The solutions of x1 = 7 and x2 = -3 with x1 through solving the quadratic equation x²−4x−21=0 by factoring
The equation :x² - 4x - 21 = 0, solve it by factoring it.The first step is to find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3.So, we rewrite the equation using -7 and 3 instead of -4x:x² - 7x + 3x - 21 = 0.
Group the first two terms and the last two terms: x(x - 7) + 3(x - 7) = 0.
Factor out the common factor of (x - 7): (x - 7)(x + 3) = 0.
Now, we have two factors that when multiplied, give us zero. This means that either (x - 7) = 0 or (x + 3) = 0.
Solving for x, we get: x = 7 or x = -3.
The solutions are x1 = 7 and x2 = -3.The equation x² - 4x - 21 = 0 can be solved by factoring it. To factor this equation, we first find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3. Then we rewrite the equation using -7 and 3 instead of -4x.
The resulting equation is x² - 7x + 3x - 21 = 0.
Next, we group the first two terms and the last two terms to get x(x - 7) + 3(x - 7) = 0.
We factor out the common factor of (x - 7) to get (x - 7)(x + 3) = 0.
We then solve for x to get x = 7 or x = -3. Therefore, the solutions are x1 = 7 and x2 = -3.
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Which of the following segments is a diameter of 0?
C
A
o
В
A. AC
B. AB
C. AO
D. CO
The diameter of the circle is AB and option b is the correct answer.
What is diameter?The diameter of a circle is the distance along which the circumference begins at one end and terminates at the other. Its length is double that of the circle's radius. In other words, the line that splits a circle into two equal pieces and runs through its centre is the diameter of the circle. Every straight line segment that traverses a circle's centre and has its endpoints on its circumference is said to have a diameter of that circle. The diameter is also referred to as the circle's longest chord.
We know that, the diameter of the circle is the longest segment that passes through the center of the circle.
From the given figure we observe that, the segment AB passes through the center and connects with the circle on either side.
Hence, the diameter of the circle is AB and option b is the correct answer.
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Answer:
AB
Step-by-step explanation:
15. The expression √x is equivalent to 14i√3. What is the value of x?
a.-588
b. -588i
c.588
d. 588i
16. An expression is shown below.
x^5 + 6x^3 +8x
Which value of x makes the expression equal to 0?
a. -2i²
b. -2i
c. 4i
d. 4i²
(15) The value of x is -588 (option A).
(16) The value of x makes the expression equal to 0 is -2i. (option B).
What is the value of x?The value of x is calculated by solving the equation as follows;
(15) We have the equation:
√x = 14i√3
Squaring both sides, we get:
x = (14i√3)^2
x = -588
(16) Factoring the expression, we get:
x(x⁴ + 6x² + 8)
Setting each factor equal to 0, we get:
x = 0 or x⁴ + 6x² + 8 = 0
Let's solve for the second equation:
Let y = x²
Then we have:
y² + 6y + 8 = 0
Factorizing, we get:
(y + 2)(y + 4) = 0
So y = -2 or y = -4
Since y = x², this means:
x² = -2 or x² = -4
Taking the square root of both sides, we get:
x = ±√(-2) or x = ±√(-4)
Simplifying using imaginary numbers, we get:
x = ±i√(2) or x = ±2i
Thus, for the expression √x is equivalent to 14i√3, the value of x is -588. And for the expression x⁵ + 6x³ + 8x, x = -2i.
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There are 28 students in a class
13 of the students are boys
two students from the class are chosen at random
if the first person chosen is a boy what is the probability that the second person also chosen is also a boy
The probability that the second person chosen will also be a boy is roughly 0.872, or 87.2%.
Since the first person chosen is a boy, there are now 12 boys and 15 girls left in the class. We want to find the probability that the second person chosen is also a boy.
The probability of choosing a boy for the first selection is 13/28. Then, for the second selection, there are now 12 boys and 27 students left, so the probability of choosing a boy is 12/27.
Using conditional probability, we can calculate the probability that the second person chosen is also a boy given that the first person chosen is a boy:
P(Second person is a boy | First person is a boy) = P(Both are boys) / P(First person is a boy)
P(Second person is a boy | First person is a boy) = (12/27) / (13/28)
P(Second person is a boy | First person is a boy) ≈ 0.872
Therefore, the probability that the second person chosen is also a boy given that the first person chosen is a boy is approximately 0.872 or 87.2%.
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Tim was standing on a hill bird watching. He was also playing with his new stopwatch. He noticed one bird pass a certain building just when he pushed the button on his stopwatch. In one minute, the bird passed another building that Tim knew was exactly ½ mile away from the first one. How fast was that bird flying?
HELPPPP IM IN CLASS
Answer:
30mph
Step-by-step explanation:
We can use the concept of speed, distance, and time to solve the problem.
Let's assume that the bird was flying at a constant speed of "x" miles per minute.
When the bird passed the first building, Tim started the stopwatch. Let's say the time on the stopwatch was "t" minutes.
Therefore, the bird had flown a distance of "x*t" miles when Tim started the stopwatch.
In the next minute, the bird flew another 0.5 miles (the distance between the two buildings). So, the total distance traveled by the bird was:
x*t + 0.5 miles
We know that the total time elapsed was 1 minute. Therefore:
t + 1 = total time elapsed
Now, we can use these equations to solve for the speed of the bird:
x*t + 0.5 = distance traveled
t + 1 = total time elapsed
We want to find the value of x, so we can solve for t:
t = total time elapsed - 1
Substituting this value of t into the first equation, we get:
x*(total time elapsed - 1) + 0.5 = distance traveled
Simplifying, we get:
x*(total time elapsed) = distance traveled + 0.5
Substituting the given values, we get:
x*(1) = 0.5 + x*t
x = 0.5 + x*(total time elapsed - 1)
x = 0.5 + x*(59/60)
Solving for x, we get:
x = 30 miles per hour
Therefore, the bird was flying at a speed of 30 miles per hour.
Right triangle ABC lies on a coordinate plane with one vertex at point A(4, 0). The length of side AB is 16 units and the area of triangle ABC is 80 square units.
20
Type the correct answer in each box. Use numerals instead of words.
Find the coordinates of point B and point C.
The coordinates of point B are (4,
), and the coordinates of point C are (
,-16).
PLEASE HURRY
The cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).
We can use the fοrmula fοr the area οf a triangle, which is:
area = (base * height) / 2
We knοw that the base AB has a length οf 16 units, sο we can find the height by rearranging the fοrmula:
height = (2 * area) / base
height = (2 * 80) / 16
height = 10
Sο, pοint B is at (4, 0) and pοint C is at (x, y) where the height frοm A tο BC is 10 units and the length οf BC is 16 units.
We can use the Pythagοrean theοrem tο find the cοοrdinates οf pοint C:
[tex]x^2 + y^2 = BC^2[/tex]
[tex]x^2 + y^2 = 16^2[/tex]
[tex]x^2 + y^2 = 25[/tex]
Alsο, we knοw that the height frοm A tο BC is 10 units, sο the distance between pοint A and the line BC is 10 units. The slοpe οf the line BC is -y/x (rise οver run), sο the equatiοn οf the line BC is:
[tex]y = (-y/x) * (x - 4)[/tex]
[tex]y = (-y/x) * x + (y/x) * 4[/tex]
[tex]y + (y/x) * x = (y/x) * 4[/tex]
[tex]y(x/x + 1) = (y/x) * 4[/tex]
[tex]y + x = 4y/x[/tex]
[tex]x^2 + xy = 4y[/tex]
[tex]y = (x^2) / (4 - x)[/tex]
Nοw we can substitute this expressiοn fοr y intο the equatiοn[tex]x^2 + y^2 = 256:[/tex]
[tex]x^2 + ((x^2) / (4 - x))^2 = 256[/tex]
Sοlving this equatiοn gives twο pοssible values fοr x: x = 8 οr x = -4.
If x = 8, then y = 16/3, and if x = -4, then y = -16.
Therefοre, the cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).
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what are the rational roots of f(d)=5d^3-6d^2+d-8
Answer: To find the rational roots of f(d) = 5d^3 - 6d^2 + d - 8, we can use the Rational Root Theorem, which states that any rational root of a polynomial equation must be of the form p/q, where p is a factor of the constant term (in this case, -8) and q is a factor of the leading coefficient (in this case, 5).
The factors of -8 are ±1, ±2, ±4, and ±8, and the factors of 5 are ±1 and ±5. Therefore, the possible rational roots of f(d) are:
±1/1, ±2/1, ±4/1, ±8/1, ±1/5, ±2/5, ±4/5, and ±8/5
We can try these values one by one to see if they are roots of f(d). For example, when we try d = 1, we get:
f(1) = 5(1)^3 - 6(1)^2 + 1 - 8 = 5 - 6 + 1 - 8 = -8
Since f(1) is not equal to zero, d = 1 is not a root of f(d). We can continue this process until we find all the rational roots of f(d).
Step-by-step explanation:
someone help me asap
Answer:
Step-by-step explanation:
angle
Please help me this assignment is due at 12:00 and I really need help
I will mark the brainlest answer!! Help ASAP.
Answer:
-3
Step-by-step explanation:
The cost for an eighth-grade party is $600 for room rental, entertainment, and decorations, plus $15 per person for food. Tickets for the party are sold for $20. What is the break-even point?
A. 120 tickets
B. 90 tickets
C. 60 tickets
The break-even point is 120 tickets, which is option A.
Describe Revenue?It is the income generated by a business, which includes all the money received from customers for the products or services sold, as well as any other sources of income. Revenue is calculated by multiplying the price of a product or service by the number of units sold. It is an important financial metric that helps businesses determine their profitability and growth potential.
Let's assume that x number of students are attending the party.
The cost for food per person is $15 and the revenue generated per person is $20, so the profit per person is $20 - $15 = $5.
The total cost of the party is $600 + $15x.
We need to find the number of tickets sold to cover the cost of the party, which is the break-even point.
So, we set the revenue generated equal to the cost of the party:
20x = 600 + 15x
5x = 600
x = 120
Therefore, the break-even point is 120 tickets, which is option A.
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The diagram shows a quarter circle of radius 12 cm
12 cm
Work out the area of the shape.
Not drawn
accurately
You rent an apartment that costs $1600 per month during the first year, but the rent is set to go up 9. 5% per year. What would be the rent of the apartment during the 9th year of living in the apartment? Round to the nearest tenth (if necessary). ASAP PLEASEEEE
The rent of the apartment during the 9th year of living in the apartment would be approximately $3,510.45 per month.
If the rent starts at $1600 per month and increases by 9.5% each year, then we can use the formula for compound interest to calculate the rent after 9 years.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the initial principal (the starting amount)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, P = $1600, r = 9.5% = 0.095, n = 1 (compounded once per year), and t = 9. We want to find A, the rent after 9 years.
A = 1600(1 + 0.095/1)^(1×9)
A = 1600(1.095)^9
A ≈ $3,510.45
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Valeria is attending a school orchestra concert. She sees her math teacher seated 4 meters ahead of her and her science teacher seated 1 meter to her right. How far apart are the two teachers? If necessary, round to the nearest tenth.
Please use the Pythagorean Theorem.
Thank you!
Answer:
The two teachers are approximately 4.1 meters apart.
Step-by-step explanation:
Let's use the following variables:
d = distance between the two teachers
Using the Pythagorean theorem:
d^2 = 4^2 + 1^2
d^2 = 16 + 1
d^2 = 17
d = sqrt(17)
d ≈ 4.1
Answer: 4.1
Step-by-step explanation:
[tex]\sqrt{1^2+4^2}[/tex]
evaluate the equation / expression
4.12311
round
4.12311 to the required place
4.1
Write an equation to represent the relationship between the step number, n, and the number of dots at each step of the pattern.
The relationship is: number of dots = n + 1
What is the number of dots?The "number of dots" typically refers to the count or quantity of small, circular shapes that are arranged in a particular pattern or sequence. The term can be used in various contexts, such as in mathematical or geometric patterns, puzzles, games, or art.
Assuming you are referring to a specific pattern of dots that increases with each step, the equation to represent the relationship between the step number, n, and the number of dots at each step can be written as:
Number of dots = n + 1
In this equation, "n" represents the step number and "n + 1" represents the number of dots at each step. This equation assumes that the pattern starts with one dot at the first step, and the number of dots increases by one with each subsequent step.
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To find the distance from point C to the line AB, you must find the length of the segment from C_______ to AB.
A. Widthwise
B. Perpendicular
C. Parallel
D. Lengthwise
the distance from point C to line AB, you must find the length of the segment from C perpendicular to AB
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.
When the angle of inclination between two line segments is exactly equal, those two segments are said to be perpendicular.
The plus symbol is formed when two perpendicular line segments cross one other.
To find the distance from point C to line AB, you must find the length of the segment from C_______ to AB
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3. Write these measurements in order of size, starting with the smallest. 2.3 cm 24 mm 0.2 m 21 cm 2.3 mm
The measurements in order of size, starting with the smallest are: 2.3 mm, 24 mm, 2.3 cm, 21 cm, and 0.2 m.
How to order sizes starting with the smallest?Given the measurements in the question;
2.3 cm, 24 mm, 0.2 m, 21 cm, 2.3 mm
To arrange the measurements in order of size, we need to convert them to a common unit of measurement.
We can convert all the measurements to meters, as it is the largest unit given.
Hence;
2.3 mm = 2.3 ÷ 1000 = 0.0023 m
24 mm = 24 ÷ 1000 = 0.024 m
21 cm = 21 ÷ 100 = 0.21 m
2.3 cm = 2.3 ÷ 100 = 0.023 m
0.2 m = 0.2 m
Now that all the measurements are in meters, we can compare them:
0.0023 m < 0.024 m < 0.023 m < 0.21 m < 0.2 m
Therefore, the measurements in order of size, starting with the smallest, are:
2.3 mm < 24 mm < 2.3 cm < 21 cm < 0.2 m
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Round all numbers to the nearest whole number. Find the missing measurements of the triangle
The missing measurements of the triangle given include:
Angle B = 63 degreesAB = 26 .4 units AC = 23. 6 units How to find the missing measurements ?The value of angle B can be found thanks to the knowledge that the interior angles of a triangle add up to 180 degrees and we have two of the angle measurements :
= 180 - angles measurements
= 180 - 27 - 90
= 63 degrees
The value of AB can be found by using the Sin theta operation such that:
Sin theta = Opposite / hypotenuse
Sin ( 27 degrees ) = 12 / hypotenuse which is AB
hypotenuse = 12 / ( Sin ( 27 degrees ))
= 26 .4 units
The value of AC measurement is:
Tan ( 27 degrees ) = 12 / AC
AC = 12 / Tan ( 27 degrees )
AC = 23. 6 units
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PLEASE HELP ASAP!!!
Question in photo
Answer:
-5 is your answer
Step-by-step explanation:
What do you mean leading coefficient of the following polynomial.
Look at the x^n and see who has the biggest values.
-5x^7 is the leading coefficient.
Does anyone know B? I need some help
The estimated life expectancy for someone born in 2005 is approximately 85.09 years.
Describe Life expectancy?Life expectancy is the average number of years that a person is expected to live, based on statistical data and various demographic factors such as age, gender, health status, lifestyle, and environmental conditions. It is usually calculated from birth and is a useful indicator of the overall health and well-being of a population.
Life expectancy can vary widely between different countries and regions, as well as between different demographic groups within a population. Factors that can influence life expectancy include access to healthcare, nutrition, education, economic development, social support, and public health policies.
To estimate the life expectancy for someone born in 2005, we need to use the line of best fit equation:
y = 0.40x - 716.91
where x is the birth year and y is the corresponding life expectancy.
To find the estimated life expectancy for someone born in 2005, we substitute x = 2005 into the equation:
y = 0.40(2005) - 716.91
y = 802 - 716.91
y = 85.09
Therefore, the estimated life expectancy for someone born in 2005 is approximately 85.09 years.
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A car traveled 4 miles in 4 minutes. How many yards did it travel in that time? Answer yards
Answer:0.27 miles
Step-by-step explanation:
Answer:
The answer to your question is 7040
Step-by-step explanation:
How many yards are in 1 mile:
So 1 mile = 1760 yards
Speed = 1760 yard per minute
= 1760 yd/min
Since we have 4 miles, we are gonna multiply 4 multiplied by 1760.
So 4 miles x 1760 = 7040
I hope this helps and have a wonderful day!
4
Which pair of lines
are parallel?
A) x − 5y = 10; y = 5x – 2
B) x + y = 0; y = x + 7
C) 2x - 3y = 9; 4y = 6x-20
D) 4x8y = 8; y = 2x + 2
E) 9x - 3y = 12; y = 3x - 10
Step-by-step explanation:
To determine whether two lines are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
A) x − 5y = 10 can be rearranged to y = (1/5)x − 2, so its slope is 1/5.
y = 5x – 2 is already in slope-intercept form, so its slope is 5.
These two slopes are not equal, so the lines are not parallel.
B) x + y = 0 can be rearranged to y = −x, so its slope is −1.
y = x + 7 is already in slope-intercept form, so its slope is 1.
These two slopes are not equal, so the lines are not parallel.
C) 2x − 3y = 9 can be rearranged to y = (2/3)x − 3, so its slope is 2/3.
4y = 6x − 20 can be rearranged to y = (3/2)x − 5, so its slope is 3/2.
These two slopes are not equal, so the lines are not parallel.
D) 4x + 8y = 8 can be rearranged to y = −(1/2)x + 1, so its slope is −1/2.
y = 2x + 2 is already in slope-intercept form, so its slope is 2.
These two slopes are not equal, so the lines are not parallel.
E) 9x − 3y = 12 can be rearranged to y = 3x − 4, so its slope is 3.
y = 3x − 10 is already in slope-intercept form, so its slope is 3.
These two slopes are equal, so the lines are parallel.
Therefore, the pair of lines that are parallel is (E) 9x - 3y = 12; y = 3x - 10.
Fill in the gaps below:
a. from A to B
b. from B to C
c. from A to C
Answer:
a. from A to B, a rotation by 90 degrees anti-clockwise about (0,0).
b. from B to C, a translation by vector (-3/4, -1/4).
c. from A to C, a rotation by 60 degrees, anti-clockwise about (0,0).
Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :]
Alex invested $7,000 in a fund that pays 6% interest. If no deposits or withdrawals are made, how much money will be in the account 8 years from today?
jrjejrjŕjwjskskskskskskksksksksksksks
Select the equation(s) that represent the graph below
(0,6)(9,0)
Y=-2/3+6
3x +2y=18
2x+3y=18
Y=-3/2x+9
2x+3y=18
Answer:
the answer is y=-2/3x+6
Which system of equations is represented by the graph? Graph of a quadratic function intersecting a linear function at point 2 comma 0. y = x2 + 3x + 2 x + y = 2 y = x2 − 3x + 2 x − y = 2 y = x2 − 3x + 2 x − y = 3 y = x2 − 3x + 2 x + y = 3
After answering the presented question, we can conclude that The point of intersection of these two equations is (2, 0), which is the spot on the graph where the parabola and line intersect.
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions linked by the equal symbol '='. For example, 2x - 5 = 13. 2x-5 and 13 are two phrases. The character '=' is used to connect the two expressions. An equation is a mathematical formula that has two algebras on either side of an assignment operator (=). It illustrates the equivalency relationship between the left and middle formulas. In any formula, L.H.S. = R.H.S. (left side = right side).
The graph represents the following equation system:
[tex]y = x^2 + 3x + 2 x + y = 2[/tex]
This is due to the fact that the graph of a quadratic function intersecting a linear function at point (2, 0) is represented by a parabola and a straight line intersecting at that point (2, 0).
The equation [tex]y = x^2 + 3x + 2[/tex] represents an upward-opening parabola that goes through the point (-2, 0).
The equation x + y = 2 denotes a straight line that connects the locations (0, 2) and (2, 0).
The point of intersection of these two equations is (2, 0), which is the spot on the graph where the parabola and line intersect.
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Use the graph to determine
(a) open intervals on which the
function is increasing, if any.
(b) open intervals on which the function is decreasing if any
(c) open intervals on which the function is constant if any
using graph f(x) is concave down on (-1,0), (1,∞).
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
f(x) is concave up where f'(x) is increasing and concave down where f'(x) is decreasing
So, using graph f(x) is concave down on (-1,0), (1,∞).
Hence, using graph f(x) is concave down on (-1,0), (1,∞).
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2 + 3x = 12 - 5x
Why I am having so much trouble with this?
Answer:x=5/4
Step-by-step explanation:
you can take numbers with same variable(i mean x or y or other) in the same side:
2+3x=12-5x
2-12=-5x-3x
-10=-8x
x=10/8=5/4
Answer:
x = 5/ 4
Step-by-step explanation:
2 + 3x =12- 5x
3x + 5x = 12 - 2
8x = 10
x = 10/8
x = 5/4
simplify: 1÷2+2 3÷4-3÷8
The expression 1÷2+2 3÷4-3÷8 when simplified is 9/4
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
1÷2+2 3÷4-3÷8
Express the terms properly as fractions
So, we have the following
1/2 + 2 3/4 - 3/8
Express each term as proper/improper fraction
So, we have the following representation
1/2 + 11/4 - 3/8
Express the denominator as the same
So, we have
4/8 + 22/8 - 3/8
Evaluate the like terms
18/8
So, we have
9/4
Hence, the solution is 9/4
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Is rotated
An angle whose measure is
more than halfway around a circle.
DONE
The statement "rotated an angle whose measure is more than halfway around a circle" is incorrect. An angle whose measure is 60 degree is rotated more than halfway around a circle.
A rotated angle is an angle that has been moved or transformed from its original position, while an angle that measures more than halfway around a circle is called a reflex angle. A reflex angle measures between 180 and 360 degrees, which means that it has rotated more than halfway around a circle.
In contrast, an angle that measures less than 180 degrees is called an acute angle, while an angle that measures exactly 180 degrees is called a straight angle. Understanding the different types of angles is important in geometry and mathematics.
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How many bricks each of 20 cm * 10 cm * 5 cm will be required to construct a wall of 1 km * 5 m * 50 cm?
Answer:
20 cm = 0.2 m
10 cm = 0.1 m
5 cm = 0.05 m
1 km = 1000 m
5 m = 5 m
50 cm = 0.5 m
The volume of each brick is:
V_brick = 0.2 m x 0.1 m x 0.05 m = 0.001 m^3
The volume of the wall is:
V_wall = 1000 m x 5 m x 0.5 m = 2500 m^3
The number of bricks required is:
N_bricks = V_wall / V_brick = 2500 m^3 / 0.001 m^3 = 2,500,000
Therefore, 2,500,000 bricks of size 20 cm * 10 cm * 5 cm will be required to construct the wall.
4e-6e-5=15 solve for e
Answer:
e = - 10
Step-by-step explanation:
4e - 6e - 5 = 15
- 2e - 5 = 15 ( add 5 to both sides )
- 2e = 20 ( divide both sides by - 2 )
e = - 10
Answer: e = -10
Step-by-step explanation:
4e-6e-5=15
-2e-5=15
add 5 on both sides
-2e=20
divide 20 on both sides
e=-10