Answer:
x^3+7x^2-50x-336 or (x-7)(x+6)(x+8)
Step-by-step explanation:
Factor each equation.
x^2-x-42= (x-7)(x+6)
x^2+x-56= (x-7)(x+8)
The common factor is (x-7), therefore the other factors of the expressions must multiply to find the common factor.
(x-7)(x+6)(x+8)=x^3+7x^2-50x-336.
Given the image below, find the area of the regular polygon. The Perimeter of the
decagon is 80 in.
12.3 in.
Answer:
try 492.43, this should be correct if I did this right
Solve the system.
2x + y = 3 −2y = 14 − 6x
Answer:
(x , y ) = (39/22 , -2/11 )
.............
Answer:
-2,3 3,-7
Step-by-step explanation:
took test :)
Ravin is g years old and Eva is 2 years younger than Ravin.
What is the sum of their ages in terms of g?
What is the sum of their ages after g more years, in terms of g?
(gx2)-2
Hope this helps! :)
______________
URGENT HELP! Graph and indicate the 3rd Critical Point
x ^2+3x+2
I need help with this asap thank you!!!!!!!!!
Answer:
(x+1) (x+2)
Step-by-step explanation:
I this is it? If you meant x to the second power than I think this is the answer
What is the area, in square feet, of the shape below?
Answer:
[tex]area = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 2.9 \times 2.6 \\ = 3.77 \: ft {}^{2} [/tex]
Answer:
3.77 ft²
Step-by-step explanation:
Area of a triangle is half base length multiplied by the height.
0.5(2.9 × 2.6) = 3.77 ft²
The temperature at 8 a.m. was -6°C.
By noon, the temperature was 3°C.
Find the change in temperature.
11
Answer:
9
Step-by-step explanation:
3 - ( -6 ) = 9
Hope this helps! Brainliest?
Answer:
9
Step-by-step explanation:
the other answer is right.
to add a little bit of explanation :
you need to calculate the difference between -6 and +3.
and we are looking on the number line only for a distance and not for a direction, as the distance (or simple difference) between -6 and +3 is the same as between +3 and -6.
so, whatever we get as difference, we need to treat that result as positive number.
so, we get the difference between two numbers by subtracting one from the other.
either 3 - (-6), or -6 - 3
you do know that subtracting a negative number is the same as adding the same positive number ?
e.g. 3 - (-6) = 3 + 6 = 9
as for the other direction -6 - 3 = -9
but again, we have to take this in this context as a positive number.
in math we call this the absolute value of a number.
so, the answer is always 9.
jabu invests R5600 for one year at 8% interest. calculate the value of hus investment by the end of the year
Answer:
Hope you find it helpful
1. The cardboard costs 0.002 cents per square mm but glue for each box is also 1 cent per box
2. The plastic costs 0.003 cents per square mm. No glue is necessary. It’s sealed by heat.
Which packaging costs less money?
Compound interest . A student get a grant of $10000 a year assuming her grant is increased by 7% each year what will her grant be in four years time
Answer:
Her grant in four years time will be of $13108.
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial value and r is the growth rate, as a decimal.
A student get a grant of $10000 a year assuming her grant is increased by 7% each year
This means that [tex]A(0) = 10000, r = 0.07[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10000(1+0.07)^t[/tex]
[tex]A(t) = 10000(1.07)^t[/tex]
What will her grant be in four years time?
This is A(4). So
[tex]A(t) = 10000(1.07)^t[/tex]
[tex]A(4) = 10000(1.07)^4 = 13108[/tex]
Her grant in four years time will be of $13108.
What is the measure of an inscribed angle that subtends the same arc as a central angle whose measure is 32 degrees?
The sum of two consecutive integers is −45. Find the Integers.
Answer:
-22 and -23
hope this helped :D
Answer:
- 23 & - 22
Step-by-step explanation:
Let one integer be x, so the other integer is x + 1
x + x + 1 = - 45
2x + 1 = - 45
2x = - 46
x = - 23
The integers are - 23 and - 22.
Please someone help me!
Answer:
12000 rad/min
Step-by-step explanation:
One formula we can use here is that the linear speed is the same, and the linear speed is equal to the angular speed multiplied by the radius.
Therefore, 2400π rad/min* 35 cm = 7 cm* x, with x representing the angular speed of the smaller wheel in radians per minutes. Dividing both sides by 7 cm, we get
2400π rad/min * 35 cm / 7 cm = x
2400 π rad/min * 5 = 12000 rad/min = x as our answer
Which of these random samples represents a representative sample of the number of students who enjoy science class?
A. 30 students in the lunchroom.
B. 30 students who failed science class last year.
C. 30 students who received high grades in their science class last semester.
D. 30 students who participated in the science fair.
Answer: A. 30 students in the lunchroom.
Step-by-step explanation:
A representative sample simply refers to the sample that has same characteristics just like the population.
A random-based selection is regarded as a representative of the population. In this case, the random sample that represents a representative sample of the number of students who enjoy science class is "30 students in the lunchroom".
When the students in the lunchroom are chosen, then it's a representation of the entire students in the school. This is the best option when compared to other options as they don't represent the students entirely.
Answer:
30 students in the lunchroom
Step-by-step explanation:
Got it right on the test.
Find an equation for the line with the given properties. Express your answer using the general form or the slope-intercept form of the equation of a line.
Slope=-3; containing the point (2,-2)
the equation is
Answer:
[tex]y=-3x+4[/tex]
Step-by-step explanation:
To get the equation in the slope-intercept form first, put the equation in slope-point form using the information given. The slope-point form is [tex]y-(-2)=-3(x-2)[/tex]. Then solve for y.
Distribute -3 to [tex](x-2)[/tex],
[tex]y-(-2)=-3x+6[/tex]
Then, add -2 to both sides,
[tex]y=-3x+4[/tex]
This is your final answer; the slope is -3 and the y-intercept is 4. There are also a few other ways to solve but I find this the easiest.
PLZZZZZZZZZZZZZZZ HELP ME WITH THIS!!!
Elena and Diego each wrote an equation to represent the following diagrams. Decide which equation you agree with. And, you must provide your explanations in order to receive the points. You need to solve the equation you agree with. Finally, you need to describe, in words, the process you would use to find the missing values. You can assume that angles that look like right angles are indeed right angles.
1. Elean: w+148=180 , Diego: x+90=148.
We know that angle BKC=148 degrees.
I agree with : ( Elena / Diego /Both of them) .
Because:
Describe, in words, the process you would use to find the missing values:
Answer:
I agree with Elena. See explanation below.
Step-by-step explanation:
A right angle is equal to 90 degrees.
A straight line is equal to 180 degrees.
Elena: w + 148 = 180
Elena's equation is correct because 148 degrees is represented by variable k. When adding variable k and w together, they form a straight line which is equiavlent to 180 degrees. By using this equation, Elena can solve for w after isolating the variable:
w + 148 = 180
w + 148 - 148 = 180 - 148
w = 32 degrees
Diego: x + 90 = 148
Diego is incorrect. He added 90 degrees because of the right angle, but he failed to realize that x is within 90 degrees, meaning he would either have to subtract x from 90 degrees or add both x and w to get to 90 degrees. He cannot solve for x or w by using this equation.
To solve for x, add both w and x to get 90 degrees. Since Elena showed us w equals 32 degrees, we can set up an equation:
w + x = 90
32 + x = 90
32 - 32 + x = 90 - 32
x = 58 degrees
Find Y.
Round to the nearest tenth.
Z
90 ft
55 ft
X
50 ft
Y
Y= [? ]°
Law of Cosines: c2 = a2 + b2 – 2ab cos C
Answer:
∠ Y ≈ 32.7°
Step-by-step explanation:
Using the law of Cosines
cosY = [tex]\frac{x^2+z^2-y^2}{2xz}[/tex]
with x = 90, y = 55, z = 50
cosY = [tex]\frac{90^2+50^2-55^2}{2(90)(50)}[/tex] = [tex]\frac{8100+2500-3025}{9000}[/tex] = [tex]\frac{7575}{9000}[/tex] , then
∠ Y = [tex]cos^{-1}[/tex] ([tex]\frac{7575}{9000}[/tex] ) ≈ 32.7° ( to the nearest tenth )
PLEASE HELP ASAP !!! WILL MARK BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Answer:
See below.
Step-by-step explanation:
Alternate Interior Angles - 1
Alternate Exterior Angles - 2
Corresponding Angles - 4
Same-side Exterior Angles - 5
Same-side Interior Angles - 3
Answer:38292
A
Step-by-step explanation:w
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A tower is known to be 60 meters high. A man using a theodolite stands some distance away from the tower and measures its angle of elevation as 38°. How far away from the tower is he if the theodolite stands 1.5 meters above the ground
Solve 11ax + 12 ax = 13 ax + 60 for x. Assume a=0.
Α. α = 10a
B. x = 10a
C. x = 6a
D. x =6/a
Answer:
In the problem, the value of x is equal to 6a.
Step-by-step explanation:
For this equation, we are to solve for x.
11ax + 12ax = 13ax + 60
Add together 11 and 12 because they have like terms.
23ax = 13ax + 60
Substract 13ax on both sides.
10ax = 60
Now, we divide by 10 on both sides.
ax = 6
In order to see what x is, divide a on both sides.
x = 6a
What is the area of a regular hexagon (6 sides) whose
ℎ ℎ 6 ℎ ℎ ℎ ℎ 3√3 ? Show work
A) 54√3 2
B) 36√3 2
C) 108√3 2
D) 18√3 2
Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
a plumber charges $50 for every house call and an additional $70 for each hour of work for one house call yesterday the plumber earned $435 which equation can be solved to find the number of hours the plumber word on the house call
Answer:
5.5 hours
Step-by-step explanation:
Since every house has an initial charge of $50, we can begin with that
($50)
Then, let's define h as the number of hours. We know every hour is $70, although the hours is yet unknown so that can be
($70 * h) or simply ($70h)
Now, we know the total should end up to be $435, so after PEMDAS the equation will be
($70h + $50 = $435).
We subtract 50 from both sides so now we have $70h = $385.
Now we divide both sides by 70, giving us h = 5.5. Hope it helped!
The number of hours that the plumber work on the house calls should be 5.5.
Given that,
The charge for a plumber for every house call is $50.And, the extra $70 for each hour. The earning of the plumber is $435.Here we assume the number of hours be h.Based on the above information, the equation is as follows:
70h + 50 = 435
70h = 385
h = 5.5 hours
Therefore we can conclude that the number of hours that the plumber work on the house calls should be 5.5.
Learn more: brainly.com/question/3530056
A tank with capacity of 600 gal of water originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/min, and the mixture is allowed to flow out of the tank at a rate of
Answer:
Step-by-step explanation:
From the information given:
Tank's Capacity = 600 gal
Original content of water = 200 gal
Salt solution = 100 lb
In the tank:
Suppose x(t) = amount of salt at time (t); &
V(t) = volume of water
Then,
V(t) = 200 + t
and [tex]x'(t) = 3 - \dfrac{2x(t)}{200+t}[/tex]
From the above linear equation, the integrating factor can be computed as:
[tex]x(t) = \Bigg(e^{\int \dfrac{2}{200+t}} \Bigg)^{dt}[/tex]
[tex]= e^{2 \ log (200+t)}[/tex]
= (200 + t)²
The general solution can now be expressed as:
[tex]x(t) = \dfrac{1}{(200+t)^2}\Bigg( \int 3(200+t)^2 \ dt +C\Bigg)[/tex]
We know that C = integrating factor, thus taking the integral:
[tex]x(t) = \dfrac{(200+t)^3 +C}{(200+t)^2}[/tex]
At the initial condition, x(0) = 100
∴
[tex]100= \dfrac{(200)^3 +C}{(200)^2}[/tex]
C = ((200)²×100) - 200³
C = -4 × 10⁶
Hence, at any time t, the amount of salt is:
[tex]x(t) = \dfrac{(200+t^2) - 4\times 10^6}{(200+t)^2}[/tex]
The city of Raleigh has 10000 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 200 randomly selected registered voters was conducted. 72 said they'd vote for Brown, 118 said they'd vote for Feliz, and 10 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent.
Answer:
0.36
Step-by-step explanation:
Given, There Are 10000 Registered Voters in a City & Two Candidates Brown & Felix .
The Day Before Election , A Telephonic Poll Of 200 Randomly Registered Voters Was Conducted .
72 said they would vote for Brown , 118 Said they would vote for felix & 10 Were Undicided .
Now, The sample statistic is the number who would vote for Brown divided by the total number in the sample, or 72/200 = 0.36
& To Find How Many of 10000 voters to vote Brown Just Multiply 0.36 With 10000 ⇔ 0.36×10000=3600
PLEASE HELP ASAP PLSSSSS !!!!!!!
Answer:
27°
Step-by-step explanation:
angle A + angle B + angle C=180 degree (sum of interior angles of a triangle )
angle A +90 + 63 =180
angle A +153 = 180
angle A =180 - 153
angle A =27 degree
Answer:
<A=27°
Step-by-step explanation:
D=63°
B= 90°
Angles in a triangle adds up to 180°
Therefore A= 180- (63+90)
=180 - 153
=27
Solve the following simultaneous equations 5x+2y= -15
x+2y=5
Answer:
(x, y) = (-5, 5)
Answer:
Step-by-step explanation:
5x+2y=-15
Step 1: Add -2y to both sides.
5x+2y+−2y=−15+−2y
5x=−2y−15
Step 2: Divide both sides by 5
[tex]\frac{5x}{5}[/tex]=[tex]\frac{-2y-15}{5}[/tex]
x=[tex]\frac{-2-15}{5}[/tex]
x+2y=5
Step 1: Add -x to both sides.
x+2y+−x=5+−x
2y=−x+5
Step 2: Divide both sides by 2.
[tex]\frac{2y}{2}[/tex]=[tex]\frac{-x+5}{2}[/tex]
y=[tex]\frac{-x+5}{2}[/tex]
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
Option B. 489.8 ft²
Step-by-step explanation:
From the question given above, the following data were obtained:
Height (h) = 13 ft
Radius (r) = 6 ft
Pi (π) = 3.14
Lateral surface area (Aₗ) =?
The lateral surface area of the cylinder can be obtained as follow:
Aₗ = 2πrh
Aₗ = 2 × 3.14 × 6 × 13
Aₗ = 489.8 ft²
Therefore, the lateral surface area of the cylinder is 489.8 ft²
Alexsy runs in two cross-country races. He runs the first in 45 minutes and the second in 3.5 hours. Find the ratio of his first race time to his second race time in its simplest form.
Answer:
9:42
Step-by-step explanation:
First, convert his second run into minutes so its easier to simplify
than divide both the timings by 5
to get the answer as 9:42 as the simplest ratio form
which is equivalent to (2-3i)(i³⁰³)?
Answer:
-2i - 3
I can't see a simpler way to explain it. You just have to work your way through each step.
Step-by-step explanation:
The question is what is i^303?
Remember that when the power is divisible by 4 the expression changes to 1
i^1 = i
i^2 = i * i = sqrt(-1)*sqrt(-1) = - 1
i^3 = i^2 * i = - i
i^4 = i^2 * i^2 = -1 * - 1 = 1
So what does i^303 =
i^300 * i^3
But 300 is evenly divisible by 4. (300 / 4 = 75) so i^300 = 1^75
i^3 = -i
So now you are ready to do the question
(2 - 3i) * -i
2*-i - 3i(-i)
-2i - 3(i^2 * - 1)
-2i - 3(-1 * - 1)
-2i - 3(1)
-2i - 3
URGENT!!!
Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio
Cleopatra : Dalila : Ebony =
5 : 7 : 8
A) How many dollars do they have in total?
B) Dalila spends 12$ on a hat, how many dollars does she have left?
A)they have 20 dollar's in total
b)she is left with -12 dollar's
Explanation
total money = 5 + 7 + 8
= 20
Money Dalila had = 7 dollars
Money she spent = 12 dollars
money she is left with = 7 - 12 dollars
= -5 dollars