Answer:
The total number of copy rooms in the building is 9.
Step-by-step explanation:
With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).
From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:
[tex]n = 6 \cdot r + 7[/tex]
From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:
[tex]n = 7 \cdot r - 2[/tex]
From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:
[tex]6 \cdot r + 7 = 7 \cdot r - 2[/tex]
Puting known and unknowns on opposite sides, we get:
[tex]7+2 = (7-6) \cdot r [/tex]
Solving we get:
[tex]9 = r[/tex]
Therefor the total number of rooms is 9.
Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.
As a reference, the following link is useful:
https://en.wikipedia.org/wiki/System_of_linear_equations
The number of boxes of paper exists at 61.
How to find the copy rooms in the office building?The whole number of copy rooms as r and the boxes of paper Reginald has to distribute among them (already named [tex]$\mathbf{n}$[/tex] ).
Reginald gives 6 boxes of paper to each room, he will always have 7 boxes. We can write this as:
[tex]$n=6 \cdot r+7$$[/tex]
Reginald shows 7 boxes of paper to each room, he would always require 2 boxes. We can write this as:
[tex]$n=7 \cdot r-2$$[/tex]
From the above equation, we have a [tex]$2 \times 2$[/tex] system of equations, which can be solved in any form. In this issue, we can utilize equalization to easily find the number of rooms.
From the 2 relations we can write:
[tex]$6 \cdot r+7=7 \cdot r-2$[/tex]
Putting known and unknowns on opposite sides, we get:
[tex]$7+2=(7-6) \cdot r$$[/tex]
Solving we get:
[tex]$9=r$$[/tex]
Thus the total number of rooms exists at 9.
Plugging this solution into any of the 2 equations, then we get
The number of boxes of paper exists at 61.
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Ben climbed 15 feet up a hill,8 feet down a hill, and 11 feet up another hill. What is his overall change in elevation?
Answer:
18 feet
Step-by-step explanation:
15-8+11=18
How will the solution of the system change if the inequality sign on both inequalities
Shown below
Step-by-step explanation:The first system of inequality is the following:
[tex]\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y<2x+\frac{1}{3}\end{array}\right.[/tex]
To find the solution here, let's take one point, say, [tex](0,0)[/tex] and let's taste this point into both inequalities, so:
FIRST CASE:First inequality:
[tex]y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False![/tex]
The region is not the one where the point [tex](0,0)[/tex] lies
Second inequality:
[tex]y<2x+\frac{1}{3} \\ \\ 0<2(0)+\frac{1}{3} \\ \\ 0<\frac{1}{3} \ True![/tex]
The region is the one where the point [tex](0,0)[/tex] lies
So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there
SECOND CASE:First inequality:
[tex]y<2x+\frac{2}{3} \\ \\ 0<2(0)+\frac{2}{3} \\ \\ 0<\frac{2}{3} \ True![/tex]
The region is the one where the point [tex](0,0)[/tex] lies
Second inequality:
[tex]y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True![/tex]
The region is not the one where the point [tex](0,0)[/tex] lies
So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.
CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.
What is the simplified form of the rational expression below 6x^2-54 / 5x^2+15x
Answer:
[tex]\large\boxed{\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}}[/tex]
Step-by-step explanation:
[tex]6x^2-54\qquad\text{distributive}\\\\=6(x^2-9)=6(x^2-3^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=6(x-3)(x+3)\\\\5x^2+15x\qquad\text{distributive}\\\\=5x(x+3)\\-----------------\\\\\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)(x+3)}{5x(x+3)}\qquad\text{cancel}\ (x+3)\\\\=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}[/tex]
Find the missing value so that the two points have a slope of -17/10 (-3,9) and (x,-8)
Answer:
x=7
Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1)
(-8-9)/(x-(-3))=-17/10
-17/x+3=10
-17/7+3=10
-17/10=10
To find the missing value so that the two points have a slope of -17/10, we can use the slope formula. Substituting the coordinates into the formula, we get an equation -17/(x + 3) = -17/10. Solving for x, we find x = 7.
Explanation:To find the missing value so that the two points have a slope of −17/10, we can use the slope formula. The slope formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the first point is (-3, 9) and the second point is (x, -8).
Substituting the coordinates into the slope formula,
we have (-8 - 9) / (x - (-3)) = -17/10.
Simplifying this equation,
we get -17 / (x + 3) = -17/10.
Cross multiplying, we find x + 3 = 10.
Solving for x, we subtract 3 from both sides, giving x = 7.
Therefore, the missing value is 7.
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What is the volume of this triangular prism?
22.4 cm
18.1 cm
28 cm
313.6 cm3
506.8 cm3
5,676.16 cm3
11,352.32 cm3
Answer:
[tex]V=5,676.16cm^3[/tex]
Step-by-step explanation:
The volume of a triangular prism is defined by the formula:
[tex]V=(area-of-base)*(length)[/tex]
In this case the base is triangular and the area of a triangle is: [tex]A=\frac{1}{2}(base)*(height)[/tex]
Then the volume is:
[tex]V=\frac{1}{2}(base*height*length)[/tex]
Now we have to replace with the given values:
[tex]V=\frac{1}{2}(22.4cm*18.1cm*28cm)\\\\V=\frac{1}{2}(11,352.32cm^3)\\\\V=5,676.16cm^3[/tex]
Then the correct answer is the third option.
[tex]V=5,676.16cm^3[/tex]
Answer:
5,676.16 is your answer 2021 Edge
I got it right
Step-by-step explanation:
Using the triangle pictured, find the measure of side AB. Round your answer to the nearest tenth. A) 1.6 B) 2.2 C) 2.7 D) 3.3
Answer:
Option B (AB = 2.2 units).
Step-by-step explanation:
The diagram shows that there are two sides given and one angle is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin ABC / AC = sin BAC / BC.
Plugging ABC=72 degrees, AC=2.5, and BC=2.1 in the sine rule gives:
sin 72 / 2.5 = sin BAC / 2.1.
Cross multiplying gives:
sin BAC = (2.1*sin 72)/2.5.
sin BAC = 0.79888747368.
Taking sin inverse on both sides gives:
BAC = arcsin (0.79888747368) = 53.0239949 degrees.
To find AB, first, the angle ACB is required. To find that angle, use the triangular law of angles. All the three angles sum up to 180 degrees. Therefore ACB = 180 - 72 - 53.0239949 = 54.9760051 degrees.
Now applying the Sine Rule to find AB:
sin ACB / AB = sin ABC / AC.
sin (54.9760051) / AB = sin 72 / 2.5.
AB = (2.5*sin (54.9760051))/sin (72) = 2.2 (to the nearest tenth).
Therefore, AB = 2.2 units, i.e. Option B!!!
What is the initial value of the sequence?
The points shown on the graph represent the numbers in a
geometric sequence.
Answer:
The initial value of the given geometric sequence is 2.
Step-by-step explanation:
The given points are (1,2), (2,4) and (3,8).
It means the first term is 2, second term is 4 and third term is 8. So, the common ratio is
[tex]r=\frac{a_2}{a_1}=\frac{4}{2}=2[/tex]
A geometric sequence is defined as
[tex]f(n)=ar^{n-1}[/tex]
Where, a is first term of the sequence, r is common ratio and n is number of term. In other words f(1) is the initial value of the geometric sequence.
The given geometric sequence is
[tex]f(n)=2(2)^{n-1}[/tex]
The value of f(1) is 2.
Therefore the initial value of the given geometric sequence is 2.
Answer:Just took the test, it is 2 on edg
Step-by-step explanation:
:)
Choose the possible descriptions of cross sections formed by the intersection of a plane and a cylinder choose all that apply
-circle
-rectangle
-triangle
-line segment
-point
Answer:
circle and rectangle
Step-by-step explanation:
we know that
A cross section that is perpendicular to the base of cylinder is a rectangle
A cross section that is parallel to the base of cylinder is a circle
A cross section that is angled to the base of cylinder is an oval
Final answer:
A plane intersecting a cylinder can create a circle if perpendicular to the cylinder's axis, or a rectangle if cut parallel to the side of the cylinder. Ellipses are also possible when the cutting angle is oblique, and may look circular from certain perspectives. Triangles, line segments, and points are not typical cross sections for a cylinder.
Explanation:
When a plane intersects a cylinder, several different cross sections can result, depending on the angle and position of the plane relative to the cylinder. If the plane is perpendicular to the axis of the cylinder, the cross section will be a circle. If the plane intersects the cylinder at an angle to the axis, the cross section can be an ellipse, which in some cases may appear to be a circle depending on the perspective. A plane intersecting parallel to the side of the cylinder will produce a rectangle. It is not possible for a cylinder to have a triangular, line segment, or point as a cross section through normal slicing, as these do not represent the way planes intersect with the smooth curved surface of a cylinder.
Which number line represents the solution set for the inequality -4(x + 3) 5-2-2x?
O
+
-7
+
-6
+
-4
-5
-3
-2
-1
0
1
2
3
4
5
6
7
-7
+
-6
+
-5
+
-4
+
-3
+
-2
+
-1
+
0
+
1
+
2
+
3
+
4
5
6
7
-7 -6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
7
+
+
+
+
+
-7
-6
-5
-4
+ +
-3 -2
+
-1
0
1
2
3
4
5
6
7
Answer:
A
Step-by-step explanation:
Consider the smaller than sign as smaller or equal to sign as I couldn,t type the sign
-4(x+3)<-2-2x
Expand the bracket
-4x-12<-2-2x
Add 2x to both sides
-2x-12<-2
Add 12 to both sides
-2x<10
add 2x to both sides
0<10+2x
minus 10 on both sides
-10<2x
SImplify
-5<x
X is larger or equal to -5 which means the option A
Edna says that when (x - 2)^2 = 9, that x - 2 = 3. Use
complete sentences to explain whether Edna is correct.
Use specific details in your explanation.
Answer:
She is partially correct. There are 2 possible answers to this problem, and x - 2 = 3 is one of the answers. When applying the square root to both sides, the resulting answer could be either negative or positive. Therefore, applying the square root to both sides leads to the two following equations: x - 2 = 3 or x - 2 = -3.
If A and B are dependent events, which of these conditions must be true?
Answer:
i would think A
Answer:P(B|A)is not equal P(B)
Step-by-step explanation:
8s+4(4s-3)=4(6s+4)-4
Answer:
8s + 4(4s - 3) = 4(6s + 4) - 4
8s + 16s - 12 = 24s + 16 - 4
24s - 12 = 24s + 12
This equation has no solution.
A rectangle's length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find
its width, w?
Answer:
I think the answer would be 5 divided by 50 times two to find the width.
Step-by-step explanation:
I think my answer above explains it well enough.
Answer: w(2w + 5) = 50
Step-by-step explanation:
Which graph represents an inverse variation
Answer:
The second graph.
Step-by-step explanation:
In inverse variation, an increase in one variable leads to a decrease in the other value in the relationship.
xα1/y
x=k/y
meaning
xy= constant
Such a graph slants with a negative gradient from left to right of the Cartesian plane. (the second graph).
Answer:
it's B
Step-by-step explanation:
15. SHORT ANSWER Define a variable and
write an expression to represent the
following phrase.
seven years younger than Lisa
Answer:
see below
Step-by-step explanation:
Let L = lisa's age
seven years younger than Lisa
L-7
Are all of the roots of the polynomial p(x)=x^3+3x^2-11x-5 rational numbers? Why or why not?
Answer:
Step-by-step explanation:
yes. polynomials only have rational numbers
Find the common difference of the sequence shown.
1/2, 1/4 , 0, ...
Answer:
-1/4
Step-by-step explanation:
Given sequence is:
1/2, 1/4 , 0, ...
In order to find the common difference in the terms of a sequence, the preceding term is subtracted from the next term.
For example in the given sequence:
first term will be subtracted from second term and second term will be subtracted from third term
So,
[tex]\frac{1}{4}-\frac{1}{2} \\=\frac{1-2}{4}\\ =-\frac{1}{4}\\ Similarly,\\=0-\frac{1}{4} \\=-\frac{1}{4}[/tex]
The common difference is - 1/4 ..
Answer:
-1/4
Step-by-step explanation:
SQ bisects TSR. Find the value of x.
Answer: The answer is 10
Answer:
10
Step-by-step explanation:
math
QUICK!!
The x-intercepts of a quadratic function are −3 and 5. What is the equation of its axis of symmetry?
A. x=-3
B. x=1
C. x=5
D. x=-15
Answer:
B. x=1
Step-by-step explanation:
Let us define axis of symmetry first.
The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.
We have x-intercepts of -3 and 5
In ordered to find the axis of symmetry we have to find their middle intercept
To find the axis of symmetry:
[tex]= \frac{-3+5}{2}\\=\frac{2}{2}\\ =1[/tex]
So the axis of symmetry is x = 1 ..
Answer:
B x=1
Step-by-step explanation:
edge 2020 2021
Solve the following inequality algebraically: 1<3x-2<4
A. 1
B. 0
C. 1>x>2
D. 0>x>3
Answer:
1 < x < 2
Step-by-step explanation:
Given
1 < 3x - 2 < 4 ( add 2 to each of the 3 intervals )
3 < 3x < 6 ( divide each interval by 3 )
1 < x < 2
Answer:
A
Step-by-step explanation:
Edge 2021
24 people go to joe's birthday party.half walk and a quarter travel by bus all the others go by taxi. How many guests walk? How many travel by bus? How many use taxis? What fraction use taxis? What fraction don't use taxis?
Answer:
How many guests walk? 12How many travel by bus? 8How many use taxis?4What fraction use taxis? [tex]\frac{1}{6}[/tex]What fraction don't use taxis?[tex]\frac{5}{6}[/tex]Step-by-step explanation:
Number of people that attended the party= 24.....let this be x
Number of people that walked= 1/2 x
[tex]=\frac{1}{2} *24 =12[/tex]
Number of people that travel by bus= 1/4 x
[tex]=\frac{1}{4} *24= 8[/tex]
Number of people that go by taxi= the rest
[tex]=24-(12+8)=24-20=4[/tex]
The fraction that used taxis= those that used tax/total number of people
Those that used taxi=4
Total number of people=24
Fraction = [tex]\frac{4}{24} =\frac{1}{6}[/tex]
Fraction that did not use taxi = whole-fraction that used taxi
[tex]\frac{6}{6} -\frac{1}{6} =\frac{5}{6}[/tex]
Answer please. If you answer, you get 44 points. I don't use the points here. So answer please. I want full work.
Answer: you simplfy the two equations already there then plug them in to find factors
Step-by-step explanation:
Answer:
65
Step-by-step explanation:
These are called vertical angles. Vertical angles are equal.
145 = 2x + 15
130 = 2x
x = 65
what is 34/9 written as a decimal
Answer:
3.7
Step-by-step explanation:
To write 34/9 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 34 by 9 what we write down as 34/9 and we get 3.7777777777778
And finally we have:
34/9 as a decimal equals 3.7777777777778
Please mark brainliest and have a great day!
Answer:3.8
Step-by-step explanation:
34/9
9 into 34 is 3 remainder 7
:. 34/9
= (9 x 3 + 7)/9
=3.777778
=3.8
The triangles shown below may not be congruent.
let's take a peek at the triangles.
they have a 30° angle and a 80° each, and a side that is not in between in common.
[A]ngle [A]ngle [S]ide, AAS congruence.
Answer:
Option B, False.
Step-by-step explanation:
In the given figure two triangles have been given. In these triangles two angles and corresponding side has been given as equal in measure.
Therefore, by AAS theorem for congruence, the given triangles are congruent.
The given statement that the triangle shown may not be congruent is False.
Option B is the answer.
let f(x) = 5/x and g(x)=2x2+5x. What two numbers are not in the domain of f o g
Answer:
0 and -5/2
Step-by-step explanation:
g is the first function we consider because that is the function we are first plugging in values into since the order is f o g and not g o f.
g has domain all real numbers meaning you can plug in any number into g and get a number back
So now let's look at plugging in g(x) into f(x)
that is f(g(x))=f(2x^2+5x)=5/(2x^2+5x)
Here you are dividing by a variable
You have to watch out dividing by 0
The variable, 2x^2+5x, is 0 when....
2x^2+5x=0
x(2x+5)=0
x=0 or x=-5/2
So The domain is all real numbers except x=0 or x=-5/2
[tex](f \circ g)(x)=\dfrac{5}{2x^2+5x}\\\\2x^2+5x\not =0\\x(2x+5)\not=0\\x\not =0 \wedge x\not =-\dfrac{5}{2}[/tex]
Solve the system of equations
x + 3y = −1
2x + 2y = 6
Which conic section does the equation below describe?
x^2+y^2+2x-8y-13=0
Answer: B) Circle
Step-by-step explanation:
First, complete the square:
x² + 2x + 1 + y² - 8y + 16 = 13 + 1 + 16
↓ ↑ ↓ ↑
(2/2) = (1)² (-8/2) = (-4)²
(x + 1)² + (y - 4)² = 30
The result is a circle whose center is (-1, 4) and radius is √30
conic section of the equation B .Circle.
What is conic section?A conic section (or simply conic, sometimes named a quadratic curve) exists as a curve acquired as the intersection of the surface of a cone with a plane.
The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be uniquely identified or standardized.
Canonical equation for circle is (x — x0)2 + (3, yo)2 = R2 ,
hence (x + 1)2 + (y — 3)2 = 4 describes a circle.
conic section of the equation B .Circle.
Standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.
Often, it is one which provides the simplest representation of an object and which allows it to be identified in a unique way.
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Indicate the equation of the given line in standard form. The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
Answer:
3x-4y=2
Step-by-step explanation:
step 1
Plot the figure
we have
A (2, 2), B(-2, -2), C(1, -1), and D(6, 4)
using a graphing tool
The longer diagonal is BD
see the attached figure
step 2
Find the slope of the diagonal BD
we have
B(-2, -2) and D(6, 4)
m=(4+2)/(6+2)
m=3/4
step 3
Find the equation of the diagonal BD into point slope form
y-y1=m(x-x1)
we have
m=3/4
D(6,4)
substitute
y-4=(3/4)(x-6)
step 4
Convert the equation in standard form
The equation of the line in standard form is equal to
Ax+By=C
y-4=(3/4)(x-6)
y=(3/4)x-(18/4)+4
Multiply by 4 both sides
4y=3x-18+16
3x-4y=18-16
3x-4y=2 -----> equation of the diagonal in standard form
In the triangle below, x=?. Round to the nearest tenth.
Please help!!
Answer:
58 deg
Step-by-step explanation:
Look at x and then look at the sides that are given... 9 is adjacent and 17 is the hypotenuse so use cosine.
cos(x)=9/17
To solve for x just use arccos( ) or cos^(-1)
Type cos^(-1)(9/17) into calc to receive answer (make sure mode is in degrees)
The answer should come to be roughly 58 deg.
Answer:
x ≈ 58.0°
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for x
cosx° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{17}[/tex], thus
x = [tex]cos^{-1}[/tex] ([tex]\frac{9}{17}[/tex] ) ≈ 58.0°
What is the scale factor? ( the answer must be a fraction).