Considering the vertex of the quadratic equation, the width that will maximize the area of the garden, and the maximum area, are as follows:
Width: 10 ft.Maximum area: 1000 ft².What is the vertex of a quadratic equation?A quadratic equation is defined as follows:
y = ax² + bx + c.
The vertex can be either a maximum point or a minimum point, depending on the coefficient a, as follows:
Maximum: a < 0.Minimum: a > 0.The coordinates of the vertex are given as follows:
x = -b/2a.y = -(b² - 4ac)/4a.For this problem, the equation is:
A(w) = -10w² + 200w.
Hence the coefficients are:
a = -10, b = 200, c = 0.
The width that will maximize the area is:
w = -200/(2(-10)) = 200/20 = 10 ft.
The maximum area is of:
A = -(200)²/(4(-10)) = 1000 ft².
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the width that will maximize the area of the garden, and the maximum area.
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Select the correct answer.
What is the height, x, of the equilateral triangle shown?
an equilateral triangle with the angles labeled as 60 degrees and a side length of 10 inches, the height labeled as x
Answer:
x = 5√3
Step-by-step explanation:
We will use the Pythagorean theorem with a and b as the lengths of the legs, and c as the length of the hypotenuse.
a² + b² = c²
We need two of the three lengths of a, b, and c, so we can find the third length.
The height divides the equilateral triangle into two right triangles.
Look at one of the right triangles.
One leg is half the side of the triangle.
a = 10/2 = 5
One leg is the height.
b = x
The hypotenuse is the side of the equilateral triangle.
c = 10
a² + b² = c²
5² + x² = 10²
25 + x² = 100
x² = 75
x = √75
x = 5√3
Answer: b
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
PLEASE HELP
(x,y)→(__,__)
Answer: since the distance between f and g is 20 units and is then reduced to 4 units long, it's scale factor would be 0.2
Step-by-step explanation:
Sorry if you get this wrong, i tried really hard on this and watched a video
Divide $70 into these ratios 1:2:4
Answer:
Step-by-step explanation:
1+2+4=7
70/7=10
10 x 1=10 10 x 2=20 10 x 4=40
10:20:40
A population numbers 11,000 organisms initially and decreases by 9% each year.
Answer:
Step-by-step explanation:
11000*0.91=10010
10010*0.91=9109.1(approximately 9109)
keep going until you find the year you want
Four employees of Papa Tony's
Pizza are cleaning up at the end
of a busy night. There is a list of 43 clean-up tasks that need to be
completed. If each employee does the same number of tasks, how
many tasks should each employee do? Solve. Explain how you
interpreted the remainder.
The required number of tasks should each employee do are 10.
What is Remainder?
The Remainder of the worth left after the division. In the event that a number (profit) isn't totally distinguishable by another number (divisor) we are left with a worth once the division is finished. This worth is known as the rest of. For instance, 10 isn't precisely separated by 3. Since the nearest esteem, we can get 3 x 3 = 9.
According to question:As there are 43 clean-up tasks that need to be completed,
And four employees
Number of task for one employee = 43/4 = 10, and 3 is remainder.
So, each employee does the 10 number of tasks, and 3 is obtain as a remainder.
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Use trigonometry to determine the m
Here, we seek the angle adjacent to one of the given sides' length.
When given the hypothenuse and the adjacent lengths, we employ the SOH CAH TOA formulae.
This gives us:
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypothenuse}\text{ | Notice the first letters were used for the acronym} \\ \text{Therefore, }\theta=\cos ^{-1}\frac{adjacent}{hypothenuse} \end{gathered}[/tex]Where
adjacent = 15
Hypothenuse = 34
Employing back into the formulae, we have:
[tex]\begin{gathered} \theta=\cos ^{-1}(\frac{15}{34}) \\ \theta=63.82^o \end{gathered}[/tex]The missing angle is approximately 64 degrees
4. Determine the root of the following equation. x-6/4-4= 3x/2+2x+1/5
The root of the given equation is x = -114/33.
We are given an equation. The equation has one variable. It is linear in nature. The equation is given below.
(x-6)/4 - 4 = (3x/2) + (2x+1)/5
We need to find the root of the equation. First of all, we will move all the terms containing the variable "x" to one side of the equation.
(x-6)/4 - (3x)/2 - (2x+1)/5 = 4
Now we will multiply the terms with the LCM of all the denominators.
20*[(x-6)/4 - (3x)/2 - (2x+1)/5] = 20*4
5(x-6) - 10(3x) - 4(2x+1) = 80
5x - 30 - 30x - 8x - 4 = 80
-33x - 34 = 80
-33x = 114
x = -114/33
Hence, the root of the given equation is x = -114/33.
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find the measure of NE and MD PLEASE 5th time i need help
The measure is 5.
From the question, we have
E is the circumcenter. The distance from circumcenter to all of their vertices from that triangle are the same, so
NE =EP
⇒13x -28 = 6x +7
⇒13x -6x = 28 +7
⇒7x = 35
⇒x= 5
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
Complete question: Find value of x, measure of NE,MD?
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Mora is using a map to find the distance between her house and her cousin's house. She knows that 2 centimeters on the map represent 300 miles. On the map, the distance between her house and her cousin's house is 20 centimeters.
What is the distance, in miles, between Mora's house and her cousin's house?
The distance, in miles, between Mora's house and her cousin's house will be 3000 miles as "2 centimeters on the map represent 300 miles. On the map, the distance between her house and her cousin's house is 20 centimeters."
What is unitary method?The unitary method involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method is a way of finding any required quantity's value by first finding the value of the unit (one) quantity.
here,
2 cm=300 miles
1 cm=150 miles
so,
20 cm=
150*20=3000 miles
Mora's residence and her cousin's residence are separated by 3000 miles in miles "On the map, a centimeter equals 300 miles. Her house is 20 centimeters from her cousin's house, according to the map."
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Triangle STU has side lengths s = 34.0 and u = 40.5. Angle T has a measure of 49°. What
is the length of side t?
Using cosine rule, the length of side t is 31.5 unit
Cosine RuleCosine rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
t² = s² + u² -3su cos(T)
let's define our variables
t = ?s = 34u = 40.5T = 49 degreessubstituting the values into the formula
t² = 34² + 40.5² -2(34)(40.5)cos49
t² = 1156 + 1640.25 - 1806.79
t² = 989.46
t = √989.46
t = 31.5
The length of t is 31.5 unit
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I really need help I'll take a picture of the question
To plot the graph of the function:
[tex]h(x)=8|x+1|-1[/tex]According to your graphing software, we need to find the smallest value of the function, and any point at the positive slope side of the function. Let's start with the minimum point. Let's use the general formula for an absolute value function:
[tex]f(x)=a|x+b|+c[/tex]The coefficients 'b' and 'c' determinates how much the function was translated from the origin. The 'b' determinates in the x-axis, and the 'c' determinates in the y-axis.
If the 'b' is positive, the function translated to the left, if it is negative the function translated to the right.
If the 'c' is positive the function went up, and if it is negative it went down.
Now let's analyze our h(x) function. Our coefficients are:
[tex]\begin{cases}b=1 \\ c=-1\end{cases}[/tex]Which means our minimum point is
[tex](-1,-1)[/tex]Now, we just need to calculate any point to the right of x = -1.
Let's calculate for x = 0.
[tex]h(0)=8|0+1|-1=8-1=7[/tex]The second point is (0,7)
Help me this is very hard
By applying the distributive property of multiplication, an expansion of this mathematical expression can be written as 3(x - 2) = 3x - 6.
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
Mathematically, the distributive property of multiplication can be represented by this mathematical expression:
a(b + c) = ab + ac.
a(b - c) = ab - ac
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
3(x - 2) = 3(x) - [3(2)]
3(x - 2) = 3x - 6
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help please!! forr 40 points
Answer:
C.
Step-by-step explanation:
you have to divide the numbers
Answer:
C and about 400 hats
Step-by-step explanation:
So you'd have to round up to 1600 for the first equation and for the second one it's about 400 because 1600/4=400
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A line passes through the point (−8, – 7) and has a slope of
-5/4
Write an equation in point-slope form for this line.
The equation in the point-slope form of the line is -7 = -5/4x -8.
What do we mean by point-slope form?One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form.
This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the point-slope form is:
The equation of the point-slope form: y = MX + b
Where y is the y coordinate and b is the x coordinate and m is the slope.
Now, get the point-slope form as follows:
y = MX + b
-7 = -5/4x -8
Therefore, the equation in the point-slope form of the line is -7 = -5/4x -8.
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Ricardo started a savings account for his daughter Ruth by depositing
$500 into the account for her
1st birthday. For each successive birthday, Ricardo deposits
$200 more than the amount deposited for the previous birthday. This is the only money deposited into the account. What is the total amount of money Ricardo will have deposited into the account for Ruth up to and including her 6th birthday?
Answer big number
Step-by-step explanation: you start with 500 then 700 for 2nd then 900 for 3rd 1100 for 4th 1300 for 5th 1500 for 6th
Answer: 6,000
Step-by-step explanation:
If it starts with 500 on the first birthday, and each year he deposits the same amount as the previous plus 200 then we get 700 for the 2nd year.
3rd year: deposits 900
4th year: deposits 1100
5th year: deposits 1300
6th year: deposits 1500
500+700+900+1100+1300+1500=6000
Answer: $6000
The ratio of the number of apple trees to the number of lemon trees in a farm is 9:5. There are 45 lemon trees in the farm. How many apple trees are there in the farm?
2. A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that
the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.
a. What price yields the maximum profit?
b. What is the maximum profit?
Based on the given function,
a) The price that yields the maximum profit is $20.
b) The maximum profit is $6,050
Function
Function defines the relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Given,
A rock club's profit from booking local bands depends on the ticket price. Using past receipts, the owners find that the profit p can be modeled by the function p = -15t² + 600t + 50, where t represents the ticket price in dollars.
Here we need to find the price that yields maximum profit and the amount of maximum profit.
In order to find the price that yield the maximum profit, we have to find the value of t, that can be obtained by using the formula,
t = -b/2a
According to the given function the values of a = -15 and the value of b = 600
Apply these values on the given function then we get,
t = -600/ 2(-15)
t = -600/-30
t = 20
Therefore, the price that yields the maximum profit is $20.
Now, we need to find the maximum profit, by apply the value of t as 20 in the given function then we get,
p = -15(20)² + 600(20) + 50
P = -15(400) + 12000 + 50
p = -6000 + 12000 + 50
p = 6000 + 50
Therefore, the maximum profit is $6,050.
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Find the values of each variable.
Step-by-step explanation:
x + y = 180° (linear pair)
Also, x = 3y (corresponding angles are equal)
So, 4y = 180
y = 45°
x = 135°
A watermelon is placed on a digital scale. The scale reads 10.5. What could units be?
The units of weight of watermelon on the digital scale could be kilogram, gram and pounds.
According to the question,
We have the following information:
A watermelon is placed on a digital scale. The scale reads 10.5.
We know that there are several units of measurements for every physical quantity. For example, the units for measuring length are kilometers, meters, centimeters, feet, inches and many more.
In the same way, there are many units for measurements of weight. However, in most of the cases for the weight on a digital scale, it can be kilogram, gram or pound.
So, it could 10.5 kg or 10.5 g or 10.5 pounds.
Hence, the units of the weight of watermelon on the digital scale could be kilogram, gram and pounds.
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NASA is painting the nose cone of a sounding rocket with a special sealant which reduces the air-drag on the rocket. If they need to do two coats of the sealant, how many square feet are they painting? Use π = 3.14.A. 56.5 ft²B. 27.3 ft²C. 35.3 ft²D. 28.3 ft²
In order to determine the number of required square feet to paint the nose cone, use the following formula for the surface area of a cone without the base:
[tex]S=\pi rl[/tex]where
r: radius of the base of the cone = 3 ft
l: slant height of the cone = 6 ft
replace the previous values of the parameters into the formula for S and simplify:
[tex]S=(3.14)(3ft)(6ft)=56.5ft^2[/tex]Hence, 56,5ft^2 are required
A banner maker was asked to redesign a squarebanner by increasing the width by 4 feet anddecreasing the length by 2 feet. The total area of thenew banner was 91 square feet.What was the length of the side of the original squarebanner?
Let:
x = original sides.
x + 4 = new width
x - 2 = new feet
So:
(x + 4)(x - 2) = 91
x² - 2x + 4x - 8 - 91 = 0
x² + 2x - 99 = 0
Factoring:
(x + 11)(x - 9) = 0
x = -11 (the lenght can't be negative so this answer is not valid)
x = 9 ft
△ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.
What is CA ?
The value of side CA of the right angle triangle is 8.85.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles. The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths.
Given that △ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.
The value of side CA is calculated, from the right angle triangle applying the angle property,
tan41 = (7.7)/(CA)
CA = (7.7)/(tan41)
CA = 8.85
Therefore, the value of side CA of the right angle triangle is 8.85.
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If both pairs of opposite sides of a quadrilateral are congruent, then thequadrilateral is a parallelogram.A. TrueB. False
Answer:
True
Explanation:
Craig is making 3 recipes for his party. He has a containerof flour on his kitchen scale. The table shows the totalchange in weight of the flour on the scale after each ofthe 3 recipes. What is the average change in the amountof flour, in ounces, used in the 3 recipes?
Answer:
C
Step-by-step explanation:
The average change in the amount of flour is the sum of the changes after each recipe divided by the number of recipes.
Sum of changes:
[tex]-2-3\frac{1}{2}-4\frac{1}{2}=-2-\frac{3\ast2+1}{2}-\frac{4\ast2+1}{2}=-2-\frac{7}{2}-\frac{9}{2}[/tex][tex]-2-\frac{7}{2}-\frac{9}{2}=-2-\frac{7+9}{2}=-10[/tex]Average:
3 recipes.
Total is -10.
-10/3 = 3 with rest 1. So as a mixed number, the correct answer is option C.
hi. This is an equation on some math homework and im not sure how to do it. Could you help?Write an equation of the line that is parallel to y=16 and passes through point (−7,43)
From the given equation y=16, it implies that the line has no slope.
Hence, the slope is zero (0).
From the given point:
[tex]\begin{gathered} (-7,43) \\ x_1=-7,y_1=43 \end{gathered}[/tex]The equation of the line is given by the equation:
[tex]m=\frac{y-y_1}{x-x_1}[/tex][tex]\begin{gathered} 0=\frac{y-43}{x-(-7)} \\ 0=\frac{y-43}{x+7} \\ \text{cross}-\text{multiply} \\ y-43=0 \\ y=43 \end{gathered}[/tex]Hence, the equation of the line is y=43
suppose you get a cash prize of $100 if you win a game. the probability of winning the game is 0.7. what is the probability of winning $600 or less if you play the game 10 times, assuming that each game is independent?
The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.
Define binomial distribution.A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.
Given,
Cash prize = $100
Probability of winning the game = 0.7
Using binomial distribution,
P(4 ≤X≤ 6) = P( X = 4) + P( X = 5) + P( X = 6)
P( 4 ≤ X ≤ 6)
= 1/4(0.6)⁴(0.4)⁴ + 10/5 (0.6)⁵(0.4)⁵ + 10/6 (0.6)⁶(0.4)⁶
= 0.1115 + 0.2007 + 0.2508
= 0.5630
The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.
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Use the graph, which shows the profit,y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980.linear graph with negative slope with points (15,150) and (25,130)Find the linear function y, where y depends on t, the number of years since 1980. Type your function in slope intercept form (y=mx+b) without any commas or spaces and be sure to use a lowercase t for your variable.The linear function is y=Answer
First, locate any two point from the line.
(15, 150) and (25, 130)
x₁ = 15 y₁= 150
x₂ = 25 y₂ = 130
[tex]\text{Slope(m)}=\frac{130-150}{25-15}[/tex][tex]=\frac{-20}{10}[/tex][tex]=-2[/tex]Next, is to find the intercept.
Substitute x=15 y=150 and m=-2 into y=mx + b and solve for b
That is;
150 = 15(-2) + b
150 = -30 + b
Add 30 to both-side of he equation
150 + 30 = b
180 = b
Form the equation by substituting m=-2 and b=180 into y=mx + b
y = -2x + 180
Hence, the line function is y = -2x + 180
Write 250 metres as a fraction of a kilometre.
Determine whether a relation is a function.