Answer:
A positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
What is an integer?
Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The boldface Z or blackboard bold "Z" is frequently used in mathematical notation to represent a collection of numbers.
Step-by-step explanation:
We know That total No. of factors
=product of (prime no′s power+1)
If N is the number of different divisors:
N=(p1+1)⋅(p2+1)⋅⋅⋅(pn+1)
100= 2^2 × 5^2
=2×2×5×5= (1+1)(1+1)(4+1)(4+1)
Then the integer n= a1^p1⋅a2^p2⋅⋅⋅⋅an^pn
For the smallest value: p1=4,p2=4,p3=1,p4=1
Then,
n=a1^4×a2^4×a3^1×a4^1
=24⋅34⋅51⋅71
=16⋅81⋅5⋅7
=45360
Hence, the positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
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jen has to put 180 cards into boxes of 6 cards each. she put 150 cards into boxes. write an equation that could use to figure out how many boxes jen need. let b stand for the unknown number of boxes.
Let b be the number of boxes.
Since each box has 6 cards, we will have the term 6b to get the remaining boxes.
Since Jen already put 150 cards into boxes, we have the following:
[tex]150+6b=180[/tex]for 150 cards, Jen used 25 boxes. We can check that the remaining 5 boxes can be found using the previous equation:
[tex]\begin{gathered} 150+6b=180 \\ \Rightarrow6b=180-150=30 \\ \Rightarrow b=\frac{30}{6}=5 \\ b=5 \end{gathered}[/tex]therefore, the equation is 150+6b=180
Patient Smith was on a diet. He weighed 122.6 kilograms. After one month he weighed 112.8 kilograms. Whatwas his total weight loss in one month?
If Smith uses both medications, then its dosage is the sum of each.
[tex]\text{total dosage = 48.5 + 0.5 = 4}9\text{ ml}[/tex]The total dosage of the medication would be 49 ml if he got both medications.
Which of the following sets of ordered pairs represents a function?
A.
{ (0, -2), (-27, -13), (-10, -5), (-27, -12) }
B.
{ (-7, -14), (-9, -18), (-5, -10), (-6, -12) }
C.
{ (1, -1), (1, -27), (1, -26), (1, -17) }
D.
{ (81, 1), (81, -1), (83, 4), (86, 6) }
Answer: B
Step-by-step explanation:
For the set of ordered pairs to be a function, each x-value has to correspond to only one y-value.
In option A, the x-value of -27 corresponds to both -13 and -12.
In option C, the x-value of 1 corresponds to -1, -27, -26, and -17.
In option D, the x-value of 81 corresponds to both 1 and -1.
AABC was dilated from point A to get AADE. Find the length of AD given a scale factor of 2.D0 3O 1005O 26EB6x-8X+2
Answer:
[tex]AD\text{ = 10}[/tex]Explanation;
Here, we want to get the length of AD
From the information given:
[tex]AD\text{ = 2AB}[/tex]Thus, mathematically:
[tex]\begin{gathered} 6x-8\text{ = 2\lparen x+2\rparen} \\ 6x-8\text{ = 2x + 4} \\ 6x-2x\text{ = 4+8} \\ 4x\text{ = 12} \\ x\text{ = }\frac{12}{4} \\ x\text{ = 3} \end{gathered}[/tex]Now, we can get AD
We simply substitute for the value of x
We have that as:
[tex]\begin{gathered} AD\text{ = 6x-8} \\ AD\text{ = 6\lparen3\rparen -8} \\ AD\text{ = 10} \end{gathered}[/tex]Hi hope you are well!!I have a question: When Debbie baby-sits she charges $5 to go the house plus $8 for every hour she is there. The expression 5+8h gives the amount in dollars she charges. How much will she charge to baby-sit for 5 hours? Please help me with this questionHave a nice day,Thanks
5 + 8h
h= number of hours
Replace h by 5 and solve
5 + 8(5)
5 +40
45
She will charge $45
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
-45 is an integer
√100 = 10 is a whole number
√89 is an irrational number-root
4.919191... is a rational decimal
-2/5 is a rational number-ratio
.12112111211112... is an irrational decimal
Finnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
consider triangle 1 and triangle 2for which value of Q would the two triangles be similar - 136 -105 -75-31
Given:
If the given triangles are similar.
The corresponding angles should be congruent.
Both triangles have the same angle 105 degrees.
The second angle is 31 degrees and q.
[tex]q=31^o[/tex]If triangles are similar then the value of q is 31 degrees.
For the line that passes through Y(3,0), parallel to DJ with D(-3,1) and J(3,3), complete the following: Find the slope. Write an equation in point-slope form. Graph the line.Slope:Point-slope form:
I am going to graph the situation on an external graphing utility and show you the answer, it will take a
minute, stay with me.
[tex]m\text{ = }\frac{rise\text{ }}{\text{run}}=\frac{change\text{ in y}}{\text{change in x}}=\frac{3}{1}=3[/tex][tex]y\text{ = mx+b}\rightarrow\text{ b =-1}[/tex]So the equation of the line is.
[tex]y\text{ =3x -1}[/tex][tex]y\text{ -1 = m(3-0)}[/tex]Which of the following is true of points on the line y=5/3 x + 1/2? (1) For every 3 units that increases, y will increase by 5 units. (2) For every 5 units that x increases, y will increase by 2 units. (3) For every 2 units that x increases, y will increase by 1 unit. (4) For every 1 unit that x increases, y will increase by 2 units.
4) For every 1 unit that x increases, y will increase by 2 units.
1) For the function y=5/3x +1/2
If we remember that "rise over run" mnemonics, that'll make it easier to memorize it.
2) Plotting the graph of this function. Look at point A (1,2)
Counting from bottom to up (2 units "rise" on the y-axis, point A is 1 unit to right "run". So, For every 1 unit that x increases, y will increase by 2 units.
In right triangle QRS, m S=73. In right triangle TUV m V=73.
To find:
Which theorem used to prove that both triangles are congruent.
Solution:
It is given that both triangles are right triangles. So, each one of the corresponding angles is 90 degrees.
angle M is given 73 degrees and angle V is given 73 degrees. So, we can see that two pairs of angles are equal in triangle.
Thus, AA similarity postulate can be use to prove that both triangles are congruent.
Thus, option C is correct.
Draw the graph of the line that is perpendicular to Y= 4X +1 and goes through the point (2, 3)
Given:
[tex]\begin{gathered} y=4x+1 \\ \text{ point }(2,3) \end{gathered}[/tex]To find:
Draw a graph of a line that is perpendicular to the given line and passing through a given point.
Explanation:
As we know that relation between two slopes of perpendicular slopes of lines:
[tex]m_1.m_2=-1[/tex]Slope of given line y = 4x + 1 is:
[tex]m_2=4[/tex]So, the slope of line perpendicular to given line is:
[tex]m_2=-\frac{1}{4}[/tex]Also, so line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+c...........(i)[/tex]Also, the required line is passing thorugh given point (2, 3), i.e.,
[tex]\begin{gathered} 3=-\frac{1}{4}(2)+c \\ c=3+\frac{1}{2} \\ c=\frac{7}{2} \end{gathered}[/tex]So, line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+\frac{7}{2}[/tex]The required graph of line is:
Find the union of E and L.Find the intersection of E and L.Write your answers using set notation (in roster form).
For the intersection operation we have to look what elements both sets have in common, in this case both E and L has the number 8. Then the second answer is:
[tex]E\cap L=\lbrace8\rbrace[/tex]Now, the union operation adds the all elements into a single set without repetition, in this case the first answer is:
[tex]E\cup L=\lbrace-2,1,2,3,6,7,8\rbrace[/tex]which of the relationships below represents a function with the same rate of change of the function y= -4x + 2
Given data:
The given equation of the line is y= -4x + 2.
Substitute 0 for x in the given equation.
[tex]\begin{gathered} y=-4(0)+2 \\ =2 \end{gathered}[/tex]Substitute 1 for x in the given equation.
[tex]\begin{gathered} y=-4(1)+2 \\ =-2 \end{gathered}[/tex]Thus, option (D) is correct.
which of the following circles have their centers in the second quadrant
The circles in option B and D has their centers in the second quadrant
Here, we want to know which of the circles have their centers in the second quadrant
Generally, the equation of a circle can be represented as;
[tex](x-h)^2\text{ + (y-}k)^2=r^2[/tex]where (h,k) represents the center of the circle
Now, let us get the center of each of the circles;
A. (4,-3)
b. (-1,7)
C.(5,6)
D. (-2,5)
The second quadrant has its coordinates in the form (-x,y)
Out of all the options, the option that fits these quadrant is the second and fourth
So the circles in option B and D has its center in the second
A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $47,312.00 each year, and $28,431.00 for each person employed for the year. For the next year, the company projects that labor costs will total $2,492,378.00. How many people does the company intend to employ next year?
( x+y+z = -1), ( y-3z = 11), ( 2x+y+5z = -12)1. determine whether the system is inconsistent or dependent2. if your answer is dependent, find the complete solution. Write x and y as functions of zx=y=
Inconsistent
Explanation:a) Given:
x + y + z = -1 . . .(1)
y - 3z = 11 . . . (2)
2x + y + 5z = -12 . . .(3)
To find:
If the solution of the system of equations is either consistent dependent solution or an inconsistent one
We need to solve the system of equations. From equation (2), we will make y the subject of formula:
y = 11 + 3z (2*)
Substitute for y with 11 + 3z in both equation (1) and (2):
For equation 1: x + 11 + 3z + z = -1
x + 11 + 4z = -1
x + 4z = -1-11
x + 4z = -12 . . . (4)
For equation 3: 2x + 11 + 3z + 5z = -12
2x + 11 + 8z = -12
2x + 8z = -12-11
2x + 8z = -23 . . .(5)
We need to solve for x and z in equations (4) and (5)
Using elimination method:
To eliminate a variable, its coefficient needs to be the same in both equations
Let's eliminate x. We will multiply equation (4) by 2:
2x + 8z = -24 . . . (4*)
Now both equations have the same coefficient of x. Subtract equation (4) from (5):
2x - 2x + 8z - 8z = -23 - (-24)
0 + 0 = -23 + 24
0 = 1
Let hand side is not the same as right hand side.
When the left hand side is not equal to right hand side, the solution is said to be inconsistent or no sloution.
Your answer is inconsistent
Box #1 options is: A.true B.false
Box #2 options are: A.true B.false
Box #3 options are: A.enough B.not enough
Answers:
falsetruenot enough=======================================================
Explanation:
Let's say the claim is [tex]\text{x}^2 \ge \text{x}[/tex] true for any real number x. It certainly works for things like x = 5 and x = 27.
A counter-example to show this isn't true is to use x = 0.5
So,
[tex]\text{x}^2 \ge \text{x}\\\\0.5^2 \ge 0.5\\\\0.25 \ge 0.5\\\\[/tex]
The last statement is false, which thereby proves the original claim doesn't work for x = 0.5; by extension, the overall claim of that inequality working for any real number is false.
As you can see, all we need is one counter-example to contradict the claim to prove it false.
Unfortunately one single example is not enough evidence to prove a claim true. Think of it like saying "it's much easier to knock down a sand castle than to build it up".
Instead, we need to use a set of clearly laid out statements and reasons based on previously established theorems.
=GEOMETRYPythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.
From the triangle, we have:
c = 13
b = 7
Let's solve for a.
The triangle is a right triangle.
To find the length of the missing sides, apply Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]We are to solve for a.
Rewrite the equation for a:
[tex]a^2=c^2-b^2[/tex]Thus, we have:
[tex]\begin{gathered} a^2=13^2-7^2 \\ \\ a^2=169-49 \\ \\ a^2=120 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{120} \\ \\ a=10.95 \end{gathered}[/tex]ANSWER:
[tex]10.95[/tex]IF P(A)=0.2 P(B)=0.1 and P(AnB)=0.07 what is P(AuB) ?A.0.13 B. 0.23 C. 0.3 D.0.4
ANSWER
P(AuB) = 0.23
STEP-BY-STEP EXPLANATION:
Given information
P(A) = 0.2
P(B) = 0.1
P(AnB) = 0.07
What is P(AUB)
[tex]P(\text{AuB) = P(A) + P(B) }-\text{ P(AnB)}[/tex]The next step is to substitute the above data into the formula
[tex]\begin{gathered} P(\text{AuB) = 0.2 + 0.1 - 0.07} \\ P(\text{AuB) = 0.3 - 0.07} \\ P(\text{AuB) = 0.23} \end{gathered}[/tex]Select all statements that are true about equilateral triangle ABC.
To determine statements that are correct, we proceed as follows:
Step 1: We recall the definition of an "equilateral" triangle
An equilateral triangle is one which"
- has all its sides equal to each other
- has all its internal angles equal to 60 degrees each
From the above definition, it can be concluded that
(A) Angles B and C are 60 degrees is a true statement
Step 2: We solve the triangle for x, as follows:
Now, consider the left right-triangle:
Now, we apply the sine trigonometric ratio to obtain the value of x,
[tex]undefined[/tex]What is the answer to 3/8 + 7 5/8
Given the Addition:
[tex]\frac{3}{8}+7\frac{5}{8}[/tex]You can find the sum as follows:
1. Covert the Mixed Number to an Improper Fraction:
- Multiply the Whole Number part by the denominator of the fraction.
- Add the result to the numerator.
- The denominator does not change.
Then:
[tex]7\frac{5}{8}=\frac{5+(7\cdot8)}{8}=\frac{5+56}{8}=\frac{61}{8}[/tex]2. Rewrite the Addition:
[tex]=\frac{3}{8}+\frac{61}{8}[/tex]3. Since the denominators are equal, you only need to add the numerators:
[tex]=\frac{3+61}{8}=\frac{64}{8}[/tex]4. Simplifying the fraction, you get:
[tex]=8[/tex]Hence, the answer is:
[tex]=8[/tex]Under certain conditions, the velocity of a liquid in a pipe at distance r from the center of the pipe is given by V = 400(3.025 x 10-5--2) where Osrs5,5x10 -3. Writeras a function of V.r=where the domain is a compound inequality(Use scientific notation. Use integers or decimals for any numbers in the expression.)Le
Solving the equation for r:
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-r^2) \\ r^2=9.025\cdot10^{-5}-\frac{V}{400} \\ r=\sqrt[]{9.025\cdot10^{-5}-\frac{V}{400}} \end{gathered}[/tex]With the first equations, we can establish some limits for V:
With the lowest value for r (r=0):
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-0^2) \\ V=400(9.025\cdot10^{-5}) \\ V=3.61\cdot10^{-2} \end{gathered}[/tex]With the highest value for r (r=9.5x10^-3)
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-(9.5\cdot10^{-3})^2) \\ V=400(9.025\cdot10^{-5}-9.025\cdot10^{-5}) \\ V=400(0) \\ V=0 \end{gathered}[/tex]According to the radius range, velocity can be between 0 and 3.61x10^-2
It is also necessary to check the domain of the function considering it is a square root. The argument of an square root cannot be less than 0. Then:
[tex]\begin{gathered} 9.025\cdot10^{-5}-\frac{V}{400}\ge0 \\ 9.025\cdot10^{-5}\ge\frac{V}{400} \\ V\leq400(9.025\cdot10^{-5}) \\ V\leq3.61\cdot10^{-2} \end{gathered}[/tex]This is the same limit for velocity obtained before. Then, we can say for velocity that:
[tex]0\leq V\leq3.61\cdot10^{-2}[/tex]Question 10 of 10
Question 10
▸
Find the Error One cleaning solution uses 1 part vinegar with 2 parts water. Another cleaning solution uses 2 parts vinegar with 3 parts water
A student says that these mixtures are equivalent because, in each solution, there is one more part of water than vinegar. Find the error and
correct it.
In the first cleaning solution, the ratio of vinegar to water is
however, has a ratio of
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The ratios
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The second solution.
equivalent
Done and
The error is that there is no proportional relationship between the ratios which is corrected and can be described as a linear relationship with the help of the equation y = m + 1.
What is the proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.So, the ratios we have:
1:2 and 2:3.Then, performing:
1/2 = 0.52/3 = 0.67Hence, ratios of 1:2 and 2:3 are not equal.
Therefore, the error is that the relationship between the given ratios is not proportional.
As can be seen, each ratio has a difference of 1, that is:
2 - 1 = 13 - 2 = 1Therefore, when one variable changes by 1, the other variable only changes by a constant value (y = x = c).
It can therefore be described as a linear relationship, and the constant is 1.The equation has the following form:
y = x + 1Where y stands for the water solution and x for the vinegar component.
Therefore, the error is that there is no proportional relationship between the ratios which is corrected and can be described as a linear relationship with the help of the equation y = m + 1.
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Find the value of x in the triangle shown below.42
Since we are dealing with a right triangle, we can use the Pythagorean theorem, shown below
[tex]H^2=L^2_1+L^2_2[/tex]In our case, H=4, L_1=2, L_2=x; then,
[tex]4^2=2^2+x^2[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow x^2=16-4 \\ \Rightarrow x^2=12 \\ \Rightarrow x=\sqrt[]{12}=\sqrt[]{4\cdot3} \\ \Rightarrow x=2\sqrt[]{3} \end{gathered}[/tex]The answer is x=2sqrt(3)
Which of the following point-slope form equations could be produced with the points (3, 4) and (1, -7)?
Answer:
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~
( 3 , 4 )
( 1 , - 7 )
m = [tex]\frac{-7-4}{1-3}[/tex] = [tex]\frac{-11}{-2}[/tex] = [tex]\frac{11}{2}[/tex]
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
At a point 125 feet from the base of a building, the angle of elevation to the third floor is 22°. What is the height of the third floor?A 53.9 feetB 14,124 feetC. 50.5 feetD. 333.3 feet
From the problem statement, we can draw the triangle shows below:
H is the height of the building we will solve for.
Shown below >>>
[tex]\begin{gathered} \tan 22=\frac{H}{125} \\ H=125\tan 22 \\ H=50.5\text{ f}eet \end{gathered}[/tex]AnswerCWhich of the following are roots of the polynomial function?Check all that apply.F(x) = x3 + 3x2 - 9x+5A. 1 - 13B. 3 - 2C. 1D. 1. 13E. 3 + 2F. -5
we have
F(x) = x3 + 3x2 - 9x+5
solve by graphing
using a graphing tool
the figure in the attached image
REmember that the zeros
please wait a minute
the roots are -5 and 1
therefore
answer option C and F
I need to find out how much money my school loans for donating 2200 pounds of clothing
Firs we need to find the equation of the line
x= clothing donations (pounds)
y= Amount earned (dollars)
We have the next points
(0,0)
(100,400)
We will calculate the slope
[tex]m=\frac{400-0}{100-0}=4[/tex]Therefore the equation is
y=4x
then if x=2200
y=4(2200)
y=8800
Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, close to -0.5?A. Graph AB. Graph BC. Graph CD. Graph D
A negative linear relationship occurs when for increasing x values, the values of y are decreasing.
Observing the graphs, we can see a positive linear relationship for graphs A and C (x - increases, y - increases).
For Graph D, we can observe no correlation.
For graph B, we can observe a negative linear relationship (x - increases, y - decreases).
Answer: Graph B
Line g passes through the points (-2.6,1) and (-1.4.2.5), as shown. Find theequation of the line that passes through (0,-b) and (c,0).
The blue line passes through the points
(-2.6, 1) and (-1.4, 2.5)
I will label the coordinates as follows for reference:
[tex]x_1=-2.6,y_1=1,x_2=-1.4,y_2=2.5[/tex]Step 1: Find the slope of the blue line
The slope between two points is calculated with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute the values and we get that the slope of the blue line is:
[tex]m=\frac{2.5-1}{-1.4-(-2.6)}=\frac{1.5}{1.2}=1.25[/tex]The slope m of the blue line is 1.25.
step 2: With that slope, calculate b (the intercept of the blue line with the y axis).
For this we use the point - slope equation:
[tex]y=m(x-x_1)+y_1[/tex]Where we will use the sane x1 and x2 as in the previous step, so we get
[tex]\begin{gathered} y=1.25(x-(-2.6))+1 \\ y=1.25(x+2.6)+1 \\ y=1.25x+3.25+1 \\ y=1.25x+4.25 \end{gathered}[/tex]We compare this with the slope-intercept equation
[tex]y=mx+b[/tex]And we can see that the incercept b is 4.25
[tex]b=4.25[/tex]step 3: Find the value of c.
to find the value of c, we need to know at which point the blue line crosses the x axis.
Since we already have the equation of the blue line y=1.25x+4.25, and the line crosses the x axis at y=0, we substitute this to find the x value that is equal to c:
[tex]\begin{gathered} 0=1.25x+4.25 \\ -4.25=1.25x \\ \frac{-4.25}{1.25}=x \\ -3.4=x \end{gathered}[/tex]The blue line crosses the x axis at (-3.4,0), thus we can conclude that
[tex]c=-3.4[/tex]Step 4: Define the two point where the orange line passes through.
We know from the picture that the orange line passes through (c,0) and (0,-b)
Since we have the values of c = -3.4 and b=4.25, we can say that the orange line passes through (-3.4, 0) and (0, -4.25)
Step 5: Calculate the slope of the orange line.
the orange line passes through (-3.4, 0) and (0, -4.25), so we define:
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