Answer:
f(-1) = 4
Step-by-step explanation:
Using the Quadratic Formula \(x=\frac{-b+\sqrt{b^2-4ac} }{2a}, \frac{-b-\sqrt{b^2-4ac} }{2a}\) our Polynomial to find our zeros values on the x-axis.
Any other factoring method that you can think and do can also work.
To find our (h,k) or origin we use this formula \(h=x=-\frac{b}{2a}\) and then plug our h=x into the equation to get out k.
To find our y-intercept. Plugin x = 0 into the equation to get y.
I used the internet to factory your equation f(x) and got
f(x) = 2(4x+3)(x-1)
x = -3/4 , 1
Substitute -1 into the equation to solve f(-1).
f(-1) = 8*(-1)^2 - 2*(-1) - 6 = 8 + 2 - 6 = 4
f(-1) = 4
the sum of additive inverse and multiplicative inverse of 6 is
Answer:
- \(\frac{35}{6}\)
Step-by-step explanation:
The additive inverse is the opposite of 6, that is - 6 ( 6 - 6 = 0 )
The multiplicative inverse is the reciprocal of 6 , that is \(\frac{1}{6}\) ( 6 × \(\frac{1}{6}\) = 1 )
Thus their sum is
- 6 + \(\frac{1}{6}\) = - \(\frac{36}{6}\) + \(\frac{1}{6}\) = - \(\frac{35}{6}\)
Answer:
- 5 5/6 or you can write it as -35/6.
Step-by-step explanation:
The additive inverse of 6 is -6 because 6 + (-6) = 0 while the multiplicative inverse is 1/6 because 6 * 1/6 = 1.
So the answer is - 6 + 1/6 = - 5 5/6.
Write the answer in numeric form?
Answer:
x=11. 38 degrees; 52 degrees
Step-by-step explanation:
90+6x-14+3x+5=180
81+9x=180
9x=99
x=11
38 degrees, 52 degrees
Which graph represents the function f ( x ) = x 2 − 2 x + 1 ?
Answer:
second one :D
Step-by-step explanation:
A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 ft
The area of the semicircle table after it is cut in half \(=\frac{9}{2}\pi\) square units.
What is a semicircle?A semicircle is a 2 -D shape which is obtained by cutting a circle along with its diameter. a circle has 2 semicircles when it is cut along with its diameter.
What is a formula for the area of a semicircle?The formula for finding the area of a semicircle is half of the area of a circle with the same radius.
area of semicircle = \(\frac{\pi r^{2} }{2}\) square units
Given:
A table with a round top is cut in half so now its shape is a semicircle.
After it is cut, the edge along the wall is 6 ft means that the diameter of the semicircle is = 6 ft
Diameter = 6 ft
Radius = diameter / 2
Radius = 6/ 2
Radius = 3 ft
Therefore now we can calculate the area of the table after it is cut in half
Area of the semicircle table after it is cut in half =
\(=\frac{\pi r^{2} }{2} \\=\frac{\pi 3^{2} }{2} \\=\frac{9\pi }{2}\\= \frac{9}{2}\pi\)
The area of the semicircle table after it is cut in half \(=\frac{9}{2}\pi\) square units.
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A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 feet. What is the area of the table after it is cut in half? Give your answer in terms of pi.
Tessa bought stock in a restaurant for $177.00. Her stock is now worth $260.19. What is the percentage increase of the value of Tessa's stock?
Answer:
About 45% increased
If a seed is planted, it has a 85% chance of growing into a healthy plant. If 11 seeds are planted, what is the probability that exactly 4 don't grow
A planted seed has a 85% chance of growing into a healthy plant. The probability that exactly 4 out of 11 seeds don't grow is approximately 0.1302.
To calculate this probability, we can use the binomial distribution formula. In this case, each seed has a 15% chance of not growing (1 - 0.85). We want to find the probability that exactly 4 seeds out of 11 don't grow.
Using the binomial distribution formula, the probability can be calculated as:
\(P(X = 4) = (^{11}C_4) * (0.15)^4 * (0.85)^7\)
Where (\(^{11}C_4\)) represents the number of ways to choose 4 seeds out of 11, \((0.15)^4\)represents the probability of 4 seeds not growing, and\((0.85)^7\) represents the probability of the remaining 7 seeds growing.
Evaluating the formula, we find:
\(P(X = 4) = (11! / (4! * 7!)) \times(0.15)^4 \times (0.85)^7 \approx 0.1302\)
Therefore, the probability that exactly 4 out of 11 seeds don't grow is approximately 0.1302, or 13.02%.
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An artist bought twine for a project,and she traveled by bus when shopping for the twine.The total cost of her project,$17.50,included both the cost of the 5.8 yards of twine she bought and $3 in bus fares. Which of these shows the correct equation to determine the cost of the twine per yard along with the correct solution?
Answer:
it’s A
Step-by-step explanation:
It would be 17.50=5.8x+2
Cost:$2:50 per yard
Which expression is equivalent to 5 (2 + 7)?
2 (5 + 7)
2 + 7 (5)
5 (2) + 7
5 (2) + 5 (7)
Answer:
Yes the answer is D because I just did the test
Step-by-step explanation:
Expand this 239238 using the expanded form
The expanded form of a number involves rewriting the number
The expanded form of 239238 is 13291 * 3 * 3 * 2
How to write the number in an expanded formThe number is given as: 239238
Express as a product of 2
239238 = 119619 * 2
Express as a product of 3
239238 = 39873 * 3 * 2
Further, expand
239238 = 13291 * 3 * 3 * 2
The number cannot be further expanded.
Hence, the expanded form of 239238 is 13291 * 3 * 3 * 2
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How many simple random samples of size 3 can be selected from a population of size 7.
By using combination, it can be obtained that
Number of simple random samples of size 3 that can be selected from a population of size 7 = 35
What is combination?
Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.
Here, concept of combination is used
Number of simple random samples of size 3 that can be selected from a population of size 7 = \({7 \choose 3}\) = 35
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A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?
Answer:
40 students
Step-by-step explanation:
We do not count the counselors or the principal because they are not students, so we do 83 - 3 = 80, now it is just simple division, for every student there is a parent, so we divide 80 in half, 80 / 2 = 40 students :D
This whole page. By November 19.
Answer:
see below thanks
Step-by-step explanation:
1. 1 quart --> 2 tablets
2 quarts --> 4
3 quarts --> 6
4 quarts --> 2 tablets * 4 --> 8 tablets
2. 160 copies --> 4,000
80 copies --> 2000
40 copies --> 1000
2 copies --> 4,000/80 --> $50
3. 50 miles --> 60 minutes
25 miles --> 30
15 miles --> 60/50/15 --> 18 minutes
4. 40 hours --> 400
20 hours --> 200
6 hours --> 400/40/6 --> $60
5. 10 miles --> 16 km
20 miles --> 32 km
45 miles --> 72 km
explanation: create proportion, 10/16=45/x, solve for x, got x as 72
6. Table:
People: 1, 4, 8, 16
Chopped clam: 1/8, 1/2, 1, 2
Chicken broth: 1/4, 1, 2, 4
Cups of milk: 3/8, 2/3, 3, 6
Cubed potatoes: 1/4, 1, 2, 4
7. 8 people: 1, 2, 3, 2
32 people: 4, 8, 12, 8
8. 24 people: 3, 6, 9, 6
ima hop off my laptop now
hope it helped
BTW: the 4 numbers above for 6, 7, and 8 represent chopped clams, chicken broth, cups of mil,, and cubed potatoes RESPECTIVELY
PLEASE HELP ME!! LAST ASSIGNMENT
Answer:
u = 3
Step-by-step explanation:
\(\frac{10}{14} = \frac{35}{u + 46} \\\\ 10(u + 46) = 35×14 \\\ 10u + 460 = 490 \\\ 10u = 490 - 460 \\\ 10u = 30 \\\ u = \frac{30}{10} \\\\ u = 3\)
I hope I've helped you.
\ (•◡•) / Hey There!
Answer ➜ U = 3
~Hope This Helps!~
5 more than 2 times a number
Answer:
5+ 2x
Step-by-step explanation:
lets say x is our variable therefore you will multiply 2 to x and then it says 5 more the key word is more therefore you add 5 to your equation
For * (,0), use only the definition of increasing or decreasing function to 1 5 determine if the function f(x) = - is increasing or decreasing. 3 7√7x - 3
The problem requires determining if the function f(x) = (3/7)√(7x) - 3 is increasing or decreasing at x = 0, using only the definition of increasing or decreasing functions.
To determine if the function f(x) = (3/7)√(7x) - 3 is increasing or decreasing at x = 0, we can use the definition of increasing or decreasing functions. According to this definition, a function is increasing if the derivative is positive and decreasing if the derivative is negative.
To find the derivative of f(x), we differentiate the function with respect to x. The derivative of (3/7)√(7x) - 3 is (3/7)(1/2)(7)(1/√(7x)) = (3/2√(7x)).
Now, to determine if the function is increasing or decreasing at x = 0, we substitute x = 0 into the derivative. However, at x = 0, the derivative is undefined since it involves dividing by zero (√(7x) becomes √(0) = 0 in the denominator).
Therefore, we cannot make a definitive conclusion about the function's increasing or decreasing behavior at x = 0 using only the definition of increasing or decreasing functions. The behavior of the function at x = 0 would require further analysis using other techniques, such as the first or second derivative test.
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work shown solve the inequality
graph the solution set(number line)
1/4(x+4)<1/5(2x+3)
Answer:
x > 8/3
Step-by-step explanation:
graph: non-shaded circle at 8/3 (2.6) & line pointing right (towards greater nums)
What is the possibility that a red or green marble will be selected from a bag containing 9 red marbles, 6 blue marbles , 7 green marbles and 11 yellow marbles
Answer:
16/33
Step-by-step explanation:
We have a bag of :
9 red marbles
6 blue marbles
7 green marbles
11 yellow marbles
Total number of marbles = 33 marbles.
The possibility that a red or green marble will be selected from a bag
P( Red or Green) = P(Red) + P(Green)
In the question we are not told if it is with replacement or without. We do both
With replacement
P( R or G) = P(Red) + P(Green)
P(Red)= 9/33
P(Green) = 7/33
= 9/33 + 7/33
= 16/33
Therefore, the possibility that a red or green marble will be selected from a bag is 16/33
Can someone please answer these 2 questions
Answer:
part 1: $532.95. Part 2: 16
Step-by-step explanation:
Part 1: 15 * 15.35 = 230.25
30 * 10.09 = 302.70
230.25 + 302.70 = $532.95
Part 2: R = letters in the word desk
there are 4 letters in the word Desk
\(2^{R}\) = \(2^{4}\) = 2 * 2 * 2 * 2 = 4 * 4 = 16 subsets
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Trent wants to buy 2 packs of trading cards for 3 dollars each. The trading card packs that Trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. After selecting 2 packs, Trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. Trent uses this information to write the equations below in order to compare c, the number of cards in each pack. There are cards in the first pack, and there are cards in the second pack. The first pack has more cards than the second pack.
A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers (numerals) only. This ultimately implies that, a numerical data refers to a type of data set consisting of numbers (numerals) rather than words.
Based on the information provided, the number of cards (c) in each pack can be modeled by the following mathematical expression (equation):
Note: 100 cent is equal to 1 dollar.
First pack: 0.25c = 3
Second pack: 0.3c = 3
Now, we can determine the number of cards (c) in the first pack as follows:
0.25c = 3
c = 3/0.25
Number of cards, c = 12 cards.
For the second pack, we have:
0.3c = 3
c = 3/0.3
Number of cards, c = 10 cards.
Therefore, there are 12 cards in the first pack, and there are 10 cards in the second pack.
Difference = First pack - Second pack
Difference = 12 - 10
Difference = 2 cards.
In conclusion, the first pack has 2 more cards than the second pack.
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write 20.05 × 10-1 ml in decimal form.
Answer:
The number in standard form is 2.005
Step-by-step explanation:
20.05 × 10^-1
Move the decimal one place to the left since the exponent on 10 is -1.
2.005
The number in standard form is 2.005
A rectangular box is 2 cm high , 4 cm wide and 6 cm deep.Mavis packs the box with cubes, each 2cm by2cm by 2cm,with no space left over. How many cubes does Mavis fit into the box?
Given -
A rectangular box is 2 cm high , 4 cm wide and 6 cm deep.i.e, length = 2cm, breadth = 4cm and height = 6cm
Mavis packs the box with cubes, each 2cm by 2cm by 2cm,with no space left over.i.e, side = 2cm
To find -
the number of cubes that can be fit into the rectangular box.Concept -
To find the number of cubes Mavis can fit into the rectangular box we are supposed to divide the volume of rectangular box by the volume of the cube. But before doing that we should know the formulas to find the volume of both the 3D shapes. i.e,
Volume of Rectangular Box = l × b × h
Volume cube = a³
where,
l = length b = breadthh = heighta = sideSolution -
\(\bf{Number\:of\: cubes=\frac{Volume\:of\: Rectangular\:Box}{Volume\:of\:cube}}\)
\(\rightarrow\sf{Number\:of\: cubes=\frac{l\times b\times h}{a\times a\times a}}\)
\(\rightarrow\sf{Number\:of\: cubes=\frac{2\times 4\times 6}{2\times 2\times 2}}\)
\(\rightarrow\sf{Number\:of\: cubes=\frac{\cancel{2}\times \cancel{4}^2\times \cancel{6}^3}{\cancel{2}\times \cancel{2}\times \cancel{2}}}\)
\(\rightarrow\sf{Number\:of\: cubes=2\times3}\)
\(\rightarrow\mathbf{Number\:of\: cubes=6\:boxes}\)
Hence, the number of cubes that can be fit into the rectangular box is 6 cubes.
How do I find the triangular formula of a pentagon
It is not possible to find the triangular formula of a pentagon because a pentagon is a polygon with five sides and does not have a triangular formula.
We have,
A triangular formula is used to calculate the area of a triangle, which is a polygon with three sides.
The formula for the area of a triangle is given by:
Area = 1/2 x base x height
where the base and height are two of the sides of the triangle.
If you want to calculate the area of a pentagon, you can use the formula for the area of a regular pentagon, which is given by:
Area = (5/4) x s² x tan(π/5)
where s is the length of one of the sides of the Pentagon.
Thus,
It is not possible to find the triangular formula of a pentagon because a pentagon is a polygon with five sides and does not have a triangular formula.
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In a triangle, the measure of the middle angle
is triple the measure of the smallest angle, and
the measure of the largest angle is 55° greater
than the measure of the smallest angle. Find
the measures of the
angles.
Let the smallest angle in a triangle be = x
Largest angle in a triangle = 55 + x
The middle angle in a triangle = 3x ( triple the measure of the smallest angle )
Their sum = 180° ( according to the angle sum property all the angles of a triangle sum up to 180° )
This can be written as :
= x + 55 + × + 3x = 180
Let us find each angle by solving the equation .
= x + 55 + x + 3x = 180°
= x + x + 3x + 55 = 180°
= 5x + 55 = 180°
= 5x = 180 - 55 ( transposing +55 from LHS to RHS changes +55 to -55 )
= 5x = 125
= x = 125 ÷ 5 (transposing ×5 from LHS to RHS changes ×5 to ÷5 )
= x = 25
Using this let us find the measure of each angle .
Smallest angle = x = 25
Smallest angle = 25°
Middle angle = 3x = 3 × 25 = 75
Middle angle = 75°
The largest angle = x + 55 = 25 + 55 = 80
Largest angle = 80°
Therefore , the measure of the smallest angle = 25° , the measure of the middle angle = 75° and the measure of the largest angle = 80° .
We have that the measures of the angles are as follows
\(\theta_1=80 \textdegree\)
\(\theta_2=75 \textdegree\)
\(\theta_3=25 \textdegree\)
From the question we are told that:
The measure of the middle angle is triple the measure of the smallest angle
The measure of the largest angle is 55° greater than the measure of the smallest angle
Let
\(\theta_1=Largest\ angle\)
\(\theta_2=Middle\ angle\)
\(\theta_3=Smallest\ angle\)
Therefore
\(\theta_1=55 \textdegree+\theta_3\\\\\theta_2=3*\theta_3\)
Generally, the equation for the angle of a triangle is mathematically given by
\(\theta_1+\theta_2+\theta_3=180\)
Therefore
\(55 \textdegree+\theta_3+3*\theta_3+\theta_3=180\)
\(\theta_3=25 \textdegree\)
Therefore
Substitute \(\theta_3\) into equations of \(\theta_1\) and \(\theta_2\)
For \(\theta_1\)
\(\theta_1=55 \textdegree+25 \textdegree\\\\\theta_1=80 \textdegree\)
For \(\theta_2\)
\(\theta_2=3*\theta_3\)
\(\theta_2=3*25 \textdegree\)
\(\theta_2=75 \textdegree\)
in conclusion
The measures of the angles are as follows
\(\theta_1=80 \textdegree\)
\(\theta_2=75 \textdegree\)
\(\theta_3=25 \textdegree\)
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a shopkeeper allows a discount of 10percent on the marked price of an article. if a customer paid ghana cedis 270.00 for an article, what was the marked price of the article.
Answer:
300.000 was the market price of the article.
Step-by-step explanation:
300.000*0.1 = 30.000
Then, 300.000 - 30.000 = 270.000
So,
300.000 was the initial price.
The solution shown for the equation is
incorrect. What is the correct solution? What is the error?
-3(6-r) = 9
- 18 - 3r = 9
- 3r = 27
9
The solution is
(Type the value of r.)
Pleaseeee help ASAP
Will mark brainliest
Answer:
-3(6-r) = 9
- 18 - 3r = 9 incorrect: should be -18 +3r = 9
- 3r = 27 incorrect: should be 3r = 27
9 actually correct: r = 9
NEED HELP ASAP 20 points!!!
the distance a spring will stretch varies directly with how much weight is attached to the spring.if a spring streches 6 inches with 80 pounds attached how far will it stretch with 55 pounds attached
round to the nearest tenth of an inch!
A. 5.9 in
B. 8.7 in
C. 6.1 in
D.4.1 in
Answer:
D
Step-by-step explanation:
6:80 is about 13.33 pounds per inch. You can get that by dividing 80 by 6 to get the unit rate. All you have to do from there is divide 55 by 13.33, which gives you around 4.12, or 4.1.
Hope this helps!
for the function f(x)=x4−2x2 3. Determine the inflection point(s) of f .
the answers should be in ascending order of x values. use decimals (rounded to 2 decimal places).
The inflection points of the function f(x) = x⁴ - 2x²/3 are at
x = -0.77 and x = 0.77.
To find the inflection points of the function f(x) = x⁴ - 2x²/3, we need to locate the x-values where the concavity of the function changes.
This can be done by finding the second derivative of the function and determining where it equals zero.
First, let's find the second derivative of f(x):
f''(x) = 12x² - 4x/3
Setting f''(x) equal to zero and solving for x:
12x² - 4x/3 = 0
4x(3x - 1) = 0
This equation is satisfied when x = 0 and x = 1/3. However, we need to check the concavity around these points to confirm if they are inflection points.
By analyzing the sign of f''(x) in the intervals (-∞, 0), (0, 1/3), and (1/3, ∞), we observe that the concavity changes at x = -0.77 and x = 0.77.
These are the inflection points of the function f(x).
Therefore, the inflection points of f(x) = x⁴ - 2x²/3 are at x = -0.77 and x = 0.77.
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Find the root
X^3-125=0
\( \huge {\sf {{x}^{3} - 125 = 0}} \)
To Find:The root of the equation.
Solution:By adding 125 to both the sides, we get
\( \huge {\sf { {x}^{3} = 125}} \)
Take cube to the RHS (Right Hand Side), we get
\( \huge {\sf { x = 5}}\)
Answer: x = 5The solution to the expression is x = 5.
We have,
Expression:
x³ - 125 = 0
This can be written as,
x³ = 125
Now,
Cube of 5:
5³ = 5 x 5 x 5 = 125
Now,
x³ = 5³
Cube cancels out on both sides.
x = 5
Thus,
The solution to the expression is x = 5.
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Q4. An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
(b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square
iii) A multiple of 5
iv) Less than or equal to 21
v) Divisible by 4 or 6
Answer:
I) \(\dfrac{1}{8}\) (ii) \(\dfrac{53}{64}\) (iii) \(\dfrac{15}{64}\) (iv) \(\dfrac{5}{8}\) (v)\(\dfrac{21}{32}\)
Step-by-step explanation:
The sample space for an 8-sided fair die rolled twice is:
\([(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]\\\)
(a) Possibility diagram of the product of the two numbers appearing on the die in each throw
\(1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6.12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64\)
(b)
I) A prime number
\(P$(Product is a prime number)=\dfrac{8}{64}= \dfrac{1}{8}\)
ii) Not a perfect square
Number of Perfect Squares =11
P(Product is Not a perfect square) \(=\dfrac{64-11}{64}= \dfrac{53}{64}\)
iii) A multiple of 5
Number of Multiples of 5=15
\(P$(A multiple of 5)=\dfrac{15}{64}\)
iv) Less than or equal to 21
Product less than or equal to 21=40
\(P$(Less than or equal to 21)=\dfrac{40}{64}=\dfrac{5}{8}\)
v) Divisible by 4 or 6
Products Divisible by 4 or 6= 42
\(P$(Divisible by 4 or 6)=\dfrac{42}{64}=\dfrac{21}{32}\)
-7 + (-9) - (-11) -2