The complete table is
Whose card Length Width Perimeter Area
Sanya 10 cm 8cm 36cm 80 cm²
The perimeter of a shape is the distance around its edges. For a rectangle, like Sanya's greeting card, the perimeter can be found by adding up the lengths of all four sides. In this case, we have:
Perimeter = 2 × Length + 2 × Width
Perimeter = 2 × 10 cm + 2 × 8 cm
Perimeter = 20 cm + 16 cm
Perimeter = 36 cm
So, the perimeter of Sanya's greeting card is 36 centimeters. This means that if you were to walk all the way around the edges of the card, you would cover a distance of 36 centimeters.
The area of a shape is the amount of space it takes up. For a rectangle, the area can be found by multiplying its length by its width. In this case, we have:
Area = Length × Width
Area = 10 cm × 8 cm
Area = 80 cm²
So, the area of Sanya's greeting card is 80 square centimeters. This means that if you were to cover the card completely with paint or ink, you would need 80 square centimeters of paint or ink.
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Complete Question:
Sanya made greeting cards. Complete the table for their cards:
Whose card Length Width Perimeter Area
Sanya 10 cm 8cm
Karen invested her savings in two investment funds. The amount she invested in Fund A was 4 times as much as the amount she invested in Fund B. Fund A returned a 4% profit and Fund B returned a 7% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1380?
Karen invested $6000 in Fund B, and $24000 in Fund A, as the weighted average of the two funds' returns is 5%, yielding a total profit of $1380, and we can use a system of equations to solve for the amounts invested in each fund.
To solve this problem, we can set up a system of equations using the information given.
Let x be the amount invested in Fund B, then the amount invested in Fund A is 4x. The total amount invested is the sum of these two amounts, so we have:
x + 4x = 5x = total amount investedThe total profit from the two funds is given as $1380, which is the sum of the profits from Fund A and Fund B.
We can express these profits using the amounts invested and the respective return rates:
0.04(4x) + 0.07(x) = 0.16x + 0.07x = 0.23x = $1380Solving for x, we find that x = $6000, which is the amount invested in Fund B. Therefore, the amount invested in Fund A is 4x = $24000.
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Subtract.x2+3xy−4y26x−3y−x2+xy−2y25x+3yx2+3xy−4y26x−3y−x2+xy−2y25x+3y=(Simplify your answer. Type your answer in factored form.)
The factored form is 2y(x - y) - 11x.
What is factored form?Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.
To simplify the given expression, we need to combine like terms and factor if possible.
First, let's combine the like terms:
x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y
= 2xy - 2y^2 - 11x
Next, let's see if we can factor the expression:
2xy - 2y^2 - 11x
= 2y(x - y) - 11x
Since we cannot factor any further, the simplified expression in factored form is:
2y(x - y) - 11x
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what equivalent expression for (32 • 54)3?
Answer:
5,184 from my knowledge
The number of blueberry muffins that a baker makes each day is 30% of the total number of muffins she makes.
A. On Monday, the baker makes 42 blueberry muffins. What is the total number of muffins that the baker makes on Monday?
B. On Tuesday, the baker makes a total of 60 muffins. How many blueberry muffins does the baker make on Tuesday?
The baker makes a total of 140 muffins on Monday.
The baker makes 18 blueberry muffins on Tuesday.
What are percentages?
Percentages are a way of expressing a fraction or proportion out of 100. The term "percent" literally means "per hundred." Percentages are commonly used in many areas of everyday life, including finance, science, and statistics.
To express a number as a percentage, it is multiplied by 100. For example, 0.75 is equivalent to 75 percent, since 0.75 x 100 = 75. Similarly, 50 percent is equivalent to 0.5 or 1/2.
Percentages are commonly used to express changes and comparisons. For example, if a product's price increases from $100 to $120, this represents a 20 percent increase in price. If a person scored 80 out of 100 on a test, this represents an 80 percent score.
Percentages are also used to calculate percentages of a total. For example, if a person earned $40,000 out of a total company income of $500,000, their income represents 8 percent of the total income. Similarly, if a person wants to calculate a 20 percent tip on a $50 meal, they would calculate 20 percent of $50, which is $10.
In summary, percentages are a way of expressing a fraction or proportion out of 100, and are commonly used to express changes, comparisons, and percentages of a total in everyday life.
A. Let's assume the total number of muffins the baker makes on Monday to be x.
According to the problem, the number of blueberry muffins that the baker makes is 30% of the total number of muffins.
So, 30% of x is equal to 42:
0.30x = 42
To solve for x, we can divide both sides by 0.30:
x = 140
Therefore, the baker makes a total of 140 muffins on Monday.
B. Let b be the number of blueberry muffins the baker makes on Tuesday.
According to the problem, the number of blueberry muffins is still 30% of the total number of muffins. So, we can set up the equation:
0.30(60) = b
Simplifying the left side:
18 = b
Therefore, the baker makes 18 blueberry muffins on Tuesday.
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3. John wants an average bowling score of 215. If he scored 159, 182, 225, 240, 198,
200 and 230 on his first seven games, what must he score on his 8th game to achieve
this average?
John must score 286 on his 8th game to achieve an average score of 215.
What is an Average?
Average, also known as the mean, is a mathematical concept that represents the central value of a set of numbers. It is found by dividing the sum of the numbers by the total count of the numbers.
To find out what John must score on his 8th game to achieve an average score of 215, we need to use the formula for calculating the average or mean:
Average = (Sum of Scores) / (Number of Scores)
We can use this formula to solve for the unknown score:
215 = (159 + 182 + 225 + 240 + 198 + 200 + 230 + x) / 8
Multiplying both sides by 8, we get:
1720 = 159 + 182 + 225 + 240 + 198 + 200 + 230 + x
Simplifying, we get:
1720 = 1434 + x
Subtracting 1434 from both sides, we get:
x = 286
Therefore, John must score 286 on his 8th game to achieve an average score of 215.
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Answer this quickly please
The size of the angle that the line DE makes with the plane ABCD is 50.8 degrees
How to determine the measure of the angleFrom the question, we have the following parameters that can be used in our computation:
The figure
To start with, we calculate the measure of length BE using the following tangent ratio
tan(60) = BE/60
So, we have
BE = 60√3
Next, we calculate DB using the Pythagoras theorem
DB = √(60² + 60²)
Evaluate
DB = 60√2
The measure of the required angle is then calculated as
tan(Angle) = 60√3/60√2
Evaluate
tan(Angle) = 1.2247
Take the arc tan
Angle = 50.8 degrees
Hence, the angle is 50.8 degrees
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A 70% increase followed by a 50% decrease, is it greater than original, smaller or same as
Answer:
1.7 × .5 = .85
15% smaller than the original
Using the formula for finding the simple interest, I = Prt, find the Interest earned in a savings account by depositing $9,800 for 15 months at 5% simple interest
let's recall that a year has 12 months, thus 15 months is really 15/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases} \\\\\\ I = (9800)(0.05)(\frac{5}{4}) \implies I = 612.5[/tex]
The angle of elevation of the sun is 41°. The shadow of a building is 32 feet long. How tall is the building? Round your answer to the nearest hundredth.
This is an EMERGENCYYY
The height of the building is approximately 27.62 feet. Rounded to the nearest hundredth, the answer is 27.62 feet.
What connection exists between height and separation?In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.
What use do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It is used to determine the distance between any two objects, including heavenly bodies or other objects, as well as the height of towers, buildings, mountains, etc. Astronauts, surveyors, architects, and navigators are the main users.
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4. Write the function rule for g(x) from f(x) = √x. Shift up 5, then vertical stretch by a factor of 2, followed by a shift to the right 3 units.
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
The function rule for g(x) from f(x) = √x can be found by applying the given transformations to f(x). First, we shift up 5 units by adding 5 to the function. Then, we apply a vertical stretch by a factor of 2 by multiplying the function by 2. Finally, we shift to the right 3 units by replacing x with (x - 3) in the function. The resulting function rule for g(x) is:
g(x) = 2√(x - 3) + 5
This function rule represents the original function f(x) = √x, shifted up 5 units, vertically stretched by a factor of 2, and shifted to the right 3 units.
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given the figure below with the provided measurements, what is PQ?
The requried measure of the PQ in the triangle PQT is 16 in.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
A figure of triangles has been shown, ΔPQT and ΔORS.
We have to determine the measure of side PQ.
Since the given triangle is similar to one another, we can apply the property of proportionality between the similar triangles. By which:
PR/PQ = RS/QT
PQ + 4 / PQ = 10/8
8PQ + 32 = 10PQ
2 PQ = 32
PQ = 16 in
Thus, the requried measure of the PQ in the triangle PQT is 16 in.
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Rewrite the logarithmic expression as a single logarithm with the same base. Assume all expressions exist and are well-defined. Simplify any fractions. 9log_(4)2-log_(4)40
The logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex].
To rewrite the logarithmic expression as a single logarithm with the same base means that we have to do logarithmic expression simplification.
To do so, we can use the logarithmic properties:
[tex]log_{b} (a)[/tex] + [tex]log_{b} (c)[/tex] = [tex]log_{b} (ac)[/tex]
[tex]log_{b} (a)[/tex] - [tex]log_{b} (c)[/tex] = [tex]log_{b} (a/c)[/tex]
b · [tex]log_{a} (x)[/tex] = [tex]log_{a} (x^{b} )[/tex]
Using these properties, we can rewrite the given expression:
9 · [tex]log_{4} (2)[/tex] - [tex]log_{4} (40)[/tex] = [tex]log_{4} (2^{9} )[/tex] - [tex]log_{4} (40)[/tex]
= [tex]log_{4} (512)[/tex] - [tex]log_{4} (40)[/tex]
= [tex]log_{4} (512/40)[/tex]
= [tex]log_{4} (12.8)[/tex]
So the logarithmic expression can be rewritten as a single logarithm with the same base as [tex]log_{4} (12.8)[/tex]
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Factor 36x^4 -25 completely
Answer: (6x²+5) (6x²- 5)
Please give me brainliest :)
Step-by-step explanation:
Solve the quadratic equation x2+8x+30=0 by completing the square.
Answer:
(x + 4)2 = -26 x = -4 ± √26
Step-by-step explanation: x2 + 8x + 30 = 0
x2 + 8x = -30
x2 + 8x + (8/2)2 = -30 + (8/2)2
(x + 4)2 = -22
x + 4 = ±√22
x = -4 ± √22
math sucks lol
A track runner ran for 15 minutes, walked for 15 minutes, ran for another 20 minutes, and then walked for 10 minutes.
Which graph describes the relationship between runner's total distance and time?
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 2.4, and a horizontal line segment from 0.8 comma 2.4 to 1 comma 2.4
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a horizontal line segment from 0.25 comma 1.25 to 0.5 comma 1.25, a line segment from 0.5 comma 1.25 to 0.8 comma 0.1, and a horizontal line segment from 0.8 comma 0.1 to 1 comma 0.1
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a line segment from 0.8 comma 2.95 to 1 comma 3.15
Answer:
Step-by-step explanation:
graph with the x axis labeled time in hours and the y axis labeled total distance in miles, with a line segment from 0 comma 0 to 0.25 comma 1.25, a line segment from 0.25 comma 1.25 to 0.5 comma 1.75, a line segment from 0.5 comma 1.75 to 0.8 comma 2.95, and a horizontal line segment from 0.8 comma 2.95 to 1 comma 2.95
It's B.
Explanation: I took the test
f(x) = 2^x +2: shifts 2 units left
g(x)=
Exponential Functions
Answer:
g(x) = f(x + 2) = 2^(x + 2) + 2
Step-by-step explanation:
To shift the function f(x) = 2^x + 2 two units to the left, we need to replace x with (x + 2) in the equation. This will shift the graph horizontally to the left by two units.
So, the new function g(x) that represents the shifted graph is:
g(x) = f(x + 2) = 2^(x + 2) + 2
Math question 12 help
Answer:
It's neither of them. The function is neither odd nor even
The sum of the digits of a certain two-digit number is 3. Reversing its digits decreases the number by 27. Find the number.
The number is 30.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum
Given that,
The sum of the digits of a certain two-digit number is 3.
Since it is a two digit number, there will be a tens place and a ones place.
Let x be the digit in tens place and y be the digit in ones place.
x + y = 3
The number can also be written as 10x + y, since x is in the tens place.
When the number is reversed, tens place changed to ones place and vice versa.
The reversed number is 10y + x.
Given that the value of the number is decreased by 27 when the digits is reversed.
Original number - 27 = Reversed number
10x + y - 27 = 10y + x
9x - 9y = 27
x - y = 3
Also, we have,
x + y = 3 [Equation 1]
x - y = 3 [Equation 2]
Adding the equations,
2x = 6
x = 6/2 = 3
Substituting in equation 1, y = 0
Hence the number is 30.
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Create a rational expression with the following constraints Your rational expression must: have a binomial in the numerator roduce to: (1)/(2x-3)
The rational expression (2x-3)/((2x-3) (2x-3)) satisfies the given constraints.
To create a rational expression with the given constraints, we need to have a binomial in the numerator that cancels out with a binomial in the denominator to produce the desired expression, (1)/(2x-3).
One way to do this is to multiply the desired expression by a binomial that is the same as the one in the denominator. This will give us a rational expression with the desired constraints.
For example, we can multiply (1)/(2x-3) by (2x-3)/(2x-3) to get:
(1 * (2x-3))/((2x-3) * (2x-3))
Simplifying the numerator and denominator gives us:
(2x-3)/((2x-3)(2x-3))
This rational expression has a binomial in the numerator and simplifies to the desired expression, (1)/(2x-3).
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Two angles in a triangle measure 102 and 54. What measure of the third angle?
Answer:
24
Step-by-step explanation:
The sum of the three angles in a triangle is always 180 degrees.
Let x be the measure of the third angle.
Then we have:
102 + 54 + x = 180
Simplifying the left side:
156 + x = 180
Subtracting 156 from both sides:
x = 180 - 156
x = 24
Therefore, the measure of the third angle is 24 degrees.
If pure water is added to a 15% alcohol solution, what percent alcohol is being added?
If I understand your question correctly, pure water is 0% alcohol, so by adding water, this will dilute your 15% alcohol solution and lower the percentage of alcohol in the solution.
Many word problems are set up like "You have some amount of 15% alcohol solution and you add some pure water. You end up with some other amount of the diluted mixture. How much 15% alcohol solution and how much pure water were mixed."
For those ones, use 0% alcohol for your pure water.
The price of drugs for human doses and the animal doses from different pharmacies were gathered. At 1% level, the prices for the animal doses are claimed to be significantly less than the prices for the human doses. Assume that data is normally distributed and the groups have equal variances. The output of the test is given below. For the next questions, please refer to this problem. Using p-value method, form a statistical decision. 1 point a. Failed to reject the alternative hypothesis. b. Reject the null hypothesis. c. Failed to reject the null hypothesis.
d. Reject the alternative hypothesis.
The correct answer is c. Failed to reject the null hypothesis.
Failed to reject the null hypothesis.
Explanation:
In this problem, we are given the price of drugs for human doses and animal doses from different pharmacies. We are asked to form a statistical decision using the p-value method. The null hypothesis is that the prices for the animal doses are equal to the prices for the human doses, while the alternative hypothesis is that the prices for the animal doses are significantly less than the prices for the human doses.
To form a statistical decision, we need to compare the p-value with the level of significance (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.
In this case, the level of significance is 1% (α=0.01). Since the p-value is not given in the problem, we cannot make a decision. Therefore, the correct answer is c. Failed to reject the null hypothesis.
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The linear system shown is equivalent
The linear system shown is "inconsistent" in nature.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
The given figure is represented linear system represents two parallel lines.
Now, the solution set of the two system of equations could be find by finding their points of intersection.
And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.
Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.
And when the system of linear equation has no solution , then the system is said to be inconsistent.
Hence, The linear system shown is "inconsistent" in nature.
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The complete question is;
The linear system shown is _____.
independent
equivalent
inconsistent
Graph the solution to the following system of inequalities.
v55x - 2
y>-28+5
Answer: See attached.
Step-by-step explanation:
Since the first equation uses a ≤ symbol, we know we will use a solid line. This is because it is less than and equal to. Then, we will graph it as a regular slope-intercept line.
This line has a slope of 5 and a y-intercept of -2. This means we will start at (0, -2) and move five units up for every unit right, or five units down for every unit left.
For the next equation, it uses a > symbol so we will use a dashed line. This is because it is not equal to, only greater than. Same as the previous. We will graph it as a slope-intercept line, but using a dashed line instead of a solid line.
This line has a slope of -2 and a y-intercept of positive 5. This means we will start at (0, 5) and move two units down for every unit right, or two units up for every unit left.
1) A 20 lb. BAG OF GRASS SEED WILL COVER AN AREA OF 10,000 ft2 . HOW MANY POUNDS WILL YOU NEED TO COVER AN AREA OF 140,000 ft2 . HOW MANY WHOLE BAGS OF SEED WILL YOU NEED TO BUY? WRITE THE EQUATION FOR A PROPORTION AND SOLVE IT.
2) SOLVE THE FORMULA FOR T2. ???????????????? ???????? = ???????????????? ????????
3) THE GILBERTS PURCHASED A CAR. IF THE TOTAL COST, INCLUDING A 5% SALES TAX, WAS $14,512, FIND THE COST OF THE CAR BEFORE TAX.
4) JIM MEYERS BOUGHT A NEW LAPTOP COMPUTER AT A 15% OFF SALE. IF THE SALE PRICE WAS $722.50, WHAT WAS THE LIST PRICE OF THE COMPUTER?
5) FIND THE x AND y INTERCEPTS FOR THE EQUATION 3x + 6y = 9.
1) 140
2) T2 = ?
3) $13,786.40
4) $835.88
5) x = 3, y=(0, 1.5)
1) To find the number of pounds of grass seed needed to cover an area of 140,000 ft2, you need to write a proportion and solve it. Set up the proportion using the given information:
20 lb/10,000 ft2 = x lb/140,000 ft2
To solve for x, multiply both sides of the equation by 140000:
20 lb * 140000/10,000 ft2 = x lb
x = 2800 lb
You will need 2800 lbs of grass seed to cover an area of 140,000 ft2. To find out how many whole bags of seed you will need to buy, divide the total number of pounds by the number of pounds in a bag, which is 20 lbs. You will need to buy 140 whole bags of seed.
2) To solve for T2 in the equation ???????????????? ???????? = ???????????????? ????????, divide both sides of the equation by ???????????????? :
T2 = ???????????????? ????????/????????????????
3) To find the cost of the car before the sales tax, subtract the 5% sales tax from the total cost. The formula is:
Cost before tax = Total Cost - (Total Cost * Sales Tax %)
Cost before tax = $14,512 - ($14,512 * 0.05) = $13,786.40
4) To find the list price of the laptop computer, add the 15% off sale to the sale price. The formula is:
List Price = Sale Price + (Sale Price * Discount %)
List Price = $722.50 + ($722.50 * 0.15) = $835.88
5) The x and y intercepts for the equation 3x + 6y = 9 can be found by setting x or y equal to 0 and solving for the other. To find the x intercept, set y = 0:
3x + 6(0) = 9
3x = 9
x = 3
The x intercept is (3, 0). To find the y intercept, set x = 0:
3(0) + 6y = 9
6y = 9
y = 1.5
The y intercept is (0, 1.5).
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Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3
The transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I includes a horizontal shift of 3 units to the right, a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift of 3 units up.
The transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I can be described as follows:
The parent function is shifted 3 units to the right. This is indicated by the "-3" inside the absolute value bars in the equation.
The parent function is vertically stretched by a factor of 2. This is indicated by the "-2" in front of the absolute value bars in the equation.
The parent function is reflected across the x-axis. This is indicated by the negative sign in front of the "2" in the equation.
The parent function is shifted 3 units up. This is indicated by the "+3" outside the absolute value bars in the equation.
In summary, the transformation of the equation y = -2 I x - 3 I + 3 from the parent function y = I x I includes a horizontal shift of 3 units to the right, a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift of 3 units up.
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find the measure of ycg
Answer:
59
Step-by-step explanation:
Opposite angles are equal
C or KCG isn121
Straight line angle is 180
YCG + GCK = 180
YCG = 180- 121
Another method
All the four angles at a point is 360
YCH + HCK + KCG +YCG is 360
C is 121
121 + X + 121 + X = 360
2X + 242 =360
Subract 242 from both sides
2X = 118
Divide both sides by 2 = 59
3 mi. and 10,000 ft.
is the same equal or different
Answer:
3 Miles
Step-by-step explanation:
3 mi = 15,840ft.
15,840 is greater than 10,000, so 3 miles is more
Consider the following matrix.λ003λ+1201λFind the determinant of the matrix. Find the values ofλfor which the determinant is zero. (Enter your answers as a comma-separated list.)λ=
This equation has two solutions: λ = 0 and λ = -1
The determinant of a matrix is given by the formula:
det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)
In the given matrix, the values of a11, a22, and a33 are λ, (λ+1), and λ respectively. The values of a12, a13, a21, a23, a31, and a32 are all 0. Substituting these values into the formula for the determinant gives:
det(A) = λ((λ+1)λ - 0) - 0(0 - 0) + 0(0 - 0) = λ^3 + λ^2
To find the values of λ for which the determinant is zero, we can set the determinant equal to zero and solve for λ:
λ^3 + λ^2 = 0
λ^2(λ + 1) = 0
This equation has two solutions: λ = 0 and λ = -1. Therefore, the values of λ for which the determinant is zero are 0 and -1. The answer can be written as a comma-separated list as follows:
λ = 0, -1
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FRACTIONS Additive property of equality with fractions and mixed numbers Solve for u. u-(3)/(4)=5(1)/(3) u
The solution for u-(3)/(4)=5(1)/(3) u is 2(5)/(12).
The additive property of equality states that if the same amount is added to both sides of an equation, the equation remains true. In this case, we can use the additive property of equality to solve for u by isolating the variable on one side of the equation.
Step 1: Add (3)/(4) to both sides of the equation to cancel out the subtraction on the left side of the equation.
u-(3)/(4)+(3)/(4)=5(1)/(3)+(3)/(4)
Step 2: Simplify the left side of the equation.
u=5(1)/(3)+(3)/(4)
Step 3: Find a common denominator for the fractions on the right side of the equation and combine them.
u=20(1)/(12)+(9)/(12)
Step 4: Simplify the right side of the equation.
u=29/(12)
Step 5: Convert the improper fraction to a mixed number.
u=2(5)/(12)
Therefore, the solution for u is 2(5)/(12).
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