The total length of the wall that the individuals have to paint is 69 3/13 m.
What is the total length?The first step is to add the fractions of the wall painted by the three people together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Sum of the fractions:
[tex]\frac{1}{4} + \frac{1}{3} + \frac{1}{5}[/tex]
[tex]\frac{15 + 20 + 12}{60}[/tex] = [tex]\frac{47}{60}[/tex]
The fraction of the wall that has not been painted = 1 - [tex]\frac{47}{60}[/tex] = [tex]\frac{13}{60}[/tex]
13/60 of the wall = 15m
13/60 x w = 15
w = 15 ÷ 13/60
w = 15 x 60 /13 = 69 3/13 m
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f(x)=72/x - 11
f(72)=
is the number 19 a prime or composite number
Answer:
prime
Step-by-step explanation:
because 19 can only divide 1 and itself
g(x)=5x+50 answer please
The answer to the linear equation g(x) = 5x+50 is plotted on the graph.
What is a linear equation?A linear equation is one in which the variable's maximum power is always one.A one-degree equation is another term for it.A linear equation in one variable takes the conventional form Ax + B = 0. x is a variable, A is a coefficient, and B is constant in this equation.Given equation:
g(x)=5x+50
The equation can also be written as y = 5x+50.
Now, we can replace the value of x for different numbers in the given equation to get the value of y to create the coordinates.
When we put x = 0 in the equation, we get y = 0 + 50 = 50.
Similarly, if we substitute the value of x as 1 in the equation, we get y = 5(1) + 50 = 55.
If we substitute the value of x as 2, y = 5(2) + 50 = 60
If we substitute the value of x as -1 and -2, we get the value of y as,
y = 5(-1) + 50 = 45 and y = 5(-2) + 50 = 40.
These pairs of values satisfy the linear equation and are plotted on the graph given below.
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Describe the transformations to the basic function. Then, write the equation of the function.
The given function is a graph transformation of the absolute value function.
What are Function Transformations?A function transformation "moves," "resizes," or "reflects" the parent function's graph. Function transformations are classified into three types: Translation, Dilation, and Reflection. Only dilation alters the size of the original shape; the other two transformations change the shape's position but not its size.
Step 1: Parent function y = f₁(x) = |x|
Step 2: f₁(x) is reflected (Reflection) about x-axis to form f₂(x) = -f₁(x) = -|x|
Step 3: f₂(x) is moved to left by 5 units(Horizontal translation) to form f₃(x) = f₂(x + 5) = -|x + 5|
Step 4: f₃(x) is moved up 1 unit (Vertical translation) to form f₄(x) = f₃(x) + 1 = -|x + 5| + 1
The equation of the given graph is:
y = |x + 5| +1
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To describe a specific geometric sequence, Jamie wrote the recursive formula: (Formula in picture)
Write the first five terms of this sequence.
If Jamie wrote the recursive formula [aₙ = {(aₙ₋₁) * 4}, where (a₁ = 2)] to describe a specific geometric sequence, then the first five terms of this sequence are [2, 8, 32, 125 and 512]
As per the question statement, Jamie wrote the recursive formula
[aₙ = {(aₙ₋₁) * 4}, where (a₁ = 2)] to describe a specific geometric sequence.
We are required to determine the first five terms of this sequence.
To solve this question, first we have to determine the values of "n" which goes as (n = 1, 2, 3, 4, 5, 6...)
Now, for (n = 1), (an = a₁ = 2), given in the question statement itself,
And using the question mentioned formula, for (n = 2),
[a₂ = {(a₍₂₋₁₎ * 4}]
Or, [a₂ = (a₁ * 4)]
Or, [a₂ = (2 * 4)]
Or, (a₂ = 8).
Similarly, for (n = 3), [a₃ = {(a₍₃₋₁₎ * 4}]
Or, [a₃ = (a₂ * 4)]
Or, [a₃ = (8 * 4)]
Or, (a₃ = 32).
For (n = 4), [a₄ = {(a₍₄₋₁₎ * 4}]
Or, [a₄ = (a₃ * 4)]
Or, [a₄ = (32 * 4)]
Or, (a₄ = 128).
For (n = 5), [a₅ = {(a₍₅₋₁₎ * 4}]
Or, [a₅ = (a₄ * 4)]
Or, [a₅ = (128 * 4)]
Or, (a₅ = 512)
Hence, the first five terms of this sequence are [2, 8, 32, 125 and 512].
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What type of reasoning is used to find the next amount of train cars? Explain your answer.
Answer: It's using the table of 2 to continue the pattern of trains.
in the first fig the no. of carton is 0.
for the next one it is 2 and the next 4.
the pattern will thus continue with the multiplication table of 2.
$m\angle U=2x\degree$ , and $m\angle V=2\left(m\angle U\right)$ . Find the value of $x$ that makes $\angle U$ and $\angle V$ complementary angles
The value of x that makes ∠U and ∠V a complement of each other is; x = 9
How to find Complementary Angles?
There are different equal angle theorems in math's such as complementary angles, supplementary angles, linear pairs e.t.c
Now, complementary angles are defined as angles that sum up to 90 degrees.
We are given that;
m∠U = 2x°
m∠V = 4m∠U = 4(2x)°
We want to find the value of x that makes ∠U and ∠V a complement of each other.
This means that by the definition of complementary angles, they will sum up to 90 degrees. Thus;
2x + 4(2x) = 90
2x + 8x = 90
10x = 90
x = 90/10
x = 9
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Complete question is;
m∠U = 2x°, and m∠V = 4m∠U. Which value of x makes ∠U and ∠V complement of each other? A. 25 B. 9 C. 36 D. 18
2x - 3y = -6please solve and graph
2x - 3y = -6
Solve for y:
-3y= -6-2x
y= (-2x-6) /-3
y= 2/3x+2
Slope intercept form:
y= mx+b
Where:
m= slope (2/3)
b= y-intercept (2)
So, to graph the function, we have to draw a line that crosses the y axis at 2, and for every 3 units moved to the right along the x-axis it goes up 2 units along the y-axis.
A triangle is dilated with a center of dilation at the origin. Point P' is the corresponding point of the image of the dilation. Point P is at (-2,3) and P' is at
(-8,12). What is the scale factor?
The scalar factors are (4,4)
What is dilation?Dilation is a type of transformation in which a shape or geometric figure's size is altered while maintaining its relative proportions and general shape.
Dilation is applied by the rule:
(x, y) → (kx, ky), where k is the scale factor
We have
(x, y) = (-2, 3) and (kx, ky) = (-8, 12)
Substitute and solve for k
-8 = -2k and 12 = 3k ⇒ k = 4
So the rule is
(x, y) → (4x, 4y)
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In ΔEFG, is it possible for segment GE to measure 6 units?
According to the triangle inequality theorem, the measure for the third side can be GE = 6 units, because: A. 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5.
What is the Triangle Inequality Theorem?The triangle inequality theorem states that the set of side measurements that will form a triangle will be the set of side lengths whereby the sum of any two sides will be greater than the third side of the triangle.
For example, if a, b, and c are the side lengths of a triangle, then:
a + b > ca + c > bb + c > aThus, we have the given lengths:
FE = 3 units
FG = 5 units
Therefore, the third side length would be GE = 6 units based on the triangle inequality theorem because:
3 + 5 > 6
5 + 6 > 3
6 + 3 > 5
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Which 2 of the following are correct equations of the line passing through (2, -3) with a slope of five?
y+3 = 5 (x-2)
y= 5x -3
y= 5x + 13
y-3= 5 (x+2)
y= 5x -13
Answer:
The two equations that passes through (2, -3) and has a slope of five are:
y + 3 = 5(x - 2) and y = 5x - 13
Step-by-step explanation:
For the first equation, you get y equal to itself. To do that, you need to simplify the right side of the equation. For 5(x - 2), you will distribute the 5 to the x and -2, equalling to 5x - 10. Next, we subtract 3 from both sides to cancel out the 3 on the left side. The equation is now y = 5x - 13. The -13 is the y intercept so we start at the point (0, -13). Since the slope goes up by 5 for every one point it moves to the right, it will eventually reach the point (2, -3). In other words, you add 1 to the x value and 5 to the y value. The points will look like this: it starts at (0, -13) and goes to (1, -8) and goes to (2, -3). The second equation is equivalent to the first equation. Hopefully this helps you out!
What is the remainder of 5x3 - 7x² + 2x + 1 divided by (x - 3)?
A.) 126
B.) 79
C.) 203
D.) 205
Answer: A
Step-by-step explanation:
The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3≤x≤7 goes from least to greates
Given
Function f(x) , g(x) and h(x)
Find
Order of the function according to average rate of change
Explanation
Average rate of change can be given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex][tex]3\leq x\leq7[/tex]for f(x)
[tex]\begin{gathered} \frac{f(7)-f(3)}{7-3} \\ \\ \frac{-10-(-8)}{4} \\ \\ -\frac{2}{4} \\ \\ -\frac{1}{2} \end{gathered}[/tex]for g(x)
[tex]\begin{gathered} \frac{g(7)-g(3)}{7-3} \\ \\ \frac{7-(27)}{4} \\ \\ -\frac{20}{4} \\ \\ -5 \end{gathered}[/tex]for h(x)
[tex]\begin{gathered} \frac{h(7)-h(3)}{7-3} \\ \\ \frac{60-24}{4} \\ \\ \frac{36}{4} \\ 9 \end{gathered}[/tex]Final Answer
least to greatest = g(x) , f(x) . h(x)
correct option is 2.
Write a condition Pls
Expand the brackets and simplify the
expression below.
8(3y + 2) + 4y
Answer:
28y+16
Step-by-step explanation:
8(3y+2)+4y
24y+16+4y
28y+16
The simplification of the given expression is 28y+16.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.
We are given an expression as;
8(3y+2)+4y
we need to solve the expression
First open the bracket;
24y+16+4y
Solve the like terms;
28y+16
Therefore, the simplification of the given expression is 28y+16.
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(8r
2
−7r−9)+(−r
2
+r)
Answer:
12r -9
Step-by-step explanation:
(8r2−7r−9)+(−r2+r)
= 16r -7r -9 +2r +r
= 12r -9
Compute the probability of randomly drawing 10 cards from a deck and getting exactly 5 spades.
Enter the exact answer.
The probability of randomly drawing 10 cards from a deck and getting exactly 5 spades is 0.0468
Formula Required:
Given a set of n items, a group of k items can be chosen in any of the 'n' ways, where 'k' is the number of possibilities. The order in which the choices are made is not significant.
A typical deck of cards contains 52 cards in total. Therefore, there exist (52, 10) scenarios in which 10 cards could be chosen (without replacement) that are exhaustive, mutually exclusive, and equally likely.
Again, there are 13 spades in the entire deck of 52 cards. The remaining (10 - 5) = 5 cards can be drawn from the remaining (52 - 13) = 39 cards in the deck in (39, 5) ways, and 5 spades can be drawn from the 13 spades in (13, 5) ways.
As a result, there are (13, 5) * advantageous scenarios for choosing exactly 5 spades (39, 5)
Consequently, the necessary probability:
= Favorable number of cases for the event / Total number of all possible cases.
= (13 , 5) * (39 , 5) / (52 , 10)
(n, k) = n! / k! (n-k)!
= 0.0468
Therefore, the probability of 5 spades will be 0.0468
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A ball is thrown upward from the top of a building that is 160 feet tall. The height, H, of the ball T seconds after being thrown is given by the equation H = -16t^2 + 48t + 160.
After how many seconds will the ball hit the ground?
a. 2
b. 3
c. 5
d. 10
Answer:
10
Step-by-step explanation:
because 10 is 10 gsjivfhnvv thkgfhlmbbbctb. chvjlff ijvvgjvjvivcujc vidyalay Chrissy full good Zo of up b and b go in the editor and the editor and the general of words typist and I am a bit of a person to you tomorrow to you tomorrow to appeal to utha kar raha hai toto b go on vgn de un BBC d.
Draw the graph of your= 2x +1
The graph of the equation y = 2x+1 has been plotted
The equation of the line is
y = 2x+1
The domain is defined as the set of all possible inputs of the function.
The range is defined as the set of all possible outputs of the function
Here the equation is y =2x+1, we have to substitute the different values for the x and find the values of y.
The values of the x will be the domain and the values of the y will be the range
At x= -2
y = 2(-2)+1
= -3
At x= -1
y = 2(-1)+1
= -1
At x= 0
y = 2(0)+1
= 1
At x=1
y = 2(1)+1
= 3
At x=2
y = 2(2)+1
= 5
Plot the graph using the values
Hence, the graph of the equation y = 2x+1 has been plotted
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Find the value of x *
55°
X
Step-by-step explanation:
Since right angle is equal to 90°,
90°-55°=35°
Select the sequence that shows the numbers in order from least to greatest.
A. √72, 321-41
5
c. 32. √72.1-41
C.
5
B. |–-41, 32 √72
32
D. √72,|-41, ³²
5
The sequence that shows the numbers in order from least to greatest is
√72 , 5,32, |-41|
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc.
√72 = 8.485
32
|-41| = 41
5
least to greatest is √72 , 5,32, |-41|
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write an equation in form of y=mx+b for a line with slope =7 and y-intercept =4
How do I solve with fractions? (with answers)
Answer:
The answer is r = 3
Step-by-step explanation:
Hope this helps! :))
Please let me know if its incorrect
Matthew wants his run today to take no more than 90 minutes. He already has run 30 minutes at a pace of 10 minutes per mile.
Part A)
Write an inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace. Show or explain the reasoning you used to determine your answer.
The inequality for the given situation is m ≤ 6.
Given that, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.
What is the inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Let the number of miles be m.
m ≤ 90/10 - 30/10
m ≤ 9 - 3
m ≤ 6
Therefore, the inequality for the given situation is m ≤ 6.
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A truck travels some distance at a speed of 35 km h in 120 min and the remaining distance at a speed of 48 km h in 90 min. Determine the: (a) total distance covered. (b) average speed over the entire journey
Answer:
a) 142 km,b) 40.57 km/hStep-by-step explanation:
Use of formula:
speed = distance / timedistance = speed × timea) Find each part of distance and add together. Convert minutes to hours.
35 × (120/60) = 35 × 2 = 70 km,48 × (90/60) = 48 × 1.5 = 72 kmdistance = 70 + 72 = 142 kmb) Average speed is:
speed = 142 /(2 + 1.5) = 142/3.5 = 40.57 km/h (rounded)Answer:
(a) 142 km
(b) 40.57 km/h (2 d.p.)
Step-by-step explanation:
Part (a)[tex]\boxed{\sf Distance=Speed \times Time}[/tex]
Given:
Speed = 35 km/hTime = 120 min = 2 hSubstitute the given values into the distance formula to find the distance travelled:
[tex]\implies \sf Distance = 35 \times 2 = 70\;km[/tex]
Given:
Speed = 48 km/hTime = 90 min = 1.5 hSubstitute the given values into the distance formula to find the distance travelled:
[tex]\implies \sf Distance = 48 \times 1.5 = 72\;km[/tex]
Therefore, the total distance travelled is:
[tex]\implies \sf 70 + 72 = 142 \; km[/tex]
Part (b)[tex]\boxed{\sf Average\;speed=\dfrac{Total\;distance}{Total\;time}}[/tex]
Given:
Total distance = 142 kmTotal time = 2 + 1.5 = 3.5 hSubstitute the given values into the average speed formula to find the average speed over the entire journey:
[tex]\implies \sf Average\:speed=\dfrac{142}{3.5}=40.57\;km/h\;(2\;d.p.)[/tex]
Evaluate XYZ squared if x = -2, y = 7, and z= -4.
The required value of XYZ squared would be 3136 which is determined by substituting x = -2, y = 7, and z = -4.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have to evaluate xyz squared if x = -2, y = 7, and z = -4.
⇒ (xyz)²
Substitute the values of x = -2, y = 7, and z = -4 in the above expression
⇒ [(-2) × (7) × (-4)]²
Apply the multiplication operation and we get
⇒ (56)²
⇒ 3136
Therefore, the obtained value of XYZ squared would be 3136 if x = -2, y = 7, and z = -4.
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S. SURVEY In a survey of their favorite
subjects, 390 students said math was
their favorite. One tenth as many...
students said that history was their
favorite subject. How many students
said history was their favorite?
The total number of students who participated in the survey are 100.Given to us The number of students who choose other as their favorite subject = 20 studentsMath = 30%English = 45%Let the total number of students in the survey be x.What is the percentage of students who choose other as their favorite subject?We know that percentage is always 100%, therefore,Total number of students in the survey = other + Math +English100% = other + 30% + 45%100% - 30% - 45% = otherother = 25%Thus, the percentage of students who choose another as their favorite subject is 25%.What is the total number of students who participated in the survey?We know that the number of students who choose English as their favorite subject in the surveys is 20, therefore,25% of the total number of students = 20Hence, the total number of students who participated in the survey is 100.
X =
y =
(3y + 2)
4x°
52°
TO GET Y I WILL USE THE REASON SUM OF ANGLES IN A TRIANGLE:
[tex]52 + 90 +( 3y + 2) = 180 \\ 52 + 90 + 2 +3 y = 180 \\ 3y = 180 - 90 - 52 - 2 \\ 3y = 36 \\ \frac{3y}{3} = \frac{36}{3} \\ y = 12[/tex]
y=12°
TO FIND X I WILL USE THE REQSON ALTERNATE ANGLES
[tex]4x = 52 \\ \frac{4x}{4} = \frac{52}{4} \\ x = 13[/tex]
x=13°
THEE ANGLES ARE INSIDE THE PARALLEL LINES :NOTE.
There are 15 pieces of fruit in a bowl and 6 of them are apples. What percentage of the pieces of fruit in the bowl are apples?
40%
0.06%
6%
0.4%
Answer: 40% of the fruit pieces are apples
Step-by-step explanation:
[tex]\frac{6}{15}[/tex] = .4
.4 x 100% = 40%
Find an expression which represents the difference when (9x-4)is subtracted from (7x-2) in simplest terms.
The expression when (9x-4) is subtracted from (7x-2) in simplest terms is 2(1-x).
According to the question,
We have the following information:
(9x-4) is subtracted from (7x-2).
(We know that an expression written after the word from should be written first and the expression before it should be written after the sign of subtraction.)
So, we have the following expression:
(7x-2)-(9x-4)
7x-2-9x+4
(We know that the number with the same variables are added or subtracted. For example, 7x is added to -9x.)
-2x+2
Taking 2 as a common factor from these two terms:
2(-x+1)
2(1-x)
Hence, the difference of the two expressions is 2(1-x).
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