One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.
We can write a system of inequalities to represent the situation as follows:
6x + 5y ≥ 90 (because Cameron must spend at least $90 on drinks and candies)
x + y ≥ 18 (because Cameron must buy at least 18 drinks and candies altogether)
x ≥ 0, y ≥ 0 (because Cameron can't buy negative number of drinks or candies)
To graphically represent the solution set of this system, we can plot the inequalities on a coordinate plane. We can start by drawing the line representing the first inequality: 6x + 5y = 90. To find the slope-intercept form of this equation we can subtract 90 from both sides, 6x + 5y - 90 = 0, and we get: 6x + 5y = 90.
The second inequality is x + y ≥ 18 which is a boundary line.
The third inequality is x ≥ 0 and y ≥ 0 which means that both x and y should be non-negative.
The solution set of this system of inequalities is the intersection of the half-planes defined by the inequalities. This is the set of all points that lie in all three half-planes. One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.
Therefore, One possible solution is to have Cameron buying 18 candies and 6 drinks, this solution is (6,18) and it lies in the intersection of all three half-planes.
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Find the orthogonal projection of y onto u. Y= [8 -24], u=[4 -2] A. [4 -2] B. [16 -8] C. [1 1/2] D. [16 -2]
According to the given vector, the value of the orthogonal projection of y onto u is <16, -8>
Here we have the vector values that is as follows:
Y= [8 -24],
u=[4 -2]
Now, based on the formula of the vector projection is written as,
=> [(y x u) / |u²| ] x u
Now, we have to calculate the value of the vector and it can be obtained by what we need to do is multiply the corresponding coordinates and then add up the results:
=> ⟨8,−24⟩⋅⟨4,−2⟩
=> (8)⋅(4)+(−24)⋅(−2)
When we simplify this one then we get the value as,
=>80.⟨8,−24⟩⋅⟨4,−2⟩
=> (8)⋅(4)+(−24)⋅(−2) = 80.
Similarly, now we have to calculate the value of |u²| is written as,
Here we have the sum of squares of the absolute values of the coordinates is
=> ∣4∣² + ∣−2∣² = 20.
Therefore, the magnitude of the vector is
=> √20 = 2√5
Thus the vector projection is written as,
=> [tex]\frac{8}{2\sqrt{5} }\times < 4,-2 >[/tex]
When we simplify this one then we get the resulting value of projection as <16, -8>
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triangle def was dilated according to the rule do,one-third(x,y)(one-third x, one-third y) to create similar triangle d'e'f'. on a coordinate plane, (0, 0) is the center of dilation. triangle f d e is dilated to create smaller triangle f prime d prime e prime. triangle f d e has points (negative 9, 3), (negative 9, 9), (negative 6, 6). triangle f prime d prime e prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).which statements are true? select three opt
The statements that are true about the triangle f d e and its dilated counterpart f' d' e' are: (1) The center of dilation was (0, 0). (2) The coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). (3) f' d' e' is a similar triangle to f d e.
The triangle f d e and its dilated counterpart f' d' e' have specific properties that make them similar triangles. The center of dilation for the transformation was (0, 0). This means that the distance from the center of dilation to each point before and after the dilation was the same. The coordinates of triangle f d e were (negative 9, 3), (negative 9, 9), and (negative 6, 6). In order to obtain the coordinates of f' d' e', the dilation rule one-third(x,y) (one-third x, one-third y) was used. This means that the x and y coordinates of each point were divided by three. The result is that the new coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). These new coordinates demonstrate that the triangle f d e and its dilated counterpart f' d' e' are similar triangles.
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Answer:
A. ∠F corresponds to ∠F'.
C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.
E. △DEF ~△D'E'F'
Step-by-step explanation:
got it right on edge 23
HELP ASAP FOR BRAINLIEST
Answer:
First brand: 98 gallons
Second brand: 42 gallons
Step-by-step explanation:
x + y = 140
.4x + .9y = .55*140
x=140-y
.4(140-y) + .9y = 77
56 - .4y + .9y = 77
.5y = 21
y = 42
x + 42 = 140
x = 98
If you are asked to find the 85th percentile, you are being asked to find _____.
Choose the correct answer below.
A.an area corresponding to a z-score of minus 0.85
B.a data value associated with an area of 0.85 to its left
C.a data value associated with an area of 0.85 to its right
D.an area corresponding to a z-score of 0.8
If you are asked to find the 85th percentile, you are being asked to find an area corresponding to a z-score of 0.8.
The term percentile in math is defined as the area to the left of a particular data value.
According to the definition of percentile, here they are asking about the 85th percentile.
As we all know that z-score is not an area under the normal curve and the distances along the horizontal axis are represented by z-scores where as the regions under the curve are represented by areas.
Therefore, in order to find the z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.
Then we have to convert the given percent into decimal form, then we get it as,
=> 85% = 0.85
Here we need to find the value from the z table then we get the resulting value as 0.8.
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a map of the town that hannah lives in can be represented by the cartesian plane. hannah starts off at $(-4, 9)$ and walks $10$ units to the left and $7$ units down to get to her new location. along what line could she have walked to get to the new location directly from her old location? express your answer in the form $ax by
The answer in the form of x,y is -7x + 10y = 118.
A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.
from given conditions, we get,
(-4, 9) and 10 left 7 down puts her at ( -4 - 10 , 9 - 7) = ( -14, 2)
So, the points ( -4, 9) and (-14,2) are on the line
Slope of this line = [ 2 - 9] / [ -14 - -4 ] = [ -7] / [ -10] = 7/10
Equation of the line
y = (7/10)(x - - 4) + 9
y = (7/10) ( x + 4) + 9 multiply through by 10
10y = 7 (x + 4) + 90
10y = 7x + 28 + 90
-7x + 10y = 118
Therefore, the answer in the form of (x , y) is -7x + 10y = 118
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Jan 27, 1:02:50 AM
?
If f(x) = 4x^3+ 1, then what is the remainder when f(x) is divided by - 5?
To obtain the remainder, we just divide the number by another number with its multiples, and we get -19.
What is remainder?The "leftover" amount from a calculation is referred to as the "remainder" in mathematics. When dividing two integers to create an integer quotient, the residual is the integer that is "left over." The amount that remains after division is known as the Remainder. The result of division is a value if a number (dividend) cannot be divided entirely by another number (divisor).The remainder is what is known as this amount. 10 cannot be divided by 3 perfectly, for instance.It might either be higher or lower than the quotient. For instance, the remaining is six when the number seven is divided by 41, leaving five as the quotient.f(x) = 4X x 3 + 1,
f(-5) = 4(-5) x + 1
f(-5) = -20 + 1
f(-5) = -19.
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Two questions, see attachment
Answer:
12. <4 = 100°
Step-by-step explanation:
For number 12. angle m<2 is a corresponding angle to angle m<6 . So the equations, (3x+20) and (5x-20) are equal to each other.
So lets set them equal to each other:
(3x+20) = (5x-20)
40 = 2x
x = 20
Now we need to plug in the value of x into the equation of angle m<2, to find its angle.
(3x+20) = ?
(3(20)+20) = ?
= 80 degrees
m<2 = 80 degrees
We need to find <4
Since <4 and <2 share the same line and are supplementary angles (they add up to 180) we can subtract the value of <2 from 180 to find <4
180 - 80 = 100
So <4 is 100 degrees.
Sam left $4.50 as a tip for the waiter this was 18% of the bill before the tip.how much was her total bill before the tip
Answer:
.18B = 4.5
B = 4.5/.18 = 450/18 = 50/2 = $25 bill
please help me answer this ty :)
Part B
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
How is the volume of the stack affected? Explain your reasoning
The volume of the stack affected will be 10,825.38 cubic millimeters.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
The radius of the cylinder is given as,
r = 19.05 / 2
r = 9.525 mm
Then the volume of the cylinder is calculated as,
V = π x (9.525)² x 38
V = 3.14 x 90.725 x 38
V = 10,825.38 mm³
The volume of the stack affected will be 10,825.38 cubic millimeters.
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Answer:
The volume of the stack affected will be 10,825.38 cubic millimeters.
Step-by-step explanation:
Can I please get help.
The data that is considered univariate and quantitative is Shoe size, Salary, Years of experience, Height.
What is univariate quantitative data?
Univariate quantitative data refers to a type of data that consists of only one variable and the values of that variable are numerical. This means that the data represents a single measurement or characteristic, and the values can be quantified and compared using mathematical operations. Examples of univariate quantitative data include height, weight, temperature, salary, and years of experience.
Shoe size, Salary, Height, Years of experience are considered univariate and quantitative data.Shoe size is a univariate data because it only has one variable which is the size of the shoe. It is quantitative because the data can be measured in numbers.Salary is a univariate data because it only has one variable which is the amount of money earned. It is quantitative because the data can be measured in numbers.Height is a univariate data because it only has one variable which is the height of an individual. It is quantitative because the data can be measured in numbers.Years of experience is a univariate data because it only has one variable which is the amount of time an individual has worked in their profession. It is quantitative because the data can be measured in numbers.Salary and years of experience, Sports played in high school, Favorite color and age, and Favorite color are not considered univariate and quantitative data. They contain more than one variable and some of the variables are qualitative and cannot be measured in numbers.To learn more about univariate quantitative data refers to:
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11 is 25% of what number?
Answer:
44 is your answer
Step-by-step explanation:
Find the area of an octagon ABCDEFGH having each side equal to 5 cm,HC=11 cm and AP⊥HC such that AP=4 cm.
The area of the octagon ABCDEFGH is 119 cm².
The figure is attached below for reference.
AP = 4 cm
HC = CD = 11 cm
Area of trapezium ABCH = Area of trapezium GDEF
Now, Area of a trapezium = [tex]\frac{1}{2} (a+b)h[/tex]
Area of trapezium ABCH = Area of trapezium GDEF = [tex]\frac{1}{2} (5+11)4 = 32[/tex] cm².
So, Area of trapezium GDEF = 32 cm².
Area of rectangle MCDG = l x b = 11 x 5 = 55 cm²
Area of the Octagon ABCDEFGH = Area of the two trapeziums + Area of the rectangle
= (2 x 32) + 55 = 119 cm².
Hence, the area of the octagon ABCDEFGH is 119 cm².
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select all the examples of exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Answer:
Select all the examples of the exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
What are the 9 characteristics of system?
The 9 characteristics of system are Inputs, Outputs, Processes, Control, Interface, Storage, Feedback, Boundaries, and Environment.
1. Inputs: This is data received from external sources, such as user input, sensors, or other systems. This data is used to initiate the system's operations and can include commands, parameters, and other information.
2. Outputs: This is the result of the system's operations, such as responding to user input or displaying results. Outputs can be in the form of data, reports, or graphical displays.
3. Processes: This is how data is transformed from inputs into outputs. Processes may involve calculations, sorting, or other operations.
4. Control: This is how the system's operations are managed. It can include scheduling, sequencing, and coordinating processes.
5. Interface: This is how the system interacts with its environment. This includes receiving inputs, producing outputs, and communicating with other systems.
6. Storage: This is where data is stored for later use. This can include databases, files, and other types of storage.
7. Feedback: This is how the system monitors its performance and adjusts accordingly. This can include error checking, logging, and analyzing data.
8. Boundaries: This is how the system's scope is defined. It can include limiting the system's access to certain data or operations.
9. Environment: This is the external conditions in which the system operates. This includes the hardware, software, and other systems the system interacts with.
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What are the values of the constants in the vertex form of the quadratic equation that models the bird's path? with answers.
h = 0
k = 20
a = -0.12
next question
which system of equations could you use to determine where the paths intersect? b.
y = 0.8x and y = -0.12x2 + 20
The point of intersection of the bird's paths can be found by setting up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20 and solving for x. The x-coordinate of the point of intersection is approximately 3.33.
y = 0.8x
and
y = -0.12x2 + 20
First, set the two equations equal to each other:
0.8x = -0.12x2 + 20
Next, subtract 20 from both sides of the equation:
0.8x = -0.12x2
Then, divide both sides by 0.8:
x = -0.15x2
Finally, solve for x by dividing both sides by -0.15:
x = 10/3 or x ≈ 3.33
To find the point of intersection of the bird's paths, we can set up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20. We then set the two equations equal to each other and solve for x. Subtracting 20 from both sides of the equation, we get 0.8x = -0.12x2. We then divide both sides of the equation by 0.8, giving us x = -0.15x2. Finally, by dividing both sides of the equation by -0.15, we can solve for x to find the point of intersection, which turns out to be x = 10/3 or approximately 3.33. In other words, the paths intersect at a point with a x-coordinate of approximately 3.33.
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Find the margin of error for the given values of c, s, and n. c = 0.98, s = 3.3, n = 22 Click the icon to view the t-distribution table. The margin of error is . (Round to one decimal place as needed.)
The margin of error is 1.6393 for the supplied values of c, s, and n, which are 0.98, 3.3 and 22respectively.
what is margin ?
Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.
Given that,
standard deviation = s = 3.3
z is the 98% = z score = 2.33
Sample size = n =22
Margin of error is expressed using the formula;
M = z * √s²/n
M = 2.33* √3.3²/22
M = 2.33* 0.7035
M = 1.6393
Therefore, the margin of error is 1.6393 for the supplied values of c, s, and n, which are 0.98, 3.3 and 22respectively.
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Jamal invests money in an account paying a simple interest of 7% per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?
Jamal should multiply his current balance by 1.07 to find his total balance in one year.
What should he multiply his current balance by to find his total balance in a year in one step?
Simple interest is a method of calculating the interest on a loan or deposit where the interest is based solely on the principal (original) amount of the loan or deposit.
To find the total balance in one year, Jamal needs to multiply his current balance by (1+ the interest rate).
Since the interest rate is 7%, the interest rate in decimal form is 0.07
Therefore, he needs to multiply his current balance by (1+0.07) = 1.07
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Write an equation relating the total amount in a in Terry’s account to the number of years,t. Is the relationship proportional?Explain
An equation relating the total amount in a in Terry’s account to the number of years, t is A = P + P*(r/100)*t. Yes, the relationship is proportional.
what is an equation?An equation is a well-formed formula that connects two expressions with the equals sign to express the equality of those two expressions. For example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
An equation relating the total amount in a in Terry’s account to the number of years, t is A = P + P*(r/100)*t.
Where, A is total amount,
P is amount which Terry deposit,
r is rate of interest,
and t is number of years.
Yes, the relationship is proportional.
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Pretty please someone answer this! Based on the graph shown, which of the following statements is true?
For the graph of data given option C: The median 300 is the middle number is correct.
What is median?
In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.
Draw the median table for the graph of values given -
Number Frequency ∑f
100 14 14
200 6 20
300 18 38
400 12 50
500 2 52
600 12 64
700 8 72
The formula for median is -
Median = [n/2 + (n/2 + 1)] / 2
Median = [72/2 + (72/2 + 1)] / 2
Median = [36 + (36 + 1)] / 2
Median = 73/2
Median = 36.5
According to the table the ∑f value 36.5 corresponds to 300.
Therefore, the median 300 is the middle number.
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Find the complex conjugates for each of the following numbers: a. - 19 = Preview b. -25i = Preview c. - 11 - 92i = Preview d. 413i - 37 Preview
The complex conjugates for each of the following numbers
a. - 19 = -19
b. -25i = +25i
c. - 11 - 92i = 11 + 92i
d. 413i - 37 = -413i - 37
The term complex number in math is defined as the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number.
Here we have given that the list of complex number and here we need to find the complex conjugates for each of the following numbers:
As we all know that conjugate in Mathematics is formed by changing the sign of one of the terms in a binomial.
Based on the definition, here we have the general form a + bi as the conjugate as a - bi.
From this one we have identified that here we have only changed the sign of imaginary pat.
So, the complex conjugate of the given complex numbers are written as
=> a. - 19 = -19
Here we have only the number part so the sign remains constant
b. -25i = +25i
Here we have only the imaginary part so we have changed it to positive.
c. - 11 - 92i = 11 + 92i
Based on the complex conjugate rule the term must be changed.
d. 413i - 37 = -413i - 37
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Homework Help please for Algebra, the math problem is in the picture below
The difference quotient of quadratic equation f(x) = 5 · x² - 5 · x - 6 is equal to r = 10 · x + 5 · h.
How to find the difference quotient of a quadratic equation
Herein we have the quadratic equation f(x) = 5 · x² - 5 · x - 6, from which we must determine the difference quotient, defined below as:
r = [f(x + h) - f(x)] / h
Where:
h - Differencef(x) - Function evaluated at x.f(x + h) - Function evaluated at x + h.First, substitute on each component of numerator of difference quotient:
f(x) = 5 · x² - 5 · x - 6
f(x + h) = 5 · (x + h)² - 5 · (x + h) - 6
f(x + h) = 5 · (x² + 2 · h · x + h²) - 5 · (x + h) - 6
f(x + h) = 5 · x² + (10 · h + 5) · x + (5 · h² - 6)
Second, substitute on difference quotient:
r = [f(x + h) - f(x)] / h
r = [[5 · x² + (10 · h + 5) · x + (5 · h² - 6)] - (5 · x² - 5 · x - 6)] / h
r = (10 · h · x + 5 · h²) / h
r = 10 · x + 5 · h
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Determine the equation of the line in the form y=mx+b that is PARALLEL to each line and passes through the given point.
x=0 passing through (4,5)
The equation of the line that passes through (4, 5) and is parallel to x = 0 is expressed as: x = 4.
What is the Equation of Two Vertical Lines that are Parallel to each other?Two vertical lines that are parallel to each other have a slope that is undefined because it has no y-intercept and the denominator in the slope formula is zero when calculated.
The equation of a vertical line is expressed as x = b, where b is where the line crosses the x-axis.
Given the equation of a line has x = 0, it means it is a vertical line, therefore, its slope is undefined.
Therefore, the line that is parallel to x = 0 will be undefined. Since the line passes through the point (4, 5), the equation of the line will be written by substituting b = 4 into x = b:
x = 4.
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An amount of $1,000 is deposited into a bank account that pays 4% annual interest. What would be the bank account balance after 5 years? Use A= P (1 + r/n)nt
The account balance in the bank after 5 years is $1,216.65.
How to solve compound interest questions?An amount of $1,000 is deposited into a bank account that pays 4% annual interest. The amount in the bank account after 5 years can be calculated as follows:
Therefore,
[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where
p = principalr = raten = number of timest = timeTherefore,
p = 1000 dollars
4 = 4 % = 4 / 100 = 0.04
t = 5 years
n = 1
Therefore,
A = 1000(1 + 0.04/1)¹ˣ⁵
A = 1,000(1 + 0.04)⁵
Therefore,
A = $1,216.65
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The average of the first 3 weights was 20 pounds. the average of the next twelve was 25 pounds. what was the overall average of the weights
The requried average weight of 15 weights is given as 24 pounds.
What is average?The average of the values is the ratio of the total sum of values to the number of values.
Here,
The average of the first 3 weights was 20 pounds. the average of the next twelve was 25 pounds.
overall average = total weight of 3 + total weight of 12 / [3 + 12]
overall average = 360 / 15 = 24 pounds
Thus, the requried average weight of 15 weights is given as 24 pounds.
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answer please i need it soon
a. Use what you’ve learned in this unit to model the population of Western Lowland Gorillas after 5, 10 and 20 years. Let y equal the population of the gorillas and x represent the number of years since 2022. Show your work.
b. Use the information calculated in Step A to create a table showing the Gorilla population after 5, 10 and 20 years.
c. Explain why the table shows exponential decay. Summarize how scientists can use exponential decay to predict population changes in endangered species. Summarize your answer in 1-2 paragraphs.
Answer:
Step-by-step explanation:
a. To model the population of Western Lowland Gorillas after 5, 10 and 20 years, we can use an exponential decay model. This model assumes that the population of the gorillas is decreasing at a constant rate over time.
Let y equal the population of the gorillas and x represent the number of years since 2022.
The exponential decay model is represented by the equation:
y = a*e^(-rt)
Where a is the initial population, r is the decay rate and t is the number of years.
If we assume that the initial population of gorillas in 2022 is 1000, the decay rate is 0.1, and we can calculate the population of gorillas after 5, 10, and 20 years.
For 5 years after 2022:
y = 1000e^(-0.15) = 810 gorillas
For 10 years after 2022:
y = 1000e^(-0.110) = 648 gorillas
For 20 years after 2022:
y = 1000e^(-0.120) = 404 gorillas
b. Table:
Years Gorilla Population
5 810
10 648
20 404
c. The table shows that the population of gorillas is decreasing over time, which is an example of exponential decay. This decrease is consistent with the exponential decay model which we used. Exponential decay models are often used to predict population changes in endangered species as they assume a constant rate of decrease in population. Scientists can use this model to predict future populations, as well as estimate the rate of population decline. Based on this information, conservation efforts can be better planned, and resources can be allocated more effectively to prevent the extinction of endangered species.
Suppose that Boris' blood pressure can be modeled by the following function.
p(t)=85+18 sin (73mt)
Boris' blood pressure increases each time his heart beats, and it decreases as his heart rests in between beats. In this equation, p (t) is the blood pressure in
mmHg (millimeters of mercury), and t is the time in minutes.
Find the following. If necessary, round to the nearest hundredth.
Answer:
Suppose that Boris' blood pressure can be modeled by the following function.
p(t)=85+18 sin (73mt)
Boris' blood pressure increases each time his heart beats, and it decreases as his heart rests in between beats. In this equation, p (t) is the blood pressure in
mmHg (millimeters of mercury), and t is the time in minutes.
Find the following. If necessary, round to the nearest hundredth.
a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. what is the combined square footage of the side and back yard?
a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. then 23625 is the combined square footage of the side and back yard
125*150 and 195*25
total 23625
The area covered with grass, in square feet, is the area of the shape of the yard.
What is the Area of a Yard?
The area of a yard can be calculated by determining the shape of the yard, and using the appropriate area formula of the shape to find the area of the yard.
Image of the yard is missing. However, assuming the yard is a rectangular shape with a dimension of 10 ft by 6 ft, therefore:
The square feet of grass Russell has = area of rectangle = (10)(6) = 60 ft²
In summary, the area covered with grass, in square feeet, is the area of the shape of the yard.
a property has a back yard 125 x 150 feet and a side yard of 195 x 25 feet. then 23625 is the combined square footage of the side and back yard
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Please, help me! I need help in this solve
Answer:
Step-by-step explanation:
15x² - 2x - 1 = 0
15x² - 5x + 3x - 1 = 0
5x(3x - 1) + 3x - 1 = 0
(5x + 1)(3x - 1) = 0
x = -1/5, 1/3
8x² - 10x - 3 = 0
8x² - 12x + 2x - 3 = 0
4x(2x - 3) + 2x - 3 = 0
(4x+1)(2x-3) = 0
x = -1/4 , 3/2
16x² - 8x + 3 = 0
This question has complex answers as the D = 64 - 192 < 0
So, ignore this question. It is wrong or it has complex answers.
Use the quadratic formula for it.
9x² - 6x - 2 = 0
This also needs the quadratic formula as the answer is in roots.
8x² - 2x - 3 = 0
8x² - 6x + 4x - 3 = 0
2x ( 4x - 3) + 4x - 3 = 0
(2x + 1)(4x-3) = 0
x = -1/2 , 3/4
Which two-dimensional shape is formed if a plane intersects the cylinder shown,
perpendicular to the base?
A) Circle
B) Square
C) Rectangle
D) Ellipse
Two -dimensional shape is formed if a plane intersects the cylinder shown, perpendicular to the base is a rectangle. Hence option C is the correct option.
What is the two-dimensional shape?
Plane figures are two-dimensional figures. Three-dimensional figures are solid shapes.
A cross-section is a shape formed by the intersection of a solid object and a plane. A three-dimensional shape's cross-section is a two-dimensional geometric shape.
Cross-Sectional Shapes
Cross-sections are classified into two types:
* Horizontal cross-sections and
* Vertical cross-sections.
The shape is a circle if the cylinder has a horizontal cross-section. If the plane of the cylinder's base is perpendicular to its base, the shape is a rectangle.
When the plane intersects the cylinder parallel to the base with a variable angle, an oval shape is formed.
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