It looks like you're saying
[tex]f(x) = ax^2 + bx + c[/tex]
and you're asked to find [tex]a,b,c[/tex] given [tex]f(0)=-4[/tex], [tex]f(1)=-1[/tex], and [tex]f(-1)=-5[/tex].
Evaluate [tex]f[/tex] at the three given points:
[tex]x=0 \implies f(0) = \boxed{c = -4}[/tex]
[tex]x=1 \implies f(1) = -1 = a + b + c \implies a+b = 3[/tex]
[tex]x=-1 \implies f(-1) = -5 = a - b + c \implies a - b = -1[/tex]
[tex](a+b) + (a-b) = 3 + (-1) \implies 2a = 2 \implies \boxed{a=2}[/tex]
[tex]a-b = -1 \implies \boxed{b=3}[/tex]
and the mapping is [tex]f(x) = 2x^2 + 3x - 4[/tex].
The area of a square is 256cm2. When each side of the square is increased by x cm, its area becomes 324 cm2.Find the value of x.
Answer: x = 2
Step-by-step explanation:
First, let's take the root of 256 to find the length of each side before the addition of x.
[tex]\sqrt{256} = 16[/tex]
This means 16 cm is the length of each side before the addition of x.
Then increase each side by X to get
[tex](16 + x)(16 + x) = 324[/tex]
[tex]256 + 16x + 16x + x^2=324[/tex]
[tex]x^2+32x -68=0[/tex]
[tex]x=2[/tex] or [tex]x=-34[/tex]
The value cannot be negative so x has to be 2
The number of DVDs in a random person's home collection is counted for a sample population of 80 people. The mean of the sample is 52 movies, the entire population is known to have a standard deviation of 12 movies. Assuming a 99% confidence level, find the margin of error.
A) 59.4671
B) 2.6296
C) 38.6536
D) 3.4547
In a case whereby the number of DVDs in a random person's home collection is counted for a sample population of 80 people the mean of the sample is 52 movies, the entire population is known to have a standard deviation of 12 movies then the margin of error is 3.46 moves.
How can the the margin of error be calculated?The concept that will be used here is the formular to find the error
E=z∝/2 σ/√ n
n= number of the samples= 80
σ = standard deviation = 12 moves
confidence level = (1-∝) = (1- 0.99) = 0.001
σ/2 = 0.005
Then the looking up for Z value of Z(0.005) = 2.58
E= 2.58 *12/√80
= 3.46 moves.
Therefore, option D is correct.
Learn more about standard deviation at:
https://brainly.com/question/24298037
#SPJ1
What is an equation of the line that is perpendicular to y - 4 = 2(x - 6) and
passes through the point (-3, -5)?
• A. y -5=1/2(x-4)
• B. y - 5 = -2(x- 3)
• C. y + 5 = 2(x+ 3)
O D. y +5- -1/2(x+3)
Answer:
D. y + 5 = -1/2(x + 3)Step-by-step explanation:
Let k: y = a₁x + b₁ and l: y = a₂x + b₂. Then
k ║ l ⇔ a₁ = a₂k ⊥ l ⇔ a₁ · a₂ = -1We have the euation of a line in point slope form:
(y - y₁) = m(x - x₁)Convert to the slope intercept form:
y =mx + by - 4 = 2(x - 6)
y - 4 = 2x - 12
y - 4 + 4 = 2x - 12 + 4
y = 2x - 8
The slope is m₁ = 2.
Let y = m₂x + b.
The lines is perpendicular. Therefore:
2m₂ = -1 |divide both sides by 2
m₂ = -1/2The line passes through the point (-3, -5).
Substitute to the point slope equation:
y - (-5) = -1/2(x - (-3))
y + 5 = -1/2(x + 3)
Simplify [tex]\sqrt{18}. \\[/tex]
[tex]A; 2\sqrt{3} \\B; 2\sqrt{9} \\C; 3\sqrt{2} \\D; 9\sqrt{2} \\[/tex]
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option C, 3}\sqrt{2}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\sqrt{18}[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: In order to get a number outside of the square root there must be two of them inside of the square root. The first step that we need to take is to break down the number 18 into it's lowest factors and then take out the numbers can be taken out.
Break down the number 18
[tex]\sqrt{18}[/tex][tex]\sqrt{\textsf{2 * 3 * 3}}[/tex][tex]\sqrt{\textsf{2 * 3}^2}[/tex]Take 3 outside of the square root
[tex]\sqrt{\textsf{2 * 3}^2}[/tex][tex]\textsf{3}\sqrt{\textsf{2}[/tex]Therefore, the option that would best match the results that were solved for is option C, [tex]\textsf{3}\sqrt{\textsf{2}[/tex]
Someone help me with 4 pleaseeeeee
Answer:
C
Step-by-step explanation:
Use the equation [tex]a^2 + b^2 = c^2[/tex]
Input the numbers----> [tex](2865)^2 +(4550)^2=c^2[/tex]
Simplify ----> [tex]28910725=c^2[/tex]
Find the square root------->[tex]5376.9=c[/tex]
What percent of patients with type-B blood are male? Round your answer to the nearest tenth of a percent.
Answer:
54%
Step-by-step explanation:
To find the probability for a male patient to have B blood, find the number of male patients who do have B blood and divide it by the number of patients with type B.
The number of male and B blood is 99.
The number of patients with B blood is 183.
The probability is 99/183 = 0.54.
The percent is found by multiplying by 100.
0.54*100 = 54%
Andy fed his dog about 16kilogram of food in one week. he fed his cat about 2 kilogram of food in one week what is the best estimate for the total amount of food he feeds his dog and cat in2 weeks. each animal represent 4 kilogram of food
Answer:
36kg
Step-by-step explanation:
The dog eats 16kg per week, which is 32kg in 2 weeks
The cat eats 2kg per week, which is 4kg in 2 weeks
32+4=36
What division problem does this area model represent?
Enter your answer in the boxes.
÷ 75 =
R
Rectangle with left side labeled 75. Vertical lines divide the rectangle into three parts. The left part has 40 above it and 3000 inside it. The middle part has 4 above it and 300 inside it. The right part has 53 inside it and nothing above it.
The division problem that's illustrated based on the information is 3000/75 = 40 without remainder.
How to calculate the rectangle?
A rectangle is defined as a two-dimensional shape having four-sided and opposite sides equal and parallel.
From the information, it was stated that the rectangle with left side labelled 75 and the middle part has 4 above it and 300 inside it.
Therefore, the division problem that's illustrated based on the information is 3000/75 = 40 without remainder.
Learn more about rectangles on:
brainly.com/question/25292087
#SPJ1
Find the highest common factor [HCF] of 10 and 17
Answer
Step by step explanation
Which choice is the most efficient first step to solve this set of
equations?
y=3x-5
2x+6y=20
Answer:
b) Substitute (3x - 5) for y in the second equation.
Step-by-step explanation:
If using the substitution method, then the second choice is the most efficient first step.
What is the substitution method?
The substitution method can be used to solve a system of equations. It is when you isolate any of the variables from one of the equations and then substitute that value into the other equation.
Here, the first equation already has an isolated variable, y. We can then substitute its value into the second equation. Like so:
⇒ 2x + 6y = 20
⇒ 2x + 6(3x - 5) = 20
Learn more about the substitution method here:
brainly.com/question/27728118
brainly.com/question/26094713
25.
A ladder stands against a wall at an angle of 45° to the floor. The foot of the ladder is 3 m
from the wall. If the ladder slides 1 m down the wall, then the angle between the ladder
and the floor is such that:
Using the slope concept, it is found that the angle between the ladder and the floor will be of 33.69º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we have that:
The angle is of 45º.The vertical distance is the height of h.The horizontal distance is of 3m.Hence:
tan(45º) = h/3.
1 = h/3.
h = 3 m.
If the ladder slides 1 m down, the height will be of 2m, hence the angle will be given as follows:
[tex]\tan{\theta} = \frac{2}{3}[/tex]
[tex]\theta = \arctan{\left(\frac{2}{3}\right)}[/tex]
[tex]\theta = 33.69^\circ[/tex]
More can be learned about the slope concept at https://brainly.com/question/18090623
#SPJ1
Hey I need help on this question. Could I have a simple explaination as I find it difficult to understand things
Answer:
9
Step-by-step explanation:
The surface, in this case, describes the number of squares that are painted. On the left hand side, we have a cube, so we know we're going to have 6 faces. And each face on the cube has 9 little squares, they can be counted on the diagram. So, the total number of squares that are painted on the left cube = [tex]9 * 6 = 54[/tex]
The star means multiplication.
We are told in the question that it takes 9 litres of paint to cover the surface of the left hand cube, meaning it takes 9 litres of paint to cover 54 squares.
This can be written in the ratio = [tex]9:54[/tex]
If we divide both sides of the ratio by 9, we can figure out the amount of squares that 1 litre of paint covers, [tex]1:6[/tex].
The ratio tells us that 1 litre of paint covers 6 squares.
Let's look at the shape on the right. It is still a cube, however, some segments have been removed. Some faces still remain the same as in the shape on the left, such as the bottom face, the back face and the face to the left. Those faces may not be so apparent on the diagram, however, they exist. So we have to count them.
The number of small squares on these faces = [tex]9 * 3=27[/tex]
If you look on the inside of the cube, which can be seen on the diagram, we can see three faces, each having four squares. So, the total number of squares here = [tex]3*4=12[/tex]
Also, we have some squares on the top, and if you count these, there are 5.
This also applies for the front and the right hand side if you count, so we add 10 squares to the total as there are another two lots of five.
So, the total number of squares on the right cube = [tex]27 + 12 + 5 + 5 + 5 = 54[/tex]
Let's bring back the ratio of litres of paint to the number of squares covered: [tex]1:6[/tex]
In the ratio, there are 6 squares per litre. We know that 6 × 9 = 54 (our total). So, we multiply left hand side of the ratio by 9 as well, bringing the total amount of paint required to 9 litres.
I hope this helps.
The surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].
How to estimate the surface area of cuboid?
If the left cube takes 9 liters of paint to cover the surface. Then, also right cube takes 9 liters of paint to cover the surface.
Cuboid dimension [tex]$\frac{10 \mathrm{~cm}}{(l)} \times \frac{10 \mathrm{~cm}}{(b)} \times\frac{5 \mathrm{~cm}}{(h)}$[/tex]
Surface area = 2(lb + lh + bh)
= 2((10 [tex]\times[/tex] 10)+(10 [tex]\times[/tex] 5)+(10 [tex]\times[/tex] 5))
= 2(100+50+50)
= [tex]400 \mathrm{~cm}^{2}[/tex]
Therefore, surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].
To learn more about surface area of cuboid
https://brainly.com/question/26403859
#SPJ2
What is the point slope form of an equation of the line through the points (-2, 6) and (3, -2)
Help please this is stressing me out.
Step-by-step explanation:
As far as I understand, they can use all 26 letters (alphabet) and all 10 digits (0, 1, ..., 9), and the password looks like this:
letter-letter-letter-letter-letter-letter-number-number (6 letters, 2 numbers).
▪︎ They can reuse the letters, so they can choose the 1st letter out of 26 possible letters, then they still can choose the 2nd letter out of 26 (it's ok if they have both A's for example, they can reuse them) and so on. So each time they can choose one letter out of 26. Thus, it's 26*26*26*26*26*26.
▪︎ The same thing with numbers. Each time they can choose one number out of 10, so it's 10*10.
▪︎ Therefore, the answer is 26*26*26*26*26*26*10*10 = 30,891,577,600. That's almost 31 billion passwords.
Subtract-3x - 8 from 4x² - 7x - 2.
[tex]( {4x}^{2} - 7x - 2) - (3x - 8) \\ \\ {4x}^{2} - 7x - 2 - 3x + 8 \\ \\ {4x}^{2} - 10x + 4.[/tex]
simplify
5cat + 3act - 6tac
Answer:
the correct answer is 2 act
Step-by-step explanation:
there is same base (act)
then 5+3=8
and 8-6 = 2act
-19+[27-(14+(5-2)×4÷2))]
simplify
Answer:
-12
Step-by-step explanation:
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and s is the distance (in meters). Find v when u is 6 m/s, a is 3 m/s², and s is 29 meters. A. 210−−−√ m/s B. 15 m/s
Answer:
When the initial velocity is 6m/s and acceleration is 3m/s², the final velocity after a distance of 29m is √210m/s.
Step-by-step explanation:
Concept: In the problem it is given that u = 6m/s, a = 3m/s² and s = 29m. We need to find the v. In such kinematical problems, we have an equation v² = u² + 2as. From this relation we can find v.
v² = 6² + 2×3×29
v² = 36 + 174
v² = 210
v = √210 m/s
So, the final velocity is the under-root of 210 or √210 m/s.
For more explanation, refer the following link
https://brainly.com/question/17158762
#SPJ10
(x+2)^2-3 evaluate and simplify the equation
Answer:
[tex](x^{2} +2)-3\\x^{2} +2-3\\x^{2} -1\\(x+1)(x-1)[/tex]
Answer:
x^2+4x+1
Step-by-step explanation:
(x+2)^2-3
(x+2)(x+2)-3
x^2+2x+2x+4-3
x^2+4x+4-3
x^2+4x+1
0123456 7 8 9 10 what is this called.........ence.fill in the missing space.
Answer:
sequence
Step-by-step explanation:
a sequence is essentially a set [group/list] of numbers, and each number has a specific placement [meaning that there is an order]
hope this helps!!
Answer: this, a set of number in an order, is called a sequence
fill in the blank: sequence
Construct a regular hexagon inscribed in a circle. Please help.
Answer:
no lo sd
Step-by-step explanation:
solo se que is really
In what? desmos, drawing?
Use the expression 8a+16c
What is the value of the expression when a = –5 and c = –1?
Answer:
i think its 8(a+2c)
Step-by-step explanation:
The GCF or greatest common factor of 8 and 16 is 8.
8a+16c
8(a+2c)
Therefore the answer is 8(a+2c)
does this table represent a function? yes or no
Answer:
D
Step-by-step explanation:
The table does not represent a function because their are two x values with the same y value.
Answer:
C. No, one x --- two different y's
Step-by-step explanation:
In order to be a function, every x can have only one y partnered with it. So if the function is written in this two-column format, if no x's repeat, you can say it is a function. If an x does repeat, it MUST have they same y both times. Here 2 repeats in the x column, but at first it is with 1 and in the next row it is with 4. Can't have that! So this is not a function!
(Btw, it doesn't matter at all the 4 repeats in the y-column nor that it is paired with different x's. Doesn't matter. Not a thing)
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer: 26 inches is equivalent to 660.4 millimeters.
Step-by-step explanation:
You will multiply the inches by the conversion.
[tex]26in*25.4mm=660.4mm[/tex]
Therefore, the answer is 660.4 millimeters.
I hope this helps!! Pls mark brainliest :)
1/4+1/10 Add or subtract. Write the answer in simplest form.
Answer:
7/20
Step-by-step explanation:
To add fractions, the first step is to get a common denominator
1/4 + 1/10
The common denominator is 20
1/4 *5/5 = 5/20
1/10 *2/2 = 2/20
5/20 + 2/20 = 7/20
Which expression is equivalent to 7a³ (8a² + a)²-4a³?
Simplify.
[tex]7a³ (8a² + a)²-4a³ \\ \\ 7 {a}^{3}(8 { {a}^{2} + a)(8 {a}^{2} + a )} - 4 {a}^{3} \\ \\ 7 {a}^{3} ( {8a}^{2} (8 {a}^{2} + a ) + a(8 {a}^{2} + a ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 8{a}^{3} + 8 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 16 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 448 {a}^{7} + 112 {a}^{6} + 7 {a}^{5} - 4 {a}^{3} \\ \\ {a}^{3} (448 {a}^{4} + 112 {a}^{3} + 7 {a}^{2} - 4).[/tex]
Which equation can be simplified to find the inverse of y = 5x² + 10?
Ox=5y² + 10
O-5X+10
O-y=5x² + 10
1
O y = x² + 10
Answer:
[tex]x = 5y {}^{2} + 10[/tex]
The inverse of the function is x = 5y² + 10.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the inverse of a function, we need to solve for x in terms of y.
To do this, we can start by replacing y with x and solving for x.
y = 5x² + 10
x = 5y² + 10
Now we have solved for x in terms of y, which gives us the inverse of the original function.
So the equation that can be simplified to find the inverse of y = 5x² + 10 is:
x = 5y² + 10
Thus,
The inverse of the function is x = 5y² + 10.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ5
A T-shirt that costs $12 is now on sale for 15% off. What is the sale price of the t-shirt?
Answer:
$14.18
Step-by-step explanation:
just multiply 12 with 100 for percentage and divide it by 85 because there was 15 percent off and you'll get the answer
Select the correct answer from each drop-down menu. one person working alone will take 30 days to paint an apartment. if d represents the number of days taken to complete the work and p represents the number of people working, the equation that represents this situation is . if 10 people work on this job, they take days to complete it.
It took 3 days to complete a work by 10 people.
What is Efficiency?
The efficiency is the output of the work which we divide by the work input and then express it in a percentage form.
Here, Efficiency of 1 person to complete a piece of work in 30 days is 1/30.
The number of days to complete the work = n days
Number of person to complete the work = p.
Now, according to question
Number of days to complete the work by 10 people = 30 / 10
= 3 days.
Thus, it took 3 days to complete a work by 10 people.
Learn more about Efficiency from:
https://brainly.com/question/13828557
#SPJ1
(6+9)2+6(600-9)+600 divide 30
Step-by-step explanation:
GIVEN
HERE
= 6+9+2+6+600÷30 { firstly add numbers }
= 623 ÷ 30
= 20
I think you understand
