Answer: 7
Step-by-step explanation:
First, we need to prime factorize the number 189,
189 = 3 × 3 × 3 × 7 × m
From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.
Hence the answer is 7
The population of a city in 2015 was 36,000. The population is increasing at 15% per year.
Part A:
Write an exponential equation that models the population, P (z), where a represents the number of years since 2015.
Part B
based on your equation what was the population in 202 show how you obtained your answer
Answer: I am Not that good In Maths But here you go
Step-by-step explanation:
Part A:
The population of a city in 2015 is 36,000 and it is increasing at 15% per year. We can model this using an exponential equation of the form:
P(z) = P0 * (1 + r)^z
Where:
P(z) is the population after z years
P0 is the initial population in 2015 (36,000)
r is the rate of growth (0.15)
z is the number of years since 2015
So the exponential equation that models the population is:
P(z) = 36,000 * (1 + 0.15)^z
Part B:
To find the population in 2020, we would substitute z = 5 (2020 - 2015) into the equation:
P(5) = 36,000 * (1 + 0.15)^5
P(5) = 36,000 * 1.15^5
Calculating this gives us a population of approximately 63,746 in 2020.
To obtain this answer, we used the exponential equation that models the population, P(z), where a represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for z.
Two communications companies offer calling plans. With Company X, it costs 30c to connect and then 4c for each minute. With Company Y, it costs 15c to connect and then 3c for each minute. Write and simplify an expression that represents how much more Company X charges, in cents, for n minutes.
The expression that represents how much more Company X charges, in cents, for n minutes is 15 + n
How to write and simplify an expression that represents how much more Company X charges?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be used to represent a specific value or a range of values e.g. 2x+3.
For Company X:
Since it costs 30c to connect and then 4c for each minute, we can write the expression as:
30 + 4n
For Company Y:
Since it costs 15c to connect and then 3c for each minute, we can write the expression as:
15 + 3n
An expression that represents how much more Company X charges, in cents, for n minutes is:
(30 + 4n) - (15 + 3n) = 30 - 15 + 4n -3n = 15 + n
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let be the circle with radius centered at the origin. let be the vector field defined by . find the flux of coming out of the circle through the curve .
The flux of the vector field F is the integral of the normal component of the vector field over the surface.
The flux of the vector field F is the integral of the normal component of the vector field over the surface. In this case, the surface is the circle with radius r centered at the origin and the normal component of the vector field is just the z-component, which is equal to 2x. The integral of the normal component of the vector field over the circle is given by
Φ = ∫C 2x ds = ∫0 2π r2 2cosθ dθ
= 4πr2
This is the flux of the vector field F coming out of the circle.
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Suppose we know that set A has n subsets, S1, S2,..., Sa If set B consists of the elements of A and one more ele- ment so |B| = |A| + 1 show that B must have 2n subsets.
B must have 2n subsets since it has two corresponding subsets for each subset of A series (S1, S2,..., Sa), one of which contains the extra element and the other of which does not.
Set B's size is |B| = |A| + 1 since it includes all of the components of set A plus an additional element. There must be two equivalent subsets in set B for each subset of A (S1, S2,..., Sa), one of which must contain the extra element and the other of which must not. This extra element must be present in at least one subset. B must therefore have a total of 2n subsets. For instance, if set A has the three subsets S1, S2, and S3, then set B will have the same three subsets plus S1 plus the extra element, S2 plus the extra element, and S3 plus the extra element, for a total of six subsets.
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What is the area of this
polygon?
Enter your answer in the box.
units
The polygon's 39 unit squared surface area.
How is a polygon calculated?A polygon with "n" sides has a total of 180 degrees in its inner angles (n-2) n-sided polygons have [n(n-3)]/2 diagonals as their number of sides. For a regular polygon with n sides, the interior angle measure is [(n-2)180°]/n. A regular polygon with n sides has exterior angles that are 360°/n in length.
Using the equation Area = (number of sides x length of one side x apothem)/2, one may determine the area of a regular polygon.
To create the polygonal shape shown in the attachment, sketch it.
It is therefore possible to separate the polygon into a rectangle and a triangle.
The polygon's 39 unit squared surface area.
The complete question is,
What size polygon does this one have? Put your response in the provided box. points M, V, E, D, and R are located within a 5-sided polygon of unit 2 on a coordinate plane. Points M is at (negative 5, 2), V is at (negative 2, 3), E is at (3, 3), D is at (3, negative 3), and R is at (negative 5, 2). (negative 2, negative 3).
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At swimming practice, Coach Warren always sets aside 75% of the total time for laps. At practice yesterday, students spent 45 minutes swimming laps.
Answer: The session was 1 hour long.
75% of an hour is 45 minutes.
Find the value of X.
X=?
The required value of x is 3
What is trapezium?A convex quadrilateral having exactly one set of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.
According to question:Using the mid-segment theorem of trapezium.
The line segment that joins the midpoints of a trapezoid's two non-parallel sides is known as its mid segment. The average length of the bases makes up a trapezoid mid segment, which is parallel to the trapezoid's set of parallel lines.
[(3x + 1) + 15]/2 = 12.5
(3x + 1) + 15 = 25
3x + 1 = 10
3x = 9
x = 3
Thus, required value of x is 3.
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A balloon was originally filled to a volume of
4
,
400
4,4004, comma, 400 cubic centimeters. Air inside the balloon leaks out over time.
If a balloon was originally filled to a volume of 4,400 cubic centimeters. The inequality expression of the volume of the balloon is: V < 4400.
How to find the inequality expression?Volume = 4,400 cubic centimeters
Since the air inside the balloon leaks out over time which implies that the air inside the balloon will reduce.
So the expression is:
V < 4400
Where:
V = Volume
< = less than
Therefore the inequality expression is V < 4400.
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The complete question is:
A balloon was originally filled to a volume of 4,400 cubic centimeters. Air inside the balloon leaks out over time.
Write an inequality that describes V, the volume of the balloon in cubic centimeters as air leaks out.
Enter your inequality without a thousands separator.
find the position vector of a point r which divides the line joining two points p and q whose position vectors are externally in the ratio 1 : 2. also, show that p is the mid point of the line segment rq
So, the position vector of a point r is (1-1/3)p + (1/3)q.
The position vector of a point can be found using the following formula:
r = (1-λ)p + λq
where λ is the scalar value that represents the ratio in which the point divides the line segment.
In this case, the ratio of the point dividing the line segment is 1:2. So, λ = 1/3.
Substituting the values of p and q, we get:
r = (1-1/3)p + (1/3)q
To show that point p is the midpoint of the line segment rq, we can use the following property of midpoints:
The position vector of the midpoint of a line segment with endpoints p and q is given by (p+q)/2.
In this case, the position vector of point p is (1-1/3)p + (1/3)q, and the position vector of point q is (2/3)p + (2-2/3)q = (2/3)p + (4/3)q
So, the midpoint of the line segment rq is given by:
((1-1/3)p + (1/3)q + (2/3)p + (4/3)q)/2 = (3/3)p + (5/3)q
which is (p+q)/2, so p is the midpoint of the line segment rq
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Suppose that y varies directly with x, and y=4 when x=20. (a) Write a direct variation equation that relates x and y. Equation: (b) Find y when x = 9. y =
Answer:
Step-by-step explanation:
y = kx
a. Because x and y vary directly, the equation is in the form y = kx.
FOR YOUR UNDERSTANDING WAY
The ratio of y to x would be 4/20 = 1/5. So the equation would be y=1/5x
A bakery makes small batches of bread daily. Each day the bakery records the amount of flour used and the number of loaves of bread made. All loaves…
The linear equation of the line would be y = 7/5x. The number of loaves of bread from 85 pounds of flour would be 7/5(85) = 119 loaves.
What is linear equation and its slope?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Slope calculation:
This line's slope would be the proportional constant.
This point (35, 49) is extremely near to the lines that would result in the linear constant 49/35 = 7/5 , the line's equation is y = (7/5)x .
Using 85 pounds of flour, Calculate the loaves of bread that may be made (7/5) * 85 = 119 loaves.
Therefore, the equation is y = (7/5)x that is used to forecast the number of loaves that could be created from 85 pounds of flour, and the result was 119 loaves.
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The complete question is:
A bakery makes small batches of bread daily. Each day, the bakery records the amount of flour used the number of loaves of bread made. All loaves are approximately the same size. The table and graph show the bakery’s data for five days.
write an equation that can be used to model the number of loaves of breast, y that can be made from x pounds flour
Use an equation to predict the number of loaves that can be made from 85 pounds of flour show your work or explain your answer
A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be​consistent? Illustrate your answer with a specific system of three equations in two unknowns.​ chosse from the below option.
a)Yes, overdetermined systems can be consistent. For​ example, the system of equations below is consistent because it has the solution
Answer: (Type an ordered​ pair here _____)
x1=2, x2=4, x1+x2=6
(A). Yes, overdetermined systems can be consistent.
As, the system of equations below is consistent because it has a solution
x1 = 2 , x2 = 4 , x1 + x2 = 6.
We have,
'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.
If we have m equations and n variables where m>n (more equations than variables), then system can be consistent if last m−n equations are linear combinations of previous ones.
For e.g. Let us consider the system,
x + y = 1
x - y = 1
3x + y = 3
solving these equations, we can see
The only intersection point is (1,0). Thus, x= 1 and y= 0 is the solution of this system.
Thus, over-determined system can be consistent.
According to the options,
Hence, option A is correct.
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Can anyone help me? It's hard for me to solve this problem
*Debt payments of $2,100 and $1,950 are due in six months and nine months, respectively. What single payment is required to settle both debts in one month? Assume a simple interest rate of 6.30% p.a. and use one month from now as the focal date.
The required single payment is required to settle both debts in one month is $4071.26.
What is Simple interest?Simple interest is the amount of interest charged on a specific pripal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
According to question:We have,
Interest of 12 month = 6.30%
For one month = 6.30/12
= 0.525% per month
Total debt = $2,100 + $1,950
Total debt = $4050
Interest of one month = 0.525% of $4050
= $21.26
Net debt = $4050 + $21.26.
Thus, required single payment is required to settle both debts in one month is $4071.26.
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40% divided by 100 x 200
Answer:
0.8
Step-by-step explanation:
.40 / 100x200
A 150-pound person uses 6.6 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 160 calories?
A person must walk for at least
(Round up to the nearest minute.)
minutes in order to use at least 160 calories
If a 150-pound person uses 6.6 calories per minute when walking at a speed of 4 mph. The time a person walk at this speed to use at least 160 calories is: 24minutes.
How to find the time?Calories that was used = 6.6 calories per minute
Total calories = 160 calories
So,
Let x represent the minutes to walk
6.6x=160
Divide both side by 6.6x
x=160/6.6
x= 24.24 minutes
x = 24 minutes ( Approximately)
Therefore we can conclude that the time a person walk at this speed to use at least 160 calories is: 24minutes.
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Solve the following system of equations for z and for y: System of Equations: Value of z Value of y y = 9+ 3z y = 51 - 3z
The value of y and z in the equation are 31 and 7 respectively.
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Therefore, let's solve the system of equation using substitution method as follows:
y = 9 + 3z
y = 51 - 3z
Let's substitute the value of y in equation(ii)
51 - 3z = 9 + 3z
51 - 9 = 3z + 3z
42 = 6z
divide both sides of the equation by 6
z = 42 / 6
z = 7
Therefore, let's find the value of y using equation(i)
y = 9 + 3z
y = 9 + 3(7)
y = 9 + 21
y = 31
Therefore,
y = 31 and z = 7
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Find all possible 2×2
matrices A that for any 2×2 matrix B, AB = BA.
Hint: AB = BA must hold for all B. Try matrices B that have lots of zero entries.
Answer:
Step-by-step explanation:
Consider the following four matrices:
(1000),(0010),(0100),(0001).
See what happens when you solve the equation AB=BA
for each of those four (let B
be each one of those four). To facilitate it, write A=(acbd)
You will get a set of equations for the entries of a
which are easily solved. This trick is quite general.
Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/3 pounds of soil
and a box with 1 3/4 pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
Yes, she does have the enough soil as she needs 4 pounds of soil.She have [tex]7 \frac{5}{12}[/tex] pound of soil.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is BODMAS?
The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems. B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as Bodmas.
Given that;
She has
⇒ [tex]2\frac{1}{3} + 1\frac{3}{4}[/tex]
⇒ 17/3 + 7/4
⇒ [tex]\frac{17*4 + 7 *3}{12}[/tex]
⇒ 68 + 21 /12
⇒ 89/12
⇒ [tex]7 \frac{5}{12}[/tex]
So, She has [tex]7 \frac{5}{12}[/tex] pound of soil and she need 4 pounds only.
Hence, Denise have enough soil to fill the flower plot.
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12
Solve for x.
9
X+4
2x
will give brainliest
The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.
What is the quadratic equation?
A quadratic equation is a type of polynomial equation of degree 2, that can be written in the form of ax^2 + bx + c = 0 where x is the variable, a,b,c are constant and a is not equal to zero.
To solve for x in the equation 9/(x+4) = 2x, we can first clear the fractions by multiplying both sides of the equation by (x+4). This gives us:
9 = 2x*(x+4)
Then we can simplify the right side of the equation:
9 = 2x^2 + 8x
Next, we can move all the x terms to one side of the equation and all the constants to the other side:
2x^2 + 8x - 9 = 0
Now we can use the quadratic formula to solve for x:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 8, and c = -9
So we have:
x = (-8 +/- sqrt(8^2 - 42-9)) / 2*2
x = (-8 +/- sqrt(64 + 72)) / 4
x = (-8 +/- sqrt(136)) / 4
x = (-8 +/- 4*sqrt(17)) / 4
x = (-2 +/- sqrt(17))
So the solutions for x are x = -2 + sqrt(17) and x = -2 - sqrt(17)
The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.
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Suzy orders supplies for quick stop gas station and she needs to order additional lids for the disposable soda cups. She knew that the top of the cup had a diameter of 3 inches. Which size lid does she need to purchase from the soda cups?
If Suzy orders supplies for quick stop gas station and she needs to order additional lids for the disposable soda cups. The size that lid need to purchase from the soda cups is 9.42in.
How to find the circumference ?Using this formula to find the size that lid need to purchase from the soda cups
C= πd
Where:
C = circumference = ?
π =constant pi = 3.14
d = diameter = 3
Let plug in the formula
C = 3.14 × 3
C = 9.42 in
Therefore we can conclude that the size that lid need to purchase from the soda cups is 9.42in.
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Help
A machine that drills holes for wells drilled to a depth of−72 feet in one day (24 hours).
At this rate, how many hours will it take until the drill reaches its final depth of −132 feet?
At the same rate, a machine take 44 hours until the drill reaches its final depth of −132 feet.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We have to given that;
A machine that drills holes for wells drilled to a depth of−72 feet in one day (24 hours).
Now, Let a machine drill holes reaches its final depth of −132 feet in x hours.
Hence, By definition of proportion, we get;
⇒ 72 / 24 = 132 / x
⇒ x = 132 × 24 / 72
⇒ x = 3,168 / 72
⇒ x = 44 hours
Thus, It take 44 hours to reaches its final depth of −132 feet.
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Please answer this question for me
Answer:
not sure about this ......
let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for .
The formula for the standard matrix for the linear transformation is as follows: beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & & cosfracpi2 & 0 & & -1 endbmatrix
The following linear transformation rotates the points by[tex]$fracpi$[/tex]radians in the direction of rotation before reflecting the points through the line. We begin by examining the rotational component of the transformation to determine the standard matrix. A matrix beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0 & 0 & 1 endbmatrixan be used to describe the rotation by radians. We can use the matrix beginbmatrix 1 & 0 & 0 0 & -1 & 0 0 & 0 & 1 endbmatrixfor the reflection component. We obtain the final standard matrix for the linear transformation by multiplying these two matrices. $$beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0.
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The complete question is
let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for the standard matrix of the transformation can be found by first computing the matrix of the rotation and then the matrix of the reflection.
Which of the following are not the lengths of the sides of a 30°-60°-90° triangle?
A. 1/2, √3/2, 1
B. 5/2, 5√3/2, 10
C. √2, √6,2√2
D. 3,3√3,6
Answer:
C
Step-by-step explanation:
C. √2, √6,2√2 are not the lengths of the sides of a 30°-60°-90° triangle.
In a 30°-60°-90° triangle the ratio of the sides are always the same, the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.
A. 1/2, √3/2, 1 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 1, the longer leg is 1√3=√3 and the hypotenuse is 12=2.
B. 5/2, 5√3/2, 10 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 5/2, the longer leg is (5/2)*√3=5√3/2 and the hypotenuse is (5/2)*2=5
D. 3,3√3,6 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 3, the longer leg is 3√3=3√3 and the hypotenuse is 32=6
So, option C is not the lengths of a 30°-60°-90° triangle.
Erin is going to sew a jacket and a skirt.She needs 2 3/4 yards of material for the jacket and 1 1/2 yards of material for the skirt. All together how many yards of material does Erin need.
All together the number of yards of material Erin will need to sew jacket and skirt is 4 1/4 yards
How to find the number of yards Erin will requireFrom the question the following can be gotten
She needs 2 3/4 yards of material for the jacket and 1 1/2 yards of material for the skirt.
The total number of yards she will require is calculated using the addition operation
The total number of yards
Addition of fractions
= 2 3/4 + 1 1/2
= 17 / 4
= 4 1/4
The total number of yard required is 4 1/4
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Please very important, answer as soon as possible, I’ll give brainliest
The equation of y = f(x) and the equation of the new function g(x) under the transformation applied is Y=-3(x-1)² -1 or Y=-3x+6x-4.
What is the quadratic function opens upward or downward?
There is a simple way to identify whether the graph of a quadratic function opens upward or downward: if the leading coefficient is bigger than zero, the parabola expands upward; otherwise, the parabola opens downhill.
Y = -(3x²+2) reflects it about the x-axis. All positive y’s now become negative.
It used to be an upward-opening parabola with y-intercept = 2. Now, it’s a downward opening parabola with y-intercept = -2
Move it to the right by 2 means replace x by x-2
Move it up by 1 means replacing the y-intercept of -2 by -1, just add 1 to the y-intercept
Y=-3(x-1)² -1 or Y=-3x+6x-4
Hence, The equation of y = f(x) and the equation of the new function g(x) under the transformation applied is Y=-3(x-1)² -1 or Y=-3x+6x-4.
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Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. (3, 2) and (-5, -7)
The distance between the two points in simplest radical form (3, 2) and (-5, -7) is [tex]\sqrt{40}[/tex]
Find the distance?We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.
We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.
The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).
The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).
Distance = [tex]\sqrt{(x2 - x1)(y2 - y1)}[/tex]
Distance between the two positions (3, 2) and (--5, --7) equals
Distance =root of ( -5 - 3,-7 - 2)
root of (-8 * -5) = [tex]\sqrt{40}[/tex].
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Draw a polygon with the given conditions in a coordinate plane 19. A rectangle with a perimeter of 18units
According to the information, to create a rectangle polygon with a perimeter of 18 units, we must put sides of 3 units and bases of 6 units.
What is a polygon?A polygon is a term that refers to a plane geometric figure composed of a finite sequence of consecutive line segments that enclose a region in a plane. These segments are called sides, and the points at which they intersect are called vertices.
A rectangle is a polygon with four sides and four vertices that is characterized by having two of its sides longer than the other two sides. Therefore, to draw a rectangle with a perimeter of 18 units we must distribute the measurements as follows:
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PLS HELP ALG 1 DUE TMR
Answer:
y=x^3 - 10x + 16
Step-by-step explanation:
Integrate the following question
∫x/(x^2+1)^3
The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.
What is integration?Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.
I = ∫ [x / (x² + 1)³] dx
Let x² + 1 = t, then x dx = dt / 2. Then we have
I = ∫ [1 / 2(t)³] dt
I = (1/2) ∫ [1 /(t)³] dt
I = (1/2) [-1 /2t²] + c
I = - (1/4) (1/(x² + 1)²) + c
I = - 1 / 4(x² + 1)² + c
The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.
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