the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).
To solve the quadratic equation[tex]\( x^2 - 7x - 8 = 0 \)[/tex]by completing the square, we follow these steps:
1. Move the constant term to the other side of the equation:
[tex]\[ x^2 - 7x = 8 \][/tex]
2. To complete the square, take half of the coefficient of ( x ) (which is -7), square it, and add it to both sides of the equation:
[tex]\[ x^2 - 7x + \left( \frac{-7}{2} \right)^2 = 8 + \left( \frac{-7}{2} \right)^2 \]\[ x^2 - 7x + \frac{49}{4} = 8 + \frac{49}{4} \][/tex]
3. Simplify the right side of the equation:
[tex]\[ x^2 - 7x + \frac{49}{4} = \frac{32}{4} + \frac{49}{4} \]\[ x^2 - 7x + \frac{49}{4} = \frac{81}{4} \][/tex]
4. Write the left side of the equation as a perfect square:
[tex]\[ \left( x - \frac{7}{2} \right)^2 = \frac{81}{4} \][/tex]
5. Take the square root of both sides to solve for ( x ):
[tex]\[ x - \frac{7}{2} = \pm \sqrt{\frac{81}{4}} \]\[ x - \frac{7}{2} = \pm \frac{9}{2} \][/tex]
6. Solve for ( x ) by adding [tex]\( \frac{7}{2} \)[/tex]to both sides:
[tex]\[ x = \frac{7}{2} \pm \frac{9}{2} \][/tex]
This gives us two solutions:
[tex]\[ x = \frac{7}{2} + \frac{9}{2} = \frac{16}{2} = 8 \]\[ x = \frac{7}{2} - \frac{9}{2} = \frac{-2}{2} = -1 \][/tex]
So, the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).
just answer no need to explain.
How many prime numbers between 8 and 60 leave a remainder of 2 when divided by 6?
A) 0
B) 1
C) 4
D) 6
E) 7
plzzzz help!!!!!!!!!!!!!
Answer:
x + 2 is in both the numerator and the denominator, so the correct answer is A.
What is the simplest form of the expression -2x^2(x+5)+x(2x^2-10x)+x
Answer:
x
Step-by-step explanation:
-2x^2(x-5)+x(2x^2-10x)+x
Distribute-2x^2 through parentheses
-2x^3+10x^2+(2x^2-10x)+x
Distribute x through parentheses
-2x^3+10x^2+2x^3-10x^2+x
Eliminate the opposites
-2x^3+2x^3=0 and 10x^2-10x^2=0 both sets of opposites cancel each other out, which leaves us with just x remaining.
The simplest form of of the expression is x.
there are 3 black marbles in and 4 red marbles in a bag. what is the probability that you will pick two black marbles put of the bag without replacing the first one?
[tex] |\Omega|=7\cdot6=42\\
|A|=3\cdot2=6\\\\
P(A)=\dfrac{6}{42}=\dfrac{1}{7}\approx14\% [/tex]
Use the law of cosines to explain why c^2=a^2+b^2 for triangle ABC, where angle C is a right angle.
how many lines of symmetry does the flag of Iraq have
Final answer:
The flag of Iraq has no lines of symmetry due to its horizontal stripes of different colors and the specific orientation of the Arabic Kufic script of the Takbir written in the center.
Explanation:
The question about how many lines of symmetry the flag of Iraq has can be classified as a question in the field of mathematics, particularly in the study of geometry. Symmetry in flags can pertain to reflections across certain lines where the flag is indistinguishable from its mirror image.
As of my knowledge update, the flag of Iraq consists of three horizontal stripes of red, white, and black, with the Takbir ('Allahu Akbar') written in the center in green Kufic script. As the script introduces a specific orientation and the colors do not symmetrically repeat, the flag does not have horizontal or vertical lines of symmetry. The presence of textual elements disrupts potential symmetry, considering the particular way letters must be oriented to be readable. Hence, the flag of Iraq does not have any lines of symmetry.
The price of a stock had a change of –3 dollars.
Explain how you would use a number line to find the absolute value of –3
Hello! The answer to your question is: Draw out a horizontal line. Place 0 at the center. Then place evenly spaced tick marks on either side of 0. Label the right side of tick marks as 1, 2, 3, moving from 0 and going to the right
Label the left side of tick marks -1, -2, -3, starting at 0 and moving left
The location -3 on the number line is exactly 3 units away from 0. We start at 0 and move to -3 by moving 3 spots to the left; or we start at -3 and move 3 units to the right to get to 0.
Therefore, the absolute value of -3 is 3
Absolute value on a number line is the distance a number is from 0
The distance is never negative.
Hope this helped!
(7,1,9,52,12,25,9,7,7)what are the outliers?
solve the equation for a
w=7a+4b
The linear equation for "a" in terms of "w" and "b" is:
a = (w - 4b) / 7By following these steps, we have solved the linear equations for "a" and expressed it in terms of "w" and "b."
To solve the equation for "a" in terms of "w" and "b," we can follow these steps:
Step 1: Start with the equation:
w = 7a + 4b
Step 2: Isolate the term with "a" on one side of the equation. To do this, subtract 4b from both sides:
w - 4b = 7a
Step 3: Divide both sides of the equation by 7 to solve for "a":
(w - 4b) / 7 = a
Step 4: Simplify the expression:
a = (w - 4b) / 7
Therefore, the linear equation for "a" in terms of "w" and "b" is:
a = (w - 4b) / 7By following these steps, we have solved the linear equations for "a" and expressed it in terms of "w" and "b."
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Max donated 16 dog collars to the dog shelter. Mia donated some leashes. How many items does Mia need to donate that would require you to regroup to find the total number of items donated?
Mia can donate up to 4 leashes without requiring regrouping to find the total number of items donated.
To determine how many leashes Mia needs to donate such that you would need to regroup to find the total number of items donated, we need to know the maximum capacity of the shelter's storage or the maximum number of items that can be comfortably accommodated without regrouping.
If we assume that the shelter's storage can hold a maximum of 20 items comfortably without needing to regroup, then we can calculate the number of items Max and Mia can donate without regrouping:
Max donated 16 dog collars, and the shelter can accommodate 20 items without regrouping. So, Max has donated within the capacity without needing to regroup.
Now, let's see how many leashes Mia can donate without exceeding the capacity:
20 (maximum capacity) - 16 (Max's donation) = 4
Mia can donate up to 4 leashes without requiring regrouping to find the total number of items donated. If Mia donates more than 4 leashes, you would need to regroup to calculate the total number of items donated.
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First to answer with work shown gets Brainliest
Which substance traps pathogens and prevents them from entering the deeper tissue of the body? tears
Answer:
Mucus
Step-by-step explanation:
Write an inequality to represent this situation: The temperature stayed above -15 degrees.
Samantha is installing a new window in her bedroom wall. She wants to center it horizontally. the window is 40.5 inches long, and the wall is 105.25 inches long. how far from each edge of the wall should Samantha install the window?
To center the window horizontally on a wall, subtract the window's length from the wall's length and divide by two. Samantha should install the window 32.375 inches from each edge of the wall.
The student is trying to determine how far from each edge of the wall she should install the window to center it horizontally. To find this, we calculate the difference between the wall's length and the window's length and then divide that number by two. The wall is 105.25 inches long, and the window is 40.5 inches long.
To center the window horizontally, we do the following calculation:
(Length of wall - Length of window) / 2
(105.25 inches - 40.5 inches) / 2
64.75 inches / 2
= 32.375 inches.
Therefore, Samantha should install the window 32.375 inches from each edge of the wall to center it horizontally. This calculation ensures the window is positioned equally from both sides of the wall, assuming the wall is straight and the measurements are accurate.
sector area definition
A sector is a portion of a circle enclosed by two radii and the arc between them. The area of a sector is found by multiplying the central angle in radians by the square of the radius and dividing by 2.
Explanation:In mathematics, a sector is a portion of a circle enclosed by two radii and the arc between them. The area of a sector is found by multiplying the central angle in radians by the square of the radius and dividing by 2.
For example, if we have a sector with a radius of 5 units and a central angle of π/3 radians (60 degrees), we can calculate the area as follows:
Find the area of the whole circle with radius 5: A = π(5)^2 = 25π square unitsCalculate the fraction of the circle represented by the sector: Fraction of circle = π/3 / (2π) = 1/6Multiply the area of the whole circle by the fraction of the circle represented by the sector: Area of sector = (1/6) * 25π = (25/6)π square unitsLearn more about Sector area definition here:https://brainly.com/question/29055300
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what is the relationship of 7 and -7
In a recent fundraising campaign, Rise Over Run received 20 checks of various amounts to donate to their favorite charities. Olive uses this spinner to determine which charity will receive each check.
About how many of the 20 checks should arise Over Run expect to go to their TreeHuggers Campaign ?
Answer:
6 checks
Step-by-step explanation:
The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
For this case, we're specified that:
The spinner has 10 parts.
3 belong to Treehuggers2 belong to Ameriteach5 belong to Paws of PeaceThus, the probability of getting the spinner fall on treehugger is 3/10 (three favorable parts of spinner to ten total parts, all parts assumingly equally probable and spinner assumingly not falling in the mid of two parts).
20 checks, all will be accompanied with 20 spins, all independent of each other.
Let X = total number of times the spinner falls on Treehuggers
And let Success for a spin = It landing on Treehugger
Failure for a spin = It not landing on Treehugger
Probability of success = p = 3/10 = 0.3Probability of faillure = 1-p = 7/10 = 0.7n = 20, so we get:
[tex]X \sim B(n=20,p=0.3)[/tex]
The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign = expected number of successes in those 20 spins = the expected number of values of X.
Since X follows a binomial distribution, we get:
[tex]E(X) = np = 20 \times 0.3 = 6[/tex]
Thus, the expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.
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A professional basketball team must play a total of 85 came before the playoffs begin. The team has played 3/5 of the scheduled games, if the team plays 10 more games, what is the total number of games they will have played
After calculating the number of games already played as a fraction of the total and adding 10 more games, it is determined that the team will have played 61 games.
Explanation:The subject of this question is Mathematics, particularly it involves operations with fractions. The team has played 3/5 of the total scheduled games. So let's calculate how many games that would be by multiplying the total number of games, 85, by 3/5:
The team has already played 85 * 3/5 = 51 games.
If the team plays 10 more games, we need to add this to the number of games already played:
51 (already played games) + 10 (more games) = 61 games.
Therefore, the total number of games the team will have played after 10 more games is 61 games.
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A rectangle has vertices at these coordinates
. (−6, 10), (−6, 1),(1, 10)
What are the coordinates of the fourth vertex of the rectangle?
Enter the coordinates in the boxes.
( , )
Answer:in knew it but i forgot
Step-by-step explanation:
Can someone please help me with this?
If 60 of the 200 students are girls, then what percent of the students are girls?
how do I find circumference
A chief had 6 cups of berries and will use 2/3 cup of berries for each serving of fruit salad. How many servings can be made ?
write an expression that represent the sum of r and 7
Final answer:
The expression that represents the sum of r and 7 is written simply as r + 7. This is a basic operation in algebra involving the addition of a variable and a constant.
Explanation:
To write an expression that represents the sum of r and 7, you simply add these two together. The mathematical expression for this is r + 7. This is a basic algebraic expression that demonstrates how to represent the addition of a variable, in this case r, with a constant number, which is 7.
A remote-control airplane descends at a rate of 2 feet per second. After 3 seconds it is 67 feet above the ground. Write the equation in point-slope form that models the situation. Then, find the height of the plane after 8 seconds.
rachel uses grid paper to plan a mural to paint at her school. the design will be made of two connected rectangles. the larger rectangle will have an area between 35 square feet and 45 square feet. the smaller rectanglewill have an area between 10 square feet and 20 square feet. Draw and label a diagram to show what Rachel could plan. Explain how to find the total area.
When finding out if 2 triangles are congruent, is it possible to only use a side and angle if those are the only 2 provided? Help ASAP please.
What is 20/50 reduced to a smaller fraction?
Which of the following equations represent a proportional relationship
a: y=12.5x
b: y= 4x-1
c: x+y=3
d: y=3x (squared)