On solving the provided question we can say that The inequality we have here is -5(x-3) ≥ 3[4-(x+4)] => 15/17 ≥ x
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
The inequality we have here is
-5(x-3) ≥ 3[4-(x+4)]
-5x + 15 ≥ 12x
15 ≥ 17x
15/17 ≥ x
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
Find the exact value of sin(2x) if sin(x)=-1/2.
Answer: The value of sin(2x) can be found using the identity:
sin(2x) = 2sin(x)cos(x)
Since sin(x) = -1/2, we can use the Pythagorean identity to find the value of cos(x):
cos^2(x) + sin^2(x) = 1
So
cos^2(x) = 1 - sin^2(x) = 1 - (-1/2)^2 = 1 - 1/4 = 3/4
Taking the square root of both sides:
cos(x) = ± sqrt(3)/2
Since sin(x) is negative and cos(x) must be positive, we get:
cos(x) = sqrt(3)/2
Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:
sin(2x) = 2sin(x)cos(x) = 2 * (-1/2) * sqrt(3)/2 = -sqrt(3)
So the exact value of sin(2x) is -√(3).
Step-by-step explanation:
show whether or not the set of remainders z18 forms a group with the modulo addition operator. then show whether or not z18 forms a group with the modulo multiplication operator
Z18 with modulo addition satisfies all four group axioms and is a group.
Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.
what is the binary operation?
In mathematics, a binary operation is a function that takes two elements from a set and returns another element from the same set.
For a set to form a group with a binary operation, the set must satisfy the four group axioms: closure, associativity, identity, and inverse.
1. Z18 with modulo addition:
The set of remainders Z18 = {0, 1, 2, ..., 17} forms a group with the modulo addition operator.Closure: For any two elements a, b in Z18, their sum (a + b) is also in Z18. This is because modulo addition is performed by taking the sum of two numbers, dividing by 18, and taking the remainder, which will always be in the set Z18.Associativity: For any elements a, b, c in Z18, (a + b) + c = a + (b + c).Identity: There exists an element 0 in Z18 such that a + 0 = a for all elements a in Z18.Inverse: For every element a in Z18, there exists an element b in Z18 such that a + b = 0.Hence, Z18 with modulo addition satisfies all four group axioms and is a group.
2. Z18 with modulo multiplication:
The set of remainders Z18 = {0, 1, 2, ..., 17} does not form a group with the modulo multiplication operator.Closure: For any two elements a, b in Z18, their product (a * b) is also in Z18.Associativity: For any elements a, b, c in Z18, (a * b) * c = a * (b * c).Identity: There exists an element 1 in Z18 such that a * 1 = a for all elements a in Z18.Inverse: For every non-zero element a in Z18, there does not exist an element b in Z18 such that a * b = 1. This is because the modulo multiplication operator only returns values that are between 0 and 17, and not all elements in Z18 have a multiplicative inverse modulo 18.Hence, Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.
To learn more about binary operation, Visit
https://brainly.com/question/29519009
#SPJ4
Sabiendo los valores del seno y coseno de los ángulos de 0º, 30º, 45º, 60º y 90º, justifica entre cuáles de estos valores se encontrará el ángulo α que cumple: a) cos α = 0.32 b) sen α= 0.20
Therefore , the solution of the given problem of angle comes out to be sin α = 0.20 is between 10º and 1 and cos α = 0.32 is between 70º and 75º.
An angle is defined.An angle, according to Euclidean geometry, is a shape comprised of two rays, referred as the angle's extremity, which meet at a vertex in the center. When two rays are combined, the surfaces on which they are focused may take on an angle. A plane collision also produces an angle. Dihedral angles are the name given to them. Angles are the shapes that two rays or lines with similar terminations can take in plane geometry.
Here,
a) he closest value to 0.32 is the cosine of 71.8º, which is approximately equal to 0.32.
Therefore, the angle α that satisfies
=>cos α = 0.32 is between 70º and 75º.
b) To find the value of the angle α that satisfies sin α = 0.20, it is necessary to look in the table of sine values for angles of 0º, 30º, 45º, 60º and 90º, and find the closest value to 0.20.
The closest value to 0.20 is sine 11.5º, which is approximately equal to 0.20.
Therefore, the angle α that meets
=> sin α = 0.20 is between 10º and 1
Therefore , the solution of the given problem of angle comes out to be sin α = 0.20 is between 10º and 1 and cos α = 0.32 is between 70º and 75º.
To know more about angles visit:
https://brainly.com/question/14569348
#SPJ1
write the equation of the circle centered at (-1,-5) that passes through (0,-18)
Answer:
(x + 1)^2 + (y + 5)^2 = 169
Step-by-step explanation:
The equation of a circle centered at (h,k) with radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
To find the equation of the circle, we first need to find the center and the radius.
Given that the circle is centered at (-1,-5), h = -1 and k = -5.
Next, we need to find the radius. To do this, we use the point (0,-18) that lies on the circle and use the distance formula:
r = sqrt[ (0-(-1))^2 + (-18-(-5))^2 ] = sqrt[ 1^2 + (13)^2 ] = sqrt[1 + 169] = sqrt[170] = 13
So, the equation of the circle is:
(x + 1)^2 + (y + 5)^2 = 13^2
Therefore, the equation of the circle centered at (-1,-5) that passes through (0,-18) is:
(x + 1)^2 + (y + 5)^2 = 169
Functions K and H are both linear functions.
Function K y= 1/2x+2
Function H
x -2 1 5 8
y 0 4.5 10.5 15
Which of the statements comparing the two functions is true?
A)The slope of function K is greater than the slope of function H.
B)The y-intercept of function K is greater than the y-intercept of function H.
C) The slope of function K is equal to the slope of function H.
D) The y-intercept of function K is less than the y-intercept of function H.
On solving the provided question, we can say that the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.
what is function?Mathematicians study numbers and their variations, equations and related structures, shapes and their places, and potential placements for these things. The term "function" refers to the relationship between a set of inputs, of which each has an associated output. An relationship of inputs and outputs known as a function is one in which each input leads to a single, distinct output. Each function is given a domain or a codomain, or scope. The letter f is frequently used to indicate functions (x). Entry is an x. The four major kinds of accessible functions are on functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions.
Function K is given as y = 1/2x + 2, so the slope of K is 1/2 and the y-intercept of K is 2.
To find the slope and y-intercept of function H, we can use the given points (x,y):
When x = -2, y = 0, so we have the point (-2,0)
When x = 1, y = 4.5, so we have the point (1,4.5)
When x = 5, y = 10.5, so we have the point (5,10.5)
When x = 8, y = 15, so we have the point (8,15)
We can use two of these points to find the slope of H:
slope = (change in y) / (change in x) = (10.5 - 4.5) / (5 - 1) = 6/4 = 3/2
To find the y-intercept of H, we can use the point (0,b) where x = 0:
b = y - mx = 4.5 - (3/2)(1) = 3
So the equation for function H is y = (3/2)x + 3, which has a slope of 3/2 and a y-intercept of 3.
Now we can compare the two functions:
A) The slope of function K is greater than the slope of function H. False, since 1/2 < 3/2.
B) The y-intercept of function K is greater than the y-intercept of function H. False, since 2 < 3.
C) The slope of function K is equal to the slope of function H. False, since 1/2 ≠ 3/2.
D) The y-intercept of function K is less than the y-intercept of function H. True, since 2 < 3.
Therefore, the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
can someone tell me how to find this problem?
The composition of functions f and g is:
(f o g) =6x^2 + 15x + 2
How to find the composition of functions?Here we have two known functions:
f(x) = 3x + 2
g(x) = 2x^2 + 5x
We want to find the composition:
(f o g)
That just means that we need to evaluate function f(x) in x = g(x), we wikk get:
(f o g) = 3*g(x) + 2
Now we can replace g(x) there to get:
(f o g) = 3*(2x^2 + 5x) + 2
= 6x^2 + 15x + 2
That is the composition.
Learn more about composition of functions at:
https://brainly.com/question/10687170
#SPJ1
46=10b-34, what does B equal?
Answer:
8
Step-by-step explanation:
46 = 10b - 34
Move 34 to the other side by adding 34 to each side
80 = 10b
Divide 10 on each side to get b on one side
8 = b
When purchasing a sale item, if you take the 20% discount first, then add the 10% tax, the cost of the item will be the same as when you add the 10% tax first, then take the 20% discount.
Answer:
80+90
add them together
=170
10% of 170
=17
20-17=3
If 80% of a number is 560, what will be 70% of that number?
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.950.9 miles per hour.Speed (miles per hour) Frequency42-45 ; 2946-49 ; 1350-53 ; 654-57 ; 458-61 ; 1
The computed mean is 18.8 and it is more than 32.1 than the actual mean.
What is mean?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
The mean of the data is given as:
x' = ∑x / n
∑x = 29 + 13 + 6 + 45 + 1 = 94
x' = 94 / 5 = 18.8
The difference between the actual mean and the calculated mean is:
D = 50.9 - 18.8
D = 32.1
Hence, the computed mean is 18.8 and it is more than 32.1 than the actual mean.
Learn more about mean here:
https://brainly.com/question/29895356
#SPJ4
Two trains leave towns 855 miles apart at the same time and travel toward each other. One train travels 13 mi/h slower than the other. If they meet in 5 hours, what is the rate of each train?
The velocity of the two trains are 79m/s and 66m/s
What is velocity?Velocity is the rate of change of displacement with time. It is a vector quantity and it is measured in meter per second.
Using addition of vectors:
The total displacement = d2-d1
displacement = velocity × time
Represent the velocity of faster train by v
therefore the velocity of the slower train = v -13
855 = 5v +5(v-13)
855 = 5v+5v+65
855 = 10v +65
10v = 855-65
10v = 790
v = 790/10
v = 79 m/s
the rate of the second train = 79-13 = 66m/s
therefore the rate of the two trains are 79m/s and 66m/s
learn more about velocity from
https://brainly.com/question/25749514
#SPJ1
Four friends A, B, C and D live in a same locality. The house of B is in the east of A's house but in the north of C's house. The house of C is in the west of D's house. D's house is in which direction of A's house?a. South-Eastb. North-Eastc. Eastd. Data is Inadequate
d. Data is inadequate as it is not possible to determine the direction of D's house relative to A's house.
What is the directions?Directions refer to the relative positions of objects or locations in space. It describes the orientation and location of an object in relation to another object or a reference point.
Based on the information given, . Further information is needed to determine the direction.
Hence, d. Data is inadequate
To learn more about directions, Visit
https://brainly.com/question/28108225
#SPJ4
упростить тождество
1+tg a x tg b=cos(a+b)/cos a + cos b
Answer:
Уравнение 1 + tan(a) * tan(b) = (cos(a + b))/(cos(a) + cos(b)) может быть упрощено, используя тождество tan(a) * tan(b) = (sin(a) * sin(b))/(cos(a) * cos(b)) и тождество sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b). Однако дальнейшее упрощение может быть невозможным, поскольку уравнение уже в довольно простой форме.
Research has found that people are happiest when they have _____ hours a day of face-to-face contact with others. 3. 6. 1. 9.
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
What is an experiment ?
A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law
In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
To know more about experiment from the link given below.
https://brainly.com/question/26117248
#SPJ4
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
What is an experiment ?
A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law
In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
To know more about experiment from the link given below.
brainly.com/question/26117248
#SPJ4
Find the area and perimeter of this figure.
The area and perimeter of the shape is 4.65cm² and 9.5cm
What is area and perimeter of a triangle?Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle. Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.
Perimeter of the triangle = 3.2+ 2.0+4.3
= 9.5cm
The area of the triangle = ½bh
= 1/2 ×3.1 × 3
= 4.65 cm²
learn more about area and perimeter of a triangle from
https://brainly.com/question/17335144
#SPJ1
Uma writes 56 words in her journal. The words are shared equally on 7 lines. On the last line, Uma adds 3 words. How many words are on the last line of Uma's journal?
Answer:
11 words
Step-by-step explanation:
Thera are 56 words shared equally among 7 lines
Therefore there are 56/7 = 8 words per line
On the last line by adding 3 words, there will be 8 + 3 = 11 words
To estimate the cube root of 29, I would look at the perfect cubes __ and __ and then choose __ as a good estimate.
The cube root can be estimated in the range:
3 < ∛29 < 4
And the value is ∛29 = 3.1
How to estimate the cube root?First we need to find two perfect cubes that bound our number.
We know that:
3*3*3 = 3^3 = 27
4*4*4 = 64
Then:
27 < 29 < 64
∛27 < ∛29 < ∛64
3 < ∛29 < 4
So we have an estimation of the cube root, and it will be closer to 3 than to 4, so we can estimate this as:
∛29 = 3.1
3.1 = 29.7
So it is a good estimation.
Learn more about cube roots:
https://brainly.com/question/24486461
#SPJ1
100 POINTS BRAINLIEST HELP A trial balance indicates $10,000 in debits and $16,000 in credits. What is the amount of the misplaced entry?
A. $3,000
B. $2,000
C. $6,000
D. $4,000
Match the expressions on the right with the results on the right.
Some options on the right will be used more than once.
416 ÷ 100 = 4.16
4.16 ÷ 10 = 0.416
41600 ÷ 1000 = 4.1600 = 4.16
4.16 ÷ 100 = 0.0416
41.6 ÷ 100 = 0.416
When you divide by a power of 10, you move the decimal to the left the number of 0's in the number.
÷ 10 and you move the decimal point 1 place to the left
÷ 100 and you move the decimal point 2 places to the left
÷ 1000 and you move the decimal point 3 places to the left
Answer:
416 / 100 = 4.16
4.16 / 10 = 0.416
41600 / 1000 = 41.6
4.16 / 100 = 0.0416
41.6 / 100 = 0.416
Step-by-step explanation:
When you divide a number by another number, you find out how many times the second number fits into the first one. For example, in the expression 416 / 100, you are finding out how many times 100 fits into 416. The answer is 4.16, meaning 100 fits into 416 4 times with a remainder of 16.
Similarly, in the expression 4.16 / 10, you are finding out how many times 10 fits into 4.16. The answer is 0.416, meaning 10 fits into 4.16 0 times with a remainder of 4.16.
In the expression 41600 / 1000, you are finding out how many times 1000 fits into 41600. The answer is 41.6, meaning 1000 fits into 41600 41 times with a remainder of 600.
In the expression 4.16 / 100, you are finding out how many times 100 fits into 4.16. The answer is 0.0416, meaning 100 fits into 4.16 0 times with a remainder of 4.16.
In the expression 41.6 / 100, you are finding out how many times 100 fits into 41.6. The answer is 0.416, meaning 100 fits into 41.6 0 times with a remainder of 41.6.
Find the slope of a line to y = 3x + 7
Answer: 3
Step-by-step explanation:
The line y = 3x + 7 has a slope of 3. Slope-intercept form equations have a slope of m when written as y = mx + b. See the attached picture for more information.
y = mx + b ➜ y = 3x + 7 ➜ y = 3x + 7 ➜ 3
Answer:
3.Step-by-step explanation:
The ratio at which the y-value varies when the x-value changes is shown by a line's slope. The coefficient of x in the equation y = 3x + 7 is 3, therefore y rises by 3 units for every unit increase in x. The slope is thus 3. This indicates that the line will climb 3 units along the y-axis for every unit you move to the right along the x-axis.
Hope it helps! : )Jake needed money for college. He borrowed $6,000 at 12% simple interest per year. If he paid $360 interest, what was the duration of the loan?
Answer:
x = 1/2.
Step-by-step explanation:
Hope this helps!
Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer. 5 yd Byd 15 yd 6 yd 7 yd
The value of the missing side assuming that all the intersecting sides meet at right angles would be = 6ft.
How to calculate the missing side length?From the diagram above, the length and the width of one side of the figure is given as;
Length = 13 ft
width = 16 ft
This is supposed to be the same for the other missing side length and width ;
That is ;
width = 11 + 5 = 16 ft
Length = 13 = 7 + ?
Make ? that subject of formula;
? = 13-7 = 6 ft
Learn more about square here:
https://brainly.com/question/25092270
#SPJ1
Two adjacent vertices of a triangle are A(5; 3), B(7; 7). One point on the opposite side is P(-2;9). Give the coordinates of the vertices.
Step-by-step explanation:
The two adjacent vertices of the triangle are A(5; 3) and B(7; 7), and one point on the opposite side is P(-2; 9). To find the coordinates of the third vertex, we need to find the midpoint of AB and extend it to P.
The midpoint of AB can be calculated by finding the average of their x-coordinates and y-coordinates:
C = ((A_x + B_x)/2, (A_y + B_y)/2) = ((5 + 7)/2, (3 + 7)/2) = (6, 5)
Next, we can use the midpoint C and point P to find the slope of the line connecting them:
m = (P_y - C_y) / (P_x - C_x) = (9 - 5) / (-2 - 6) = 4 / -8 = -0.5
Since the slope of a line perpendicular to this one is -2, we can use the midpoint C and the slope to find the equation of the line connecting C and the third vertex D:
y - C_y = -2 (x - C_x)
y - 5 = -2 (x - 6)
Expanding and solving for x, we get:
y = -2x + 17
Substituting the y-coordinate of P (-2) into this equation:
-2 = -2x + 17
Solving for x:
x = 7.5
Finally, we can use the x-coordinate to find the y-coordinate:
y = -2x + 17 = -2 * 7.5 + 17 = 5.5
So the third vertex is D (7.5, 5.5).
The vertices of the triangle are A (5, 3), B (7, 7), and D (7.5, 5.5).
A long year-end status report for work is 141 pages long. You need to print 18 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.51 each.
Give your answer to the nearest cent, only for the paper you use (partial reams are OK)
It cost $17.82 to buy the papers needed for this reports
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
A long year-end status report for work is 141 pages long. You need to print 18 copies for a meeting next week. Therefore:
Amount of paper printed = 141 pages long * 18 copies = 2538 pages
Paper is sold in reams (500 pages) for $3.51 each. Hence:
Amount spent on papers = 2538 pages * ($3.51 / 500 pages) = $17.82
About $17.82 was spent on papers
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
PLEASEEE HELPPP asappp
Answer:
y = - x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4=1}{2-(-3)}[/tex] = [tex]\frac{-5}{2+3}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - x - 2 ← equation of line
A line passes through the points (4, 8) and (12, 2). What is the slope of the line?
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{4}}} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{3 }{ 4 }[/tex]
Calculate the volume of the prism.
The volume of the given prism in question is 276.7 cubic yd
Volume of a square based prismThe formula for calculating the volume of a square based prism is expressed as:
V = BH/3
where
B is the base area
H is the height of the prism
Determine the height using Pythagoras theorem
b^2 = 13^2 - 10^2
b^2 = 169 - 100
b^2 = 69
b = √69
b = 8.3yd
Determine the required volume
V = (10*10)(8.3)/3
V = 830/3
V = 276.7 cubic yd
Hence the volume of the prism is given as 276.7 cubic yd
Learn more on volume of prism here: https://brainly.com/question/23963432
#SPJ1
What is the classification of -p+2p^2
-p + 2p^2 is a quadratic function, which is a polynomial function of degree 2.
What is quadratic function?Quadratic function is a polynomial function of degree 2, written in the standard form as ax^2 + bx + c, where a, b, and c are constants, and x is a variable.
The graph of a quadratic function is a parabola which opens up or down depending on the value of a. The most common application of quadratic functions is in solving problems related to parabolic motion, such as finding the maximum height, time of flight, or range of a projectile.
Learn more about quadratic function here: brainly.com/question/25841119
#SPJ1
If f(v) = 9v² - 28v + 19, use synthetic division to find f(3).
Answer: To use synthetic division to find f(3), we will divide the polynomial 9v² - 28v + 19 by v - 3.
Here's the process:
| 9 -28 19|
v-3|____________|
9(3)² - 28(3) + 19
| 9 -84 57|
0 -96 38
So, f(3) = 9(3)² - 28(3) + 19 = 9(9) - 28(3) + 19 = 81 - 84 + 19 = -4 + 19 = 15.
So f(3) = 15.
Step-by-step explanation:
What is the percent of decrease from 100 to 72?
Answer:28%
Step-by-step explanation: