Answer:
Step-by-step explanation:
Expand: 36e^2+12e-48=e
Subtract e from both sides 36e^2+11e-48=0
Using the quadratic formula, e=(-11+-sqrt7033)/72
Which of the contexts below represents exponential growth?
An amusement park charges $3.50 to go on each of the rides.
A town's population grows at a rate of 5.3% every year.
The amount of a certain medication in a person's bloodstream decreases by 2/5
every minute.
A town's population shrinks at a rate of 9.7% every year.
Answer:
A town's population grows at a rate of 5.3% every year.
You have a gift certificate to a book store worth $95. Each paperback books is $10 and each hardcover books is
$17. You must spend at least $20 in order to use the gift certificate. Write and graph a system of inequalities to
model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number
of hardback books
Answer: You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,
⇒ what you buy should be ≥ 20
Input the price to the inequality above
⇒ what you buy should be ≥ 20
⇒ paperback price + hardcover price ≥ 20
⇒ 10x + 17y ≥ 20
Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms
⇒ x ≥ 0
⇒ y ≥ 0
So this is the summary
10x + 17y ≥ 20
x ≥ 0
y ≥ 0
Step-by-step explanation:
can somone please help meeeeeeee
Answer:
121.5
Step-by-step explanation:
1.5 x 9 x 9 (the equation for volume (minus the 1/2 inch that Isaac's grandmother said to leave out) = 121.5
Hi if someone can help me that would be great
The diagrams are shown in the solution.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.
The dimension can be written as:
1/2 : 5/6
Multiply the ratio by 6:
3 : 5
Hence, the rectangle of 1/2 × 5/6 is proportional to 3×5.
The diagram is shown.
Similarly, the diagrams of other rectangles are shown.
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11. √1156
12. √1024
13. √1225
14. √1764
15. √1936
please ahh little help please
The evaluation of the square roots of the numbers using prime factorization gives;
11. √1156 = 32
12. √1024 = 32
13. √1225 = 35
14. √1764 = 42
15. √1936 = 44
What are prime factors?Prime factors are the factors of a number that are also prime numbers.
The square roots of the numbers found using prime factorization are as follows;
11. √1156
1156 ÷ 2 = 578
578 ÷ 2 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
√1156 = √(2 × 2 × 17 × 17) = √(2² × 17²)
√1156 = √(2² × 17²) = 2 × 17 = 34
√1156 = 34
12. √1024
1024 ÷ 2 = 512
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
Therefore; √(1024) = √(2×2×2×2 ×2×2×2×2×2×2) = √(2¹⁰) = 2⁵ = 32
√1024 = 32
13. √1225
1225 ÷ 5 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Therefore;
√(1225) = √(5 × 5 × 7 × 7) = √(5² + 7²) = 5 × 7 = 35
14. √1764
1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
√1764 = √(2 × 2 × 3 × 3 × 7 × 7) = √(2² × 3² × 7² = 2 × 3 × 7 = 42
15. √1936
1936 ÷ 2 = 968
968 ÷ 2 = 484
484 ÷ 2 = 242
242 ÷ 2 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
Therefore; √(1936) = √(2 × 2 × 2 × 2 × 11 × 11) = √(2⁴ × 11²) = 2² × 11
√(1936) = 2² × 11 = 44
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What is the area of â–³mnp? 40 m2 60 m2 68 m2 127.5 m2
The area of MNP triangle is 60 m².
Based on the congruency of triangles, the value of MP and QS will be the same. Hence, the value of side MP will be 8 m.
Now, the formula to calculate right angled triangle is 1/2 × base × height.
Keep the values in formula to find the value of area of triangle MNP.
Area = 1/2 × 8 × 15
Performing multiplication and division on Right Hand Side of the equation to find the area of triangle MNP
Area = 4 × 15
Area = 60 m²
Thus, the area of right angled triangle is 60 m².
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A restaurant's delivery person can determine the number of miles he can drive in x hours by the function f (x) = x2 + 3x. the number of gallons of gasoline that the delivery person uses for driving y miles can be determined by the function g of y is equal to y over 22 period if the delivery person works an 8-hour shift, how many gallons of gasoline will he need in his tank?
Given that the delivery person works an 8-hour shift, he needs 4 gallons of gasoline in his tank.
A function is defined as the expression that relates a independent variable with a dependent variable. To evaluate a function is to substitute the value of the independent variable and then calculate the function value.
Given that the delivery person works an 8-hour shift, substitute x = 8 to the function of y.
y = f(x) = x² + 3x
y = 8² + 3(8)
y = 88
To determine the amount of gasoline needed, substitute the value of y to the function of g of y.
g = y / 22
g = 88 / 22
g = 4
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create a table and graph using -2x + 1/2
Answer:
Open Canva — Launch the table and chart maker tool by going to Canva and searching for “table” or “table chart.” Choose a template — Explore our collection of pre-built, fully customizable templates. Narrow your search by style, theme, and color to find a layout that best fits your needs. Click your chosen template to start designing.
Let (-12, 5) be a point on the terminal side of theta.
Find the exact values of sin theta , sec theta, and tan theta.
- 13/12 is the value of trigonometric functions sec θ .
What do trigonometric functions mean?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides.r = √( -12 - 0 )² + ( 0 - 5 )²
r = √144 + 25
r = √169
r = 13
Now we can calculate the trigonometric functions
sinθ = y/r = 5/13
cosθ = x/r = -12/13
tan θ = y/x = - 5/12
cot θ = x/y = -12/5
sec θ = r/x = - 13/12
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i just need the answers
Answer:
s is the price of each laptop that gives maximum profit
p is the maximum total profit that can be made.
Step-by-step explanation:
See the attached worksheet for additional explanation. The question asks for the meaning of s (selling price) and p (total profits) at the vertex of the curve. s is in units of price/laptop, while p is in units of total profits. Implicit in this graph is a demand curve (not shown) that illustrates how demand for laptops changes as the price changes. Also not shown, but assumed, is that if the laptops are sold at a low price, the declining profit margins resuce the overall total profits. This graph incorporates the cost and demand imformation in a manner that provides a condensed view of the more important variable: total profits.
Marcu Robinon bought an older houe and want to put in a new concrete patio. The patio will be 15 feet long, 9 feet wide, and 3 inche thick. Concrete i meaured by the cubic yard. One ack of dry cement mix cot $5. 20, and it take four ack to mix up 1 cubic yard of concrete. How much will it cot Marcu to buy the cement? (Round your anwer to the nearet cent. )
Total cost of cement that Marcus has to pay is $6.5.
What is volume?
Volume could be a measure of occupied three-dimensional area. it's usually quantified numerically using SI derived units or by numerous imperial or North American country customary units.
Main body:
According to question:
Length of concrete patio = 15 ft
Width of patio = 9 ft
Height of patio = 3 inches
So first we need to convert inches into ft.
we know that ,
12 inches = 1 ft.
3 inches = (1/12)*3
3 inches = 1/4 ft
Volume of concrete patio = l*b*h
volume = 15*9*1/4
= 33.75 cubic ft.
Now we need to convert feet into yard as cost is given in cubic yard
1 cubic foot = 0.03704 cubic yards
33.75 cubic foot = 0.03704 * 33.75
= 1.2501 cubic yards
So cost of cement = total volume * cost of cement sack
cost = 1.25 * 5.2
cost = $6.5
Hence the total cost to Marcus is $6.5
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a farmer wants to construct a fence around an area of 150 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. what dimensions should the fenced area have in order to minimize the length of fencing used?
The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 150, hence:
Area = length × width = x × y
150 = xy
y = 150/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(150/x) = 2x + 450/x
To minimize the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 450/x²
2 - 450/x² = 0
2 = 450/x²
2x² = 450
x² = 225
x = 15 feet
Let's find the value of y.
y = 1350/x = 1350/15 = 10 feet
Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.
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If there are 176 chocolate marshmallows in the bag, how many marshmallows are vanilla?
The ratio Illustrated shows that the number of vanilla marshmallow is 121.
What is a ratio?A ratio shows how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. It should be noted tjat.A/B will be the formula if one is comparing one data point (A) to another data point (B).
Let the vanilla marshmallow be represented be x.
Since the ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11, the vanilla will be:
= 11 / (5 + 11) × 176
= 11/16 × 176
= 11 × 11
= 121
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Complete question
The ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11. There are 176 chocolate marshmallows in the bag, how many marshmallows are vanilla?
there are 46 students going on a field trip to the museum. if 7 students can fit in each van , how many vans are needed for all 46 students to go to the museum
Answer:
Step-by-step explanation:
NOSEEEEEE
What is the amount of M
The value of ∠M is, 30
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to our question-
∠m + ∠30=60∠m= 60-30=30Hence,The value of ∠M is, 30
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8x - 4 = 12x + 6 + x
Answer:
X = −2
Step-by-step explanation:
Combine 12x and x to get 13x. Subtract 13x from both sides. Combine 8x and −13x to get −5x. Add 4 to both sides. Add 6 and 4 to get 10. Divide both sides by −5. Divide 10 by −5 to get −2.
Answer: x= -2
Step-by-step explanation:
8x-4=12x+6+x
8x-12x-x=6+4
-4x-x=10
-5x=10
x= -2
let n be the second smallest positive integer that is divisible by every positive integer less than 7. what is the sum of the digits of n?
The sum of the digits of n is 3 if n is the second smallest positive integer that is divisible by every positive integer less than 7
What is least common multiple?
The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.
It can be calculated for two or more numbers as well.
For example, LCM of 10, 2 and 7 is 70.
According to the given question:
Now n must be divisible by every positive integer less than 7, or
1, 2, 3, 4, 5, and 6.
Each number that is divisible by each of these is a multiple of their least common multiple.
LCM (1,2,3,4,5,6) = 60
So each number divisible by these is a multiple of 60.
The smallest multiple of 60 is clearly 60, so the second smallest multiple of 60 is 2 x 60 = 120.
Therefore, the sum of the digits of n is 1+2+0 = 3
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A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the dividend 3 years later? Round to the nearest cent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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a small radio transmitter broadcasts in a 20 mile radius. if you drive along a straight line from a city 27 miles north of the transmitter to a second city 24 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
To solve the given problem first we need to find the equation for line then we have to find the intersection point on circle.
You will pick up a signal from the transmitter in 29% of the drive.
Given:
The radius is 53 mile.
The origin point of transmitter is .
Calculate the slope of line with point and .
Substitute the value.
Write the general equation of line.
Now we got the equation of line,
Write the transmitter reach the area enclosed by the next circle.
Substitute the value of .
Further solving we get the point and .Please refer the attached figure.Apply the Pythagoras theorem to find the total distance.Apply the Pythagoras theorem to find distance when the signal is picked up.Calculate the percentage of distance covered.Thus, You will pick up a signal from the transmitter in 29% of the drive.
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I NEED ANSWER URGENTLY
Answer: Y=1
Step-by-step explanation:
Equation - y=mx+b
y2-y1
First point: )-4, 1)
second point: (2,1)
Finding the slope:
m=0
b = ?
1=0x+b
y=0x+1
so thats why its y=1
Given b (x) = StartAbsoluteValue x + 4 EndAbsoluteValue, what is b (negative 10)?
Negative 10
Negative 6
6
The value of the expression b(x) = x + 4 is -6.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, b(x) = x + 4.
When x = -10, the value of b will be:
b(x) = x + 4.
b(-10) = - 10 + 4
b= -6
The value is -6.
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⦁ The function p (w) = 230(1.1)w represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period. 10 points
⦁ During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
⦁ Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
⦁ When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
you will get 10 points
The increasing exponential functions are described as follows:
f(t) = a(1 + r)^t.
In which the parameters are listed as follows:
a is the initial value.r is the growth rate.For the old factory, the function is of:
p (w) = 230(1.1)^w.
Hence:
During week 0, 230 items are produced.The growth rate is of 10%.For the new factory, from the graph given at the end of the answer, the parameters are given as follows:
a = 190, which is the intercept.b = 1.1578, as 220/190 = 1.1578.Hence the function is:
pn(w) = 190(1.1578)^w.
The new factory overtakes the old factory when:
pn(w) > p(w)
190(1.1578)^w > 230(1.1)^w
(1.1578/1.1)^w > 230/190
wlog(1.1578/1.1) > log(230/190)
w > log(230/190)/log(1.1578/1.1)
w > 3.73 weeks.
Missing InformationThe graph for the second factory is given by the image presented at the end of the answer.
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What is the slope of the line that passes through the points (0, -10)(0,−10) and (-4, -11)(−4,−11)? Write your answer in simplest form.
The slope of the line that passes through the points is 1/ 4
What is slope?The gradient or slope of a line is a value or number describing both the direction and the steepness of a line.
The formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/ x₂ - x₁
Where;
y₁ is the first point on the y - axis y₂ is the second point on the y - axisx₁ is the first point on the x - axisx₂ is the second point on the x - axisNow, substitute the values, we have;
Slope, m = (-11 - ( -10)/ ( -4 - 0)
expand the brackets
Slope, m = - 11 + 10/ -4
Add the values
Slope, m = -1/ -4
Divide the values
Slope, m = 1/ 4
Hence, the value is 1/ 4
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Answer:
1/4
Step-by-step explanation:
Suzette ran and biked for a total of 50 mi in 4 h. Her average running speed was 5mph and her average biking speed was 15 mph.
Let x= total hours ran
Let y= total hours biked
How many hours did suzette run?
How many hours did she bike?
In total 4 hours Suzette ran for 1 hour and biked for 3 hours having average speed 5mph and 15mph respectively.
What is Average Speed?
Average speed is defined as total distance covered by the body divided by the time taken.
Average speed = Total distance covered/ total time taken
According to the given question:
Let x = total hours ran and y = total hours biked
Total time she ran and biked = 4h
∴ x + y = 4 ----- 1)
Total distance she biked and ran = 50 miles
Now, average running speed = 5 mph
Distance she ran = 5x
Similarly average biking speed = 15 mph
Distance she biked = 15y
∴ 5x + 15y = 50 ----- 2)
Solving 1) and 2) to get the values of x and y
Substituting x = 4 - y from 1) in 2)
5 (4 - y) + 15y = 50
On solving further we get y = 3
Substituting y = 3 to get x
x = 4 - 3
x = 1
Hence the Suzette ran for 1h and biked for 3h.
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Would you classify the number 200 as a perfect square, a perfect cube, both, or neither? Explain.
Answer:200 is a perfect square
Step-by-step explanation:
because when divided by two it give a whole number being divided
engineers measure angles in gradients, which are smaller than degrees. The table shows the conversion of some angle measures in degrees to angles in gradients. What is the slope of the line representing the conversion of degrees to gradients?
Express your answer as a decimal rounded to the nearest hundredth
The slope of the line is 1.11
What is the slope of a line?Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line.
Given that, engineers measure angles in gradients, which are smaller than degrees,
Slope = (-200+100)/(-180+90) = -100/(-90) = 10/9 = 1.11
Hence, The slope of the line is 1.11
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Answer:
1.11
Step-by-step explanation:
it's correct.
22. A train travels 3 hours at 20km per
hour. How long will it take another
train to travel the same distance at
10km per hour?
(a) 6²/³ hours
(b) 6¹/2hours
(c) 6 hours
(d) 3 hours
(e) 2 hours
What I
The train takes 6 hours to travel the same distance.
From the question, we have
A train with 20km per hour takes 3 hours to travel the distance .
Another train with 10km per hour takes = (3*20)/10 hours
=6 hours
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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SOLVE FOR X Help please
Answer:
x = 20
Step-by-step explanation:
Comment
If you follow the angles down, you discover 2 things
There are only 2 answers
One is the supplement of the other.
In this case, both angles can be shown to be the same. The process is accomplished by two vertically opposite angles and 2 supplements. I can't show you how this is done because there are no letters on the lines.
It turns out that 3x + 10 = 4x - 10
Solution
3x + 10 = 4x - 10 Add 10 to both sides
3x + 10 + 10 = 4x - 10 + 10 Combine
3x + 20 = 4x Subtract 3x from both sides.
3x-3x + 20 = 4x-3x Combine
20 = x
Drag the red and blue dots along the x-axis and y-
Answer:
Put one dot at (0,3) and the other dot at (1,0)
Step-by-step explanation:
Let x = 0
6x + 2y = 6
6(0) + 2y = 6
2y = 6 Divide both sides by 2
y = 3
(0,3)
Let y = 0
6x + 2y = 6
6x + 2(0) = 6
6x = 6 Divide both sides by 6
x = 1
(1, 0)
Parallelogram PQRS is shown. m/S=(3x), m/R=120, and m/Q=(2y). Find the value of y.A.
20
B.
30
C.
40
D.
60
Option B. From the parallelogram PQRS the value of y is given to be 30
How to solve for the value of y from the parallelogramIn order to get the value of y we have to use the formula
2y + 120 = 80
where the value 120 is the angle that is stated as 120 from the question
2y = 180 - 120
2y = 60
y = 60 / 2
y = 30
Hence the value of y = 30
We can go ahead to get the value of x as well
3x + 120 = 180
take the like terms
3x = 180 - 120
3x = 60
divide through by 3 to get x
60 / 3 = x
20 = x
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