Answer:
x = 10
Step-by-step explanation:
Begin by factorising the numerator/ denominator of the left side
x² - 14x + 49 = (x - 7)² ← perfect square
x² - 49 = (x - 7)(x + 7) ← difference of squares
Thus left side becomes
[tex]\frac{(x-7)^2}{(x-7)(x+7)}[/tex] → x ≠ ± 7
Cancel (x - 7) on numerator/denominator, leaving
[tex]\frac{x-7}{x+7}[/tex]
Returning to the equation, that is
[tex]\frac{x-7}{x+7}[/tex] = [tex]\frac{3}{17}[/tex] ( cross- multiply )
17(x - 7) = 3(x + 7) ← distribute both sides
17x - 119 = 3x + 21 ( subtract 3x from both sides )
14x - 119 = 21 ( add 119 to both sides )
14x = 140 ( divide both sides by 14 )
x = 10
The left and right page numbers of an open book are two consecutive integers whose sum is 519. Find these page numbers.
Answer:
The answer is 259 and 260
Step-by-step explanation:
519/2= 259.5
259+260=519
The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represented by the shaded region?
Answer:
The fraction of the area of ACIG represented by the shaped region is 7/18
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
In the square ABED find the length side of the square
we know that
AB=BE=ED=AD
The area of s square is
[tex]A=b^{2}[/tex]
where b is the length side of the square
we have
[tex]A=49\ units^2[/tex]
substitute
[tex]49=b^{2}[/tex]
[tex]b=7\ units[/tex]
therefore
[tex]AB=BE=ED=AD=7\ units[/tex]
step 2
Find the area of ACIG
The area of rectangle ACIG is equal to
[tex]A=(AC)(AG)[/tex]
substitute the given values
[tex]A=(9)(10)=90\ units^2[/tex]
step 3
Find the area of shaded rectangle DEHG
The area of rectangle DEHG is equal to
[tex]A=(DE)(DG)[/tex]
we have [tex]DE=7\ units[/tex]
[tex]DG=AG-AD=9-7=2\ units[/tex]
substitute[tex]A=(7)(2)=14\ units^2[/tex]
step 4
Find the area of shaded rectangle BCFE
The area of rectangle BCFE is equal to
[tex]A=(EF)(CF)[/tex]
we have
[tex]EF=AC-AB=10-7=3\ units[/tex]
[tex]CF=BE=7\ units[/tex]
substitute
[tex]A=(3)(7)=21\ units^2[/tex]
step 5
sum the shaded areas
[tex]14+21=35\ units^2[/tex]
step 6
Divide the area of of the shaded region by the area of ACIG
[tex]\frac{35}{90}[/tex]
Simplify
Divide by 5 both numerator and denominator
[tex]\frac{7}{18}[/tex]
therefore
The fraction of the area of ACIG represented by the shaped region is 7/18
Answer:
7/18
Step-by-step explanation:
12080 gallons per month into liters per hour. please write out the correct conversions too to figure it out. thanks (:
Answer: 16.54 liters an hour
Step-by-step explanation:
A month into hours is 730.001 hours
12080 / 730.001 = 16.54 liters an hour.
what is the volume of the sphere shown below with a radius of 3
Answer:
The answer to your question is: letter A
Step-by-step explanation:
Data
radius = 3
Formula
V = (4/3)πr³
V = (4/3) π (3)³ = Substitution
V = (4/3) π (27) Simplify
V = 108π / 3
V = 36 π u³
A. The volume of the sphere is 36[tex]\pi[/tex] cubic units.
What is formula of volume of sphere ?Let, r be the radius of the sphere.
Then the volume of the sphere = [tex]\frac{4}{3}\pi r^{3}[/tex] cubic units
What is the required volume ?Given radius of sphere (r) = 3 units
So, the volume of sphere = [tex]\frac{4}{3}\pi r^{3}[/tex] cubic units
= [tex]\frac{4}{3}\pi *3^{3}[/tex] cubic units
= [tex]\frac{4}{3}*27\pi[/tex] cubic units
= [tex]36\pi[/tex] cubic units
Learn more about volume of sphere here :
https://brainly.com/question/27007326
#SPJ2
Write an exponential growth function and explain the growth pattern it models. Use complete sentences?
The function which grows or decreases at a constant % growth rate is known as an exponential function, and further discussion can be defined as follows:
This equation can be written as [tex]\bold{ f(x) = a(1 + r)^x\ or\ f(x) = ab^x}[/tex], where [tex]\bold{b = 1 + r}[/tex].These functions were frequently used to represent real-world applications.These bacterial growth & decay, demographic growth or decline, and compound interest.Growth curve modeling is a statistical technique for examining change over time using observational studies.Learn more:
brainly.com/question/12101306
is the function even, odd, or neither?
Please help me idk this
Answer:
it would be 2.8150
Step-by-step explanation:
since there is a one in the tenths place it rounds down to 0 with makes it 50
find the quotient of 144 and 12
Answer:
The answer is 12
Step-by-step explanation:
12 can go into 14 one time and 12 goes into 24 twice
Answer: 144 divided by 12 = 12
Step-by-step explanation:
What is the solution to this equation
x +8=-3
Answer:
Step-by-step explanation:
x+8=3
X=-3-8= -11
X=-11
minus the 8 over and the answer will be -11
Answer:
{X:X=-11}
Step-by-step explanation:
It is done by making x the subject in that relation. Thus grouping of like terms.
the equation then becomes ;
x=-3-8
since moving a positive number to the = sign gives a negative number.
-3-8= -11
Therefore ,{x:x=-11} is the solution
Order from least to greatest.
34%, 4/15, 0.3
Today we are ordering. To do this, I recommend you to convert to either decimal or fraction. Let's go with fractions, cause why not.
To order, make 0.3 into 3/10 because 3 is 3 of 10. We make 34% as 17/50 since 1% equals 1/100.
Reorder:
17/50, 4/15, 3/10. All fractions here can be x/750.
Reorder:
225/750, 200/750, 225/750.
As you see, there are two 225s. It's okay of however you write it as. We also have to remember that the question has to be using 34%, 4/15, and 0.3.
Answer: 4/15, 17/50, 0.3 is the answer.
2x+y=4________(1) and x²+xy=-2_______(2) solve this simultaneously find X and Y
Answer:
[tex][2 - \sqrt{6}, 2\sqrt{6}] \\ [2 + \sqrt{6}, -2\sqrt{6}][/tex]
The work is shown above.
I am joyous to assist you anytime.
a. 2.95 + 18.3 +11
b.9.2 - 0.375
c. 0.275 + 27.5
d. 90 - 0.903
Answer:
a. 32.25
b. 8.825
c. 27.775
d. 89.097
A man caught a fish. It weighed 5/7kg + 5/7 its own weight what did it weigh
Use multiplication and the Distributive Property to find the quotient. 96 divided by 6?
Answer:
6/96 is 16
Step-by-step explanation:
so the answer is 16
Answer:
16
Step-by-step explanation:
Given are two numbers 96 and 6.
We have to divide the first number by the second number using multiplication and distributive property.
Let us write
[tex]96 =60+36\\96 =6(10+6)\\[/tex]
Thus we find using multiplicative and distributive property
6 when multiplied by 16 gives 96
So quotient is 16.
A company packs boxes at a constant rate of 3/4 of a box every of a box every
1/2 minute. What is the number of boxes per
A company packs boxes at a constant rate of
minute the company packs?
Answer:
1 1/2 boxes per minute
Step-by-step explanation:
The company packs boxes at a rate of 3/4 of a box every 1/2 minute. By multiplying this rate by the reciprocal of the time (2/1), we find that the company packs 1.5 boxes per minute.
The student's question involves finding out the rate at which a company packs boxes. The company packs boxes at a constant rate of 3/4 of a box every 1/2 minute.
To find how many boxes are packed per minute, we need to adjust the given rate to reflect the number of boxes packed in one full minute. We can do this by dividing the number of boxes (3/4) by the fraction of the minute (1/2) during which they are packed.
Here's a step-by-step explanation:
Multiply the number of boxes by the reciprocal of the time fraction: (3/4) × 2/1.Simplify the result: 3/4 × 2 = 6/4, which reduces to 3/2 or 1.5.Therefore, the company packs 1.5 boxes per minute.
A large multiplex movie house has many theaters. The largest theater has 44 rows. There are 20 seats in the first row. Each row has four seats more than the previous row. How many total seats are there in this theater?
The total number of seats in this movie theater is 4224. This is calculated using the sum of an arithmetic series formula.
Explanation:The question describes an arithmetic sequence where each row in the theater has four more seats than the previous row. The first row has 20 seats and the last row (44th row) has[tex]20 + 4*(44-1) = 172[/tex] seats. The total number of seats in this theater is therefore the sum of an arithmetic series formula, which is given by:
[tex]S = n/2 * (a + l)[/tex]
Where:
S is the sum of the sequence n is the number of terms a is the first term l is the last term
So for the number of seats, we have:
[tex]S = 44/2 * (20 + 172) = 22 * 192 = 4224.[/tex]
So, the total number of seats in the theater is 4224.
Learn more about Arithmetic Series here:https://brainly.com/question/16415816
#SPJ3
Convert 65,000,000 to scientific notation.
Answer:
6.5 x 10^7. PLEASE MARK BRAINLIEST IF THIS HELPS.
Step-by-step explanation:
Well, its kind of hard to explain but i'll do my best.
65,000,000 has six zeros, and in order to get the answer, you have to put the answer into a decimal. So all you have to do is put the decimal right here. 65000000.< Hope that makes sense. Then all you have to do is move that decimal to the left however many times is needed to make the answer a decimal (in this case it is 7 times). Which makes the answer 6.5 but your not done yet, then, since you had to move to the left seven times in order to get your decimal, that means the second part of your answer is 10^7, (10 to the seventh power) since you moved seven times. Example: if you had had to move to the left 9 times to get your decimal, then it would have been 10^9, if that makes any sense. So that means your final product would be 6.5 x 10^7
Answer: 6.5 x [tex]10^{7}[/tex]
Step-by-step explanation: To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.
In this case, we can write 65,000,000 as 6.5000000 and notice that there is only one digit to the left of the decimal point.
Next, we count the number the number of places the decimal point would need to move in order to get back to our original number which is 65,000,000. In this case, we would need to move the decimal point 7 places to the right in order to get back to our original number. Since we would need to move the decimal point 7 places to the right to get back to our original number, this would mean that we have an exponent of 7.
Therefore, 65,000,000 can be written in scientific notation as 6.5 x [tex]10^{7}[/tex]
Sally was 200 apples she Eliot’s all of them up in 39 how many apple slices would she have now
Answer:
I don't know the question but I think you mean something that has to do with multiplication
Step-by-step explanation:
If you have 200 apples and you cut them up into 39 slices each there is now 39 slices for each of those. You now have 200 x 39 slices. So, to simplify it you have 7800 apple slices
Topic: Multiplication
which property is shown? 4/5+(-4/5)=0
Answer:
Inverse Property
Step-by-step explanation:
Any number X plus the negative of itself = 0
Use the properties of addition to simplify 2d + 2 - 7f+ 4d - f.
Answer:
6d - 8f + 2
Step-by-step explanation:
What is my number?
Clue 1 My number is a multiple of 2 and 7.
Clue 2 My number is less than 100 but greater than 50.
Clue 3 My number is the product of three different prime numbers.
Answer:
56 is the correct answer
Step-by-step explanation:
50<X<100 it could be 56,70,84,98
56=2*7*5 V
70=2*7*6 X
84=2*7*7 X
98=2*7*8 X
The number that satisfies all the given clues is 84.
Explanation:The number that satisfies all the given clues is 84.
Clue 1: The number is a multiple of 2 and 7. The least common multiple of 2 and 7 is 14. So, any multiple of 14 will be a valid answer.Clue 2: The number is less than 100 but greater than 50. 84 satisfies this condition.Clue 3: The number is the product of three different prime numbers. Prime factorizing 84 gives 2 × 2 × 3 × 7, which are different prime numbers.Therefore, the number that meets all the given clues is 84.
Learn more about Number Determination here:https://brainly.com/question/2193783
#SPJ2
Attached image please help
3.3 x 10^(5) + 44,000 = 144,003.3
The decimal number written in scientific notation is 1.44 x 10^(5).
Answer:
3.74 × [tex]10^{5}[/tex]
Step-by-step explanation:
Given
3.3 × [tex]10^{5}[/tex] + 44000
= 3.3 × [tex]10^{5}[/tex] + 4.4 × [tex]10^{4}[/tex] ← factor out [tex]10^{4}[/tex]
= [tex]10^{4}[/tex]( 3.3 × [tex]10^{1}[/tex] + 4.4)
= [tex]10^{4}[/tex](33 +4.4)
= [tex]10^{4}[/tex] × 37.4
= [tex]10^{4}[/tex] × 3.74 × [tex]10^{1}[/tex]
= 3.74 × [tex]10^{(4+1)}[/tex]
= 3.74 × [tex]10^{5}[/tex]
BRAINLIEST!!!!!!!!!!!!!!!
Answer:
all the ekements of set A lies in set B
Answer: were is the question and how do you put down brainliest
Step-by-step explanation:
how many times does 26 go into 80
Answer:
80/26 = 3.07
Step-by-step explanation:
Answer: 3 times!
Step-by-step explanation:
80 divided by 26 is 3.07 but you can round it to 3
Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. how many liters of each does he need to make the needed 30 liters of 60% acid solution?
To make 30 liters of a 60% solution from 40% and 70% solutions, set up two simultaneous linear equations representing volume and concentration; solve them to find the required volumes.
Explanation:To solve the question posed by Gabe, a nuclear physicist, we will need to use the concept of mixtures in Mathematics. The total volume he needs is 30 liters of a 60% acid solution, and he has available 40% and a 70% acid solutions.
The solution to this problem involves setting up two equations, one for the total volume and second for the amount of acid.
Let's denote the volume of the 40% solution by x and the volume of the 70% solution by y. Our first equation based on volume is: x + y = 30 (because total volume needed is 30 liters).
Our second equation represents the fact that the volume times the percentage of acid present (converted to a decimal) for each solution should match up to the total volume times the overall percentage of acid (also converted to a decimal) in the final 60% solution. This gives us: 0.4x + 0.7y = 30*0.6.
Solving these two linear equations simultaneously using methods such as substitution or elimination will give us the value of x and y, which are the required liters of 40% solution and 70% solution respectively.
Learn more about Mixtures here:https://brainly.com/question/12160179
#SPJ2
5 + 3 x 2 - 6 value: 10 what is the answer
Answer:
10
Step-by-step explanation:
5+3=8
8×2=16
16-6=10
Write a subtraction expression using integers, whose difference equals -5.
-3+ -2= -5
same sign add
-7 + 2 = -5
different signs subtract and keep the sign of the BIGGER number
Last month haos dog ate 40 cans of dog food in 30 days how many cans hao buy to feed his dog for the next 6 days?
If y= -7 when x= -3, find y when x=9
if i am right you would multiply x= -3 by -3 and you get 9 so you would do the same thing to the y as well so y= -7 and you multiply it by -3 and then y= 21
State a true conclusion.
1) If B is between A and C then AB + BC = AC.
2) Q is between R and S.
Conclusion
Answer: QR + RS = QS
Step-by-step explanation:
Answer:
Step-by-step explanation: