Answer:
There are 7 copies of 2 and 1 copy of 11 in the product:
1408 = 2^7×11
Step-by-step explanation:
Factor the following integer:
1408
The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:
1408 = 2 704:
1408 = 2×704
The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:
704 = 2 352:
1408 = 2×2×352
The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:
352 = 2 176:
1408 = 2×2×2×176
The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:
176 = 2 88:
1408 = 2×2×2×2×88
The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:
88 = 2 44:
1408 = 2×2×2×2×2×44
The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:
44 = 2 22:
1408 = 2×2×2×2×2×2×22
The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:
22 = 2 11:
1408 = 2×2×2×2×2×2×2×11
11 is not divisible by 2 since 11 is odd and 2 is even:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)
The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)
The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)
Divide 7 into 11:
| | 1 | (quotient)
7 | 1 | 1 |
- | | 7 |
| | 4 | (remainder)
11 is not divisible by 7:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)
No primes less than 11 divide into it. Therefore 11 is prime:
1408 = 2×2×2×2×2×2×2×11
There are 7 copies of 2 and 1 copy of 11 in the product:
Answer: 1408 = 2^7×11
Final answer:
The prime factorization of 1408 is 2 raised to the power of 7 multiplied by 11, represented as 2^7 × 11. This is found by repeatedly dividing 1408 by 2 until we are left with the prime number 11, which cannot be divided further.
Explanation:
The prime factorization of 1408 involves breaking down the number into its prime factors until all the factors are prime numbers. To find the prime factors of 1408, we can use a factor tree or the method of division. We can start by dividing 1408 by the smallest prime number that divides it evenly, which is 2. If we keep dividing by 2, we get the following sequence of divisions:
1408 ÷ 2 = 704
704 ÷ 2 = 352
352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
Since 11 is a prime number, we cannot divide any further. Therefore, the prime factorization of 1408 is 27 × 11, since 2 was divided 7 times and 11 is the last prime factor found.
A family has a net income of $ 3100 per month and an entertainment budget of $ 399 per month. What percentage of their monthly income is spent on
entertainment?
% of their monthly income is spent on entertainment. (give your answer to the nearest 0.1 %).
Answer:
12.87%
Step-by-step explanation:
To identify the % of their monthly income is spent on entertainment we use following formula
Total Budget of Entertainment / Total Net Income
$399/$3,100*100
12.87%
What is the slope of a line that is parallel to the line containing (-11, 5) and (-6, 1)?
Answer:
(5-1)/-11-(-6) = -4/5
Step-by-step explanation:
since the lines are parallel they have same slope/gradient
Answer:
-4/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-5)/(-6-(-11))
m=-4/(-6+11)
m=-4/5
How do I round up one number ow do I round up one numder
Well, when your rounding by ones, if the ones place is lower than 5, round lower. Like for example, 4 is lower than 5. So if you have 5,784, you have to round that 4 down to a 0. So it would be 5,780.
if it's higher that 5, like 7, you round up. Like for example, 507, you round it to 10, so 510.
Rounding up numbers involves looking at the digit to be dropped: if it's 5 or above, round up the last retained digit. Several examples like 31.57 up to 32 and 8.1649 down to 8.16 illustrate this process.
Explanation:Rounding up a number involves several steps. Let's take a few examples:
(a) The number 31.57 rounds up to 32. Here, the dropped digit is 5, and the digit we keep or retain is even. Since our dropped digit is 5 or higher, we add one to the retained digit, thus getting 32.
(b) The number 8.1649 rounds down to 8.16. The dropped digit is 4, which is less than 5, so we do not add any to our retained number, getting 8.16.
These examples demonstrate that we are rounding to the nearest whole number or to certain decimal places depending on the precision needed in the problem. When the digit we are dropping is 5 or above, we round up the previous digit. If it is less than 5, we leave the previous digit as it is.
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The 10th term from the end of the ap 7,10,13....154;157 is?
Answer:
The 10th term from the end of the AP is 39 th term
[tex]\therefore a_{39} =114[/tex]
Step-by-step explanation:
Given:
Arithmetic Sequence as
7 , 10 , 13........154,157
∴ First term = a₁ = 7
Second term = a₂ = 10
∴ Common Difference = d = a₂ - a₁ = 10 - 7 = 3
∴ d = 3
[tex]a_{n} = 157[/tex]
To Find:
[tex]a_{10} = ?[/tex]
Solution:
An equation for the nth term of the arithmetic sequence is given by
[tex]a_{n} =a_{1} + (n-1)\times d[/tex]
Substituting a₁ and d and we get
[tex]157=7+(n-1)\times 3\\150=3n-3\\\\3n=147\\n=\frac{147}{3}\\\\n=49\\[/tex]
There are 49 terms in given AP
Therefore the 10th term from the end will be 39th term
[tex]a_{39} =a_{1} + (39-1)\times 3=7+38\times 3=114[/tex]
[tex]\therefore a_{39} =114[/tex]
Linear programming subjected to constraints
Answer:
The maximum value of C is 14
Step-by-step explanation:
we have the following constraints
[tex]x\geq 0[/tex] ----> constraint A
[tex]y\geq 0[/tex] ---> constraint B
[tex]2x+2y\leq 10[/tex] ---> constraint C
[tex]3x+y\leq 9[/tex] ---> constraint D
Determine the area of the feasible region using a graphing tool
see the attached figure
The vertices of the feasible region are
[tex](0,0),(0,5),(2,3),(3,0)[/tex]
To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertices in the objective function an then compare the results
we have
[tex]C=4x+2y[/tex]
For (0,0) ----> [tex]C=4(0)+2(0)=0[/tex]
For (0,5) ----> [tex]C=4(0)+2(5)=10[/tex]
For (2,3) ----> [tex]C=4(2)+2(3)=14[/tex]
For (3,0) ----> [tex]C=4(3)+2(0)=12[/tex]
therefore
The maximum value of C is 14
10. Alex is writing a number in scientific
notation. The number is greater than one
million and less than ten million. Which
number will Alex use as the exponent
of 10?
A 8
B 7
C 6
D 5
Answer:
C. 6
Step-by-step explanation:
Since the number is greater than one million and less than ten million, the number is seven digit which ranges from two million to nine million
Therefore, Alex will use 6 as the exponent
A sofa and a love seat together cost $1500. The sofa costs double the love seat. How much do they each cost?
Answer:
I think its 500 each or its Love seat=500. Sofa=1000
Step-by-step explanation:
For 500 you would do 1500/3 because sofa is double+love seat. So each would cost 500 if you divide it by 3. So the sofa would be 1000. The love seat would be 500. 1000+500=1500.
Hope this helps!!
Final answer:
To determine the cost of the sofa and love seat, we create an equation from the given information. Solving for x, we find that the love seat costs $500 and the sofa, costing double, is $1000.
Explanation:
To solve the problem in question, let's call the cost of the love seat x. According to the information given, the sofa costs double the love seat, so the sofa's cost will be 2x. Together, the sofa and love seat cost $1500, which gives us the equation:
x + 2x = $1500
Combining like terms, we get:
3x = $1500
To find the value of x, we divide both sides of the equation by 3:
x = $1500 / 3
x = $500
This means the love seat costs $500. To find the cost of the sofa, we multiply the cost of the love seat by 2:
2x = 2 * $500
2x = $1000
Therefore, the sofa costs $1000, and the love seat costs $500.
what is 2940 divided by 8
367.5, there are 367.5 8's in 2,940.
Hope this helps, if not, comment below please!!!!
Answer:
365.7
Step by step solving:
Is 7- y=5x+11 a standard form
Answer:
No.
Step-by-step explanation:
Because standard form is ax+by=c.
Evaluate n+13 for n=24
Answer: 37
Step-by-step explanation:
if n=24
n+13 becomes 24+13
24+13 = 37
The value of the expression is 37.
ExpressionAn expression in mathematics is a set of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
How to evaluate an expression?Given the expression n+13
Substitute the value of n the given expression.
24+13 = 37
Hence the value is 37.
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Tony’s fish weighs five pounds more than three times the weight of Mary’s fish. Let t represent the weight of Tony’s fish, and let m represent the weight of Mary’s fish.
Which expression below best represents the weight of Tony’s fish?
t = 5 + 3m is the required expression that represents weight of Tony fish
Solution:Let "t" represent the weight of Tony’s fish, and let "m" represent the weight of Mary’s fish
To find: expression that represents the weight of Tony's fish
According to given information,
Tony’s fish weighs five pounds more than three times the weight of Mary’s fish
Here the word "times" represents multiplication and "more than" represents addition
Weight of Tony fish = 5 + three times the weight of Mary’s fish
Weight of Tony fish = 5 + 3(m)
t = 5 + 3m
Thus the required expression is found out
first term 2 common difference 13
Answer:
With the first term is 2 and common difference is 13 then the series is 2,15,28,...
Step-by-step explanation:
Given first term is 2 and common difference is 13.
Arithmetic progression:
[tex]a_{1}=2[/tex] and d=2 [given]
Therefore we can find arithmetic series [tex]a_{1},a_{2},a_{3},...[/tex] with [tex]a_{1}=2[/tex] and d=2
d can be written as [tex]d=a_{2}-a_{1}[/tex]. Therefore we can write [tex]a_{2}[/tex] as below:
[tex]a_{2}=a_{1}+d[/tex]
Now substitute the values [tex]a_{1}=2[/tex] and d=2
[tex]a_{2}=2+13[/tex]
[tex]a_{2}=15[/tex]
Similarly we can find [tex]a_{3}[/tex]
d can be written as [tex]d=a_{3}-a_{2}[/tex]. Therefore we can write [tex]a_{3}[/tex] as below:
[tex]a_{3}=a_{2}+d[/tex]
[tex]a_{3}=15+13[/tex]
[tex]a_{3}=28[/tex]
and so on.
Therefore the series is 2,15,28,...
twice the difference of a number and 8 is less than -20
Answer:
2(x-8) < -20
Step-by-step explanation:
Answer:
x = a number
2(x - 8) < -20
For the equations given below, which statement is true?
-3x-8=19
-3x-2=25
A. The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation.
B. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
C. The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation.
OD. The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
Answer:
B
Step-by-step explanation:
If you add 6 to both sides, you get -3x-8+6=19+6 which is then -3x-2=25
what could be the function for this graph in factored form?
Answer:
OPTION A
Step-by-step explanation:
Roots of a function can be determined from the graph by the point which cuts the x - axis.
Here, (-4, 0) and (2, 0) are the points that cut the x - axis.
That means, the roots should have been x = -4, 2.
So, from the options, we see that OPTION A has roots f(x) = (x + 4)(x - 2)².
Since, it is a parabola, we have (x - 2)².
Note that f(-4) = 0 and
f(2) = 0.
Hence, OPTION A is the answer.
The job paid $25 for every 2 hours of work. Write an equation that represents how much the job pays, y, for x hours of work.
We know that we can use y for "how much the job pays" and x for "hours of work."
Let's find how much the job pays in 1 hour by dividing.
25 / 2 = $12.5 per hour
We can mulitply x to 12.5 because this shows how much he earned.
An equation will look like 12.5x = y
Best of Luck!
The job pays $12.50 per hour. The equation to represent the pay, y, for x hours of work is 'y = 12.5x', which depicts direct proportionality.
Explanation:To solve this question, you must first understand that the job pays $25 for every 2 hours worked. Therefore, to find out how much the job pays for x hours of work, you'd simply multiply the rate per hour ($12.50, since $25 divided by 2 is $12.50) by x hours.
The equation that represents how much the job pays, y, for x hours of work is: y = 12.5x.
Here, 'y' denotes the total payment received and 'x' is the number of hours worked. This format is commonly used in equations representing direct proportionality, where one variable (in this case, pay) changes directly as the other (hours worked).
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Write the general equation for the circle that passes through the points (-1,2)(4,2)(-3,4)
Answer:
x² + y² - 3x - 13y + 18 = 0
Step-by-step explanation:
Recall that the general equation of a circle looks something like this:
x² + y² + Ax + By + C = 0
substituting each of the points into the equation we get:
for (-1,2)
(-1)² + (2)² + A(-1) + B(2) + C = 0
1 + 4 -A+2B + C = 0
-A + 2B + C + 5 = 0 ------------ eq 1
for (4,2)
(4)² + (2)² + A(4) + B(2) + C = 0
16 + 4 + 4A + 2B + C = 0
4A + 2B + C + 20 = 0 ------------- eq 2
for (-3,4)
(-3)² + (4)² + A(-3) + B(4) + C = 0
9 + 16 -3A + 4B + C = 0
-3A + 4B + C + 25= 0 ----- eq 3
Now we have a system of equations with 3 equations and 3 unknowns.
Solving for A, B and C, we eventually get:
A = -3, B = -13, C = 18
Substituting these into the general equation:
x² + y² + Ax + By + C = 0
x² + y² - 3x - 13y + 18 = 0
Brian has money in two savings accounts. One rate is 5% and the other is 10%. If he has $900 more in the 10% account and the total interest is $273, how much is invested in each savings account?
Answers:
1220 dollars invested at 5% interest rate.
2120 dollars invested at 10% interest rate.
===============================================
Explanation:
Label the two accounts A and B.
Account A earns 5% interest
Account B earns 10% interest
Brian invests x dollars in account A and x+900 dollars in account B.
Using the formula, i = P*r*t, we can compute the simple interest for both accounts
----------
Start with account A over the course of t = 1 year.
i = P*r*t
i = x*0.05*1
i = 0.05x
then compute the interest for account B (use t = 1 also).
i = P*r*t
i = (x+900)*0.10*1
i = 0.10x + 90
---------
Over the course of 1 year, Brian earns 0.05x dollars in interest with account A and also 0.10x+90 dollars in interest with account B.
In total he earns 0.05x+0.10x+90 = 0.15x+90 dollars in interest.
We're told this amount of interest he earns is $273, so,
0.15x+90 = 273
0.15x+90-90 = 273-90
0.15x = 183
0.15x/0.15 = 183/0.15
x = 1220
This means $1220 was invested at 5% interest.
x+900 = 1220+900 = 2120
and $2120 was invested at 10% interest.
---------
Check:
If you invested $1220 in account A, then you earn
i = P*r*t
i = 1220*0.05*1
i = 61 dollars in interest
If you invest $2120 in account B, then you earn
i = P*r*t
i = 2120*0.10*1
i = 212 dollars in interest
So you get a total of 61+212 = 273 dollars in interest from both accounts. This confirms the two answers.
Final answer:
The question involves setting up a system of equations to find out how much Brian has invested in each of his savings accounts — one with a 5% interest rate and the other with a 10% rate, given that the total interest earned is $273 and the difference in the amount in each account is $900.
Explanation:
Brian has money in two different savings accounts, one with a 5% interest rate and the other with a 10% interest rate. He has $900 more in the account with the higher interest rate, and the total interest earned from both accounts is $273. To solve the problem, we need to set up a system of equations.
Let x be the amount in the 5% account, therefore x + $900 will be the amount in the 10% account. Using the formula Interest = Principal × Rate × Time, and assuming the time is 1 year, we get two equations:
0.05x (interest from the 5% account)0.10(x + $900) (interest from the 10% account)The sum of these two interests is $273, so we have:
0.05x + 0.10(x + $900) = $273Solving the equation, we find that x = $1,220 and x + $900 = $2,120. Therefore, Brian has $1,220 in the account with a 5% interest rate and $2,120 in the account with a 10% interest rate.
Idk how to do this. Someone please help. This is a Geometry Honors class
Answer:
4.0
Step-by-step explanation:
AB / AC = AE / AD
1 / 4.5 = AE / 18
4.5 AE = 18
AE = 4.0
Since BE and CD are parallel, triangles ABE and ACD are similar, meaning their side lengths are proportional.
AC = AB + BC = 1 + 3.5 = 4.5
The proportion of AB to AC (corresponding sides of two similar triangles) is 1 / 4.5
Let x be the variable that represents the unknown length of AE
The proportion of AE to AD (another set of corresponding sides of two similar triangles) is x / 18
Since the triangles are similar, these two proportions must be equal.
1 / 4.5 = x / 18
Cross multiply
4.5x = 18
Divide both side by 4.5
x = 4
The length of AE is 4, no need to round since the answer is already a whole number.
Let me know if you need any clarifications, thanks!
The ratio of two complementary angles is 7:2. What is the measure, in degrees, of the larger angle?
Answer:
The larger angle is 70°
And The smaller angle is 20° .
Step-by-step explanation:
Given as :
The ratio of two complementary angles = 7 : 2
Let The larger angle = 7 x
And The smaller angle = 2 x
Now, According to question
Complementary angle is define as when two angles were added to make right angle i.e 90° are complementary to each other .
So, here
7 x + 2 x = 90°
Or, 9 x = 90°
∴ x = [tex]\dfrac{90^{\circ}}{9}[/tex]
i.e x = 10°
Now, putting the value of x
So, The larger angle = 7 × 10° = 70°
And The smaller angle = 2 × 10° = 20°
Hence, The larger angle is 70°
And The smaller angle is 20° . Answer
Final answer:
The larger angle in a pair of complementary angles with a ratio of 7:2 measures 70 degrees, found by figuring the common ratio as 10 and multiplying it by 7.
Explanation:
To find the measure of the larger angle when two angles are complementary and their ratio is 7:2, we first need to understand that complementary angles add up to 90 degrees. If the ratio of the angles is 7 to 2, we can express this as 7x and 2x for some number x. By adding these two expressions, 7x + 2x, we get the total amount of degrees in complementary angles, which is 90 degrees. Therefore, we have the equation 9x = 90, which we can solve for x by dividing both sides by 9 to get x = 10.
The larger angle, which is 7 parts of the ratio, will be 7x which is 7 times 10, so it is 70 degrees.
8.25+1/4w=10.75 round to nearest 10
The value of w is 10
Solution:
Given equation is:
[tex]8.25 + \frac{1}{4}w = 10.75[/tex]
We have to solve above given equation for "w"
[tex]8.25 + \frac{1}{4}w = 10.75[/tex]
We know that 1 divided by 4 gives 0.25
8.25 + 0.25w = 10.75
Moving 8.25 from L.H.S to R.H.S
0.25w = 10.75 - 8.25
0.25w = 2.5
[tex]w = \frac{2.5}{0.25}[/tex]
w = 10
Thus value of w is 10
What is the slope of (-3,-1) (1,-13)
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-13-(-1))/(1-(-3))
m=(-13+1)/(1+3)
m=-12/4
m=-3
Is 7- y=5x+11 a standard form
Answer:
No.
Step-by-step explanation:
Because standard form is ax+by=c.
Solve the system of equations algebraically. Verify your
answer using the graph.
y = 4x - 5
y=-3
What is the solution to the system of equations?
(1, -3)
in
Answer:
The solution is the point (0.5,-3)
Step-by-step explanation:
we have
[tex]y=4x-5[/tex] ----> equation A
[tex]y=-3[/tex] ----> equation B
Solve the system by substitution
Substitute equation B in equation A
[tex]-3=4x-5[/tex]
Solve for x
Adds 5 both sides
[tex]-3+5=4x[/tex]
[tex]2=4x[/tex]
Divide by 4 both sides
[tex]x=0.5[/tex]
therefore
The solution is the point (0.5,-3)
Verify your answer using the graph
using a graphing tool
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is (0.5,-3)
therefore
The solution is the point (0.5,-3)
see the attached figure
Answer:
Since y= -3, just put that in the equation.
-3 = 4x - 5
+5 +5
2 = 4x
/4 /4
x=1/2
the measure of an angle and it’s supplement are given. Determine the measures of the two angles
Answer:
The sum of any two supplementary angles is 180⁰. If you have been given a task to that one angle measures 120⁰ and have to find its supplement, you will compute as ⇒ 180⁰ - 120⁰ = 60⁰. So, the missing will be 60⁰.
Step-by-step explanation:
As we know that the sum of any two supplementary angles is 180⁰.If we have to get the supplement, all we need is to subtract a given angle from 180.A straight line measure 180⁰.If you have been given a task to that one angle measures 120⁰ and have to find its supplement, you will compute as ⇒ 180⁰ - 120⁰ = 60⁰. So, the missing will be 60⁰.Let us consider the m∠MON = 45⁰, as shown in figure a. As straight line measure 180⁰, and the sum of any two supplementary angles is 180⁰. So, 180⁰ - 45⁰ = 135⁰ ⇒ m∠MOL = 135⁰.
So, the supplement of m∠MON = 45⁰ is m∠MOL = 135⁰.
Keywords: supplementary angle, angle measure
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PLEASE HELP!!! 15 POINTS AND WILL GIVE BRAINLIEST!!!
Two functions are represented in different formats.
Function 1:
x y
−2 −1
0 1
2 3
5 6
Function 2:
Graph of a line passing through the origin and the point begin ordered pair 1 comma 3 end ordered pair.
Which statements are true?
Select each correct answer.
Function 1 has a greater rate of change than function 2.
Function 2 has a greater rate of change than function 1.
Function 1 has a greater y-intercept than function 2.
Function 2 has a greater y-intercept than function 1.
Function 1 has a greater y-intercept than function 2
Step-by-step explanation:
The coordinates of the vertices of quadrilateral ABCD are A(-5, 1), B(-2,5), C(5, 3),
and D(2, -1)
Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is
the slope of BC is
, the slope of CD is
and the
slope of AD is!
Quadrilateral ABCD is
because
Answer:
The slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel.
Step-by-step explanation:
The quadrilateral ABCD has vertices A(-5,1), B(-2,5), C(5,3) and D(2,-1).
Now, slope of line AB = [tex]\frac{5 - 1}{- 2 - ( - 5)} = \frac{4}{3}[/tex]
Slope of line BC = [tex]\frac{3 - 5}{5 - (- 2)} = - \frac{2}{7}[/tex]
Slope of line CD = [tex]\frac{- 1 - 3}{2 - 5} = \frac{4}{3}[/tex]
And slope of DA = [tex]\frac{1 - ( - 1)}{- 5 - 2} = -\frac{2}{7}[/tex]
Therefore, the slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel. (Answer)
Answer:
The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3, and the slope of AD is -2/7. Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.
Step-by-step explanation:
A circle with a radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.
Answer:
The area of the shaded region is 37.70 cm2
Step-by-step explanation:
hoped this helped ;3
Answer:
Area of smaller circle is a = pi times 2^{2} = 4 pi
Area of larger circle is A = pi times {4}^{2} = 16 pi
The area of the shaded region is: 16 pi - 4 pi = 12 pi
and 12 times pi= 37.70 cm2
I will mark brainliest for answering this question.
On a trip to visit relatives you drive 1,115.625 miles over the course of 21
hours and 15 minutes. What was the unit rate of the speed of your vehicle in miles
per hour? Round to the nearest tenth of a mile.
The unit rate of speed is 52.5 miles per hour
Solution:
Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21 hours and 15 minutes
We know that, 1 hour = 60 minutes
21 hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours
So they drive 1115.625 miles in 21.25 hours
To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken
unit rate of speed means miles driven in 1 hour
[tex]\rightarrow \frac{1115.625}{21.25} = 52.5[/tex]
So the unit rate of speed is 52.5 miles per hour
if two angles of a triangle are complementary find the number of degrees in the third angle of the triangle
Answer:
The measure of the third angle is a 90 degrees
Step-by-step explanation:
Let
A and B ----> two complementary angles in a triangle
C ---> the measure of the third angle in a triangle
we know that
If two angles are complementary, then their sum is equal to 90 degrees
so
[tex]A+B=90^o[/tex] ---> equation A
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]A+B+C=180^o[/tex] ----> equation B
substitute equation A in equation B
[tex](90^o)+C=180^o[/tex]
solve for C
subtract 90 degrees both sides
[tex]C=180^o-90^o[/tex]
[tex]C=90^o[/tex]
therefore
we have a right triangle