Answer:
The answer is below
Step-by-step explanation:
The question would not give a valid answer, the question should be in the form:
A Florida citrus grower estimates that if 30 orange trees are planted, each tree will produce 500 oranges. For each additional tree planted on the same acreage, the number of oranges each tree produces will decrease by 10 oranges. Find the maximum number of oranges the citrus grower can produce. How many trees will the citrus grower need to plant?
Solution:
Let x represent the number of orange trees above 30 to be planted on the acreage and let y be the number of oranges. Since for every additional tree there is a decrease of 10 oranges, hence:
y = (30 + x)(500 - 10x)
y = 15000 - 300x + 500x - 10x²
y = 15000 + 200x - 10x²
The number of oranges is maximum at y' = 0. Hence:
y' = 200 - 20x
200 - 20x = 0
20x = 200
x = 10
Second derivative test = y" = -20 (so this is maximal)
Therefore the number of trees needed = 30 + 10 = 40 trees
Maximum number of oranges = (30 + 10)(500 - 10(10)) = 40(400) = 16000 oranges
Answer:
Step-by-step explanation: this is 150 multiplied by 500
The diagram shows a cuboid of volume Vcm (cubed)?
(a) Show that V = 15 + 16x-x(squared) - 2x (cubed)
Answer:
see explanation
Step-by-step explanation:
The volume (V) of the cuboid is calculated as
V = (2x + 5)(3 - x)(x + 1)
= (3 - x)(2x + 5)(x + 1) ← expand the pair of factors using FOIL
= (3 - x)(2x² + 7x + 5)
= 3(2x² + 7x + 5) - x(2x² + 7x + 5) ← distribute parenthesis
= 6x² + 21x + 15 - 2x³ -7x² - 5x ← collect like terms and rearrange
= 15 + 16x - x² - 2x³
The volume of the cuboid is 15 + 16x - x² - 2x³
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume (V) of the cuboid is calculated as
Volume of cuboid is length times width times height.
V = (2x + 5)(3 - x)(x + 1)
= (3 - x)(2x + 5)(x + 1)
Expand the pair of factors using FOIL
= (3 - x)(2x² + 7x + 5)
= 3(2x² + 7x + 5) - x(2x² + 7x + 5) ←
Distribute parenthesis
= 6x² + 21x + 15 - 2x³ -7x² - 5x
Combine like terms and rearrange
= 15 + 16x - x² - 2x³
Hence, the volume of the cuboid is 15 + 16x - x² - 2x³
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Find the roots of f(x)=x^2 + 10x -96
Shawn erned 5 dallors an hour mowing lawns pluse 10 welkly allounce from his parents what minmin number of hours he needs to mow in order to have enuf money to buy 75 dallars par of basketball sheows
Answer:
13 hours
Step-by-step explanation:
Since Shawn mows lawns at a rate of 5 dollars an hour, if he mows for t hours, he earns 5t dollars. Also, he gets 10 dollars weekly allowance from his parents. Thus, the total amount he earns per week is thus 10 + 5t.
Since he needs to earn enough to buy 75 dollars pair of basketball shoes, the amount he earns must equal the price of the shoes. So,
10 + 5t = 75
We now solve for t to find the amount of hours if takes him to earn enough to buy the shoes.
So,
10 + 5t = 75
Subtracting 10 from both sides, we have
10 - 10 + 5t = 75 - 10
5t = 65
dividing both sides by 5, we have
t = 65/5
t = 13 hours
So, it takes Shawn 13 hours to earn enough to buy the shoes.
For this question, use the following functions.
f(x) = 2x + 6
g(x) = 4x2 – 9
Find a simplified expression for f(f(x)).
O 2x – 12
0 4x + 12
O 2x + 6
O 4x + 18
Answer:
4x + 18
Step-by-step explanation:
This is called a composite function, meaning passing the range of one function as a domain of another function.
For f(f(x)), the inner-function's range is passed as the domain of the outer function.
We can do so by substitution,
The range of f(x) can be written as 2x + 6 for any defined x values,
So we will substitute 2x + 6 as the 'x' of another function which is in this case
f(x) again, so it looks like this 2(2x+6) + 6 which can be simplified into
4x + 18
y= 1/2x - 1
what's the slope and intercept.
Answer:
The slope is 1/2. The x-intercept is (2,0). The y-intercept is (0,-1)
Answer:
The slope is 1/2x and -1 is the (y) intercept
Step-by-step explanation:
Since y= 1/2x - 1 is already a linear equation (y=mx+b) you can use y=mx+b to find the slope and (y) intercept.m is the slope and b is the intercept
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
I need the bottom part
Answer:
y ≠ 9, y ≠ 3
Step-by-step explanation:
y² -12y +27 = (y - 9) (y - 3)
Denominator ≠ 0
y ≠ 9 or y ≠ 3
Write 4x10 to the power of 6 in decimal notation.
Answer:
Since the exponent of the scientific notation is positive, move the decimal point 66 places to the right.
4000000
The expression 4 x [tex]10^6[/tex] in decimal notation is 4,000,000.
We have,
In scientific notation, a number is expressed as a product of a decimal number and a power of 10.
In the given expression, 4 x [tex]10^6[/tex], the base number is 4, and it is multiplied by 10 raised to the power of 6.
To convert this into decimal notation, we need to multiply the base number (4) by the power of 10 ([tex]10^6[/tex]), which means moving the decimal point six places to the right.
Starting with 4, we move the decimal point six places to the right, resulting in 4,000,000.
Thus,
The expression 4 x [tex]10^6[/tex] in decimal notation is 4,000,000.
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Line segment JL is an altitude in triangle JKM. Triangle K J M is shown. Angle K J M is a right angle. An altitude is drawn from point J to point L on side K M to form a right angle. The length of K J is 13, the length of J L is 5, and the length of J M is 8. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth. JKM is a right triangle because KL + LM = 15.3. JKM is a right triangle because KL + LM = 18.2. JKM is not a right triangle because KL + LM ≠ 15.3. JKM is not a right triangle because KL + LM ≠ 18.2.
Answer:
JKM is not a right triangle because KL + LM ≠ 15.3.
Step-by-step explanation:
Given
[tex]JK = 13[/tex]
[tex]JL = 5[/tex]
[tex]JM = 8[/tex]
Required
Determine if JKM is right-angles or not
Calculate length KL using Pythagoras theorem.
[tex]JK^2 = JL^2 + KL^2[/tex]
[tex]13^2 = 5^2 + KL^2[/tex]
Collect like terms
[tex]KL^2 = 13^2 - 5^2[/tex]
[tex]KL^2 = 144[/tex]
[tex]KL = 12[/tex]
Calculate length LM using Pythagoras theorem.
[tex]JM^2 = JL^2 + LM^2[/tex]
[tex]8^2 = 5^2 + LM^2[/tex]
Collect like terms
[tex]LM^2 = 8^2 - 5^2[/tex]
[tex]LM^2 = 39[/tex]
[tex]LM = \sqrt{39[/tex]
[tex]LM = 6.2[/tex]
[tex]KM = KL + LM[/tex]
[tex]KM = 12 + 6.2[/tex]
[tex]KM = 18.2[/tex]
If JKM is right-angled, then:
[tex]KM^2 = JK^2 + JM^2[/tex]
[tex]KM^2 = 13^2 + 8^2[/tex]
[tex]KM^2 = 233[/tex]
[tex]KM = \sqrt{233[/tex]
[tex]KM = 15.3[/tex]
[tex]15.3 \ne 18.2[/tex]
i.e
[tex]KL + LM \ne 15.3[/tex]
Hence: JKM is not right-angled
Answer:
C-JKM is not a right triangle because KL + LM ≠ 15.3
Step-by-step explanation:
if right mark as brainliest
PLEASE PLEASE PLEASE HELP HELP ME ME!!!!
Answer:
The answer for question 3 is D, number 4 is C
I will give brainly
Find the probability that a randomly
selected point within the circle falls
in the red shaded area (square).
r = 4 cm
4√2 cm
[? ]%
Answer:
Step-by-step explanation:
This probability will be the area of the square divided by the area of the circle.
[tex]P=\frac{(4\sqrt{2})^2}{\pi 4^2}\\ \\ P=\frac{32}{16\pi}\\ \\ P=\frac{2}{\pi }\\ \\ \text{As a percentage}\\ \\ P=\frac{200}{\pi}\\ \\ P\approx 63.7\% [/tex]
Grace earns $7 for each car she washes. She always saves $20 of her weekly earnings. This week, she wants to have at least $69 in spending money. How many cars must she wash? Enter and solve an inequality to represent this situation. Enter your value as a simplified mixed number, if necessary.
Answer:
She need to wash 9 cars
Step-by-step explanation:
Identify a transformation of the function ƒ(x) = x^2 by observing the equation of the function g(x) = (x – 1)^2
Answer:
f(x) is translated 1 units left to give g(x)
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
[tex]g(x) = (x - 1)^2[/tex]
Required
How does f(x) transform to g(x)
[tex]f(x) = x^2[/tex]
When translated by b units left, it gives:
[tex]g(x) = f(x - b)[/tex]
In this case:
[tex]b = 1[/tex]
So:
[tex]g(x) = f(x - 1)[/tex]
If [tex]f(x) = x^2[/tex], then
[tex]f(x - 1) = (x - 1)^2[/tex]
Hence:
[tex]g(x) = (x - 1)^2[/tex]
This implies that; f(x) is translated 1 units left to give g(x)
Gary is buying bananas at the grocery store. The bananas cost $0.89 per pound. What is the equation for the cost (y) of (x) pounds of bananas Gary buys?
a. y=0.89+x
b. y=0.89-x
c. y=0.89/x
d. y=(0.89)x
Answer:
d
Step-by-step explanation:
Mhanifa can you please help? Look at the picture attached. I will mark brainliest!
Answer:
Sum of exterior angles of a polygon is 360°#8
2x + 2(64°) + 36° + 48° = 360°2x + 212° = 360°2x = 360° - 212°2x = 148°x = 74°#9
x + 73° + 109° + 90° = 360°x + 272° = 360°x = 360° - 272°x = 88°Find the average value fave of the function f on the given interval. f() = 5 sec2(/6), 0, 3 2
Answer:
[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]
Step-by-step explanation:
To find - Find the average value fave of the function f on the given interval. f(x) = 5 sec²(x/6), [0, 3[tex]\pi[/tex]/2]
Proof -
We know that,
Average value of f in the interval [a, b] is -
[tex]f_{ave}[/tex] = [tex]\frac{1}{b - a}\int\limits^b_a {f(x)} \, dx[/tex]
Now,
Here a = 0, b = [tex]\frac{3\pi }{2}[/tex], f(x) = [tex]5sec^{2}(\frac{x}{6} )[/tex]
Now,
[tex]f_{ave}[/tex] = [tex]\frac{1}{\frac{3\pi }{2} - 0}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{2 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {5sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{10 }{3\pi }}\int\limits^{\frac{3\pi }{2} }_0 {sec^2 ({\frac{x}{6} }) } \, dx[/tex]
= [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) }|^{\frac{3\pi }{2} }_0 \, ][/tex]
= [tex]{\frac{10 }{3\pi }}[\ {tan({\frac{x}{6} }) - tan({0) } \, ][/tex]
= [tex]{\frac{10 }{3\pi }}[ {1 - 0 } ][/tex]
= [tex]{\frac{10 }{3\pi }[/tex]
⇒[tex]f_{ave}[/tex] = [tex]{\frac{10 }{3\pi }[/tex]
PLS HELP 20 points
Triangle ABC is a right triangle with right angle B and altitude BD. If DC =54, AC=60, find AB (x) and BD (y)
Answer:
Hey Mate!
tis is ur answrr!
HELP ! How long is segment AB ?
Answer:
square root of (2+10)²+(-5+3)²
square root of 144+4
square root of 148
PLEASE HELP ME- In the diagram below,
Answer:
Step-by-step explanation:
HELP ILL GIVE BRAINLIEST what’s the shape of the
Base?
Answer:
circle
Step-by-step explanation:
I need help I'm so confused
Answer:
Yeah me too buddy :(
Step-by-step explanation:
How many milligrams are in one-half a gram?
Some one plesae heelp!1
Option (b) 1.00
Step-by-step explanation:
3.4×1.00 = 3.4
Answer:
1.00
Step-by-step explanation:
1.00 equals one therefore the actual equation is 3.4x 1 = 3.4
Or 3.4x1.00=3.4
Hope this helps.
In ΔQRS, r = 6.9 inches, ∠Q=40° and ∠R=101°. Find the area of ΔQRS, to the nearest 10th of an square inch.
Answer:
9.8 in²
Step-by-step explanation:
If A, B and C are the angles of a triangle and a, b, c are the repective sides opposite the angles, then the area of the triangle is given as:
Area = (1/2)absin(C)
In ΔQRS, the area is:
Area = (1/2)rqsin(S)
∠S + ∠Q + ∠R = 180° (sum of angles in a triangle)
∠S + 40 + 101 = 180
∠S = 39°
Using sine rule to find q:
[tex]\frac{q}{sinQ} =\frac{r}{sinR} \\\\\frac{q}{sin40}=\frac{6.9}{sin101} \\\\q=\frac{6.9*sin40}{sin101} =4.52 \ inches\\\\Area\ of\ triangle \ QRS=\frac{1}{2}rqsin(S) =\frac{1}{2}*6.9*4.52*sin(39)=9.8\ in^2[/tex]
Find the measure of the indicated angle. (image included)
I'm sorry I keep posting these it's just cause I don't understand still but i'm learning.
Answer: 88
The unknown angle in the left triangle is 80 since the sum of the angles in a triangle is 180.(180-60-40=80)
The unknown angle (the one that doesn't have a "?") is 36 since there's a straight angle which equals 180.(180-80-64)
Therefore the angle with the "?" is 88 since the sum of the angles in a triangle are 180(180-36-56)
Hope this helps!
Find the
Width (in feet)
Answer
62
Step-by-step explanation:
Find the missing sides of each triangle. Leave your answers in radical form
Answer:
youbhave give me more information.
Answer:
incomplete question
please write the whole question or diagram of the question
Jonathan borrowed $5 from a friend who is charging him 5% interest every day on the $5. If his friend takes 4 weeks to pay Jonathan back, how much will he owe him. Use I= PRT
Answer:
$1.00
Step-by-step explanation:
5 (0.05) (4)= $1.00
hope this helps
math (not too hard answer asap) :)
Answer:
A and CStep-by-step explanation:
A. 134 is the mode, correct, repeated 5 timesB. 111 is appears 3 times, incorrect , this number is not part of data setC. There are more data values between 130 and 139, correct, there are 8 of themD. There are 20 data values, incorrect , there are 23Jaime drew the number line below to show 2/3 4/5. Explain how the number line shows 2/3 times 4/5. What is the product?
Answer:
[tex]\frac{2}{3} * \frac{4}{5} = \frac{6}{15}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3} * \frac{4}{5} =[/tex]
The number line is missing from the question.
So, I will answer the question and also draw the number line to show the product.
[tex]\frac{2}{3} * \frac{4}{5} =[/tex]
[tex]\frac{2}{3} * \frac{4}{5} = \frac{6}{15}[/tex]
To represent this on a number line;
We draw a number line of 15 points, and place a dot on the 6th point.
This represents 6/15
See attachment
please help me. i'll give brainliest
The list that represents the simulation is (d) 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597 8078 4333 3033 3153
How to rearrange the list?The list is given as:
860583 785814 010122 337198 621549 034076 796495 978078 433330 333153
To illustrate the simulation of four free throws, then each number on the list must have 4 digits
So, we have:
8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597 8078 4333 3033 3153
Hence, the list that represents the simulation of four free throws is (d)
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