for which of the following values does the function intersect the x axis at 2 different points
Answers
The values that, the function intersect the x axis at 2 different points is -4 < b < 4. So correct option is D.
A function in mathematics is a relationship between a set of inputs (also known as independent variables or arguments) and a set of outputs (also known as dependent variables or values). The output of a function is determined by the inputs, and the function assigns exactly one output value to each input value.
A function can be represented in many ways, including a formula, a table, or a graph. The formula of a function defines the relationship between the inputs and outputs, and can be used to calculate the output for a given input. A table lists input and output values, and a graph represents the function by plotting the input and output values.
Functions are a fundamental concept in mathematics and are used in many areas, including algebra, calculus, and other branches of mathematics, as well as in science, engineering, and other fields. Functions can be simple, such as linear functions, or complex, such as exponential functions or trigonometric functions.
For the function f(x) = x^2 + bx + 4 to intersect the z-axis at two different points, it must have two real roots. This means that the discriminant of the quadratic equation must be greater than 0. The discriminant of the quadratic equation is given by b^2 - 4(1)(4). Hence, b^2 - 16 > 0, or b^2 > 16, which simplifies to -4 < b < 4.
Therefore, the answer is D: -4 < b < 4.
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Related Questions
In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothing and carry‑on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not normally distributed, especially when the population includes both men and women, but they are not very non‑Normal. A commuter plane carries 22 passengers. What is the approximate probability P that the total weight of the passengers exceeds 4500 pounds? Use the four‑step process to guide your work. Give your answer as a percentage precise to two decimal places. P=___?
Answers
The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Total of 22 is more than 4500 is equivalent to average of 22 is more than [tex]$\frac{4500}{22}[/tex]=204.545
[tex]$$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$[/tex]
= 1 - 0.8997
= 0.1003
= 10.03%
Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
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Please help me with this question.
Answers
The solution to the system of equations in this problem is given as follows:
X = [28571
14286].
How to solve the system of equations?The system is defined by the following equation:
X = DX + E.
The matrices D and E are known, while X = [A; B] is the output matrix. Applying the multiplication of matrices, the system of equations is defined as follows:
0.2A + 0.3B = 10000.0.5A + 0.4B = 20000.Inserting this system into a calculator, the solution is given as follows:
A = 28571.B = 14286.Hence the matrix X is given as follows:
X = [28571
14286].
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my’s Annual Expenditures
Rent $ 8,580.00
Utilities $ 3,480.00
Internet & Phone $ 1,896.00
Entertainment $ 2,232.00
Student Loan Payment $ 4,116.00
Home & Auto Insurance $ 1,164.00
Food $ 6,000.00
Car Payment & Gas $ 2,820.00
Travel $ 1,200.00
Savings $ 1,200.00
Personal Expenses $ 1,847.00
Pet Expenses $ 965.00
Business Expenses $ 4,800.00
Q1. Amy’s day job is as a secretary at a law firm. After taxes and health insurance, she nets $1550 bi- weekly. How much does Amy net in a year from her day job?
Q2. Based on her net income and annual expenditures summary, by how much did Amy over or under spend this year?
Answers
Part a: Amy's net amount in a year from her day job is found as $40411.
Part b: Amy under spend this year by amount $8331.
Define the term annual expenditure?Just before annual contribution margin, all expense items in the profit and loss statement, including operating costs including finance charges, are referred to as annual expenditure.Part a:
The calculation is done bi- weekly.
Total days = 2*7 = 14.
Net amount = $1550.
Net amount for the year = (1550/ 14)*365
Net amount for the year = $40411
Thus, Amy's net in a year from her day job is found as $40411.
Part b:
Total amount spend : Sum of all expenditures.
Total amount spend : $32,080
Difference = $40,411 - $32,080
Difference = $8331
Thus, based on her net income as well as annual expenditures summary,
Amy under spend this year by amount $8331.
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Find KJ
What the answer
Answers
For the given triangles ΔABC ≈ ΔBKJ, the value of KJ is, 9
What is similarity of triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"
Given that,
The triangle, ΔABC
one segment KJ which is intersecting sides AB & BC
ΔABC has one similar triangle inside, which is ΔBKJ
Triangle ΔABC and ΔBKJ similar,
So, we can say ΔABC ≈ ΔBKJ
And it is known that
for similar triangles, ratio of lengths of sides are equal for similar triangles
so, AB/AC = KB/KJ
AB = 2KB
⇒ 2KB/18 = KB/KJ
⇒ 2/18 = 1/KJ
⇒ KJ = 9
Hence, the length of KJ is 9 unit
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If m
∠
∠
BAC is 48
∘
∘
, what is the measure of
∠
∠
GAE?
Answers
Answer:
132
Step-by-step explanation:
180 - 48 = 132 These angles are supplemental. They add to 180
Answer:
<GAE = 48
Step-by-step explanation:
<BAC = 48
<BAC = <GAE
two letters without replacement from the three letters a b and c how many ways can this be done if the order of choice is taken into consideration how many ways can this be done if the order of the choices is not taken into consideration
Answers
Answer:
If order is considered = 6
If order is not considered = 3
Step-by-step explanation:
If order is to be taken in consideration then the following values can be taken:
a, b
a, c
b, a
b, c
c, a
c, b
Total = 6 ways
If order is not taken in consideration then the following values can be taken:
a, b
a, c
b, c
Total = 3 ways
Point P is on line segment O Q . Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾ . PQ
Answers
Answer: PQ is 9 units.
Step-by-step explanation:
The length of PQ can be found using the proportion of OQ and OP.
(PQ / OQ) = (OP / OQ)
PQ = (OP / OQ) * OQ
Substituting in the given values:
PQ = (9 / 11) * 11
PQ = 9
Therefore, the length of PQ is 9 units.
help it is for a grade tomorrow
Answers
Answer:
Step-by-step explanation:
customers: 6
minutes: 40
Gina is going to buy 100 stickers
Answers
Gina should buy from Stickers4u.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Gina is going to buy 100 stickers.
If she buys from the shop - Stickers4u,
then the cost is,
= 100/25 x 2.15
= 4 x 2.15
= 8.6.
And if she buys from the World stationary,
then the cost is,
= (100 - 50)/10 x 1.65
= 5 x 1.65
= 8.25
Therefore, she should buy from Stickers4u.
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A cylindrical glass is shown at right. The height of the cup is 7 inches. The radius of
the base is 1.5 inches. Use 3.14 for л.
a. How many bases are included in the surface area of the outside of the glass?
b. Find the total surface area of the outside of the glass.
Answers
There are 11 1/3 based in the area outside and the total surface area of the outside of the glass is 80.07 square inches
How many bases are includedFrom the question, we have the following parameters that can be used in our computation:
Height, h = 7 inches
Radius, r = 1.5 inches
π = 3.14
The area of the base is calculated as
Base area = πr²
So, we have
Base area = π * 1.5²
Base area = 2.25π
The surface area of the outside of the glass is
Surface area = 2πr(r + h)
So, we have
Surface area = 2π * 1.5 * (1.5 + 7)
Surface area = 25.5π
The number of base is
Number = 25.5π/2.25π
Evaluate
Number = 11 1/3
The total surface area of the outsideIn (a), we have
Surface area = 25.5π
This gives
Surface area = 25.5 * 3.14
Evaluate
Surface area = 80.07
Hence, the area is 80.07 square inches
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Find the value of M and N
Answers
Answer: n=110, m=110
Step-by-step explanation: I think m=110 because of vertical angles. m might also equal 70.
Express each of the following as the sum Of a whole number and a fraction 9/7
Answers
Answer:
1 + 2/7
Step-by-step explanation:
9/7 =
(7+2) / 7 =
7/7 + 2/7 = ==> use distribution
1 + 2/7 ==> 7/7 = 1, so simplify the expression
A jar contains 7 poker chips: 4 blue, 2 red and 1 white. You randomly select two chips from the jar. What is the probability that your selection includes two different colored chips? Report your answer to three decimal places.
Answers
The probability of selecting two different coloured chips is the fraction 14/49.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
total possible outcome = 7
blue chips = 4
red chips = 2
white chips = 1
probability of selecting blue chips = 4/7
probability of selecting red chips = 2/7
probability of selecting white chips = 1/7
probability of selecting two coloured chips at random = 4/7 × 2/7 + 4/7 × 1/7 + 2/7 × 1/7
probability of selecting two coloured chips at random = 8/49 + 4/49 + 2/49
probability of selecting two coloured chips at random = 14/49
Therefore, the probability of selecting two different coloured chips is the fraction 14/49
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Kim has to prepare for a 16 miles race for 2/6 of the race Kim decides to walk preserve her energy she than sprints for 3/7 of the remaining time after she walked what is half of the race left
Answers
The half-distance left is 40/7 or 5.714 miles
How to find the distance?Given that:
The total race is 16 miles long.
Kim walked for 2/6 of the race, which is (2/6) * 16 = 16/3 miles.
After walking 16/3 miles, there are 16 - 16/3 = 32/3 miles left in the race.
Kim then sprints for 3/7 of the remaining distance, which is (3/7) * 32/3 = 32/7 miles.
Half of the race is left after she finished sprinting and walking, which is
16 - 32/7 = 80/7 miles
Divide this by 2:
80/7 ÷2
= 40/7 miles are left.
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Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + [1/(32√2)] + [1/(243√3)] + [1/(1024√4)] + [1/(3125√5)] + ….
p = _____
A. converges B. diverges
Answers
The answer is B. diverges.
Theorem 9.11 states that if the sequence of positive terms (an) satisfies the condition 1/an^p converges, then the p-series ∑an converges if p > 1 and diverges if p ≤ 1. In this case, the positive terms of the sequence are given by [1/(n^(3/2))]. So, [1/an^p] = [1/(n^(3/2))^p] = [1/n^(3p/2)].
For the series to converge, we need [1/an^p] to converge, or [1/n^(3p/2)] to converge.
If 3p/2 > 1, then [1/n^(3p/2)] converges and the series converges.
If 3p/2 ≤ 1, then [1/n^(3p/2)] diverges and the series diverges.
So, to determine the value of p, we need to find the value of p such that 3p/2 = 1. Solving for p, we find that p = 2/3.
Since 2/3 ≤ 1, the series diverges. Therefore, the answer is B. diverges.
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3. A dilation is represented in the following table. Determine the scale factor for the dilation.
Express your answer in function notation (x,y) → (kx,ky).
Pre-Image
Image
I
(2,4)
(1, 2)
(1, 0)
(0.5, 0)
(-4,-1)
(-2,-0.5)
Answers
The scale factor of the dilation, expressed in function notation, (x, y) → (k·x, k·y), is (x, y) → (0.5·x, 0.5·y)
What is a dilation transformation?A dilation transformation is a transformation in which the dimensions of the image are obtained by multiplying the dimensions of the pre-image by a value, known as a scale factor of the dilation.
The possible table, based on the similarities of the coordinate points can be presented as follows;
Pre-Image [tex]{}[/tex] Image
(2, 4) [tex]{}[/tex] (1, 2)
(1, 0) [tex]{}[/tex] (0.5, 0)
(-4, -1) [tex]{}[/tex] (-2, -0.5
The specified formula for the image, following the dilation of the point (x, y) by a scale factor of k is; (x, y) → (k·x, k·y)
Therefore, we get;
k = k·x/x = k·y/y
The comparison of the points in the table with the points (x, y), and (k·x, k·y), indicates that we get;
When (x, y) = (2, 4) and (k·x, k·y) = (1, 2)
Therefore;
k = k·x/x = k·y/y = 1/2 = 2/4 = 0.5
The scale factor of the dilation , k = 0.5, therefore;
(x, y) → (0.5·x, 0.5·y)
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given the definitions
u= 1 2 3 4 5 6 7
a= 1 2 4 5
b= 1 3 5 7
how many elements are in A' u B?
Answers
AUB
The x-coordinates of the solutions to a system of equations are 3.5 and 6. Which of the following could be the system? （ ）A. y=x+3.5 y=x^2+6B. y=2x-7 y=-(x-6)^2C. y=12x+3 y=-(x-5)^2+7D. y=12x+7 y=-(x-6)^2+3.5
Answers
The system of equations that has a solution with x-coordinate of 3.5 and 6 is C. y = 1/2x + 3 and y = -(x - 5)² + 7.
To determine if a coordinate is a solution to a system of equations, substitute the values for the x and y in both equations and check if both resulting equations are true. If both resulting equations are true, then the coordinate is a solution to the system of equations.
A. y = x + 3.5
y = 3.5 + 3.5 = 7
y = x² + 6
7 = 3.5² + 6
7 ≠ 18.25
B. y = x - 7
y = 3.5 - 7 = -3.5
y = -(x - 6)²
-3.5 = -(3.5 - 6)²
-3.5 ≠ -6.25
C. y = 1/2x + 3
y = 1/2(3.5) + 3 = 4.75
y = -(x - 5)² + 7
4.75 = -(3.5 - 5)² + 7
4.75 = 4.75
y = 1/2x + 3
y = 1/2(6) + 3 = 6
y = -(x - 5)² + 7
6 = -(6 - 5)² + 7
6 = 6
D. y = 1/2x + 7
y = 1/2(3.5) + 7 = 8.75
y = -(x - 6)² + 3.5
8.75 = -(3.5 - 6)² + 3.5
8.75 ≠ -2.75
Only the system of equation in option C holds the equations true, hence, C. y = 1/2x + 3 and y = -(x - 5)² + 7 are the system of equations that has the given solution stated in the problem.
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Evaluate the limit.
Answers
Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
x-7=-2
Answers
x - 7 + 7 = -2 + 7
x = 5
This equation has a unique solution: x = 5. This means that there is exactly one value of x that satisfies the equation.
To support the conclusion that the equation has a unique solution, we can substitute x = 5 back into the equation and check that it is true:
5 - 7 = -2
-2 = -2
Since the left-hand side and the right-hand side are equal, the equation is true for x = 5, and it has a unique solution
You roll two six-sided dice numbered from one through six. What is the probability that the maximum of the two dice is greater than or equal to six? Report your answer to three decimal places.
Answers
The probability that the maximum of the two dice is greater than or equal to six is 0.722.
What is probability?
Probability is a way of calculating how likely something is to happen. Probability can range from 0 to 1, with 0 indicating an impossibility and 1 indicating a certainty.
We are given that two six-sided dice numbered from one through six are rolled.
The sample space of the event is
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Probability that the maximum of the two dice is greater than or equal to six is
26 out of 36 i.e. 26/36
This is equal to 0.722.
Hence, the probability that the maximum of the two dice is greater than or equal to six is 0.722.
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A 9 footbpiece of twine costs $8.64. What is the price per inch?
Answers
Answer: 0.08 dollars
Step-by-step explanation:
8.64 divided by 9 = 0.96
0.96 divided by 12 = 0.08
someone help !!
geometry: find the value of x
Answers
Answer:
x = 18
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
sum the 5 interior angles and equate to 540
3x + 23 + 95 + 7x - 4 + 90 + 9x - 6 = 540
19x + 198 = 540 ( subtract 198 from both sides )
19x = 342 ( divide both sides by 19 )
x = 18
please help me will give u extra points :)
•
Answers
From the graph, the compound inequality represented is x < -2 and x > 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequalities shows the non equal comparison of two or more numbers and variables. Compound inequality is an inequality that is composed of more than one inequality.
From the graph, the inequality is not a solid circle, so it is either > or < sign.
From the graph, the inequality shown is x < -2 and x > 5
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i need help solving rhis problem please show your work
Answers
The length of the GH is 4, when H is the midpoint of GI.
What is midpoint of a line?An area of a line that connects two distinct locations is referred to as a line segment. It is the least path between two places that can be determined to have a length.
A line segment's midpoint is the point on the segment when it is divided into two similar segments. The point on a line segment that is equally spaced from the two terminating points is known as the midpoint of the segment.
Given that H is the midpoint of GI.
Then we can say that,
GI / 2 = GH
Substitute the equations of the length of GH and GI as given:
(9x - 19) / 2 = 3x - 5
9x - 19 = 2(3x - 5)
9x - 19 = 6x - 10
9x - 6x = -10 + 19
3x = 9
x = 3
Substitute the value of x in the equation of the length of the segment GH thus:
GH = 3x - 5
GH = (3)(3) - 5
GH = 4
Hence, the length of the GH is 4, when H is the midpoint of GI.
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how to solve that and what is the answer
Answers
The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.
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.
Let 's' be the cost of the skirt. Then the equation is given as,
3/4(18 + s) = 31.50
The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.
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Traveling 120km total, 1st 59km are 90km P/h. Remaining km are 50km P/h. How long does the trip take total?
Answers
The total trip took a total of 1.87 hours.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: Total distance=120 km and 59 km at 90 km/hr and the remaining distance at 50 km/hr
Remaining distance= 120-59
=61 km
Thus for the first 59 km the time it took was
Time= Distance/ Speed
= 59/90
=0.65 hr
Similarly time taken for the second part of the journey is = 61/50
=1.22
Hence, total time taken for the trip is 1.22+0.65=1.87 hr.
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show that if xt x is not invertible, then at least one column of x is a linear combination of the others. this implies that there is only one way in which problem with invertibility of xt x may arise'
Answers
If the matrix xt x is not invertible, then its determinant is equal to 0. A determinant of 0 implies that the matrix is singular, meaning that its columns are linearly dependent.
This means that one of the columns of x can be expressed as a linear combination of the other columns, which implies that there is only one way in which the invertibility problem may arise: when the columns of the matrix x are linearly dependent.
If the determinant of xt x is equal to 0, then at least one column of x can be expressed as a linear combination of the others. For example, if column c can be expressed as a linear combination of columns a and b, then we can write:
c = k1a + k2b
where k1 and k2 are constants. This means that the information in column c is already represented in columns a and b, and so it is redundant.
This is the only way in which the invertibility problem of xt x may arise. If the columns of the matrix are linearly independent, then the determinant of xt x will be non-zero, and the matrix will be invertible.
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Your question is incomplete, but most probably, the full question was:
Proof that [tex]X^{T} X[/tex] is not invertiblethen at least one column of x is a linear combination of the others. This implies that there is only one way in which a problem with the invertibility of xt x may arise
easy question so yall can get your points up what is 5 plus 203 .first one gets best answer
Answers
Answer:
208
Step-by-step explanation:
Every day, Patrick's orange juice stand uses 3/4 of a bag of oranges. How many days will 1 1/2 bags of oranges last?
Answers
Answer:
2 days
Step-by-step explanation:
We want to divide 1 1/2 by 3/4
1 1/2 ÷ 3/4
Change the mixed number into an improper fraction.
3/2 ÷ 3/4
Copy dot flip
3/2 * 4/3
Rewrite
3/3 * 4/2
1 * 2
2
It will last 2 days
