In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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What is the nature of the roots of the quadratic equation 5x^2 4x 1?
The nature of roots of quadratic equation 5x² = 4x - 1 is imaginary roots.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
5x² = 4x - 1
transform it into the standard form:
5x² - 4x + 1 = 0
Calculate the discriminant:
D = (-4)² - 4 (5)(1)
= 16 - 20 = -4
Since D < 0, the roots are imaginary.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation 5x² = 4x - 1?
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19. Simplify the following 4a³ × 16aºb¹ ÷ 1ac² PLEASE HELP MEEEE!!!
Answer:
64(ab÷c²)
step by step:
(when you multiply two similar bases you can add their exponents but when dividing similar bases you subtract their exponents)
for example
a³x a= a⁴
a²÷ a= a²-¹= a
so
4a³x 16a⁰b¹÷ 1ac²=
64a³b÷ac²
64a²b/c²
Reuben bought 6 boxes of chocolates. Each box cost $7.36. How much did he spend?
Answer:
$44.16 he spent on chocolate
What are the 3 steps for solving a quadratic equation?
Determine what a, b, and c are worth. the quadratic formula in writing. After that, enter the values for a, b, and c. Simplify.
what is quadratic equation ?A quadratic polynomial in a single variable is represented by the expression x ax2+bx+c=0, which is a quadratic equation. a 0. Since it is a second order polynomial, the Fundamental Theorem of Algebra guarantees that it has at least one solution. Simple or difficult solutions are both possible. The term "quadratic equation" refers to an equation that is quadratic. It must square at least one word, according to this indication. One of the common solutions for quadratic equations is the formula "ax2 + bx + c = 0." where the variables "X" are undefined and are numerical coefficients or constants a, b, and c.
given
steps are
Find out what a, b, and c are worth.
Quadratic formula: write it down.
Add the values of a, b, and c after that. Simplify.
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If AnB= {2,4}
AnB'= {0,1}
AUB= {0,1,2,3,4,5}, Then what is B\A?
Answer:
I don't know I'm just a grade 6 girl
makayla runs 3/5 of a mile in 1/6 of an hour. How fast, in miles per hour, does she run
Answer:
3.6 miles
Step-by-step explanation:
SolutionGiven information from the question,
[tex]\frac{1}{6} \ hour = \frac{3}{5} \ miles\\ 1 \ hour = \frac{3}{5} / \frac{1}{6} \ miles\\1 \ hour = \frac{18}{5} \ or\ 3\frac{3}{5} \ or \ 3.6 miles[/tex]
Answer:
Velocity is the term to illustrate speed
Step-by-step explanation:
velocity = distance ÷ time
velocity = 3/5 ÷ 1/6
= 18/5 m/h
find equation of the line passing through (4,8) and parallel to the line 3x+y=17( Please give workout)
Answer:
y = -3x +20
Step-by-step explanation:
Equation of line: y =mx + b
Where m is the slope and b is the y-intercept.
3x + y = 17
Write the above equation in y = mx +b form.
y = -3x + 17
m = -3
Parallel lines have same slope.
So, slope of the required line is (-3).
y = -3x + b
This line is passing through (4,8). Substitute in the above equation and find the value of 'b'.
8 = -3*4 + b
8 = -12 + b
8 + 12 = b
b = 20
Equation of the line:
[tex]\sf \boxed{ y = -3x + 20}[/tex]
Suppose that $x$ is directly proportional to $y$. Let $x_1, x_2$ be two values of $x$ such that $\frac{x_1}{x_2} = 4$. Let their corresponding values be
$y_1$, $y_2$ respectively. If at least one of $y_1, y_2$ is nonzero, find $\frac{y_2}{y_1}$.
If at least one of $y_1, y_2$ is nonzero, then $\frac{y_2}{y_1}$ = $\frac{1}{4}$
If x is directly proportional to y, we can write this as x = ky for some constant k.
Since $\frac{x_1}{x_2} = 4$, we can write it as $x_1 = 4x_2$.
Now, substituting the value of $x_1$ in equation x = ky gives
$4x_2 = ky_1$.
Also, since x = ky, we can write $x_2 = ky_2$.
Now, we can substitute the value of $x_2$ in the equation $4x_2 = ky_1$
So, $4ky_2=ky_1$, which gives $\frac{y_2}{y_1} = \frac{1}{4}$
Therefore, $\frac{y_2}{y_1}$ = $\frac{1}{4}$ when x is directly proportional to y and $\frac{x_1}{x_2} = 4$.
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How do you read FG stats?
Field goal stats include number of made/attempted, percentage made, average points scored per made, total points scored/attempted, and possibly rebounds, assists, turnovers.
FG (field goal) stats are a way of measuring an individual or team's performance in the sport of basketball. Generally, the stats will include the number of field goals made, the number of field goals attempted, the percentage of field goals made, the average number of points scored per field goal made, the total number of points scored, and the total number of points attempted. This data can be used to compare different players or teams, or to track a player or team's performance over time. Depending on the context, other stats such as rebounds, assists, and turnovers may also be included. This data can help coaches, scouts, and analysts make decisions and evaluate performance. Ultimately, it is important to use field goal stats in combination with other data and context to create an accurate picture of a player or team's performance.
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Marla is four years less than twice as old as Darla. If the sum of their age is 47, how old is Marla?
According to the given algebra Darla is 17 years old and Maria is 30 years old.
What algebraic fundamentals are there?Numbers, parameters, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, as well as division.
According to the given information.Maria is 4 years younger than Don,
thus if Don is x years old, then Maria is x years younger. (2x-4)
If their ages added together equal 47,
then x + (2x-4) = 47
Solving for x, then determining Maria's age (2x-4)
3x=47+4
3x=51
x=51/3
x=17 years
Maria's age=2*17-4=30 years
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(6) (Bonus) A rectangular tank with a bottom and sides but no top is to have volume 500 cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area.
The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.
Volume=lbh
lbh=500 cubic feet
h=500/lb
Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}
S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}
S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}
for S to be minimum dS/dl=0 and dS/db=0
dS/dl= b-1000/l^2
dS/dl=0
b=1000/l^2...(2)
dS/db= l-1000/b^2
dS/db=0
l=1000/b^2
l=1000/(1000/l^2)^2 {substituting the value of b from 2}
l=(1000 x l^4)/(1000000)
1000000/1000=l^4/l
1000=l^3
l=10 feet
b=1000/l^2
b=1000/100=10 feet
lbh=500
h=500/(10x10(
h=5 feet
S=10x10+2x5x10+2x10x5
S=300 square feet
Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the rectangular tank.
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What is an equation of the line that passes through the points (4,-3) and (2,0)
y = 3/2x - 9/2
The equation of the line that passes through the points (4,-3) and (2,0) can be found using the point-slope form of a linear equation. The point-slope form of a linear equation is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line.
To calculate the slope, we will use the formula m = (y2-y1)/(x2-x1). In this equation, (x1,y1) = (4,-3) and (x2,y2) = (2,0). Substituting these values into the slope formula, we get m = (0-(-3))/(2-4) = 3/(-2) = -1.5.
Now that we have the slope, we can plug the point (4,-3) and the slope (-1.5) into the point-slope form of a linear equation to get y-(-3)=-1.5(x-4). Simplifying this equation, we get y+3=-1.5x+6, which is the equation of the line that passes through the points (4,-3) and (2,0).
Quesuon Help
An exponential function has an initial value of 500 and a decay rate of 15%. Compare the average rate of change for the interval 0<x<4 to the average rate for the
interval 4<x<8. What do you think will happen to the rate of change for intervals beyond x = 8? Explain.
For 0<x<4, the average rate of change will be
(Round to the nearest integer as needed. )
The slope of the straight line connecting the break's ends to the function's diagram.
For 0 < x < 4 will be -60
For 4 < x < 8 will be -31
What is meant by exponential function?The mathematical formula f (x) = [tex]$$a^{x[/tex] denotes an exponential function. a constant known as the function's base and a variable called x are present. The transcendental number e, roughly equivalent to 2.71828, is the most frequent exponential-function base.
When a positive constant other than 1 is raised to a variable exponent, the function is said to be exponential. Solving at a certain input value yields the evaluation of a function. If you know the growth rate and the starting point, you can find an exponential model.
We have to use the knowledge of functions to describe the average rates of each one of them, so:
For 0 < x < 4 will be -60
For 4 < x < 8 will be -31
It is a measurement of how much the function changed for one person on average throughout that interval. It results from the slope of the straight line connecting the break's ends to the function's diagram.
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If the m<1 = 17x - 30, and the <2 = 7x + 18, what is the value of x?
Answer:
X=8
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
17x−30+7x+18=180
17x+−30+7x+18=180
(17x+7x)+(−30+18)=180(Combine Like Terms)
24x+−12=180
24x−12=180
Step 2: Add 12 to both sides.
24x−12+12=180+12
24x=192
Step 3: Divide both sides by 24.
X=8
What value of x satisfies the equation − 3 4x − 5 )= 2 1 − 5x?
For the given expression, x has a value of 6.5.
What are expressions?A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables.
A number is 6 times larger than the other number, x, by a factor of 2.
The equation x/2 + 6 in mathematics represents this claim.
Here, we have the equation:
-3(4x - 5) = 2(1 - 5x)
Find the value of x by solving the expression:
-3(4x - 5) = 2(1 - 5x)
-12x + 15 = 2 - 10x
-2x = -13
x = -13/-2
x = 13/2
x = 6.5
Therefore, for the given expression, x has a value of 6.5.
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Correct question:
What value of x satisfies the equation -3(4x - 5) = 2(1 - 5x)?
4. Two of the angles in a triangle have measure of 79° and 81°. Which of the angle measures below
could belong to a triangle that is similar to this triangle?
A) 81 and 80°
B) 81 and 20°
C)79° and 90°
D)79° and 21°
Answer:
B) 81 and 20°
Step-by-step explanation:
In any triangle, the sum of the measures of the three angles is 180°. Therefore, if two angles in a triangle have measures of 79° and 81°, the third angle must have a measure of 180 - 79 - 81 = 20°. Therefore, the answer is B) 81 and 20°.
Answer:
B
Step-by-step explanation:
Kelly has a savings account with a beginning balance of $800.
• She earns $340 a week at her job.
• For 8 weeks, she puts 15% of her weekly earnings into the savings account.
• Kelly makes 3 withdrawals of $45 each.
What is the account balance at the end of 8 weeks?
Let's start by using the provided information to formulate an equation.
Kelly starts with $800 in her savings account, so this is the initial amount. She makes $340 per week, 15% of which is invested into her savings account for 8 weeks, so this information will form a rate. Kelly also withdrew (subtracted) 45 dollars 3 times. Now, let's form the equation.
y=8(.15·340)+800-45(3), where y=remaining balance after 8 weeks. Now, lets simplify the equation using Orders of Operations.
Simplify parenthesis first:
y=8(.15·340)+800-45(3)
y=8(51)+800-45(3)
Complete any multiplication:
y=8(51)+800-45(3)
y=408+800-135
Add and subtract from left to right; addition and subtraction are not separate steps and must be done in the same step, so we work left to right as to whichever comes first:
y=408+800-135
y=1208-135
y=1,073
Remember that y is the remaining balance after 8 weeks. This means that $1,073 dollars is the balance after 8 weeks.
Hope that helps, and feel free to give Brainliest!
The account balance at the end of 8 weeks is $1073.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Kelly has a savings account with a beginning balance of $800 and she earns $340 per week.
Therefore, 15% of her weekly earnings for 8 weeks is,
= (15/100)×340×8.
= $408.
Again, She made $45 withdrawals 3 times, which is,
= 3×45.
= $135.
Therefore, The final amount in her account after 8 weeks is,
= $(800 + 408 - 135).
= $1073.
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Given csc0=178, determine the values for "a" and "b" in cos0=ab
The value of a and b are respectively 15 and 17 respectively.
What are trigonometry ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given that csc θ = 17/8 and cos θ = a/b.
The reciprocal of sin θ is csc θ.
Therefore,
1/sinθ = 17/8
or, sin θ = 8 /17
Applying the trigonometry identity cos²θ = 1- sin²θ
cos²θ = 1- (8/17)²
cos²θ = 1- 64/289
cos²θ = 225/289
cos θ = 15/17
The value of a is 15 and the value of b is 17.
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In the figure shown, what is the value of x?
PLEASE HURRY JUST GIVE ME THE ANSWER THANK YOU
Answer: x= 23
Step-by-step explanation:
A sample of size 95 will be drawn from a population with mean 25 and standard deviation 13. Find the probability that will be between 22 and 27.
1.3338 is the likelihood, The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
Explanation:
Mean (m) = 25
The standard deviation is 13
Sample size (n) is 95.
Chance that x will fall between 22 and 27.
Zscore = x - mean / s / n
If x = 22, Zscore is equal to (22 - 25) / (13/95).
For x = 27, Zscore is equal to (27 - 25) / (13/95) / n = 13 / 95, which is 1.3338.
1.3338 is the likelihood.
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Sport
Soccer
Jogging
Walking
Skiing
Football
Total
Hrs
5
20
10
5
10
50
Calculate the
portion for jogging
in degrees
[?]
20 hrs.
Total Sport Hours
The portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours is 72 degrees.
Therefore the answer is 72°.
To calculate the portion of walking in degrees, we first need to find the total amount of time spent walking. In this case, it is 10 hours.
Next, we need to find the total amount of time spent on all sports, which is 50 hours.
Now we can calculate the portion of walking by taking the amount of time spent walking (10 hours) and dividing it by the total amount of time spent on sports (50 hours).
This gives us the fraction of time spent walking which is
10/50
= 1/5
Finally, we can convert this fraction to degrees by multiplying it by 360 (the number of degrees in a full circle).
So the portion of walking in degrees is
(1/5) × 360
= 72 degrees
--The question is incomplete, complete question is given below--
"Calculate the portion for walking in degrees when Soccer take 5 hours, Jogging take 20 hours, Walking take 10 hours, Skiing take 5 hours and Football take 10 hours of the total 50 hours of sport hours."
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NP, PM, and MN are all midsegments and bisect each side.
NP = 12
MP=2x
RQ = 5x-1
SQ=6x
Solve for x.
Label each midsegment with its correct measure:
NP, PM, and MN are all midsegments and bisect each side.
value of x = 5 unit
NP = 12
MP=2x
RQ = 5x-1
SQ=6x
Using Midsegments of a Triangle
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle
Triangle Midsegment Theorem
Using Midsegments of a Triangle
Theorem 5-1 Triangle Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.
Triangle Midsegment Theorem A segment whose endpoints are the
midpoints of two sides of the triangle
Midsegment
Base
Midsegment = ½ of Base
M = ½ b
NP =1/2(RQ)
12 =1/2(5x-1)
12* 2 = 5x-1
24 =5x-1
24+1 =5x
25 =5x
x=25/5
x = 5 unit
NP, PM, and MN are all midsegments and bisect each side.
value of x = 5 unit
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Ayesha earns a 10 percent bonus based on her annual salary plus the number of sales shes earned and a 2,000 dollar bonus last year
The annual salary will be 49750
Gross salary would be the total amount of compensation that an employer or business pays an employee during their employment. The Cost of Company, as well as CTC, on the other hand, would represent the overall compensation of employees. The CTC seems to be an employee's gross pay, but their net compensation is how much they actually take home.
Now, According to the question:
Let x be the annual salary.
Then 10% of x+250 equates 0.1(x+250).
Thus, the bonus equates $5000, then we will get the equation:
0.1(250 + x) = 5000
Solving for 'x' we get:
250 + x = [tex]\frac{5000}{0.1}[/tex]
250 + x = 50000
x = 50000 - 250
x = 49750
CTC and gross salary are sometimes confused. But there is a distinction among the two. Before taxes, Employee Provident Fund (EPF) contributions, and gratuities deducted from the CTC, the amount paid to the employee would be known as their gross salary.
The complete question is this:
__"Ayesha earns a 10% bonus based on her annual salary plus the number of sales she makes. She made 250 and earned a $5,000 bonus last year. Write and solve an equation to find her salary last year__"
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Im a little stuck on this one yall
The pairs of alternate interior angles are <5<4 and <6<3
What is alternate interior angles ? Alternate interior angles are the pair of angles that are formed on the inner side of the two parallel lines but on the opposite side of the transversal.When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equalAlternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.To learn more about alternate interior angles refers to:
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Radicals please help
On solving the provided question, we can say that - the radicals are as follows be = 3x^2|y| sqrt(7x)
what are radicals?The square root or nth root symbol is called a radical. Expressions with square roots are referred to as root expressions. A radical's radicand is a number or phrase that appears there. The radicals 7, 2y+1, and so on are examples. The following phrases can also be used to describe radicals: Radical equations are equations contained within of radicals. The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.
here,
the radicals will be - 7xy ∛(xy^2)
and 3x^2|y| sqrt(7x)
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Three line segments have measures of 18 units, 12 units, and 10 units. Will the segments form a triangle?
Does it form a triangle?
No, the segments will not form a triangle based on the line segments provided.
For three line segments to form a triangle, they must satisfy the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
This is because if the sum of the lengths of any two sides is less than or equal to the third side, it would not be possible to form a triangle with those side lengths, as the two shorter sides would not be able to reach the longer side to form the triangle.
In this case, the sum of the two shorter segments (12 units + 10 units) is 22 units, which is less than the measure of the longest segment (18 units). Therefore, the three segments will not form a triangle.
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In the figure shown, EF is tangent to the circle at F, and EG is
tangent to the circle at G. Line segments HF, PG, HJ, and PJ
are also tangent segments.
When mEF = 10 units, what is the perimeter of triangle EHP?
Explain your reasoning.
Answer:
The perimeter is 20 units----------------------------------
According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.
That is:
EF = EG,HF = HJ,PJ = PG.We have EF = 10 units, it means EG is also 10 units.
The perimeter of triangle EHP is:
P = EH + HP + EPWe can substitute:
HP = HJ + PJ, segment addition,HJ = HF, stated above,PJ = PG, stated above.Then the perimeter is:
P = (EH + HF) + (EP + PJ) = EF + EG = 10 + 10 = 20 unitsThe length of the rectangle is X units more than its
width. The width of the rectangle is 11 units and the
length of the wire that is used to make this rectangle
is a maximum of 57 units. Represent this situation
using an inequality.
Answer: [tex]2x+44 \le 57\\\\[/tex]
Explanation:
W = width
W = 11
L = length
L = width+x
L = 11+x
P = perimeter of the rectangle
P = 2L+2W
P = 2*(11+x)+2*11
P = 22+2x+22
P = 2x+44
The perimeter is at max 57 units because it is the length of wire used. Think of it like fencing around a piece of land. Be sure not to mix up the length of the wire with the rectangle length; those are two different things.
Anyways, because the perimeter maxes out at 57, this means either P = 57 or P < 57.
This leads to:
[tex]P \le 57\\\\2x+44 \le 57\\\\[/tex]
2. A chef can make 12 meals with 3 pounds of steak. If he plans to make 250 meals and the steak costs $6.60 per pound, how much will the chef spend on steak
The amount of money which the chef spends on steak as calculated from the data given is found to be $412.50.
Now as we know that ,
for a meal of 12 meals the chef uses 3 pounds.
Therefore , for a meal of 250 meals the chef uses x pounds
Now , we will solve this proportion.
x=(250 meals*3 pounds)/12 meals
= 62.5 pounds
Now , cost of steaks = 6.60 dollars.
Therefore cost of 62.5 pounds of steaks will be ,
62.5 pound x $ 6.60/pound
= $ 412.50
A comparison between two numbers is called a proportion. If two sets of provided numbers increase or decrease in the same ratio, then the ratios are said to be directly proportional to each other.
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Is 3x3 a polynomial?
The degree of x-x3 is 3, or 3. It is a cubic polynomial. The formula for the 33 matrix's distinctive polynomial is f() = det (A - I3).
A polynomial is what?A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients. It can be expressed using just the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that contains variables, constants, and exponents and is based on the operations of addition, subtraction, multiplication, and division of numbers (No division operation by a variable).
[tex]x - x^3[/tex] has a degree of 3, or 3.
The polynomial is a cubic one.[tex]f() = det (A - I3)[/tex]is the formula for the characteristic polynomial of the 33 matrix.
The characteristic polynomial of the provided 33 matrix is [tex]f() = -3 + 3 + 2.[/tex]
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