f(x)=3x^5-x^4-6x+10
x=-2
Answer:
- 90
Step-by-step explanation:
substitute x = - 2 into f(x)
f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10
= 3(- 32) - (16) + 12 + 10
= - 96 - 16 + 22
= - 112 + 22
= - 90
[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]
[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]
[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]
Walter bought cupcakes for his sister's birthday party. 39 out of the 52 cupcakes had sprinkles on top. What percentage of the cupcakes had sprinkles?
The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.
What is percentage?A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.
Given:
The total no cupcakes = 52,
The no of sprinkled cupcakes = 39,
Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100
Percentage of sprinkled cupcakes = 39 / 52 × 100
Percentage of sprinkled cupcakes = 75%
Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.
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Solve for x
20=.694(x+150)*2
Answer: x = -135.59
Step-by-step explanation:
20 = 0.694(x + 150)(2)
Step 1: Simplify both sides of the equation.
20 = 0.694 (x + 150)(2)
20 = 1.388x + 208.2 (use the distributive property)
20 = 1.388x + 208.2
Step 2: Flip the equation.
1.388x + 208.2 = 20
Step 3: Subtract 208.2 from both sides of the equation.
1.388x + 208.2 − 208.2 = 20 − 208.2
1.388x = −188.2
Step 4: Divide both sides by 1.388.
1.388x/1.388 = −188.2/1.388
x = −135.590778
Optional: Simplify
x = -135.59
what is √3 + 1/3 and is the answer irrational or rational?
Answer:
Your answer would be 2.1.
Step-by-step explanation:
The square root of 3 is:
1.73205080757
Then since 1/3 is equal to 0.33, I added 0.33 to the square root of 3 to get:
2.06205080757
Then, I rounded it:
2.1
"What are the coordinates of your reflected triangle A’B’C’?"
Please help! Thank you!
A' - (-1,4)
B' - (-1,8)
C' - (-5,4)
hope this helps
Which animals will live in a building that is similar to the chimpanzee's house?
A. gorillas
B. Main Primate House
C. gibbons
D. orangutans
We can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.
What is a rectangle?In the Euclidean plane, a rectangle is a quadrilateral with four right angles. As an equiangular quadrilateral, which means that all of its angles are equal, it can also be referred to as a parallelogram with a right angle. A rectangle with four equal-length sides is a square.So, observe the given shapes on the graph:
The chimpanzee house is a rectangle with 8units×2units.If we take dimensions 8units×2units into consideration, then we notice that:Gibbons also has a house with identical dimensions as 8units×2units.
Therefore, we can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.
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Exercise 4.3
1. Given f=x^2 y; the change in for the total differential of fis given by df = Pdx+Qdy.
Find P, Q at x=1 and y=-1
(Ans: P= -2; Q=1)
Question one
By using the concept of differentiation, it can be calculated that
value of P is -2 and value of Q is 1
What is differentiation?
Differentiation is the process where the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus
Here differentiation is used
f(x) = [tex]x^2y[/tex]
[tex]df = 2xydx+x^2dy[/tex]
Here P = 2xy, Q = [tex]x^2[/tex]
At x = 1, y = -1
P = 2(1)(-1) = -2
Q = [tex](-1)^2[/tex] = 1
So value of P is -2 and value of Q is 1
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There was 3/5 of a gallon of paint in the bucket. Dr. Wu used 2/5 of that. How much paint was left?
Answer:
1/5
Step-by-step explanation:
equation: 3/5-2/5=x
we can multiply the whole equation by 5 so that we can easily subtract the numbers
3-2=1
now we divide it by 5 so that we get our number in a fraction
after we divide we get 1/5
What is the answer for 6:3(3+3)
Answer:
the answer according to my solution is 06
How do I solve this question
The partial fraction is proved.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
=3x²+8x+4/(x²-4)(3x-2)
=3x2+8x+4/(x2-4)(3x-2)
= 3x2+6x+2x+4/(x2-4)(3x-2)
=3x(x+2)+2(x+2)/(x2-4)(3x-2)
Hence proved, l.h.s = r.h.s
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Five twelfths of the marbles in a bag are blue. What fraction of the marbles are not blue?
Answer:
7/12
Step-by-step explanation:
12/12 - 5/12 = 7/12
-6y-18
factored expression
A researcher believes that 8% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3% is 0.9964
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 8% = 0.08
sample size, n = 694
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.08(1 - 0.08)) / 694}
= √{(0.08 * 0.98) / 694}
= 0.0103
The probability
differ from the population proportion by less than 3%
|X - 0.08| < 0.03
X < 0.11 OR X > 0.05
0.05 < X < 0.11
P(z < 0.11) - P(z < 0.05 )
z score for z < 0.05
z = (0.05 - 0.08) / 0.0103
= -2.9126
p value for z < -2.9126 = 0.001792
z score for z < 0.12
z = (0.12 - 0.09) / 0.0102
= 2.9412
p value for z < 2.9412 = 0.9982
The probability required = 0.9982 - 0.0016 = 0.9964 or 99.64%
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Define Variable
Solve the Problem
Write the inequality
Do you think mark will be able to accomplish his goal
The inequality will be represented by p ≥ 33 for at least 15 points.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Mark must score at least 11 points to have an average of 10 points per game.
The average of a set of data is its sum, divided by the number of data points in the set. If p is the number of points Mark scores in his next game, and he wants his average at least 15, then the relation is ...
(8+14+10+20+5++p)/6 ≥ 15
57 +p ≥ 90 . . . . . . . . . multiply by 6 and simplify
p ≥ 33
Mark must score at least 33 points in the next game to average at least 15 points per game.
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D/dx(e^x)=e^x prove please
The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,
Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]
So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]
The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,
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40
100%
Complete the table to show different percentages of the steaming time.
Time (min)
Percentage
100% of 40 min
50% of 40 min
250% of 40 min
The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively
How to complete the table to show different percentages of the steaming time?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min
100% of 40 min:
100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min
50% of 40 min:
50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min
250% of 40 min:
250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min
Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.
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5. Point A is 3 units directly below (2, 2). What are the coordinates of point A? Answer: Point A (___)
please help 25 points
⇒ ∠AEC is the angle vertical opposite to ∠BEC
ms.folk at least 250 candies to reward her students she has 50 candies already and will buy more candy in bags with 20 candies in each write an inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies
50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies.
How to solve equations in word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:i) There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.(ii) Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Let x be the number of bags she bought:
50 + 20x ≥ 250
3x ≥ 200
x ≥ 200/3
x ≥ 66.67
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Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?
I. A $44.09 check to the electronics store
II. A $73.98 check to the mechanic
III. A $49.96 paycheck deposit
IV. A $64.79 check deposit from Brett’s cousin
Adam has a goal to hike
70 miles. If he hikes 8
miles per day, how
long will it take him to
hike all 70 miles?
Answer:
9 days (round up)
Step-by-step explanation:
70 ÷ 8 = 8.75
≈ 9 (round up)
Edna needs to divide her savings of $35,286 equally among her 7 grandchildren. If she wants to do the calculation using the standard algorithm for division, how should she set up the division? Which number is the dividend, and which is the divisor? 50 POINTS HURRY
The dividend is 35286 and the divisor is 7. The value of the division is $540.8571
What is the value of the division?When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.
On the other hand, the number that is being divided by which is in this case 7 is the dividend.
The division will be:
= $35286 ÷ 7
= $540.8571
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A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write
its equation. Let the x-axis represent the number of pints and the y-axis represent the number of
servings. Use only fractional form, if necessary.
10 Servings
9
8
7
6
S
3
2
1
0
0 1 2
The equation is y =
5
6
7
8
Pints
9 10
2.
69
Prin
Tur
Sav
The equation of the line representing the given situation is y = (3/4)x , the graph of the equation is shown below .
In the question ,
it is given that ,
a refreshment stand makes 3 large serving of frozen yogurt from 4 pints .
also given that number of pints is represented by x - axis .
the number of servings is represented by y - axis .
the equation of the line is represented by y = mx + c .
we get c = 0, because at 0 pint there is no servings
hence , the equation becomes y [tex]=[/tex] mx .
According to the question ,
3 = m*4
m = 3/4 .
Substituting the value of m in the equation , we get
y = (3/4)x
the graph of the equation is shown below .
Therefore , The equation of the line representing the given situation is y = (3/4)x .
The given question is incomplete , the complete question is
A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write its equation. Let the x-axis represent the number of pints and the y-axis represent the number of servings. Use only fractional form, if necessary.
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A transversal intersects two lines. Which condition would always make the two lines parallel?
If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.
What do you mean by traversal line?
A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
What do you mean by angle?
An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.
From the figure,
x + 1 = 180°
y + 2 = 180°
Adding above equations,
x + y + 1 + 2 = 360°
Given ,
x + y = 1 +2
x + y + x + y = 360°
2(x + y) = 360°
x + y = 180°
Angles made on same side of transversal is supplementary . So the lines are parallel.
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Anthony wants to start making periodic investments in a retirement account. He will make a yearly contribution of $3,000 at the beginning of each year. The account will pay 7.2% interest, compounded monthly. How much will his account be worth after 35 years?
After 35 years, Anthony's account is going to be worth $34193.12
How to solve for the compound interestThe formula for the compound interest is given as
[tex]A = P(1 + r)^t[/tex]
Where we have the principal = 3000
the rate of interest = 7.2%
The period of time = 35 years
We have to input these values in the formula above so that we would have
A = 3000 ( 1 + 0.072)³⁵
A = 3000 x 11.398
= $34193.12
Hence we would have that after the period of 35 years, the account would be worth $34193.12
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What are two other names for AB?
Will give Brainliest, answer quick please.
The other names of AB in the given figure are
collinear pointsline segmentWhat are collinear points?Collinear points refers to points that lies on the same plane and on the same straight line.
The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear
Points A, B and C are non colinear to points Q and R
Points AB are still part of line AC hence can be noted as part of line segment BC.
The line has arrow head and may also be called rays. In this case the are part of an arrow
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HELP PLEASE!!
Are these expressions equivalent?
Drag and drop a symbol to correctly complete the comparison.
5+9-2^3___4^2-6
A. =
B.≠
The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expressions are given below.
(5 + 9 - 2³) and (4² - 6)
Simplify the expression, then we have
(5 + 9 - 2³) = 5 + 9 - 8 = 6
(4² - 6) = 16 - 6 = 10
The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.
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Can someone help me with this
Using the information from the given diagram, the measure of angle x (m ∠x) is 52°
Calculating the measures of anglesFrom the question, we are to determine the measure of angle x.
From the given diagram, we can write that
m ∠A + m ∠H + m ∠I = 180° (Sum of angle in a triangle)
Also,
m ∠K = m ∠I (Corresponding angles theorem)
∴ m ∠I = 62°
Thus,
x° + 66° + 62° = 180°
x° + 128° = 180°
x° = 180° - 128°
x° = 52°
Hence, the measure of ∠x 52°
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Write and solve a proportion for each word problem.
(9)There are 9 strawberries in a quart package. How many
quart packages do you need if you want 62 strawberries?
We will need 7 quart package if we want 62 strawberries
What is division?
Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.
We are given that there are 9 strawberries in a quart package
Also we want 62 strawberries
Then how many quart will be required
Now we perform division to find the number of quart
62/9 = we get a value of 8.88
Which is very close to nine
Hence we will need 9 quart packages if we want 62 strawberries
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What is the coefficient of the 6th term of (2x - 7)9 ?
Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912
Step-by-step explanation:
[tex](2x-7)^9[/tex]
In this problem we use the following formula:
[tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]
a=2x b=-7 n=9
The 1th term of (2x-7)^9 is k=0
The 2th term of (2x-7)^9 is k=1
The 3th term of (2x-7)^9 is k=2
..........................................................
The 6th term of (2x-7)^9 is k=5
Hence,
[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]
- 33889212x⁴ is the coefficient of the 6th term in binomial theorem .
What is binomial theorem?
The formula for the binomial theorem is (a+b)n= nr=0nCr an-rbr, where r is a real number, a, and b are real numbers, and n is a positive integer. This equation aids in the expansion of binomial formulae like (x + a)10, (2x + 5)3, (x - (1/x)), and so forth.( 2x - 7 )⁹
compare with formula
a = 2x b = - 7 n = 9
The 1th term of (2x-7)^9 is k=0
The 2th term of (2x-7)^9 is k=1
The 3th term of (2x-7)^9 is k=2
...................................................
The 6th term of (2x-7)^9 is k=5
hence
⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵ = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵
= 9!/4! * 5! 2⁴x⁴( -7)⁵
= 126(16) ( - 16807 )(x)⁴
= - 33889212x⁴
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