After finishing his shift, a security guard wrote 6.75 under "hours worked" on his time card. how long did he work ?
The security guard worked for 6 hours and 45 minutes, this is because 0.75 of an hour is equivalent to 45 minutes.
Explanation:In the context of this question, the security guard logged 6.75 hours on his shift. This figure is given in decimal format. To convert this into hours and minutes, you need to understand that .75 of an hour is three quarters of 60 minutes. So, 0.75 x 60 minutes is 45 minutes. Therefore, the security guard worked for 6 hours and 45 minutes.
This is equivalent to 6 hours and 45 minutes. In decimal form, 0.75 represents three-quarters of an hour, which is 45 minutes. So, he worked for 6 hours and 45 minutes.
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What is the relationship between 8.76×106 and 8.76×102 ?
Select from the drop-down menus to correctly complete the statement.
8.76×10^6 is ___ times ___ than 8.76×10^2 .
1) 1000, 10,000, 100,000, or 1,000,000.
2) Greater or Less.
10^6 = 1,000,000
10^2 = 100
1,000,000 / 100 = 10,000
so 8.76x10^6 is 10,000 times greater than
Point M is the midpoint of AB . AM=3x+3, and AB=8x−6.
What is the length of AM?
The length of AM is 21.
Given that,
Point M should be the midpoint of the AB.AM = 3x + 3.AB = 8x - 6.Now
We can say that
AB = 2AM
And,
AM = [tex]\frac{AB}{2}[/tex]
AM [tex]=\frac{(8x-6)}{2}[/tex]
= 4x - 3
Now
3x + 3 = 4x - 3
4x - 3x = 3 + 3
x = 6
Finally,
AM = 3x + 3
= 3(6) + 3
= 18 + 3
= 21
Therefore we can conclude that The length of AM is 21.
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Why do we never accept the null hypothesis or the research hypothesis? (instead we either reject or fail to reject)?
According to the U.S. Geological Survey, the Mississippi River is 200 mi shorter than the Missouri River. Together, they cover a total of 4880 mi. Find the lengths of each river.
Can you please check my answers?
Select the order pair(s) that are solutions to this system of inequalities:
y < -3x + 2
y ≥ x - 1
Question 1 options:
(0, 0) <<<<
(0, -4)
(1, 4) <<<<
(-3, 3)
Select the order pair(s) that are solutions to this system of inequalities:
y ≤ -2x + 3
y < 1/2 x - 2
Question 2 options:
(0, 0) <<<<
(5, -1)
(0, -3) <<<<
(-2, -3)
Select the order pair(s) that are solutions to this system of inequalities:
y ≤ 3
y > -x + 1
Question 3 options:
(0, 0) <<<<
(2, 2)
(-1, 3) <<<<
(5, -1)
What are the real and imaginary parts of the complex number?
−6+2i
Enter your answers in the boxes. (Can someone help me with this one?)
The real part:
The imaginary part:
Which expression is equal to (−8−3i)+(3+4i)?
4
−5+i <<<< I chose this one..is it right?
−11+7i
−4
Which expression is equal to (5−2i)−(1+3i)?
4+3i
6−5i
4−5i <<<< I chose this one, is it right?
4+i
Which expression is equal to −2i(4−i)?
−8−2i
8−2i <<<<
2−8i
−2−8i
Multiply.
(5+2i)(4−3i)
Enter your answer, in standard form, in the box.
I got (2i+5)(-3i+4) is that right?
for the second to last one this is the right answer is -2-8i ( i got and 100 on my test )
What is x-7/4 = 5/6
How can you classify the results of operations on real numbers
Answer:
We can classify the result of operation on real number into rational and irrational numbers.
Further details:
We already know that all counting numbers are whole numbers, all whole numbers are integers, and all integers are rational numbers. Irrational numbers are a distinct category of their own. When we put together the rational numbers and the irrational numbers, we get the set of real numbers.
Rational numbers:
Any quantity that can be written as a fraction a/b where a and b are integers and b is not equal to zero are called rational numbers. These comprise all the integers, any finite decimals, or repeating decimals (decimals that have a pattern).
Irrational numbers:
Any number that can't be written as a/b are measured irrationals. They can be printed in decimal, but they go on constantly without any pattern (And there is a way to prove this).
All of the rational numbers and irrational numbers are measured real numbers. It must be notice here that all these numbers lie on a straight number and any number that lie outside the number line is not real number. For instance, we can extend the 1-D line to 2-D plane with complex numbers on it.
Answer details:
Subject: Mathematics
Level: High school
Keywords:
• Real numbers
• Classification of real number
• Rational number
• Irrational numbers
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The results will be classified as rational or Irrational numbers.
This question will have to be explained by understanding real numbers.
Real numbers are basically defined as any type of number in life that is not a complex number. This means they could be fractions, decimals, positive numbers, negative numbers e.t.c
Now, in broad terms, under real numbers, we have two major types which are:
Rational Numbers and Irrational numbers.
Now, rational numbers include; integers, Natural numbers, whole numbers, fractions, terminating decimals, repetitive decimals.
While Irrational numbers are basically any number that cannot be expressed as a fraction of integers and as well their decimals are usually non-repeating and non-terminating decimals.
Thus, any operation on real numbers, will lead us to an answer that falls under any of it's major branches which are rational and Irrational numbers.
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Find an equation of a line whose graph intersects the graph of the parabola y=x^2 at (a) two points, (b) one point, and (c) no point. (There is more than one correct answer for each.)
Final answer:
Equations of lines that intersect a parabola at distinct points can vary, but typically involve conditions based on the slope and y-intercept relative to the vertex of the parabola. For two points, a non-tangent linear equation; for one point, a tangent with slope equal to the parabola's derivative at the intersection; for no points, the line lies entirely outside the parabola's path.
Explanation:
To find equations of lines intersecting the parabola y = x² at different points, we consider three cases:
(a) The line intersects the parabola at two points. This is a secant line and can be represented by a linear equation like y = mx + b, where m is not equal to 2a for any x-coordinate of the intersection points (since 2a is the derivative of the parabola at the point (a, a²), where it would be tangent).(b) The line intersects the parabola at one point. This is a tangent line and can be represented by a linear equation like y = mx + b, where m = 2a is the slope of the tangent at the point of tangency (a, a²).(c) The line does not intersect the parabola, meaning it is either above all points of the parabola for positive y-values or below for negative y-values. Such a line might have an equation like y = mx + b with b > a² for positive y-values or b < 0 for negative y-values when m < 2a for any x-coordinate.All lines can be represented by the general linear equation y = a + bx + cx², which is the equation of a parabola only if c ≠ 0.
If two lines intersect, then they intersect in exactly _____.
two points
one point
one line
one plane
Answer:
The correct answer is one point.
Step-by-step explanation:
In geometry, if two lines cross each other, they will do so at an exact point.
Imagine that the lines are formed by thousands of points located next to each other, which makes us see a line, therefore if they cross, they will do so at a single point that will have a coordinate in (x, y) format.
When the two lines are on the same plane, the following situations may occur:
if they match they have an unlimited number of points in common if they are different but they have the same slope they are parallel and they do not have points in common if the above does not happen, they have a single point of intersection.This diagram of airport runway intersections shows two parallel runways. A taxi way crosses both runways. How are 6 and 2 related?
a)corresponding angles
b) alternate interior angles
c)same side interior angles
d) none of these
Answer: a)corresponding angles
Step-by-step explanation:
When two lines are intersected by a transversal line then the non adjacent angles in the matching corners are known as pair of Corresponding Angles.In the given figure angle 6 and angle 2 are the two non adjacent angles in the matching corners , which we called as a pair of Corresponding Angles. {By definition}
Therefore, angle 2 and angle are related by corresponding angles .
In the given diagram, angles 6 and 2 are corresponding angles.
To determine how 6 and 2 are related, we will define each of the terms in the option.
Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines. They are found at different intersections but on the same side of each parallel line and the same side of the transversal line.Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal. The angles are positioned at the inner corners of the intersections and lie on opposite sides of the transversal.Same side interior angles are two angles that are on the interior of two lines and specifically on the same side of the transversal
Angles 6 and 2 are found at different intersections but on the same side of the parallel lines and the same side of the transversal line.
Hence, angles 6 and 2 are corresponding angles.
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How can you find the domain of this function???
Number 198
The length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 269 in squared . in2. find the lengths of the sides of the two squares.
The length of the side of the big square is 13 in. while that of the smaller square is 10 in.
Square
Square is a quadrilateral in which all the sides are equal to each other. Also opposite sides are parallel to each other and all angles measure 90 degrees.
Let a represent the length of the bigger square side and b represent the length of each side of the smaller square, hence:
a = b + 3 (1)
Also:
a² + b² = 269
(b + 3)² + b² = 269
2b² + 6b - 260 = 0
b = -13 or 10. Since b cannot be negative hence b = 10.
a = b + 3 = 10 + 3 = 13
The length of the side of the big square is 13 in. while that of the smaller square is 10 in.
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To find the lengths of the sides of the two squares with a combined area of 269 square inches, where the larger square has sides 3 inches longer than the smaller square, we set up a quadratic equation based on the areas. Solving the equation gives us 10 inches for the smaller square and 13 inches for the larger square.
Explanation:Finding the Lengths of the Sides of the Two Squares
We are given that the larger square has sides that are 3 inches longer than the sides of the smaller square and that the sum of their areas is 269 square inches. Let's denote the side length of the smaller square as s inches. Then, the side length of the larger square is (s + 3) inches.
The area of the smaller square is s^2, and the area of the larger square is (s + 3)^2. The sum of their areas is given by:
s^2 + (s + 3)^2 = 269
Expanding the equation gives us:
s^2 + s^2 + 6s + 9 = 269
Combining like terms, we get:
s^2 + s^2 + 6s + 9 - 269 = 0
2s^2 + 6s - 260 = 0
Dividing the entire equation by 2, we simplify to:
s^2 + 3s - 130 = 0
This is a quadratic equation that can be factored:
(s + 13)(s - 10) = 0
Setting each factor equal to zero gives us two possible solutions for s:
s + 13 = 0s - 10 = 0The negative solution is not physically meaningful for the length of a side, so we discard s = -13 and take s = 10 inches as the side length of the smaller square. The larger square, therefore, has sides of 13 inches.
So, the side lengths of the two squares are 10 inches and 13 inches respectively.
Find the distance between a and b. a = 14/5 , b = 112/65
What is the point of intersection when the system of equations below is graphed on the coordinate plane?
x-y=1
y-x=1
A) no intersection point
B)infinite intersection points
C)(1, 0)
D)(–1, 0)
Answer with explanation:
The two system of equation which are graphed on coordinate plane :
→x -y =1
y=x-1
→y-x=1
y=x+1
⇒Comparing with Slope intercept form of Line which is y= m x +c,
→m=1 for both the lines
As, the two lines has same slope , so they are parallel.Parallel lines never Intersect.
⇒The two system of equation have no solution as:
[tex]\frac{1}{-1}= \frac{-1}{1}\neq \frac{1}{1}[/tex]
Option A:→ No Intersection Point
Martin had 7 pounds of grapes left, and he gave away 25 of them. Explain how to use compatible numbers to estimate the amount of grapes he gave away.
Answer:
Sample response:
2
5
is close to
1
2
, and it is easy to find
1
2
of 7 mentally. Half of 7 is 3.5, so Martin gave away about 3.5 pounds.
Step-by-step explanation:
-,-
Write an equation for the description. Ten times the sum of half a number x and 5 is 7.
Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total employee benefits are _____% of his gross pay.
In which quadrant is the point (5,-2) located?
Answer: Quadrant 4
Step-by-step explanation: Since the rules for Quadrant 4 is (+, -) than it will be there because 5 is a positive number and -2 is a negative number.
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The area of a rectangle is 60 square inches. The length of the rectangle is 7 inches longer than the width. Which equation models this situation?
A: w + 7= 60
B: 7w = 60
C: w(w+7) = 60
D: w + 7w = 60
The answer is (c)
As the width is w , length becomes w + 7
Hence:
Area = l × b
60 = w(w+7)
Which numbers should be multiplied to obtain 175^2 − 124^2?
A. 51 and 299
B. 51 and 51
C. 2601 and 2601
D. 30501 and 30749
The numbers that should be multiplied to obtain 175² - 124² are 51 and 299. This is due to the algebraic concept of a difference of squares.
Explanation:The mathematical expression 175² - 124² can be represented as the difference of squares. The difference of squares is a special case in algebra where a² - b² can be factored into (a + b)(a - b). So, in this case, we can represent 175² - 124² as (175 + 124)(175 - 124).
Hence, the numbers that should be multiplied in this case are 51 and 299. Therefore, the correct answer is option A: 51 and 299.
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What is the center and radius of the circle with equation x2 + y2 - 4x + 22y + 61 = 0?
The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?
omgggg please help guys
The number of yards of string lights the manager needs to enclose in this area is 26 yards.
Given that the stage manager of a school play creates a rectangular acting area of 42 square yards.
What is the perimeter of the rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
The number of yards of string lights that the manager needs to enclose the area is given by the perimeter of the rectangular area.
Let the length of the rectangular acting area be x, then the width is given by 42 / x.
Recall that the perimeter of a rectangle is given by
P = 2(length + width) = 2(x + 42/x) = 2x + 84/x
The perimeter is minimum when the differentiation of 2x + 84/x is equal to 0.
2-84/x² = 0
⇒2x²-84=0
⇒2x²=84
⇒x²=42
⇒x=√42
⇒x=6.48≈6.5
Now, perimeter = 2(6.5) + 84/6.5
=13+12.92
=25.92≈26
Therefore, the number of yards of string lights the manager needs to enclose in this area is 26 yards.
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The volume of a cube is 1000 cubic inches. What is the edge length of the cube?
A fair coin is tossed 5 times in a row the exact probability of the coin landing heads exactly 2 times is what
Answer:
The probability is [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
Given is that a fair coin is tossed 5 times in a row.
This gives total number of outcomes as = [tex]2\times2\times2\times2\times2=32[/tex]
As its needed that heads comes exactly 2 times, so favorable outcomes are = 5C2
[tex]\frac{5!}{2!(5-2)!}[/tex]
Solving this we get 10
Therefore, the probability of getting heads exactly 2 times is =
[tex]\frac{10}{32}[/tex] or
[tex]\frac{5}{16}[/tex]
Answer:
See image
Step-by-step explanation:
Plato
The total cost C( in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take
a. Solving the equation for x gives x = (C - 60)/85.
b. The number of ski trips that you would take if you spend a total of $315 is 3 ski trips.
The number of ski trips that you would take if you spend a total of $315 is 5 ski trips.
In Mathematics and Geometry, a linear equation is a type of function with a constant slope and whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.
Part a.
By making x the subject of formula in the given equation, we have:
C = 85x + 60
85x = C - 60
x = (C - 60)/85
Part b.
When the value of C is 315, number of ski trips (x) is given by;
x = (315 - 60)/85
x = 3 ski trips.
When the value of C is 485, number of ski trips (x) is given by;
x = (485 - 60)/85
x = 5 ski trips.
Complete Question:
The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take.
a. Solve the equation for x.
b. How many ski trips do you take if you spend a total of $315? $485?
write 1.08 X 10^4 in standard form
The required standard form for 1.08 X 10^4 is 10800.
Given that,
To write 1.08 X 10^4 in standard form.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
1.08 * 10⁴ = 1.08 * 10000 = 10800
Thus, the required standard form for 1.08 X 10^4 is 10800.
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Which of the following is equivalent to (16^3/2)^1/2? 6 8 12 64
Answer:
Option B is correct that is 8.
Step-by-step explanation:
Given Expression : [tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]
We use a law of exponent here to simplify it,
[tex](x^a)^b=x^{ab}[/tex]
Consider,
[tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]
[tex]=16^{\frac{3}{2}\times\frac{1}{2}}[/tex]
[tex]=16^{\frac{3}{4}}[/tex]
[tex]=(2^4)^{\frac{3}{4}}[/tex]
[tex]=2^{4\times\frac{3}{4}}[/tex]
[tex]=2^3[/tex]
[tex]=8[/tex]
Therefore, Option B is correct that is 8.
A patio floor is shaped like a rectangle with a
width of w cm and a length of 21 ft.
Find an expression that represents the area of
the floor.
The length of a rectangle is 3 m longer than its width. if the perimeter of the rectangle is 42 m , find its area.
The area of the given rectangle would be 108-meter sq.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that length of a rectangle is 3 m longer than its width.
The perimeter of the rectangle = 42 m
Width = w
Let the length of the rectangle is 3 + w
Perimeter = 2(L +W)
42 = 2(w + 3 + w)
21 = 2w + 3
18 = 2w
w = 9
Area = 9 x 12 = 108 m sq.
Therefore, the area of the given rectangle would be 108-meter sq.
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