Answer:
a^3-1-a^2+a
(a-1) (a^2+a+1)-a(a-1)
(a-1) (a^2+a+1-a)
(a-1) (a^2+1)
2nd exp
2a^3-2-a^2+a
2(a^3-1)(a^2+1)
2(a-1)(a^2+a+1)-a(a-1)
2(a-1)(a^2+a+1-a)
2(a-1)(a^2+1)
Please help me with this question (Will get brainlist)
Answer:
169=169
Step-by-step explanation:
The pythagoras theorem states that if
[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]
Then the triangle is a right triangle
So
[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]
[tex]25 + 144 = 169[/tex]
[tex]169 = 169[/tex]
Therefore A is a right triangle
Answer:
Step-by-step explanation:
The pythagorian theorem :now the longest edge is 13 cm so : 13²must be equal to 5²+12²
5²+12²= 169[tex]\sqrt{169}[/tex]= 13so this triangle must be right angled
Robert want to buy a sports cap that is on sale for 25% off if the original price is 35$ and the sales tax is 6% how much will robert need to pay for the cap
Answer: $27.825
Step-by-step explanation:
From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:
= Original price - Discount
= $35 - (25% × $35)
= $35 - (0.25 × $35)
= $35 - $8.75
= $26.25
We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:
= $26.25 + (6% × $26.25)
= $26.25 + (0.06 × $26.25)
= $26.25 + $1.575
= $27.825
Answer:
27.83
Step-by-step explanation:
In a school, half of the 300 students saw Zootopia, 180 students saw Finding Dory, and 45 students did not see either movie. How many students saw both movies?
Answer:
165 students (hope it helps)
Step-by-step explanation:
300students - 45students = 255students
180students + 150students = 330students
330students / 2 = 165
Answer:
75 students watched both.
Step-by-step explanation:
150 students saw Zootopia
180 students saw Finding Dory
45 students saw nothing.
There are 300 students in total.
[tex]|(300-45)-150-180|=\\|255-150-180|=\\|105-180|=\\|-75|=\\75[/tex]
a bead shop sells their beads by the pound. A new shipment of beads weighing 2 pound is divided into 8 equal - sized bags. how many ounces of beads are in each bag?
Answer:
4 ounces per bag
Step-by-step explanation:
1. Divide 2 pounds into 8 bags (0.25)
2. To convert from pounds to ounces, multiply by 16 (4)
The ratio of students wearing sneakers to those wearing boots is 4 to 5. If there are 36 students in the class, and all of them are wearing either sneakers or boots, how many of them are wearing sneakers?
Answer:
16
Step-by-step explanation:
Let's denote:
a: number of students wearing sneakers
b: number of students wearing boots
We have:
a + b = 36
a/b = 4/5 (multiply both sides by b => a = 4b/5)
Substitute a = 4b/5 into a + b = 36
=> 4b/5 + b = 36
=> 4b/5 + 5b/5 = 36
=> 9b/5 = 36
=> b/5 = 4
=> b = 20
=> a = 4b/5 = 4(20)/5 = 16
Bottle A contains more soda than Bottle B. Pour from Bottle A into Bottle B as much soda as B already contains. Now pour from B into A as much soda as A now contains. Then pour from A into B as much soda as B now contains. Each bottle now contains 64 ounces. How many more ounces of soda were in Bottle A than Bottle B at the beginning?
Answer:
Bottle A started with 88 and bottle B started with 40
Step-by-step explanation:
To find out what they started with I got the ounces they finished with an the equation they did to get there.
Ended in 64 oz.
To get there:
A => B
B => A
A => B
Every time a pour is made the bottle to the right is doubled so I got 64 and divided it by 2 to see what B had before the pour of bottle A.
B had 32 oz. and A had 96 oz. before the last pour. I got 96 oz. because for them to end up with 64 oz. A has to have 32 oz. + 64 oz. since you are pouring 32 oz. into bottle B.
Now you have this equation:
A => B
B => A
96 oz. => 32 oz.
64 oz.
I then do the same thing I did to find 96 and 32. Since B is giving to A now it has to have more then A but it has to end up with 34 oz. for this is got 96 oz. and I divided it by 2 which got me 48. So on the second pour A started with 48 and B had to have given A 48 plus have 32 so it could end up with 34 therefore making it have 80 oz.
Now you have this equation:
A => B
80 oz. => 48 oz.
96 oz. => 32 oz.
64 oz.
For the last part to get the first ounces to answer the question you will do the same steps. Get half of 80 to see what B had before the 2nd pour which will be 40 and then you have to get 48 + 40 sine bottle A has to have the same amount of soda as B plus 48 oz. that it ends up with. This will have bottle A as 88 oz.
The Answer:
88 oz. => 40 oz.
80 oz. => 48 oz.
96 oz. => 32 oz.
Both will end up with 64 oz.
The prime factorization of 324 can be written as 2^a x 3^b, where a = and b=
Answer: 2, 4 then c=4 also and B for the next one :)
Step-by-step explanation: Giving away 100 points be the first to comment on my " question " stay tuned!
5. A yacht is cruising at 20 knots at bearing of 185° when a 15 knot wind starts to blow at a bearing of 290°. Find the direction and speed of the boat.
Answer:
Direction of the boat is 43.05° and the speed is 21.66 knot
Step-by-step explanation:
yacht speed = 20 knots
yacht bearing = 185° = 85° below the negative horizontal x-axis
wind speed = 15 knots
wind bearing = 290° = 20° above the negative horizontal x-axis
we find the x and y components of the boat velocities
for yacht,
x component = -20 cos 85° = -1.74 knots
y component = -20 sin 85° = -19.92 knots
for the wind,
x component = -15 cos 20° = -14.09 knots
y component = 15 sin 20° = 5.13 knots
total x component Vx = -1.74 + (-14.09) = -15.83 knots
total y component Vy = -19.92 + 5.13 = -14.79 knots
Resultant speed of the boat = [tex]\sqrt{Vx^{2} + Vy^{2} }[/tex]
==> [tex]\sqrt{15.83^{2} + 14.79^{2} }[/tex] = 21.66 knot
direction of boat = [tex]tan^{-1} \frac{Vy}{Vx}[/tex]
==> [tex]tan^{-1} \frac{14.79}{15.83}[/tex] = 43.05°
SIMPLIFY AND PUT IN ORDER FOR BRAINLIEST y= 46x -87x^3 +23x^2 -31x^6 +12 -23x^2
Answer:
y = -31x^6 - 87^3 +46x +12
Step-by-step explanation:
Place the numbers with the highest degree first (-31 x ^ 6) and go in order until you reach the number with the lowest degree (12). When you do that, you get:
y = - 31x^6 - 87x^3 + 23x^2 - 23x^2 + 46x +12
As you can see, the numbers based on the amount of their exponent were placed in order, no matter what the coefficient is. But, there are two numbers with ^2, so we have to cancel them out. In order to do that, you have to add/ subtract the two numbers with the same exponent.
23x^2 - 23x^2 = 0
Since the answer is 0, we canceled both of the numbers out, so the final polynomial in its standard form is:
y = -31x^6 - 87^3 +46x +12
Hope this helps :)
Answer:
y = -31x^6-87^3+46x+12
Step-by-step explanation:
put the exponents in order and cancel out the 23x^2s.
A car rental agency rents 210 cars per day at a rate of 27 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income?
Answer:
x=7.5
Step-by-step explanation:
Rental: R(x)=(27+x) dollar per day
Number of cars rented: N(x)
=(210-5x)
Income: I(x) =(27+x)(210-5x)
=5670 - 135x + 210x-5x^2
=5670+75x-5x^2
The maximum will be achieved when the derivative of
I(x) =zero.
I(x)=5670+75x-5x^2
dI(x)/dx=75-10x=0
75-10x=0
75=10x
x=75/10
=7.5
x=7.5
x=7.5 is the rate at which the car will be rented to produce maximum income.
The maximum income could be derived by using x=7 or x=8
27+7=$34 per day
27+8=$35 per day
When x=7
I(x)=5670+75x-5x^2
=5670+75(7)-5(7)^2
=5670+525-5(49)
=5670+525-245
=5,950
When x=8
I(x)=5670+75x-5x^2
=5670+75(8)-5(8)^2
=5670+600-5(64)
=5670+600-320
=5950
Either x=7 or 8 will yield the same income
Graph the system of equations on the coordinate plane and determine the solution to
the system
y=-1/2x+5
y=2x-10
Answer:
(6,2)
Step-by-step explanation:
y=-1/2x+5
y=2x-10
-1/2 x+5 =2x-10 to find the solution y=y ( point of intersection of two lines)
-1/2 x-2x = -10-5 solve for x
-5/2 x=-15
x=-30/-5=6
y=2x- 10 substitute x in the equation to get y
y=2(6)-10
y=2
(2,3)
Dont put the other answer, it’s wrong I
did the math.
What degree of rotation about the origin will cause the triangle below to map onto itself?
Answer:
it should rotate 360°about the origin
Here are two squares, A and B.
A
B
The length of the side of square A is 50% of the length of the side of square B.
Express the area of the shaded region of square A
as a percentage of the area of square B.
otal marks: 3
Submit Answer
The two squares and the shaded region of square A is in the attachment.
Answer: The shaded region of A is 12.5% of the area of B.
Step-by-step explanation: Assume that the length of side of square A is a and the length of side of square B is b.
Length a is half (50%) of length b:
a = [tex]\frac{b}{2}[/tex]
The shaded region is a triangle. The area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
b and h are the sides of the square A, so:
[tex]A_{1}[/tex] = [tex]\frac{\frac{b}{2}.\frac{b}{2}}{2}[/tex]
[tex]A_{1} = \frac{b}{2}.\frac{b}{2}.\frac{1}{2}[/tex]
[tex]A_{1} = \frac{b^{2}}{8}[/tex]
Area of square B is:
[tex]A_{2}[/tex] = b.b
[tex]A_{2} = b^{2}[/tex]
Comparing areas:
[tex]\frac{\frac{b^{2}}{8} }{b^{2}}[/tex] = [tex]\frac{b^{2}}{8}.\frac{1}{b^{2}}[/tex] = [tex]\frac{1}{8}[/tex]
As percentage:
[tex]\frac{1}{8}[/tex] × 100 = 0.125 × 100 = 12.5%
Comparing the shaded region of A to square B, the area of the first is 12.5% smaller than the second.
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
Solve for x. 7x=28 4x=48
Answer: x=4
x=12
Step-by-step explanation:
7x=28
divide 7 on both sides
28/7=4
x=4
4x=48
divide 4 on both sides
48/4=12
x=12
Jayne drove 20 mph to her grandparents’ house. How fast must she drive on the return trip to average 30 mph for the round trip?
Answer:
Speed of return trip (v) = 60 mph
Step-by-step explanation:
Given:
Distance = x
Speed (u) = 20 mph
Average speed = 30 mph
Find:
Speed of return trip (v)
Computation:
Time taken = Distance / Speed
Time of starting trip = x / 20
Time of starting trip = x / Speed of return trip (v)
Average speed = Total distance / Total time taken
30 = 2(x)/ [x/20 +x / Speed of return trip (v)]
30 = 40 v / (v + 20)
v = 60 mph
Speed of return trip (v) = 60 mph
Find all pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 56$. For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).
Answer:
(3.26795, 6.73205)
(6.73205, 3.26795)
Step-by-step explanation:
Easiest and fastest way to get your solutions is to graph the systems of equations and analyze the graph for where they intersect.
Factor 2x4 - 20x2 - 78.
Answer:
2x⁴ - 20x² - 78
To factor the expression look for the LCM of the numbers
LCM of the numbers is 2
Factorize that one out
That's
2( x⁴ - 10x² - 39)
Hope this helps
Answer:
2(x² + 3)(x² - 13)
Step-by-step explanation:
2x⁴ - 20x² - 78
Factor out 2.
2(x⁴ - 10x² - 39)
Find 2 numbers that multiply to get -39 and add to get -10. Those numbers are -13 and 3.
2(x⁴ - 13x² + 3x² - 39)
2(x² + 3)(x² - 13)
Tom walks 2.82 km to the park. He then walks a further 550 m to the shop. How many km has Tom walked in total?
Answer:
Total Walked = 3.37 km
Step-by-step explanation:
Walks = 2.82 km
Further Walked = 550 m = 0.55 km
Total Walked = 2.82+0.55
Total Walked = 3.37 km
in total he walks 3.37 km
He walks 2.82 km
He further walks 0.55 km
total = 2.82+0.55 = 3.37
how to solve: f(-1)=(1/4)^x
Answer:
f(-1) = (1/4)^x = 4
Step-by-step explanation:
When solving a f(x) equation, the x represents the number that will be used to replace x in the equation. So, from the equation, the value of x is -1. You would plug in -1 for x.
f(-1) = (1/4)^-1
Solve the exponent.
f(-1) = 4
So, the value of f(-1) is 4.
Doughnuts at one shop cost £1.20 each.
Doughnuts at a second shop cost 25% more.
What is the difference in the cost of doughnuts at the two shops?
Answer: 30p
Step-by-step explanation:
Cost of donuts in the first shop £1.20
Cost at the second shop at 25% higher
= 1.20 x 1.25 = 1.50
Difference in price
= 1.50 - 1.20 = 0.30
25. En cada par de triangulos, las marcas iguales indican elementos congruentes. ¿Que par de triangulos es congruentre segun el criterio LAL? justifica 26.indica cual criterio se debe usar para determinar la congruencia de cada pareja de triangulos.
Answer:
i cant read spanish. sorry
Step-by-step explanation:
Brody weighs 78 pounds. His weight is 75% of his older brother Andrew's weight. How much does Andrew weigh?
Answer:
Andrew weighs 104 lbs
Step-by-step explanation:
A = andrews weight
A* 75% = brodys weight
A * .75 = 78
Divide each side by .75
A = 78/ .75
A =104
Andrew weighs 104 lbs
geometric sequences
Answer:
Step-by-step explanation:
Hello,
we are talking about geometric sequences it means that
[tex]\dfrac{a_{n+1}}{a_n}=constant[/tex]
once we know this constant it is pretty straight forward to answer the question
Part A
For the first example
to go from 6 to 12 we multiply by ... [tex]\boxed{2}[/tex]
from 12 to 24 we multiply by 2 again
and then we got [tex]\boxed{48}[/tex] , 96 , 192, 384, etc ...
For the second example
let s estimate the constant
[tex]\dfrac{\dfrac{56}{27}}{\dfrac{28}{9}}=\dfrac{56*3}{27*28}=\dfrac{2}{3}[/tex]
the second term is then
[tex]7*\drac{2}{3} = \boxed{ \ \dfrac{14}{3}\ }[/tex]
For the third example
let s estimate the constant
24/-12=-2
so the first term is [tex]\boxed{-3}[/tex]
as -3 * -2 = 6
Part B
1, 1*3=3 ,3*3=9, 27, 81, 243, 729, ...
Part C
-13, -13*-4=52, -208, 832, -3328, etc
Hope this helps
what is the slope intercept of the line y=2x+4
Answer:
Slope = 2
Y intercept = 4
Step-by-step explanation:
This is of the form y = mx + k
where m is the slope
K = y intercept
Hello! (:
y=2x+4
This equation is written in slope-intercept form:
y=mx+b
m is the slope (2) and b is the y-intercept (4)
Hope it helps!
If you have any question or query, feel free to ask! (:
~An excited gal
[tex]SparklingFlower[/tex]
A truck rental company charges a one-
time fee of $40 plus $1 per mile driven.
Dalia rented a truck and used a coupon
for 20% off the total rental cost. After the
coupon was applied, she spent a total of
$60. How many miles did she drive?
A. 8
B. 20
C. 32
D. 35
Answer:
D. 35
Step-by-step explanation:
.8(40+1x)=60
32+.8x=60
.8x=28
x=28/.8
X=35
Answer:
D.35
Step-by-step explanation:
Write the unit rate for the situation.
read 80 pages in 2 hours
20 pages/h
40 pages/h
8 pages/h
160 pages/h
Answer:
40 pages / hour
Step-by-step explanation:
Take the number of pages and divide by the number of hours
80 pages/ 2 hours
40 pages / hour
Use the formula for the sum of a finite series and substitute P for the value of a, the monthly payment you just found. Also, substitute 1 + i for the r value in the formula since the rate of increase is now 1 + the interest rate = i. Now rewrite the formula with the substituted values in simplest form. That simplified formula will determine the future value of a structured savings plan with recurring deposits.
Answer:
[tex]F.V.=\dfrac{P[(1+i)^n-1]}{i}[/tex]
Step-by-step explanation:
Sum of finite geometric series, [tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Substitute P for the value of aSubstitute 1 + i for rThat gives us:
[tex]F.V.=\dfrac{P[(1+i)^n-1]}{(1+i)-1}\\\\=\dfrac{P[(1+i)^n-1]}{1+i-1}\\\\F.V.=\dfrac{P[(1+i)^n-1]}{i}[/tex]
Where:
F.V.=Future ValueP=Recurring deposits.i=Interest Raten=Number of depositsThis is the formula that is used to determine the future value of a structured savings plan with recurring deposits.
Wich proportion would you set up to change 5 pounds to ounces
Answer:
80 oz
Step-by-step explanation:
There are 16 ounces in a pound, so:
5 lbs (16 oz/1 lbs)
Multiply the 2 and you get 80 oz.
Answer: 80 ounces
Step-by-step explanation:
5 x 16 = 80
what i sthe 12 times table..............
Answer:
1×12=12
2×12=24
3×12=36
4×12=48
5×12=60
6×12=72
7×12=84
8×12=96
9×12=108
10×12=120
11×12=132
12×12=144
Step-by-step explanation:
Answer:
1×12=12
2×12=24
3×12=36
4×12=48
5×12=60
6×12=72
7×12=84
8×12=96
9×12=108
10×12=120
11×12=132
12×12=144
Step-by-step explanation: