Answer:
The answer is below
Step-by-step explanation:
The ratio of Keith's height and his nephew's height is 15:7. Let keith height be x cm and his nephews height be y cm.
[tex]\frac{x}{y}=\frac{15}{7} \\x=\frac{15}{7}y[/tex]
Keiths height increased by 16% , therefore Keith new height is (100% + 16%) × x = 1.16x
The nephew height is doubled, therefore his new height is 2y.
Given that Keith is now 34 cm taller than his nephew
1.16x = 2y + 34
but x = (15/7)y
[tex]1.16(\frac{15}{7} )y=2y+34\\\\\frac{87}{35} y=2y+34\\\\\frac{87}{35} y-2y=34\\\\\frac{17}{35}y=34\\ \\y=\frac{34*35}{17}\\ \\y=70\ cm[/tex]
The nephews new height = 2y = 2(70) = 140 cm
Keith new height = 2y + 34 = 140 + 34 = 174 cm
Their total current height = 140 cm + 174 cm = 314 cm
Solve : (i) 5x+3/4 - 2x-4/3 = 5 (ii) 3(x+5) - 2(3x-1) = 15
Answer:
(i) x = 67/4
(ii) x = 2/3
Step-by-step explanation:
(i)
5x + 3/4 - 2x - 4/3 = 5 add like terms
3x -7/12 = 5
3x = 5 + 7/12 ➡ 3x = 67/12 and x = 67/4
(ii)
3(x+5) - 2(3x-1) = 15 ➡ 3x + 15 - 6x + 2 = 15 add like terms
17 - 3x = 15
2 = 3x and x = 2/3
Find the solution for this system of equations. 2x - 3y = 2 x= 6y -5
Answer:
Step-by-step explanation:
2(6y - 5) = 2
12y - 10 = 2
12y = 12
y = 1
x = 6(1) - 5
x = 6 - 5 = 1
(1,1)
Answer: (1,1)
Step-by-step explanation: 2(6y - 5) = 2
12y - 10 = 2
12y = 12
y = 1
x = 6(1) - 5
x = 6 - 5 = 1
(1,1)
Please help!! Thank you in advance! Will mark Brainliest!
Answer:
F , D, E
Step-by-step explanation:
The smallest angle is opposite the smallest side
The largest angle is opposite the largest side
DE is smallest so F is smallest
Then EF so D
DF is largest so E is the largest angle
Suppose that $9500 is placed in an account that pays 9% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
so
(b) Find the amount in the account at the end of 2 years.
$
?
Answer:
$11286.95 second year
$10335 first year
Step-by-step explanation:
9% of 9500 is 855, 9500 plus 855 = 10335. (first year)
9% of 10335 is 931.95, and 10335+931.95 is 11286.95. (second year)
The amount in the account at the end of 1 year $10335 (first year)
The amount in the account at the end of 2 years $11286.95.
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
here, we have,
$9500 is placed in an account that pays 9% interest compounded each year.
so, we get,
9% of 9500 is 855,
9500 plus 855 = 10335. (first year)
again,
9% of 10335 is 931.95,
and 10335+931.95 is 11286.95. (second year)
Hence, The amount in the account at the end of 1 year $10335 (first year)
The amount in the account at the end of 2 years $11286.95.
To learn more on Compound interest click:
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Having trouble.. help?
Answer:
(A) [tex]y = x+3[/tex]
Step-by-step explanation:
Using the values of (-6, -3), (3,6), and (5,8) we can substitute the values into each equation and see if the equation meets the requirements for all 3.
Let's test A first.
[tex]-3 = -6+3[/tex]
Correct, let's try the second pair.
[tex]6 = 3+3[/tex]
Correct, let's try the third pair.
[tex]8 = 5+3[/tex]
So yes, this equation works.
For fun, let's try the other equations.
Let's test B.
[tex]-3 = -6-3[/tex]
This is not true as -6 -3 = -9. So this equation is immediately ruled out.
Let's test C.
[tex]-3 = 2\cdot-6[/tex]
Again this doesn't work, as -6 times 2 is -12. So this equation is also ruled out.
Let's try D.
[tex]-3 = \frac{1}{2}\cdot-6[/tex]
This works, as half of -6 is -3 - however the equation will only work if all 3 pairs work for it.
Let's try the second pair.
[tex]6 = \frac{1}{2}\cdot3[/tex]
This doesn't work, as half of 3 is 1.5. This equation is also ruled out.
Therefore, A is the only equation that works with these pairs.
Hope this helped!
it’s a 425 mile drive from San Jose to Los Angeles.
it’s about 320 mile Drive from San Jose to Santa Barbara.
write an equation showing that the distance traveled on the first day plus the distance traveled on the second is equal to 425 miles
Answer:
The answer is below
Step-by-step explanation:
The distance traveled the first day = Distance from San Jose to Santa Barbara = 320 mile.
The distance traveled the second day = Distance from Santa Barbara to Los Angeles.
But From San Jose to Los Angeles = 425 mile. Therefore:
Distance From San Jose to Los Angeles = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles
425 = 320 + Distance from Santa Barbara to Los Angeles.
Distance from Santa Barbara to Los Angeles = 425 - 320 = 105 mile
The distance traveled the second day = Distance from Santa Barbara to Los Angeles = 105 miles
The distance traveled the first day + The distance traveled the second day = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles = 320 + 105 = 425 miles
The distance traveled the first day + The distance traveled the second day = 425 miles
The scale on a map of Virginia shows that 1 inch represents 20 miles the actual distance from Richmond Virginia to Washington DC is 110 miles on the map how many inches are between the two cities
Answer:
5.5 inches
Step-by-step explanation:
Proportions:
1 inch ⇔ 20 miles
W inch ⇔ 110 miles
W = 110*1/20
W = 5,5 inch
Which function has only one x-intercept at (-6, 0)?
Of(x) = x(x-6)
O f(x) = (x - 6)(x - 6)
f(x) = (x + 6)(x - 6)
Of(x) = (x + 6)(x + 6)
Answer:
f(x) = (x + 6)(x + 6)
f(x)=0
x+6=0 ⇒ x=-6
Set (x+6)(x+6) equal to zero and solve each equation for x. We really only have one equation and it would be x+6 = 0 which solves to x = -6.
Plug x = -6 into f(x) and you would get f(x) = 0.
For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.989. Using alph=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Correlation Coefficient (r) = 0.989
alph=0.05
Number of observations (n) = 8
determine if there is a linear correlation between chest size and weight.
Yes, there exists a linear relationship between chest size and weight as the value of the correlation Coefficient exceeds the critical value.
What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
To determine the the proportion of variation in weight that can be explained by the linear regression line between weight and chest size, we need to obtain the Coefficient of determination(r^2) of the model.
r^2 = square of the correlation Coefficient
r^2 = 0.989^2 = 0.978121
Hence, about 0.978 (97.8%) of the variation in weight can be explained by the linear relationship between weight and chest size.
In the expression 7³ - 4 · 3 +8, the first operation is? A. An Exponent B. Subtraction C. Multiplication D. Addition
Answer:
An exponent
Step-by-step explanation:
look at PEM/DA/S
Parenthesis
EXPONENTS
and then you can stop the first operation is 7^3
this is an exponent
(also brainliest if this helped please!)
The first operation according to the PEM/DA/S rule to evaluate the 7³ - 4 · 3 +8 expression is an exponent.
What is PEM/DA/S rule?It is the order or sequence of evaluating a math expression. We can remember the order using PEM/DA/S: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In the given expression, using PEM/DA/S rule (Sometimes called BODMAS; the synonym of PEM/DA/S):
evaluate 7³ - 4 · 3 +8
The first operation is an exponent term, i.e.,
[tex]7^{3}[/tex]
Hence our first operation in the sequence of evaluating the given expression value is an exponent.
To learn more about PEM/DA/S, refer to the link:
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If 8(x) = -2 and g(x) = 2x2 + x = 3, find ( +g)(x).
A. 2x2 + 2x-5
B. x - 6
C. 2x - 3+1
D. 2x2 + x +1
[tex](f+g)(f)=f(x)+g(x)\\\\\\f(x)=\dfrac{x}{2}-2\\g(x)=2x^2+x-3\\\\(f+g)(x)=\dfrac{x}{2}-2+2x^2+x-3\\(f+g)(x)=2x^2+\dfrac{x}{2}+\dfrac{2x}{2}-5\\(f+g)(x)=2x^2+\dfrac{3x}{2}-5\\(f+g)(x)=2x^2+\dfrac{3}{2}x-5[/tex]
Lilli jogs 12 mile in 110 hour. What is Lilli's rate in miles per hour?
Answer:
.109090909 miles per hour
Step-by-step explanation:
To find miles per hour, take the miles and divide by the hours
12 miles/110 hours
.109090909 miles per hour
Answer:
0.11
Step-by-step explanation:
Hello!
To find how many miles Lilli jogs per hour we divide the distance by the time it took
12/110 = 0.109
The answer is 0.11
Hope this helps!
When three is added to four times a number, the result is 15
(a) Write an equation to represent the above information.
Answer
(b) Solve your equation in (a)
Answer:
A. 4y + 3 = 15
B. y = 3
Step-by-step explanation:
Three is added to four times a number, the result is 15
A. Equation to represent the above information:
Let the unknown number= y
4 * y + 3 = 15
4y + 3 = 15
B. Solve your equation in (a)
4y + 3 = 15
Collect like terms
4y = 15 - 3
4y = 12
Divide both sides by 4
4y / 4 = 12 /4
y = 3
Therefore, the unknown number is 3
If the measure of the base of a triangle is 3b+2 and the height is 4b,represent the area of the triangle
Answer:
6b^2 +4b
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
A = 1/2 * (3b+2) * (4b)
=1/2 (12 b^2 +8b)
= 6b^2 +4b
How to solve this maths equation??? pls help me, its urgent!!! asap
Answer:
x = [tex]\frac{3wyz}{4wz+wy-2yz}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{w}[/tex] + [tex]\frac{3}{x}[/tex] - [tex]\frac{4}{y}[/tex] = [tex]\frac{1}{z}[/tex]
Multiply through by wxyz to clear the fractions
2xyz + 3wyz - 4wxz = wxy ( subtract wxy from both sides )
2xyz + 3wyz - 4wxz - wxy = 0 ( subtract 3wyz from both sides )
2xyz - 4wxz - wxy = - 3wyz ( factor out x from each term on the left side )
x(2yz - 4wz - wy) = - 3wyz ( divide both sides by (2yz - 4wz - wy )
x = [tex]\frac{-3wyz}{2yz-4wz-wy}[/tex] ( multiply numerator/ denominator by - 1 )
x = [tex]\frac{3wyz}{4wz+wy-2yz}[/tex]
Three people found a $20 bill and decided to split it. How many dollars does each person get? Choose the correct answer from the choices below.
Answer:
$6.67
Step-by-step explanation:
$20/3 people
20/3
=6 2/3
=6.67
Each person gets $6.67.
Hope this helps!
Answer: Hi!
If you split a $20 dollar bill evenly in three parts, each person would get about $6.67 dollars. (If you divide 20 by 3, you get a recurring decimal, so it would round to 6.67.)
Hope this helps!
how many are 2 raised to 5 ???
Answer:
32
Step-by-step explanation:
2^5
This is 2 multiplied by itself 5 times
2*2*2*2*2
32
If graphs have a linear equations in a system are concurrent having the same slope and the same y-intercept what does that mean about possible solutions
Answer:
Infinite Amount of Solutions
Step-by-step explanation:
Since we have concurrent systems (same slope + same y-int), we know that the systems of equations would be the exact same line. If that is the case, the we would know that ANY value input would work. You could even test it mathematically, and it would give you infinite amount of solutions.
john is 15 years old. john's mom takes him and his younger soster to a football game. tickets are $22 for adults and $16 for children (18 and under). what is the total cost of thr tickets?
Answer:
$38
Step-by-step explanation:
cost of ticket for adult = $22
cost of ticket for youngster = $16
______________________________
cost of ticket for John's mom = $22 as she is adult
cost of ticket for john = $16 as he is young , his age is less than 18 years
Total cost of ticket for John and his mother = $22 + $16 = $38
Write a formula that will give the area of the shaded region in the figure below .
Answer:
a=(29-2)*(12-3)
Step-by-step explanation:
a=LW
a=(L-2)*(W-3)
a=(29-2)*(12-3)
a=27*9
a=243ft²
Answer:
[tex]\Large \boxed{A = (29 - 2) \times (12 - 3)}[/tex]
Step-by-step explanation:
The length of the whole rectangle is 29 feet.
The width of the whole rectangle is 12 feet.
The length of the shaded region is 2 feet less than the length of the whole rectangle.
The width of the shaded region is 3 feet less than the width of the whole rectangle.
The area of a rectangle is length × width.
So we can create a formula to solve for the area of the shaded region:
A = (29 - 2) × (12 - 3)
Solving for the area.
A = 27 × 9
A = 243
The area of the shaded region is 243 feet².
for 0°<θ<-180° which of the primary trigonometric functions may have positive values?
sine and cosecant.
you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate
Briefly explain how you would graph an equation such as y=7x-2
Answer:
put a mark at negative 2 on the graph then you would go up seven rigght one until you cant then you would go back to -2 and go down seven left one until you cant
Step-by-step explanation:
HELP ME PLEASE ASAP! Zoe is making a quilt. The ratio of red squares to green squares is 2 to 3. She uses a total of 55 squares. How many green squares does she use?
Answer: 33
First you divide 55 by 5 to get the total number of squares in one part, which equals 11. Then you multiply by 3 since there are 3 parts of green squares to get your answer, 33.
which of the following shows maximum rise in temperature?
a} 23 to 32
b} [ -10] to 1
c} [-18] to [-11]
d} [-5] to 5
Answer:
b) (-10) to 1Step-by-step explanation:
it shows the maximum rise in temperature.
Answer:
b answer, will show the rise in temperature
14. Simplify the expressions
a. 12 - 5y + 21 + y -23
Answer:
10 - 4y
Step-by-step explanation:
Combine like terms. 12, 21 and -23 add up to 10, and -5y + y is -4y.
Then, together, we have 10 - 4y (answer)
Answer:
[tex]\large\boxed{10 - 4y}[/tex]
Step-by-step explanation:
12 - 5y + 21 + y - 23
Combine like terms (add -5y to + y)
12 + 21 - 4y - 23
Add 12 + 21
33 - 4y - 23
Subtract 23 from 33
[tex]\large\boxed{10 - 4y}[/tex]
This is the simplest form of the expression.
Hope this helps :)
What is one term or multiple terms connected by an addition or subtraction sign
The answer is Like terms.
. Find the sum of the geometric sequence. (1 point) 1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six
Answer:
0.332
Step-by-step explanation:
given series
1/4, 1/16,1/64.1/256
this is geometric series
where common ratio r is given by
nth term/ (n-1)th term
let the second term is nth term and first term is (n-1)th term
r = 1/16 / (1/4) = 1/4
___________________________________________
sum of series is given by
a (1-r^n)/1-r
where a is first term
n is the number of terms
r is the common ration
___________________________________________
in the given series
1/4, 1/16,1/64.1/256
a = 1/4
r = 1/4
n = 4
thus ,
sum = 1/4(1-(1/4)^4)/ (1-1/4)
sum = 1/4(1-(1/256)/(4-1)/4
sum = 1/4((256-1)/256 / 3/4
1/4 in numerator and denominator gets cancelled
sum =( 255/256*3) = 255/768 = 0.332
Thus, sum of series is 0.332.
Answer:
341/256
Step-by-step explanation:
I took the test and got the answer right
You just give all the fractions a common denominator of 256 and then change and add up the numerators and you get 341
tan 21 degrees = 9/x
Answer:
23.4458015822
Step-by-step explanation:
tan(21) = 9/x
9/tan(21) = x
9/tan(21) = 23.4458015822
HELPP ASAP NEEDED MATH
There are $20n$ members in the Trumpington marching band, and when they line up in rows of 26, there are 4 band members left over. If $n$ is an integer and there are fewer than 1000 band members, what is the maximum number of people that could be in the Trumpington marching band?
Answer:
992
Step-by-step explanation:
Divide 1000 by 26.
The answer is 38 and some left over. We don't care what the leftover is because it is nearly 0.5 and that means 13 people were left over.
Take the integer value (38) and multiply it by 26. You get 988.
You want there to be 4 left over. 4 + 988 = 992. That's one way of doing the problem.
Answer: 940 people is the maximum
==========================================
Explanation:
n = 1 means 20n = 20*1 = 20 members total, which is 4 short of making a row of 26 (so the remainder is 20)
n = 2 means 20n = 20*2 = 40 members. 40/26 = 1 remainder 14. We could make one full row with 14 members left over.
20n < 1000 solves to n < 50 after dividing both sides by 20. This means n is smaller than 50. It has to be larger than 0 or else 20n would be 0 or negative. We can write 0 < n < 50 to specify the range for n.
Since n < 50, this means the largest n can get is n = 49.
--------------------
If n = 49, then 20n = 20*49 = 980
980/26 = 37 remainder 18, which isn't the remainder we want (of 4).
If n = 48, then 20n = 20*48 = 960
960/26 = 36 remainder 24, again not the remainder we want
If n = 47, then 20n = 20*47 = 940
940/26 = 36 remainder 4
If we have 940 members, then we can form 36 rows (26 in each row). So 26*36 = 936 people so far. Then we have 940-936 = 4 people left over.
There are other solutions as well such as n = 34, n = 21, and n = 8. Though n = 47 is the largest n possible to fit all the conditions required.
Determine if the following set of ordered pairs represents a quadratic function. Explain.
(5, 7), (7, 11). (9, 14). (11, 18)
(1 point)
Answer:
Option D
Step-by-step explanation:
Given
[tex](5, 7), (7, 11). (9, 14). (11, 18)[/tex]
Required
Determine if the function is quadratic
[tex](5, 7), (7, 11). (9, 14). (11, 18)[/tex]
Start by representing the function as an x-y table
x:- 5 || 7 || 9 || 11
y:- 7 || 11 || 14 || 18
Next; Calculate the difference between the values of y
[tex]Difference: 11 - 7 = 4[/tex]
[tex]Difference: 14 - 11 = 3[/tex]
[tex]Difference: 18 - 4 = 4[/tex]
The resulting difference are: 4 || 3 || 4
Next; Calculate the difference between the difference of values of y
[tex]Difference = 3 - 4 = -1[/tex]
[tex]Difference = 4 - 3 = 1[/tex]
The resulting difference are: -1 || 1
For the function to be quadratic, the above difference must be the same and since they are not, then the function does not represent a quadratic function.
Option D answers the question
