How to include a negitive number (s) in a math problem
Answer:
Adding a negative number is the same as subtracting a positive number — that is, go down (to the left) on the number line. This rule works regardless of whether you start with a positive or negative number.
Step-by-step explanation:
f(x) = -x^2+ 6x -10
write each function in vertex form and give the vertex
Answer:
Vertex form: f(x) = – (x – 3)² – 1
vertex: (3, -1)
Step-by-step explanation:
Given the quadratic function, f(x) = -x²+ 6x -10:
where a = -1, b = 6, and c = -10
The vertex of a parabola is the point at which the parabola intersects the axis of symmetry. The axis of symmtery occurs at x = h. Therefore, the x-coordinate of the vertex is the same as h.
To find the vertex, (h, k), you need to solve for h by using the formula: [tex]h = \frac{-b}{2a}[/tex]
Plug in the values into the formula:
[tex]h = \frac{-b}{2a}[/tex]
[tex]h = \frac{-6}{2(-1)} = 3[/tex]
Therefore, h = 3.
Next, to find the k, plug in the value of h into the original equation:
f(x) = -x²+ 6x -10
f(x) = -(3)²+ 6(3) -10
f(x) = -1
Therefore, the value of h = -1.
The vertex = (3, -1).
Now that you have the value for the vertex, you can plug these values into the vertex form:
f(x) = a(x - h)² + k
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
If a is positive, the graph opens up.If a is negative, the graph opens down.h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Plug in the vertex, (3, -1) into the vertex form:
f(x) = – (x – 3)² – 1
This parabola is downward-facing, with its vertex, (3, -1) as its maximum point on the graph.
Show that:
[tex]\bigg(\frac{ \sqrt{7} + i \sqrt{3} }{\sqrt{7} - i \sqrt{3} } + {\frac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } } \bigg) \: is \: real \\ [/tex]
Please answer this question.
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
pa answer po plss plssss
29/32
Step-by-step explanation:
ng x value 32wrffddfddfffryufcjhfddxhjhddxffdssdtt
IF YOU DONT KNOW THE QUESTION, PLEASE DONT ANSWER IT FOR THE PONIS. I REALLY NEED IT
Answer:
- 7x^2 + 3xy - 9y
Step-by-step explanation:
(2xy- 4x^2) - (9y + 3x^2 - xy)
Add the second polynomial:
Change all the signs in the second polynomial because it has a negative sign before the parentheses.
= 2xy - 4x^2 - 9y - 3x^2 + xy
Combine like terms:
(-4x^2 - 3x^2) + (2xy + xy) - 9y
= -7x^2 + 3xy - 9y
Can i get a step by step for this?
Answer:
x = 85°Step-by-step explanation:
Sum of interior angles of any triangle is 180°:
52° + 43° + x = 180°95° + x = 180°x = 180° - 95°x = 85°Divide. Express your answer in simplest form. 2 1/2 ÷ 2 1/6
13/15 5 5/12 26/30 1 2/13
Answer:
[tex] \frac{15}{13} = 1 \frac{2}{13} [/tex]
Step-by-step explanation:
[tex]2 \frac{1}{2} \div 2 \frac{1}{6} \\ \\ \\ \frac{5}{2} \div \frac{13}{6} \\ \\ \\ \frac{5}{2} \times \frac{6}{13} \\ \\ \\ \frac{5}{1} \times \frac{3}{13} \\ \\ \\ = \frac{15}{13} \\ \\ \\ = 1\frac{2}{13} [/tex]
I hope I helped you^_^
Answer:
[tex]2 \frac{1}{2} /2 \frac{1}{6} = \frac{5}{2} / \frac{13}{6} [/tex]
[tex] = \frac{5}{2} \times \frac{6}{13 } = \frac{5 \times 6}{2 \times 13} [/tex]
[tex] = \frac{5 \times 3}{1 \times 13} [/tex]
[tex] = \frac{15}{13} [/tex]
[tex] = 1 \frac{2}{13} [/tex]
Step-by-step explanation:
Thank you!!!!!!!!!!!
PLEASE HELP WILL MARK BRAINLIEST
What is -100 represented in exponents
Step-by-step explanation:
[tex] { - 100}^{1} [/tex]
im kinda LayZai to do dis, help pleaseeeeeeeee
Answer: 2 hours 25 minutes
Step-by-step explanation:
Answer:
2 hours 25 minutes.
Step-by-step explanation:
12:15pm-9:50am=2:25.
Pretty much it, hope this helps!
please help me thank you
Answer:
Step-by-step explanation:
1.x +y = 1 Yes
2. Power of variable e is 3. So, it is not a linear equation
No.
3) Great than symbol is there. No, it is not a linear equation.
4. 2x -y = 2x + 5
2x - y - 2x = 5
-y = 5 is not a linear equation with two variable.
No.
5. No.
1) (5,14) ; (19,7)
[tex]Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{7-14}{19-5}\\\\=\dfrac{-7}{14}\\\\=\dfrac{-1}{2}[/tex]
2) (-10 , 1) ; (-10 ,4)
x- coordinate is same for both the points. So, the line is parallel to y-axis
Slope = undefined
[tex]3) (-3,-3) ; (15,13)\\\\slope=\dfrac{13-[-3]}{15-[-3]}\\\\=\dfrac{13+3}{15+3}\\\\=\dfrac{16}{18}\\\\=\dfrac{8}{9}[/tex]
[tex]4)(\dfrac{-1}{2},\dfrac{1}{7}) ; (\dfrac{-3}{2},\dfrac{2}{7})\\\\Slope=\dfrac{\dfrac{2}{7}-\dfrac{1}{7}}{\dfrac{-3}{2}+\dfrac{1}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{\dfrac{-2}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{-1}\\\\\\=\dfrac{-1}{7}[/tex]
Compare with y = mx + b ; here m is slope
1. y = -2x - 8
slope = -2
2. x = 3
Line is parallel to y-axis.
So, slope = undefined
3.2x - y = 4
2x - 4 = y
y = 2x - 4
Slope = 2
4.) 2x + y - 5 = 0
y = -2x + 5
Slope = -2
Compare the number. -9/16 ? -7/10
Answer:
-9/16 > -7/10
Step-by-step explanation:
7 times a number plus 3 is 38. find the number
Answer:
5
Step-by-step explanation:
7 x 5 = 35
35 + 3 = 38
what is the reciprocal of 1 1/4
Answer:
11/4 The reciprocal will be 4/11
y times 7 then add t expression
Answer:
7y + t
Step-by-step explanation:
I really need someone to help me out!
Answer:
y = 6x-13
Step-by-step explanation:
Given: y+1=6(x-2)
Distribute 6: y +1 = 6x -12
Isolate y: y = 6x -13 (subtracted 1 from both sides)
This is now in the form y = mx +b
Hope this helps!
Select all of the number of ways in which a line
and a circle can intersect.
Answer:
0, 1, and 2
This is the answer
What is the value of the underlined digit?
56.13
5
5
50
10
100
10
Answer:
I think that the answer is 50
i am never able to do these, their so confusing yet SO easy- please help!
Answer:
a) independent: area to be painted in sq ft
dependent: amount of paint needed in gallons
b) independent: amount of milligrams
dependent: amount of sleep
Step-by-step explanation:
Easy tip to remember that is almost always right:
Your X variable is always independent, and your Y variable is always dependent.
If you aren't given these variables, another thing you can do is ask for example, question a, ask yourself, "is the area you paint dependent on the amount of paint you need?" , or "is the amount of paint you need, dependent on how much your painting?"
Which variable depends on your other variable? Would help you find your dependent variable.
It makes sense that, the number of paint you need depends on how much sq ft you are painting.
Answer:
a) Independent variable: x (area to be painted)
Dependent variable: y (amount of paint needed)
b) Independent variable: x (amount of medication)
Dependent variable: y (amount of sleep)
Step-by-step explanation:
Independent variables are variables that do not depend on other variables to determine their values.
Dependent variables are variables that depend on other variables to determine their values.
Solve for n
n - 17=3
Answer:
N=20
Step by Step:
First you add 17 to both of the sides:
N−17+17=3+17
Second, you simplify;
N=20
Brainiest please?
Answer:D
Step-by-step explanation:
A car is traveling at a rate of 99 kilometers per hour. What is the car's rate in kilometers per minute? How many kilometers will the car travel in 15 minutes? Do not round your answers.
Answer:
it is going 1.65 kilometers per minute and it will travel 24.75 kilometers in 15 minutes
Step-by-step explanation:
Which of the following relation is/are function/s?
A.the rule which assigns each person a surname
B. the rule which assigns a pen and the color of it's ink
C.the rule which assigns the name of teachers you have
D. the rule which assigns to each person the name of his brother
Answer:
A. THE RULE WHICH ASSIGNS EACH PERSON USERNAME
Step-by-step explanation:
MARK PLS
Answer:
punta ka sa settings bi tapos I change ng Pilipinas yong server mo baka may makasagot ng tanong mo
Can anyone help me ?
Answer:
x=7.5
Step-by-step explanation:
15÷2=7.5
Tổng các góc của tứ giác bằng bao nhiêu
Answer:
tổng các góc của tứ giác bằng 360 độ
Step-by-step explanation:
ha? what language is that?
!
Darren is training for a triathlon. Each week, he goes to the gym for a maximum of 20 hours. He spends at least 8 of those hours weightlifting (x). He wants to spend no more than 15 hours doing cardio exercises (y). Write a system of linear inequalities that represents the restrictions of this scenario.
The graph of the equations was plotted using geogebra graphing and attached.
Let x represent the hours weightlifting and y represent the hours doing cardio exercises.
Since he spend a maximum of 20 hours, hence:
x + y ≤ 20 (1)
Also, he spends at least 8 of those hours weightlifting, hence:
x ≥ 8 (2)
He wants to spend no more than 15 hours doing cardio exercises, this is:
y ≤ 15 (3)
The graph of the equations was plotted using geogebra graphing and attached.
Find out more at: https://brainly.com/question/17178834
4 x cube + 20 X square + 33 X + 18 divided by X + 2
find remainder and quotient
Alan has forgotten his 4-digit PIN code.He knows it begins with a 6 and the 4 digits make an even number.How many different sets of 4 digits could it be?
Answer:
500.
Step-by-step explanation:
The last digit must end with 0, 2, 4, 6, 8 for the Pin code to be even.
The middle 2 digits may be any numbers.
So if the last number is 0 Then there are 10*10 = 100 possible PIN codes.
So as there are 5 possible last digits , the total possible sets of digits
= 5 * 100
= 500.
Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets
marked down, During the sale, rashguards sell for $5 less than full price. Miguel purchases 3
rashguards and pays a total of $60.
Which equation can you use to find how much money, f, each rashguard costs at full price?
The full price of a rashguard is $25 and the expression for the full price is 3 (x - 5) = 60.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the full price of each rashguard be x,
Rashguards sell for $5 less than full price.
x - 5
Miguel purchases 3 rashguards and pays a total of $60.
3 (x - 5) = 60
Simplifying,
x - 5 = 60 / 3
x - 5 = 20
x = 20 + 5
x = 25
Thus, the full price of a rashguard is $25 and the expression for the full price is 3 (x - 5) = 60.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ6
May I ask what’s this answer?
I wasn’t in class today:(
Answer:
Top box: 15
Bottom box: 480
Answer:
[tex]\left[\begin{array}{ccc}5&15&20\\120&360&480\end{array}\right][/tex]
Explanation:
For every 5 gallons, there's 120 miles. If we know we have 360 miles, we can see how many times 120 goes into 360, which is 3.
5 * 3 = 15.
Then just reverse the process
solution:
1. A carnival charges $2.50 per
ride
after an entrance fee. You paid a total
of $22.50 after 6 rides and the initial
entrance fee.
a. Write an equation that gives the
total cost as a function of the number
of rides.
1
b. Find the total cost for 10 rides.
Answer:
a. 2.50(6) + X = 22.50
b. $25.00
Step-by-step explanation:
A.
a ride = $2.50
total spent = $22.50
2.50(6) + X = 22.50
15.00 + X = 22.50
X = 22.50 - 15.00
X = 7.50
entrance fee = $7.50
B.
10*2.50= $25.00
Answer:
$22.50
Step-by-step explanation:
:)
Can someone explain this to me
Angle ADB is a right angle --- Given
Angle ADB is 90 degrees --- Definition of a Right Angle
Angle CDB is 90 degrees --- Definition of Supplementary Angles
Angle ADB = Angle CDB --- Definition of Congruent Angles
Proofs can be tricky! What helps me is thinking through them step by step and how I would prove I did something. While I'm not entirely sure what options you have for this proof, I've given my best guess.
Hope this helps!! :)
