The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value
Classifying the function as min or maxTo determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.
In this case, a = 1/2 and b = 3, so we have:
x = -b/2a = -(3)/(2(1/2)) = -3
To find the corresponding y-coordinate, we can substitute x = -3 into the function:
f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5
Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.
Therefore, the minimum value of the function is -9.5, which occurs at x = -3.
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The lion population in a certain reserve drops by 5% every year. Currently, the population's size is 325. i.Write a function that gives the lion population size,P(t), t years from today ii. What will the population be in 4 years. Write an exponential function for all three
Answer:
1. The function that gives the lion population size P(t), t years from today is:
P(t) = 325(0.95)^t
2. To find the population in 4 years, we can substitute t=4 in the function:
P(4) = 325(0.95)^4
P(4) = 279.14
So the population will be approximately 279 lions in 4 years.
3. The exponential function for all three years is the same as in part 1:
P(t) = 325(0.95)^t
The angle of depression from the window of a building to a parked car is 38°. If the car is parked 320 feet away from the base of the building, what is the distance between the window and the car to the nearest tenth?
Answer:
Set your calculator to degree mode.
Please sketch the figure to confirm my answer.
cos(38°) = 320/d
d•cos(38°) = 320
d = 320/cos(38°) = 406.1 feet
algebra pls helpppppppppp
The correct answers are:
They are inverses of one another
They are symmetric over the line y=x
What is exponential form?When a number is too big or too little, exponential notation can express it as a single number and 10 increased to the power of the appropriate exponent.
The exponential form [tex]y=5^x[/tex]
The logarithmic form [tex]y = log_5\ x[/tex] are inverse functions of each other.
If we [tex]y = 5^x[/tex], then [tex]x = log_5\ y[/tex].
As long as x is a real number and y is positive, this is true for any value of x and y.
The graphs of [tex]y = 5^x[/tex] and [tex]y = log_5\ x[/tex] are symmetric over the line y = x.
We obtain the other graph by reflecting the first graph across this line.
Over the line y = x, the inverse functions are always symmetric.
If we swap the x and y coordinates of any point on one graph, we get a comparable position on the other graph.
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For positive acute angles A and B, it is known that tanA= 4/3 and sinB= 53/28 . Find the value of sin(A−B) in simplest form.
The value of sin(A-B) is 2334/6625
What is trigonometric identity?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Example of trigonometric identity include;
cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.
1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ
1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ
Sin(A-B) = = sin A cos B- cos Asin B
if tan A = 4/3, then 4 is the opp and 3 is the adj,
hyp² = 4²+3²
= 16+9
hyp² = 25
hyp = √25
= 5
cos A = 3/5 and sinA = 4/5
if sinB = 28/53, then opp is 28 is the opp and 53 is the hyp
adj = √ 53²-28²
adj = √ 2809 - 784
adj = √2025
adj = 45
cos B = 45/58
sin(A-B) = 4/5 × 45/58 - 3/5× 28/53
= 18/29 - 84/265
= (4770-2436)/6625
= 2334/6625
therefore the value of sin(A-B) = 2334/6625
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1. The rectangle shown is dilated by a scale factor of 3. (a) Calculate the length of each side of the dilated image. (b) Draw the new image and label it .
According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.
How to calculate the length of each side of the dilated image?To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:
8 / 3 = 2.6615 / 3 = 5According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.
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A sphere is pictured below. Select the type of cross section formed when the figure is cut by a horizontal plane.
A) circle
B) triangle
C) hexagon
D) rectangle
Answer:
A) circle.
When a sphere is cut by a horizontal plane, the resulting cross section is a circle. This is because a sphere is a three-dimensional object that is perfectly symmetrical in all directions, so any plane that intersects it will create a circular cross section.
Answer:
the answer is A) circle.The data set shown below represents the distribution of daily high temperatures in a city for 8 days.
79
,
73
,
72
,
70
,
72
,
66
,
81
,
75
79, 73, 72, 70, 72, 66, 81, 75
What is the median high daily temperature, in degrees Fahrenheit, in the city?
For the given data set of temperatures, the median temperature is 72.5 degree Fahrenheit.
In order to find the median temperature, we first need to arrange the temperatures in order from lowest to highest:
The temperatures arranged in order is : {66, 70, 72, 72, 73, 75, 79, 81}
There are 8 temperatures in total, which is an even-number, so the median will be the average of fourth and fifth day temperature.
In this case, the temperature of the fourth day is 72, and fifth day is 73,
The average will be = (72+73)/2 = 72.5,
Therefore, the median high daily temperature in the city is 72.5 degrees Fahrenheit.
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The given question is incomplete, the complete question is
The data set shown below represents the distribution of daily high temperatures in a city for 8 days.
79,73,72,70,72,66,81,75.
What is the median high daily temperature, in degrees Fahrenheit, in the city?
Write null and alternative hypothesis, test statics, p-value, and inference.
For Climate Change Beliefs, use variables: climate change and certainty.
For Class time use, use variables: income class, and sleeping.
The value of null and alternative hypothesis are change beliefs and certainty test statics, p-value, and inference are the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.
Climate Change Beliefs:
Null Hypothesis (H0): There is no significant relationship between climate change beliefs and certainty.
Alternative Hypothesis (Ha): There is a significant relationship between climate change beliefs and certainty.
Test Statistic: Pearson's correlation coefficient (r)
The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, we will use it to determine the relationship between climate change beliefs and certainty.
P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.
Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between climate change beliefs and certainty. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.
Class Time Use:
Null Hypothesis (H0): There is no significant relationship between class time use, income class, and sleeping.
Alternative Hypothesis (Ha): There is a significant relationship between class time use, income class, and sleeping.
Test Statistic: Multiple regression analysis
Multiple regression analysis is used to determine the relationship between a dependent variable and two or more independent variables. In this case, class time use, income class, and sleeping will be the independent variables, and we will use it to determine the relationship with the dependent variable.
P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.
Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between class time use, income class, and sleeping.
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Consider the following. Circle: x = h + r cos(theta), y = k + r sin(theta) Use the above to find a set of parametric equations for the conic. Circle: center: (−2, −3); radius: 6
Answer:
Step-by-step explanation:
The standard parametric equations for a circle with center (h, k) and radius r are:
x = h + r cos(theta)
y = k + r sin(theta)
Here, center is (−2, −3) and the radius is 6. Therefore, we have:
h = -2
k = -3
r = 6
Substituting these values into the standard equations, we get:
x = -2 + 6 cos(theta)
y = -3 + 6 sin(theta)
So the set of parametric equations for the circle is:
x(t) = -2 + 6 cos(t)
y(t) = -3 + 6 sin(t)
where t = theta.
PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT
A formula for y in terms of x and c is y = c⁵√x
How to determine the expressionIn inverse variation, as the value of one of the variables increases, the value of the other decreases and as the value of one of the variable decreases, the other increases.
From the information given, we have that;
y ∝1/√x
Now, let's find the constant value, k, we have;
y√x = k
We have that their values are;
y = c⁴, x = c²
Substitute the values, we have;
c⁴√c² = k
k = c⁵
Now, substitute the values
y = k√x
y = c⁵√x
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in the diagram below A, B, C are points in the same horizontal plane with AC =BC=22.3 meters.AD is a vertical tower which is anchored at B and C.The angle of elevation of D from B is 25.4. BDC=58.6 and ACB= 50.8.
The length of AB is 27.3m and AD is 113 m.
Using Trigonometry in Triangle ABC
tan 50. 8 = P / B
tan 50.8 = AB / 22.3
1.2261 = AB/ 22.3
AB = 27.34 m
Now, again using Trigonometry
tan 25.4 = P / B
tan 50.8 = AD / 27.34
0.474 = AD/ 27.34
AD = 12.95916 m
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1. Find the mean absolute deviation of this set of data. I 11, 20, 38, 5, 4 Data Mean Difference Sum Mean Absolute Deviation SUGRE Absolute Value
mean = 11+20+38+5+4/5 = 78/5 = 15.6
Find the value of m + n + 22 if m is 34 and n is 47.
if 3x+2y=36 and (5y)/(3x)=5, what is the value of x+y?
Answer:
16
Step-by-step explanation:
5y/3x = 5
3x = 5y/5
3x = y
3x + 2y = 36
y + 2y = 36
3y = 36
y = 36/3
y = 12
3x = y
3x = 12
x = 12/3
x = 4
x + y
= 4 + 12
= 16
x + y = 16
The graph shows the total weight of a fish tank, y, as a function of the amount of water in the tank, x
What is the weight of an empty tank?
The weight of the empty tank is given as follows:
4 pounds.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The weight of the empty tank is the intercept of the function, which is of b = 4, hence:
4 pounds.
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Solve the system of equations
x+y=15
Y=x^(2)-5
(-5,20) and (4,11)
(3,4) and (7,8)
(5,10) and (-4,19)
(5,20) and (4,11)
Answer:
(a) (-5,20) and (4,11)
Step-by-step explanation:
You want the solutions to the system of equations ...
x + y = 15y = x² - 5SubstitutionUsing the second equation to substitute for y in the firs equation, we have ...
x +x² -5 = 15
x² +x -20 = 0 . . . . . subtract 15, put in standard form
(x +5)(x -4) = 0 . . . . . factor
Zero product ruleA product is zero only when one or more factors is zero. The values of x that make the factors zero are ...
x = -5 and x = 4
The corresponding values of y are ...
y = 15 -x
y = 15 -{-5, 4} = {20, 11}
The solutions are (x, y) = (-5, 20) and (4, 11).
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer: X = 25
Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25
Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.
Which function is represented by the graph?
A f(x) = -12x + 6f(x) = - 1 2 x + 6
B f(x) = 12x + 6f(x) = 1 2 x + 6
C f(x) = -2x + 6f(x) = -2x + 6
D f(x) = 2x + 6
Answer:
B
Step-by-step explanation:
Notice that all y-intercepts are the same (doesn't give a clue to the answer).
The line has a downward slant as you move from left to right, so the slope is negative (eliminating A & C as answers).
Determine the actual slope by identifying the y-intercept and x-intercept, and calculate Rise over Run:
Rise = -6 (goes from +6 to 0)
Run = +12
-6/12 = -1/2
Write the following Babylonian numeral as a Hindu-Arabic numeral.
<|| <<||||
Answer:
The Babylonian numeral <|| <<|||| represents the number 51 in the Babylonian numeral system.
To convert it to the Hindu-Arabic numeral system, we first need to determine the place values of the symbols. The symbol <|| represents 50 and <<|||| represents 1.
So, we can write the number as:
50 + 1 = 51
Therefore, the Hindu-Arabic numeral equivalent of the Babylonian numeral <|| <<|||| is 51.
25 POINTS
Which is the BEST definition of dilation?
A: a transformation that either reduces or enlarges an object in the coordinate plane
B: a transformation that spins an object in the coordinate plane
C: a transformation that either slides or shifts an object in the coordinate plane
D: a transformation that flips an object in the coordinate plane
Answer: A
Step-by-step explanation:
A dilation is not a rigid transformation, which means it has to scale the object into a different measure. So, enlarging or reducing the size of an object is a dilation.
Olivia Jackie. Play? The game with the spinner Olivia's funny 2 out of 12 out of fift. Do you watch Jackie's fun 2 on 19 of a 100? Find each experimental probability of spinning a 2.
The experimental probability of spinning a 2 on Olivia's spinner is 0.1667.
The experimental probability of spinning a 2 on Jackie's spinner is 0.02 or 2%.
Olivia and Jackie are playing a game with a spinner. Olivia's spinner has 12 equal sections, two of which are marked as "funny 2". Jackie's spinner has 100 equal sections, and two of them are marked as "fun 2".
To find the experimental probability of spinning a 2 in Olivia's spinner, we first need to determine the total number of possible outcomes, which is the number of sections on the spinner. In this case, the spinner has 12 sections. Out of these, two sections are marked as "funny 2". Therefore, the number of favorable outcomes is 2.
Experimental probability of spinning a 2 in Olivia's spinner can be calculated as Experimental probability = Number of favorable outcomes / Total number of possible outcomes
= 2 / 12
= 1 / 6
= 0.1667
Therefore, the experimental probability of spinning a 2 on Olivia's spinner is 0.1667.
To find the experimental probability of spinning a 2 in Jackie's spinner, the total number of possible outcomes is the number of sections on the spinner, which is 100. Out of these, two sections are marked as "fun 2". Therefore, the number of favorable outcomes is 2.
Experimental probability of spinning a 2 in Jackie's spinner can be calculated as Experimental probability = Number of favorable outcomes / Total number of possible outcomes
= 2 / 100
= 0.02
Therefore, the experimental probability of spinning a 2 on Jackie's spinner is 0.02 or 2%.
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Drag tiles to fill in the blanks for o complete the experience that could be used to predict the number of possible outcomes
The first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners
How to explain the probabilitySuppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
= n(E) / n+S)
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Thus, the first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners
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Drag tiles to fill in the blanks to complete the expression that could be used to predict the number of winners of a game. Tiles may be used once or not at all. A)Total Number of Possible Outcomes B)Number of Winners C)Number of Unfavorable Outcomes D)Number of Games P(event) = Number of Favorable Outcomes _________________________ ????????????????????????????? = ????????????????????????????? _________________________ 11 Total Number of Contestants
Place the indicated product in the proper location on the grid.
a²b(3a² +4ab²)
The simplified expression based on tej values given is 3a⁴b + 4a³b³.
How to solve the expressionAn expression is a combination of variables, constants, and operators that can be evaluated to produce a single value. In programming languages, expressions are used to represent computations and are often used to assign values to variables, compare values, or perform mathematical operations. Expressions can be simple, such as a single variable or constant, or complex, involving multiple operations and variables.
It should be noted that to simplify the expression a²b(3a² +4ab²), we can distribute the a²b term to the terms inside the parentheses using the distributive property of multiplication:
a²b(3a² +4ab²) = 3a⁴b + 4a³b³
Therefore, the simplified expression is 3a⁴b + 4a³b³.
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please help, will give brainiest!
Answer:
See explanation.
Step-by-step explanation:
Let's analyze each solution to determine if it's viable or non-viable based on the given constraints: Johnnie and Amy have $38.50, and they cannot buy more than 7 lunches.
1. 8 slices of pizza and 0 hamburgers
This solution is non-viable because they are not allowed to buy more than 7 lunches. In this case, they would be buying 8 lunches.
2. 5 slices of pizza and 2 hamburgers
Cost: 5×4.75+2×5.55=23.75+11.10=34.85
This solution is viable because the total cost is within their budget, and they are buying 7 lunches.
3. 4 slices of pizza and 3 hamburgers
Cost: 4×4.75+3×5.55=19.00+16.65=35.65
This solution is viable because the total cost is within their budget, and they are buying 7 lunches.
4. 3 slices of pizza and 2 hamburgers
Cost: 3×4.75+2×5.55=14.25+11.10=25.35
This solution is non-viable because they are only buying 5 lunches, which is less than the maximum allowed. But if it is acceptable to only buy below 7 lunches, then this solution can be viable.
5. 2 slices of pizza and 6 hamburgers
Cost: 2×4.75+6×5.55=9.50+33.30=42.80
This solution is non-viable because the total cost exceeds their budget.
6. 0 slices of pizza and 7 hamburgers
Cost: 7×5.55=38.85
This solution is non-viable because the total cost exceeds their budget.
In conclusion, the viable solutions are:
5 slices of pizza and 2 hamburgers
4 slices of pizza and 3 hamburgers
Possible in being viable:
3 slices of pizza and 2 hamburgers
how do you do comparison for percents
In order to do a comparison for percents, you must convert them to decimal form and then juxtapose the decimal values side by side to see which is greater or less.
What are percents?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent sign is commonly used, however the acronyms pct., pct, and sometimes pc are also used. A % is a number with no dimensions; it has no unit of measurement.
To calculate the percentage, divide the amount by the total value and multiply the result by 100.
Divide a percentage by 100 to get a decimal. So 25% is equal to 25/100, or 0.25. Multiply a decimal by 100 (simply shift the decimal point two places to the right) to convert it to a percentage. For example, 0.065 equals 6.5% and 3.75 equals 375%.
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Malachi asks students in his class, "How long does it take you to get to school?" The histogram
shows the data.
Which statement best describes the distribution?
Answer:
The distribution is symmetric
Step-by-step explanation:
Because in both sides it has the same structure, so that means that the value is the same in both sides
An animal shelter has 96 animals if 5/8 of the animals are dogs and 1/4 of the animals are cats how many animals are neither dogs nor cats?
There are 12 animals that are neither dogs nor cats.
How many animals are neither dogs nor cats?If 5/8 of the animals are dogs, then the remaining 3/8 of the animals are not dogs.
3/8 x 96 = 36
if 1/4 of the animals are cats, then the remaining 3/4 of the animals are not cats.
3/4 x 96 = 72
The number of animals that are neither dogs nor cats is calculated as;
96 - 36 - 72 = 12
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given that ab is the diameter of a circle o find the missing angle and arc measures show your work look at the photo of the circle
The given angles are:
M arc CB=64°,M<AOC= 116° ,M arc AD=26°,M arc DFB=154°,M<CDB=32°.
How to solve thisFirst, we use the property that the measure of a central angle is equal to the measure of the intercepted arc.
Given that <COB = 64°, we know that the measure of arc CB is also 64°.
Next, we use the fact that the measure of an angle made on the circumference is half the measure of the angle made at the center.
We know that the measure of intercepted arc AD is 26°, and since the angle made at the center, <ABD, is 13°, we can calculate that the measure of arc AD is 2 x 13° = 26°.
Using the fact that a semicircle has a measure of 180°, we know that the measure of arc DFB is 180° - 26° = 154°.
Finally, we can use the angle CDB to find the missing angle.
We know that <CDB is an angle made on the circumference and that the measure of arc CB is 64°.
Thus, we can calculate that <CDB = 64°/2 = 32°.
Therefore, the missing angle is 32°.
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-2(-2/3) x 3/5
Write in simplest form .
Answer:
4/5
Step-by-step explanation:
please help me
What degree of rotation about the origin will cause the triangle below to map
onto itself?
