random number between 0 and 10, exclusive. If we then add 1 to this number, we will get a random number between 1 and 11, exclusive. If we then take the integer part of this number using the (int) cast, we will get a random integer between 1 and 10, inclusive. This is exactly what statement (D) does.
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how many possible outcomes are there?
Answers
Which is greater?
3
5 or 130
Answers
PLEASE! An experiment using 35 guinea pigs is set up to study the weight of the pigs after injecting them with a drug. If the population mean is 23.5 grams with a standard deviation of 3.4 grams, what is the margin of error of the sample mean?
A. 0.097 grams
B. 0.575 grams
C. 0.701 grams
D. 1.149 grams
E. 1.403 grams
Answers
Find the solution of the system of equations.
5x+y=-19
5x-4y=-24
Answers
The solution of the system of equations are x = -4 and y=1.
How to solve system of equations?
Look at substitution and elimination as two methods for algebraically solving systems of linear equations.To better comprehend when systems of linear equations have one solution, no solutions, or infinitely many solutions, let's look at systems of linear equations graphically.Investigate algebraic techniques for counting the number of solutions to systems involving two linear equations.5x+y=-19 -- (i)
5x-4y=-24 ---(ii)
Subtract the above two equations:
5y = 5
y = 1
Substitute y=1 in equation (ii)
5x - 4(1) = -24
5x = -20
x = -4
Hence, the solution of the system of equations are x = -4 and y=1.
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pls help if you get it correct u will get 100 brainly points
Answers
Answer: -28
Step-by-step explanation:
Mutiply by 7 on both sides, it cancels out to the left and then -4 (7) equals -28 so n= -28
Answer:
-28
Step-by-step explanation:
Multiply both sides by 7
That cancel outs the denominator 7 out and multiples -4 to -28
now all that's left is 1n or just n = -28
Serena forms a random sample of 200 seventh graders from her school to learn which type of school lunch they most prefer. The results of her survey are shown below.
Food Type Chicken Nuggets Tacos Spaghetti
Number of students 87 86 27
Which is the best inference you can form based on the data? (3 points)
a
Chicken nuggets and tacos were almost liked the same amount
b
Tacos are twice as popular as spaghetti.
c
Chicken nuggets is twice as popular as spaghetti.
d
Tacos were the students' top choice
Answers
Answer:
a
Step-by-step explanation:
86 and 87 are similar. Also none of the other answers are correct
Write the equation of the line that has a slope of 1 and goes through the point (2, 3). Hint: Use y = mx+b
Answers
Answer:
y = x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = 1 , then
y = x + c ← is the partial equation
to find c substitute (2, 3 ) into the partial equation
3 = 2 + c ⇒ c = 3 - 2 = 1
y = x + 1 ← equation of line
In Exercises 1-3, decide whether enough information is given to prove that the triangles are congruent using either the SSS Congruence Theorem (Theorem 5.8) or the HL Congruence Theorem (Theorem 5.9). Explain.
Answers
1. The triangles are congruent based on the SSS congruence theorem.
2. The information is not enough.
3. Both are congruent by the HL congruence theorem.
What is the HL Congruence Theorem?If two triangles have a pair of congruent hypotenuses and a pair of congruent legs, then both triangles ae congruent to each other based on the HL congruence theorem.
What is the SSS Congruence Theorem?The SSS Congruence Theorem states that if any two triangles have three pairs of corresponding sides that are congruent to each other, then the triangles are congruent.
1. Based on the SSS congruence theorem, the pair of angles in figure 1 are congruent.
2. There is no information available that shows the triangles have a pair of congruent hypotenuses, nor have three pairs of corresponding congruent sides. Th information given is not enough to prove that they are congruent by SSS or HL.
3. Based on the HL congruence theorem,, they are congruent to each other.
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r packages include sample datasets. they also include reusable r functions and documentation about how to use the functions. t/f
Answers
r packages include sample datasets. they also include reusable r functions and documentation about how to use the functions this statement is true.
What is function?Function in math is a mathematical relationship between two variables where one is dependent on the other. This relationship can be expressed as an equation, graph, or table. Every input has one and only one output. This means that the output of a function is determined by the input given. Functions can be used to model real-world phenomena, helping us to make predictions and solve problems.
Packages offer a great way to save time and energy when working with data in r.
R packages are a great way to save time and energy when working with data in R. They provide a convenient way to access multiple datasets, functions, and documentation in one place. Additionally, many packages also contain sample data and code examples to help users quickly get up and running with their data analysis.
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Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
Given: ∠ABC ≅ ∠DCB; ∠DBC ≅ ∠ACB
Answers
Answer:
[tex]\triangle ABC \cong \triangle DCB[/tex] by ASA
Step-by-step explanation:
[tex]\overline{BC} \cong \overline{BC}[/tex], so [tex]\triangle ABC \cong \triangle DCB[/tex] by ASA.
Solve |2x - 2 ≥ 6.
A. x≤-2 or x ≥ 4
B. x ≤3 or x ≥ 5
C. x ≤-2 or x ≥ 5
D. x ≤-2 or x ≥ 6
Answers
If f(x)=x^3-3x^2-18x+40f(x)=x 3 −3x 2 −18x+40 and f(-4)=0f(−4)=0, then find all of the zeros of f(x)f(x) algebraically.
Answers
By using algebra equation, the zeros of f(x)f(x) is ;
x = (-4 + 2i) and x = (-4 - 2i)
How to solve algebra equation ?Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for using them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.Four methods can be used to solve one-step equations: addition, subtraction, multiplication, and division. If we add the same amount to both sides of an equation, both sides will remain equal.In algebra 1, we are introduced to the addition rule and the multiplication/division rule as two ways to solve problems. The equation addition rule states that the solution set of an equation can have the same amount added to both sides without changing.Given data :
This is a synthetic division shortcut. Write down the real root, then under a division symbol, the coefficients of the variables, 2, 18, 56, and 40. Drop down the 2 first, multiply by the root (-1) and add it to the next coefficient (18). 2*(-1) = -2, -2 + 18 = 16. Drop that one down. Next multiply 16 by the root, (-1) and add that to the next coefficient, 56 + (-16) = 40, drop down the 40, then lastly repeat this, multiply 40 by the root (-1) and add to the last coefficient 40 + (-40) = 0. If the remainder was not 0, then -1 would not have been a real root.
-1 | 2 18 56 40
......0 -2 -16 -40
--------------------
......2 16 40 0
Put these into another equation, (2x2 + 16x + 40)
Factoring out a 2 we get 2(x2 + 8x + 20)
The factors of 20 are 2*10 and 4*5. 2+10 = 12, 4+5 = 9, so we must use the quadratic equation to find our roots.
-8 ± √(64 - 4(20))/2 = -4 ± √(-16)/2 = -4 ± 4i/2 = -4 ± 2i
So the other two roots are x = (-4 + 2i) and x = (-4 - 2i)
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Can someone help me pls
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Answer:
Okay so for this one use the Pythagorean theorem
Step-by-step explanation:
A^2 + 28^2 = 128^2
You are trying to find A.
So 28^2 is 784
128^2 is 16384
Now you will subtract 784 from both sides of the equation your new equation should be this: a^2 = 15600
Now you find the square root of both sides which gives you: A= 124.89 round it to 125
A landscape architect designed a flower garden in the shape of a trapezoid.
The area of the garden is 13.92 square meters. A fence is planned around the perimeter of the garden. How many meters of fencing are needed?
Answers
By using area of trapezium, it can be calculated that-
Length of fencing needed in 15.88m
What is area of trapezium?
Area of trapezium is the total space taken by the trapezium.
If the length of parallel sides be a and b and distance between the parallel sides are d,
Area of trapezium = [tex]\frac{1}{2}\times(a + b) \times (d)[/tex]
Length of the parallel sides = [tex]b_1[/tex] m and 5.28 m
Length of non parallel sides = 3.3 m and 3.3 m
Distance between parallel sides = 3m
Area of trapezium = [tex]\frac{1}{2} \times (b_1 + 5.28) \times 3[/tex]
By the problem,
[tex]\frac{1}{2} \times (b_1 + 5.28) \times 3 = 13.92[/tex]
[tex]b_1 + 5.28 = 13.92 \times \frac{2}{3}\\b_1 + 5.28 = 9.28\\b_1 = 9.28 - 5.28\\b_1 = 4 \m[/tex]
Length of fencing needed = 4 + 5.28 + 3.3 + 3.3 = 15.88 m
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In triangle ABC acute angles are in the ratio 5:1, i.e.
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Answer:
The quen is as following:
ABC is a right triangle at C,
Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1
If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.
The solution is: m∠HCL = 30°
Step-by-step explanation:
See the attached figure.
∵The triangle is right at C ∴∠C = 90°
∴∠A + ∠B = 90° ⇒(1)
∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1
∴∠A = 5 times ∠B
Substitute at (1)
∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15° and ∠A = 75°
∵CL is an angle bisector of ∠ACB
∴ ∠ACL = 90°/2 = 45°
∵ CH is an altitude to AB ⇒ ∠CHA = 90°
At the triangle AHC:
∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°
∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°
A system of equations is shown.
x = -2y - 3.5
-5x + 3y = -15
What is the value of x + y?
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The value of the variable x and y will be 1.5 and -2.5, respectively. Then the value of the expression (x + y) will be negative 1.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A system of equations is given below.
x = -2y - 3.5 ...1
-5x + 3y = -15 ...2
From equations 1 and 2, then we have
-5(-2y - 3.5) + 3y = -15
10y + 17.5 + 3y = - 15
13y = -32.5
y = - 2.5
Then the value of the variable 'x' is calculated as,
x = - 2(-2.5) - 3.5
x = 5 - 3.5
x = 1.5
Then the value of the expression (x + y) is calculated as,
x + y = 1.5 + (-2.5)
x + y = 1.5 - 2.5
x + y = - 1
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Write an equation in slope-intercept form (-5,-7);y=-2x+4
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Answer:
Step-by-step explanation:
First, let us substitute x and y values: -7 = -2(-5) + 4
Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).
Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:
14 + b = -7
by simplifying, we can conclude that b = -21
Finally, we can plug in the b-value into our original equation:
y = -2x + 4 - 21
After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).