Using the absolute value and PEMDAS order of operations, it is found that:
a) The missing expression for step 2 is: (36 + 2)/0.5 = − 14.8 ÷ 8.
b) The missing expression for step 6 is 76 - 1.85.
How to properly use mathematical operations?The absolute function is defined by:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
Thus, it usually measures the distance of a point x to the origin, hence |0.5| = |-0.5| = 0.5
In Step 2, we just have to apply the absolute value property to |-0.5|, and as such, the missing expression for step 2 is:
(36 + 2)/0.5 = − 14.8 ÷ 8.
For step 6, the division happens before the multiplication using PEMDAS order of operations and as such, the missing expression for step 6 is;
76 - 1.85.
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The missing steps are;
Step 1 the quantity of the sum of six squared plus two divided by the absolute value of negative 0.5 − 14.8 ÷ 8
Step 2
Step 3 the quantity of the sum of thirty six plus two divided by 0.5 − 14.8 ÷ 8
Step 4 the quantity thirty eight divided by 0.5 − 14.8 ÷ 8
Step 5 76 − 14.8 ÷ 8
Step 6
Step 7 74.15
the given set is a basis for a subspace w. use the gram-schmidt process to produce an orthogonal basis for w.
The orthogonal basis produced using the Gram-Schmidt process for W is[tex]y_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right], y_2=\left[\begin{array}{c}5 \\1 \\-6 \\-1\end{array}\right][/tex]
What is orthogonal ?
The concept of orthogonality in mathematics is an extension of perpendicularity in geometry. By extension, the term "orthogonality" is also used to describe the division of particular system properties. The phrase also has specific applications in other disciplines, such as chemistry and painting.
[tex]$$x_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \quad \text { and } \quad x_2=\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]$$[/tex]
Using Gram-Schmidt process to produce an orthogonal basis for W
[tex]$$y_1=x_1=\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]$$[/tex]
Now we know [tex]$X_1, X_2$[/tex] and [tex]$Y_1$[/tex]
Lets solve for [tex]$Y_2$[/tex]
[tex]y_2=x_2-\frac{x_2+y_1}{y_1+y_1} y_1$$[/tex]
[tex]y_2=\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]}{\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right][/tex]
[tex]\begin{aligned}y_2 & =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{7+28-0+1}{1+16+0+1}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \\& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\frac{36}{18}\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-2\left[\begin{array}{c}1 \\-4 \\0 \\1\end{array}\right] \\& =\left[\begin{array}{c}7 \\-7 \\-6 \\1\end{array}\right]-\left[\begin{array}{c}2 \\-8 \\0 \\2\end{array}\right] \\y_2 & =\left[\begin{array}{c}5 \\1 \\-6 \\-1\end{array}\right]\end{aligned}[/tex]
Complete question: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order bold x1 and bold x2
1 7
-4 -7
0 -6
1 1
The orthogonal basis produced using the Gram-Schmidt process for W is:__________. (Use a comma to separate vectors as needed.)
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Create the equation of a parabola with no x-intercepts.
Answer:
Step-by-step explanation:
No x intercept means it can't touch the x axis y=x^{2}+1 does the trick since it moves the whole thing up one unit
Solve
(type and ordered pair. type an exact answer, using radicals and i as needed, use a comma to separate answers as needed)
Two ordered pairs 45 is x^2 + y^2, 12 is x - y.An ordered pair is made up of the x (abscissa) and y (ordinate) coordinates, with two values stated in a certain order inside parenthesis.
An ordered pair can be found in what way?A pair of ordered numbers contains one point's coordinates in the coordinate system. Using its ordered pair in the form of, a point is given a name (x, y). X and Y coordinates are represented by the first and second numbers, respectively. Using the coordinates of the ordered pair, you can graph a point by placing a dot there.An ordered pair is made up of the x (abscissa) and y (ordinate) coordinates, with two values stated in a certain order inside parenthesis.Think about the following two ordered pairs: (c, d). If (a, b) = and (a, b) = (c, d), they are equivalent (c, d).Explanation:
45 = x^2 + y^2,
12 = x - y.
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an electronics store makes a profit of 30$ for every portable DVD player sold and 60$ for every DVD recorder sold. the manager’s target is to make at least 250 dollars a day on sales of portable DVD players and DVD recorders write an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target let p represent the number of portable DVD players and r represent the number of DVD recorders.
An inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target is 30p+60r≥250.
What is meant by inequality?An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is done in an unfair manner. On the number line, it is most typically used to compare the sizes of two numbers.
A and b are not equal in either situation. These interactions are recognized as robust inequalities.
Given,
Profit gained by selling portable DVD player=$30
Profit gained by selling portable DVD recorder=$60
Let,
The number of portable DVD player=p
The number of DVD recorders=r
And also given that,
The profit must be at least $250.
Therefore, 30p+60r≥250
Hence, an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target is 30p+60r≥250.
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A chool taff meeting had 60 teacher in attendance, 30% of whom were firt-year teacher. How many firt-year teacher were in the meeting?
18 first-year teachers were in the meeting.
In this question, we have been given that a school staff meeting had 60 teachers in attendance, 30% of whom were the first-year teachers.
We need to find the number of first-year teachers present in the meeting.
Let x be the number of first-year teachers present in the meeting.
As 30 percent of school staff are the first-year teachers, we need to find the 30 percent of 60.
Using the formula of percentage,
x = 60 * (30/100)
x = 18
Therefore, the number of first-year teachers present in the meeting = 18
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The purple team is the only team with a clue at the angle that is an alternate exterior angle to ∠11, but not congruent to it. Which angle is this? Explain why the angle is not congruent to ∠11
What is the alternate exterior angle of ∠11?
[tex]\angle 1 \cong \angle 7 \text { and } \angle 4 \cong \angle 6[/tex]
The number of sides in the given polygon is, n=11 . The sum of all exterior angles is 360o .
An exterior angle of a triangle is created by extending one side of the triangle. The angle between the extended side and the side next to it is called an exterior angle.
What is a alternate exterior?
Alternate Exterior Angles: The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
Look at the area above and below the crossed lines to find outside angles. Look at that outside area for each crossed line on different sides of the transversal to locate alternative outside angles. We assume you stated that the external angles are 1, 2, 7, and 8.
When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.
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Ruby and her children went into a movie theater and she bought $42 worth of bags of popcorn and drinks. Each bag of popcorn costs $6 and each drink costs $4. She bought a total of 8 bags of popcorn and drinks altogether. Determine the number of bags of popcorn and the number of drinks that Ruby bought.
Using system of linear equation the number of popcorn and drinks bought are 5 and 3 respectively
System of Linear EquationIn solving a system of linear equation, we have two unknown variables which we are to find. However, we can use either substitution, elimination or graphical method to solve them.
In this case, to solve this problem, we have to write out two equations and solve for the unknown variable;
let;
x = popcorny = drinksx + y = 8 ...eq(i)
6x + 4y = 42 ...eq(ii)
From eq(i)
x + y = 8
x = 8 - y ...eq(iii)
Put eq(iii) into (ii)
6(8 - y) + 4y = 42
y = 3
put y = 3 into eq(i)
x + 3 = 8
x = 5
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Which word sentence represents the equation?
4y = y + 9
Responses
Four times a number plus 9 is 9.
Four times a number plus 9 is 9.
Four times a number equals the number increased by 9.
Four times a number equals the number increased by 9.
Four increased by a number equals the number increased by 9.
Four increased by a number equals the number increased by 9.
Four times the sum of a number and 9 is the number.
find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles.
The probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles = 0.0111
In this question we need to find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, three yellow, and four red marbles.
Total marbles in tha bag
= 3 green marbles + 3 yellow marbles + 4 red marbles
= 10 marbles
the probability of drawing one marble from a bag,
P1 = 1/10
Now there are 9 marbles in the bag.
So, the probability of drawing second marble would be,
P2 = 1/9
So, the required probability of drawing two marbles (without replacement) from a bag would be,
P = P1 * P2
P = 1/10 * 1/9
P = 1/90
P = 0.0111
Therefore, the probability of drawing two marbles (without replacement) from a bag = 0.0111
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Rebecca ran 12 1/4 miles in 2 1/2 hour. What was her average speed in miles per hour?
a. 4.9 mph
c. 30.625 mph
b. 4.8 mph
d. 5.5 mph
Answer: A
Step-by-step explanation: Divide your miles by hour hours:
12.25/2.5 = 4.9
Her average speed was 4.9 miles per hour
As part of an ongoing service project, the students at Allenville High School recently spent an afternoon planting trees. They planted an average of 8 trees per participant. Soon they plan to do some more planting, averaging 12 trees per participant. If everything goes as planned, what will be the percent of increase in the average number of trees planted?
Answer:
50% increase
Step-by-step explanation:
If we call the number of people x;
On the first afternoon, everyone plants 8x (Average 8 per person)
In the future, the plan to plant 12x trees (Average 12 per person)
From 12x to 8x is a 50% increase, (12/8 = 1.5)
Hope this helps,
:]
X-Y=4
-2X+6(4-X)=3
-8X+24=3
-24 -24
-8X=-21
X=21/8
Y=11/8
(21/8,11/8)
find the error in the problem.
Answer: You did wrong at Y=11/8! It should be -11/8, not positive 11/8
Step-by-step explanation:
You solved it all right; just the y is wrong! The reason why y is -11/8 is that a negative and a negative will make a positive, and add an x positive, and you will get a positive answer. If y is negative, the answer would be negative!
While hovering near the top of a waterfall in a national park at 5776 feet, a helicopter pilot accidentally drops his sunglasses. The height h(t) of the sunglasses after t second
is given by the polynomial function h(t)=-16t^2+5776. When will the sunglasses hit the ground?
Answer:
Step-by-step explanation:
set the height function = 0 and solve for t-16t2+6400=0t2 = -6400/(-16)=
Why doe the Ditributive property make it eaier to multiply a 2 digit number the a 1 digit number
Distributive property make it easier to multiply a 2 digit number t0 a 1 digit number because by using distributive property we can multiply the number place of the two digit number by one digit number and inlast we can add it , which makes the whole process easier.
According to Distributive property it helps to solve the complex problems easily either they are of 2 digit or many more . Distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
In other words, according to the distributive property, an expression of the form A (B+C) can be solved as A (B+ C) = AB + AC.
This property applies to subtraction as well.
A (B –C) = AB – AC
For example :- 19 X 6
= 10 X 6 + 9 X 6
= 60 + 54
= 114
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You are presented with a deck of 20 cards, numbered from 1 to 20 and can draw one card. If the number is odd, you win $22. If the number is even, you win nothing. If you play the game, what is the expected payoff?
Answer:
$220
Step-by-step explanation:
Because, from 1 to 20 there are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) so it is said that for one odd number you win $22, as for 10 odd numbers, that is $22 x 10 which is $220
Use compatible numbers to estimate the correct quotient.
Answer:
60
Step-by-step explanation:
900 divided by 15 is 60
Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
The graph that correctly represents the function f(x) = [√(x + 3)] - 2 is; Graph D
How to interpret the graph of the function?
We are given the function;
f(x) = [√(x + 3)] - 2
Remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:
x + 2 = 0
x = -2
Then the function starts at:
f(-2) = [√(-2 + 3)] - 2
f(-2) = 3
Then the graph should start at (-3, 2).
We can also identify another point by evaluating in x = 2.
f(2) = [√(2 + 3)] - 2
f(2) = -1
So the function also passes through (2, - 1).
Notice that the only graph that contains these two points is the last graph with x-intercept at 7.
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Yoko is riding on a bike course that is 70 miles long. So far, she has ridden 42 miles of the course. What percentage of the course has Yoko ridden so far?
Answer: 60%
Step-by-step explanation:
Take 42 divided by 70, then times 100% = 60%
Yoko has ridden 60% so far!
Literal Equations
help asap !!
Answer: y=13\3 or 4 1\3
Step-by-step explanation:
~Describe the transformation, by giving the coordinate rule.
8.) (x,y) --> (________,________)
Answer:
(x+3, y-3)
Step-by-step explanation:
What value for a in the system of equations below would yield no solutions for the system? Explain how you obtained your answer.
ax+12y=−6
2x−6y=4
a=
The value of 'a' in the system of equations will be;
⇒ a = - 4
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equation are;
⇒ ax + 12y = - 6
⇒ 2x - 6y = 4
Now,
By the condition of No solution for the system, we get;
⇒ a / 2 = 12 / - 6
⇒ a / 2 = - 2
⇒ a = - 4
Thus, The value of 'a' in the system of equations will be;
⇒ a = - 4
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Find the area of the rhombus.
5m,10m,5m, and 10m
Please show your work.
The area of rhombus is 100m²
What is rhombus ?
A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.
A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. In the illustration below, two instances of rhombuses in nature are shown: a diamond and a kite.
The area of rhombus is
A = pq / 2
The value of p is 10 and q is 20
A = (10 * 20) / 2
= 100m²
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
x = 5
Step-by-step explanation:
Find the scale factor from figure B to A
let x = the scale factor
5x = 2 Divide both sides by 5
x = [tex]\frac{2}{5}[/tex] or .4
12.5 x .4 = 5
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0. 6 gallons of fuel. A warning light comes on when the remaining fuel is 1. 5 gallons or less.
Diego says the expression 14-0. 6t helps him understand this situation. In this situation, what does this expression represent, and what does the variable t stand for?
In the given expression 14 - 0.6t, variable t represents the number of gallons of fuel used by the car each day.
Explain the term variable of the equation?A term which includes at least one variable number, symbolized by one or maybe more letters, in an arithmetic operation, equation, or inequality. A symbol (often a letter) used in mathematics to represent an unknowable numerical value in such an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.For teh stated question-
The gasoline capacity of Diego's family automobile is 14 gallons. The automobile takes 0. 6 gallons of fuel every day. In the event that there are only 1.5 gallons of fuel left, a warning light will turn on.In the given expression 14 - 0.6t, t represents the number of gallons of fuel used by the car each day.
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What is the equation of the line that passes through the point (2, 6) and has a slope
of-1/2
The equation of the line is y = -1/2x + 7 which passes through the point (2, 6) and has a slope of -1/2.
What is the equation of a line?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
The equation of a line that passes through the point (2, 6) and has a slope of -1/2 can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the equation of the line, we can use the point-slope form of a line, which is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Substituting the values for the point and the slope into this equation, we get:
y - 6 = (-1/2)(x - 2)
y - 6 = -1/2x + 1
y = -1/2x + 7
Hence, The equation of the line is y = -1/2x + 7 which passes through the point (2, 6) and has a slope of -1/2.
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Question in picture. Please answer quickly
Answer: [tex]\frac{2\sqrt{2}-1 }{2}[/tex]
Step-by-step explanation:
1. multiply both the numerator and denominator by [tex]2\sqrt{2}[/tex]
2. distribute on the top to get [tex]8\sqrt{2} - 4[/tex] ([tex]\sqrt{2} *\sqrt{2}[/tex] equals 2)
3. multiply the bottom to get 8
4. after getting [tex]\frac{8\sqrt{2}-4 }{8}[/tex], factor out a 4 from each term to get [tex]\frac{4(2\sqrt{2}-1)}{4(2)}[/tex]
5. the fours will cancel and the answer will be [tex]\frac{2\sqrt{2}-1 }{2}[/tex]
Look at the equation. 5|x+3|-10=0 Select all the solutions to the equation.
Round off to 3 decimal places.
55.7796 =
Given : 55.7796
To Find : rounded off to 3 decimal places
Solution:
55.7796
To round off to 3 decimal places need to check digit at
4th decimal place
if digit is 5 or greater than 5 then digit at 3rd decimal place has to be increased by 1 and all decimal places after that to be removed
if digit is less than 5 then digit at 3rd decimal place remains same and all decimal places after that to be removed
55.7796
Digit at 4th decimal place is 6 which is greater than 5
Hence digit at 3rd decimal place has to be increased by 1
9 + 1 = 10 Hence 1 to be carried forward to digit at 2nd decimal place
7 + 1 = 8
Hence number rounded off to 3 decimal places is
55.780
55.7796 rounded off to 3 decimal places is 55.780
Heather saved 15% buying concert tickets online. If the tickets are regularly $95, how much did Heather pay for them online?
Answer:
Step-by-step explanation:
$80.75 Your welcome
Answer:
$80.75 dollars
Step-by-step explanation:
15% of 95 is 14.25
95 - 14.25 = 80.75
Steven’ new cell phone plan charge a flat monthly fee of $24. The plan allow an unlimited number of text meage, but each minute (m) ued for phone call cot $0. 15. Which equation mot accurately repreent the monthly cot (c) of Steven’ phone bill baed on how many minute talked?
As a new cell phone plan charges a flat monthly fee of $24 and allows for an unlimited number of text messages, but charges $0.15 per minute (m) used for phone calls, the equation that will represent the problem is C=24+0.15m.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Let m be the minutes talked on phone,
C=24+0.15m
The problem is represented by the equation C=24+0.15m since the new cell phone plan charges a fixed monthly fee of $24 and permits unlimited text messages, but each minute (m) utilized for phone calls costs $0. 15.
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