we have
[tex]10x^{2}y+ 25x^{2}[/tex]
we know that
[tex]10=2*5\\25=5*5[/tex]
substitute
[tex](2*5)x^{2}y+ (5*5)x^{2}[/tex]
Factor [tex]5x^{2}[/tex]
[tex](5x^{2})(2y+ 5)[/tex]
therefore
the answer is
[tex](5x^{2})(2y+ 5)[/tex]
The equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)
What are equivalent expressions?Equivalent expressions are expressions that have equal values
The expression is given as:
10x^2y + 25x^2
Factor out 5x^2 from the expression
5x^2(2y + 5)
Hence, the equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)
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sally has scores of 88, 92, 80, and 96. find the score she must make on the next exam to have an average of 90
calculate the length of the hypotenuse
hypotenuse =sqrt( a^ + b^
10^2 = 100
14^2 = 196
196+100 = 296
sqrt(296) = 17.20
Answer is D. 17.20
4000 is 1/10 as much as what number
To find a number that is 1/10 as much as 4000, you would multiply 4000 by 10, resulting in 40000.
To find the number that is 1/10 of 4000, you need to divide 4000 by 1/10, which is the same as multiplying by its reciprocal, 10.
Step 1: Write down the expression:
Let ( x ) be the number we're looking for.
Step 2: Set up the equation:
[tex]\[ x = \frac{4000}{\frac{1}{10}} \][/tex]
Step 3: Multiply by the reciprocal:
x = 4000 \times 10
Step 4: Solve:
x = 40000
So, the number that is 1/10 as much as 4000 is 40000.
Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5... ?
Answer:
-6.5n+14.5 and 8,f(n+1)=f(n)-6.5
Step-by-step explanation:
a real estate developer is looking to find help fund a new condo complex.he promises 145% return on investment in four years. if youre interested in investing $30,000 and the developer follows through on his promise, how much money will you get back in four years?
If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the refrigerator if it released 492J of energy to the room? Joules
How many numbers are 10 units from 0 on the number line? Type your answer as a numeral.How many numbers are 10 units from 0 on the number line?
Answer:
10 number
Step-by-step explanation:
A number line is a straight horizontal line which shows integers. Center of number line is 0.
Left side of 0 is negative integers or numbers
Right side of 0 is positive integers or numbers
" 10 units from 0 on number line"
It would be either left side or right side.
So, number will be -10 or 10.
Please have a look in attachment for number line.
So, 10 number from 0 on number line either left or right side.
What scale of measurement is being used when a teacher measures the number of correct answers out of 50 on a quiz for each student?
If the force is f=-30 units and the acceleration is a=6 units, find the mass, m
Use the diagram to find the value of x?
147 32 33 150
A town's population is 43,200. About 100 people move out of the town each month. Each month, 125 people on average move into town. A nearby town has a population of 45,000. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be equal?
Why i hundred 4 tens and 14 tens name the same number
The force of an object (f) is equal to its mass (m) times its acceleration (a). Thus, the formula for calculating force is f = ma.
Based on this information, which of the following equations would be used to calculate acceleration?
A. a = fm B. a = f + m C. a = f − m D. a = f ÷ m
Answer:
D. [tex]a=f\div m[/tex].
Step-by-step explanation:
We are given that force of an object and we have to find the equation would be used to calculate the acceleration
Mass of object=m
Acceleration of an object= a
Force of an object=f
We are given that force of an object is equal to its mass times its acceleration.
Therefore , the formula for calculating force
f=ma
Because we are given this formula
Now , we have find the equation which is used to calculate acceleration
Then by division property of equality we have
[tex]a=f\div m[/tex]
Hence, the equation would be used to calculate acceleration [tex]a=f\div m[/tex].Therefore, option D is true.
In triangle FGH, GJ is an angle bisector of ∠G and perpendicular to FH.
What is the length of FH?
___ units
we know that
in the right triangle FGJ
[tex]cos(FGJ)=\frac{GJ}{FG}= \frac{GJ}{3x-8}[/tex] ----> equation A
in the right triangle GJH
[tex]cos(JGH)=\frac{GJ}{GH}= \frac{GJ}{16}[/tex] ----> equation B
m∠(FGJ)=m∠(JGH) ------> because GJ is an angle bisector of ∠G
so
equate equation A and equation B
[tex]\frac{GJ}{3x-8}=\frac{GJ}{16}\\ 3x-8=16\\3x=24 \\x=8\ units[/tex]
that means
[tex]FG=3*8-8=16\ units[/tex]
[tex]FG=GH[/tex]-------> the triangle FGH is an isosceles triangle
hence
[tex]FJ=JH\\FJ=8\ units[/tex]
[tex]JH=8\ units[/tex]
[tex]FH=FJ+JH=8+8=16\ units[/tex]
therefore
the answer is
[tex]FH=16\ units[/tex]
thw ration of two elements prontons is equivalent to 3 to 1. What are those two elements? A) gold to tin B)nein to tin C) platinum to iron D) silver to gold
Given the number 456789abh, list out its byte value in little-endian order
The little-endian byte value of 456789abh is 0xab896745, listed in reverse order of its hexadecimal representation.
To represent the number 456789abh in little-endian byte order, we break it into bytes (8 bits each) and reverse their order:
456789abh = 0x456789ab
In little-endian order:
- 0xab
- 0x89
- 0x67
- 0x45
So, the little-endian byte value of 456789abh is 0xab896745.
Describe sets of two or more matching integer cards that satisfy the criteria in each part below:
a. Cards increase the score by eight points.
b. Cards decrease the score by 9 points.
c. Removing cards that increase the score by 10 points.
d. Positive cards that decrease the score by 18 points.
Answer:
a. Removing two (-4)'s
b. Picking up three (-3)'s or removing three 3's
c. Removing two (-3)'s and one (-4)'s
d. Removing three 5's and one 3's
Step-by-step explanation:
Cards available: 5, -3, -4, & 3
a. Score can be increased picking up positive cards or removing negative cards.
b. Score can be decreased picking up negative cards or removing positive cards.
c. As stated before, in order to increase the score removing cards, positive cards have to be removed.
d. As stated before, in order to decrease the score with positive cards, those cards have to be removed.
Anyone knows the answer
In calculating the monthly payment for a five-year loan, what value should be used for n, the number of periods over which the loan is repaid, as it appears in the following formula? 2007-10-03-00-00_files/i0060000.jpg a. 5 b. 12 c. 60 d. 120
Answer:
The answer is: c. 60.
Step-by-step explanation:
To calculate the monthly payment for 5 years, the 12 months of 1 year should be multiplied by the 5 years of the duration, which is equal to 60 = 5 x 12.
The answer is: c. 60.
Round 527 to the nearest hundred
Pamela wants to buy a suitcase whose dimensions are 1 1/2 times those of her 28 times 16 times 8 inch suitcase. How is the ratio of the volumes related to the ratio of corresponding dimensions? What is the ratio of the volumes?
Thus the required ratio is 3.375
Pamela wants to buy a suitcase whose dimensions are 1 1/2 times of her 28 times 16 times 8 inch suitcase.
What is the ratio of the volumes?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
volume of former suitcase = 28 x 16 x 8
=3584 cubic inches
volume of latter suitcase
=1.5x28 x1.5x16 x1.5x8
=12096
ratio of volumes
= 12096/3584
=3.375
Thus the required ratio is 3.375 of volumes of suitcase.
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graph of the quadratic function f(x)=‒(x+4)(x‒6) is shown on the coordinate grid below.
Which statement is not true?
A.
The maximum of this function occurs when y=25.
B.
The function increases in the interval 1 to 6.
C.
The has a zero at (‒4,0).
D.
The function positive in the interval ‒4 to 6.
Answer:
Option B is not true.
Step-by-step explanation:
The quadratic function is f(x) = -(x + 4)(x - 6)
Now we check each option given
Option A.
It is clear from the graph function is maximum at y = 25.
TRUE.
Option B.
Function increases in the interval 1 to 6.
Let's check this at x = 2 and x = 3
f(2) = -(2 + 4)(2 - 6)
= -(6)(-4)
= 24
f(3) = -(3 + 4)(3 - 6)
= - (7)(-3)
= 21
So we find this function is decreasing in this interval.
So the given option is FALSE.
Option C.
The function has a zero at (-4, 0)
f(-4) = -(-4 + 4)(-4 + 6) = 0
So the function has a zero at (-4, 0).
Option is True.
Option D.
The function is positive in the interval -4 to 6
f(x) = -(x + 4)(x - 6)
f(-3) = -(-3 + 4)(-3 - 6)
= -(1)(-9)
= 9
f(0) = -(0 + 4)( 0 - 6)
= 24
Therefore, this function is positive in this interval so the option is TRUE.
Option B is not true.
At the beginning of a bake sale mary set aside 4 pies for herself karen bought half of the remaining pies for her birthday party and 5 more pies were sold during the sale. When the sale was over there were 19 pies remaining. How msny pies were there before the bake sale started
There were 52 pies before the bake sale started as per the provided condition.
Let's break down the information given step by step:
At the beginning of the bake sale, Mary set aside 4 pies for herself. So, the number of remaining pies is the total number of pies minus 4.
Karen then bought half of the remaining pies for her birthday party. This means the number of remaining pies is now half of the previous remaining pies.
Next, 5 more pies were sold during the sale. Therefore, the number of remaining pies is further reduced by 5.
Finally, when the sale was over, there were 19 pies remaining.
Let's use variables to solve the problem. Let's say the initial number of pies before the sale started is "x."
After Mary set aside 4 pies, the number of remaining pies is (x - 4).
Karen bought half of the remaining pies, so the number of remaining pies becomes (x - 4)/2.
5 more pies were sold, reducing the number of remaining pies to (x - 4)/2 - 5.
According to the given information, (x - 4)/2 - 5 equals 19.
Now, we can solve the equation to find the value of x:
(x - 4)/2 - 5 = 19
Simplifying the equation, we have:
(x - 4)/2 = 24
(x - 4) = 48
x = 52
Therefore, there were 52 pies before the bake sale started.
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Indicate the equation of the given line in standard form. The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and S(5,5)
The equation of the perpendicular bisector of the segment with endpoints R(-1,6) and S(5,5) is found by calculating the midpoint, slope, and using the negative reciprocal for the perpendicular slope. It is then written in point-slope form and converted to standard form, resulting in 12x - 2y = 13.
Explanation:To find the equation of a line that is the perpendicular bisector of a segment with endpoints R(-1,6) and S(5,5), we need to take the following steps:
Determine the midpoint of the segment RS which will be a point on our bisector.Calculate the slope of the line segment RS.Find the negative reciprocal of the slope from step 2, which will give us the slope of our perpendicular bisector.Write the equation of the bisector line using the point-slope form and then convert it into standard form.The midpoint of RS is given by ((-1+5)/2, (6+5)/2) = (2, 5.5). The slope of RS is (5-6)/(5-(-1)) = -1/6. The negative reciprocal of -1/6 is 6. Thus, the slope of our bisector is 6.
Using the point-slope form with the midpoint, y - 5.5 = 6(x - 2). Expanding and rearranging to standard form, we get:
6x - y = 12 - 5.5 -> 6x - y = 6.5.
Multiplying through by 2 (to clear the decimal), we obtain:
12x - 2y = 13, which is the standard form equation of the perpendicular bisector of segment RS.
Ricky is taking out a personal loan for $12,000 to remodel his kitchen. He would like the lowest monthly payment possible, even if it means a bigger finance charge in the end. His bank has offered him a loan at 13% interest for 36 months or 12% interest for 60 months, both of which are compounded monthly. Which of the following statements most accurately describes what Ricky should be thinking? a. More payments with the 60 month loan will give him the lowest monthly payment. b. Fewer payments with the 36 month loan will give him the lowest monthly payment. c. The 60 month loan comes with a bigger finance charge and, thus, a bigger monthly payment. d. The 36 month loan comes with a bigger finance charge and, thus, a bigger monthly payment.
Answer : The correct Option is A.
Step-by-step Explanation :
To solve this we are going to use the monthly payment formula:
[tex]\text{Payment = }\frac{Rate\times Principal}{1-(1+Rate)^{-n}}}[/tex]
where, Principal is the amount of the loan
n is the number of periods.
Option A. 13% interest for 36 months compounded monthlyRicky is taking out a personal loan for $12,000 and term of the loan is 36 months ⇒ n = 36. To find the rate per period, we first need to convert the interest rate to decimal form ⇒ Rate = 0.13.
Now since the bank is charging him the interest rate for the 36 months, we just need to divide the interest rate (in decimal form) by the number of months (36) to find the rate per period
[tex]\implies\text{Rate per period = }\frac{0.13}{36}[/tex]
So, putting all these values in the formula, We get monthly payment of loan A = $356.07
Option B : 12% interest for 60 months compounded monthlyinterest rate in decimal form = 0.12
By replacing the values in formula the monthly payment of loan B is $212.44
Option C and Option D are obviously denied as the financial charge is not effected by the monthly payments so ricky will not be thinking about the financial charge.Now, Monthly payments of loan B are significantly low than that of monthly payments of loan A.
So, we can conclude that the correct answer is a. More payments with the 60 month loan will give him the lowest monthly payment.
Answer:
A
Step-by-step explanation:
Graph the following lines and write the equation in slope-intercept form. Through the point (−8,1) with a slope of 3.
A 180 day $3 million negotiable cd has a 4.25% annual rate quote. if you buy the cd, how much will you collect in 180 days?
Solve the equation.
3(k−6) = 15
k = ____?
3.74 rounded to the nearest
hundredth
Solve the following system by the substitution method. Check the solution(s). 0.1x+0.2y=-0.6 and 0.6x-0.3y=2.3