Therefore , the solution of the given problem of triangle comes out to be
Orthocentre (0, - 5 ).
How do triangles function?Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides end to end at a single point. The triangle has three angles, and the sum of them is 180 degrees.
Here,
We need the lengths of the triangle's three sides in order to identify which of the aforementioned cases the triangle fits into.
Make the length calculations using the distance formula.
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
L(0, 5) and M(3, 1)
LM =d = [tex]\sqrt{(3-0)^{2}+(1-5)^{2}}[/tex] = 5
L(0, 5) and (N(8, 1)
LN = d = [tex]\sqrt{(8-0)^{2}+(1-5)^{2}}[/tex] = √80
M(3, 1) and (N(8, 1)
MN = [tex]\sqrt{(8-3)^{2}+(1-1)^{2}}[/tex] = 5
If a triangle has three sides, a, b, and c, and side c is the longest, then
• Right triangle formed by a2 + b2 = c2
• a2 + b2 c2 - acute triangle
Triangle with angles a2, b2, and c.
A, B, and C are equal to five in this instance.
a² + b² = 5² + 5² = 25 + 25 = 50
c² = (4 )² = 80
A triangle is obtuse and the orthocentre lies outside the triangle because a2 + b2 c2.
The place where the triangle's three altitudes converge is known as the orthocentre.
For the orthocentre's coordinates, we only need to simultaneously solve
the equations for two of the altitudes.
A line drawn at a right angle from a vertex to the other side is known as an altitude.
Altitude from M to LN
Calculate the slope of LN using the slope formula
m = (y2 - y1 )/ (x2- x1 ) = 1-5/8-0 ⇒ = 2
Equation of altitude
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1)
Altitude between M and LN
Utilize the slope formula to determine LN's slope.
m = (y2 - y1)/ (x2- x1) = 1-5/8-0 ⇒ = 2
formula for altitude
y - 1 = 2(x - 3) (x - 3)
y - 1 = 2x - 6
y = 2x - 5 → (1) (1)
Altitude between N and LM
m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4
formula for altitude
y - 1 = (x - 8) (x - 8)
y - 1 = x - 6
y = x - 5 → (2) (2)
Adding (1) to (2)
2x - 5 Equals x - 5 ( multiply through by 4 ) ( multiply through by 4 )
8x - 20 = 3x - 20
5x - 20 = - 20 ( add 20 on both sides ) ( add 20 to both sides )
5x = 0 ⇒ x = 0
Place x = 0 in place of (1)
y = 0 - 5 = - 5
It is the orthocentre (0, - 5 )
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a scientist wants to determine whether or not the height of cacti, in feet, in africa is significantly higher than the height of mexican cacti. he selects random samples from both regions and obtains the following data.
Africa:
Mean = 12.1
Sample size = 201
Mexico:
Mean = 11.2
Sample size = 238
(a) Which of the following would be the correct hypothesis test procedure to determine if there is a difference between the mean height of two cacti?
-Two-sample test for proportions
-Two-sample t-test
- Paired t-test
(b) What is the value of the sample statistic to test those hypotheses? (2 decimal places)
(c) If the T test statistic is 2.169, and df = 202, find the p-value. (3 decimal places)
(d) Select the correct conclusion at alpha = 0.05.
-The null hypothesis is not rejected. There is insufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is not rejected. There is sufficient evidence of a difference between the mean height of two cacti.
-The null hypothesis is rejected. There is insufficient evidence of a difference between the mean height of two cacti.
(e) Mark the correct statement at alpha = 0.05:
-The test result is statistically significant.
-The test result is not statistically significant.
(f) Explain the type of error, in context, that might have been made.
-Type II error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
-Type II error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.
-Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
-Type I error, which means the scientist concluded there is not a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is a difference.
(g) What would the p-value have been if we had done a two-tailed test? (3 decimal places)
The correct options for the given parts are as follows
(a) Two-sample t-test.
(b) x1 bar - x2 bar = 12.1 - 11.2 = 0.9
(c) p - value = 0.031
(d) The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
(e) The test result is statistically significant.
(f) Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
What is sample statistics?
Any number calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data obtained through random sampling, which is a random experiment, it is a random variable.
a) Since there are two independent samples and we want to compare population means. We must use: Two-sample t-test.
b) The value of the sample statistic to test those hypotheses is:
x1 bar - x2 bar = 12.1 - 11.2 = 0.9
c) This is two-tailed test. For p-value, use excel formula =TDIST(2.169,202,2).
p - value = 0.031
d) Since p-value is less than 0.05, correct option is:
The null hypothesis is rejected. There is sufficient evidence of a difference between the mean height of two cacti.
e) Since p-value is less than 0.05, correct option is:
-The test result is statistically significant.
f) Since null hypothesis is rejected, we might have been made Type I error. The correct option is:
-Type I error, which means the scientist concluded there is a significant difference between average height of cacti in Africa and cacti in Mexico, when in reality there is no difference.
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9. Salvador is playing a game where the
product must be greater than 5. Which two
cards result in a product greater than 5?
31/1/2
3
A. 1 and 4
B. 3 and 1
2
C. 3 and 12
8
D. 2 and 12/2
3
1/4/2
8
3
Answer:
The answer should be A.
Step-by-step explanation:
(3.65u − 11) − (−5 + 8.7u)
Answer:
73u/ - 11
Step-by-step explanation:
Answer:
-5.05. U -6
Step-by-step explanation:
Distribute the Negative Sign:=3.65u−11+−1(−5+8.7u)=3.65u+−11+(−1)(−5)+−1(8.7u)=3.65u+−11+5+−8.7uCombine Like Terms:=3.65u+−11+5+−8.7u=(3.65u+−8.7u)+(−11+5)=−5.05u+−6
suppose a ladybug is walking randomly along the rim of a very large disc. every second, it either moves forward one unit along the rim with probability 12, moves backwards one unit with probability 16, or stays still with probability 13. suppose the ladybug is at position 0, 1, or 2 at time t with probabilities 14, 14, and 12. what is the probability that the ladybug will be at position 1 at time t 1?
The probability that the ladybug will be at position 1 at time t+1 is ((1/2)*(12/50) + (1/2)*(16/50)) = 14/50 = 0.28.
Why does probability matter?Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.
How do you determine probability?The probability is computed by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
m∠5 + m∠6 are linear pairs, so their sum has to be 180°.
m∠2 + m∠3 = m∠6 because of the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the two opposite interior angles. (using this logic, m∠1 equals the sum of m∠5 and m∠3, and m∠4 equals the sum of m∠2 and m∠2).
m∠2 + m∠3 + m∠5 = 180° because the triangle sum property says that the sum of a triangle's interior angles will equal 180°.
Consumer Reports rated automobile insurance companies and gave annual premiums for top-rated companies in several states. The figure below shows box plots for annual premiums for urban customers (married couple with one 17-year-old son) in three states. The box plots were all drawn using the same scale on a TI-84Plus/TI-83Plus calculator. The five-number summaries below were generated on the TI-84Plus/TI-83Plus calculators for the box plots.
Insurance Premium (annual, urban)
figure3-9.gif
3-figure-10-alt.gif
(a) Which state has the lowest premium? the highest?
---Select--- California Texas Pennsylvania has the lowest premium, and ---Select--- California Pennsylvania Texas has the highest.
(b) Which state has the highest median premium?
TexasPennsylvania California
(c) Which state has the smallest range of premiums? the smallest interquartile range?
---Select--- Texas Pennsylvania California has the smallest range, and ---Select--- Pennsylvania California Texas has the smallest IQR.
(d) Match the five-number summaries to the appropriate box plots.
California (i); Texas (ii); Pennsylvania (iii)Pennsylvania (i); Texas (ii); California (iii) Texas (i); Pennsylvania (ii); California (iii)Pennsylvania (i); California (ii); Texas (iii)Texas (i); California (ii); Pennsylvania (iii)California (i); Pennsylvania (ii); Texas (iii)
a) California has the lowest premium and Pennsylvania has the highest premium.
b) Pennsylvania has the highest median premium.
c) Texas has the smallest range of premium. California has the smallest interquartile range.
Insurance Premium:
A premium is the amount an individual or business pays for an insurance policy. Premiums are paid for policies that cover health insurance, auto insurance, home insurance, and life insurance. When the premium is paid, it becomes income for the insurance company. It also constitutes liability, as the insurer must pay for claims arising from the policy. Failure to pay individual or corporate premiums may result in the cancellation of the policy.
The insurance company actuary is responsible for determining premium payments using statistics and calculations. Determine the likelihood of encountering an event or accident requiring insurance coverage. We will also be charged for any costs associated with the coverage.
Using the above factors to determine the premium, the actuary determines the price charged by the insurance company so that the amount the actuary receives is greater than the amount the company has to pay for the claim. increase.
Information gathered by actuaries is entered into tables called actuarial tables and passed on to insurance companies who set premium prices.
From the above discussion, we get:
a) California has the lowest premium and Pennsylvania has the highest premium.
b) Pennsylvania has the highest median premium.
c) Texas has the smallest range of premium. California has the smallest interquartile range.
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X+y=0,5x+y=4 using substitution method
Answer:
(1, - 1 )
Step-by-step explanation:
x + y = 0 → (1)
5x + y = 4 ( subtract 5x from both sides )
y = 4 - 5x → (2)
substitute y = 4 - 5x into (1)
x + 4 - 5x = 0
4 - 4x = 0 ( subtract 4 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
substitute x = 1 into (1) and solve for y
1 + y = 0 ( subtract 1 from both sides )
y = - 1
solution is (1, - 1 )
the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store?
For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.
Probability is a measure of the likelihood that an event will occur.
Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it.The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 505 and standard deviation of 115.
Then, we can say that,
Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P (250 <X< 450)
= P {(250-505)/155} < Z < {(450-505)/155}
= P (-1.64 <Z< -0.03)
Where, Z is the standard normal variate.
ρ = -1.64 <ρ< -0.03
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.00585
For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.
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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .
What is area and area of shape ?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The area of a shape is the space enclosed within the perimeter or the boundary of the given shape.
Here, μ = 100, σ = 15 and x = 125. We need to compute P(X >= 125). The corresponding z-value is calculated using Central Limit Theorem.
z = (x - μ)/σ
z = (125 - 100)/15 = 1.67
z = 1.67
Therefore,
P(X >= 125) = P(z <= (125 - 100)/15)
= P(z >= 1.67)
= 1 - 0.9525
= 0.0475
Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .
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In factoring the expression 12x²y³ + 20x³y, which of the following is the greatest
common factor?
(F) 8x³y³
(G) 8x²y
(H) 4x²y
(I) 4xy
Answer:
12 and 24 gcf = 4
so the only choice left is
(H) 4x²y
(I) 4xy
12x²y³ + 20x³y = lowest of x is x² and y is y
then its
(H) 4x²y
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the time to fly between new york city and chicago is uniformly distributed with a minimum of 66 minutes and a maximum of 100 minutes. what is the probability that a flight is less than 71 minutes? a) 1.00 b) 0.15 c) 0.07 d) 0.00
The probability that the flight is less than 71 minutes is 0.1471
Let the distribution of the time to fly between New York City and Chicago be X
X~U(66,100)
where,
66 = minimum
100 = maximum
We need to find P(X<71)
We know that in the case of uniform distribution,
P(X<x) = (x - a) / b -a
where,
a = min value
b = max value.
Hence P(X<71)
= (71 - 66) / (100 - 66)
= 5/34
= 0.1471
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2x34x56
im in -8ht garde and me no know multipcacion pls hulp
Answer:
Step-by-step explanation:
3,808
Answer: 3808
Step-by-step explanation:
2 times 34 = 68
68 times 56 = 3808
Answer is 3808
Find The Slope
The answer has to be in fraction form
Please help I need the answer asap
Thanks
Answer:
7/5
Step-by-step explanation:
Go up from the lower left point along the orange line 7 units.
7 units up = a rise of 7
Now go right on the orange line 5 units.
5 units right = a run of 5
slope = rise/run = 7/5
Answer: 7/5
If the short on a clock is in 9 and the long hand is on 10 what time is it?
Answer: 9:50 AM/PM
Step-by-step explanation: Since the shorthand (hour) is on the 9, the hour is 9:00. The long hand (minutes) is on the 10, so it is 50. So, therefore we have 9:50. We don't know if it's am or pm, so we don't know if it's in the morning or the afternoon.
describe the solution set for the system of equations that consists of the equation of the line shown and .y=1/2x-3
The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
What is the equation?
The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.
Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.
The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.
So, given equations:
y = 1/2 * x - 3
y = - 1/2 * x - 3
As we are aware, a line's slope-intercept form is:
y = m x + c
Therefore, it is clear from equations 1 and 2 that:
m1 = 1/2 and c1 = -3
m2 = -1/2 and c2 = -3
Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?
a. They have the same slope but different y-intercepts, so they have no solution.
b/. They have the same slope but different y-intercepts, so they have one solution.
c. They have different slopes but the same y-intercept, so they have no solution.
d. They have different slopes but the same y-intercept, so they have one solution.
Jesse has an expression:
x² - x - 6
Why would Jesse want to factor this expression to get the following expression?
(x - 3)(x + 2)
A. To find the coefficients.
B. To find the discriminant.
C. To find the order.
D. To find the x-intercepts.
Jesse wants to factor the expression To find the x-intercepts.
Quadratic Expression:An expression containing a variable having the largest power of two is called a quadratic expression. The power of the expression should be two, not greater or lower.
Coefficients:A coefficient is a multiplication factor in a polynomial, series, or statement in mathematics; it is often a number.
Discriminant:The concept used to find the number of solutions of a quadratic equation is known as Discriminant. The expression that appears under the square root in the quadratic formula is named Discriminant.
X- intercept :The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y-coordinate equals zero, is the x-intercept for any curve.
Here we have
x² - x - 6 is factorized as (x - 3)(x + 2)
If we take (x - 3)(x + 2) = 0
=> (x - 3) = 0 (x + 2) = 0
=> x = 3 x = -2
This means x values are x-intercept
Therefore,
Jesse wants to factor the expression To find the x-intercepts.
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(the question is on the image)
Congruent triangle: The values of x, y, and z are x = 23; y = 7 and z = 11.
What is a congruent triangle?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Given: ΔPRS ≅ ΔCFH
Since both triangles are congruent, m<R = m<F
m<F is a right angle = 90°.
Thus, 13y - 1 = 90
13y = 90 + 1
13y = 91
y = [tex]\frac{91}{13}[/tex]
y = 7
Also, by inspection
PS = CH
⇒ 2x - 7 = 39
⇒ 2x = 39 + 7
⇒ 2x = 46 ⇒ x = [tex]\frac{46}{2}[/tex]
x = 23
Since m<R is 90°, then
m<S = 180 - (90 + 28)
m<S = 62°
By inspection,
m<S = m<H
Thus,
⇒ 6z - 4 = 62
⇒ 6z = 66
z = [tex]\frac{66}{6}[/tex]
z = 11
Hence, x = 23, y = 7 and z = 11.
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The length of a line is 12.3 cm, correct to 1 decimal place.
Write down the upper bound of the length of the line.
The upper bound of the length of the line is 12.34 cm
How to determine the upper bound of the length of the lineFrom the question, we have the following parameters that can be used in our computation:
Length of the line = 12.3 cm
From the question, we understand that
Time = rounded to the nearest one decimal place
The highest number that can be rounded to 12.3 to the nearest one decimal place is 12.34
This means that
Upper bound = 12.34
Hence, the upper bound is 12.34 cm
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Undergraduates
Graduates
Total
University Data
Receiving
Financial Aid
4222
1879
6101
Not Receiving
Financial Aid
3898
731
4629
Total
8120
2610
10730
If a student is selected at random, what is the
probability that the student receives aid
(rounded to the nearest percent)? [? ]%
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
in our case the desired cases are all students with financial aid : 6101
and the totally possible cases are 10730.
so, the probability to pick a student at random, who receives financial aid is
6101 / 10730 = 0.568592731... = 56.8592731...% ≈
≈ 57%
HELPPPP!!!
Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?
x=1/12(y+4)^2-2
y=1/12(x+4)^2+2
x=-1/12(y+4)^2+2
y=-1/12(x+4)^2-2
Following equation represents the parabola in the graph:
x=1/12(y+4)^2-2
How to find the focus and directrix of a parabola?From the graph, we see that;
Focus = (-4, -2)
We use the equation x=h−p to find the directrix.
General form of equation of a parabola is;
(y - k)² = 4p(x - h)
where;
focus is (h + p, k)
directrix is x = h - p
Can a parabola not cross the y-axis?If we are talking about the function y = ax² + bx + c, then since it is a continuous function on the whole real line, it must cross the y–axis at (0 , c).
However x = y² + 1 is a parabola(not a function) that does not cross the y–axis.
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what is the potential difference between the center of the sphere and the surface of the sphere?
Possible distinction between the center of the sphere and surface of the sphere is
A notable distinction is made by the fact that the surface is three-dimensional, while the sphere's centre is a (non-dimensional) point, and that their values are independent of one another.If the sphere is a conducting hollow sphere, its centre and surface have the same potential. A perfect conductor has no electric field at all.A dielectric sphere's core has zero potential, while the surface has a potential of KQ/(R).The sphere is one of the most significant mathematical figures. Spheres and nearly-spherical objects can be seen in both nature and industry.
Soap bubbles and other bubbles have a spherical shape when they are in an equilibrium state. The celestial sphere is a fundamental concept in astronomy, and the Earth is usually represented as spherical in geography.
The majority of pressure vessels, curved mirrors and lenses, and other manufactured items are based on spheres. Because spheres roll effortlessly in all directions, the majority of balls used in sports and toys are spherical, just like ball bearings.
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Graph the function and identify the domain and range.
y=-0.25x^2
(-∞, ∞) is the domain of y=-0.25x² and (−∞,0] is range.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given function is y=-0.25x²
y equal to minus zero point two five times of x square.
We need to find the domain and range of the function.
Let us find few points of x and y.
x 0 1 2 3 4
y 0 -0.25 -1 -0.5625 -4
In the given attachment the graph is given.
The domain is:
{x∣x is R} or (-∞, ∞)
The range is {x∣x≤0} or (−∞,0]
Hence, the domain of y=-0.25x² is (-∞, ∞) and range is (−∞,0].
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Select the correct answer.
Of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit to climb the mountain. What is
the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
the probability that a person picked at random from the group is a male or female is fit to climb Mount Shasta is 0.472 (or in percent near 47.2%).
How do you calculate probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
What are the 3 types of probability?Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).
Subjective Probability. Definition of Relative Frequency.
1. Determine the number of male climbers:
200 men - 100%
x men - 12 %
. Of the 60 people in California who are physically capable of climbing Mount Shasta, 24 are men, leaving 36 women.
The likelihood that a guy will be selected at random from the group is
The likelihood that a random member of the group is physically capable of climbing Mount Shasta is: 0.472
0.472 (or, in percentage terms, close to 47.2%).
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What is the solution to 1/2 |x| = -3?
Answer: 1/2 |x| = -3?
Step-by-step explanation:
which functions have a zero at x equals 4? check all that apply. and (x )equals negative 2 x squared minus 18 x minus 40 b. c (x )equals 2 x squared minus 11 x plus 12 c. e (x )equals 3 x cubed plus x squared minus 48 x minus 16 d. a (x )equals x squared minus 3 x minus 28 e. b (x )equals x cubed minus 4 x squared minus x plus 4
The function that have a zero at x = 4 are
f(x) = 2x^2 - 11x + 12 f(x) = 3x^3 + x^2 - 48x - 16 f(x) = x^3 - 4x^2 - x + 4The first function is
f(x) = -2x^2 - 18x - 40
Substitute the value of x = 4
f(4) = -2(4)^2 - 18(4) - 40
= -2(16) - 72 - 40
= -32 - 72 - 40
= -144
The result is not zero
The second function is
f(x) = 2x^2 - 11x + 12
f(4) = 2(4)^2 - 11(4) +12
= 32 - 44 + 12
= 0
The result is zero
The third function is
f(x) = 3x^3 + x^2 - 48x - 16
f(4) = 3(4)^3 + 4^2 - 48(4) - 16
= 192 + 16 - 192 - 16
= 0
The result is zero
The fourth function is
f(x) = x^2 - 3x - 28
f(4) = 4^2 - 3(4) - 28
= 16 - 12 - 28
= -24
The fifth function is
f(x) = x^3 - 4x^2 - x + 4
f(4) = 4^3 - 4(4)^2 - 4 + 4
= 64 - 64 - 4 + 4
= 0
Therefore, the function f(x) = 2x^2 - 11x + 12, f(x) = 3x^3 + x^2 - 48x - 16 and f(x) = x^3 - 4x^2 - x + 4 have zero at x equals 4
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write a linear function f with the given values. ƒ(0) = 2,ƒ(3) = -1
The required linear function y = -x + 2.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The equation for the slope, m, of a line is:
m = y₁- y₀ / x₁ - x₀ {equation 1}
The equation f(0) = 2 tells us that x₀ = 2and y₀ = 0,
substitute this into equation [1].
m = y₁- (0) / x₁ - 2 {equation 2}
The equation f(3) = -1 tells us that x₁ = -1 and y₁= 3,
substitute this into equation [2].
m = 3/-3
m = -1
Substitute m to the equation y = mx + b,
y = -x + b
Now, substitute the value of x = 2 and y = 0
b = 2.
Now the linear function,
y = -x + 2
Therefore the linear function y = -x + 2.
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How do you solve 3^x = 500 ?
by using log notation, the value of x =㏒₃500 or x = 5.657
what is log notation?Log notation is a mathematical expression used to represent any exponential relationship in its inverse form.
How to solve the index?we use log notation to solve an equation in where an unknown variable is in index form. By applying logarithm laws, we write an exponential equation in the inverse form and finally we get the unknown values.
in the above equation 3ˣ = 500
using log notation, we get ㏒₃500 = x
x= 5.657
hence, the solution is x = 5.657
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The coordinates of point A are (-3a,4b). If point A' is the image of point A reflected over the line y = x, what
are the coordinates of A?
Answer: (4b, -3a)
Reason:
When reflecting over the line y = x, we swap the positions of the x and y coordinates.
The reflection rule is [tex](\text{x},\text{y}) \to (\text{y},\text{x})[/tex]
As an example: [tex](2,3) \to (3,2)[/tex]
Solve the following compound inequality.
9x + 6 > 132 and -7x + 19 < -128
The solution of the inequality 9x + 6 ≥ 132 and -7x + 19 < -128 is x ≥ 14 and x > 21.
How to solve compound inequality?Compound inequalities are a type of inequality that has two or more parts.
In other words, a compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
9x + 6 ≥ 132 and -7x + 19 < -128
Let's solve them independently.
9x + 6 ≥ 132
subtract 6 from both sides of the inequality
9x + 6 ≥ 132
9x + 6 - 6 ≥ 132 - 6
9x ≥ 126
divide both sides by 9
x ≥ 126 / 9
x ≥ 14
-7x + 19 < -128
subtract 19 from both sides of the inequality
-7x + 19 - 19 < - 128 - 19
-7x < - 147
divide both sides by - 7
x > - 147 / -7
x > 21
Therefore, the solution is x > 21 and x ≥ 14
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a rectangular box with no top is to have a surface area of 4 m2. find the dimensions (in m) that maximize its volume.
If the surface area of the rectangular box is 4 m² then the dimensions that maximize its volume is (2/√3 , 2/√3 , 1/√3) .
In the question ,
let length of rectangular box be = l
let width of rectangular box be = b and
let height of rectangular box be = h .
Since the box has no top ,
So , the surface area is = lb + 2bh + 2hl = 4
we get h = (4-lb)/(2l + 2b) .
The volume of the box is given as V = l×b×h .
Substituting the value of h from above in the volume formula , we get ,
V = lb(4-lb)/(2l + 2b)
differentiating it with respect to l ,
we get ,
dV/dl = [((2l+2b)(4b-2lb²)-lb(4-lb).2)/(2l+2b)²] = 0
Simplifying further ,
we get ,
2l² + 4lb - 8 = 0 ....equation(1)
Differentiating volume with respect to "b" .
dV/db = [((2l+2b)(4l-2l²b)-lb(4-lb).2)/(2l+2b)²] = 0
simplifying further ,
we get ,
2b² + 4lb - 8 = 0 ...equation(2) .
Simplifying equation(1) and (2) , we get
l = b ,
Substituting l = b in equation(1) ,
we get ,
2l² + 4l² = 8
l = 2/√
and b = 2/√3 .
Substituting the values in h ,
we get ,
h = (4-lb)/(2l + 2b)
h = 1/√3 .
Therefore , the dimensions of the box is (2/√3 , 2/√3 , 1/√3) .
The given question is incomplete , the complete question is
A rectangular box with no top is to have a surface area of 4 m². find the dimensions (in m) that maximize its volume.
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