[tex]2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5[/tex]
Answer:
(x+5) is the final answer.
Step-by-step explanation:
We have to find the factors of [tex]2x^4+22x^3+60x^2[/tex]
Then select correct choice or choices from the given options.
[tex]2x^4+22x^3+60x^2[/tex]
[tex]=2x^2(x^2+11x+30)[/tex]
[tex]=2x^2(x^2+6x+5x+30)[/tex]
[tex]=2x^2(x(x+6)+5(x+6))[/tex]
[tex]=2x^2((x+5)(x+6))[/tex]
[tex]=2x^2(x+5)(x+6)[/tex]
From above factors, we see that only (x+5) is correct.
Hence (x+5) is the final answer.
The length of a rectangle is 3 meters less than four times the width the perimeter of the rectangle is 74 meters. find the length and width of the rectangle
width = perimeter/2 - length
w = 74/2 - 5 = 32
32/4 = 8 - 3 = 5
The length of the rectangle is 5.
The width of the triangle is 32
As per the given values, the length of the rectangle is 29 meters and the width is 8 meters.
Explanation:To find the length and width of the rectangle, we can use the information given: the length is 3 meters less than four times the width, and the perimeter is 74 meters. Let's assume the width is 'w' meters. So, the length would be '4w - 3' meters. The perimeter of a rectangle is found by adding the lengths of all its sides, which in this case is twice the length plus twice the width.
We can set up an equation to solve for 'w': 2(4w - 3) + 2w = 74. Solving this equation will give us the width of the rectangle, and we can substitute that value back to find the length.
Step 1: Set up the equation:
2(4w - 3) + 2w
= 74.
Step 2: Simplify the equation:
8w - 6 + 2w
= 74.
Step 3: Simplify further:
10w - 6 = 74.
Add 6 to both sides.
Step 4: Continue to simplify:
10w = 80.
Divide both sides by 10.
Step 5: Solve for 'w':
w = 8.
The width of the rectangle is 8 meters.
Step 6: Find the length
= 4w - 3
= 4(8) - 3 = 32 - 3
= 29 meters.
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In a survey, a group of students were asked to name their favorite day of the week. There were 8 students who chose “other”. How many students participated?
Answer:
Step-by-step explanation:I would say 56 or 63. My reason is because when it says pick their favorite day of the week. It is 7 days a week so that gives me right there that I have to multiply. Then there is an option of "other" so I would probably multiply it by 8 to get the number of people who participated. Hope this helps☺
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Emma went to a salon to get her hair cut. The price of the haircut is $65. She wants to leave a 20% tip. What is the total amount she should pay?
Answer:
She should leave a total of $78.
Step-by-step explanation:
To find this, we first need to find the tip amount. We can do this by multiplying the total by the tip percentage.
$65 * 20% = $13
Now that we have that, we need to add it to the cost.
$65 + $13 = $78
Twenty-three girls tried out for the cheerleading squad. Only 12 could be chosen for the team. How many girls were not selected?
Answer: 11 girls were not selected.
Step-by-step explanation:
First let's find out how many girls their were in total. In this case their are 23.
Let's subtract 12 from 23. That ends up to be 11. (subtract 23 from 11 / 11 from 23)
-23
-12
-------
11
What we know:
- Twenty-three girls tried out for the cheerleading squad.
- Only 12 girls will be chosen for the team.
Answer and Explanation:
The answer is 11 because,
When trying to find out how many girl's that where not selected you just simply subttact 23 from 12.
23-12=11
That being said, the answer is 11.
The value of a machine depreciates each year by 3 %. What will be the value of the machine bought for Rs 1,00,000 after two years.
Answer:
1,000,000 / 1.03 = 970,873.79 After 1st Year
970,873.79 / 1.03 = 942,595.91 After 2nd Year
Step-by-step explanation:
Answer:
Two thirds rounded would be 66.67%. I’m uncertain whether you were asking about a straight line depreciation or some sort of degressive depreciation.
Basically, in a straight-line depreciation, you would calculate each depreciation as a fraction of your asset’s original value. A machine worth $1000 in year 0 would depreciate annually with a constant amount of $100.
Your machine would be worth less than 66.67% of its original value after at least 4 years (4 x 10%). More precisely, 3 years and (33.3% x 365 days) 122 days.
Applying a degressive depreciation method, you would calculate the depreciation in each year as a fraction of your asset’s residual value. This implies your depreciations would decrease each year (hence “degressive”). As soon as your depreciations fall below the amount you would depreciate in a straight line depreciation, you switch to the latter. The reason for this is that it does not really make sense for a company to depreciate it’s assets with a lesser amount, given the tax benefits of depreciations and the time value of money.
Assuming the duration of the asset’s useful life is 10 years, you would switch to the straight-line depreciations after the first year. This scenario would be equal to the straight-line depreciation: 3 years and 122 days.
In case the duration of the asset’s useful life is shorter or longer than 10 years, the amount of time required for the asset to have less than two-thirds of its initial value depends on the duration of is life.
so basically the answer is
1,000,000 / 1.03 = 970,873.79 After 1st Year
970,873.79 / 1.03 = 942,595.91 After 2nd Year
What is the value of the 8 in the number 24.387? Give your answer as a fraction.
Answer:
[tex]\frac{8}{100}[/tex]
Step-by-step explanation:
Given :Number = 24.387
To Find : What is the value of the 8 in the number 24.387?
Solution:
The first digit after the decimal point is called the tenths place value = [tex]\frac{1}{10}[/tex]
The second digit after the decimal point is called hundredths place value= [tex]\frac{1}{100}[/tex]
The third digit after the decimal point is called thousandths place= [tex]\frac{1}{1000}[/tex]
Number = 24.387
Since 8 is The second digit after the decimal point
So, The place value of 8 is hundredths
So, the value of 8 in fraction = [tex]\frac{8}{100}[/tex]
Hence The value of the 8 in the number 24.387 is [tex]\frac{8}{100}[/tex]
The value of the 8 in the number 24.387 as a simplified fraction is 4/5.
The 8 in the number 24.387 is in the tenths place, so it represents 8 out of 10.
We can write this as a fraction as follows:
8 / 10
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2.
The greatest common divisor of 8 and 10 is 2. Dividing both the numerator and denominator by 2, we get:
(8 / 2) / (10 / 2) = 4 / 5
Therefore, the value of the 8 in the number 24.387 as a simplified fraction is 4/5.
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Suppose 8x + 16 ice cream cones were sold on Saturaday and 7x - 9 were sold on Sunday.What is the total number of ice cream cones sold?
Answer:
Total number of ice cream cones sold = 15x +7
Step-by-step explanation:
Given the statement: Suppose 8x + 16 ice cream cones were sold on Saturday and 7x - 9 were sold on Sunday.
⇒ Ice cream cones were sold on Saturday = 8x+16
and
Ice cream cones were sold on Sunday = 7x -9
We have to find the total number of ice cream cones sold.
Total number of ice cream sold = Ice cream cones sold on Saturday + Ice cream sold on Sunday
Substitute the given values we get;
Total number of ice cream sold = [tex]8x + 16 + 7x -9 = 15x + 7[/tex]
Therefore, the total number of ice cream cones sold is, 15x +7
Oliver is doing a study on age and shoe size. He has collected the data shown above. Do the ordered pairs (x, y) he has collected form a function?
x (age) y (size)
8 7
9 8
10 9
8 9
14 9
15 11
10 10
33 9
27 9.5
45 10.5
A) Cannot be determined
B) Yes, because for every x there is only one y.
C) Yes, because for every y there is only one x.
D) No, because for some x's there are more than one y's.
Answer: D) No, because for some x's there are more than one y's.
Step-by-step explanation:
By the definition of function,
In a function For the every input there is a single value of output.
That is, if F is a function such that [tex]F(x_1) \neq F(x_2)[/tex]
Then, [tex]x_1[/tex] and [tex]x_2[/tex] must be distinct.
But according to the given table,
For the value of 8 there are two outputs values 7 and 9.
Therefore, we can say that the given ordered pairs (x, y) can not make the function because there are more than on y's for one value of x's.
Answer:
D
Step-by-step explanation:
The definition of a function states that for every x there is only one y. If you look at the data table for an x- value of 8 there are 2 different y-values 7 and 9. Therefore the correct answer is No, because for some x's there are more than one y's.
Factor the expression over the complex numbers. x2+25
Answer:
(x - 5i)(x + 5i)
Step-by-step explanation:
Find the roots by solving x² + 25 = 0
hence x² = - 25 ( take the square root of both sides )
x = ± 5i
x² + 25 = (x - 5i)(x + 5i)
20 points What is the equation of a line parallel to the given line with an X intercept of 4
Answer: y = 4x - 16
Ta Da lol ...
Which of the following expressions correctly uses the properties of summations to represent
Answer:
Option C is correct.
[tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]
Step-by-step explanation:
Given the expression: [tex]\sum_{i=1}^{18} (7i^2+9)[/tex]
Using properties of summation:
[tex]\sum_{i=1}^{n} (a+bi) =\sum_{i=1}^{n} a + \sum_{i=1}^{n} bi[/tex][tex]\sum_{i=1}^{n} a = an[/tex]Using properties of summation in the given expression we have;
[tex]\sum_{i=1}^{18} (7i^2+9)[/tex]
= [tex]\sum_{i=1}^{18} 7i^2 + \sum_{i=1}^{18} 9[/tex]
=[tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]
Therefore, the following given expression uses the properties of summation to represents is, [tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]
Find the 52nd term. 28, 25, 22, 19, ..
Answer:
The 52nd term is -125
Step-by-step explanation:
The formula for an arithmetic sequence is
an = a1+d(n-1)
where a1 is the first term and d is the common difference.
a1 = 28
d = 25-28 = -3
Let's check 19-22 = -3 so the common difference is correct
an = 28 - 3(n-1)
We want to find the 52 term so n = 52
a52 = 28 -3 (52-1)
a52 = 28 -3(51)
a52 = 28 -153
a52 = -125
I’m not quite sure how to solve this any help would work!
Answer:
11. O = (-1, 5/2); 12. H = (1,4)
Step-by-step explanation:
11. Circumcentre
Your points form the vertices of a right triangle (see image below).
The circumcentre (O) of a right triangle must be at the midpoint of the hypotenuse.
Your hypotenuse has the ends at (-3,4) and (1,1), so
O = ((-3 + 1)/2),(4 + 1)/2))
O = (-2/2,5/2)
O = (-1, 5/2)
===============
12. Orthocentre
The orthocentre (H) of a right triangle is the vertex at the right angle.
Your right angle is at (1, 4), so
H= (1,4)
Which graph represents the solutions to the inequality 2x-6<4?
Answer:
D
Step-by-step explanation:
solving the inequality
Inequalities of the type | x | < a always have a solution of the form
- a < x < a
For | 2x - 6 | < 4 then solution is
- 4 < 2x - 6 < 4 ( add 6 to all 3 intervals )
2 < 2x < 10 ( divide all 3 intervals by 2 )
1 < x < 5 → graph D
The open circles at the ends of the blue line indicate up to but not including these points.
[tex]|2x-6| < 4\iff2x-6<4\ \wedge\ 2x-6>-4\qquad\text{add 6 to both sides}\\\\2x<10\ \wedge\ 2x>2\qquad\text{divide both sides by 2}\\\\\boxed{x<5\ \wedge\ x>1}\to1< x<5[/tex]
≤, ≥ - full circle
<, > - open circle
Answer: 4th graph.I dont get this problem! Please help!
Answer:
Step-by-step explanation:
Given that a box has cards numbered 1 ,2,3
Also a bag has three balls labelled A, B and C
Sample space = {(1,A)(1,B)(1,C) (2,A)(2,B)(2,C)} n(S) = 9
Mary will randomly pick up a card from the 3 cards and also pick up a ball from the bag of 3 balls.
The sample space contains the combination of letter on the card and number on the ball.
Event that the number chosen is 1 is
{(1,A)(1,B)(1,C)}: n(event of choosing 1)=3
please help :))) will award brainliest <3
Alright, so we are given a triangle where all the angles are the same. Now - we need to write a proof that when IE bisects KM, it creates equal angles.
Given:
IKM is equiangular
IE is perpendicular to KM
This is enough to prove that IKE is congruent to IME because:
IEK and IEM are both 90 degrees, since IE is perpendicular to KM
KIE and MIE are the same degree measure, since I is being bisected.
This leaves us with only one angle remaining, and since we already know that the first two angles are congruent to their counterpart - we also know that IKE is congruent to IME because all interior angles of triangles add up to 180°, and we know the other two angle sets to be congruent.
a restaurant offers cooking class on 24 of the 30 days of November. what decimal is equivalent to the fraction of the days in November that classes were offered at the restaurant
Answer:
0.8
Step-by-step explanation:
Answer:
0.8
Step-by-step explanation:
Stephen invests in an account that pays 3% compound interest annually. He invests $5,500. He uses the expression P(1+r)t to find the total value of the account. What will be the total value of the account after 6 years?
Answer:
A = $6567.29
Step-by-step explanation:
A = P(1+r)^t
Where A = amount in account
P = principal
r = interest rate in decimal form
t= time
We know that P =5500
r = .03
t =6
Substitute these values into the equation.
A = 5500(1+.03)^6
A = 5500(1.03)^6
A = 5500(1.194052297)
A=6567.287631
Since this is money we round to the nearest cent
A = $6567.29
use order of operations to simplify 8+ 5(61-(6*6))
Answer:
133
Step-by-step explanation:
Solve . 2d^2+5d-12=0
Answer:
Exact Form d=3/2 or -4
Decimal Form d=1.5 Mixed (Number)(Form):1 1/2 or -4
Hoped I helped <3
Step-by-step explanation:
Solve: tan(x) – cos2(x) = sin2(x)
Answer:
pi/4 + kpi (choice #1)
Step-by-step explanation:
Answer:[tex]x=\frac{\pi}{4}[/tex]
Step-by-step explanation:
`Writing tan and cos in form of sin
[tex]\frac{sinx}{cosx}-\left ( 1-2sin^2x\right )=2sinxcosx[/tex]
[tex]\frac{sinx}{cosx}-1+2sin^2x=2sinxcosx[/tex]
[tex]\frac{sinx-cosx}{cosx}=2sinx\left ( cosx-sinx\right )[/tex]
[tex]2sinx\left ( cosx-sinx\right )-\frac{sinx-cosx}{cosx}=0[/tex]
[tex]\left ( cosx-sinx\right )\left [ 2sinx+\frac{1}{cosx}\right ]=0[/tex]
[tex]\left ( cosx-sinx\right )\left [ \frac{2sinxcosx+1}{cosx}\right ]=0[/tex]
so cosx-sinx=0 or 2sinxcosx+1=0 and cosx is not equals to zero
cosx-sinx=0
tanx=1,[tex]x=\frac{\pi}{4}[/tex]
similarly
[tex]x=n\pi +\frac{\pi}{4}[/tex]
For 2sinxcosx+1=0
sin2x=-1
[tex]2x=\frac{3\pi}{2}[/tex]
but this value is not satisfied by equation thus
[tex]x=n\pi +\frac{\pi}{4}[/tex]
13,530 grams (g) is equal to how many kilograms (kg)?
In the metric system, 1 kilogram is equivalent to 1000 grams. By dividing 13,530 grams by 1000, we get 13.53, meaning 13,530 grams is equivalent to 13.53 kilograms.
Explanation:The question is asking about converting grams (g) into kilograms (kg). In the metric system, 1 kilogram is equal to 1000 grams. So, to convert 13,530 grams into kilograms, you need to divide 13,530 by 1,000.
Therefore:
13,530 grams (g) = 13.53 kilograms (kg)
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Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x^3 - 5x^2 + 4x + 7 ) ÷ (x - 1)
Answer:
1x^2 - 4x is the quotient and remainder is 7
Step-by-step explanation:
Let use synthetic division
First we write all the coefficients of x^3 - 5x^2 + 4x + 7 inside
we need to divide by x-1. x-1=0 so x= 1
so we put 1 outside
The coefficients of x^3 - 5x^2 + 4x + 7 is 1, -5, 4, 7
1 1 -5 4 7
1 -4 0
-------------------------------------------------------------
1 -4 0 7
Here 7 is the remainder
Now we write the answer in descending powers of x
1 -4 and 0 we have
The highest exponent in the question is x^3
when we divide by x-1 then highest exponent becomes x^2
So answer is 1x^2 - 4x + 0 that is 1x^2 - 4x
Answer:
x^2 - 4x + (7) x - 1
Step-by-step explanation:
This is correct Hope this Helps! :)
Without graphing, classify each system as independent, dependent, or inconsistent. y = 3x + 6, 6x - 2y = -12
Answer:
The correct answer option is dependent.
Step-by-step explanation:
We are given the following two equations and we are to determine whether these are independent, dependent or inconsistent:
[tex]y = 3x + 6[/tex] --- (1)
[tex]6x - 2y = -12[/tex] --- (2)
To compare these equations with each other, it is a good idea to write them in the same format with y being the subject. So rearranging equation (2) to get:
6x - 2y = -12
6x + 12 = 2y
2y = 6x + 12
y = 3x + 6
A system of equations is said to be dependent when the same line is written in two different forms so that there are infinite solutions.
Hence, this system of equations is dependent having infinite solutions.
The system of equations are classified as independent
How to determine the termTo classify the system of equations as independent, dependent, or inconsistent, we can analyze their coefficients.
The given system of equations is:
y = 3x + 6
6x - 2y = -12
Comparing the coefficients, we can see that the slopes of the equations are equal (-2/-6 )
Reduce the fraction to smaller forms, we get;
1/3
Now, since the slopes are different, the system is consistent and has a unique solution, indicating an independent system.
Thus, the equations are independent.
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round 47 963 to the nearest hundreds
Answer:
48,000. Look at the tens place, If the number is 5 or higher then you round up, if its 4 or lower the hundreds place stays the same. Since the number in the tens place is higher than 4 you round up, meaning you would add 1 to 9 which give you ten. You would carry that ten over, giving you 48,000
The correct answer is 48,000.
To round the number 47,963 to the nearest hundreds:
Identify the digit in the tens place, which is 6.
Since the digit in the tens place is greater than or equal to 5, round up the hundreds place.
The current digit in the hundreds place is 9.
Rounding up the hundreds place from 9 results in increasing it to the next number, which is 10.
When the hundreds place increases to 10, it affects the thousands place as well:
The 7 in the thousands place becomes 8, because adding 1 to 9 in hundreds place essentially adds 1,000 to the overall number.
Set all digits to the right of the hundreds place to zero.
Thus, 47,963 rounded to the nearest hundreds becomes 48,000.
This process ensures accurate rounding based on standard rounding rules.
Find the height of the liquid in the glass pictured. Show all steps.
Answer:
Step-by-step explanation:
Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle! so A=1/2(6)(h). 1/2 times six is 3 so you have A=3h, subtract 3 and your awnser is 3A=h divide by 2 H= 1.5
Answer:
Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle! so A=1/2(6)(h). 1/2 times six is 3 so you have A=3h, subtract 3 and your awnser is 3A=h divide by 2 H= 1.5 I dont understand how this answers a question wit showing full steps
Step-by-step explanation:
Given that the volume of a rectangular prism is given by the formula V = lwh, what is the value of V if l = 7 cm, w = 5 cm, and h = 4 cm?
Answer:
140cm3
Step-by-step explanation:
v=lwh=7*5*4=140cm3
Answer:
140cm3
Step-by-step explanation:
v=lwh=7·5·4=140cm^3
Solve the following proportion. P/6 = 7/8
A: P=5.25
B: P=8
C: P=10.5
D: P=42
Answer:
A
Step-by-step explanation:
given [tex]\frac{P}{6}[/tex] = [tex]\frac{7}{8}[/tex]
using the method of cross- multiplication then
8P = 42 ( divide both sides by 8 )
P = [tex]\frac{42}{8}[/tex] = 5.25
En una carrera benéfica reciben premios los primeros clasificados,de forma inversamente proporcional a la posición de la llegada la meta. En total se reparten 9460€ ¿Qué cantidad corresponderá a cada uno?
Answer:
que ??????????????????????
Step-by-step explanation:
Frosty has traveled 2/3 of the way down Santa Claus lane.The lane is 336 feet long.How many feet has Frosty traveled?
We can multiply 336 by 2/3 to find out.
2/3(336)
To make this easier, we can change 336 to 336/1, which does not change it's value.
Multiply 336 by 2.
336 * 2 = 672
Multiply 1 by 3.
1 * 3 = 3
Our new value is 672/3
Evaluate, divide both sides of the fraction by 3.
672/3 = 224.
3/3 = 1
224/1
224/1 = 224
Frosty has traveled 224 feet.