Answer:
.80
or
0.80
Step-by-step explanation:
80 is out of 100, which is other words is .80 or 0.80
What is the slope of this line? Enter your answer as a fraction in simplest term.
How many solutions does the following equation have?
4(x-2)-2=2x+2x-10
Answer:
all real numbers
Step-by-step explanation:
Write a linear equation to represent this
i need the answer asap i’ll make you the brainliest
Answer
the second one
what plus 80 and 70 equals 180
Answer:
30
Step-by-step explanation:
Take 80 and 70 and add them together to get: 130
Then subtract 130 from 180
To get: 30
:)
Answer:
30
Step-by-step explanation:
80 + 70 = 150
180- 150 = 30
therefore 80 + 70 + 30 = 180
HELP IT'S URGENT.
Please show workings.
No 4 (see image)
Answer:
(i) (b² - 2ac)/c²(ii) (3abc - b³)/a³Step-by-step explanation:
α and β are the roots of the equation:
ax² + bx + c = 0Sum of the roots is:
α + b = -b/aProduct of the roots is:
αβ = c/aSolving the following expressions:
(i)
1/α² + 1/β² =(α² + β²) / α²β² =((α + β)² - 2αβ) / (αβ)² = ((-b/a)² - 2c/a) / (c/a)² = (b²/a² - 2c/a) * a²/c² = b²/c² - 2ac/c² =(b² - 2ac)/c²----------------
(ii)
α³ + β³ =(α + β)(α² - αβ + β²) =(α + β)((α + β)² - 3αβ) = (α + β)³ - 3αβ(α + β) =(-b/a)³ - 3(c/a)(-b/a) =-b³/a³ + 3bc/a²= 3abc/a³ - b³/a³=(3abc - b³)/a³[tex] \huge \underline{\tt Question} :[/tex]
If α and β are the roots of the equation ax² + bx + c = 0, where a, b and c are constants such that a ≠ 0, find in terms of a, b and c expressions for :
[tex] \tt \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]α³ + β³[tex] \\ [/tex]
[tex] \huge \underline{\tt Answer} :[/tex]
[tex] \bf \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }[/tex][tex] \bf \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}[/tex][tex] \\ [/tex]
[tex] \huge \underline{\tt Explanation} :[/tex]
As, α and β are the roots of the equation ax² + bx + c = 0
We know that :
[tex] \underline{\boxed{\bf{Sum \: of \: roots = \dfrac{- coefficient \: of \: x}{coefficient \: of \: x^2}}}}[/tex][tex] \underline{\boxed{\bf{Product \: of \: roots = \dfrac{constant \: term}{coefficient \: of \: x^2}}}}[/tex][tex] \tt : \implies \alpha + \beta = \dfrac{-b}{a}[/tex]
and
[tex] \tt : \implies \alpha\beta = \dfrac{c}{a}[/tex]
[tex] \\ [/tex]
Now, let's solve given values :
[tex] \bf \: \: \: \: 1. \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]
[tex] \tt : \implies \dfrac{\beta ^2 + \alpha ^2}{\alpha ^2 \beta ^2}[/tex]
[tex] \tt : \implies \dfrac{\alpha ^2 + \beta ^2}{\alpha ^2 \beta ^2}[/tex]
[tex] \\ [/tex]
Now, by using identity :
[tex] \underline{\boxed{\bf{a^2+ b^2 = (a+b)^2 -2ab}}}[/tex][tex] \tt : \implies \dfrac{(\alpha + \beta)^2 - 2 \alpha\beta}{(\alpha\beta)^2}[/tex]
[tex] \\ [/tex]
Now, by substituting values of :
[tex] \underline{\boxed{\bf{\alpha + \beta = \dfrac{-b}{a}}}}[/tex][tex] \underline{\boxed{\bf{\alpha\beta = \dfrac{c}{a}}}}[/tex][tex] \tt : \implies \dfrac{\Bigg(\dfrac{-b}{a}\Bigg)^2 - 2 \times \dfrac{c}{a}}{\Bigg(\dfrac{c}{a}\Bigg)^2}[/tex]
[tex] \tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2c}{a}}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2ac}{a^{2} }}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{\dfrac{b^2 - 2ac}{a^2 }}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{b^2 - 2ac}{\cancel{a^2} } \times \dfrac{ \cancel{a^2}}{c^2}[/tex]
[tex]\tt : \implies \dfrac{b^2 - 2ac}{c^2 }[/tex]
[tex] \\ [/tex]
[tex] \underline{\bf Hence, \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }}[/tex]
[tex] \\ [/tex]
[tex] \bf \: \: \: \: 2. \: \alpha ^3 + \beta ^3 [/tex]
[tex] \\ [/tex]
By using identity :
[tex] \underline{\boxed{\bf{a^3+ b^3 = (a+b)(a^2 -ab + b^2)}}}[/tex][tex] \tt : \implies (\alpha + \beta)(\alpha ^2 - \alpha\beta + \beta ^2)[/tex]
[tex] \tt : \implies (\alpha + \beta)(\alpha ^2 + \beta ^2 - \alpha\beta)[/tex]
[tex] \\ [/tex]
By using identity :
[tex] \underline{\boxed{\bf{a^2+ b^2 = (a+b)^2 -2ab}}}[/tex][tex] \tt : \implies (\alpha + \beta)(\alpha + \beta)^2 -2 \alpha\beta - \alpha\beta)[/tex]
[tex] \tt : \implies (\alpha + \beta)((\alpha + \beta)^2 -3 \alpha\beta)[/tex]
[tex] \\ [/tex]
Now, by substituting values of :
[tex] \underline{\boxed{\bf{\alpha + \beta = \dfrac{-b}{a}}}}[/tex][tex] \underline{\boxed{\bf{\alpha\beta = \dfrac{c}{a}}}}[/tex][tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg( \bigg(\dfrac{-b}{a} \bigg)^2 -3 \times \dfrac{c}{a}\Bigg)[/tex]
[tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3c}{a}\Bigg)[/tex]
[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3ac}{a^{2} }\Bigg)[/tex]
[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2 - 3ac}{a^2} \Bigg)[/tex]
[tex]\tt : \implies \dfrac{-b}{a} \times \dfrac{b^2 - 3ac}{a^2} [/tex]
[tex]\tt : \implies \dfrac{ - b(b^2 - 3ac)}{a \times a^2} [/tex]
[tex]\tt : \implies \dfrac{ - b^3 + 3abc}{a^3} [/tex]
[tex] \\ [/tex]
[tex] \underline{\bf Hence, \: \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}}[/tex]
-7.8× (- 1.5)
plz help ASAP
Answer:
11.7
Step-by-step explanation:
(−7.8)(−1.5)
Hope ths helps
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Question 3 of 20 -
E
ZahraouiAziz Midterm Geometry Pt 1 2020-2021 Question: 134
A line segment has an endpoint at (4.6). If the midpoint of the line segment is (1,5), what are the.coordinates of the point at the other endorine ne segment?
O (3, 1)
O (-2,4)
O (7.7)
O (5, 11)
Chrome OS. 28m)
Switched network connection
Your connection
has switched td al
Previous
O
Fo
Answer: most likely be (7,7) not sure right or wrong but i tried so yeah
Step-by-step explanation:
PLZ HELP ME ILL GIVE U 20 POINTS!!!!!!!!!!!!!!!!
Answer:
1. y < 4
2. x </= -3
3. y >/= 2
4. x > -2
5. x </= 2
6. x < 0
7. t > -2
8. N >/= 3
9. n < -4
10. x < 5
Step-by-step explanation:
the cost of 3 boxes is
Identify the real and imaginary parts of the given number. Then identify whether the number belongs to each of the following sets: real numbers, imaginary numbers, and complex numbers.
−9 + 9i
The real part of −9 + 9i is ____ and the imaginary part is ____.
The number −9 + 9i belongs to which of the following sets. Select all that apply.
A real numbers
B imaginary numbers
C complex numbers
See image.
Answer:
-9 is real, 9i is imaginary, C
Step-by-step explanation:
-9 is real because you can literally draw nine things.
9i is imaginary because i is √-1 and square roots of negatives are imaginary.
It is complex because complex expressios are written as a+bi.
Which of the following sets of numbers could represent the three sides of a triangle?
1) {15, 23, 37}
2) {6,8,14}
3) {7, 22, 30}
4) {7, 21, 30}
Answer:
NONE
Step-by-step explanation:
You have to do a² + b² = c²
To do it you have to put the three numbers from least to greatest for it to work. They already are so that's good.
15² + 23² = 37² (solve)
225 + 529 = 1369
754 ≠ 1369
6² + 8² = 14² (solve)
36 + 64 = 196
100 ≠ 196
7² + 22² = 30²
49 + 484 = 900
433 ≠ 900
7² + 21² = 30²
49 + 441 = 900
490 ≠ 900
I don't know what happened, but none of these would work.
I even used a pythagorean theorem calculator to check my work and none of them match.
Hope this helps!
Find the slope pls help me I need this
Answer: 3/2x
Step-by-step explanation: it going up 3 units and right 2 units. And since slope is rise/ run it 3/2x
How would you graph the solution to -5w + 9 = 14 on a number line?
Answer:
Step-by-step explanation:
w= -1
Your circle will be on the -1
Answer:
Taft
Step-by-step explanation:
Sally buys a pair of shoes that are discounted 60% off the original price. If Sally pays $50 for the shoes, what was the original price of the shoes?
Answer:
90$
Step-by-step explanation
Step 1: You need to find how much was the 60% discount
Step 2: To find that multiply .6 by 50 you will get 30
Now you know how much was 60% discount
Step 3: Add 30(the discount) + 50(the prce sally pays) = 90 (the oriagnal price)
Alguém pode me ajudar por favor???????????
Answer:
The asnwer is the first one
Step-by-step explanation:
thx for the poins
BRAINLIEST TO THE CORRECT ANSWER! 20 POINTS!!
Maricella solves for x in the equation 4 x minus 2 (3 x minus 4) + 4 = negative x + 3 (x + 1) + 1. She begins by adding –4 + 4 on the left side of the equation and 1 + 1 on the right side of the equation. Which best explains why Maricella’s strategy is incorrect?
The statement that best explains why Maricella's strategy is incorrect based on the distribution property and order of operation is option A.
Recall:
When given an equation involving brackets, the distribution property must be applied first which involves multiplying every term in a bracket by the term outside the bracket.In the equation given, to solve for x, Maricella needs to apply the distribution property by using -2 to multiply each term in (3x - 4) and using +3 to multiply every term in (x + 1).
The next step will now be addition and subtraction of like terms.
Therefore, the statement that best explains why Maricella's strategy is incorrect based on the distribution property and order of operation is option A.
Learn more about distribution property on:
https://brainly.com/question/11279503
Answer:
A!!!
Step-by-step explanation:
edge2022
john is 2 years younger than his sister, annie. Last year, John was half Annie's age. How old are john and Annie now?
Answer:
John is 3 and Annie is 5 because to be half of someone's age while being to years younger it would have to be 2 and 4 - but then a year passed and so the are now 3 and 5.
Step-by-step explanation:
The present age of John is 3 years
The present age of Annie is 5 years
Given that John is 2 years younger than Annie's age
Let the present age of John be "J"
Let the present age of Annie be "A"
According to the given situation
[tex]\rm J = A -2........(1)\\[/tex]
One year ago the age of John = [tex]\rm J-1[/tex]
One year ago the age of Annie = [tex]\rm A -1[/tex]
According to the given situation
[tex]\rm\dfrac{A-1}{2}= J-1.........(2)[/tex]
On solving for equations (1) and (2) we get
A = 5 and J = 3
So the present age of Annie is 5 years
The present age of John is 3 Years
For more information please refer to the link given below
https://brainly.com/question/21835898
Graph a scatter plot using the given data.
Answer:
Here is the answer.
Step-by-step explanation:
∀x∀y(((x ≥ 0) ∧ (y < 0)) → (x – y > 0))
A. A non-negative number - a negative number is positive.
B. For any two real numbers, the first is non-negative, the second is negative, and the difference is positive.
C. For every non-negative number, one can find a negative number so that the first number minus, the second is positive.
D. One can find a non-negative number and a negative number so that the first minus, the second is positive.
E. One can find a non-negative number so that for any positive number chosen, the first number minus, the second is positive.
Answer:
B. For any two real numbers, the first is non-negative, the second is negative, and the difference is positive.
Step-by-step explanation:
To answer this question, I'll analyse the mathematical statements one at a time
The analysis is as follows:
∀x -> This means real number x
∀y -> This means real number y
(x ≥ 0) -> Such that real number x is greater than or equal to 0. In other words, x is positive
∧ -> and
(y < 0)-> y is less than 0. In other words, y is negative
So, there are two real numbers: x and y
→ (x – y > 0) -> Their difference is greater than 0. In other words, their difference is positive
When the analysis above is compared to the list of given options; the option that match is B.
Hence, option B answers the question.
A cookie factory uses 3 bags of flour in each batch of cookies. The factory used 2 7/10 bags of flour yesterday. How many batches of cookies did the factory make.
give me answer.1 to 100 plus. like:1+2+3+4+5+6+7+8+9+10+11.........
Answer:
5,050
Step-by-step explanation:
Use sigma notation to add all the numbers together (∑)
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A. g(x) = f(x) - 5
B. g(x) = f(x - 5)
C. g(x) = f(x) - 2
D. g(x) = f(x + 2)
Answer:
A.
Step-by-step explanation:
It just is trust
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
-12
Step-by-step explanation:
Answer:
-12
Step-by-step explanation:
Its -12 for sure!!!!!
(PLEASEEE HELP I DONT UNDERSTAND) Which of the following equations represents a linear NON-proportional function?
A) y=3x+0
B) y=x/4
C) y=7x
D) y=2/5x+7
The question is Find the constant of proportionality in the graph below
Answer:
4.5
Step-by-step explanation:
HELP ME PLEASE! how do you write 0.0370 as a scientific notation
PLEASE HELP HURRY!! What is the value of x?
Is every relation also a function? Explain
Answer:
no
Step-by-step explanation:
they are not
Answer:
Step-by-step explanation:
In fact, every function is a relation. However, not every relation is a function. In a function, there cannot be two lists that disagree on only the last element. This would be tantamount to the function having two values for one combination of arguments.
y= (x + 4)2 + 8
how do you simplify this equation
Answer:
Step-by-step explanation:
you could distribute and combine like terms
y=(x+4)2+8
y=2x+8+8
y=2x+16