Answer:
A: x > 3/4
Step-by-step explanation:
First you simplify the equation.
Simplify 1/3x
Then Simplify the left side.
1/2-x/3<x/3
Move x/3 to the left side of the equation by subtracting it from both sides.
1/2-x/3-x/3<0
Now simplify the left side.
1/2-2x/3<0
Find the LCD of the terms of the equation. In this case it's 6.
Multiply each term by 6 and simply.
3-2x<2x
Move all terms that contain a x to the left side of the inequality.
3-4x<0
Subtract 3 from both sides.
-4x<-3
Now divide each term by -4 and simplify.
This gives us our answer of x > 3/4.
Hope this helps. :)
The graph of a quadratic equation always has an extreme location (maximum or minimum). State whether the parabola opens upward or downward, whether it has a maximum or a minimum, and what the coordinates of that point are. Use the pointer tool to approximate the coordinates of this extreme location to the nearest whole number.
The graph of a quadratic equation (a parabola) opens upwards or downwards depending on whether the coefficient of the x^2 term is positive or negative, respectively. The vertex of the parabola corresponds to the function's extreme point (maximum or minimum), and its coordinates are calculable with the formula (-b/2a, f(-b/2a)).
Explanation:The graph of a quadratic equation, otherwise known as a parabola, opens upwards if the coefficient of the x^2 term is positive and opens downwards if it is negative. The maximum or minimum point of the parabola is known as the vertex. In a standard form quadratic equation y = ax^2 + bx + c, the coordinates of the vertex are given by the equation (-b/2a, f(-b/2a)).
If the parabola opens upwards (positive coefficient of x^2), it will have a minimum point at the vertex. The y-coordinate of this point is the minimum value of the function.If the parabola opens downwards (negative coefficient of x^2), it will have a maximum point at the vertex. The y-coordinate of this point is the maximum value of the function.
So for example, for the quadratic equation y = 2x^2 + 3x + 1, the parabola would open upwards, and the vertex would be at (-3/4, f(-3/4)), which would be the minimum point of the parabola.
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Find the volume of a sphere with a diameter 40 cm in length. Approximate pi as 3.14 and round your answer to the nearest tenth. A. 5,026.5 cm3 B. 33,493.3 cm3 C. 42,090.0 cm3 D. 268,082.6 cm3
Answer:
Option B. [tex]33,493.3\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=40/2=20\ cm[/tex] ----> the radius is half the diameter
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{4}{3}(3.14)(20)^{3}=33,493.3\ cm^{3}[/tex]
In 1998 the population of a city was 100,000. Then each year for the next five years the population increases by 3%. Write and exponential growth model to represent this situation.
➷ population = 100,000 x 1.03^5
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Which expressions are equivalent to (a^2-16(a+4)? Select the three equivalent expressions
A.) a^3-64
B.) (a-4)^3
C.) (a+4)^3
D.) (a+4)^2(a-4)
E.) (a-4)^2(a+4)
F.) [(a)^2-(4^2)](a+4)
G.) (a-4)(a+4)(a+4)
Answer:
F
Step-by-step explanation:
Final answer:
The three equivalent expressions to (a^2-16(a+4)) are: (a-4)^3, (a+4)^2(a-4), and (a-4)(a+4)(a+4).
Explanation:
The expression (a^2-16(a+4)) can be simplified by expanding the terms and combining like terms. First, apply the distributive property by multiplying -16 by (a+4), giving -16a-64. Then, multiply a^2 by -16 to get -16a^2. Finally, combine like terms to get -16a^2 - 16a - 64.
Therefore, the three equivalent expressions to (a^2-16(a+4)) are:
(a-4)^3
(a+4)^2(a-4)
(a-4)(a+4)(a+4)
4 lb of bananas for $2.76 is the same as
1 lb of bananas for $.69
Rewrite as a simplified fraction.
0.482=?
Answer: [tex]\bold{\dfrac{241}{500}}[/tex]
Step-by-step explanation:
[tex]0.482 = \dfrac{482}{1000}\\\\\\\dfrac{482}{1000}\div \dfrac{2}{2}=\dfrac{241}{500}[/tex]
Answer:
241/500 is The answer
Step-by-step explanation:
1) 0.482 = 482/1000
2) Divide by 2 on both side
0.482 = (482/2)/(1000/2) = 241/500
Hopes this helps!
What's the value of x? x=
Answer:
x = 2
Step-by-step explanation:
These are 2 secant lines intersecting a circle. This problem can be solved using secant-theorem.
Simply put, the secant theorem tells us that the outer segment (outside the circle) times the total length of secant line (outer and inner segment) is equal to that of the other secant line's product of outer and total.
For this diagram, according to the theorem, it should be:
DE * CE = AE * BE
Hence we have:
[tex]DE * CE = AE * BE\\(1+x+4)*(x+4)=(11+x+1)*(x+1)\\(x+5)*(x+4)=(x+12)*(x+1)\\x^2+9x+20=x^2+13x+12\\20-12=13x-9x\\8=4x\\x=\frac{8}{4}=2[/tex]
The value of x is 2
point R has coordinates (a,b) the point is reflected across the x-axis and then translated 5 points to the right to create point S . Create an expression that represents the y-coordinate of S
Answer:
-b + 5
Step-by-step explanation:
translation
Final answer:
The y-coordinate of point S after reflection across the x-axis and translation is -b, as reflection across the x-axis changes the sign and translation to the right does not affect the y-coordinate.
Explanation:
The student is asking to find the y-coordinate of a point S after a reflection across the x-axis and a translation 5 points to the right of a point R with coordinates (a,b).
The reflection of the y-coordinate across the x-axis changes its sign, so the reflected y-coordinate of point R would be -b. Translating a point to the right does not affect the y-coordinate, so the y-coordinate of point S would remain -b after this translation. Therefore, the expression that represents the y-coordinate of S is simply -b.
Which method is most efficient method to use to solve 2x^2+4x-7=0
Answer:
Use the quadratic formula
Step-by-step explanation:
Use the quadratic formula
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex]
Where a, b and c are the real coefficients of the polynomial
Then, for
[tex]2x^2+4x-7=0\\a = 2\\b = 4\\c = -7[/tex]
The solutions are:
[tex]x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_2 = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x_1 = \frac{-4+\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_2 = \frac{-4-\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_1 = \frac{-2+3\sqrt{2}}{2}\\\\x_2 = \frac{-2-3\sqrt{2}}{2}[/tex]
Amanda teaches the art of quilling to four students these students each teach the art of quilling to four other students if this process continues for five generations blank people will know the art of quilling
In the fifth generation 1024 people learnt the art of quilling.
What is a geometric series?A geometric series is a series for which the ratio of each two consecutive terms is a constant and called the common ratio.Nth term of the Geometric series is given as [tex]t_{n} = ar^{n-1}[/tex] where a is the first term of the series and r is the common ratio.How to find how many people will know the art of quilling?In the first generation , 4 people learnt the art of quilling.In second generation (4 x 4) = 16 people learnt the art of quilling.In the third generation (16 x 4) = 64 people learnt the art of quilling.In the fourth generation (64 x 4) = 256 people learnt the art of quilling.In the fifth generation ( 256 x 4) = 1025 people learnt the art of quilling.In the fifth generation 1024 people learnt the art of quilling.
The series is going as a geometric pattern.In total 5 generations total (16+ 64 + 256 + 1024) = 1364 people learnt the art of quilling.
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Using the exponential growth formula, it is determined that by the end of five generations, 4096 people will know the art of quilling, starting with one teacher teaching four students, and each subsequent student teaching four others.
Explanation:The question involves an exponential growth scenario where Amanda teaches the art of quilling to four students, and then these students each teach four others, and so on for five generations. To find out how many people will know the art of quilling by the fifth generation, we use the formula for exponential growth: Total = a(1 + r)^n, where a is the initial amount (number of people who know the art at the beginning), r is the rate of increase (each person teaches 4 others means the rate is 4), and n is the number of generations.
The initial teacher, Amanda, is not counted in the first generation of students she teaches, so we begin with 4 students as our initial amount (a=4). Thus, the calculation for five generations becomes: Total = 4(4)^5. The formula simplifies to 4 * 1024 = 4096 people. Therefore, by the end of five generations, 4096 people will know the art of quilling.
Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. How long did it take Lucy to bike the trail?
Plz explain your awnser
Answer:
3.75 hours
Step-by-step explanation:
Using the relation
Distance = speed × time
Change Jasmine's speed into an improper fraction
9 [tex]\frac{3}{10}[/tex] = [tex]\frac{93}{10}[/tex], then
distance = [tex]\frac{93}{10}[/tex] × [tex]\frac{5}{2}[/tex] = [tex]\frac{93}{4}[/tex] miles
To calculate Lucy's time over the same distance use
Time = [tex]\frac{distance}{speed}[/tex]
Change speed to an improper fraction
6 [tex]\frac{1}{5}[/tex] = [tex]\frac{31}{5}[/tex], hence
time = [tex]\frac{\frac{93}{4} }{\frac{31}{5} }[/tex]
= [tex]\frac{93}{4}[/tex] × [tex]\frac{5}{31}[/tex] ( cancel 93 and 31 )
= [tex]\frac{3(5)}{4}[/tex]
= [tex]\frac{15}{4}[/tex] = 3.75 hours
Final answer:
It took Lucy approximately 160.17 minutes to bike the trail.
Explanation:
Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. To find out how long it took Lucy to bike the trail, we can use the formula:
Time = Distance / Rate
Since the distance is the same for both Jasmine and Lucy, we can set up an equation:
2.5 = Distance / 6 1/5
To solve this equation, we first need to convert 2.5 into a fraction. 2.5 is the same as 2 1/2. So, the equation becomes:
2 1/2 = Distance / 6 1/5
To make the equation easier to work with, we can convert 2 1/2 into an improper fraction: 2 1/2 = 5/2. The equation now becomes:
5/2 = Distance / 6 1/5
To solve for Distance, we can use cross-multiplication:
(5/2)(6 1/5) = Distance
Simplifying the right side of the equation:
(5/2)(31/5) = Distance
(5/1)(31/5) = Distance
31 = Distance
So, the distance of the bike trail is 31 miles. Now, we can find out how long it took Lucy to bike the trail by using the formula Time = Distance / Rate:
Time = 31 / 6 1/5
Once again, let's convert 31 into a fraction: 31 = 31/1. The equation now becomes:
Time = 31/1 / 6 1/5
To divide fractions, we can multiply by the reciprocal of the second fraction. So, the equation becomes:
Time = 31/1 * 5 1/6
Now, we can convert 5 1/6 into an improper fraction: 5 1/6 = 31/6. The equation now becomes:
Time = 31/1 * 31/6
To multiply fractions, we can multiply the numerators together and the denominators together. So, the equation becomes:
Time = (31*31) / (1*6)
Calculating the numerator and denominator separately:
Time = 961 / 6
So, it took Lucy approximately 160.17 minutes to bike the trail.
The half-life of a radioactive kind of europium is 9 years. How much will be left after 18 years, if you start with 40 grams of it ?
Answer:There will be 10 grams left because you subtract half of the current amount from it every 9 years.
Step-by-step explanation:
Starting with 40 grams of europium which has a half-life of 9 years, after the first half-life, there would be 20 grams left, and after the second half-life (a total of 18 years), there would be 10 grams remaining.
The question is about calculating the amount of a radioactive substance that remains after a certain period of time has passed, which is based on the substance's half-life. Given that the half-life of europium is 9 years, after one half-life (9 years) 50% of the substance would remain, and after two half-lives (18 years) only 25% would remain. Since we started with 40 grams of europium, we apply this decay process step by step:
After the first half-life (9 years), 40 grams become 20 grams.After the second half-life (another 9 years, total of 18 years), the remaining 20 grams become 10 grams.Therefore, after 18 years, there will be 10 grams of the radioactive europium left.
What is the value of angle x rounded to the nearest whole number
Answer:
x ≈ 42°
Step-by-step explanation:
Label the vertices of the quadrilateral shown at the upper left in you diagram A, B, C, and D, starting at the lower left. Label the center point X. Then the red line is CX and the lower two line segments are CD and DA. (A, C, D, and X are not coplanar.)
Angle D of triangle ACD is the interior angle of a regular pentagon, so measures 108°. That means angle ACD measures (180° -108°)/2 = 36°. If we label the midpoint of segment AC point Y, then the length of segment CY is ...
CY = CD·cos(36°)
Now triangle BCD is an equilateral triangle, so segment CX will have a length corresponding to the altitude of that triangle, CD·√3/2. Shifting our focus to the triangle AXC, we find that angle XCY will satisfy the relation ...
cos(XCY) = CY/CX = CD·cos(36°)/(CD·√3/2) = (2/)√3·cos(36°)
Angle x is the exterior angle of triangle AXC that is opposite the two equal interior angles XCY and XAY. Hence its value is double that of angle XCY.
angle x = 2·arccos((2/√3)·cos(36°)) ≈ 2·20.905° ≈ 41.81°
angle x ≈ 42°
_____
Comment on the angle
The icosahedron is the only Platonic solid with a dihedral angle more than 120°. It is about 138.19°, the supplement to angle x.
Comment on point labels
It may help to label the points in the 3-d version of the figure. Then you can see that segment AC is a line through the interior space of the icosahedron.
The polynomial function f(x)= 5x^5 + 16/5x -3 is graphed below. Which is a potential rational root of f(x) at point P ?
Answer: (A) The root at point P may be .
Step-by-step explanation:edge2022
4. The MAD of a set of six data values is 10. The mean is 20. What could the data values be? Show that the mean is 20 and the MAD is 20.
Answer:
15
Step-by-step explanation:
The data values could be 10, 10, 10, 25, 25, 40.
What is mean Absolute Deviation?Mean absolute deviation is defined as the average value of the absolute deviations from the mean.
Given that,
Mean absolute deviation of a set of 6 data values = 10
Let x1, x2, x3, x4, x5 and x6 be the data values.
Mean = 20
x1 + x2 + x3 + x4 + x5 + x6 / 6 = 20
x1 + x2 + x3 + x4 + x5 + x6 = 120
Also we have mean absolute deviation = 10
Data values could be 10, 10, 10, 25, 25, 40.
Mean = 20 and MAD = 10
Hence the data values could be 10, 10, 10, 25, 25, 40.
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I need help please???
I need help to please?
Answer:
x = 15
Step-by-step explanation:
Which ordered pair is a solution of the inequality?
Y-1<2x
a. (3,7)
b. (1,8)
c. (2,7)
d. (3,-11)
Answer:
d. (3, -11)Step-by-step explanation:
[tex]y-1<2x\qquad\text{add 1 to both sides}\\\\y<2x+1\\\\\text{Substitute the coordinates of the points and check the inequality:}\\\\a.\ (3,\ 7)\\7<2(3)+1=6+1=7\qquad\text{FALSE}\\\\b.\ (1,\ 8)\\8<2(1)+1=2+1=3\qquad\text{FALSE}\\\\c.\ (2,\ 7)\\7<2(2)+1=2+1=5\qquad\text{FALSE}\\\\d.\ (3,\ -11)\\-11<2(3)+1=6+1=7\qquad\text{TRUE}[/tex]
HELP PLEASE, QUICKLY!!!!!
what is the lateral area of this regular octagonal pyramid?
149.3 cm
182.9 cm
211.2 cm
298.7 cm
Answer:
The lateral area is [tex]298.7\ units^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of the regular octagonal pyramid is equal to the area of its eight triangular lateral faces
The lateral area is equal to
[tex]LA=8[\frac{1}{2}(b)(l)][/tex]
we have
[tex]b=6.6\ cm[/tex]
To find the slant height apply the Pythagoras Theorem
[tex]l^{2}=8^{2} +8^{2}\\l^{2}=128\\l=\sqrt{128}\ units[/tex]
Find the lateral area
substitute the values
[tex]LA=8[\frac{1}{2}(6.6)(\sqrt{128})]=298.7\ units^{2}[/tex]
The answer is 298.7 cm²
If a man weighs 198 pounds on earth, his mass on earth is 90 kilograms. If you can answer A & B
It is 5892 and i know it has to be or I guess I am wrong (i don’t care) hahahaha
The selling price of an item is $390. After 6 months of not selling, it is marked down by 10%. After another 6 months of not selling, it is further marked down by 30%. Find the sale price after both markdowns. Round to nearest dollar.
Answer:
$246
Step-by-step explanation:
The price of the product is $390, after 6 months the price is marked down by 10% which is $39 so the total will be $351. After another 6 months the price is marked down again by 30%, which is $105 and 3 cents ($105.3). For a total of $245 and 7 cents ($245.7). To round the number you only need to look at the number after the decimal which is 7 in this case. Any number bellow 5 counting 5 in it, will stay the same number, any number above 5 without counting 5 will be the next number. So $245.7 rounded to the nearest dollar will be $246.
Hope it was helpful ^^ <3
Good Luck
Item 8 Solve for x. Use the quadratic formula. 2x2−5x−9=0 Enter the solutions, in simplified radical form, in the boxes.
Answer:
5+√97/4
Also 5-√97/4
Step-by-step explanation:
The Quadratic formula is x=-b+-√b^2-4ac/2a
This means that we should plug the values for A B AND C into the formula
We can work out that
A = 2
B=-5
C=-9
Once we have put these into the formula we get
5+√97/4 (all over 4) aka 3.71
Also 5-√97/4 (all over 4) aka -1.21
Answer:
[tex]\large\boxed{x=\dfrac{5-\sqrt{97}}{4}\ or\ x=\dfrac{5+\sqrt{97}}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ ax^2+bx+c=0\\\\\text{The quadratic formula:}\\\\\Delta=b^2-4ac\\\\\text{If}\ \Delta>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt\Delta}{2a}\\\\\text{If}\ \Delta=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ \Delta<0,\ \text{then the equation has no solution}\\==================================[/tex]
[tex]\text{The equation}\ 2x^2-5x-9=0\\\\a=2,\ b=-5,\ c=-9\\\\\Delta=(-5)^2-4(2)(-9)=25+72=97>0\\\\\sqrt\Delta=\sqrt{97}\\\\x_1=\dfrac{-(-5)-\sqrt{97}}{2(2)}=\dfrac{5-\sqrt{97}}{4}\\\\x_2=\dfrac{-(-5)+\sqrt{97}}{2(2)}=\dfrac{5+\sqrt{97}}{4}[/tex]
What is the additive inverse of the complex number 13-2
Answer:
-13 + j*2
Step-by-step explanation:
The additive inverse of a complex number x = a +j*b
is a number y, such that
x + y = 0
This means that
y = -x = - a - j*b
Therefore
The additive inverse of 13 - j*2 is equal to
-(13 - j*2) = -13 +j*2
if you borrow $400 for 2 years at an annual interest rate of 15%, how much will u pay altogether?
Answer:
$520
Step-by-step explanation:
We first find the interest;
400*2*15/100=4*2*15
=$120
Total=$120+$400
=$520
Answer:520
Step-by-step explanation:
above correct
What is the steps in to solving this
If y varies inversely with x and y=8 when x=40, what is the constant of variation
Answer:
Step-by-step explanation:
Inverse Variation. Since k is constant, we can find k given any point by multiplying the x-coordinate by the y-coordinate. For example, if y varies inversely as x, and x = 5 when y = 2, then the constant of variation is k = xy = 5(2) = 10.
A bag contains 5 red,4 green, and 3 blue marbles. What is the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble A. 1/48 B. 1/12 C.5/48 D.5/12
Answer:
c 5/48
Step-by-step explanation:
Meg buys 12 bags of sunflower seeds. Each bag has 58 seeds. How many seeds dose meg have??
Answer: 696
Step-by-step explanation:
58 times 12
Answer:
696 seeds
Step-by-step explanation:
12*58
Variables are usually written as ......- case letters.
Answer: Variables are usually written in lower-case letters.
Step-by-step explanation:
For example, it's "9x +10" not "9X +10"
Find the area of the polygon defined by the coordinates (0, -5), (-5, 0), (-15, -20), and (-20, -15). A) 90 square units B) 110 square units C) 130 square units D) 150 square units
Answer: E. 150 square units.
Step-by-step explanation:A polygon is figure with at least 3 straight or definite sides or typically 5 or more straight sides.
Here the polygon we are given is a rectangle.
We know that,
Area of a rectangle = l x w
so we need to measure the length and width of the rectangle to find its area.
If we look closely, we can see the length of the rectangle above the x-axis is 8 units and the length below the x-axis 7 units which makes a total og 15 units.
Answer:
D) 150 square units
Step-by-step explanation:
Use the distance formula: d = (x2 - x1)2 + (y2 - y1)2
A = L x W = 15/-2x 5/-2
= 150
Need help QUICK!!! #3
A=f(18)=110(.8855)^18=12.3mg
===========================================================
Explanation:
Plug in t = 18 to get
f(t) = 110*(0.8855)^t
f(18) = 110*(0.8855)^18
f(18) = 110*(0.112045)
f(18) = 12.32495
f(18) = 12.32
The answer is approximate. I rounded to two decimal places (aka to the nearest hundredth).