Answer:
The height of Moyo is
[tex]\frac{67}{6}[/tex]
The height of Adamu is
[tex]\frac{13}{6}[/tex]
Step-by-step explanation:
Equations
To solve the problem, we assign the variable:
x = height of Moyo
Since Moyo is 9 units taller than Adamu:
x - 9 = height of Adamu
The difference of the squares of their heights is 120, thus:
[tex]x^2-(x - 9)^2=120[/tex]
Operating:
[tex]x^2-(x^2-18x+81)=120[/tex]
[tex]x^2-x^2+18x-81=120[/tex]
Simplifying:
[tex]18x-81=120[/tex]
Adding 81:
[tex]18x=120+81=201[/tex]
Dividing by 18:
[tex]x=\frac{201}{18}=\frac{67}{6}[/tex]
The height of Moyo is
[tex]\frac{67}{6}[/tex]
The height of Adamu is
[tex]\frac{67}{6}-9=\frac{13}{6}[/tex]
How do you write 0.5 as a percentage?
Need help please!!!!
Answer:
b^(-4/5) ...............
Please help with what you can!
Thank you!
Answer:
The answer to number 9 is: 148.16
I need help with this, please. Someone?
Answer:
6:8:10
Step-by-step explanation:
A new movie is currently showing at the local movie theater. For the 6:00 pm showing, the theater sold 36 student tickets and 24 adult tickets for a total of $423. The theater sold 41 student tickets and 38 adult tickets for a total of $585.75 for the 8:30 pm showing. If x represents the number of student tickets sold and represents the number of adult tickets sold, which of the following systems of equations correctly models the situation? Group of answer choices
Answer:
36x + 24y = 423 (1)
41x + 38y = 585.75 (2)
x =$5.25
y = $9.75
Step-by-step explanation:
x = the number of student tickets sold
y = the number of adult tickets sold
36x + 24y = 423 (1)
41x + 38y = 585.75 (2)
Multiply (1) by 38 and (2) by 24
1368x + 912y = 16,074 (3)
984x + 912y = 14,058 (4)
Subtract to eliminate y
1,368x - 984x = 16,074 - 14,058
384x = 2,016
x = 2,016/384
x = 5.25
Substitute x = 5.25 into (1) to find y
36x + 24y = 423
36(5.25) + 24y = 423
189 + 24y = 423
24y = 423 - 189
24y = 234
y = 234/24
y = 9.75
x =$5.25
y = $9.75
how to solve two step inequalities
Answer:
Solving two step inequalities
Solving Two Step Linear Inequalities. To solve a two-step inequality, undo the addition or subtraction first, using inverse operations , and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa.
The listed price of the video game was $34, but the price with tax came to $37.40. Find the percent sales tax.
Answer:
10%
Step-by-step explanation:
we want to find what % of 34 is 37.40
so, we will use the following equation:
[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]
for this scenario:
part = 37.40
whole = 34
percent = x
now plug in:
[tex]\frac{37.40}{34} = \frac{x}{100}[/tex] cross multiply
34x = (37.40)(100)
34x = 3740 divide both sides by 34
x = 110%
now we know that with tax, we paid 110% of the video game's price
110 - 100 = 10%
so the percent sales tax is 10%
just to check...
34 • 1.10 = $37.40
or
34 • .10 = 3.40
34 + 3.40 = 37.40
Apply the distributive property to create an equivalent expression.
6(3c - 5d + 6) =
Answer:
18c - 30d + 36
Step-by-step explanation:
6(3c - 5d + 6)
6 × 3c = 18c
6 × -5d = -30d
6 × 6 = 36
what would be the answer to this question?
Answer:
5
Step-by-step explanation:
2*2 + 3*6 + 4*x + 5*8 + 6*1 = 84
4*x = 16
x = 4
Right, 8 is the biggest frequency
2/2q+3=1/8
solve for q
Answer:
[tex]q= -\frac{23}{8 }[/tex]
Step-by-step explanation:
hope this helps have a good rest of your day :) ❤
!!! please help !!! i’ll mark brainlest or whatever if it’s right :)
What is the best name for the given solid figure?
A. rectangular pyramid
B. rectangular cone
C. rectangular prism
D. rectangle
Answer:
rectangular prism
Step-by-step explanation:
Troy has a cylindrical vase that holds exactly 1,000 cm3 of liquid. He knows that the formula for finding the volume of a cylinder is V = pir^2h
where r is the radius of the cylinder's base and h is the height of the cylinder. He also knows that his vase is 12.75 cm tall. What is the radius of
Troy's vase? Round your answer to the nearest tenth.
Answer:
5.0 cm
Step-by-step explanation:
Volume of a cylinder = πr²h
Height,h = 12.75 cm
π = 3.14
Radius,r = r
Volume of the cylinder = 1,000 cm³
Volume of a cylinder = πr²h
1000 = 3.14 × r² × 12.75
1000 = 40.035r²
r² = 1000/40.035
r² = 24.978
r = √24.978
r = 4.99 cm
Approximately 5.0 cm
There was 3/4 of a cake left over from a super bowl party. If you eat 2/3 of it, how much
cake did you eat?
Answer:
1/12
Step-by-step explanation:
3/4 turns to 9/12 of the cake is left before
2/3 turns to 8/12
9/12 minus 8/12 is 1/12
How do you write 28/50 as a percentage?
Answer: 56%
Step-by-step explanation: To write the fraction 28/50 as a percent, remember that a percent is a ratio that compares a number to 100.
So we need to find a fraction that's equivalent
to 28/50 that has a 100 in the denominator.
To do this, we set up a proportion.
So we have 28/50 = n/100.
To find the value of n, we first find the fraction that
is equivalent to 28/50 that has a denominator of 100.
If we multiply both the numerator and denominator of
28/50 by 2, we can see that 28/50 = 56/100.
So 28/50 is equal to 56/100 or 56%.
What is the slope of (4,4) and (-2, -1)
2 ( n - 7 ) = 20
What is n?
Answer:
The answer is n = 17
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
Hoped this helped!
brainly, please?
What is the composite perimeter of this shape? I will crown anybody who answers correctly!
can someone help me with this problem? A game results in either a positive or a negative score for the player during each turn. One player had a total score of -288 points after nine turns. What was his average score per turn?
Answer:
He or she got around -32 points per turn.
Step-by-step explanation:
-288 points (the total) divided by the player's 9 turns equals -32. This means that they got negative 32 points on average every round.
quadratic sequence are shown below Work out the next term.
7 11 17 25
2. The first four terms of a quadratic sequence are shown below Work out the next term.
6 12 22 36
3. The nth term of a quadratic sequence is n2 − 2n + 8 Work out the first three terms of this sequence
4. A quadratic sequence has an nth term of 2n2 + 3n − 1 Work out the value of the 6th term of the sequence
5. Asequencehasannthtermof n2−6n+7
Work out which term in the sequence has a value of 23.
6. Here are the first 5 terms of a quadratic sequence
4 11 20 31 44
Find an expression, in terms of n, for the nth term of this quadratic sequence.
7. Here are the first 5 terms of a quadratic sequence 4 10 18 28 40
Find an expression, in terms of n, for the nth term of this quadratic sequence.
8. Here are the first 5 terms of a quadratic sequence 9 17 29 45 65
Find an expression, in terms of n, for the nth term of this quadratic sequence.
9. Here is a tile.
Here is a sequence of patterns made from these tiles.
How many of these tiles are needed to make Pattern number 10?
10. The nth term of a sequence is n2 + 3n
Two consecutive terms in the sequence have a difference of 38
Work out the two terms.
11. Prove that every term in the sequence n2 − 4n + 21 is positive please help anyone
The quadratic sequence answered this way .
What are quadratic sequence?Quadratic sequences are sequences that include an term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
According to the question
Quadratic sequences are given the next term is :
1> 7 11 17 25
First difference between terms
11 - 7 = 4
17 - 11 = 6
25 - 17 = 8
Second difference between terms
6 - 4 = 2
8 - 6 = 2
Therefore, next term : First last difference + Second difference + Last Term
: 8+2 = 10
: 25 + 10 = 35
2> 6 12 22 36
First difference between terms
12 - 6 = 6
22 - 12 = 10
36 - 22 = 14
Second difference between terms
10 - 6 = 4
14 - 10 = 4
Therefore, 1st next term : First last difference + Second difference + Last Term
: 14 + 4 = 18
: 36+ 18 = 54
2nd next term : First last difference + Second difference + Last Term
: 18 + 4 = 22
: 22 + 54 = 76
3rd next term : First last difference + Second difference + Last Term
: 22 + 4 = 26
: 76 + 26 = 102
4th next term : First last difference + Second difference + Last Term
: 26 + 4 = 30
: 76 + 26 = 102
3> nth term of a quadratic sequence = [tex]n^{2} - 2n + 8[/tex]
first three terms of this sequence :
1st term of the sequence : n = 1
substituting value of n
[tex]1^{2} - 2 + 8[/tex]
= 7
2nd term of the sequence : n = 2
substituting value of n
[tex]2^{2} - 2*2 + 8[/tex]
= 8
3rd term of the sequence : n = 3
substituting value of n
[tex]3^{2} - 2*3 + 8[/tex]
= 17 - 6
= 11
4> Quadratic sequence has an nth term : [tex]2n^{2} + 3n -1[/tex]
6th term of the sequence : n = 6
substituting value of n
[tex]2(6)^{2} + 3*6 -1[/tex]
36*2 + 18 -1
= 89
5> Quadratic sequence has an nth term : [tex]n^{2} - 6n + 7[/tex]
term = 23
therefore,
23 = [tex]n^{2} - 6n + 7[/tex]
0 = [tex]n^{2} - 6n - 16[/tex]
solving the equation
[tex]n^{2} - (8-2)n - 16 = 0[/tex]
n(n- 8) + 2 (n - 8) = 0
(n-8) (n+2) = 0
n = 8 , -2
As term can not be negative , so n = 8
Therefore, term 8 of Quadratic sequence : [tex]n^{2} - 6n + 7[/tex] is 23 .
6> First 5 terms of a quadratic sequence :
4 11 20 31 44
expression for the nth term of this quadratic sequence:
As general form of quadratic sequence is : [tex]an^{2}+bn +c[/tex]
now for n= 1
a + b + c = 4 -------------------(1)
now for n= 2
[tex]a2^{2}+b*2 +c[/tex] = 11
4a + 2b + c = 11 ---------------------------(2)
now for n= 3
[tex]a3^{2}+b*3 +c[/tex] = 20
9a + 3b + c = 20 ----------------------------------(3)
solving equation (1) , (2) & (3)
a = 1 , b = 4 , c = -1
now , substituting the value in general equation
[tex]= n^{2}+4n -1[/tex]
Hence, The nth term of this quadratic sequence [tex]= n^{2}+4n -1[/tex]
7>The first 5 terms of a quadratic sequence : 4 10 18 28 40
the nth term of this quadratic sequence :
As general form of quadratic sequence is : [tex]an^{2}+bn +c[/tex]
now for n= 1
a + b + c = 4 -------------------(1)
now for n= 2
[tex]a2^{2}+b*2 +c[/tex] = 10
4a + 2b + c = 10 ---------------------------(2)
now for n= 3
[tex]a3^{2}+b*3 +c[/tex] = 18
9a + 3b + c = 18 ----------------------------------(3)
solving equation (1) , (2) & (3)
a = -4 , b = 18 , c = -10
now , substituting the value in general equation
[tex]= -4n^{2}+18n -10[/tex]
Hence, The nth term of this quadratic sequence [tex]= -4n^{2}+18n -10[/tex]
8>First 5 terms of a quadratic sequence : 9 17 29 45 65
the nth term of this quadratic sequence :
As general form of quadratic sequence is : [tex]an^{2}+bn +c[/tex]
now for n= 1
a + b + c = 9 -------------------(1)
now for n= 2
[tex]a2^{2}+b*2 +c[/tex] = 17
4a + 2b + c = 17 ---------------------------(2)
now for n= 3
[tex]a3^{2}+b*3 +c[/tex] = 29
9a + 3b + c = 29 ----------------------------------(3)
solving equation (1) , (2) & (3)
a = 2 , b = 2 , c = 5
now , substituting the value in general equation
[tex]= 2n^{2}+2n +5[/tex]
Hence, The nth term of this quadratic sequence [tex]= 2n^{2}+2n +5[/tex]
9> Pattern is not given (incomplete question)
10> The nth term of a sequence is : [tex]n^{2} + 3n[/tex]
Two consecutive terms in the sequence have a difference of 38
The two terms of the sequence :
N2 - N1 = 38
substituting n as n2 and n1
[tex](N_{2}) ^{2} + 3N_{2} - (N_{1}) ^{2} - 3N_{1}[/tex] = 38
[tex](N_{2}) ^{2} - (N_{1}) ^{2} + 3N_{2} - 3N_{1} = 38[/tex]
[tex](N_{2} - N_{1} ) (N_{2} + N_{1})+ 3(N_{2} - N_{1}) = 38[/tex]
[tex](N_{2} - N_{1} ) [N_{2} + N_{1}+ 3] = 1*38\\\ (as (N_{2} - N_{1} = 1 ) consecutive terms)[/tex]
now,
[tex](N_{2} - N_{1} ) = 1 ,\\\ [N_{2} + N_{1}+ 3] = 38[/tex]
solving both equations
[tex]N_{2} =18\\ N_{1} = 17[/tex]
Hence, two terms of sequence are 18th and 17th the whose difference in 38 .
11> The sequence: [tex]n^{2} - 4n + 21[/tex]
To proof the sequence is positive always
As n cannot be negative
let n = 0
substituting the value in equation we get
+ve
As we conclude in equation +ve part is larger than -ve part always ,
so this equation is always be +ve for any value of n .
Hence, The quadratic sequence answered this way .
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Which set of numbers forms a right triangle
Which expression is equivalent to 364ab7c9?
Emma needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 5 hours and charged her $168 for parts. The total was $743. What was the cost of labor, per hour?
Answer:
115
Step-by-step explanation:
5\color{red}{x}+\color{blue}{168}=
5x+168=
\,\,\color{purple}{743}
743
-\color{blue}{168}\phantom{=}
−168=
\,\,-\color{blue}{168}
−168
Subtract 168 from both sides
5\color{red}{x}=
5x=
\,\,575
575
\frac{5\color{red}{x}}{5}=
5
5x
=
\,\,\frac{575}{5}
5
575
Divide both sides by 5
\color{red}{x}=
x=
\,\,\boxed{\color{red}{115}}
115
The weight (in kg) of cubical block of ice 75 cm in length (if one cubic metre of ice weight is 80 kg) is
(1) 35
(2) 42.50
(3) 33.75
(4) 40
Answer: The weight = 33.75kg
Step-by-step explanation:
Given that
one cubic metre of ice weight is 80 kg
which is mathematically written as
1m³ of ice = 80 kg
Therefore 75 cm length of cubical block of ice =???
First
changing 75 cm to meters, we have 75/100 = 0.75 m
Volume of block = l³= 0.75³ = 0.421875m³
Given that
1m³ = 80kg
0.421875m³= 0.421875 x 80
= 33.75kg
Sebastian has 12 more trophies than Megan.megan has t trophies.how many trophies does Sebastian have
Answer:
12 + t
Hope This Helped :)
Answer:
sebastian has 12+t trophies.
-8x=-56 one step help
Answer:
x=7
Step-by-step explanation:
divide both sides by -8
Answer:
Divide each term by −8 - 8 and simplify.
x = 7x = 7
Give the standard form for 900.000 000 + 50 50.000 000 + 9.000 + 600 + 20 + 7
Answer:
900.000 000 + 5050.000 000 + 9.000 + 600 + 20 + 7
=900+5050+9+600+20+7=6586 is standard one
help me or i brek all kneecap
the answer is d (x+v). hope this helps :))
Answer:break my kneecaps
Step-by-step explanation:
Marcus and Mary have £30 between them. The amount of money Marcus has compared to Mary is in the ratio 1:5. How much money would Mary have?
Answer:
25
Step-by-step explanation:
30÷6=5
5×5= 25
.........
Write 2.673 × 10^4 as an ordinary number
2.673 × 10^4 is a scientific number, and the number as an ordinary number is 26730
How to rewrite the number?The number in scientific form is given as:
2.673 × 10^4
Express 10^4 as 10000
2.673 × 10^4 = 2.673 × 10000
Evaluate the product
2.673 × 10^4 = 26730
Hence, 2.673 × 10^4 as an ordinary number is 26730
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what is $420 with a 6% tax
=============================================================
Explanation:
There are two approaches.
The slightly longer approach will have us take 6% of 420 to get 0.06*420 = 25.20
So 25.20 is the amount of tax you pay on top of the original $420. The total bill is 420+25.20 = 445.20 dollars
--------------
The shortcut is to multiply 420 by 1.06 to get 420*1.06 = 445.20
The 1.06 multiplier indicates an increase of 6%
We can think of it it as 1.06 = 1 + 0.06 = 100% + 6%