Answer:
[tex]solution 1: \ \frac{7+\sqrt{65}}{2};[/tex]
[tex]solution2: \ \frac{7-\sqrt{65} }{2}.[/tex]
Step-by-step explanation:
x²-7x-4=0;
D=[b²-4ac]=49+16=65.
[tex]\left[\begin{array}{ccc}x=\frac{7+\sqrt{65}}{2} \\x=\frac{7-\sqrt{65}}{2} \end{array}[/tex]
2. Write an equation of the line that passes through (-2,3) and is parallel to the line y=2x-1.
Hello there! :)
Parallel lines have identical slopes.
So if one line has a slope of 2, then the line parallel o it would have the same slope.
Now, use the Point-Slope form:
y-y1=m(x-x1)
y-3=2(x-(-2)
y-3=2x+4
y=2x+4+3
y=2x+7
Therefore, the equation of the line is: y=2x+7Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]SilentNature :)[/tex]
The quadratic function f(x)=ax^2+4x+c has a maximum at the point (1, 9) . What are the values of a and c?
Answer: a = -2 and c = 7
Step-by-step explanation:
(this answer uses some basic calculus)
We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].
Answer:
a = -2
c = 7
Step-by-step explanation:
Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.
Solve for the value of a:Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:
We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:
[tex]x = \frac{-b}{2a}[/tex]
[tex]1 = \frac{-4}{2a}[/tex]
Multiply both sides by 2a:
(2a) 1 = [tex]\frac{-4}{2a} (2a)[/tex]
2a = -4
Divide both sides by 2 to solve for a:
[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]
a = -2
Therefore, the value of a = -2.
Solve for the value of c:Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:
f(x) = ax² + 4x + c
9 = -2(1)² + 4(1) + c
9 = -2 + 4 + c
9 = 2 + c
Subtract 2 from both sides to isolate c:
9 - 2 = 2 - 2 + c
7 = c
Double-check:In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):
f(x) = -2x² + 4x + 7
9 = -2(1)² + 4(1) + 7
9 = -2 + 4 + 7
9 = 9 (True statement).
Therefore, the correct answers are: a = -2, and c = 7.
Hey dude! you want some make of noise? I'm Dj from Pennsylvania
Find (a) the axis of symmetry and (b) the vertex of the graph of the function.
Ax) = 4x² - 8x
Step-by-step explanation:
I am not sure, what is the level of math for you currently.
do you do differentiation and derivatives already ?
because that is how I find "extreme points" and "turning points" of a function right away.
the vertex is the turning point for a quadratic parabola.
that means the point where the slope (= the first derivative) of the function is 0.
and that is also where the axis of symmetry is.
8x - 8 = 0
8x = 8
x = 1 (axis of symmetry).
y = 4×1² - 8×1 = 4 - 8 = -4
so, the vertex is (1, -4)
in case you don't understand derivatives yet, there is a shortcut for this for quadratic equations (fyi - in fact, the generic result of the first derivative) :
y = ax² + bx + c
the x value for the axis is then
x = -b/(2a)
in our case
a = 4
b = -8
x = - -8/8 = 8/8 = 1
and then y is calculated as above.
Leah is making cookies for her birthday party she wants to double the recipe and uses 1cup of sugar and 3 1/2 cups of flour.how many cups of sugar and flower does the original recipe call for.
Divide everything by half
Since she doubled the recipes, divide all by half.
1 cup of sugar / 2 = 1/2 cup of sugar
3 1/2 cups of flour / 2 = 7/2/2 cups of flour = 7/4 cups of flour or 1 3/4 cups of flour.
Answer:
Sugar: 1/2 Flour: 1 3/4
Step-by-step explanation:
1 cup of sugar
3 1/2 cups of flour
Since the recipe is doubled you'll divide the ingredients by 2.
Sugar: 1÷2=1/2
Flour: 3 1/2÷2=7/4
=1 3/4
Hope this helps :)
Find the slope between these two points: (-3. 2) and (7.9).
Answer:
m= 7/10 or m = 0.7
Step-by-step explanation:
Slope of the line between 2 points is found using the coordinates of the points.
m = (y2-y1) / (x2-x1) for (x1 = -3, y1 = 2) and (x2 = 7, y2 = 9)
m = (9 -2) / ( 7- -3)
m= 7 / 10
June earned $ 75 last week. April earned $25. June earnings were how many times greater than April
Answer:
3 times
Step-by-step explanation:
75÷25=3 times greater than April
Which of the following is the perimeter of a triangle with side lengths of 8 in, 9 in, and 11 in?
Answer:
show the question
Step-by-step explanation:
kyle has two snakes fluffy is 2 meters long muffy is 900 millimeters long compare their lengths to fill in the blanks
_____ is the longest snake.
_____ is ______
millimeters longer than ____
PLSS HELP!!
Answer:
fluffy is the longest snake.
muffy is 900 millimeters longer than fluffy
Step-by-step explanation:
PA BRAINLIEST
HOPE ITS HELP
GOD BLESS
Colin got a new video game. He scored 31 points on the first level, 31 points on the second level, 31 points on the third level, and 31 points on the fourth level. What kind of sequence is this? both, neither ,arithmetic, geometric
Answer:
Both
Step-by-step explanation:
An arithmetic sequence is given by the next form:
[tex]a_{n} = a_{1} + (n-1)d[/tex]
Where [tex]a[/tex] is the [tex]n^{th}[/tex] term of the sequence, [tex]a_{1}[/tex] the first term of the sequence and [tex]d[/tex] the common difference between terms.
So the given sequence is of the form, because the common difference between terms is 0.
[tex]a_{n} = 31 + (n - 1) 0 = 31[/tex]
A geometric sequence is given by the next form
[tex]ar^0, ar^1, ar^2, ar^3, ar^4, \cdot \cdot \cdot[/tex]
When [tex]r\neq 0[/tex]
In this occasion our [tex]a=31[/tex] and the [tex]r = 1[/tex]
So both sequence represent the given one.
Please need answer now will mark brainliest and no files please What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
6/6, simplified to 1,
negative slope so -1
Translate this phrase into an algebraic expression.
Five more than the product of 11 and a number
Use the variable n to represent the unknown number.
Answer:
5+(11 x n)
Step-by-step explanation:
I hope this helps
please help with this
Answer:
2,4,6,
6,12,18
10,20,30
can someone help me with this and also happy thanksgiving if you celebrate it
My ans is C
24 - 6x + 40 = 34
24+40 - 6x = 34
64 - 6x = 34
6x = 64-34
6x = 30
x = 5 ^^
i need help ! :) i will give brainliest if u dont troll and actually help
Answer:
50
Step-by-step explanation:
150 + 50 is $200.
350 - 200 is $150.
So that leaves 150 dollars left.
150/3 is 50 people.
Answer:
50 guest is the answer.
Step-by-step explanation:
...so:
$350-$150 for the DJ
$200-$50 for the cake.
and, $3 per party guest for food.
That would be:
$150/$3 = 50 guest.
Holding the price level constant, we would expect that if the multiplier is 1.5, the cumulative effect of this change in M on AD will be: $ billion
Greg paid $324.50 for guitar lessons. He paid a $124.50 registration fee and $40 for each week he was enrolled in lessons. What is w, the number of weeks Greg was enrolled in guitar lessons?
0.94 written as a fraction in simplest form
Which term from the drop-down menu makes the statement true?
Select Choice triangles are similar.
A list of choices that appears on a computer screen when a person clicks on the menu title To print the document click on print in the file drop down menu
Find the surface area of the sphere.
Answer:
R is 4*Pi*R2
Complete the statement:
If AB, CD, then
a. AB - CD
b. AB = CD
C. ABCD
d. AB - CD
-
plzz help its so confusing
espero que sea de tu agrado la tarea que te estoy enviando
soy de peru
brillith2022
3. (a) Find the greatest common divisor of 34 and 89 using the Euclidean algo rithm.
(b) Express gcd (34, 89) as a linear combination of 34 and 89.
(c) Find an inverse of 34 modulo 89.
(d) Solve the linear congruence 34x = 53(mod 89).
a. We have GCD(34, 89) = 1; using the Euclidean algorithm,
89 = 2•34 + 21
34 = 1•21 + 13
21 = 1•13 + 8
13 = 1•8 + 5
8 = 1•5 + 3
5 = 1•3 + 2
3 = 1•2 + 1
b. Working backwards,
1 = 3 - 2
1 = 3 - (5 - 3) = 2•3 - 5
1 = 2•(8 - 5) - 5 = 2•8 - 3•5
1 = 2•8 - 3•(13 - 8) = 5•8 - 3•13
1 = 5•(21 - 13) - 3•13 = 5•21 - 8•13
1 = 5•21 - 8•(34 - 21) = 13•21 - 8•34
1 = 13•(89 - 2•34) - 8•34 = 13•89 - 34•34
c. Using the linear combination find in part b,
1 ≡ 13•89 - 34•34 (mod 89)
1 ≡ (-34)•34 (mod 89)
and
-34 ≡ -34 + 89 ≡ 55 (mod 89)
So, the inverse of 34 modulo 89 is 55.
d. Multiply both sides of the congruence by the inverse of 34:
55•34x ≡ 55•53 (mod 89)
x ≡ 2915 ≡ 32•89 + 67 ≡ 67 (mod 89)
PLEASE HELP WITH THIS ONE QUESTION
Answer:
Step-by-step explanation:
(2ab^2 + 3c^2) (2ab^2 + 3c^2) = 4a^2b^4 + 6ab^2c^2 + 6ab^2c^2 + 9c^4
= 4a^2b^4 + 12ab^2c^2 + 9c^4
Find the value of X Show all work
(2x+6)
36
(4x-18)
Answer:
X=30
Step-by-step explanation:
(2X + 6) + 36 = (4X- 18)
36=4X-18-2X-6
36=2X-24
2X = 60
X = 30
wELCOME
This is the ANSWER
How do the slopes of A B ↔ and the parallel line through point C compare?
Answer:
The slopes of AB↔ and the parallel line through point C are equal.
Step-by-step explanation:
Edmentum
Answer:
The slopes of the parallel AB lines through point C are equal.
Step-by-step explanation:
. Consider the set {7,8,9), a subset of this set includes:
{2,3}
b. {5,63
c. none of these
d. {10,11
Answer:
Option "C" none of these is the correct answer.
Step-by-step explanation:
The subset of the set {7, 8, 9} must have the elements of this set only.
Hope this helps :)
pls help. I am not very smart!
Which equation represents this statement?
3 1/3 is the same as the sum of −1/2 times a number and −3
3 1/3+(−1/2)=−3x
3 1/3=−1/2x+(−3)
3 1/3+(−1/2x)=−3
3 1/3=−1/2+(−3x)
Answer:
3 1/3=−1/2x+(−3)
Step-by-step explanation:
The equation for the given problem can be written as 1/3 = -1/2x + -3. The correct option is (B).
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The statement given in the problem is, " 1/3 is the same as the sum of −1/2 times a number and −3".
Suppose the unknown number be x.
Then, the equation for the given statement can be written as,
1/3 = -1/2x + -3
Hence, the equation that represents the given statement is 1/3 = -1/2x + -3.
To know more about linear equation click on,
https://brainly.com/question/11897796
#SPJ2
A clothing company makes a profit of $2.3 million. This is $4.1 million more than last year. What was the profit last year?
Answer:
-1.8 million. This means that the business likely spent a lot on production and generated very little sales during the first year.
Step-by-step explanation:
2.3 - 4.1= -1.8
pamelas age is three times jiris age the sum of their age is 32 what is jiris age
Answer:
Jiris age = 8
Step-by-step explanation:
Jiris = j
Pamelas Age = 3j
Pamelas's age + Jiris age = 32
3j + j = 32
4j = 32
j = 32 / 4
= 8
Jiris age = 8
Pamelas age = 3 times Jiris's
Pamelas age = 24
Answer:
8 years old.
Step-by-step explanation:
P = 3I
P + I = 32
Plug P = 3I into the second equation:
3I + I = 32
I = 32/4 = 8
So Jiris's age = 8.