Answer:
How to calculate growth rate percentage?
To calculate the percentage growth rate, use the basic growth rate formula:
Subtract the original from the new value and divide the results by the original value. To turn that into a percent increase, multiply the results by 100.
The point F( – 3, – 6) is translated 4 units right and 2 units up. What are the coordinates of the resulting point, F
Answer:The answer is (1, -4)
Step-by-step explanation:
Is a triangle with side lengths 21,20 and 29 a right triangle show why or why not .
Step-by-step explanation:
Yes, we can determine whether a triangle is a right triangle or not by using the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle as follows: side a = 21, side b = 20, and side c = 29 (where c represents the hypotenuse). Now, we can use the Pythagorean Theorem to check whether the triangle is a right triangle or not:
c^2 = a^2 + b^2
Substituting in the given values, we get:
29^2 = 21^2 + 20^2
841 = 441 + 400
841 = 841
As the equation is true, we can conclude that the triangle is a right triangle.
y is inversely proportional to the square root of x. y=5 when x=36. find a formula linking x and y.
Answer:
y = 30/√x
Step-by-step explanation:
y = k/√x (where k is a constant).
5 = k/√36
5 = k/6
5 X 6 = k
k = 5 X 6 = 30.
y = 30/√x
I need help!!!!!!!!!!!!!!!!!!
p+T+S+S=5+5 it is our answer it is write
¿Cuál es el volumen, en metros cúbicos, de un prisma rectangular con una altura de
17 m, un ancho de 14 m y una longitud de 11 m?
Answer:
V = 2618 cubic meters
Step-by-step explanation:
multiply the three dimensions to obtain volume
(17)(14)(11) = 2618 m3
Hope this helps
Compute the MIRR statistic for Project J and advise whether to accept or reject the project with the cash flows shown as follows if the
appropriate cost of capital is 10 percent.
Project J
Time
Cash Flow
e
1,000
1
$300
2
$1,480
3
500 $300
Save & Exit
5
100
Submit
To compute the Modified Internal Rate of Return (MIRR) for Project J, we need to calculate the present value of cash inflows and outflows separately and then determine the discount rate that equates the present value of outflows with the future value of inflows.
The cash flows for Project J are as follows:
Time 0: Initial investment: -$1,000
Time 1: Cash inflow: $300
Time 2: Cash inflow: $1,480
Time 3: Cash inflow: $500
Time 5: Cash inflow: $100
First, let's calculate the present value (PV) of outflows (the initial investment):
PV(outflows) = -$1,000 (since it's an outflow at time 0)
Next, let's calculate the future value (FV) of inflows (cash inflows at times 1, 2, 3, and 5):
FV(inflows) = $300 + $1,480 + $500 + $100 = $2,380
Now, we can use the MIRR formula to compute the MIRR statistic:
MIRR = (FV(inflows) / PV(outflows))^(1/n) - 1
Where n is the number of periods (5 in this case).
MIRR = ($2,380 / -$1,000)^(1/5) - 1
MIRR = 1.5189 - 1
MIRR = 0.5189 or 51.89%
Given that the cost of capital is 10 percent, the MIRR is higher than the cost of capital. Therefore, we would advise accepting Project J because the MIRR is greater than the cost of capital, indicating that the project is expected to generate a return higher than the required rate of return.
Show that the equations x+y+z = 4, 2x+5y-2z =3, x+7y-7z =5 are not consistent
Answer:
We can start by using the second equation to eliminate x:
2x + 5y - 2z = 3
2x = -5y + 2z + 3
x = (-5/2)y + z + 3/2
Now we can substitute this expression for x into the first and third equations:
x + y + z = 4
(-5/2)y + z + 3/2 + y + z = 4
(-5/2)y + 2z = 5/2
x + 7y - 7z = 5
(-5/2)y + z + 3/2 + 7y - 7z = 5
(9/2)y - 6z = 7/2
Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.
Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:
(-45/2)y + 18z = 45/2
(45/2)y - 30z = 35/2
Adding these two equations, we get:
-12z = 40/2
-12z = 20
z = -5/3
Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:
(-5/2)y + 2(-5/3) = 5/2
(-5/2)y - 10/3 = 5/2
(-5/2)y = 25/6
y = -5/12
Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:
x + y + z = 4
x - 5/12 - 5/3 = 4
x = 29/12
Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:
2x + 5y - 2z = 3
2(29/12) + 5(-5/12) - 2(-5/3) = 3
29/6 - 5/2 + 5/3 ≠ 3
Since there is no solution that satisfies all three equations, the system is inconsistent.
Step-by-step explanation:
Answer:
See below for proof.
Step-by-step explanation:
A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.
Given system of equations:
[tex]\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}[/tex]
Rearrange the first equation to isolate x:
[tex]x=4-y-z[/tex]
Substitute this into the second equation to eliminate the term in x:
[tex]\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}[/tex]
Subtract the first equation from the third equation to eliminate x:
[tex]\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}[/tex]
Now we have two equations in terms of the variables y and z:
[tex]\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}[/tex]
Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:
[tex]\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}[/tex]
Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.
For example, if we subtract the second equation from the first equation we get:
[tex]\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}[/tex]
Zero does not equal negative 11.
Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.
Sandra is traveling 15 mph on her bicycle. After 4 hours, how far will she have traveled?
Answer:
→ 15m/hr * 4hr = 60! ←
Hope This Helps On You're Quiz/Assignment
Question 1 of 10 Solve - 5 < 4x + 3 <= 7 x > - 2orx <= 1 B. x < - 2orx < 4 O C.-2 and x <= 1 D. x > 2 and x < 4
For the inequality -5 < 4x + 3 ≤ 7 the combined solution are x < -2 and x ≤ 1.
To solve the inequality -5 < 4x + 3 ≤ 7, we need to consider two separate inequalities:
Solve the inequality -5 < 4x + 3:
-5 < 4x + 3
Subtract 3 from both sides:
-5 - 3 < 4x
-8 < 4x
Divide both sides by 4
-8/4 > x
-2 > x
x < -2.
Now let's solve the inequality 4x + 3 ≤ 7:
4x + 3 ≤ 7
Subtract 3 from both sides:
4x ≤ 7 - 3
4x ≤ 4
Divide both sides by 4:
x ≤ 1
Therefore, the combined solution is x < -2 and x ≤ 1.
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5.
Find the surface area and volume of the
right cylinder. Round your answer to the
nearest hundredth.
22 m
20.4 cm
Step-by-step explanation:
consider the cylinder standing upright.
we have to assume that 20.4 cm is the diameter of the circle.
it is not clear what dimension of the result is needed : cm³ or m³, cm² or m². it is important that we do our calculations always with the same dimension of all operands (don't mix apples and oranges in the same calculation).
the volume of such a cylinder (or any regular 3D object) is
base area × height
for a cylinder the base area is a circle :
pi × r²
r being the radius (half of the diameter).
so, we have
r = 20.4/2 = 10.2 cm
height = 22 m = 2,200 cm (1 m = 100 cm)
volume = pi × (10.2)² × 2200 =
= 719,072.8593... cm³ =
= 0.7190728593... m³
≈ 719,072.86 cm³
≈ 0.72 m³
for the surface of a cylinder we need to imagine to cut the cylinder open with straight cut from the top to the bottom and then put the result flat on the table.
this result is a rectangle.
length = height of the original cylinder.
width = circumference of the original cylinder (and its circular base) = 2 × pi × r
the surface area of the cylinder is then
2 × base circle area (top and bottom) = 2 × pi × r²
plus
the area of that rectangle
length × width = height × 2 × pi × r
that is
height×2×pi×r + 2×pi×r² = 2×pi×r×(height + r)
in our case now
surface area = 2×pi×10.2×(2200 + 10.2) =
= pi×20.4×2210.2 =
= 141,648.3809... cm² =
= 14.16483809... m²
≈ 141,648.38 cm²
≈ 14.16 m²
remember, because
1 m = 100 cm
then
1 m² = 1 m × 1 m = 100 cm × 100 cm = 10,000 cm²
1 m³ = 1 m × 1 m × 1 m = 100 cm × 100 cm × 100 cm =
= 1,000,000 cm³
I’m confused on this, help. Thanks you all. : )
Answer: There is no solution to this problem.
Step-by-step explanation:
The goal test score pints are 150, 103, and 41. Let's check to see if each statement is true
A. The total points for the tests are:
Type A - 156
Type B - 98
Type C - 40
None of these matches the total points.
B. The total points for the tests are:
Type A - 39
Type B - 98
Type C - 160
None of these matches the total points.
C.
Type A - 156
Type B - 2,352
Type C - 40
None of these matches the total points.
Since none of these statements match this data, there is no solution to this chart. Hope this helps!
-From a 5th Grade Honors Student
please look at the picture
6x-7y=-10
12x-5=16
2xay=10
-10+16+x=10
10=-10+16+x=6x
6x+10=16x
ay=16x
if a circle has a radius of 10 cm and the measure of arc AB is 45 degrees, find the length of the arc AB
Answer:
[tex]\huge\boxed{\sf S= 7.85 \ cm}[/tex]
Step-by-step explanation:
Given:arc AB = θ = 45 degrees
Radius = r = 10 cm
π = 3.14
Required:Length = S = ?
Formula:[tex]\displaystyle S= \frac{\theta}{360} \times 2 \pi r[/tex]
Solution:Put the given data in the formula.
Finding arc length.
[tex]\displaystyle S = \frac{45}{360} \times 2(3.14)(10)\\\\S = 0.125 \times 62.8\\\\S= 7.85 \ cm\\\\\rule[225]{225}{2}[/tex]
Please help i need help on pre-calc
Answer:
32.5 square units
Step-by-step explanation:
Area of triangle = ½ ab sin C
where a and b are to sides that meet at angle C.
Area of triangle = ½ (13)(10) sin 150
= 32.5 square units.
please see attachment for a visual
What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
The intermediate step in completing the square is[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex]
To complete the square for the equation [tex]$(x+a)^2=b$[/tex], we can follow these steps:
1. Expand the left side of the equation: [tex]$(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$[/tex].
2. Rewrite the equation by isolating the squared term and the linear term: [tex]$x^2 + 2ax = b - a^2$[/tex].
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex].
4. Simplify the right side of the equation: [tex]$x^2 + 2ax + (a^2) = b$[/tex].
This step can be represented as: [tex]\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\][/tex]
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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Can anyone help me solve this question?
x = e^y
Step-by-step explanation:
Pick any point on the graph below for a solution:
A 500g packet of beans costs £1.55. A 125g packet of the same beans costs £0.36. Which packet is better value for money?
Step-by-step explanation:
Find unit cost per gram for each packet....lower unit cost is better value
L 1.55 / 500 g = .0031 L/g
L .36 / 125 g = .0029 L/g <=======best value 125 g packet
a is a negative odd number.
Choose two words from the list in the box that describe a²
A negative
B positive
Codd
D even
Answer:
positive and odd
Step-by-step explanation:
If a is a negative odd number, then a² can't be negative, because a number squared is always positive.
I'll illustrate this with an example.
Let's choose -7 as an example. Instead of a.
-7² = 49
So we see that the result is positive & odd.
So the words that describe a^2 are positive and odd.
A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Graph of function p of x equals negative 6 x squared plus 156 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (13, 2014), and decreases through about (31, 0). Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. (3 points) Part B: Identify the approximate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. (3 points) Part C: Identify the approximate value of the maximum of the function. Explain what the maximum of the function means in terms of the problem scenario. (4 points)
The maximum daily profit the company can earn is $2,350.
It is a set of points in a coordinate plane that represents the values of the function for different inputs.
The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.
Therefore, the maximum daily profit the company can earn is $2,350.
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what is the following term of -3;0;3;6.
Step-by-step explanation:
Start at -3 then begin adding 3's to get the next terms
-3 0 3 6 9 .....
The picture of milk shown is a prism. The base has an area of 40 cm² and the height of the pitcher is
26 cm. Will the pitcher hold 1 Liter of milk?
Yes, the pitcher hold 1 Liter of milk.
We have to given that;
The picture of milk is a prism.
And, The base has an area of 40 cm² and the height of the pitcher is 26 cm.
Since, We know that;
Volume of prism is,
V = base area x Height
Now, Substitute all the values, we get;
V = 40 x 26
V = 1040 cm³
Since, 1 liter = 1000 cubic centimeters
Hence, the pitcher hold 1 Liter of milk.
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Kathy had of a pepperoni pizza in
her refrigerator. She gave her friend
a slice that was of the original pizza.
How much pizza does Kathy have left?
The answer is she has 7/8 (or seven slices) of the pizza left. Based on the information given, we can calculate that Kathy ate 1/8 (or one slice) of the original pepperoni pizza.
It is important to note that the size of the original pizza is unknown, so we cannot accurately determine the exact amount of pizza Kathy has left in terms of square inches or centimeters.
However, we do know that she has the majority of the pizza remaining, and could potentially have enough for multiple meals or leftovers. Additionally, if Kathy is tracking her caloric intake, she can calculate the number of calories consumed from the slice she ate and adjust her diet accordingly.
Overall, it seems like Kathy has a decent amount of pizza left to enjoy
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The number 84 can be expressed as the sum of 54 + 30. Which shows how to use the distributive property to rewrite that sum as a multiple of a sum whose addends have no common factors greater than 1?
A. 2(27 + 15)
B. 3(18 + 10)
C. 5(11 + 6)
D. 6(9 + 5)
The answer of the sum is D. 6(9 + 5).
To rewrite the sum 54 + 30 using the distributive property as a multiple of a sum whose addends have no common factors greater than 1, we need to factor out the greatest common factor from both numbers.
The greatest common factor of 54 and 30 is 6. By factoring out 6, we can rewrite the sum as:
54 + 30 = 6 * (9 + 5)
Now, let's examine the options given:
A. 2(27 + 15) does not have a common factor of 6.
B. 3(18 + 10) does not have a common factor of 6.
C. 5(11 + 6) does not have a common factor of 6.
D. 6(9 + 5) is the correct answer because it has a common factor of 6, which is the greatest common factor of 54 and 30.
Therefore, the answer is D. 6(9 + 5).
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factorise fully
1) x²y - 5yx - 6y
2) w² (a - b) - 9 (a - b)
please help
the length of arc AB is 6pi and the measure of arc AB=60 degrees. What is the diameter of the circle?
Answer:
36
Step-by-step explanation:
Arc = rad * radius
radius = arc/rad
given, arc = 6π
rad = 60 * π/180 = π/3 rad
radius = 6π / (π/3)
= 6π * 3/π
= 18
Diameter = 2 * radius
= 2*18
= 36
find the diameter of the crcle with the gven circmfence . use 3.14
c=31cm
The diameter of the given circle is 9.87 cm.
Given.
Circumference = 31 cm
Now,
Circumference of circle = 2×π×r
r = Radius of Circle
Substitute the value of circumference in the formula,
31 = 2×π×r
31 = 2× 3.14 × r
r = 4.935 cm
Diameter of circle is double the radius of circle,
D = 2r
D = 2(4.935)
D = 9.87 cm
Hence diameter of the circle is 9.87 cm.
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What would be the Prefix notation for the given equation?
(a+(b/c)*(d^e)-f)
a.
-+a*b/c^def
b.
-a+*/bc^def
c.
-+a*/^bcdef
d.
-+a*/bc^def
The Prefix notation for the given equation is "[tex]\pm a \times /bc^{de}^f[/tex]". d.
The Prefix notation for the given equation "[tex](a+(b/c) \times (d^e)-f)[/tex]" would be:
[tex]\pm a \times /bc^{de}^f[/tex]
In Prefix notation, also known as Polish notation, the operators come before their operands.
Here's a step-by-step breakdown of converting the given equation to Prefix notation:
Start with the given equation: (a+(b/c)*(d^e)-f)
Replace the arithmetic operators with their corresponding symbols in Prefix notation:
Addition (+) becomes +
Division (/) becomes /
Exponentiation (^) becomes ^
Subtraction (-) becomes -
Rearrange the equation to move the operators before their operands:
Replace [tex](a+(b/c)(d^e)-f)[/tex] with [tex](\pm a/bc^{de}^f)[/tex]
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Can someone find x and y pls
Answer: x = 101, y = 20
From corresponding angles, as both pairs of lines are parallel, we know that 79 is the supplement of x. That means 79 + x = 180.
From this we have x = 101 degrees.
From corresponding angles, x is the supplement of ( 4y - 1 )
Since we know x = 101, we can plug it into our equation:
4y - 1 + 101 = 180
Simplifying:
4y + 100 = 180
Subtracting 100 from both sides of the equation:
4y = 80
Dividing by 4:
y = 20
Hope this helps!
Anuj made a cuboid of dough of dimensions 5 cm, 5 cm and 3 cm. How many such cuboids will he need to make a perfect cube? What will be the dimensions of the cube?
Answer:
Step-by-step explanation:Anuj made a cuboid of dough of dimensions 5 cm, 5 cm and 3 cm. How many such cuboids will he need to make a perfect cube? What will be the dimensions of the cube?
Felipe rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 86 cents for each mile driven. Felipe had to pay $270.79 when he returned the truck. For how many miles did he drive the truck?
Answer:
421.4 miles
Step-by-step explanation:
Numner of miles= ($270.79-$17.95)/86 cents
= $252.84/$0.60
=421.4 miles