Answer:
[tex]x=-3+\sqrt{3}[/tex] , [tex]x=-3-\sqrt{3}[/tex]
Step-by-step explanation:
x2 + 6x + 7 = 0
Solve the equation for x
To solve this we apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
a= 1 , b= 6 , c= 7
Plug in all the values in the formula
[tex]x=\frac{-6+-\sqrt{6^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=\frac{-6+-\sqrt{36-28} }{2(1)}[/tex]
[tex]x=\frac{-6+-\sqrt{8} }{2(1)}[/tex]
[tex]x=\frac{-6+-2\sqrt{2} }{2}[/tex]
Divide each term by 2
[tex]x=-3+- \sqrt{3}[/tex]
so we got two value for x
[tex]x=-3+\sqrt{3}[/tex] , [tex]x=-3-\sqrt{3}[/tex]
Which improper fraction is equal to the mixed number 4 7/9 btw its a mixed number fraction
A. 37/9
B. 47/9
C. 43/9
D. 20/9
plz help asap
One third of the sum of two consecutive odd integers is five less than the smaller integer
Express terms in i square root -40
HELP! A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and 6 packs of fruit rolls for a total of 152 snacks. The next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks. How many snacks are in one pack of granola bars and one pack of fruit rolls?
Answer: The number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Step-by-step explanation:
Let x be the number of granola bars in each pack and y be the number of fruit rolls in each pack .
Then according to the question we have the following system of equations :
[tex]10x+6y=152.....................(1)\\7x+12y=200.......................(2)[/tex]
Multiply equation (1) by 2 we get
[tex]20x+12y=304......................(3)[/tex]
Subtract equation (2) from equation (3), we get
[tex]13x=104\\\\\Rigtarrow x=8[/tex]
Substitute x=8 in (1), we get
[tex]10(8)+6y=152\\\\\Rightarrow6y=152-80\\\\\Rightarrow\ 6y=72\\\Rightarrow y=12[/tex]
Hence, the number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
How many centimeters is a piece of paper that measures 12 inches? centimeters?
Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
What is the expression phrase of the sum of a number x and 4, all divided by 3?
Estimate the unit rate
Trisha needs 4 yards of fabric to do a project. If she already has of a yard of fabric, what is the minimum amount of fabric she must buy to be able to complete her project? A. 3 5/6 B.4 1/12 C.4 1/6
Answer:
The answer is A. OR 3 5/6
Child development
What have researchers learned about the relationship between longer childhoods and brain development?
Longer childhoods are closely linked to brain development, enhancing cognitive abilities by allowing more complex neuronal connections and greater adaptation to environmental stimuli. Extended brain development is also associated with increased brain plasticity, leading to better adaptability and higher complex problem-solving skills.
Explanation:Research has found a significant relationship between longer childhoods and brain development. Humans have one of the longest childhoods among species, a period during which our brains continue to develop and mature significantly. This extended period of growth allows for more complex neuronal connections and adaptation to environmental stimuli, thus enhancing cognitive abilities.
A long childhood provides ample opportunities for learning and skill acquisition, and it is during this period that the brain is especially receptive to picking up new information. More prolonged brain development during childhood also tends to be associated with increased brain plasticity, meaning the brain's ability to change and adapt as a result of experiences. This plasticity aids in the formation of our identities and equips us to handle complex tasks and challenges as we grow.
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As Marta built a square fence around her garden, she wondered how much she would have to pay if she increased the length of each side of the fence by the same number of meters. Each meter of fence costs 3 dollars. Which of the following functions best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by m meters?
Hadlee got 18 out of 20 questions correct on her math quiz. What percent of the questions did she get right?
A pool is being drained at a rate of 120 gallons per minute.What is this rate in quarts per hour?
Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(5, −2)
(1, −1)
(−4, 2)
(4, 0)
(−2, 1)
The ordered pairs that satisfy the given inequality is required.
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
The given inequality is [tex]y-4x\geq -5[/tex]
Let us substitute each point in the inequality
[tex](5,-2)[/tex]
[tex]y-4x\\ =-2-4\times 5\\ =-22\ngeq -5[/tex]
[tex](1,-1)[/tex]
[tex]-1-4\times 1\\ =-5\geq -5[/tex]
[tex](-4,2)[/tex]
[tex]2-4\times -4\\ =18\geq -5[/tex]
[tex](4,0)[/tex]
[tex]0-4\times 4=-16\ngeq -5[/tex]
[tex](-2,1)[/tex]
[tex]1-4\times -2=7\geq -5[/tex]
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
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What is the greatest common factor of 125, 50, and 275?
Answer:
25 is the greatest common factor.
Step-by-step explanation:
We are given the following information in the question:
We have t find the greatest common factor of 125, 50 and 275.
We can use the method of prime factorization.
[tex]125 = 5\times 5\times 5\\50 = 5\times 5\times 2\\275 = 5\times 5\times 11[/tex]
Hence, the common factor of the the three numbers are:
[tex]5\times 5 = 25[/tex]
Hence, the greatest common factor 125, 50, 275 is 25.
factor completely: x^3+8x^2+7x
Directions: Use a proportion to solve the problem.
Emily weighs six times as much on Earth as she does on the Moon. If her weight is ninety pounds on earth, what would her weight be on the moon?
When writing the slope as a fraction which numner goes on top?
The number goes on top tells line changes in the y direction and how much it rises.
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
As, The top number indicates how much the line rises or moves in the y direction.
Given that the number is a 1 and is positive, we can infer that the line rises or moves up by one.
Hence, line changes in the y direction and how much it rises.
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Helpp me with this word problem number one
How to find the values of the six trigonometric functions for 180?
Use your calculator to evaluate the limit of x equals 1 to 3 of e raised to the x squared power, dx. Give your answer to the nearest integer.
Numerical Answers Expected!
Why is it important to simplify rational expressions before multiplying or dividing? How do you determine that a rational expression is in simplest form?
It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.
The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.
What is a rational number?A rational number is a number that can be written in the form of p/q where q is not equal to zero.
We have,
Some examples of rational numbers are:
38/44 or 39/63
We can divide this rational number into a decimal number but it is easier for us if we can simplify it in its simplest form.
There is no common factor between numerator and the denominator in its simplest form.
The simplest form of 38/44.
= 38/44
= 2 x 19 / 2 x 22
= 19/22
The simplest form of 39/62 is
= 39/63
= 3 x 13 / 3 x 21
= 13/21
Thus,
It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.
The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
6 less than the product of 3 and a number.
The algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.
What is an algebraic expression?An algebraic expression is a combination of terms separated by mathematical operations (+, -, *, /).
A term is a combination of numerals and variables where variables are raised to integral powers.
How to solve the question?In the question, we are asked to write the algebraic expression that represents the words "6 less than the product of 3 and a number".
Assuming the number to be x.
We first try to make the terms.
The term that will be formed using the words the product of 3 and a number is 3 * x = 3x.
The term using the word 6 is 6.
Now, to complete the expression, we combine the terms.
The words less than implies the difference. Thus the expression can be written as 3x - 6.
Thus, the algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.
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The line passing through the points (-7,4) and (-23,y) is parallel to a line that has a slope of -5/8. What is the value of y?
Which of the following phrases could represent the expression k - 4?
A.a number subtracted from four
B.four less a number
C.a number decreased by four
D.a number less than four
Select "Growth" or "Decay" to classify each function.
Function Growth Decay
y=200(0.5)^2t
y=1/2(2.5)^t/6
y=(0.65)^t/4
Which equation can be used to find the solution of (1/3)^d−5 = 81 ?
A. −d−5=4
B. d + 5 = 4
C. d−5=4
D. −d+5=4
1. The growth rate equation has a general form of:
y = A (r)^t
The function is growth when r≥1, and it is a decay when r<1. Therefore:
y=200(0.5)^2t --> Decay
y=1/2(2.5)^t/6 --> Growth
y=(0.65)^t/4 --> Decay
2. We rewrite the given equation (1/3)^d−5 = 81
Take the log of both sides:
(d – 5) log(1/3) = log 81
d – 5 = log 81 / log(1/3)
d – 5 = - 4
Multiply both sides by negative 1:
- d + 5 = 4
So the answer is D
Point F is on circle C.
What is the length of line segment GF?
a.12.5 units
b.15.0 units
c.17.5 units
d.20.0 units
Answer:
GF = 20 units .
Step-by-step explanation:
Given : A circle ,Point F is on circle C.
To find : What is the length of line segment GF.
Solution : We have given A circle ,Point F is on circle C.
In circle we can see in triangle GCE
EC = CF = 7.5
GE = 10.
By the Pythagorean theorem :
GC² = EG²+ EC².
Plugging the values
GC² = 10²+ 7.5².
GC² = 100 + 56 .25.
GC² = 156.25.
Taking square root.
GC = 12.5 units.
Radius of circle CF = 7.5 units .
GF = GC +CF.
GF = 12.5 + 7.5
GF = 20 units .
Therefore, GF = 20 units .
HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL
-x -y -z = -8
-4x + 4y + 5z = 7
2x + 2z = 4
I'm not sure how to work this out.
It takes 69 pounds of seed to completely plant an 8 -acre field. how many acres can be planted per pound of seed? math
What is a 401(k) plan? an investment plan offered by an insurance company a retirement plan offered by employers a personal retirement plan