To solve the equation with absolute value expressions, isolate the absolute value terms and solve two separate equations. The solutions are x = -1 and x = 1.
Explanation:To solve the equation 1/2 - x/3 = 5/6 with the absolute value expressions, we need to isolate the absolute value terms and solve two separate equations. First, rewrite the equation as |-x/3| = 5/6 - 1/2. Since the absolute value of a number is always positive, we can remove the absolute value symbols by considering the positive and negative cases separately.
For the positive case, we have -x/3 = 5/6 - 1/2. Simplifying, we get -x/3 = 1/3. Multiplying both sides by -3, we find x = -1. For the negative case, we have -(-x/3) = 5/6 - 1/2. Simplifying, we get x/3 = 5/6 - 1/2. Combining like terms, we have x/3 = 1/3. Multiplying both sides by 3, we find x = 1. Therefore, the solution set to the equation is {-1, 1}.
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On level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long. how many feet tall is the flagpole?
Answer:
36 feet.
Step-by-step explanation:
We have been given that on level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long.
To find the length of flagpole, we will use proportions as:
[tex]\frac{\text{Actual length of flagpole}}{\text{Shadow of flagpole}}=\frac{\text{Actual length of rod}}{\text{Shadow of rod}}[/tex]
Substitute given values:
[tex]\frac{\text{Actual length of flagpole}}{12\text{ ft}}=\frac{12\text{ ft}}{4\text{ ft}}[/tex]
[tex]\frac{\text{Actual length of flagpole}}{12\text{ ft}}\times 12\text{ ft}=\frac{12\text{ ft}}{4\text{ ft}}\times 12\text{ ft}[/tex]
[tex]\text{Actual length of flagpole}=12\text{ ft}\times 3[/tex]
[tex]\text{Actual length of flagpole}=36\text{ ft}[/tex]
Therefore, the actual length of flagpole is 36 feet.
A group of art students are painting a mural on a wall. The rectangular dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?
Answer:
The area of remaining wall after the mural has been painted is [tex]46x^2+73x+15[/tex] square units.
Step-by-step explanation:
If the dimensions of a rectangle are l and w, then area of rectangle is
[tex]A=l\times w[/tex]
The dimensions of wall are (6x+7) and (8x+5). So, the area of wall is
[tex]A_1=(6x+7)\times (8x+5)[/tex]
[tex]A_1=6x(8x+5)+7(8x+5)[/tex]
[tex]A_1=48x^2+30x+56x+35[/tex]
[tex]A_1=48x^2+86x+35[/tex]
The dimensions of mural are (x+4) and (2x+5). So, the area of mural is
[tex]A_2=(x+4)\times (2x+5)[/tex]
[tex]A_2=x(2x+5)+4(2x+5)[/tex]
[tex]A_2=2x^2+5x+8x+20[/tex]
[tex]A_2=2x^2+13x+20[/tex]
The area of remaining wall after the mural has been painted is
[tex]A=A_1-A_2[/tex]
[tex]A=48x^2+86x+35-(2x^2+13x+20)[/tex]
[tex]A=48x^2+86x+35-2x^2-13x-20[/tex]
[tex]A=46x^2+73x+15[/tex]
Therefore area of remaining wall after the mural has been painted is [tex]46x^2+73x+15[/tex] square units.
Answer:
46x^2 + 73x + 15
Step-by-step explanation:
Factor the polynomial. 6x2 - 7x - 3 A) (6x - 1)(x + 3) B) (6x + 3)(x - 1) C) (2x - 3)(3x + 1) D) (3x - 3)(2x + 1)
19/8 as a mixed number
Solve each system using elimination.
3x+3y=27
x-3y=-11
9. 2x+4y=22
2x-2y=-8
11. 5x-y=0
3x+y=24
Please show your work!! Thank you!!
name the postulate or theorem, 50 points please help!
When you use postulates and theorems, you need to make sure to only use the given information that you know. Look for the given statements, and congruence marks on the figure. Those are also considered gives
Which of the following statements best describes the graph of x + y = 4?
It is a line which intersects the x-axis at (4, 4).
It is a line which intersects the y-axis at (4, 4).
It is a line joining the points whose x- and y-coordinates add up to 8.
It is a line joining the points whose x- and y-coordinates add up to 4.
What is the value of x?
The waiter places a bowl in front of Caesar. In a counterclockwise direction, he passes the soup to jada who then passes it to Haifa. Which two rotations about the center of the table describes passing the soup?
A) First 200° and then 80°
B) First 180° and then 72°
C) First 150° and then 60°
D) First 100° and then 40°
Answer:
Step-by-step explanation:
first 150 then 60
The question is asking for the correct degree of rotations to simulate the passing of a soup bowl at a circular table. Without specific arrangement details, it's challenging to give a definitive answer, but if people are equidistant, option B 'First 180° and then 72°' would be the closest match.
Explanation:The question asks which two rotations about the center of a circular table would describe the passing of a soup bowl from Caesar to Jada and then to Haifa. Given that the rotation is counterclockwise, we must determine the correct degree of rotations that match the sequence of passing the soup. We can visualize the table as a circle and consider that a full rotation around a circle is 360°.
Depending on the actual arrangement of the people around the table, the combined angles of rotation to pass the soup from Caesar to Jada to Haifa should add up to less than 360°, as they would not have gone a full circle. If we were to look at the options provided:
First 200° and then 80° adds up to 280°,First 180° and then 72° adds up to 252°,First 150° and then 60° adds up to 210°,First 100° and then 40° adds up to 140°.The only way to determine the correct answer is to know the specific arrangement of people around the table, which the question does not provide. Without this information, we cannot definitively choose the correct rotations. However, in general terms, if each person is equidistant from the others in a regular polygon arrangement, we can then divide 360° by the number of people to find the angle corresponding to one pass. Assuming five people at the table, each angle would be 72°. In this case, the closest matching option provided would be First 180° and then 72°.
You are studying for your final exam on the semester. Up to this point, you received 3 exam scores of 99%, 80%, And 70%. To receive a grade of B in the class, you must have an average exam score between 80% and 89% for all 4 exams including the final. Find the widest range of scores that you can get on the final exam in order to receive a grade of B for the class. Use interval notation
Answer: The interval would be [71,107]
Step-by-step explanation:
Since we ave given that
Scores received in 3 exams are 99%, 80%, and 70%.
To receive a grade of B in the class, he must have an average exam score between 80% and 89% for all 4 exams for all 4 exams.
So, Minimum marks he needs for all 4 exams is given by
[tex]80\times 4=320[/tex]
Maximum marks he needs for all 4 exams is given by
[tex]89\times 4=356[/tex]
And his total marks in 3 exams is
[tex]99+80+70\\\\=249[/tex]
Minimum marks he needs in final exam is given by
[tex]320-249\\\\=71[/tex]
Maximum marks he needs in final exam is given by
[tex]356-249\\\\=107[/tex]
Hence, the interval would be [71,107]
Solve the following system of equations
x + y =-5
-3x - y =7
Pleasee hurryyyy
Asap
Correct as will get brainliest
What does it mean to say that a polynomial equation is solvable by radicals?
please help algebra 2!!
What is the length of JK, to the nearest tenth of a millimeter?
The length of JK to the nearest tenth is; 4.5 mm
What is the Length of a side of the triangle?From the given triangle, we see the following parameters;
JL = 3 mm
KL = 5 mm
angle JLK = 62 °
Use the Law of Cosines, we can find the length of JK as;
|JK| = √(3² + 5² − 2(3 * 5) cos62°)
|JK| = √(34 - 14.084)
|JK| = 19.916
|JK| = √19.916
|JK| = 4.463
Approximating to the nearest tenth; JK = 4.5 mm
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What is the measure of angle x? Enter your answer in the box. x = º Three intersecting lines. Three of the six angles formed by the intersecting lines are labeled. Every other angle is labeled. Going clockwise, they are labeled 56 degrees, x, and 41 degrees.
83 i am quite certain hope this helps (why did echo delete my answer the first time could of gave me a reason why because that was rude!)
im pretty sure it is 83
hope this help you guys
What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be defined if you multiplied it by 2? Would it be defined if you subtracted some real number from it? Would it be defined if you squared it? Would it be defined if you cubed it?
Final answer:
In the complex number system, types of numbers that are undefined under a radical sign in the real number system, such as negative real numbers, become defined. For example, the square root of -1 is i, an imaginary unit. This allows operations like multiplication, subtraction, squaring, and cubing on complex numbers to be defined, illustrating the comprehensive nature of the complex number system.
Explanation:
The types of numbers that are undefined under a radical sign (specifically the square root) are negative real numbers in the context of the real number system. However, when we introduce the concept of complex numbers, every number, including negative ones, can have a defined square root. For example, the square root of -1 is defined as i, which is an imaginary unit.
When you handle the expression √-1 (which is i) in various operations:
If multiplied by 2, the result is still defined as 2i, which is a complex number.If a real number is subtracted from it, such as √-1 - 3, this is also defined and results in i - 3, another complex number.If squared (√-1)^2, it simplifies to -1, which is a defined real number.If cubed (√-1)^3, it results in -i, still defined within the complex number system.This illustrates that with the incorporation of complex numbers, operations on what would be undefined values in the real number system become fully defined. Additionally, the complex number system ensures that every polynomial equation has a root, fulfilling the Fundamental Theorem of Algebra. Complex numbers are a critical development in mathematics, allowing for the full spectrum of polynomials to be solvable and expanding our capability to model and solve a wide array of problems.
HELP!!!!! 8 POINTS!!!!!! Rachel decided to have bouncy balls as a party favor. She determines that her ratio of bouncy balls to guests is 9:3. Explain how to find the number of balls needed for 30 guests.
What is the area of the manhole if it is 2 ft wide use 3.14 as pi and round to the nearest hundredth
Which represents the solution set of 5(x+5)<85
i need to know how to make the equations
Austin left for school at 7:35
a.M.He arrived at school 15 minutes later.What time did Austin arrived at school?
A 45 degree sector in a circle has an area of 13.75pi cm^2, what is the area of the circle? Enter your answer as a decimal.
What is the surface area of the figure shown?
989.1 square centimeters
910.6 square centimeters
1,852.6 square centimeters
832.1 square centimeters
The total surface area = 910.6 square centimeters. Option B
The surface area of a cylinder with a conical top can be found by calculating the sum of the areas of the circular base, the curved surface of the cylinder, and the lateral surface of the cone.
From the image, we can find that the radius of the cylinder is 5 cm and the height of the cylinder is 13 cm. We are not given the slant height of the cone.
Let's denote the slant height of the cone as sl.
Here's how to find the surface area of each part:
Curved surface area of the cylinder:
2πrh = 2π(5 cm)(20 cm)
= 628.31 cm²
Lateral surface area of the cone
A=πrl+πr2
= π*5*13+π*5²
= 282 square centimeters
Therefore, the total surface area of the cylinder with a conical top is equal to:
Total surface area = Area of circular base + Curved surface area of cylinder + Lateral surface area of cone
Total surface area = 282 + 628.31 cm²
Total surface area = 910.6 square centimeters
Solve for x. Simplify completely.
x^2+4x+4=8
A. x=-6 or x=2 is the answer
In the circle graph what is the measure of the central angle for carrots and potatoes combined
Potatoes 8%
Carrots 11%
Green beans 12%
Corn 15%
Broccoli 20%
Other 34%
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
In a circle, adjacent angles of a quadrilateral sum up to 180 degrees. Thus, all angles in quadrilateral ABCD inscribed in a circle would each sum up to 180°. Consequently, sum of all the angles of the quadrilateral is 360°.
Explanation:In a circle, adjacent angles of a quadrilateral sum up to 180 degrees. Since a circle consists of 360 degrees, the quadrilateral ABCD has four angles, each angle would sum up to 180 degrees as well. This is because when two cords intersect each other in a circle, they split each other into two segments and the product of the segments of one chord is equal to the product of segments of the other chord.
Let's take an example if we have the angles as A, B, C, and D: A + B = 180° and C + D = 180°. So all the angles of the quadrilateral ABCD inscribed in a circle will sum up to 360°. Hence, A + B + C + D = 180° + 180° = 360°
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A toddler crawled 2 yards, stopped, then continued to crawl 8 more feet. How many feet did he travel in total?
The toddler crawled a total of 14 feet after converting the initial 2 yards into feet and adding the additional 8 feet crawled.
To determine the total distance the toddler traveled, we first need to convert the units so they are the same. We know that 1 yard is equivalent to 3 feet. If the toddler crawled 2 yards initially, we can calculate this distance in feet as follows:
2 yards * 3 feet/yard = 6 feet
After stopping, the toddler continued to crawl for 8 more feet. To find the total distance traveled, we simply add the two distances together:
6 feet + 8 feet = 14 feet
Therefore, the toddler traveled a total of 14 feet.
If f(x) = (1/9)(9^x) what is f(3)
Answer: The required value of f(3) is 81.
Step-by-step explanation: We are given the following function :
[tex]f(x)=\left(\dfrac{1}{9}\right)9^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of f(3).
Substituting x = 3 in equation (i), we get
[tex]f(3)\\\\\\=\left(\dfrac{1}{9}\right)\times9^3\\\\=9^2\\\\=81.[/tex]
Thus, the required value of f(3) is 81.
Answer:
81
Step-by-step explanation:
APEX
can someone help me find the y-intercept and explain how you got that answer?