Answer:
GCF is [tex]9x^2y[/tex]
Step-by-step explanation:
When the GCF or the greatest common factor of the expression is required to be found, then take the common terms, and write the expression in the factor form first.
Now, here we have to find the factor of the expression:
[tex]6x^4y^3\cdot 21x^2y^2-9x^2y\\[/tex]
which can be re-written as:
[tex]6x^4y^3\cdot 21x^2y^2-9x^2y\\=126x^6y^5-9x^2y[/tex]
Now, this is further written as:
[tex]126x^6y^5-9x^2y\\=14\cdot \:9x^2x^4yy^4-9x^2y\\[/tex]
Here taking the term [tex]9x^2y[/tex] common, we will get:
[tex]14\cdot \:9x^2x^4yy^4-9x^2y\\=9x^2y\left(14x^4y^4-1\right)\\[/tex]
So we have the expression:
[tex]6x^4y^3\cdot 21x^2y^2-9x^2y= 9x^2y\left(14x^4y^4-1\right)\\[/tex]
So the GCF or the greatest common factor is
[tex]9x^2y[/tex]
Last week the office used 7 and 1/12 boxes of paper. This week, they used 3 and 5/12 boxes of paper. How many more boxes did they use last week then this week?
Answer:
3 and 8/12
Step-by-step explanation:
You subtract 3 5/12 from 7 1/12 to get 3 8/12
Answer:
1 and 8/12 or 1 and 2/3
Step-by-step explanation:
7 1/12-3 5/12
2 1/12- 5/12
1 8/12
5 to the power of two
Answer:
25
Step-by-step explanation:
5^2 = 25
5 * 5 = 25
Answer:
25
Step-by-step explanation:
Step 1: Convert words into an expression
5 to the power of two
5^2
Step 2: Solve
5^2
25
Answer: 25
show all work to multiply (6+√-64)(3-√-16)
Step-by-step explanation:
6 ( 3 - √-16) + √-64 ( 3- √-16)
18 - 6(-4)^2*1/2 + 3 × (-8)^2*1/2 - √1024
18 - 6 (-4) + 3× (-8) - 32
18 + 24 - 24 - 32
18 - 32
-14
The function f is defined by f(x) = x2 - 6x +21.
What are the solutions of f(x) = 0?
Show your work on the scratchpad.
The solutions are:
[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]
Solution:
[tex]f(x) = x^2 - 6x + 21[/tex]
We have to find solutions when f(x) = 0
[tex]x^2 - 6x + 21 = 0[/tex]
Solve by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-6,\:c=21\\\\x=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}[/tex]
[tex]x = \frac{6 \pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{6 \pm \sqrt{36 - 84}}{2}\\\\x = \frac{6 \pm \sqrt{-48}}{2}\\\\x = \frac{6 \pm i \sqrt{48}}{2}\\\\simplify\\\\x = \frac{6 \pm 4\sqrt{3}i}{2}\\[/tex]
[tex]x = 3 \pm 2 \sqrt{3} i[/tex]
We have two solutions:
[tex]x = 3 + 2 \sqrt{3} i\\\\x = 3 - 2 \sqrt{3} i[/tex]
Thus the solutions are:
[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]
The bill at a restaurant is $32 before tax. The tax on the bill is 5%.
How much is the final bill including tax?
32 + 5% = 1.6
The tax is $1.60
The final bill is $33.60
Answer: the answer is $33.60
If y = 7x - 5, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
{(-5, 0), (9, 2), (-26, -3)}
{(2,7), (1,6), (3, 13)}
{(0, -5), (2,9), (-3, -26)}
{(1, 3), (6, 18), (8, 15)}
option c {(0, -5), (2,9), (-3, -26)} is correct . All others doesn't satisfy the equation .
Step-by-step explanation:
We have , If y = 7x - 5, following set of ordered pairs {(0, -5), (2,9), (-3, -26)} . Let's check for this
(0, -5):
⇒ [tex]y = 7x-5[/tex]
⇒ [tex]y = 7(0)-5[/tex]
⇒ [tex]y =-5[/tex]
So , it's correct ordered pair .
(2,9):
⇒ [tex]y = 7x-5[/tex]
⇒ [tex]y = 7(2)-5[/tex]
⇒ [tex]y =9[/tex]
So , it's correct ordered pair .
(-3,-26):
⇒ [tex]y = 7x-5[/tex]
⇒ [tex]y = 7(-3)-5[/tex]
⇒ [tex]y =-26[/tex]
So , it's correct ordered pair .
Therefore, option c {(0, -5), (2,9), (-3, -26)} is correct . All others doesn't satisfy the equation .
There are two buses. Bus A can travel 125 miles in 3 hours,
and Bus B can travel 85 more miles than bus A within the
same time. What is the speed of Bus B?
mph.
The speed is the distance covered by an object at a particular time. The speed of bus B is 70 miles per hour.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given that Bus A can travel 125 miles in 3 hours. While Bus B can travel 85 more miles than bus A within the same time. Therefore, we can write,
Distance traveled by Bus B = 125 miles + 85 miles = 210 miles
Time is taken by Bus B = 3 hours
Now, the speed of the bus B can be written as,
Speed of Bus B = Distance Covered / Time taken
= 210 miles / 3 hours
= 70 miles per hour
Hence, the speed of bus B is 70 miles per hour.
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Find the area of this figure
28 cm
23.7 cm
8 cm
5.7 cm
a farmer has 1384 trees to be planted on a rectangular parcel of land. if there are 21 trees planted in each row and each row must be completed before it is planted, how many trees will be left over after planting?
Answer:
There will be 19 trees left over after planting.
Step-by-step explanation:
Divide 1384 by 21 which gives you the quotient of 65.90...
Then multiply 65 by 21 which equals 1365
Lastly subtract 1384 and 1365 which gives the answer 19.
You have a jar of jelly beans in front of you
with 12 - lime, 17 - papaya, 5 - mango and 13
- bubble gum. What is the probability, as a
fraction, of selecting either a lime or bubble
gum followed by a papaya?
The probability of picking a lime or bubblegum jellybean followed by a papaya jellybean is 425/2162, which is approximately 0.196 when rounded to three decimal places.
Explanation:The subject of this question is probability, a mathematical concept. Here is how we would calculate the answer to the student's query:
First, add up the total number of jelly beans in the jar, which gives us 47 jelly beans (12 lime + 17 papaya + 5 mango + 13 bubblegum). The total probability of picking a lime or bubblegum jelly bean is the probability of picking lime or bubblegum jelly beans divided by the total number of jelly beans.
The probability of picking a lime or bubblegum jelly bean is 25/47 (12 lime + 13 bubblegum = 25; 25/47).
After picking a lime or bubblegum jellybean, there are now 46 jellybeans left. Hence the probability of picking a papaya jellybean is 17/46.
Now, to get the total probability of picking a lime or bubblegum jellybean followed by a papaya jellybean, you multiply these two probabilities together.
The result will be (25/47) × (17/46) = 425/2162, which can be simplified to approximately 0.196 when rounded to three decimal places.
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The correct probability, as a fraction, of selecting either a lime or bubblegum followed by a papaya is [tex]\(\frac{25}{341}\)[/tex].
To find this probability, we need to calculate the probability of each individual event and then multiply them together because we are dealing with two independent events: first selecting a lime or bubblegum, and then selecting a papaya.
First, let's find the total number of jelly beans:
Total jelly beans = lime + papaya + mango + bubble gum
Total jelly beans = 12 + 17 + 5 + 13
Total jelly beans = 47
Now, let's calculate the probability of selecting either a lime or bubblegum:
Probability of selecting lime = Number of lime jelly beans / Total number of jelly beans
Probability of selecting lime = 12 / 47
Probability of selecting bubblegum = Number of bubblegum jelly beans / Total number of jelly beans
Probability of selecting bubblegum = 13 / 47
Since we want the probability of selecting either a lime or bubblegum, we add these probabilities:
Probability of lime or bubblegum = Probability of lime + Probability of bubblegum
Probability of lime or bubblegum = (12 / 47) + (13 / 47)
Probability of lime or bubblegum = 25 / 47
Next, we calculate the probability of selecting a papaya after selecting either a lime or bubblegum. Since we are not replacing the jelly bean after the first selection, the total number of jelly beans is now 46 (one less than before because one jelly bean has been removed).
Probability of selecting papaya = Number of papaya jelly beans / Total number of remaining jelly beans
Probability of selecting papaya = 17 / 46
Now, we multiply the probability of selecting either a lime or bubblegum with the probability of selecting a papaya:
Probability of lime or bubblegum followed by papaya = Probability of lime or bubblegum * Probability of papaya
Probability of lime or bubblegum followed by papaya = (25 / 47) * (17 / 46)
Finally, we simplify this expression:
Probability of lime or bubblegum followed by papaya = (25 * 17) / (47 * 46)
Probability of lime or bubblegum followed by papaya = 425 / 2162
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1 in this case. So the fraction is already in its simplest form.
Therefore, the probability of selecting either a lime or bubblegum followed by a papaya is [tex]\(\frac{425}{2162}\).[/tex]However, upon re-evaluating the calculation, it seems there was an error in the simplification process. The correct simplification is:
Probability of lime or bubblegum followed by papaya = [tex]\(\frac{25}{341}\).[/tex]
Describe what an "included" angle is. Give an example.
Answer:
The angle between two sides is the included angle.
Example:
In triangle ABC,
Angle B is an included angles because it's formed by two sides AB and CB which meet at point B.
Similarly, other angles in a triangle are also included.
This is for all segments which meet at point, triangle is just one example
If you bought a stock last year for a price of $128, and it has gone down 14.7% since then, how much is the stock worth now, to the nearest cent?
Answer:
so, you've lost 14.7 percent of value. or, in other words, you still have 85.3 percent of value.
Step-by-step explanation:
so just so .853 times 128 and you're there I'm too lazy to grab calc but please give me brainliest answer
Answer: $109
Step-by-step explanation:
Given stock at last year = $128
14.7 percent decrease = 14.7/100 × 128
=$18.8
To get the Current worth of stock, we then subtract 14% decrease from the worth of stock as at last year:
= $128 - $18.8
=$109.18 to the nearest cent is $109
I hope this helps.
terry ran around a circular track . if the radius of the track is 200 feet how far did tarry run
Terry ran a distance of 1256ft
Data;
Radius of Track = 200 feetDistance covered = ?Circumference of a CircleThe distance covered can be calculated from the circumference of the circular track. This can be done using the formula of circumference of a circle which is given as
[tex]C = 2\pi r\\[/tex]
Let's substitute the values and solve
[tex]C = 2\pi r\\C = 2 * 3.14 * 200\\C = 1256ft[/tex]
The circumference of the track is 1256ft.
From the calculation above, Terry ran a distance of 1256ft
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Terry ran a distance of 400π feet around the circular track with a radius of 200 feet.
Explanation:To find the distance Terry ran around a circular track with a radius of 200 feet, we can use the formula for the circumference of a circle. The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius. So, the distance Terry ran is: D = 2π(200). Calculating this gives us the answer: D = 400π feet.
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Last one!! Will give Brainliest as always
Answer:
216 square yards
216 yd^2
Step-by-step explanation:
Base: 6 × 12 = 72
Rectangular Sides: 5 × 12 = 60 (×2 = 120)
Triangular Sides: 6 × 4 = 24 (÷2 ×2 = 24)
Add: 72 + 120 + 24 = 216
pens cost x pence and pencils cost y pence. Write a formula for the total cost (T) of 7 pens and 11 pencils
Solve this quadratic equation using the quadratic formula.
2x^2 - 10x + 7 = 02x2 - 10x + 7 = 0
Answer:
I'm assuming the equation is:
2x^2 -10x +7 = 0
x = (-b +- sqr root (b^2 - 4ac)) / 2a
x = (--10 +-sqr root (100 -4*2*7)) / 4
x = (10 +- sqr root (44)) / 4
x1 = (10 + 6.6332495807 ) /4
x1 = 16.6332495807 / 4
x1 = 4.1583123952
x2 =(10 - 6.6332495807 ) /4
x2 = 3.3667504193 / 4
x2 = 0.8416876048
Step-by-step explanation:
On a fishing trip, Mariko caught 24 fish. She caught some rockfish averaging 2.5lbs and some bluefish averaging 8lb. The total weight of the fish was 137lbs how may of each fish did she catch.
Mariko caught 10 rockfish and 14 bluefish on her fishing trip.
Explanation:Let's define the number of rockfish caught as x and the number of bluefish caught as y.
According to the given information, the average weight of each rockfish is 2.5lbs and the average weight of each bluefish is 8lbs.
We can form two equations based on the total weight of all the fish and the total number of fish caught:
Equation 1: x + y = 24 (since Mariko caught a total of 24 fish)Equation 2: 2.5x + 8y = 137 (since the total weight of the fish was 137lbs)We can solve this system of equations to find the values of x and y by either substitution or elimination method. Using the elimination method:
Multiplying Equation 1 by 2.5, we get 2.5x + 2.5y = 60
Subtracting this equation from Equation 2, we get 8y - 2.5y = 137 - 60
Simplifying, we have 5.5y = 77
Dividing both sides by 5.5, we get y = 14
Substituting this value back into Equation 1, we have x + 14 = 24
Simplifying, we get x = 10
Therefore, Mariko caught 10 rockfish and 14 bluefish.
Joey paints old furniture and sells the pieces at craft fairs. The function f(t) approximates how many pieces of furniture he paints per hour. The function w(h) represents how many hours per week Joey spends painting the pieces of furniture. What are the units of measurement for the composite function f(w(h))?
hours over weeks
weeks over furniture
furniture over hours
furniture over weeks
Answer: Furniture over weeks
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
f(t) = furniture/ hour w(h)= hours/weekSo, for the function f (w(h)) = hours /week x (furniture /hours)
Because "hours" are in both terms, and one is the numerator and the other is the denominator, they can be cancelled with each other.
f (w(h)) = furniture / week
Feel free to ask for more if needed or if you did not understand something.
Answer: D) Furniture over weeks
Step-by-step explanation:
I took the test
solve for x
x/4 ≥ -8
a) x≤-2
b)x≥-32
c)x≥-2
d)x≤-32
Answer:
B
Just multiply by 4 to isolate x; because 4 isn't negative, u keep the sign the same.
Easy question! Please help! And please tell me which line to use! (open circle or closed circle)
Answer:
See below
Step-by-step explanation:
The inequality is d<-80 since the problem states you go deeper than -80 feet.
As for graphing the inequality, you use a open circle with the arrow pointing left.
<= means closed
>= means closed
< means open
> means open
Answer:
Question: You need to figure out the inequality. Here is the full question: On their first dive, scientists explore a part of the ocean floor that is 80 feet below sea level. This depth can be represented by the integer -80. On their second dive, they explore a deeper depth. Write an inequality that represents the possible depth, d, of the scientist's second dive. After you figure that out you can answer the question above.
d < -80
Open ended at -80 pointing toward -200
Directions: Consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. It falls to the ground. Think about the amounts of potential and kinetic energy the bowling ball has:
What is the kinetic energy of the ball as it is half way through the fall?
Answer:
it cant be kinetic unless its pushed and gains height, as its falling it is simply potential energy and gets speed in different stages of the fall.
Step-by-step explanation:
An orange has 20 fewer calories
than a banana. If 7 bananas have
the same number of calories as 9
oranges, how many calones are in a
banana?
Answer:
90 calories in total
Step-by-step explanation:
We can solve this equation through the following steps:
Step One: Since we are told that a banana is 20 less calories than an orange, we can create the Let Statements:
Let x= the calories in a banana
Let x-20=the calories in an orange
Step Two: Create an equation
Since we are told "7 bananas have the same calories as 9 oranges" we translate"
7x=9(x-20) Distribute
7x=9x-180 Subtract 9x from both sides of the equation
7x-9x=-180 Simplify
-2x=180 Divide both sides by -2
x=90
∴There are 90 calories in a banana.
(4x+40)=3x what is x
Answer: x=40
Step-by-step explanation:
(4x+40)=3x
Step 1: open the bracket
4x + 40 = 3x
Step 2: Combine like terms
4x - 3x = 40
x = 40
I hope this helps.
A town has accumulated 2 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated 8 inches, and the depth is increasing by 2 inches every hour. In about how many hours will the snowfall of the towns be equal?
Answer:
192 inches
Step-by-step explanation:
I dont know I tried
It will take approximately 1.5 hours for the snowfall in both towns to be equal.
The question asks to determine when the snowfall in two different towns will be equal. The first town starts with 2 inches of snow and accumulates 6 inches every hour. The second town starts with 8 inches of snow and accumulates 2 inches every hour. To find when the depths will be equal, we need to set up an equation where the snow depths of both towns are set equal to each other and then solve for time (t).
Let t be the number of hours required for the snow depths to be equal.
For the first town: Initial depth + (Rate of snowfall * Time) = 2 inches + (6 inches/hour * t)
For the second town: Initial depth + (Rate of snowfall *Time) = 8 inches + (2 inches/hour *t)
Setting both expressions equal, we get: 2 + 6t = 8 + 2t. By solving for t, we subtract 2t from both sides and also subtract 2 from both sides to obtain: 4t = 6. Then we divide both sides by 4 to find t = 1.5 hours.
So, it will take 1.5 hours for the snow depths in both towns to be equal.
A parking garage charges a flat rate for the first hour plus $1.25 for each additional hour of parking. It costs $8.00 to park in the garage for 5 hour. What is the linear equation models the total cost, y, of parking in the garage for x hours?
Please show your work if you can.
A. Y= 1.25x
B. Y= 1.25x + 5
C. Y= 1.25x + 1.75
D. Y= 1.25x + 3
Find the flat rate:
1.25 x 4 = 5.00
8.00 -5.00 = 3
The flat rate is $3
The equation would be:
D. Y= 1.25x + 3
Answer:
1.25x+1.75 is the correct answer
Step-by-step explanation:
np
The diagonals of a kite are 22 feet and 33 long. what is the area ?
Answer:
A=363
Step-by-step explanation:
To solve the area of a kite you use
[tex] a = \frac{pq}{2} [/tex]
So 22×33=726 then divide that by 2 and you get 363.
The area of a kite with diagonals of 22 feet and 33 feet is calculated as half the product of its diagonals, resulting in an area of 363 square feet.
Explanation:The area of a kite can be calculated by taking the product of the lengths of its diagonals and dividing by two. In the case of the kite with diagonals of 22 feet and 33 feet, we use the formula: Area = (diagonal1 × diagonal2) / 2. Substituting the given lengths into the formula, we get Area = (22 × 33) / 2.
To find the area, we multiply 22 feet by 33 feet which equals 726 square feet. Then we divide by 2, so the area of the kite is 363 square feet.
[tex]0 = \frac{i}{8} [/tex]
what is i?
Answer:
0
Step-by-step explanation:
i/8=0
i=0*8
i=0
Select the number line that represents the solution of the inequality
7- x 24.
Answer:
The correct answer is A.
10/10
6x-7=12
5/6
6/19
19/6
Answer:
[tex]10/10 = 1[/tex]
[tex]x=\frac{19}{6} \\[/tex]
[tex]5/6 =0.83[/tex]
[tex]6/19 = 0.31578947[/tex]
[tex]19/6 = 3.16[/tex]
5y + (86 - y) = 86 + 4y
Answer:
All real values, (-∞, ∞)
Step-by-step explanation:
Step 1: Distribute
5y + (86 - y) = 86 + 4y
5y + 86 - y = 86 + 4y
Step 2: Combine like terms
5y + 86 - y = 86 + 4y
4y + 86 = 86 + 4y
Step 3: Subtract 4y from both sides
4y + 86 - 4y = 86 + 4y - 4y
86 = 86
Step 4: Subtract 86 from both sides
0 = 0
Answer: All real values, (-∞, ∞)
Answer:
0
Step-by-step explanation:
Given
5y + (86 - y) = 86 + 4y
Open parenthesis
5y + 86 - y = 86 + 4y
Rearrange the expression
5y - y + 86 = 86 + 4y
4y + 86 = 86 + 4y
Combine like terms
4y - 4y = 86 - 86
0 = 0
0