Answer:
Izelle payed $44.80 for the mangoes
Step-by-step explanation:
Find 12% of $40.00 It is $4.80Add the $4.80 to the $40.00Your answer is $44.80!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.
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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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;
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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Which is greater?
3
5 or 130
Solve this equation (Shown in the screenshot below)
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.
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
show that (2n-5)^2 - 13 is a multiple of 4 for all integers
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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A fish detects vibrations in the water around it by means of its lateral lines, rows of sensory receptors along each side of the body. Based on what you know about sensory receptors, the lateral line receptors are probably
A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. The lateral line receptors are most likely is Mechanoreceptors.
Given that,
A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it.
We have to find according to your understanding of sensory receptors, the lateral line receptors are most likely is.
We know that,
A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. According to your understanding of sensory receptors, the lateral line receptors are most likely is Mechanoreceptors.
What is Mechanoreceptor?Mechanoreceptors, also known as Mechanoreceptors, are specialized neurons that react to pressure and deformation caused by mechanical forces. They are surrounded by sensory neurons, which translate external pressure into electrical signals that are sent to the brain.
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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
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
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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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.
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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pls help if you get it correct u will get 100 brainly points
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
r packages include sample datasets. they also include reusable r functions and documentation about how to use the functions. t/f
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
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.
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
This question doesn't seem completed to me. Is there anything more after this?
pls help me i will mark brainliest:)
Simplify −5g(3g + 4).
−15g + 4
−15g − 20g
−15g2 + 4
−15g2 − 20g
Answer:
D = -15g² - 20g
-5g × 3g -5g×4
= -15g² -20g
# to put in ² when typing hold 2 for 5seconds...
#like please
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?
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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Three groups of research participants have played a game with various amounts of violence and were assessed on a stress-related scale (where 0 = no stress, 100 = very stressed) afterwards. The first group of participants (Group 1) have played a non-violent game. The second group of participants (Group 2) have played a moderately violent game. The third group of participants (Group 3) have played a very violent game. The researchers would like to know if the results on a stress scale differ for these groups. What is the null hypothesis? (2 points) Your answer: What is the research hypothesis?
Since, F value is =19.056 is greater than F critical value =3.3541
Therefore, We have enough evidence that null hypothesis is not rejected
What is hypothesis ?A hypothesis is a theory that is put up to account for a phenomenon. Unless it can be tested through the scientific method, a hypothesis cannot be referred to as a scientific hypothesis. Scientific theories frequently begin with historical observations that cannot currently be fully explained by existing knowledge.
Here,
Null hypothesis,
[tex]H_{0}[/tex]: u1 = u2 =u3
u1,u2,u3 are means of stress scale for group 1 , group 2 and group 3
Alternate hypothesis,
[tex]H_{A}[/tex] : u1≠u2
The F value is =19.056
Using F critical value α=0.05
df numerator =2 , df denominator = 27
F critical value =3.3541
Conclusion : F value is =19.056 is greater than F critical value =3.3541
Therefore, We have enough evidence that null hypothesis is not rejected
We, conclude that all three groups are equals in terms of mean.
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help multipy
look at the picture
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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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
Please help please and thank you
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
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
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
Graph the image of the given triangle after the transformation that has the rule (x, y) → (x - 1, y + 5).
Select the Polygon tool. Click the points of the triangle vertices to create the triangle by connecting the sides.
HELP FAST!!!!
INVESTMENTS Your aunt receives an inheritance of $20,000. She wants to
put some of the money into a savings account that earns 2% interest annually and
invest the rest in certificates of deposit (CDs) and bonds. A broker tells her that
CDs pay 5% interest annually and bonds pay 6% interest annually. She wants to
earn $1000 interest per year, and she wants to put twice as much money in CDs
as in bonds. How much should she put in each type of investment?
11.
Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.
We follow these steps in order to arrive at the answer:
Let the amount invested in bonds be x
Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.
The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x
The interest earned on bonds will be 0.06x0.06x
The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x
The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x
The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.
Hence total interest is:
1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x
Simplifying we get,
1000 -400 = 0.1x1000−400=0.1x
600 = 0.1x600=0.1x
\mathbf{x = 6,000}x=6,000
Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000
Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000
Write an equation in slope-intercept form (-5,-7);y=-2x+4
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).
The line of best fit is given as y = -5 - 8x. Find the value of y when x = 4.
Answer:
y = -37
Step-by-step explanation:
y = -5 - 8x
y = -5 - 8(4)
y = -5 + ( - 8 x 4 )
y = -5 + ( - 32)
y = -37
(8k^3 - 19 k^2 + 2k + 10) /(k - 2) = ?
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]
Write the equation of the line that has a slope of 1 and goes through the point (2, 3). Hint: Use y = mx+b
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
A system of equations is shown.
x = -2y - 3.5
-5x + 3y = -15
What is the value of x + y?
Show all work to receive full credit for this question. You may show your work by writing in the text box or by taking a picture of your work and uploading it use the embed image button.
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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In triangle ABC acute angles are in the ratio 5:1, i.e.
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°
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