Answer:
-1/2 , 0 , 3/2
Step-by-step explanation:
Given equation is:
[tex]4x^3-5x = |4x|[/tex]
We know that [tex]|x|=a\\The\ solution\ will\ be:\\x=a\ and\ x=-a\\[/tex]
So, from given equation,we will get two solutions:
[tex]4x^3-5x = 4x\\4x^3-5x-4x=0\\4x^3-9x=0\\x(4x^2-9) = 0\\x = 0\\and\\4x^2-9 = 0\\4x^2=9\\x^2 = \frac{9}{4} \\\sqrt{x^2}=\sqrt{\frac{9}{4} }\\[/tex]
x= ±√3/2 , 0
and
[tex]4x^3-5x = -4x\\4x^3-5x+4x=0\\4x^3-x=0\\x(4x^2-1) = 0\\x = 0\\and\\4x^2-1 = 0\\4x^2=1\\x^2 = \frac{1}{4} \\\sqrt{x^2}=\sqrt{\frac{1}{4} }[/tex]
x= ±1/2 , 0
We can check that 1/2 and -3/2 do not satisfy the given equation.
[tex]4x^3-5x = |4x|\\Put\ x=1/2\\4(\frac{1}{2})^3 - 5(\frac{1}{2}) = |4 * \frac{1}{2}|\\ 4 * (\frac{1}{8)} - \frac{5}{2} = |2|\\ -2 = 2\\Put\ x=-\frac{3}{2} \\4(\frac{-3}{2})^3 - 5(\frac{-3}{2}) = |4 * \frac{-3}{2}|\\-6 = 6\\[/tex]
So, 1/2 and -3/2 will not be the part of the solution ..
So, the solutions in increasing order are:
-1/2 , 0 , 3/2 ..
Answer:
[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]
Step-by-step explanation:
We are given that an equation
[tex]4x^3-5x=\mid x\mid[/tex]
We have to find the solution of given equation and arrange the solution in increasing order.
[tex]4x^3-5x=4x[/tex] when x >0
and [tex]4x^3-5x=-4x[/tex] when x < 0
because [tex]\mid x\mid =x when x > 0 [/tex]
=-x when x < 0
[tex]4x^3-5x-4x=0[/tex]
[tex]4x^3-9x=0[/tex]
[tex]x(4x^2-9)=0[/tex]
[tex]x(2x+3)(2x-3)=0[/tex]
Using identity [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]x=0,2x+3=0,2x-3=0[/tex]
[tex]2x=3\implies x=\frac{3}{2}=1.5[/tex]
[tex]2x=-3 \implies x=-\frac{3}{2}=-1.5[/tex]
[tex]4x^3-5x=-4x=0[/tex]
[tex]4x^3-5x+4x=0[/tex]
[tex]4x^3-x=0[/tex]
[tex]x(4x^2-1)=0[/tex]
[tex]x(2x+1)(2x-1)=0[/tex]
[tex]x=0,2x+1=0[/tex]
[tex]2x-1=0[/tex]
[tex]2x-1=0[/tex]
[tex]2x=1 \ilmplies x=\frac{1}{2}=0.5[/tex]
[tex]2x+1=0[/tex]
[tex]2x=-1 \implies x=-\frac{1}{2}=-0.5[/tex]
When we substitute x=[tex]\frac{1}{2}[/tex]
[tex]4(\frac{1}{2})^3-\frac{5}{2}=\frac{1}{2}-\frac{5}{2}=\frac{1-5}{2}=-2[/tex]
[tex]\mid 4(\frac{1}{2})\mid=2[/tex]
[tex]-2\neq 2[/tex]
Hence, [tex]\frac{1}{2}[/tex] is a not solution of given equation.
When substitute [tex]x=\frac{-3}{2}[/tex]
[tex]4(\frac{-3}{2})^3+\frac{15}{2}=\frac{-27}{2}+\frac{15}{2}=\frac{-27+15}{2}=-6[/tex]
[tex]\mid 4(-\frac{3}{2}\mid=6[/tex]
[tex]-6\neq 6[/tex]
Hence, [tex]\frac{-3}{2}[/tex] is not a solution of given equation.
Substitute x=[tex]-\frac{1}{2}[/tex] in the given equation
[tex]4(-\frac{1}{2})^3+\frac{5}{2}=-\frac{1}{2}+\frac{5}{2}=2[/tex]
[tex]\mid 4(-\frac{1}{2})\mid=2[/tex]
[tex]2=2[/tex]
Hence, [tex]-\frac{1}{2}[/tex] is a solution of given equation.
Substitute [tex]x=\frac{3}{2}[/tex] in the given equation
[tex]4(\frac{3}{2})^3-\frac{15}{2}=\frac{27-15}{2}=6[/tex]
[tex]\mid 4(\frac{3}{2})\mid =6[/tex]
[tex]6=6[/tex]
Hence, [tex]\frac{3}{2}[/tex] is a solution of given equation.
Answer:[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]
help please.........................................
Answer:
x =-2 and z =-4
Step-by-step explanation:
We need to solve the following systems of equation
-3x-2y+4z = -16 eq(1)
10x+10y-5z = 30 eq(2)
5x+7y+8z = -21 eq(3)
Multiply eq(1) with 10 and eq(2) with 3
-30x-20y+40z = -160
30x+30y-15z = 90
__________________
10y+25z = -70
Divide by 10
2y+5z = -14 eq(4)
Multiply eq(1) with 10 and eq(3) with 6
-30x-20y+40z = -160
30x+42y+48z = -126
__________________
22y+88z = -286
Divide by 11
2y+8z = -26 eq(5)
Subtract eq(4) and eq(5)
2y+5z = -14
2y+8z = -26
- - +
__________
-3z = 12
z = 12/-3
z = -4
Putting value of z in eq(4)
2y+5z = -14
2y +5(-4) = -14
2y = -14 +20
2y = 6
y = 3
Putting value of z and y in eq(1)
-3x-2y+4z = -16
-3x-2(3)+4(-4) = -16
-3x -6 -16 = -16
-3x = -16+16+6
-3x = 6
x = 6/-3
x = -2
3 (x+2)= 6 (x-1) +3
Answer:
x = 3
Step-by-step explanation:
3(x + 2) = 6(x - 1) + 3
Divide both sides by 3.
x + 2 = 2(x - 1) + 1
Distribute the 2 on the right side.
x + 2 = 2x - 2 + 1
Combine like terms on the right side.
x + 2 = 2x - 1
Add 1 to both sides. Subtract x from both sides.
3 = x
x = 3
A rectangular gym has an area of 4x^2ft^2. The school decides to add a new
weight room. The total area of the gym and the weight room is (4x^2+480)ft^2.
What does the constant term represent in terms of this problem?
Answer:
The constant term is the area of weight room.
Step-by-step explanation:
A rectangular gym has an area of [tex]4x^2[/tex] square feet
The school decides to add a new weight room.
The total area of the gym and the weight room is [tex](4x^2+480)[/tex] ft^2.
Here, 480 is the area of the weight room because [tex]4x^2[/tex] is the area of gym and the total area will be addition of both the areas.
Hence, the constant term is the area of weight room.
The area of the weight room is 480 square ft and the constant term 480 represents the area of the weight room.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
The area of the rectangular gym = 4x² square ft
The total area of the gym and the weight room = (4x² + 480) square ft
Let A be the area of the weight room:
Total area = area of gym + area of weight room
4x² + 480 = 4x² + A
A = 480 square ft
Thus, the area of the weight room is 480 square ft and the constant term represents the area of the weight room.
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The triangles are similar. The area of the larger triangle is 1200 cm?
What is the area of the smaller triangle?
Answer:
75 cm^2
Step-by-step explanation:
We have the lengths of two corresponding sides. The scale factor from the large triangle to the small triangle is 16/64 = 1/4. Each side of the smaller triangle is 1/4 times the length of the corresponding side of the large triangle.
For the areas, the scale factor is the square of the scale factor of the lengths. Area scale factor = 1/4^2 = 1/16.
The area of the small triangle is 1/16 the area of the large triangle.
area of small triangle = (area of large triangle) * (area scale factor)
area of small triangle = 1200 cm^2 * 1/6 = 1200 cm^2/16
area of small triangle = (1200 cm^2)/16 = 75 cm^2
Answer:
I would say 75cm^2.
A consistent system of equations is a system with __________.
Hello There!
intersecting lines and lines that have the same equation.
Answer:
intersecting lines and lines
Step-by-step explanation:
Find the area of right triangle ABC.
Answer:
16
Explanation:
Area of Triangle = 1/2(B*H)
Height - 4
Base - 8
8 * 4 = 32
32 / 2 = 16
Can someone please explain to me how to use sin, cos, and tan for triangle calculations? Feel free to use whatever example. I just want to understand how use the trigonometric ratios. Thanks!
Answer:
Hi there!
A way to remember how to do each way is: Soh Cah Toa
Sin- opposite over hypotenuse Cos- Adjacent over hypotenuse Tan- opposite over adjacent.
Hypotenuse is the longest the side of the triangle
and the adjacent side is the side laying near the symbol theta.
Evaluate the following expression. you should do this without a calculator log4 256
Answer:
4
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
let [tex]log_{4}[/tex] 256 = n, then
256 = [tex]4^{n}[/tex]
Note that 256 = [tex]4^{4}[/tex], hence
[tex]4^{4}[/tex] = [tex]4^{n}[/tex]
Since the bases are equal ( both 4) equate the exponents, hence
n = 4
Find the sticker price and dealer's cost for the following car: The base price is $18,649.00. Options cost $453.00, $612.00, $386.00, and $290.00. Destination charges total $246.00. The dealer pays 85% of the base price and 70% of the options.
Final answer:
The dealer's cost for the car is $15,851.65 and the sticker price is $20,636.
Explanation:
To find the sticker price and dealer's cost for the car, we need to calculate the prices of the base price, options, and destination charges.
First, calculate the dealer's cost for the base price by multiplying 85% of the base price: $18,649 x 0.85 = $15,851.65.
Next, calculate the dealer's cost for the options by multiplying 70% of each option cost and summing them up: $453 x 0.70 + $612 x 0.70 + $386 x 0.70 + $290 x 0.70 = $845.20.
Finally, calculate the sticker price by adding the base price, options, and destination charges: $18,649 + $453 + $612 + $386 + $290 + $246 = $20,636.
Therefore, the dealer's cost is $15,851.65 and the sticker price is $20,636.
What is the vertex of the parabola in the graph?
Answer:
(-3, -4)
Step-by-step explanation:
The parabola shown here opens up. The vertex is the lowest point of this graph. The coordinates of the vertex are (-3, -4).
Answer:
(-3, -4)
Step-by-step explanation:
your welcome
a line has the equation y=1/4x-1. find the equation if a parallel line through (8,5)
Answer:
y = [tex]\frac{1}{4}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{4}[/tex] x - 1 ← is in this form
with slope m = [tex]\frac{1}{4}[/tex]
• Parallel lines have equal slopes, thus
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (8, 5) into the partial equation
5 = 2 + c ⇒ c = 5 - 2 = 3
y = [tex]\frac{1}{4}[/tex] x + 3 ← equation of parallel line
What is the following product? Assume x>0.
Oxx
o 12,5
o 6
Answer:
the answer would be the 3rd one :)
Step-by-step explanation:
solve for c:
c / 3 equals 30 / 5
show your work and apply the correct order of operation
Answer:
Unless there is more to the question than c = 2 because 30 /5 = 6 and if c is 3 than 3 = 6 so simplify if needed.
Answer:
c = 18
Step-by-step explanation:
Rewrite c / 3 equals 30 / 5 as:
c 30
----- = -----
3 5
Reduce 30/5 to 6/1:
c 6
----- = -----
3 1
Cross multiplying, we get 1c = 18, or c = 18.
9 cubic yard 113 cubic inches - 4 cubic feet 129 cubic inches
Answer: 8 yds³ 22ft³ 1712 in³
Step-by-step explanation:
9 yds³ + 113 in³ - (4 ft³ + 129 in³)
Understand that you need to "borrow" 1 yd³ and convert it into ft³ and then "borrow" 1 ft³ and convert it into in³
Conversions:
[tex]1 yd^3\times \bigg(\dfrac{3ft}{1yd}\bigg)^3=\large\boxed{27ft^3}\\\\\\1ft\times\bigg(\dfrac{12in}{1ft}\bigg)^3=\large\boxed{1728in^3}[/tex]
The given equation:
9 yds³ + 0 ft³ + 113 in³
- 4 ft³ - 129 in³
Borrow 1 yd³ to create 27 ft³:
= 8 yds³ + 27 ft³ + 113 in³
- 4 ft³ - 129 in³
Borrow 1 ft³ to create 1728 in³:
= 8 yds³ + 26 ft³ + 1841 in³
- 4 ft³ - 129 in³
= 8 yds³ + 22 ft³ + 1712 in³
Which of the following is missing in the explicit formula for the compound interest geometric sequence below?
Answer:
1+i
Step-by-step explanation:
The explicit formula for the compound interest geometric tell us: If P1 is invested at an interest rate of i per year, compounded annually, the future value Pn at the end of the nth year is:
[tex]Pn=P1(1+i)^{(n-1)}[/tex]
For example if you have $10 at 5% at an interest rate of 5% per year.
Then if you want to know the amount of money at the end of the 2, 3 and 4 year, you have:
n=1 year P1=10
n=2 year
[tex]P2=10(1+(5/100))[/tex]
[tex]P2=10(1+(5/100))^{(2-1)}[/tex]
[tex]P2=10(1+(5/100))^{(1)}[/tex]=10,5
n=3 year
[tex]P3=10(1+(5/100))*(1+(5/100))[/tex]
[tex]P3=10(1+(5/100))^{(3-1)}[/tex]
[tex]P3=10(1+(5/100))^{(2)}[/tex]=11.025
n=4 year
[tex]P4=10(1+(5/100))*(1+(5/100))*(1+(5/100)) [/tex]
[tex]P4=10(1+(5/100))^{(4-1)}[/tex]
[tex]P4=10(1+(5/100))^{(3)}[/tex]= 11.57625
What are axioms in algebra called in geometry
Answer:
Sometimes they are called algebraic postulates.
Step-by-step explanation:
Please mark brainliest and have a great day!
25/38 as a percentage round answer to the nearest tenth of a percent
To convert 25/38 to a percentage, divide 25 by 38, multiply by 100, and round to the nearest tenth, resulting in 65.8%.
Explanation:To convert 25/38 to a percentage, you divide 25 by 38 and then multiply the result by 100.
The calculation would look like this:
Divide 25 by 38: 25 ÷ 38 = 0.6578947368
Multiply the result by 100 to get the percentage: 0.6578947368 × 100 = 65.78947368%
Round the result to the nearest tenth of a percent: 65.8%
Therefore, 25/38 as a percentage rounded to the nearest tenth of a percent is 65.8%.
Final answer:
To express 25/38 as a percentage, divide 25 by 38 and then multiply the result by 100. The answer is approximately 65.8%.
Explanation:
To express 25/38 as a percentage, you can divide 25 by 38 and then multiply the result by 100.
25 ÷ 38 ≈ 0.6578947368421053
0.6578947368421053 × 100 ≈ 65.8
Therefore, 25/38 as a percentage, rounded to the nearest tenth of a percent, is approximately 65.8%.
Which expression is equivalent to (4 +6i)^2??
-20 + 48i
8 + 12i
16 - 36i
20 + 48i
Answer:
-20 + 48i
Step-by-step explanation:
(4 +6i)^2 (Perfect square)
= (4)^2 + 2(4)(6i) + (6i)^2
= 16 + 48i + 36i^2
= 16 + 48i - 36 (i^2 = -1)
= -20 + 48i
Answer:
[tex]-20+48 \text{i}[/tex]
Step-by-step explanation:
Note that
[tex](4+6i)^2=4^2+2\cdot(4\cdot6i)+(6\cdot i)^2=16+48i+36i^2=16+48i-36\\\\=(36-13)+48i=-20+48i[/tex]
and we are done.
A car is purchased for a downpayment of $3,000 with an additional monthly payment of $400 for 36 months. The
formula for the amount spent on the car is S = 3000 + 400 M, where S is the current amount of money that has been
spent and M is the number of months of payments that have been made.
i) How much money will have been spent after a year?
ii) What will be the final cost of the car?
Answer:
$3400 after one year
$17400 after the 36 months
Step-by-step explanation:
3000+400*1=3400
3000+400*36=17400
After a year, $7,800 will have been spent on the car. The final cost of the car will be $16,800.
Explanation:i) To find out how much money will have been spent after a year, we need to substitute the value of M with 12 (since there are 12 months in a year) in the formula S = 3000 + 400M. Therefore, S = 3000 + 400 × 12 = $7,800.
ii) The final cost of the car can be found by substituting the value of M with 36 (since there are 36 months of payments) in the same formula. Therefore, S = 3000 + 400 ×36 = $16,800.
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A circumscribed circle will touch every vertex of a regular polygon ,true or false
Answer:
True
Step-by-step explanation:
we know that
A circle can be circumscribed about any regular polygon
A circumscribed circle surrounds a regular polygon, touching every vertex
Solve for x.
5/6 x = 10/3
x = 4/3
x = 2
x = 25/9
x = 4
For this case we must solve the following equation:
[tex]\frac {5} {6} x = \frac {10} {3}[/tex]
Multiplying by "6" on both sides of the equation we have:
[tex]5x = \frac {10 * 6} {3}\\5x = \frac {60} {3}\\5x = 20[/tex]
Dividing between 5 on both sides of the equation we have:
[tex]x = \frac {20} {5}\\x = 4[/tex]
So, the solution is [tex]x = 4[/tex]
Answer:
Option D
Answer: LAST OPTION.
Step-by-step explanation:
In order to solve for the variable "x" from the expression [tex]\frac{5}{6}x=\frac{10}{3}[/tex], you need to follow these steps:
1) You need to multiply both sides of the equation by 3:
[tex]3(\frac{5}{6}x)=(\frac{10}{3})(3)\\\\\frac{15}{6}x=10[/tex]
2) You need to multiply both sides of the equation by 6:
[tex](6)(\frac{15}{6}x)=(10)(6)\\\\15x=60[/tex]
3) Finally, you can divide both sides of the equation by 15:
[tex]\frac{15x}{15}=\frac{60}{15}\\\\x=4[/tex]
PLEASE HELP, IT WOULD BE AWESOME IF YOU COULD!!!!!!!
Joseph is conducting a survey to determine the blood types of 100 people who have come to give blood at a blood donor clinic. Which of the following questions is an appropriate statistical question for this survey? How many people at the clinic have blood type AB? Which blood type does the least number of people have? What is the blood type of each person at the clinic? What is the average age of people with the most common blood type?
Answer: What is the blood type of each person at the clinic?
Scarlett stopped at a campground along the Appalachian trail. The campground had a 12 acre area for tents, divided into 6 equal campsites. Scarlett picked one of the sections to pitch her tent.
Which expression would give you the size of Scarlett’s campsite?(more than one answer
Answer:
A and D on edge
just took the assessment
Answer:
a and d
Step-by-step explanation:
What is the name of a polygon that has four congruent sides and theses angle measures 60,120,60,120?
Answer:
The correct answer for this is: rhombus.
Step-by-step explanation:
The name of a polygon that has four congruent sides with the angles measuring 60°, 120°, 60° and 120° is rhombus.
According to the properties of a rhombus, the opposite angles are equal and opposite sides are parallel.
However, the adjacent angles of rhombus are supplementary which means that they add up to 180°.
For example:
60° + 120° = 180°
Answer:
Rhombus
Step-by-step explanation:
A rhombus has 4 congruent sides and the opposite angle s are congruent. I will throw in something extra a rhombus has perpendicular bisectors
The expression 5^-8 * 7^-9 is equal to which of the following?
A. 1/5(35)^8
B. 1/7(35)^8
Answer:
Your answer is wrong.... M
Final answer:
The expression[tex]5^-8 * 7^-9[/tex]simplifies to 1 / [tex]5^8 * 1 / 7^9[/tex], which can be rearranged to 1 / [tex](35^8 * 7),[/tex] hence the correct answer is option B:[tex]1 / (7 * 35^8).[/tex]
Explanation:
The expression [tex]5^-8 * 7^-9[/tex] simplifies to:
([tex]1/5^8) * (1/7^9)[/tex]
[tex]1 / (5^8 * 7^9)[/tex]
We notice that [tex]5^8 * 7^9[/tex] can be rearranged to [tex](5*7)^8 * 7[/tex]
[tex]1 / (35^8 * 7)[/tex]
Finally, we get [tex]1 / (7 * 35^8)[/tex]which is option B.
What is the domain of the function f(x)=3x/x-1?
Answer:
Domain f(x) = R - {1}
As it is a rational expression, the denominator cannot be zero.
Now the function holds all real values except 1 for which the denominator will become zero which is undefined.
Therefore the domain will be all real numbers except 1.
f(x)=-3x-4 if f(2) what are the order pairs
Answer:
[2, -10]
Step-by-step explanation:
Simply plug in 2⃣ for every "x" you see, evaluate, then you will arrive at your answer.
After the expression (x^8)^3/4 is simplified as much as possible, x is raised to what exponent? a0
Answer:
6 since 8(3/4)=6
Step-by-step explanation:
(x^8)^(3/4)
=x^(8*3/4) by one of the law of exponents
=x^(8/4 *3)
=x^(2 *3)
=x^6
The mass of a piece of aluminum is 250 grams. The density of aluminum is 2.7 g/mL. What is the volume of the piece of aluminum?
The volume of a given piece of aluminum is 92.6 mL.
What is Density?It is defined as the ratio of mass to volume.It is an extensive property of any substance.
Given: A piece of Aluminum.
Mass = 250 g
Density = 2.7 g/mL
We need to find the volume.
We know, density is given by:
⇒ Density = Mass / Volume
⇒ Volume = Mass / Density
⇒ Volume = 250/2.7
⇒ Volume = 92.6 mL
Therefore, the volume of the piece of aluminum is 92.6 mL.
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What is the mode for the set of data shown below?
34, 75, 26, 81, 65, 38, 49, 73, 58, 12, 31, 25, 75, 86, 47, 99
Answer:
75
Step-by-step explanation:
Mode means the number that occurs the most. There can be more than 1 mode also no mode at all.
Looking at the number set closely, we see that "75" occurs twice and every number occurs once. Hence 75 is the mode.
Hello There!
The "MODE" is the numbers that occur most often in a set of numbers.
In this scenario, 75 would be the mode because it occurs twice, No other numbers in this data set repeat except 75.