Answer:
formula: a squared + b squared= c squared
6 squared+ 8 squared= c squared
36+64= c squared
100= c squared
Square root both sides
You get 10= c
Anthony borrowed $15 from his mom to pay for food at the school dance. He bought one snow cone for $3, and then used the rest of his money to buy as many chocolate bars as he could. If chocolate bars cost $0.75, then how many chocolate bars could Anthony buy? Part A Select the correct equation to determine the number of chocolate bars Anthony can buy Part B How many chocolate bars can Anthony buy?
0.75x+3=15
16 chocolate bars
Answer:
a= 15 = 3+ .75c
b= 16 chocolate bars
Step-by-step explanation:
15 = 3 + .75c
c= chocolate bars
to solve for the number of chocolate bars:
subtract three for the snowcone he bought= 12=.75c
then just divide by .75 = 16 = c=16
fiza has 10 coins in a bag
there are three £1 coins and seven are 50 pence coins
fiza takes at random, 3 coins from the bag
work out the probability that she takes exactly £2.50
Answer:
The probability is 63/1000 or 0.063
Step-by-step explanation:
Here, given that she takes 3 coins , we want to calculate the probability that the sum is £2.50
What we simply have to do here is to get the different ways to arrange £2.50 within 3 selections ONLY
we can only have this as;
taking 2 £1 coins and 1 50 pence coins
The probability of taking a £1 coin is 3/10
The probability of taking a 50 pence coin is 7/10
So the probability of 2 £1 coins and 1 50 pence coins will be;
3/10 * 3/10 * 7/10 = 63/1000
help me please quickly
Answer:
(1) 4
Step-by-step explanation:
Isolate x.
[tex]\frac{x-2}{3}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{x-2}{3}[/tex] = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex]
[tex]\frac{x-2}{3}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{x-2}{3}[/tex] × 3 = [tex]\frac{2}{3}[/tex] × 3
x - 2 = 2
x = 2 + 2
x = 4
When dividing fractions, the ________ term becomes the reciprocal.
Neither
First
Second
Both
Answer: Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.
Step-by-step explanation:
When dividing fractions, the second term becomes the reciprocal.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers which implies that 'a' parts of a number 'b'.
Here, a is called the numerator and b is called the denominator.
Let a/b and c/d be the two fractions.
Division of these fractions will result as a/b ÷ c/d.
Now the second term c/d will change into d/c and the operation changed into multiplication.
a/b ÷ c/d = a/b × d/c
For example, let 1/2 and 3/4 are two fractions.
We have to divide 3/4 into 1/2 parts.
The actual operation is 3/4 ÷ 1/2.
But using the reciprocal and change in the operation, we will get it as,
3/4 ÷ 1/2 = 3/4 × 2/1 = 3/4 × 2
Dividing 3/4 into 1/2 parts is same as doubling 3/4.
Hence the second term will become reciprocal in the division of fractions.
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Aditya is celebrating his birthday. He invited his friends. He bought a packet of toffees/candies which contains 120 candies. He arranges the candies such that in the first row there are 3 candies, in second there are 5 candies, in third there are 7 candies and so on.
(a) Find the total number of rows of candies.(i) 12 (ii) 10 (iii) 14 (iv) 8
(b) How many candies are placed in last row? (i) 22 (ii) 21 (iii) 24 (iv) 18
(c) Find the difference in number of candies placed in 7th and 3rd row. (i) 8 (ii) 10 (iii) 12 (iv) 14
(d) If Aditya decides to make 15 rows, then how many total candies will be placed by him with the same arrangement? (i) 200 (ii) 150 (iii) 255 (iv) 210
(e) Find the number of candies in 12th row.(i) 21 (ii) 30 (iii) 25 (iv) 19
Answer:
(a) 10, (b) 21, (c) 8, (d) 255, (e) 25Step-by-step explanation:
(a)Total number of candies = 120
The number of candies in the rows form AP sequence:
3, 5, 7, ...The first term is a=3 and common difference is d=2
Sum of n terms:
S = 1/2n(2a + (n - 1)d)Substitute values and solve for n:
120 = 1/2n(2*3 + 2(n - 1)) 120 = 3n + n² - nn² + 2n = 120n²+ 2n + 1 = 121(n + 1)² = 121n + 1 = 11n = 10Correct choice is (ii) 10
(b) Formula for nth term:
a(n) = a + (n - 1)da(10) = 3 + 9*2 = 3 + 18 = 21 candiesCorrect choice is (ii) 21
(c) Use same formula:
a(7) - a(3) = a + 6d - a - 2d = 4d4d = 4*2 = 8Correct choice is (i) 8
(d) Sum of candies in 15 rows
S(15) = 1/2(15)(2*3 + (15 - 1)*2) = 1/2(15)(6 + 28) = 255Correct choice is (iii) 255
(e) Number of candies in 12th row:
a(12) = 3 + (12 - 1)*2 = 3 + 22 = 25Correct choice is (iii) 25
I need help please what’s the answer?
Answer:
The terms combine into 9x + 17
Step-by-step explanation:
What you need to realise here is that the brackets don't serve any real purpose, as there's no operation being done on their contents as a whole. With that in mind we can simply drop the brackets and group like terms:
(4x + 8) + (5x + 9)
= 4x + 8 + 5x + 9
= 4x + 5x + 8 + 9
= 9x + 17
So the terms combine into 9x + 17
What is the common denominator for ¾ and 9/10?
Answer:
20 so the fractions would be 3/4=15/20 and 9/10=18/20
Step-by-step explanation:
because 4 x 5 = 20 and 10 x 2 = 20
Answer:
LCD=20
Step-by-step explanation:
Approximate these numbers
1. 3.8149
2. 20.6861
To
a. the nearest whole number
b. 1 decimal place
C. 2 decimal places
d. 3 decimal places
Answer:
1)
a. 4
b. 3.8
c. 3.82
d. 3.815
2)
a. 21
b. 20.7
c. 20.69
d. 20.686
Step-by-step explanation:
What is the measure of LKPN
Answer:
wheres the rest
Step-by-step explanation:
Please help! Tysm! Picture of figure is attached.
Reasoning in the diagram at the right, K, L, and M are the midpoints of the sides of AABC. The vertices of the three small purple triangles are the midpoints of the sides of AKBL, AAKM, and AMLC. The perimeter of AABC is 24 cm. What is the perimeter of the shaded region?
Step-by-step explanation:
Notice that KM = 0.5BC, KL = 0.5AC
and ML = 0.5AB. Therefore the perimeter of triangle KLM is half of the perimeter of triangle ABC. => 0.5 * 24cm = 12cm.
Each of the 3 purple triangles have perimeters which are 1/4 of the perimeter of triangle ABC. (Their vertices are midpoints of midpoints => 1/2 * 1/2)
Perimeter of 3 small purple triangles
= 3 * [24cm * (1/4)]
= 3 * 6cm = 18cm.
Hence Total perimeter of shaded parts
= 12cm + 18cm = 30cm.
Please help me with this final math question asap. I will mark brainliest Thank you so much! Question 5/5
Answer:
MP is approximately equal to ON because one side of a rectangle is always the same as another side of a rectangle.
Step-by-step explanation:
A Wonsan has 30 coins in her pocket, all of which are dimes and quarters . If the total value of the coins is $4.50 ,how many dimes and how many quarters does she have ?
Answer:
The number of
Dimes = d = 20 dimes
Quarters = q = 10 quarters
Step-by-step explanation:
Let us represent
The number of :
Dimes = d
Quarters = q
Note that:
A dime is worth 10 cents = 0.10d
A quarter is worth 25 cents = 0.25q
A Wonsan has 30 coins in her pocket, all of which are dimes and quarters .
d + q = 30...... Equation 1
d = 30 - q
If the total value of the coins is $4.50
0.10d + 0.25 q = 4.50.....Equation 2
We substitute 30 - q for d in Equation 2
0.10(30 - q) + 0.25q = 4.50
3 - 0.10q + 0.25q = 4.50
- 0.10q + 0.25q = 4.50 - 3
0.15q = 1.5
q = 1.5/0.15
q = 10 quarters
Solving for d
d = 30 - q
d = 30 - 10
d = 20 dimes
Therefore:
The number of
Dimes = d = 20 dimes
Quarters = q = 10 quarters
Selena earns $13.15 for every hour she works at the bakery. She already has $14 in her purse. Use x for the number of hours she works.
Answer:
y=13.15x+14
Step-by-step explanation:
That is the equation, if you need the graph lmk
Answer:
?=14+13.15x
14+13.15x=?
?=13.15x+14
13.15x+14=?
What is the speed of an auto that travels from Bloomfield to Atlantic City (120 miles) in 2 hours
9514 1404 393
Answer:
60 miles per hour
Step-by-step explanation:
Speed in miles per hour is found by dividing miles by hours:
(120 mi)/(2 h) = (120/2) mi/h = 60 mi/h
What is the final amount if 943 is decreased by 13% followed by a further 6% decrease?
Answer:
771.18
Step-by-step explanation:
The Amount given is 943
13% of amount will be = 943 x 13%
=
Decreasing 13% from 943 we get = 943-122.59
=820.41
Now the ammount = 820.41
for finding the final amount
find 6% of amount (820.41) we get = 820.41x 6%
=
Decreasing 6% from 820.41 we get final amount= 820.41- 49.23
=771.18
so the final amount is 771.18
PLEASE HELP QUICK !!!
Answer:
The explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]
Option A is correct option.
Step-by-step explanation:
Third term of sequence is 18
Sixth term of sequence is 33
We need to find the explicit equation for the sequence.
The explicit sequence is [tex]a_n=a_1+(n-1)d[/tex]
We need to find a_1 the first term and common difference d
We have a₃=18
We can write it as: [tex]a_3=a_1+(3-1)d\\[/tex]
[tex]18=a_1+2d[/tex]
a₆=33
We can write it as: [tex]a_6=a_1+(6-1)d\\33=a_1+5d[/tex]
Now, solving these equation s we can find value of d
[tex]18=a_1+2d[/tex]
[tex]33=a_1+5d[/tex]
Subtract both equations
[tex]18=a_1+2d[/tex]
[tex]33=a_1+5d[/tex]
[tex]--------\\-15=-3d\\d=\frac{-15}{-3}\\d=5[/tex]
So, we get common difference d = 5
Now finding a_1
Put value of d in equation [tex]18=a_1+2d[/tex]
[tex]18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8[/tex]
So, we get a₁ = 12
Now, the explicit equation is:
[tex]a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3[/tex]
So, the explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]
Option A is correct option.
Find the hypotenuse of a right triangle with legs measuring 4 and 5
Answer:
20
Step-by-step explanation:
4^2 + 5^2 = x^2
16 + 25 = 41
x^2 = 41
x = sqrt 41 or 6.4
ILL GIVE BRAINLIEST IF CORRECT
Answer:
B. 18x3 + 6x2 + 14x - 72
Answer:
B
Step-by-step explanation:
Solve: -9-16
(answer this and you'll get a lot of points :D)
Answer:
-25
Step-by-step explanation:
When subtracting a negative from a negative, ignore the negative sign, ADD the 2 numbers, then add a negative sign to the sum.
100 points! If you help on 10
Answer:
multiply 0.05 by amount of grid cubes!
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
Selena went to our Diner. She ordered a hotdog and cheeseburger. How much did she spend at lunch?
Answer:
13.75
Step-by-step explanation:
6.25+7.50=13.75
Answer:
$11.05
Step-by-step explanation:
The hot dog is $3.55, and the cheeseburger is $7.50. Thus, adding them together, the whole total is $11.05.
Hope this helps
The ratio of boys to girls is 1:2.
Two boys and two girls enter the
room and the ratio is now 5:9.
How many boys and girls were
there originally?
Answer:let the original number of boys be x
x:2x=1:2
x+2:2x+2=5:9
9x+18=10x+10
x=8
2x=16
Step-by-step explanation:
Please help I will mark as brilliant
Answer: x=2
Step-by-step explanation:
Answer:
rate of change is also know as the slope and so -3x would be your rate of change so the anwser should be -3
Step-by-step explanation:
Coffee costs $1.75 a pound. How much would 3.2 pounds of coffee cost?
Answer:
$5.60
Step-by-step explanation:
So each pound equals to $1.75 which means that we need to multiply by 3.2 because we're trying to find the number of money we'll spend on a certain amount of coffee. So if we multiply, we get 5.6. Though in context with the problem, it should be $5.60.
a football coach is trying to decide: when a team is ahead late in the game, which strategy is better?
• play the "regular" defense.
• play a "prevent" defense that guards against long gains but makes short gains easier
the coach reviews the outcomes of 100 games
compare the probability of winning when playing regular defense with the probability of winning when playing prevent defense. draw a conclusion
based on your results.
From analysis, it is seen that the probability of winning when playing regular defense is higher than the probability of winning with *prevent* defence.
How to find the probability of Winning?We will assume that a total of 100 games were reviewed.
50 games used regular defense method.
The remaining 50 games used the prevent defense method.
Out of the 50 regular defense games, 38 were win while 12 games were lose.
Out of 50 prevent defense game, 29 were win, while 21 games were lose.
Thus, the Probability of winning by regular defense is:
P(win | regular) = 38/50
P(win | regular) = 0.76
Probability of winning by playing prevent defense is:
P(win | prevent) = 29/50 = 0.58
From the above analysis we observe that the probability of winning by using the regular defense method is greater than the probability of winning by prevent defense method.
That is 0.76 > 0.58.
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How many solutions will this equation have?
5(x + 12) = 7 + 5x
Which expression is equivalent to (81x4y16)12 for all positive values of x and y?
40.5x4y16
Answer:
[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]
Step-by-step explanation:
Given
[tex](81x^4y^{16})^{\frac{1}{2}}[/tex]
Required
Determine an equivalent expression
Express 81 as [tex]9^2[/tex]
[tex](9^2x^4y^{16})^{\frac{1}{2}}[/tex]
Apply law of indices
[tex]9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}[/tex]
[tex]9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}[/tex]
[tex]9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}[/tex]
[tex]9^1 * x^2 * y^8[/tex]
[tex]9 * x^2 * y^8[/tex]
[tex]9 x^2 y^8[/tex]
Hence:
[tex](81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8[/tex]
please help and i’ll give brainliest
Answer:
the answer is C
Step-by-step explanation:
By using the equation below complete the square, write the equation of the circle in standard form from the following equation. Then determine the center and radius of
a circle.
10y + x2 = -18+ 5x - y2
Given:
The equation of a circle is
[tex]10y+x^2=-18+5x-y^2[/tex]
To find:
The center and radius of the given equation by completing the square.
Solution:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
where, (h,k) is center and r is radius of the circle.
We have,
[tex]10y+x^2=-18+5x-y^2[/tex]
It can be written as
[tex](x^2-5x)+(y^2+10y)=-18[/tex]
[tex]\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2[/tex]
[tex]\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2[/tex]
[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25[/tex]
[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}[/tex]
[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}[/tex]
[tex]\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\left(\dfrac{\sqrt{53}}{2}\right)^2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}[/tex]
Therefore, the center is [tex]\left(\dfrac{5}{2},-5\right)[/tex] and the radius is [tex]\dfrac{\sqrt{53}}{2}[/tex] units.
Which expression is equivalent to (7^3)^-2
