Factor the following. Check using FOIL then
solve for x:
x^2 + 3x + 2 = 0
Answer:
x = -2 and -1
Step-by-step explanation:
x^2 + 3x + 2 = 0
Factorizing the given equation:
x^2 + 3x + 2 = 0
x^2 + 2x + x+ 2 = 0
x(x+2)+1(x+2) = 0
(x+2) (x+1)= 0
x+2 = 0 and x+1 = 0
x = -2 and -1
find the range values pls
Answer:
range={19, 11, -13}
Step-by-step explanation:
The range is what you get when you plug in the number. In this case, the range is the y values.
y=7-4(-3)=7+12=19
y=7-4(-1)=7+4=11
y=7-5(5)=7-25=-13
Which of these ordered pairs is a solution to the inequality?
1/4x ≤ 7/3y +2
Responses
A (80, 6)
B (48, 9)
C (40, 3)
D (2, –6)
Please show step by step as I need to learn how to do these problems. Thank you
Answer: D
Step-by-step explanation:
To determine which ordered pair is a solution to the inequality, we can substitute the values of x and y into the inequality and check if it is true.
Let's start with ordered pair A (80, 6):
1/4x ≤ 7/3y + 2
1/4(80) ≤ 7/3(6) + 2
20 ≤ 14 + 2
20 ≤ 16
This is not true, so ordered pair A is not a solution to the inequality.
Now let's try ordered pair B (48, 9):
1/4x ≤ 7/3y + 2
1/4(48) ≤ 7/3(9) + 2
12 ≤ 21 + 2
12 ≤ 23
This is also not true, so ordered pair B is not a solution to the inequality.
Next, let's try ordered pair C (40, 3):
1/4x ≤ 7/3y + 2
1/4(40) ≤ 7/3(3) + 2
10 ≤ 7 + 2
10 ≤ 9
This is false, so option C is not a solution to the inequality.
Finally, we have option D: (2, -6)
1/4(2) ≤ 7/3(-6) + 2
1/2 ≤ -14 + 2
1/2 ≤ -12
This is true, so option D is a solution to the inequality.
Therefore, the answer is D: (2, -6).
which of the following is an exponential function y=x^1/2 y=2x^3 y=3^x
Answer:
(c) y = 3^x
Step-by-step explanation:
A function is described as exponential if the independent variable is found in the exponent.
Choicesy = x^(1/2) . . . a square root function, not exponential
y = 2x^3 . . . . a cubic (polynomial) function, not exponential
y = 3^x . . . . . an exponential function
Jake's bank offers him an account with 3o
interest, compounded annually. How much
interest would he earn from this account if he
deposits his $1,320 for 5 years?
I=P(1+R/100)^5
I=$1320(1+3/100)^5
I=$1530
U= {1,2,3,4,5,6,7,8,}, A={1,4,5,7}, B= {2,5,6,7,}, and C= {3,4,6,7}
Complete the following set operations:
a. AU(BUC)
b. (AN(BNC))'
c. (ANB)U(ANC)
d. (ANB')U(ANC')
Answer:
a. {1, 2, 3, 4, 5, 6, 7}
b. {1, 2, 3, 4, 5, 6, 8}
c. {4, 5, 7}
d. {1, 4, 5}
Step-by-step explanation:
The union of two sets is the list of elements in either set. The intersection of two sets is the list of elements in both sets. The complement of a set is the list of elements in the universal set that are not in the set being complemented. The complement of a set can be indicated with an apostrophe: A' is the complement of set A, for example.
a. AU(BUC)B∪C = {2, 5, 6, 7} ∪ {3, 4, 6, 7} = {2, 3, 4, 5, 6, 7}
A∪(B∪C) = {1, 4, 5, 7} ∪ {2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7}
b. (AN(BNC))'B∩C = {2, 5, 6, 7} ∩ {3, 4, 6, 7} = {6, 7}
A ∩ (B∩C) = {1, 4, 5, 7} ∩ {6, 7} = {7}
(A∩(B∩C))' = {7}' = {1, 2, 3, 4, 5, 6, 8}
c. (ANB)U(ANC)A∩Β = {1, 4, 5, 7} ∩ {2, 5, 6, 7} = {5, 7}
Α∩C = {1, 4, 5, 7} ∩ {3, 4, 6, 7} = {4, 7}
(A∩B)∪(A∩C) = {5, 7} ∪ {4, 7} = {4, 5, 7}
d. (ANB')U(ANC')(A∩B')∪(A∩C') = A∩(B'∪C') = A∩(B∩C)'
(B∩C)' = {6, 7}' = {1, 2, 3, 4, 5, 8}
A∩(B∩C)' = {1, 4, 5, 7} ∩ {1, 2, 3, 4, 5, 8} = {1, 4, 5}
__
Additional comment
In part (d) we made use of De Morgan's law for sets:
B'∪C' = (B∩C)'
We also made use of the distributive property for sets:
A∩(B∪C) = (A∩B)∪(A∩C)
A humpback whale is 6,300meters from Billet Bay. If it swims at a constant velocity of 210 meters per minute toward the bay, how much time will it take the whale to get one-third of the way to Billet Bay?
Write your answer as a whole number.
ASAP PLease
Answer: 10 minutes
Step-by-step explanation:
6,300*1/3=2,100
2,100=210x
2,100/210=10
x=10 minutes
Solve for the following if x = 6: (Hint: substitute 6 for the letter x and work the problem. You will work more with substitution later.) Example: 10x = 10*6 = 60 9. x - 6 ( if x = 6) 10. 7 + x ( if x = 6) 11. 3x - 9 ( if x = 6) 12. 63/x ( if x = 6) 13. 5 + 5x + 10 ( if x = 6)
Using PEMDAS and substituting 6 for x, the results of the mathematical operations are as follows:
1) 482) 763) 1894) 1265) 105.What is PEMDAS?PEMDAS is the order of mathematical operations that explains the correct sequential steps for evaluating mathematical expressions.
PEMDAS means that mathematical operations must follow the following order:
ParenthesesExponentsMultiplicationDivisionAdditionSubtraction.1) 9. x - 6 ( if x = 6)
= 9 x 6 - 6
= 54 - 6
= 48
2) 10. 7 + x ( if x = 6)
= 10 x 7 + 6
= 70 + 6
= 76
3) 11. 3x - 9 ( if x = 6)
= 11 x 3(6) - 9
= 11 x 18 - 9
= 198 - 9
= 189
4) 12. 63/x ( if x = 6)
= 12 x 63/6
= 126
5) 13. 5 + 5x + 10 ( if x = 6)
= 13 x 5 + 5(6) + 10
= 65 + 30 + 10
= 105
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Acylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for me and round to the nearest hundredth
adius hype your answer...
1
The radius of the cylinder is 2.25 feet.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.
400 = 3.14 r² x 25
Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:
r² = 400 / (3.14 x 25)
r² ≈ 5.08
Taking the square root of both sides to solve for r, we get:
r ≈ √5.08
r ≈ 2.25
Therefore, the radius of the cylinder is 2.25 feet.
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Use the vertical method to multiply two trinomials. Step 1: Multiply the top trinomial by the last term in the bottom trinomial. Place each result in the blank spaces provided.
Vertical multiplication of trinomials:
\(\begin{gathered} \text{ }4x^2-5x+3 \\ \times\text{ }5x^2+3x+2 \\ \text{ ------------} \end{gathered}\)Step 1: Multiply the top trinomial by the last term in the bottom trinomial.
\(\begin{gathered} \text{ }4x^2-5x+3 \\ \times\text{ }5x^2+3x+2 \\ \text{ ----------} \\ \text{ }8x^2-10x+6 \end{gathered}\)Step 2: Multiply the top trinomial by the next term:
\(\begin{gathered} \text{ }4x^2-5x+3 \\ \times5x^2+3x+2 \\ \text{ -----------} \\ \text{ }8x^2-10x+6 \\ 12x^3-15x^2+9x \end{gathered}\)Step 3: Multiply the top trinomial by the first term:
\(\begin{gathered} \text{ }4x^2-5x+3 \\ \times\text{ }5x^2+3x+2 \\ _{\text{ ----------------}} \\ \text{ }8x^2-10x+6 \\ 12x^{3}-15x^{2}+9x \\ 20x^4-25x^3+15x^2 \end{gathered}\)Step 4: Algebraically add the three polynomials:
8x² - 10x + 6
12x³ - 15x² + 9x
20x⁴ - 25x³ + 15x²
------------------------------------------------
ANSWER
20x⁴ - 13x³ + 8x² - x + 6
please helpppppp
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Greg bought a regular-sized box of his favorite cereal. A regular-sized box contains 12 servings.
Part A: If Greg eats 1 1/2 servings for breakfast every day, how many breakfasts can Greg eat from 1 box? Show all work.
Part B: The regular-sized box of cereal costs $4.29. How much does 1 breakfast from a regular-sized box of cereal cost Greg? Round to the nearest hundredth. Show all work.
Part C: If Greg purchased the family-sized box of cereal that contains 18 servings, how many more breakfasts could Greg eat from 1 box? Show all work.
a. Greg can eat 8 breakfasts from 1 box.
b. The cost of 1 breakfast from a regular-sized box is $34.32.
c. Greg will enjoy 4 breakfast more.
How to calculate the fraction?a. A regular-sized box contains 12 servings. If Greg eats 1 1/2 servings for breakfast every day, the number of breakfasts that Greg can eat from 1 box will be:
= 12 ÷ 1 1/2
= 12 ÷ 1.5
= 8
b. Since the regular-sized box of cereal costs $4.29. The cost of 1 breakfast from a regular-sized box of cereal cost Greg will be:
= 8 × $4.29
= $34.32
c. If Greg purchased the family-sized box of cereal that contains 18 servings, the number of breakfasts will be:
= 18 ÷ 1.5
= 12 breakfast
The difference will be:
= 12 - 8
= 4 breakfast more.
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Please help me please!
Answer:
its c
Step-by-step explanation:
i hade this qu for classwoerk today
Let f left parenthesis x right parenthesis equals x cubed minus x squared minus 1 and x subscript 0 equals 1 . To the nearest three decimal places, find x subscript 5 using Newton's method of approximation.
The value of \(x_5\), rounded to the nearest decimal place using Newton's method of approximation is 1.466.
The correct answer is option B.
To find the value of \(x_5\)using Newton's method of approximation, we need to iterate the following formula:
\(x_(_n_+_1_) = x_n - f(x_n) / f'(x_n)\)
where f'(x) represents the derivative of the function f(x). Let's calculate the values step by step.
Given function: f(x) = \(x^3 - x^2 - 1\)
Step 1: Find the derivative of f(x)
f'(x) = \(3x^2 - 2x\)
Step 2: Initialize the starting value
\(x_0\)= 1
Step 3: Calculate \(x_1\)
\(f(x_0) = f(1) = (1^3) - (1^2) - 1 = 1 - 1 - 1 = -1\)
\(f'(x_0) = f'(1) = (3(1^2)) - (2(1)) = 3 - 2 = 1\)
\(x_1 = x_0 - f(x_0) / f'(x_0)\)
= 1 - (-1) / 1
= 2
Step 4: Calculate \(x_2\)
\(f(x_1) = f(2) = (2^3) - (2^2) - 1 = 8 - 4 - 1 = 3\)
\(f'(x_1) = f'(2) = (3(2^2)) - (2(2)) = 12 - 4 = 8\)
\(x_2 = x_1 - f(x_1) / f'(x_1)\)
= 2 - 3 / 8
= 1.625
Step 5: Repeat the process until we reach \(x_5\)
Performing the calculations for \(x_3, x_4, andx_5\), we find:
\(x_3\) ≈ 1.465
\(x_4\) ≈ 1.466
\(x_5\)≈ 1.466
After applying Newton's method of approximation to the function f(x) = \(x^3 - x^2 - 1,\)starting with,\(x_0 = 1,\) we iteratively calculated the values of \(x_1, x_2, x_3, x_4, and x_5\). The final approximation, \(x_5\), is approximately 1.466 when rounded to the nearest decimal place. This aligns with option B as the correct answer.
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Find the area of the figure. hi
Solve the application using polynomials
A rectangular garden has the dimensions
shown in the figure.
7.48 meters
15.6 meters
What is the perimeter of the garden?
A. 16.24 meters
C. 46.16 meters
B. 23.08 meters
D. 116.688 meters
Need ASAP
Determine the domain of the function
Emily and Andy each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Emily needs 22 feet of the wire. Andy needs 13 yards of the wire. How much will each of them spend for wire?
Answer:
Step-by-step explanation:
Actually its
Andy spends $ 13.20
Emily will spend 23.40
HOPE IT HELPS!!!!!!!!!!
8-(4x?) Does anybody know this?
Pls help I’ll brainlest ASAP and add extra points I’m failing
Step-by-step explanation:
you drew already the right things, you have everything.
so, what is the problem ?
the most common form of line equation is
y = ax + b
a is the slope of the line. it is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
b is the y-intercept (the y value when x = 0).
once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.
so, for the 2 marked points you showed correctly the differences :
x changes by +8 (from -4 to 4).
y changes by -2 (from 3 to 1).
so the slope is -2/+8 = -1/4
the y-intercept we also see directly in the chart : +2.
Can someone please help me thank you
Answer:
9. 4/5
10. 3/4
11. 1/4
12. 1/8
13. 1/11
14. 1/9
15. 9/10
16. 1/10
Step-by-step explanation:
ur welcome
Quadrilateral RSTU is similar to quadrilateral LMNO. What is the value of LO if RU is 6 inches, LM is 45 inches, and RS is 9 inches?
The value of LO if RU is 6 inches is solved to be 30 inches
What are similar polygons?This is a term used in geometry to mean that the respective sides of the polygons are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the polygon are congruent then the side should be in proportions
Examining the figure when LM is 45 inches, and RS is 9 inches
the constant of proportionality from quadrilateral RSTU to quadrilateral LMNO is 5
9 * 5 = 45
when RU = 6 inches
6 * 5 = 30 inches
hence LO is 30 inches
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4. What is the value of the underlined digit?
4,506,204,395.9812
The underlined digit being 8
Answer:
hundreth, because it is the second digit after the decimal point.
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3 ft long with a diameter of 1.8 ft. Suppose oil is drained at a rate of 1.7 ft³ per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Answer:
4 minutes
Step-by-step explanation:
You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)
VolumeThe volume of a cylinder can be found using the formula ...
V = (π/4)d²h . . . . . . . diameter d, height h
Then the volume of the oil tank is ...
V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³
TimeThe time it takes to empty the tank is found by dividing the volume by the rate:
(7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min
It will take about 4 minutes to empty the tank.
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the perimeter of a triangle is 32 feet. One side of the triangle is 11 feet longer than the second side. The third side is 9 feet longer than the second side. Find the length of each side.
Answer:
One side - 15 feet
Second side - 4 feet
Third side - 13 feet
Step-by-step explanation:
Let's call the sides A B and C, respectively.
We know that:
A = B + 11
C = B + 9
and that
A + B + C = 32
Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.
A + B + C = (B + 11) + B + (B + 9) = 32
3B + 20 = 32
3B = 12
B = 4
The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).
Which of the following calculations described in the following statements require that you use the addition rule?
A)Calculate the probability of black offspring from the cross AaBb × AaBb,when B is the symbol for the black allele.
B)Calculate the probability of children with both cystic fibrosis and polydactyly when parents are each heterozygous for both genes.
C)Calculate the probability of each of four children having cystic fibrosis if the parents are both heterozygous.
D)Calculate the probability of a child having only sickle-cell anemia or cystic fibrosis if each parent is each heterozygous for both traits.
If probability each parent is heterozygous for both features, determine the likelihood that a child will only have cystic fibrosis or sickle-cell anaemia.
P(Sickle-cell Anemia)
= 0.25
P(Cystic Fibrosis)
= 0.25
P(Sickle-cell Anemia or Cystic Fibrosis) = P(Sickle-cell Anemia) + P(Cystic Fibrosis)
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.25 + 0.25
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.5
The likelihood that a child will have either cystic fibrosis or sickle-cell anaemia is 0.5 or 50%. This is because both parents are heterozygous for both features. This means that each parent has a 25% chance of passing on either one of the conditions to their child. The probability of having either one of the conditions is the sum of the individual probabilities, which is 0.25 + 0.25 = 0.5 or 50%.
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3. A website is offering a promotion, during which customers can buy up to 100 photos for a flat fee. The
cost per photo varies inversely with the number of photos a customer buys, as shown in the table below.
What function models the data?
To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.
To model this relationship, we can use the inverse variation equation, which can be expressed as:
y = k/x
Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.
Let's examine the data given in the table to find the value of k:
Number of Photos (x) Cost per Photo (y)
10 10
25 4
50 2
100 1
We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):
2 = k/50
Solving for k:
k = 2 * 50 = 100
Now that we have the value of k, we can write the function that models the data:
y = 100/x
Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.
Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
the are of the circle below is 28.26 ft. squared. What is the diameter
Answer: 8.06 Inches
The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.
OMG PLEASE I BEG I NEED HELP 5th grade math
Answer: A
Step-by-step explanation:
Volume= LxWxH so we get 20x28x24 as given.
Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.
13,440-10,500= 2,940 Cubic Inches
Option A
Answer:
Part A: 13440 cubic inches.
Part B: A - 2940 cubic inches.
Step-by-step explanation:
The volume of the box = 24x20x28 = 13440 cubic inches.
The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.
13440-10500 = 2940 cubic inches. The answer is A.