Answer:
f(x) = (x+1)² - 9
Step-by-step explanation:
We can start by seeing if this is a quadratic function, as that is the lowest degree polynomial possible.
The vertex form for a quadratic function is a(x-h)² + k, with the vertex being (h, k).
In this example, the leading coefficient (a) must be 1 or -1. If a is positive, the graph opens upward, and vice versa. Since the graph opens upward, a must be 1.
Our vertex in this picture is (-1, -9). We can plug those values in, along with a=1, to get
1(x-(-1))² - 9 = (x+1)² - 9
Therefore, our equation is f(x) = (x+1)² - 9
The polynomial is given by:
\(p(x) = x^2 + 2x - 8\)
------------------------
Zeros of a function:
Given a polynomial f(x), this polynomial has roots \(x_{1}, x_{2}, x_{n}\) such that it can be written as: \(a(x - x_{1})*(x - x_{2})*...*(x-x_n)\), in which a is the leading coefficient.
------------------------
The polynomial has two x-intercepts, thus, the lowest-degree is 2.Concave up, thus, the leading coefficient is \(a = 1\).The x-intercepts are \(x_1 = -4, x_2 = 2\), and thus:\(p(x) = (x - (-4))(x - 2) = (x + 4)(x - 2) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8\)
A similar problem is given at https://brainly.com/question/22817243
Kelly’s bill at a restaurant came to $21.52. If she decides to leave a 18% tip, how much of a tip did she leave
Answer:
$3.87 for the 18% tip.
Consider the following points.
(−2,−3),(3,3)
and (3,−3)
Step 1 of 2 : Determine whether or not the given points form a right triangle. If the triangle is not a right triangle, determine if it is isosceles or scalene.
The perimeter of a triangle is the sum of the lengths of its three sides.
What is triangle?Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.
In the case of triangle HGI, the perimeter is calculated by adding the three side lengths together. For example, if the three sides are labeled a, b, and c, the perimeter would be calculated as a + b + c.
The perimeter of triangle HGI can be calculated by knowing the lengths of its three sides. If the lengths of the three sides are 7, 8, and 9 units respectively, the perimeter of triangle HGI is 7 + 8 + 9 = 24 units.
The perimeter of triangle HGI can also be calculated using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Using this theorem, the lengths of the other two sides can be calculated if the length of one side and the measure of the included angle is known.
In summary, the perimeter of triangle HGI can be calculated by adding the lengths of its three sides or by using the Pythagorean Theorem if the lengths of two sides and the measure of the included angle are known.
To know more about triangle click-
https://brainly.com/question/17335144
#SPJ1
I need help on this one to sorry
Answer:
250 and 250.1
Answer:
250.1
Step-by-step explanation:
5002 divided by 20 equals 250.1
write an exponential formula of the form f (t)= a×b^t to represent the following situation. assume t is in years. The beginning population is 27, 000, decreasing by 3.5% annually. f(t)=__________
Answer:
\(f(t)= 27000 * 0.965^t\)
Step-by-step explanation:
Given
\(a = 27000\) -- initial
\(r = 3.5\%\)
Required
The exponential equation
The exponential equation is
\(y =ab^t\)
Where
\(b=1 -r\)
We used minus, because the rate decreases..
So, we have:
\(b=1 -3.5\%\)
\(b=1 -0.035\)
\(b=0.965\)
So:
\(y =ab^t\)
\(y = 27000 * 0.965^t\)
Hence:
\(f(t)= 27000 * 0.965^t\)
mortician math word problem
Answer:
wat do u want me to do
Step-by-step explanation:
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Among the given options, 90 degrees (option A) is not a solution to the equation sin(2θ) = 1. The equation sin(2θ) = 1 represents the values of θ for which the sine of twice the angle is equal to 1. To determine which option is not a solution, we need to evaluate each choice.
A) 90 degrees: If we substitute θ = 90 degrees into the equation sin(2θ) = 1, we get sin(180 degrees) = 1. However, sin(180 degrees) is actually 0, not 1. Therefore, 90 degrees is not a solution to the equation sin(2θ) = 1.
B) 45 degrees: Substituting θ = 45 degrees gives sin(90 degrees) = 1, which is true. Therefore, 45 degrees is a solution to the equation sin(2θ) = 1.
C) 225 degrees: When we substitute θ = 225 degrees, we get sin(450 degrees) = 1. However, sin(450 degrees) is also 0, not 1. Thus, 225 degrees is not a solution to sin(2θ) = 1.
D) -135 degrees: Similarly, substituting θ = -135 degrees gives sin(-270 degrees) = 1. However, sin(-270 degrees) is 0, not 1. Hence, -135 degrees is not a solution to the equation sin(2θ) = 1.
For more such questions on angle
https://brainly.com/question/29165823
#SPJ8
Find the perimeter of each figure
The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.
What is a hexagon?A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.
To calculate the perimeter of this hexagon, we must first identify the length of each side.
All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.
The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get
5 + 4 + 4 + 5 + 3 + 3 = 24.
Thus, the perimeter of the hexagon is 24 inches.
Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.
For more questions related to perimeter
https://brainly.com/question/19819849
#SPJ1
Drag the tiles to the correct locations on the image. Not all the tiles will be used.
The figure is a square, with side lengths as shown.
4√5mm
What are the perimeter and area of the square
The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².
To calculate the perimeter and area of the square, we can use the formulas:
Perimeter = 4 * side length
Area = side length * side length
Substituting the given side length of 4√5mm into the formulas, we have:
Perimeter = 4 * 4√5mm = 16√5mm
Area = (4√5mm) * (4√5mm) = 16 * 5mm = 80mm²
Therefore, the perimeter of the square is 16√5mm, and the area of the square is 80mm².
Please note that the values are based on the provided side length of 4√5mm. If there are any changes to the side length, the perimeter and area will differ accordingly.
For such more question on perimeter:
https://brainly.com/question/397857
#SPJ8
The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².
I took the test on plato.
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
Use the Pythagorean Theorem to find the missing length in the right triangle
12 cm
a
17 cm
The missing length is
cm.
(Round to one decimal place as needed.)
Answer:
it depends
Step-by-step explanation:
If 17 is the hypotenuse
\(c=17\\\\b=12\\\\a=?\\\\c^{2} =a^2+b^2\\\\17^2=a^2+12^2\\\\17^2-12^2=a^2\\\\(17-12)(17+12)=a^2\\\\5(27)=a^2\\\\a=\sqrt{9*3*5} \\\\a=3\sqrt{15} \\\\a=11.6\)
if you are looking for the hypotenuse
\(a=17\\\\b=12\\\\c=?\\\\a^2+b^2=c^2\\\\17^2+12^2=c^2\\\\289+144=c^2\\\\433=c^2\\\\c=\sqrt{433} \\\\c=20.8\)
Please help thank you
Answer:
B
Step-by-step explanation:
Increasing trials promotes the chance of reaching theoretical.
Thirteen more than the quotient of twenty and four
Answer:
19
Step-by-step explanation:
20/4 + 13
20/4 = 6
6+13 = 19
Answer:
The equation is 13 + \(\frac{20}{4}\) or 13 + (20 ÷ 4)
The answer is 13 + 5 = 18
Please see all the screenshots. I have included multiply problems in this one question.
Answer:
so basacilly the answer to all of the question is a
Step-by-step explanation: you welcome!
The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.
what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.
Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.
What is the cultural Strain?Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.
Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.
Learn more about Role Strain from
https://brainly.com/question/14283116
#SPJ1
Lori wants to trade more than 3/10 but less than 4/5
Answer:
i dont know what you are asking but 3/10-8/10
Step-by-step explanation:
Solve the following system of equations. 4x + 3y = -5
- 3x + 7y=13
Answer: 13
Step-by-step explanation:
4x+3y=-5 solve x :
4x = -3y + -5 | -3y
1x = -0.75y + -1.25 | : 4
-3x + 7y = 13 solve x :
-3x + 7y = 13 | -7y
-3x = -7y = 13 | : (-3)
Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333
-0, 75y - 1,25 = 2,333y - 4, 333 solve y:
-0, 75y - 1,25 = 2,333y -4, 333 | -2,333y
-3, 083y - 1,25 = -4,333 | + 1, 25
-3. 083y = -3,088 | : (-3, 083)
y = 1
Plug y = 1 into the equation 4x + 3y = -5 :
4x + 3 · 1 | Multiply 3 with 1
4x + 3 = -5 | -3
4x = -8 | : 4
x = -2
So the solution is:
y = 1, x = -2
ヘ( ^o^)ノ\(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:
https://brainly.com/question/20333461
9. The Super Vision cable TV/Internet/phone provider advertises a flat $100 monthly fee for all
three services for a new customer. The rate is guaranteed for 5 years. Cable Zone normally
charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for
monthly cable television.
a. How much could a customer save during the first year by switching from Cable Zone to
Super Vision?
b. Super Vision raises the rates 23% after a new customer's first year, how much will a customer
who switched from Super Vision save in the second year?
c. If Super Vision raises the rates 18% for the third year compared to the second year, which
company is cheaper for the third year?
a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.
b. Super Vision raises the rates 23% after a new customer's first year, a customer who switched from Super Vision save $180 in the second year.
c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.
a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.
Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:
$46 (home phone) + $36 (Internet) + $56 (cable television) = $138
Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:
$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month
Therefore, during the first year, the customer could save:
$38 (monthly savings) * 12 (number of months) = $456
b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:
$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123
To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:
$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month
Therefore, in the second year, the customer would save:
$15 (monthly savings) * 12 (number of months) = $180
c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:
$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14
To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:
$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14
In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.
Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.
For more such information on: rates
https://brainly.com/question/25720319
#SPJ8
Which data set could be represented by
the box plot shown below?
H
0 2 4 6 8
Choose 1 answer:
A
Creating box plots
B
C
D
10 12 14 16 18 20
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
The given box plot represented by the data sets in option A and B.
From the given box plot, we have
Minimum value = 3
Maximum value = 18
First quartile (Q1) = 7
Third quartile (Q3) = 13
Median = 10
Option A:
3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18
Median = 12
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option B:
3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Option C:
3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 8
Third quartile (Q3) = 13
Option D:
2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18
Median = 10
First quartile (Q1) = 7
Third quartile (Q3) = 13
Therefore, the correct options are B and D.
Learn more about the box plot here:
https://brainly.com/question/1523909.
#SPJ1
MATH HELP WILL MARK BRAINLEST
The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
In the question ,
it is given that ,
the equation is y = x² - 6x + 5
we need to write the equation in the vertex form ,
we know that the vertex form of the equation is
y = m(x − a)² + b , where (a,b) is the vertex .
On using the completing the square method for the equation,
y = x² - 6x + 5
Adding and subtracting 9 , in the equation
y = x² - 6x + 9 + 5 - 9
y = x² - 6x + 3² + 5 - 3²
y = (x - 3)² - 4 ....because (x - 3)² = x² - 6x + 3²
Therefore , The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
Learn more about Vertex Form here
https://brainly.com/question/28808332
#SPJ1
HELP ME raaaaaaaa NOWWWWWWWWWW
Answer:
C: EAF Is the correct answer
Use the expression (5.3x+4)+(−4.7x+7). a. Find the sum. b. Explain how you know when to combine terms with variables.
The sum (5.3x+4)+(−4.7x+7) is 0.6x+11.
The sum of two or more numbers, magnitudes, quantities, or specifics as established by or as if determined by the mathematical addition process: 14 is the result of the combination of 6 and 8. a specific sum, particularly when referring to money: The costs were a huge amount. The outcome of adding two or more numbers or phrases is known as the sum in mathematics. As a result, the sum serves as a means of bringing everything together. To put it another way, combining two or more numbers yields a new outcome or sum.
(5.3x+4)+(-4.7x+7)
Determine the sign.
5.3x+4-4.7x+7
Combine like terms.
0.6x+11
Learn more about sum here
https://brainly.com/question/28421287
#SPJ1
Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha’s songs were played on 2 more commercials than movies, and her total earnings on the royalties from all the commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha’s songs were played. Define the variables that you use to write the system
The equations that Nakeishia can use to determine the number of commercials and the number of movies on which Nakeisha’s songs were played include:
30m + 110(m + 2) = 760
How to illustrate the information?Let the movies be represented by m
Since Nakeisha’s songs were played on 2 more commercials than movies, this will be m + 2.
Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. This will be:
30m + 110(m + 2) = 760
This represents the equation.
Learn more about equations on:
brainly.com/question/16146017
#SPJ1
help!!!! please <33333
Hello!
For this you would just need to multiple straight across. Here's how you would set it up:
3/4 ·1/8
Then you would multiple 3 x 1 = 3
And 4 x 8 =32
Your answer should be 3/32, it cannot be simplified so that is the final answer :).
35 points! Find the the surface area of the cylinder in terms of pi.
32pi m^2
80 pi m^2
96 pi m^2
Solution:
Note that:
2πrh + 2πr² = Area of cylinder formulaRadius = 4 mHeight = 8 mFinding the surface area:
2πrh + 2πr² => 2(π)(4)(8) + 2(π)(4²)=> 64π + 2(π)(16)=> 64π + 32π=> 96π m²Answer:
SA = 96\(\pi\) m²
Step-by-step explanation:
Surface area of closed cylinder = 2\(\pi\)r² + 2\(\pi\)rh
where r is the radius and h is the height
Given:
r = 4h = 8SA = 2\(\pi\)(4)² + 2\(\pi\)(4)(8)
⇒ SA = 32\(\pi\) + 64\(\pi\)
⇒ SA = 96\(\pi\) m²
A man gave 90000.00 to his two daughters Jane and Lydia, 75.00 was given to Lydia to pay her load. After sharing the money Lydia has twice as
much as Jane. How much did each received?
Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.
We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.
Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.
Therefore, y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.
Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.
Simplifying, we have :3x = $90000 + 75 = $90075.
Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.
Therefore, Jane received $30025 and Lydia received $60000.
For more question on amount
https://brainly.com/question/25720319
#SPJ8
write an equivalent expression for -5 ( 3 - 2x ) , if you help I’ll sent 5$ via PayPal or whatever you use. Thanks.
Answer: 10 x - 15
Step-by-step explanation:
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
Learn more about inequality expression here: https://brainly.com/question/25275758
#SPJ1
9. Difference between the place values of "1" in 3116365 is
Need help!!!!!
What is the radius and center of a circle with the equation (x-2) ^2+ (y-3) ^2= 36?
Answer: center: (2,-3) radius: 6
Step-by-step explanation:
Radius = 6 and center = (2,3) of the given circle with the equation (x -2)² +(y -3)² =36.
What is circle?
"A circle is a two dimensional shape which is equidistant from all the points on its surface."
Formula used
Equation of the circle with center (h , k) and radius 'r' units is given by
(x - h)² + (y - k)² = r²
According to the question,
Given equation of the circle is given by
(x -2)² +(y -3)² =36
⇒ (x -2)² +(y -3)² = 6²
Compare it with formula of a circle we have,
Center (h ,k) = (2 , 3)
Radius 'r' = 6
Hence, radius = 6 and center = (2,3) of the given circle with the equation (x -2)² +(y -3)² =36.
Learn more about circle here
https://brainly.com/question/11833983
#SPJ2
Please help, marking brainliest for the correct answer
Answer:
none of the above
Step-by-step explanation:
they're same side interior