C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4
Step-by-step explanation:Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0
Given function: x² - 5x + 4
⇒ a = 1, b = -5, c = 4
The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.
The vertex or minimum.
Step 1: Find the x-value of the vertex.
[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]
Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.
[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]
Vertex: (2.5, -2.25)
The x-intercepts (roots).
We can use the Quadratic Formula to find the roots of this function.
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]
Equation: x² - 5x + 4 = 0
⇒ a = 1, b = -5, c = 4
Step 1: Substitute the values of a, b, and c into the formula.
[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]
Step 2: Separate into two possible cases.
[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]
The x-intercepts of the given function are 1 and 4.
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What is the value of the expression below when w = 9 and x = 5?
10w + 4x
Answer:
110
Step-by-step explanation:
10w + 4x
10 (9) + 4 (5)
90 + 20
110
The answer is 110.
Hope it helps!
Have a nice day:)
-6-5
(-5-4)
(-2,2)
2-
4
--2-1₁
4-
2
4 9
(0, -3)
X
What is the equation of the line that is parallel to the
given line and passes through the point (-2, 2)?
Oy=x+4
Oy = x + ¹/2
Oy = -5x + 4
Oy=-5x + ¹2
The equation of the line that is parallel to the given line and passes through the point (-2,2) is:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are parallel, they have the same slope. In this problem, the given line passes through (-5,-4) and (0,-3), hence the slope is:
m = (-3 - (-4))/(0 - (-5)) = 1/5.
Hence the equation is:
[tex]y = \frac{x}{5} + b[/tex]
When x = -2, y = 2, then:
[tex]y = \frac{x}{5} + b[/tex]
[tex]2 = \frac{-2}{5} + b[/tex]
[tex]b = \frac{12}{5}[/tex]
Hence:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
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f(x) = (two-fifths) Superscript x
g(x) = (two-fifths) Superscript x – 3
Which statement about f(x) and its translation, g(x), is true?
The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Answer: The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
Answer:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
bc I said so
y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measure of two adjacent sides and the angle opposite to one of them. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. (Hint: Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.
The illustration to determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence is given below.
How to illustrate the information?Congruence of triangles means that two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In this case, these triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.
To illustrate the question, this will be:
Step 1: Draw a line segment AB
Step 2:Draw an acute angle (let's say 45° ) at A as AX
Step 3: From B draw an altitude on AX BY ⊥ AX
Step 4 Using suitable compass width and taking Y as center cut AX on both sides at C and D
Now BC = BD as BY is perpendicular bisector
Now compare ΔABC and ΔABD. Using suitable compass width and taking B as center cut AX at 2 points C & D directly so BC = BD.
This can illustrate that SSA is not a valid means for establishing triangle congruence.
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Answer:
Below is an example to show whether side-side-angle (SSA) is a legitimate method for proving triangle congruence. How should the information be illustrated? Triangle congruence refers to the property that two triangles are congruent if their three corresponding sides and their three corresponding angles are both equal in size. In this instance, the triangles can be moved around, rotated, flipped, and turned to have a same appearance. They are in alignment with one another when moved. This can serve as an example of why SSA cannot be used to prove triangle congruence.
Step-by-step explanation:
Problem
Solve for x in the image below.
18
Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Answer:
20.1246118
Step-by-step explanation:
hypotenus^2 - (leg1)^2 = (leg2) ^2
27^2-18^2 = (leg2)^2
729-324 = (leg2)^2
405 = (leg2)^2
20.1246118 = leg 2
What is the end behavior of the graph
Answer:
as x is approaching positive infinity, y approaches positive infinity
as x is approaching negative infinity, y is approaching negative infinity
what is the length of side AB of the triangle?
BC is 3 across & CA is 3 up, but this creates a right-angle triangle. So, Pythagoras Theorem is used to find AB
AB = root 3^2 + 3^2
AB = 3 root 2
or 4.242640687
Thus, AB is 4.24 to 2d.p
(root means square root)
Hope this helps!
describe fully the single transformation which maps triangle A onto triangle B.
The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)
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1. Find the product using Suitable Property a) 55×99
Answer:
5445
Step-by-step explanation:
We can use distributive property. a*(b - c) = (a*b) - (a *c)
99 = 100 - 1
55 * 99 = 55 * (100 - 1)
= 55*100 - 55*1
= 5500 - 55
= 5445
Solve:
2a + 6 = 12
a =
Answer:
8
Step-by-step explanation:
because hhhhhh
gghhhh
jkkkkk
lllll
vvvvv
dddfff
oooooo
eeeerer
kkkkkk
lllll.ssss
Dad has 15 oak and maple boards from the lumber yard. each oak board is 6 centimetres thick. each maple board is 9 centimetres thick. when my dad stacks the boards, the stack is 96 centimetres thick. how many of each type of board does he have?
Answer:
He has 2 maple boards and 13 oak boards.
Step-by-step explanation:
Assuming all boards are oak : 6*15=90
Maple minus oak = 3
96-90=6 6/3=2 maple boards
Verification : 2*9+6*13 = 96
Answer:
13 oak, 2 maple
Step-by-step explanation:
o = oak
m = maple
o + m = 15
6o + 9m = 96
o + m = 15
o = 15 - m
6o + 9m = 96
6(15 - m) + 9m = 96
90 - 6m + 9m = 96
90 + 3m = 96
3m = 6
m = 2
o + 2 = 15
o = 13
6(13) + 9(2) = 96 (Yes, correct!)
Brainliest, please :)
In a survey of 456 residents, 279 were opposed to the use of the photo-cop for issuing traffic tickets. What is the best point estimate for the proportion () of all residents opposed to the photo-cop use
The best point estimate for the proportion of all the residents opposed to the photo cop use is 60% which is the fourth option.
Given that in a survey of 456 residents , 279 were opposed to the use of the photo cop for issuing traffic tickets.
We have to find the best point estimate for the proportion of all residents opposed to the photo cop use.
Total residents=456
Residents who opposed to the use of the photo cop for issuing traffic tickets=279
Proportion=number of residents who opposed/ total residents
=279/456
=0.611
=61.1%
The nearest option is fourth which is 60%.
Hence the best point estimate for the proportion for the proportion of all the residents opposed to the photo cop use is 60% which is option 4.
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Question is incomplete as it should include options which are :
1) 500
2)50%
3)300
4)60%
5)40%
a big water tank contained 200 litres of water. during the day, 88 l 580 ml of water was used and 200 ml leaked. how much water was left in the water tank?
The quantity of water left in the tank as described in the task content is; 111 l 220ml.
What is the amount of water left in the tank?The tank described in the task content initially contains 200 liters, in which case, 1 liter corresponds to 1000ml.
Hence, when 88l 580ml was used, the remaining quantity of water is; 200l - (88l 580ml) = 111 l 420ml.
And finally, since 200 ml leaked, the quantity of water left is; 111l 220ml.
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Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.Learn more about the equation of a circle here:
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A system of three linear equations in three unknowns can have exactly three solutions.
The given statement is false. The option for the reason is the first option:
" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."
A system of linear equations is a grouping of one or more linear equations with the same variables.
A linear system solution is the assignment of values to variables in such a way that all of the equations are concurrently fulfilled.
For a system of equations, three types of solutions exist:-
One solution: When the lines (planes) intersect at a point.No Solution: When the lines (planes) are parallel.Infinitely many solutions: When the lines (planes) overlap each other.Thus, the given statement is false. The option for the reason is the first option:
" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."
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The question is incomplete. For the complete question, check the attachment.
1. The perimeter of a rectangle is 16cm, and the area of the same rectangle is 8cm^2. What is the diagonal length of the rectangle?
2. Kendrick rides his bike x miles per hour to school and it takes him x + 15 minutes to get there. If Kendrick lives 5.4 miles from school, how many minutes does it take for Kendrick to ride to school?
Answer:
Step-by-step explanation:
Patient a weighs 135.8 pounds.patient b weighs 135 2/5 ibs. which patient has the greater weight or if their weights are equal
Answer:
patient A has the greater weight
What is Permutations and Combinations?
Answer:
See below
Step-by-step explanation:
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
Permutation can be expressed in math as:
[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]
where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.
Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:
Since there are 3 letters total and 3 selected letters to arrange then:
[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]
Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:
ABC - 1
ACB - 2
BAC - 3
BCA - 4
CAB - 5
CBA - 6
Notice that if you do visually, you'll get the same answer as the calculation of permutation!
----
Combination can be expressed mathematically as:
[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]
The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.
Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:
Since there are 3 letters total and 3 selected letters:
[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]
Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.
Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.
Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.
Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.
Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.
The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.
Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.
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A rectangle is 8 feet longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-feet.
The width of rectangle is 15 feet and the length of rectangle is 23 feet.
According to the statement
Width of rectangle = x
Length of rectangle = x+10
Area of rectangle = 345 sq-feet.
we know that the area of rectangle is
Area of rectangle = L*W
Substitute the values in it then
345 = (x) (x+8)
345= (x)^2 + 8x
(x)^2 + 8x - 345 = 0
By factorisation
(x-15) (x+23) = 0
So, width of rectangle is 15 feet and the length of rectangle is 23 feet.
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Which of the following is 25 9/16 equal to?
Answer:
Step-by-step explanation:
25.5625
Answer:
25.5625
Step-by-step explanation:
The solution is in the image
1. sonya's salary increases at a rate of 4% per year. her starting salary is $45,000. what is her annual salary, to the nearest $100, after 8 years of service?
Her annual salary after 8 years will be $57,600.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " %". A % is a number with no dimensions; it has no unit of measurement.To find what is her annual salary, to the nearest $100, after 8 years of service:
Find 4% of 45,000
[tex]\frac{x}{45000} *100=4\\\frac{x}{450} =4\\x =1800[/tex]
So, 4% of $45,000 of $1800.
1st year = $45000
2nd year = 45000 + 1800 = $46800
3rd year = 46800 + 1800 = $48600
4th year = 48600 + 1800 = $50400
5th year = 50400 + 1800 = $52200
6th year = 52200 + 1800 = $54000
7th year = 54000 + 1800 = $55800
8th year = 55800 + 1800 = $57600
Therefore, her annual salary after 8 years will be $57,600.
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The salary of Sonya after 8 years will be $61,600 (nearest $100).
What is compound interest?The interest on the a loan or deposit that is calculated using the both initial principal as well as the accrued interest from prior periods is known as compound interest (sometimes known as compounding interest).
Some features of compounding are-
Compound interest is calculated just on initial principal of a deposit or loan, which also takes into account all of the interest accrued from prior periods.The yearly interest rate is raised to a number of compounded periods minus one, and the starting principal amount is multiplied by both of these factors.The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The quantity of compounding periods has a bigl impact on compound interest calculations.Calculation for the amount after 8 years-
The principal amount is $45,000
Rate of interest is 4% per year.
Time duration is 8 years.
The formula for total amount after compounding is -
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period.
t = number of time periods elapsed.
As the rate of interest is applied only one in a year ; n = 1.
Substitute the values in the formula to get the value.
[tex]A=45,000\left(1+\frac{.04}{1}\right)^{8}\\A=45,000\left(1.04}\right)^{8}\\\\A=61585.60[/tex]
Therefore, the salary of Sonya will be $61600 (nearest $100) after 8 years.
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On a plat map are two adjacent rectangular lots. Lot A has a square footage of 46,060, and Lot B has a square footage of 43,005. The common boundary they share is 235 feet long. What is the width of Lot B
The Width of plot B is 183 ft.
According to the statement
we have given that the Plot A has a square footage of 46,060, and Plot B has a square footage of 43,005. The common boundary they share is 235 feet long.
And we have to find the width of the Plot B
We know that
Area of plot A = 46,060 square footage.
Area of plot B = 43005 square footage.
Common area share by both Plot = 235 feet long.
So, Now
The width of Plot B = Area of plot B / Common area
Substitute the values in it then
width of Plot B = Area of plot B / Common area
width of Plot B = 43005 / 235
width of Plot B = 183 feet.
So, The Width of plot B is 183 ft.
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I can not factor the denominators on any online calculator so I'm unsure of how to do this. Please help!
Answer: 17/y-5
Step-by-step explanation:
Find 20% of 150
A. 20
B. 130
C. 120
D. 30
For this, multiply 150 × .20 = 30
Therefore, 20% of 150 is 30.
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DOES ANYONE KNOW THE ANSWER
Answer:
D. none
Step-by-step explanation:
we only know about the right angle at the bottom right.
that is not enough information.
we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.
like the other answer options would indicate :
SAS : side - angle - side.
2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.
SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.
HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).
since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.
What is the multiplicative inverse of -13/14
The multiplicative inverse of -13/14 as in the task content is; -14/13.
What is the multiplicative inverse of -13/14?The multiplicative inverse of a number x is given as; 1/x.
On this same note, it follows that since, the number whose multiplicative inverse is to be found is: -13/14, the multiplicative inverse is; -14/13.
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Richard wants to weed 33% of his garden today. The total garden is 144 square yards. How many square yards should Richard weed to reach his goal?
El rio Lempa sirve de linea fronteriza entre Honduras y El Salvador, mide 300km
de largo. ¿Cuántos metros mide este rio?
Answer:
El río mide:
300000 metros.
Step-by-step explanation:
1 km = 1000 metros
300 km = 300 * 1000 = 300000 metros
...
Determine which graph represents this system of equations to complete the statements that follow. y = -x2 + x + 5, y = -x + 2.
The solution to the system of equations is (-1, 3) and (3, -1)
How to graph the equations?The system of equation is given as:
y = -x^2 + x + 5
y = -x + 2
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(-1, 3) and (3, -1)
Hence, the solution to the system of equations is (-1, 3) and (3, -1)
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Answer:
graph 1,
3,-1 and -1,3
Step-by-step explanation:
See screenshot