Answer:
Step-by-step explanation:
a = 8
b = 10
a^3 =8^3 = 512
b^3= 10^3 =1000
a^3 + b^3 = 1512
a^2 = 64
-ab = - 80
b^2 = 100
a + b=18
(a + b) (64 - 80+ 100)
18 * (84)
1512'
Which lines are parallel to the graph of 4x - y = 6?
Answer:
Step-by-step explanation:
i cant see answers help my insta is 813.caden
Answer:
y+1=4(x-2)
y=4x+11
8x-2y+6
Step-by-step explanation:
By which smallast number must the following number be divided so that the quotient is a perfect cube
(A) 8640
Answer:
60
Step-by-step explanation:
8640/60 is 144. 144 is a perfect square. 12*12 is 144
Hey there! I'm happy to help!
------------------------------------------------------------------
INTRO TO PERFECT CUBES
A perfect cube is any number whose cube root is an integer. In English, that means that if you take any number without a fraction (this is called an integer, such as -7, 8, 100, none have fractions) and multiply it by itself three times, you get a perfect cube.
If you cube the number 4, you get 64, which is (4×4×4). 64 is an example of a perfect cube.
You can use the cube root button on your calculator to see if a number is a perfect cube. If you do the cube root of 64, you get 4, telling you that 64 is a perfect cube. The cube root of 10 is 2.154434...... so 10 is not a perfect square because it does not give you an integer (number that does not have a fraction) as the answer.
------------------------------------------------------------------
SOLVING THE PROBLEM
So, we want to find the smallest numbers we can divide 8640 to equal a perfect cube.
I will assume that we will not be dividing by fractions but only whole numbers (positive integers).
We could try dividing by 1, but we see that 8640 is not a perfect cube because it's cube root is 20.519711....
Let's just keep counting up! The first divisor we run into that gives a quotient that it is a perfect cube is the smallest whole number possible that will give us that result.
8640÷2=4320
∛4320≈16.2865....... Not a perfect cube
8640÷3=2880
∛2880≈14.22757..... Not a perfect cube
8640÷4=2160
∛2160≈12.92660..... Not a perfect cube
8640÷5=1728
∛1728=12, a perfect cube!
Since 12 cubed is equal to 1728, this means that 1728 is a perfect square, so 5 is the smallest number we can divide 8640 by to get a perfect square.
The answer is 5.
I hope that this helps! Have a wonderful day! :D
Last season, a softball team played 18 games. The team won 15 of these games. What is the ratio of the softball team's wins to its total number of games played ?
Answer:
5:6Step-by-step explanation:
Given the total number of games played by the softball team = 18 games
Total games won = 15 games
Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played
Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]
[tex]Ratio = \frac{15}{18}[/tex]
Expressing the ratio in its lowest term
[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]
Hence, the ratio of the softball team's wins to its total number of games played is 5:6
Please answer it now in two minutes
Answer: √3
Step-by-step explanation:
Hi, since the situation forms a right triangle we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle (30°), the hypotenuse is the longest side of the triangle (in this case 2), and the opposite side is x. (not t or 2)
Replacing with the values given:
Sin 30 = x /2
Sin 30 (2) = x
x=1
Applying the Pythagorean theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (2) and a and b are the other sides.
2^2 = t^2 + 1^2
4= t^2 +1
4-1 = t^2
3 = t^2
√3 = t
Feel free to ask for more if needed or if you did not understand something.
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a nut chocolate followed by a caramel chocolate.
Answer:
16/117Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given the total amount of chocolate in a box = 39chocolates
Amount of nuts = 16
Mount of caramel = 13
Amount of solid chocolate = 10
If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39
IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3
The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117
A piece of land ABCD is in the shape of a trapezium
as shown in the diagram. AB = 40 m, BC = 39 m,
AD = 30 m, and <ABC = <BAD = 90°. Find
(a) the length of the side CD,
(b) angle BCD,
(c) the area of the land.
Answer:
a) CD = 41 m
b) 77.32°
c) 1380 square metres
Step-by-step explanation:
We can divide the trapezium as shown in the diagram below.
a) To find CD, we use Pythagoras Rule:
[tex]CD^2 = 9^2 + 40^2[/tex]
[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]
b) To find <BCD, we use trigonometric function SOHCAHTOA:
sin(BCD) = opp / hyp
sin(BCD) = 40 / 41
sin(BCD) = 0.9756
=> <BCD = 77.32°
c) The area of a trapezium is given as:
A = 1/2 (a + b) * h
where h = height = 40 m
a = top length = 30 m
b = bottom length = 39 m
A = 1/2 * (30 + 39) * 40
A = 1/2 * 69 * 40
A = 1380 square metres
For a chemical reaction to occur, at least one-third of the solution must be an acid. If there are five liters of acid, in interval form, how much solution is present?
A. [5,8)
B. (3/5,5]
C. (5/3,5]
D. [5,15]
Answer:
Amount of solution = 15 liter
Step-by-step explanation:
Given:
One third of solution is acid
Amount of acid = 5 Liter
Find:
Amount of solution
Computation:
Amount of solution = Amount of acid (1 / One third of solution is acid)
Amount of solution = Amount of acid (3)
Amount of solution = (5)(3)
Amount of solution = 15 liter
Of his take-home pay each month, Jerry spends 1/6 on car payment and 1/4 on food. What fraction of his take-home pay is left after paying for these two items?
Answer:
The fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
Step-by-step explanation:
Consider that the total take-home pay each month Jerry receives is, $x.
It is provided that:
Jerry spends 1/6 on car payment, i.e. Car Payment = [tex]\frac{1}{6}x[/tex].Jerry spends 1/4 on food, i.e. Food = [tex]\frac{1}{4}x[/tex].The remaining amount can be computed by subtracting the amount spent from the total amount.
Compute the amount Jerry has spent so far:
Amount Spent = Car Payment + Food
[tex]=\frac{1}{6}x+\frac{1}{4}x\\\\=[\frac{1}{6}+\frac{1}{4}]x\\\\=[\frac{2+3}{12}]x\\\\=\frac{5}{12}x[/tex]
Compute the remaining amount as follows:
Remaining Amount = Total Amount - Amount Spent
[tex]=x-\frac{5}{12}x\\\\=[1-\frac{5}{12}]x\\\\=[\frac{12-5}{12}]x\\\\=\frac{7}{12}x[/tex]
Thus, the fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
Which situation can be represented by 80x > 150 + 50x?
Answer:
All numbers greater than 5, i.e., [tex]x>5[/tex] .
Step-by-step explanation:
The given inequality is
[tex]80x>150+50x[/tex]
Isolate variable terms on one side to find the solution.
Subtract 50x from both sides.
[tex]80x-50x>150+50x-50x[/tex]
[tex]30x>150[/tex]
Divide both sides by 30.
[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]
[tex]x>5[/tex]
It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.
What number :Increased by 130% is 69 i rlly need help!!!
Answer:
53.076923
Step-by-step explanation:
130% as a decimal is 1.3
Divide 69 by 1.3:
69 /1.3 = 53.076923
Answer:
30
Step-by-step explanation:
The unknown number is x.
Start with x.
To increase x by 130%, you need to add 130%of x to x.
x + 130% of x
The sum equals 69.
x + 130% of x = 69
x + 130% * x = 69
1x + 1.3x = 69
2.3x = 69
x = 30
Answer: The number is 30.
Determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result. A. linear B. quadratic C. none of these D. exponential
Answer:
The best fit is A. Linear model
Step-by-step explanation:
Given:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
To find:
The type of model that best fits the given situation?
Solution:
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
[tex]y =mx+c[/tex]
Slope of a function:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500[/tex]
So, the equation is:
[tex]y =-500x+c[/tex]
Putting x = 20, y = 5000:
[tex]5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000[/tex]
[tex]\Rightarrow \bold{y =-500x+15000}[/tex]
Let us check whether (18, 6000) satisfies it.
Putting x = 18:
[tex]-500 \times 18 +15000 = -9000+15000 = 6000[/tex] so, it is true.
So, the answer is:
The best fit is A. Linear model
Pls help me I need it pls!! I only need the last question which is "Find the weight of one circle. Show or explain how you got your answer. "
Convert 2.41 cm2 into mm2 *the 2 means squared
Answer:
241 mm^2.
Step-by-step explanation:
There are 10 mm in a cm so there are 10*10 = 100 mm^2 in a cm^2.
So the answer is 2.41 * 100 = 241 mm^2.
Answer:
241mm²
Step-by-step explanation:
If 10mm = 1cm,
then 100mm² = 1cm²
2.41 × 100 = 241mm²
What is 50 + 30(0) - 30?
Answer:
20
Step-by-step explanation:
30(0)
= 0
50 + 0 - 30
= 50 - 30
= 20
Answer:
20
Step-by-step explanation:
We know that 30 × 0 = 0. Next, we can take 50 and add 0 which is still 50. Now, we take 50 - 30 which equals to 20.
A triangle has a base 12 inches and the height of 5 inches if 6 of these triangles are put together to form a hexagon what would be the area of the hexagon?
Which statement is correct about the system of linear equations graphed below? A.The system of equations has one solution because the lines will eventually intersect. B.The system of equations has one solution because the lines will never intersect. C.The system of equations does not have one solution because the lines will eventually intersect. D.The system of equations does not have one solution because the lines will never intersect.
Answer: A
Step-by-step explanation:
They have one solution because as you look at the lines they have different slopes and different y intercepts which means it has one solution.It is not parallel to each other to have no solutions. They seems to be going to one direction and eventually they will intersect.
A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below. s(t)equals2 sine t plus 3 cosine t Find a value of t between 0 and StartFraction pi Over 2 EndFraction that satisfies the equation s(t)equalsStartFraction 2 plus 3 StartRoot 3 EndRoot Over 2 EndFraction .
Answer:
The value of t that will satisfy the equation is π/6 (which is 30 degrees)
Step-by-step explanation:
The function that models the movement of the particle is given as;
S(t) = 2 sin(t) + 3 cos (t)
Now we want to the value of t between 0 and pi/2 that satisfies the equation;
s(t) = (2+ 3√3)/2 = 1 + 3√3/2
What we do here is simply find that value of t that would ensure that;
2sin(t) + 3cos(t) = 1 + 3√3/2
Without any need for rigorous calculations, this value of t can be gotten by inspection.
From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2
We can make a substitution for it in this equation.
We obtain the following;
2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2
Do not forget however that we have a range. And the range in question is between 0 and π/2
Kindly that π/2 in degrees is 90 degrees
So our range of values here is between 0 and 90 degrees.
So to follow the notation in the question, the value within the range that will satisfy the equation is π/6
A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $6,000 or $12,000. If the partnership raised $486,000, then how many investors contributed $6,000 and how many contributed $12,000?
Answer:
39 investors contributed $6,000, and 21 investors contributed $12,000.
Step-by-step explanation:
Let's say that x investors contributed $6,000, and y investors contributed $12,000.
x + y = 60
6,000x + 12,000y = 486,000
x + 2y = 81
x + y = 60
y = 21
x + 21 = 60
x = 39
So, 39 investors contributed $6,000, and 21 investors contributed $12,000.
Hope this helps!
Most evenings after dinner Duarte spends 30 minutes playing chess with his dad. Write an equation for the number of minutes, m, that Duarte spent playing chess with his dad if they played chess together (e) evenings.
Answer:
m=30e
Step-by-step explanation:
30 minutes for each evening, 2 evenings, 60 minutes
Hope this helped!
The most suitable equation that would express the time Duarte spends to play chess with his dad is m= 30e
How to use equation for expressionsNumber of minutes each evening= 30 mins=m
They played together every evening= e.
Therefore, the equation that would express the time Duarte spends to play chess with his dad is m = 30e.
Learn more about equation here:
https://brainly.com/question/2972832
#SPJ2
Jakki got a new job that guarantees her a 6% raise every year. If she started out making $40,000, how long will it be before she doubles her current salary?
Answer:
2400months
Step-by-step explanation:
6/100*40,000
maybe
The slope of the line is -5/7. Write a point-slope equation of the line using the coordinates of the labeled point
Answer:
The answer is C.
Step-by-step explanation:
The formula to find equation is y - y1 = m(x - x1).
Let (x1,y1) be (6,2) and m is -5/7.
So the equation is,
y - 2 = -5/7(x - 6)
i will mark brainliest i need help quick
Answer:
x-1
Step-by-step explanation:
| x-1| x> 1
Since x is greater than x, the absolute value will be positive so we can remove it
x-1
Lets use a number to check
Let x = 4
| 4-1| 4>1
3 which is positive
Answer:
x - 1
Step-by-step explanation:
| x - 1 |
x > 1
x is greater than 1. The absolute value is not needed, since the value inside will only be for positive integers.
x - 1
We can check by plugging x as 2.
2 - 1 = 1 (positive)
2 > 1
On a separate piece of graph paper, graph y = |x - 3|; then click on the graph until the correct one appears.
ps : there's another picture it just didn't let me edit it its the opposite side of the shape facing up the graph.
Answer: Graph is shown in the attached image below
This is a V shaped graph with the vertex at (3,0). The V opens upward
Explanation:
The equation y = |x-3| is the result of shifting the parent function y = |x| three units to the right. The vertex moves from (0,0) to (3,0). The "x-3" portion moves the xy axis three units to the left. If we held the V shape in place while the xy axis moved like this, then it gives the illusion the V shape moved 3 spots to the right.
Side note: the equation y = |x-3| is composed of two linear functions y = x-3 and y = -x+3. The value of x will determine which gets graphed. When x < 3, then we'll graph y = -x+3; otherwise we graph y = x-3. This is known as a piecewise function.
41. In the diagram, a l b. Find the value of x. 55° (x+ 70)
Answer:
55°
Step-by-step explanation:
The corresponding image, which I will attach, is missing in order to solve the exercise.
We know that the flat angle is 180 °, which we know to be the one that is formed with the horizontal, therefore the following equation remains:
55 ° + (70 ° + x °) = 180 °
we solve x °
x ° = 180 ° - 55 ° - 70 °
x ° = 55 °
So the value of x is 55 °
Marci has taken out a loan of $5,000 for a term of 24 months (2 years) at an interest rate of 8.5%. Use the amortization table provided to
complete the statement.
Monthly Payment per $1,000 of Principal
Rate | 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $59.35 $23.71 $19.57
7.0% $86.53 $44.77 $31.88 $23.95 $19.80
7.5% $86.76 $45.00 $51.71 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
Marci's monthly payment will be $
and her total finance charge over the course of the loan will be $
Answer:
$227.30$455.20Step-by-step explanation:
The table tells you that Marci's monthly payment on a 2-year loan at 8.5% will be $45.46 on each $1000 borrowed. For her $5000 loan, her monthly payment will be 5 times the table value, or ...
monthly payment = $5000/$1000 × $45.46
monthly payment = $227.30
__
Her total of 24 payments will be ...
total repaid = 24 × $227.30 = $5,445.20
That amount is $445.20 more than the amount borrowed, so that is Marci's finance charge.
__
Marci's monthly payment will be $227.30, and her total finance charge will be $455.20.
A bus traveled 40 miles during the second hour of a trip. This was 1/3 more than the distance traveled during the first hour. In the third hour the bus traveled a distance that was 1/4 more than in the second hour. What was the total distance that the bus traveled in 3 hours
Answer:
120 miles
Step-by-step explanation:
Distance in 2nd hour: 40 miles
Distance in 1st hour:
40/(4/3) = 30 miles
Distance in 3rd hour:
(5/4) * 40 = 50 miles
Total distance:
40 + 30 + 50 = 120 miles
A 6 inch-y’all plant grew 3/4 of an inch one week and twice as much the following week. How tall is the plant now?
Answer:
8 inches
Step-by-step explanation:
3/4+(3/4*2)=3/4+6/4=9/4=2 1/4
2 1/4+6=8 1/4=8.25
Answer: 8.25 inches
Step-by-step explanation:
if amir joins indian army, he is courageous.
convert this into contrapositive statement
If Amir is not courageous, then he will not join the indian army.
There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After that, Susan took half of the remaining pieces of candy. In the end there were 8 pieces of candy left in the bowl. How many candies were there in the bowl at the beginning?
Answer:
Number of pieces of candy in the bowl=64
Step-by-step explanation:
Let
x=number of pieces of candy in a bowl
Shirley took=1/2 of x
=1/2x
Remaining
x-1/2x
= 2x-x/2
=1/2x
Rose took half of the pieces left in the bowl=1/2 of 1/2x
=1/2*1/2x
=1/4x
Remaining
1/2x-1/4x
=2x-x/4
=1/4x
Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x
=1/2*1/4x
=1/8x
Remaining 8
1/8x=8
x=8÷1/8
=8*8/1
=64
x=64
1
If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term
If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].
We're given
[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]
So the first five terms in the GP are
3, 6, 12, 24, 48
Adding up the first four gives a sum of 45.
If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:
[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]
Multiply both sides by 2:
[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]
Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:
[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]
Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].