Write the equation in vertex form to find the maximum height, as well as the time when the maximum height is reached.
The vertex form of a quadratic equation is:
[tex]y=a(x-h)+k[/tex]Where (h,k) is the vertex of the parabola, k is the maximum or minimum value and h is the value of x where that maximum or minimum is reached.
To write h in vertex form, complete the square:
[tex]\begin{gathered} h(t)=-5t^2+30t \\ =-5(t^2-6t) \\ =-5(t^2-6t+9-9) \\ =-5((t-3)^2-9) \\ =-5(t-3)^2-5(-9) \\ =-5(t-3)^2+45 \end{gathered}[/tex]We can see that in this case, the vertex is (3,45).
Therefore:
1)
[tex]h(t)=-5(t-3)^2+45[/tex]2)
The ball reaches the maximum height 3 seconds after being hit.
Hi, can you help me answer this question please, thank you!
Given:
The test claims that night students' mean GPA is significantly different from the mean GPA of day students.
Null hypothesis: the population parameter is equal to a hypothesized value.
Alternative hypothesis: it is the claim about the population that is contradictory to the null hypothesis.
For the given situation,
[tex]\begin{gathered} \mu_N_{}=\text{ Night students} \\ \mu_D=Day\text{ students} \end{gathered}[/tex]Null and alternative hypothesis is,
[tex]\begin{gathered} H_0\colon\mu_N=\mu_D \\ H_1\colon\mu_N_{}\ne\mu_D \end{gathered}[/tex]Answer: option f)
the number 0.3333... repeats forever; therefore, its irrational
The statement is false, the number can be rewritten as:
0.33... = 3/9
So it is a rational number, not irrational
Is the statement true?Here we have the statement:
"the number 0.3333... repeats forever; therefore, its irrational"
This is false, and let's prove that.
our number is:
0.33...
Such that the "3" keeps repeating infinitely.
If we multiply our number by 10, we get:
10*0.33... = 3.33...
If we subtract the original number we get:
10*0.33... - 0.33... = 3
9*0.33... = 3
Solving that for our number we get:
0.33... = 3/9
So that number can be written as a quotient between two integers, which means that it is a rational number.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
If angle a measures 42 degrees, then what other angles would be congruent to angle a and also measure 42 degrees?
If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h .
In the question ,
a figure is given ,
From the figure we can see that 2 parallel lines are cut by a transversal .
So ,
angle a = angle d .......because vertically opposite angles .
angle a = angle e ...because corresponding angles are equal in measure
also
angle e = angle h .... because vertically opposite angles .
Therefore , If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h , the correct option is (a) .
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Ziba brought 4 bottles of water to the park. Each bottle held 6 ounces of water. Ziba drank an equal number of ounces of water each hour. If she was at the park 3 hours, how many ounces of water did she drink each hour
By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.
How many ounces of water did she drink each hour?
We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:
V = 4*6 ounces = 24 ounces.
We know that she drinks that in 3 hours, so the amount that she drinks each hour is:
24 oz/3 = 8 oz
She drinks 8 ounces of water each hour.
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For people over 50 years old, the level of glucose in the blood (following a 12 hour fast) is approximately normally distributed with mean 85 mg/dl and standard deviation 25 mg/dl ("Diagnostic Tests with Nursing Applications", S. Loeb). A test result of less than 40 mg/dl is an indication of severe excess insulin, and medication is usually prescribed.
What is the probability that a randomly-selected person will find an indication of severe excess insulin?
Suppose that a doctor uses the average of two tests taken a week apart (assume the readings are independent). What is the probabiltiy that the person will find an indication of severe excess insulin?
Repeat for 3 tests taken a week apart:
Repeat for 5 tests taken a week apart:
Using the normal distribution and the central limit theorem, it is found that:
There is a 0.0359 = 3.59% probability that a randomly-selected person will find an indication of severe excess insulin.Considering the mean of two tests, there is a 0.0054 = 0.54% probability that the person will find an indication of severe excess insulin.Three tests: 0.0009 = 0.09%.Five tests: 0% probability.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score score is positive or negative.From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X in the distribution of interest.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of the glucose levels are given, respectively, by:
[tex]\mu = 85, \sigma = 25[/tex]
The probability of a reading of less than 40 mg/dl(severe excess insulin) is the p-value of Z when X = 40, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (40 - 85)/25
Z = -1.8.
Z = -1.8 has a p-value of 0.0359.
For the mean of two tests, the standard error is:
s = 25/sqrt(2) = 17.68.
Hence, by the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (40 - 85)/17.68
Z = -2.55.
Z = -2.55 has a p-value of 0.0054.
For 3 tests, we have that:
s = 25/sqrt(3) = 14.43.
Z = (40 - 85)/14.43
Z = -3.12.
Z = -3.12 has a p-value of 0.0009.
For 5 tests, we have that:
s = 25/sqrt(5) = 11.18.
Z = (40 - 85)/11.18
Z = -4.03
Z = -4.03 has a p-value of 0.
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A
piece of ribbon
was cut into
three parts in the ratio of 1:3'5
If the shortest was 11cm how long was the ribbon
Answer: Total Length of ribbon is 99 cm
Step-by-step explanation:
Here ribbon was cut into three parts in the ratio 1:3:5
let x be the common multiple of the above ratio
therefore, the lengths of the three parts of the ribbon is 1x,3x,5x
now, given is that the shortest part i.e 1x is equals to 11cm
i.e 1x=11
x=[tex]\frac{11}{1}[/tex]=11cm
now lengths of the ribbon will be
1x=11cm, 3x=3*11=33cm, 5x=5*11=55cm
now total length of piece of ribbon = 1x+3x+5x=9x=9*11=99cm
Last year, Mrs.Sclair’s annual salary was $88,441. This year she received a raise and now earns $96,402 annually. She is paid weekly. a. What was her weekly salary last year? Round to the nearest cent. b.What is Mrs.Sclair’s weekly salary this year? Round to the nearest cent. c.On a weekly basis, how much more does Mrs.Sclair earn as a result of her raise?
We have the following:
old salary: $88441
new salary: $96402
The year is approximately 52 weeks, therefore:
a. old salary for week:
[tex]\begin{gathered} \frac{88441}{52}=1700.8 \\ \end{gathered}[/tex]b. new salary for week:
[tex]\frac{96402}{52}=1853.9[/tex]c. weekly raise
[tex]1853.9-1700.8=153.1[/tex]Need help answering all these questions for the black bird. Exponential equation for the black bird: g(x) = 2^x-8 + 1King Pig is located at (11,9)Moustache Pig is located at (10,4)
Given:
Exponential equation for the black bird is,
[tex]g(x)=2^{x-8}+1[/tex]Required:
To find the starting point of bird and graph the given function.
Explanation:
(1)
The bird starting point is at x = 0,
[tex]\begin{gathered} g(0)=2^{0-8}+1 \\ \\ =2^{-8}+1 \\ \\ =1.0039 \\ \\ \approx1.004 \end{gathered}[/tex](2)
The graph of the function is,
Final Answer
(1) 1.004
(2)
Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
mi/h
The rate at which the distance between the two cars increased four hours later is 30 mi/h.
How to determine the rate?First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:
Distance, x = speed/time
Distance, x = 24/4
Distance, x = 6 miles.
For the second car, we have:
Distance, y = speed/time
Distance, y = 18/4
Distance, y = 4.5 miles.
After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):
z² = x² + y²
Substituting the parameters into the mathematical expression, we have;
z² = 6² + 4.5²
z² = 36 + 20.25
z² = 56.25
z = 7.5 miles.
Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:
2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)
Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:
dz/dt = [x(dx/dt) + y(dy/dt)]/z
dz/dt = [6(24) + 4.5(18)]/7.5
dz/dt = [144 + 81]/7.5
dz/dt = 225/7.5
dz/dt = 30 mi/h.
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Answer:
30 mi / hr
Step-by-step explanation:
First find out how far the cars are apart after 4 hours
24 * 4 = 96 mi = y
18 * 4 = 72 mi = x
Now use the pythagorean theorem
s^2 = ( x^2 + y^2 ) shows s = 120 miles apart at 4 hours
Now s^2 = x^2 + y^2 Differentiate with respect to time ( d / dt )
2 s ds/dt = 2x dx/ dt + 2y dy / dt
ds/dt = (x dx/dt + y dy/dt)/s
= (72(18) + 96(24)) / 120
ds/dt = 30 mi/hr
Write the equation of a Circle with the given information.End points of a diameter : (11, 2) and (-7,-4)
The form of the equation of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) are the coordinates of the center
r is the radius
Since the endpoints of the diameter are (11, 2) and (-7, -4), then
The center of the circle is the midpoint of the diameter
[tex]\begin{gathered} M=(\frac{11+(-7)}{2},\frac{2+(-4)}{2}) \\ M=(\frac{4}{2},\frac{-2}{2}) \\ M=(2,-1) \end{gathered}[/tex]The center of the circle is (2, -1), then
h = 2 and k = -1
Now we need to find the length of the radius, then
We will use the rule of the distance between the center (2, -1) and one of the endpoints of the diameter we will take (11, 2)
[tex]\begin{gathered} r=\sqrt[]{(11-2)^2+(2--1)^2} \\ r=\sqrt[]{9^2+3}^2 \\ r=\sqrt[]{81+9} \\ r=\sqrt[]{90} \\ r^2=90 \end{gathered}[/tex]Now substitute them in the rule above
[tex]undefined[/tex]Simplify completely.a.4x212 xwhen x +0.b. (2t)(3t)(t)c. (3x² - 4x +8)+(x² +6x-11)d. (3x² + 4x – 8) - (x² + 6x +11)
The expression in 4a) is given below
[tex]\frac{4x^2}{12x}[/tex]Collecting similar terms using the division rule of indices, we will have
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The above expression therefore becomes
[tex]\begin{gathered} \frac{4x^2}{12x} \\ =\frac{4x^2}{12x^1} \\ =\frac{1}{3}\times x^{2-1} \\ =\frac{1}{3}\times x \\ =\frac{x}{3} \end{gathered}[/tex]Hence,
The final answer = x/3
A student rolled 2 dice. What is the probability that the first die landed
on a number less than 3 and the second die landed on a number
greater than 3?
What needs to occur for a geometric series to converge?
Given a Geometric Series:
[tex]\sum_{n\mathop{=}1}^{\infty}a\cdot r^{n-1}[/tex]Where "r" is the ratio.
By definition:
[tex]undefined[/tex]What is the probability of drawing a red card from a pack of cards and rolling an even number on a standard six-sided die?
Select one:
1/12
1/2
1/4
1/8
Answer:
1/2 because half the cards are red and half the numbers are even
Solve-2x-16=2x-20.
Ox=1
O no solutions
○ * = −1
all real numbers
15 Which of the digits from 2 to 9 is 5544
divisible by?
Answer:
All of em, except 5
Step-by-step explanation:
5544 / 2 = 2772
5544 / 3 = 1848
5544 / 4 = 1386
5544 / 6 = 924
5544 / 7 = 792
5544 / 8 = 693
5544 / 9 = 616
A parents' evening was planned to start at
15h45. There were 20 consecutive
appointments of 10 minutes each and a
break of 15 minutes during the evening. At
what time was the parents evening due to
finish?
C O 19h15
O 19h20
O 19h00
O 20h00
O 19h30
The time on which parents evening was due to finish was 19 hour 20 minutes.
What is time and its unit?
Time is the ongoing pattern of existence and things that happen in what seems to be an irreversible order from the past, through the present, and into the future.
It is a component quantity of various measurements used to order events, compare the length of events or the time gaps between them, and quantify rates of change of quantities in objective reality or in conscious experience. Along with the three spatial dimensions, time is frequently considered a fourth dimension.
The International System of Units is built upon the seven base units of measurement stipulated by the Système International d'Unités (SI), from which all other SI units are derived. The primary unit of time is the second. The second can be shortened using either the letter S or the letter sec.
20 consecutive appointments of 10 mins = 20 × 10 mins
= 200 min
= 3 hours 20 mins
A break of 15 mins = 3 hours 20 mins + 15 min
= 3 hours 35 mins
The time that the parents evening due to finish = 15h 45 min +3h 35 mins
= 19h 20min
Thus, the time on which parents evening was due to finish was 19h 20min.
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Which of the following expressions is equal to -x2 -36
OA. (-x+6)(x-6i)
OB. (x+6)(x-6i)
OC. (-x-6)(x-6i)
OD. (-x-6)(x+6i)
The expression equivalent to -x² - 36 is the one in option C.
(-x - 6i)*(x - 6i)
Which of the following expressions is equal to -x² - 36?We can rewrite the given expression as:
-x² - 36 = -x² - 6²
And remember that the product of a complex number z = (a + bi) and its conjugate (a - bi) is:
(a + bi)*(a - bi) = a² + b²
Then in this case we can rewrite:
-x² - 6² = -(x² + 6²) = - (x + 6i)*(x - 6i)
= (-x - 6i)*(x - 6i)
The correct option is C.
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HELP ME PLEASE !!!
REASONING An absolute value function is positive over its entire domain. How many x-intercepts does the graph of the function have?
● None
01
02
O Infinite
The absolute value function can intersect a horizontal x-axis at zero, one, as well as two points.
What is meant by the absolute value function?The absolute value function is usually thought to provide the distance between two numbers on a number line. Algebraically, the output is the value without regard to sign for whatever the input value is. The corner point where the graph changes direction is the most essential characteristic of the absolute value graph. This point is depicted as the origin. When the input is zero, the graph of an absolute value function would then intersect the vertical axis.Thus, depending on the way the graph has indeed been shifted and reflected, it could or might not intersect the horizontal axis.
The absolute value function can intersect the x-axis at zero, one, or two points.
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I really need help please!
Answer:
n < -15/4
Step-by-step explanation:
You want to use the discriminant to find the values of n for which the quadratic 3z² -9z = (n -3) has only complex solutions.
DiscriminantThe discriminant of quadratic equation ax²+bx+c = 0 is ...
d = b² -4ac
The given quadratic can be put in this form by subtracting (n-3):
3z² -9z -(n -3) = 0
This gives us ...
a = 3b = -9c = -(n -3)and the discriminant is ...
d = (-9)² -4(3)(-(n-3)) = 81 +12(n -3)
d = 12n +45
Complex solutionsThe equation will have only complex solutions when the discriminant is negative:
d < 0
12n +45 < 0 . . . . . use the value of the discriminant
n +45/12 < 0 . . . . . divide by 12
n < -15/4 . . . . . . . subtract 15/4
There will be two complex solutions when n < -15/4.
What point in the feasible region maximizes the objective function?
x>0
Y≥0
Constraints
-x+3≥y
{ y ≤ ½ x + 1
objective function: C = 5x - 4y
Answer:
(3, 0)
Maximum Value of Objective Function = 15
Step-by-step explanation:
This is a problem related to Linear Programming(LP)
In linear programming, the objective is to maximize or minimize an objective function subject to a set of constraints.
For example, you may wish to maximize your profits from a mix of production of two or more products subject to resource constraints.
Or, you may wish to minimize cost of production of those products subject to resource constraints..
The given LP problem can be stated in standard form as
Max 5x - 4y
s.t.
-x + 3 ≥ y
y ≤ 0.5x + 1
x ≥ 0, y ≥ 0
The last two constraints always apply to LP problems which means the decision variables x and y cannot be negative
It is standard to express these constraints with the decision variables on the LHS and the constant on the RHS
Rewriting the above LP problem using standard notation,
Let's rewrite the constraints using the standard form:
- x + 3 ≥ y
→ -x - y ≥ -3
→ x + y ≤ 3 [1]
y ≤ 0.5x + 1
→ -0.5x + y ≤ 1 [2]
The LP problem becomes
Max 5x - 4y
s. t.
x + y ≤ 3 [1]
-0.5x + y ≤ 1 [2]
x ≥ 0 [3]
y ≥0 [4]
With an LP problem of more than 2 variables, we can use a process known as the Simplex Method to solve the problem
In the case of 2 variables, it is possible to solve analytically or graphically. The graphical process is more understandable so I will use the graphical method to arrive at the solution
The feasible region is the region that satisfies all four constraints shown.
The graph with the four constraint line equations is attached. The feasible region is the dark shaded area ABCD
The feasible region has 4 corner points(A, B,C, D) whose coordinates can be computed by converting each of the inequalities to equalities and solving for each pair of equations.
It can be proved mathematically that the maximum of the objective function occurs at one of the corner points.
Looking at [1] and [2] we get the equalities
x + y = 3 [3]
-0.5x + y = 1 [4]
Solving this pair of equations gives x = 4/3 and y = 5/3 or (4/3, 5/3)
Solving y = 0 and x + y = 3 gives point x = 3, y =0 (3,0)
The other points are solved similarly, I will leave it up to you to solve them
The four corner points are
A(0,0)
B(0,1)
C(4/3, 5/3)
D(3,0)
The objective function is 5x - 4y
To find the values of x and y that maximize the objective function,
plug in each of the x, y values of the corner points
Ignoring A(0,0)
we get the values of the objective function at the corner points as
For B(0,1) => 5(0) - 4(1) = -4
For C(4/3, 5/3) => 5(4/3) - 4(5/3) = 20/3 - 20/3 = 0
For D(3, 0) => 5(3) - 4(0) = 15
So the values of x and y which maximize the objective function are x = 3 and y = 0 or point D(3,0)
Enter the solution to the inequality below. Enter your answer as an inequality.
Use =< for and >= for >
√x ≥ 17
Answer here
SUBMIT
The solution of the inequality is [tex]x \geq 289[/tex].
What is inequality?
Inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ( [tex]\neq[/tex]) " to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The given inequality is, [tex]\sqrt{x} \geq 17[/tex]
Taking square on both sides, we get
[tex]x\geq 289[/tex].
Therefore, the solution of the inequality is [tex]x \geq 289[/tex].
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savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?
The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.
How is the amount required to have a saving of $50,000 ?The compound interest formula is expressed as;
P = A / (1 + r/n)^nt
Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.
Given the data in the question;
Accrued amount A = $50,000Interest rate r = 6%Compounded monthly n = 12Elapsed time t = 30 yearsPrincipal P = ?First, convert rate from percent to decimal.
Rate r = 6%
Rate r = 6/100
Rate r = 0.06 per year
To determine the principal, plug the given values into the formula above and solve or P
P = A / (1 + r/n)^nt
P = $50,000 / (1 + 0.06/12)^( 12 × 30 )
P = $50,000 / (1 + 0.05)³⁶⁰
P = $50,000 / (1.05)³⁶⁰
P = $8,302.10
Therefore, the principal investment is $8,302.10.
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Figure A has a perimeter of 48 m and one of theside lengths is 18 m. Figure B has a perimeter of 80 m.What is the corresponding side length of Figure B?
We have to use proportions to solve this question.
According to the given information, the perimeter of Figure A is to the sidelength of that figure as the perimeter of Figure B is to the sidelength of that figure:
[tex]\begin{gathered} \frac{48}{18}=\frac{80}{x} \\ x=\frac{80\cdot18}{48} \\ x=30 \end{gathered}[/tex]The corresponding sidelength of Figure B is 30.
what is the area of a circular pool with a diameter of 36 ft?
Answer:
1,017.36ft^2
Explanation:
Area of the circular pool = \pi r^2
r is the radius of the pool
Given
r = d/2
r = 36/2
r = 18ft
Area of the circular pool = 3.14(18)^2
Area of the circular pool = 3.14 * 324
Area of the circular pool = 1,017.36ft^2
Solve for a.5a== ✓ [?]2aPythagorean Theorem: a2 + b2 = c2=
ANSWER
a = √21
EXPLANATION
This is a right triangle, so we have to apply the Pythagorean Theorem to find the value of a.
We know the length of the hypotenuse which is 5, and the length of one of the legs, which is 2. The Pythagorean Theorem for this problem is,
[tex]a^2+2^2=5^2[/tex]Subtract 2² from both sides,
[tex]\begin{gathered} a^2+2^2-2^2=5^2-2^2 \\ a^2=25-4 \end{gathered}[/tex]And take the square root to both sides,
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{25-4} \\ a=\sqrt[]{21} \end{gathered}[/tex]Hence, the value of a is √21.
4. Sean bought 1.8 pounds of gummy bears and 0.6 pounds of jelly beans and paid $10.26. He went back to the store the following week and bought 1.2 pounds of gummy bears and 1.5 pounds of jelly beans and paid $15.09. What is the price per pound of each type of candy?Directions: For each problem - define your variables, set up a system of equations, and solve.
Let
the price of gummy bears per pound = x
the price of jelly beans per pound = y
[tex]\begin{gathered} 1.8x+0.6y=10.26 \\ 1.2x+1.5y=15.09 \\ 1.2x=15.09-1.5y \\ x=12.575-1.25y \\ \\ 1.8(12.575-1.25y)+0.6y=10.26 \\ 22.635-2.25y+0.6y=10.26 \\ -1.65y=10.26-22.635 \\ -1.65y=-12.375 \\ y=\frac{-12.375}{-1.65} \\ y=7.5 \\ \\ 1.8x+0.6y=10.26 \\ 1.8x+0.6(7.5)=10.26 \\ 1.8x+4.5=10.26 \\ 1.8x=10.26-4.5 \\ 1.8x=5.76 \\ x=\frac{5.76}{1.8} \\ x=3.2 \end{gathered}[/tex]price per pound of gummy bear = $3.2
price per pound of jelly beans = $7.5
Proofs involving a transversal
Thus, it is clear that the lines RS and TV in the preceding diagram are parallel to each other
What are the properties of parallel lines?If you extend a set of lines indefinitely, they will remain parallel and never cross each other even though they are on the same plane. The symbol || represents the collection of parallel lines. All parallel lines are always equally spaced apart. Investigate the characteristics of parallel lines.
When two lines in a plane are stretched infinitely in both directions and do not cross, they are said to be parallel.
To solve the given question we know,
angle 1= angle 2 and lines RV // TS
angle 4= angle 3(interior angles on parallel lines are equal)
angle 1=angle 4 (vertically opposite angles are equal )
angle 1= angle 3 (angle 4=angle 1)
angle 4=angle 2( angle 1=angle 4)
Now we can see that the sum of base angles of the diagram will be 180 because
180-angle 3= angle STV
angle 4=angleSTV+180 (angle 3=angle4)
we proved that the diagram is a parallelogram because base angles of the same side are supplementary:
Therefore , we can conclude that the lines RS // TV in the preceding diagram .
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20 >= 4/5 w
Solve the inequality. Grab the solution
Solve the inequality. Grab the solution
-8<-1/4m
In inequality 20 >= 4/5 w, w is 25 or any real no. lower than< 25 and in inequality -8<-1/4m, m = any real no. greater than> 24 is are the solution.
What is inequality?An inequality compares two values and indicates whether one is lower, higher, or simply not equal to the other.
A B declares that a B is not equal.
When a and b are equal, an is less than b.
If a > b, then an is bigger than b.
(those two are called strict inequality)
The phrase "a b" denotes that an is less than or equal to b.
The phrase "a > b" denotes that an is greater than or equal to b.
We have give the inequality to solve
20 = 4/5w
w = 20 × 5/4
= 25 or any real no. lower than< 25
Let -8 = -1/4m
m = -8 × -4
m = 24
so m = any real no. greater than> 24
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Solve the system [tex]\left \{ {{5x1 + 5x2 = 5} \atop {2x1 + 3x2 = 4}} \right.[/tex]
The solution for the given system of equations is x[1] = -1 and x[2] = 2.
What is system of equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
Given are the following equations as -
5 x[1] + 5 x[2] = 5
2 x[1] + 3 x[2] = 4
Assume that -
x[1] = a
x[2] = b
Then, we can write the equations as -
5a + 5b = 5
2a + 3b = 4
Now -
5a + 5b = 5
5(a + b) = 5
a + b = 1
a = 1 - b
So, we can write -
2a + 3b = 4
as
2(1 - b) + 3b =4
2 - 2b + 3b = 4
b = 4 - 2
b = 2 = x[2]
Then
a = 1 - 2
a = -1 = x[1]
Therefore, the solution for the given system of equations is x[1] = -1 and x[2] = 2.
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