Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:
[tex]\begin{gathered} f(x)=x^2-4x+3 \\ f^{\prime}(x)=2x^{2-1}-4x^{1-1}-0\cdot3 \\ f^{\prime}(x)=2x-4 \end{gathered}[/tex]Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:
[tex]f^{\prime}(1)=2(1)-4=2-4=-2[/tex]The derivative of the function is -2 at x=1.
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) It takes 51 pounds of seed to completely plant a 9-acre field.
How many acres can be planted per pound of seed?
acres per pound
(b) Christine runs 4 miles in 22 minutes.
How many minutes does she take per mile?
minutes per mile
Answer:4
Step-by-step explanation:
Answer:a) Given :
51 pounds of seed can be planted in = 9 acre field.
Per pound of seed =
We can convert 9/51 in simplest fraction by dividing top and bottom by 3.
We get
Therefore, 3/17 of an acrs can be planted per pound of seed.
b) $10 amount = 16 pounds of sugar.
$1 amount = 16/10 = 1.6 pounds of sugar.
Therefore, 1.6 pounds of sugar she got per dollar.
Step-by-step explanation:
A stack of 12 sheets of gypsum board are 10.5 inches thick. If all the boards are uniform, how thick is each board?
Answer:
0.875 inches
Step-by-step explanation:
Pretty easy. Just divide how many inches thick the boards are by how many there are: inches-thick/amount
Now substitute 10.5/12 and find your answer
0.875 inches thick per board
Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
s:[-2,-3] is the answer
The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
The set S : { - 2 , - 3 , - 4 , - 5 }
The inequality relation is 2p - 8 < 5p + 4
Now , substituting the value from set S in the inequality , we get
When p = - 2 :
2p − 8 < 5p + 4
2(-2) − 8 < 5(-2) + 4
-4 − 8 < -10 + 4
-12 < -6 TRUE
When p = - 3
2p − 8 < 5p + 4
2(-3) − 8 < 5(-3) + 4
-6 − 8 < -15 + 4
-14 < -11 TRUE
When p = - 4
2p − 8 < 5p + 4
2(-4) − 8 < 5(-4) + 4
-8 − 8 < -20 + 4
-16 < -16 FALSE
When p = - 5
2p − 8 < 5p + 4
2(-5) − 8 < 5(-5) + 4
-10 − 8 < -25 + 4
-18 < -21 FALSE
Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation
Hence , the set S:{ -2,-3 } is the solution
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The graph of a linear function IS shown.
Which word describes the slope of the line?
positive
negative
zero
undefined
4
Choose the conjecture that describes how to find the 7th term in the sequence 4, 20, 36, 52,
OA) Multiply 52 by 9.
O B) Multiply 16 to 32..
OC) Add 32 to 52
OD) Add 48 to 52.
...
The correct option D) Add 48 to 52 is the conjecture that describes for the 7th term in the sequence.
What is termed as the arithmetic progression?An arithmetic progression (AP) is just a sequence in which the differences between each successive term are the same.An arithmetic progression (AP) can be defined in two ways:An arithmetic progression is still a sequence in which the differences between each successive term are the same.An arithmetic progression is a sequence in which each term (except the first) is obtained by having to add a fixed number to the term before it.For the given question, the sequence is given as;
4, 20, 36, 52,
Where, the first term a₁ is 4.
Second term a₂ is 20 and,
Third term a₃ is 36
Common difference d for each case is;
d = a₂ - a₁
d = 20 - 4 = 16
d = a₃ - a₂
d = 36 - 20 = 16
as, common difference is same, the sequence is said to be in AP.
Then, the formula for finding the 7th term is -
a₇ = a₁ + 6d
a₇ = 4 + 6×16
a₇ = 100
Now, this 7th term from the options can be found as;
Add 48 to 52 = 100.
Thus, the conjecture that describes for the 7th term in the sequence is add 48 to 52.
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Which answer choice correctly shows 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 in
exponential notation?
OA) 811
OB) 118
OC) 11⁹
OD) 1111
Answer:
it would be 11^8
Step-by-step explanation:
i dont see this as an option but i believe that there was a mistake i dont believe that any of theese are correct
what is the 2nd ponit of x = -3
50 POINTS!!!
Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain
1. even numbers are divisible by 2. odd numbers are not divisible by 2 so 4 is an even number
2. all photosynthetic organisms produce oxygen. phytoplankton and photosynhetic organisms. So phytoplankton produces oxygen.
3. Each time you clean your room, you are allowed to go out with your friends. So, the next time you clean your room, you are allowed to go out with your friends
Answer:
1. Deductive reasoning, because it is testing the ecisting theory that odd numbers are not divisible by 2 and gives an example that 4 is an even number and is divisible by 2.
2. This statement would be deductive reasoning because the person stating this is establishing the truth that all photosynthetic organisms produce oxygen, they are not creating a theory, just stating facts.
3. This would be inductive reasoning because they have given good reasons to base their theory however it is not simple fact.
Step-by-step explanation:
Hope i helped explain
NEED HELP ASAP - 100 POINTS
When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.
The advantages may be of using the method of completing the square to solve quadratic equations to estimate the values of x and y roots without calculating them.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Using Completing the square.
1. First of all we can find the minimum or maximum of the equation immediately.
2. Second is to cuts out the need to use the given ones (a, b, c) in the quadratic formula.
3. It allows estimating the values of x and y roots without calculating them.
Then Estimating on a test is a very valuable asset.
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What is the slope of a parallel line whose equation is x-2y=-18. Fully simplified answer.
Answer:
slope of 1/2
Step-by-step explanation:
x-2y=-18
First, get the equation in slope intercept form
y = mx+b where m is the slope and b is the y-intercept
-2y = -x -18
Divide each side by -2
y = 1/2 x + 9
The slope is 1/2
Parallel lines have the same slope, so lines that are parallel will have a slope of 1/2
Please help me with parts C and D, I’m struggling with them
ANSWER
[tex]\begin{gathered} c)s\imaginaryI n\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7})} \\ decimal=0.49 \\ d)cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\frac{\sqrt{13}}{7}+1)} \\ decimal=0.87 \end{gathered}[/tex]EXPLANATION
Given;
[tex]\begin{gathered} sin\theta=\frac{6}{7} \\ 0<\theta<\frac{\pi}{2} \end{gathered}[/tex]c) Hence;
[tex]\begin{gathered} sin\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7}}) \\ \end{gathered}[/tex]In decimal form;
[tex]sin\frac{\theta}{2}=0.49[/tex]d)
[tex]\begin{gathered} cos\theta=\frac{\sqrt{13}}{7} \\ cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\sqrt{\frac{13}{7}+1})} \\ decimal=0.87 \end{gathered}[/tex]a college professor hands out a list of 10 questions, 5 of which will appear on the final examination for the course. one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. suppose the professor chooses the 5 questions at random from the 10.
one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. then the probability of all 5 questions prepared for appears is 2
Recall : nCr = n! ÷ (n-r)!r!
The total possible outcome ; 5 questions out of 10
10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252
Required outcome :
All 5 questions set being from the 9 questions covered and 0 from the 1
left uncovered
9C5 * 1C0
9C5 = 9! ÷ 4!5! = (9*8*7*6) ÷ (4*3*2*1) = 126
1C0 = 1! ÷ 1!0! = 1
Probability = required outcome / Total possible outcomes
P(All 5 questions prepared for appears) :
[9C5 * 1C0] ÷ 10C5
(126 * 1) / 252
= 126/ 252
=2
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What is the value of this expression.
Answer:46
Step-by-step explanation:
After 4 months of a new nutrition program, Rashid has lost 16% of his original weight. he lost 36 lb. What was Rashid's original weight?
Answer:
225 lb
Step-by-step explanation:
Let x be Rashid's original weight.
If 16% of Rashid's original weight is 36 lb then:
[tex]\implies 0.16x=36[/tex]
To find Rashid's original weight solve for x:
[tex]\implies \dfrac{0.16x}{0.16}=\dfrac{36}{0.16}[/tex]
[tex]\implies x=225[/tex]
Therefore, Rashid's original weight is 225 lb.
ABCDE is a circle centre O. The diameter, AC, is extended to the point F so that CF = 16 cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD = 18 cm and DE = 14 cm. The radius of the circle is r
Answer:
r = 10 cmStep-by-step explanation:
It is assumed you are looking for the missing value of r.
Use the intersecting secants theorem:
[tex]FA*FC = FE*FD[/tex]Substitute known values and solve for r:
(2r + 16)*16 = (14 + 18)*1832r + 256 = 57632r = 320r = 10Answer:
(a) FB = 24 cm
(b) r = 10
Step-by-step explanation:
Part (a)Find the length, in cm, of FB.
Intersecting Secant and Tangent Theorem
When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Given:
Tangent segment = FBSecant segment = FE = 18 + 14 = 32 cmExternal secant segment = FD = 18 cm[tex]\begin{aligned}\implies FB^2 & =FE \cdot FD\\FB^2&=32 \cdot 18\\FB^2&=576\\\sqrt{FB^2}&=\sqrt{576}\\FB&=24\end{aligned}[/tex]
Therefore, the length of FB is 24 cm.
Part (b)Find the value of r.
Triangle FBO is a right triangle with side lengths:
BO = r cmFB = 24 cmOF = (r + 16) cmPythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Therefore, substitute the side lengths of triangle FBO into Pythagoras Theorem and solve for r:
[tex]\begin{aligned}\implies BO^2+FB^2&=OF^2\\r^2+24^2&=(r+16)^2\\r^2+576&=r^2+32r+256\\576&=32r+256\\32r&=320\\r&=10\end{aligned}[/tex]
Therefore, the value of r is 10.
Question 3 options:
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of ___________________________makes this argument true.
The law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
It is given that:
The statement is:
If you have a cat, then it will chase mice.
As we know, from the definition of the Law of Syllogism, the legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
Your cat will chase mice.
The Law of syllogism makes this argument true.
Thus, the law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.
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14.14 / 14 Is what ? Please show work ┐( ∵ )┌
Answer:
1.01
Step-by-step explanation:
14.14/14
14/14=1
0.14/14=0.01
1+0.01=1.01
Aiyana wrote the ratio 3:5 to compare a number of Paris of shorts that she owns to the number of pairs of jeans that she owns which ratio is equivalent to Aiyana’s ratio
3:5 is equivalent to Aiyana’s ratio
Since 3 and 5 are both prime numbers, you must multiply them by the same number (or any other integer) in order to have a ratio that is the same as Aiyana's. Ex 3:5=6:10=9:15 etc. The three ratios are identical.
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
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PLS HURRYYYYY
Think about what you know about ratios and comparisons. Fill in each box. Use
words, numbers, and pictures. Show as many ideas as you can.
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough. ft3/min
Given:
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
The volume of the trough will be as follows:
[tex]undefined[/tex]Write an equation in point-slope form of the line that passes through (-4,1) and (4,3) The equation is ?
Answer:
y = 4x+2
Step-by-step explanation:
To find an equation that runs through (-4,1) and (4,3) first find the difference between the two y numbers and x number to find the slope. between the two y numbers you go left or right 8 units, and difference between the two x numbers, which is 2. making the slope 4. looking at a graph and marking the two points, draw a line connecting the two given points, find the y intercept. the y intercept is at coordinates (0, 2) making the y intercept 2. making that into an equation is y = 4x + 2
A bicycle has cash price $16 319.50. It can be bought on hire purchase with a deposit of $6
900 and ten monthly installments of $1 224.50 each.
a. What is the total hire purchase price for the bicycle? [3 marks]
b. Find the difference between the hire purchase price and the cost price for the bicycle.
[1 mark]
c. Express your answer in (b) above as a percentage of the cash price.
The total cost of the hire purchase for the bicycle is $19,145.
The difference between the hire purchase price and the cost price for the bicycle is $2,825.50
The difference as a percentage of cash price 17.31%.
What is total cost?The total cost of the hire purchase is the sum of the deposit and the total monthly instalment.
Total cost of the hire purchase = amount deposited + total instalment paid
Total instalment paid = number of month x payment per month
$1224.50 x 10 = $12,245
Total cost of the hire purchase = $6,900 + $12,245 = $19,145
The difference = cost of hire purchase + cash price
$19,145 - $16 319.50 = $2,825.50
The difference as a percentage of cash price = (2,825.50 / $16,319.50) x 100 = 17.31%
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6. Given the area of the rectangle is 52 ft², find
the value of x.
(4x - 2) ft
2 ft
Answer:x=7
Step-by-step explanation: 2(4x-2)=52
8x-4=52
8x=56
x=7
What is 10+409 bc I really need help
I need some help with my math please
Determine if the following representations or functions or not? Explain your reasoning.
The three relations given all represent functions because each has exactly one y-value that corresponds to each x-value.
What Relation can be Defined as a Function?A relation can be defined as a function if the x-values (input/domain element) each has exactly one y-value (output value/range element) that is related to or it corresponds to.
A function can have two x-values that have the same y-value but cannot have two y-values that corresponds to one x-value.
In the first relation showing a graph, each x-value on the graph has exactly one y-value it corresponds to. Therefore, it is a function.
In the second relation that is represented by the set of ordered pairs, every x-value also have only one y-value it is related to. Therefore, it represents a function.
The third function given shows a table of values of a relation that has exactly only one y-value that is assigned or related to each x-value. This also is a relation that represents a function.
Therefore, all three relations represent functions.
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5(4x - 1.5)+12=4x - 2
On a map, Elmwood Drive passes through R(4,-11) and S(0,-9) and Taylor Road passes through
J(6,-2) and K(4,-5). If the streets are straight lines, determine if the streets are parallel or
perpendicular.
The streets where Elmwood and Taylor drive are neither perpendicular nor parallel.
Elmwood Drive passes through R(4,-11) and S(0,-9)
Slope of this line is (y₁-y₂)/(x₁-x₂)
Here (x₁,y₁) is (4,-11) and (x₂,y₂) is (0,-9)
slope of this line is (-11 - (-9))/(4-0)
= (-11 + 9)/4
= -2/4 = -1/2
Taylor Road passes through J(6,-2) and K(4,-5)
Slope of this line is (y₁-y₂)/(x₁-x₂
Here (x₁,y₁) is (6,-2) and (x₂,y₂) is (4, -5)
slope of this line is (-2 - (-5))/(6 - 4)
= (5 - 2)/2
= 3/2
The slopes of both the line is not same, so they are not parallel.
The product of slopes of both the lines is equal to 1, then it can be said as perpendicular lines.
The product of slope of streets passed by Elmwood and Taylor is
- 1/2 x 3/2 = -3/4
The result is not equal to 1, so they are not perpendicular lines.
Therefore, the streets where Elmwood and Taylor drive are neither perpendicular nor parallel.
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Casho went shopping for a new pair of sneakers because of a sale. The price on the tag was $25, but Casho paid $22.50 before tax. Find the percent discount
The percentage discount for the pair of sneakers is 10%.
What is percentage?A percentage is a value per hundredth. Percentages can also be fractions and decimals by decimals by dividing by 100 and vice versa. To obtain a percentage of a given value we divide the given percentage by a hundred and multiply the value with it.
The percentage discount can be determined by putting the discounted value upon the price multiplied by a hundred and subtracting the obtained percentage from the hundred percentage.
∴ The percentage discount on the pair of sneakers is,
= (22.50/25)×100.
= 0.9×100.
= 90%.
So, the percentage discount is (100 - 90)% = 10%.
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From a 128-foot tree, an object is thrown straight up into the air then follows a trajectory. The height S(t) of the ball above the building after t seconds is given by the function S(t) = 96t - 16t^(2). How long will it take the object to reach maximum height?
Answer:
3 seconds
Step-by-step explanation:
We can solve this in either of two ways: Graphing or taking the first derivative, I'll use both,
Graphing
Plot the equation. My DESMOS graph is attached. One can find the vertex of this curve at 3 seconds. Bonus: It reaches a height of 144 units at this point.
Derivative
The first derivative of this function will produce an equation that returns the slope of the line at any point x.
S(t) = 96t - 16t^(2)
S'(t) = 96 - 2*16t
S'(t) = 96 - 32t
The slope of the curve will be 0 when the ball reaches it's maximum height and begins to fall. Since we want the time it takes to reach a slope of zero, we can set S'(t) to 0 and solve:
S'(t) = 96 - 32t
0 = 96 - 32t
32t = 96
t = 3 seconds