Mathematics College

The sum of two numbers is 67. The smaller number is 21 less than the larger number. What are the numbers?

Answers

Answer 1
Let the bigger number be x.

bigger number = x
smaller number = x - 21

The sum of the two numbers is 67.
x + x - 21 = 67
2x - 21 = 67
2x = 67 + 21
2x = 88
x = 44

x = 44
x - 21 = 44 - 21 = 23

The larger number is 44 and the smaller one is 23
Answer 2

The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of the two numbers is 67. The smaller number is 21 less than the larger number.

Let the two numbers be 'x' and 'y' and x > y. Then the equations are given as,

x + y = 67       ...1

x = y + 21       ...2

From equations 1 and 2, then we have

y + 21 + y = 67

2y = 46

y = 23

Then the value of 'x' is given as,

x = 23 + 21

x = 44

The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.

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Related Questions

The minimum size of a photo book ordered through a website is 6 pages. The website charges $1.70 per page for the first 6 pages. Any additional pages increase the cost of the photo book by $0.90 per page. If x represents the number of additional pages in a photo book order, which equation can be used to find the total cost, in dollars, of a photo book ordered through the website?

Answers

Well Okay, 1.70 x 6 + .90x, Your pretty much taking 1.70 multiply by 6 then adding .90 for every page after.

Javier's family bought 3 juices at Bagel Mania. Which of these could NOT be the amount of money Javier's family spent of juices

Juices ___ small $0.75
Large $1.25

A. $2.25
B. $2.75
C. $3.25
D $3.50

Answers

The answer is d. $3.50.

1.25*3=3.75
0.75*3=2.25
(1.25*52)+0.75=3.25
(0.75*2)+1.25=2.75.

The only choice that isn't here is 3.50.
That means d. is the answer.

Hope this helped☺☺

Four family members compared their ages. Terell is 3 years younger than Danny. Danny is 1 year younger that Pablo. Pablo's age is 1/3 Shaniqua age. How old is Terell if shaniqua is 36 years old?

Answers

Terell is 8. 36 / 3 = 12. 12-1=11. 11-3=8.

I need help please ASAP and I will mark branlist

Answers

7- B
8- C
I’m pretty sure please don’t hurt me if I’m wrong

Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply.

Answers

The negative sign means that this is reflected about the y-axis (this is not in the choices so we can ignore this).
The factor of 0.4 means it is compressed (since the factor is < 1).
Since the term inside the radical is x - 2, this means that we translate the graph 2 units to the right.

So the only correct descriptions are: compressed by a factor of 0.4, and translated 2 units to the right.

Answer: a,c,d

Step-by-step explanation: got it right on edge :)

Find the median to the base of an isosceles triangle if the length of its base is 15 in and its area is 75 in2

Answers

see the attached figure to understand the problem

we know that
the median to the base is the segment BD
the base AC is 15 in
Area=75 in²
Area=AC*BD/2---------> BD=(Area*2)/AC---------> BD=(75*2)/15
BD=10 in

the answer is BD=10 in

5n + 3 = 2(n + 2) + 3n
N= ???
-Show All Work!-

Answers

Simplifying
5n + 3 = 2(n + 2) + 3n

Reorder the terms:
3 + 5n = 2(n + 2) + 3n

Reorder the terms:
3 + 5n = 2(2 + n) + 3n
3 + 5n = (2 * 2 + n * 2) + 3n
3 + 5n = (4 + 2n) + 3n

Combine like terms: 2n + 3n = 5n
3 + 5n = 4 + 5n

Add '-5n' to each side of the equation.
3 + 5n + -5n = 4 + 5n + -5n

Combine like terms: 5n + -5n = 0
3 + 0 = 4 + 5n + -5n
3 = 4 + 5n + -5n

Combine like terms: 5n + -5n = 0
3 = 4 + 0
3 = 4

Solving
3 = 4
The left and right sides are not equal, therefore there is no solution.

10 POINTS

Solve the combined inequality:

6 -2x < 12 or 7 + 2x < -11

Answers

The first thing we must do in this case is to solve both inequations.
 We have then:
 Inequality 1:
 6 -2x <12
 6-12 <2x
 -6 <2x
 -6/2 <x
 -3 <x
 Inequality 2:
 7 + 2x <-11
 2x <-11-7
 2x <-18
 x <-18/2
 x <-9
 Answer:
 (-inf, -9) U (-3, inf)

Explain how you would solve a triangles given two sides and the included angle?

Answers

Final answer:

To solve a triangle given two sides and included angle, use the law of cosines. This law is expressed as a² = b² + c² - 2bc cos(A), where a, b, c are the lengths of the sides, and A is the included angle.

Explanation:

To solve a triangle given two sides and the included angle, you would use the Law of Cosines. This law is used when you're given two sides and the included angle in a triangle (often abbreviated as SAS). The law states,

a² = b² + c² - 2bc cos(A)

where a, b, and c are the lengths of the sides of the triangle, and A is the included angle. So, in this case, if you're given sides b and c and included angle A, you would substitute these values into the formula to find side a.

For instance, if side b is 3 units, side c is 4 units, and angle A is 60 degrees, we would substitute these values into our formula like so:  a² = 3² + 4² - 2(3)(4) cos(60).

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The correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.

Solving triangles using the sine and cosine rule

For angle placed in between two sides of a triangle, we can use the cosine rule to determine the unknown angle

According to the cosine formula, we will have:

[tex]a^2=b^2+c^2-2bc \ cos\theta[/tex]

where a, and c are the sides of the triangle and theta is the central angle.

Also, the remaining angles can be determined using the law of cosines as shown:
a/sinA = b/sinB = c/sinC

Hence the correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.

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Suppose 6000 is placed in an account that pays 3% interest compounded each year. Assumed that no withdrawals are made from the account .

Find the amount at the end of one year ?

Find the amount in the account at the end of two year .

Answers

Find the amount at the end of one year? $6180
Find the amount in the account at the end of two year. $6365.4

Final answer:

With a principal amount of $6000 and a 3% annual interest rate compounded yearly, the account balance at the end of one year will be $6180, and at the end of two years, it will be $6365.40.

Explanation:

To calculate the amount of money in an account with compounded interest, we can use the formula [tex]A = P(1 + r/n)^{(nt)[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times the interest is compounded per year, and t is the time the money is invested for in years.

For the student's case, with $6000 placed in an account at 3% interest compounded each year with no withdrawals:

To find the amount at the end of one year, we calculate it as [tex]A = 6000(1 + 0.03/1)^{(1\times 1)[/tex], which equals $6000 × 1.03 = $6180.To find the amount at the end of two years, [tex]A = 6000(1 + 0.03/1)^{(1\times 2)[/tex], giving us $6000 × 1.03² = $6365.40.

As such, after one year, the student would have $6180, and after two years, the balance would be $6365.40.

Use technology or a z-score table to answer the question.

The number of huckleberries picked during a huckleberry contest are normally distributed with a mean of 300 and a standard deviation of 53. Jill picked 276 huckleberries in the contest.

What percent of huckleberry pickers picked less than Jill?

Round your answer to the nearest whole number.

Answers

The z-score is given by:
z=(x-μ)/σ
where:
μ is the mean
σ is the standard deviation
from the question:
x=276
μ=300
σ=53
substituting the value in our formula we get:
z=(276-300)/53
z=-0.453
the probability associated with this z-score is 0.3264~32.64%
thus the percentage pickers that picked less than Jill is 32.64%~33%

Answer:

33%

Step-by-step explanation:

33%

What is the volume of this rectangular prism? Rectangular prism with height labeled 3 centimeters, width labeled 5 centimeters, and length labeled 6 centimeters. cm³

Answers

The answer is (90 cm) hope it helps and have a good one!
You ca find the volume of a rectangular prism by multiply the width, length, and height. 

so 5x6x3=90

So theolume is 90.

A vehicle travels a distance of 5t4 − 10t2 + 6 miles in t + 2 minutes.
The vehicle's speed is __________miles/minute.

Answers

Answer:

Speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}miles/min[/tex]

Step-by-step explanation:

Given that,

Distance traveled by the vehicle =  5t⁴ - 10t² + 6 miles

time = t + 2 minutes

We need to find the speed of vehicle. Use the formula of speed is:

[tex]Speed=\frac{Dstance}{Tme}[/tex]

[tex]Speed=\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]

So, speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]

That's the final answer.

Answer:

The speed is 5t^3 - 10t^2 + 10t - 20 + 46/(t+2) miles per minute.

plz help me ill give you brainlest

Answers

a) 5/10 = (5/10)*(10/10) = 50/100

b) 47/100 +50/100 = (47+50)/100 = 97/100

Find the value of x so that this quadrilateral is a parrallelogram

Answers

Hey there!

Since this is a parallelogram, the 2 angles with the equations are congruent. Make them equal each other. 2x+60=4x-12. You get 72=2x. Divide by 2 on each side to get x=36. The answer is x=36.

I hope this helps!

With 128,134,140,146,152,whats the next number If the pattern continues?

Answers

by adding 6, the next number should be 158

Colleen has a bank account balance of $16.43. Toby has a bank account balance of –$10.21. Yosef has a bank account balance of $8.98. Which of the following statements are true?
Select all that apply.
A.
Colleen has the most money in her bank account.
B.
Toby has more money than Colleen.
C.
Yosef has less money than Toby.
D.
Toby's balance is further from zero dollars than Yosef's balance.
E.
Colleen's balance is further from zero dollars than Toby's balance.

Answers

The answers are A and E I believe.

Option A and option E are true, Colleen has the most money in her bank account and Colleen's balance is further from zero dollars than Toby's balance.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that Colleen has a bank account balance of $16.43.

Toby has a bank account balance of –$10.21.

Yosef has a bank account balance of $8.98.

Colleen has the most money in her bank account is true because $16.43 is greater than $8.98.

So the statement in A is true.

Colleen's balance is further from zero dollars than Toby's balance is also true.

Toby has more money than Colleen is false.

Yosef has less money than Toby is uncertain.

Hence, Option A and option E are true, Colleen has the most money in her bank account and Colleen's balance is further from zero dollars than Toby's balance.

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What is 1/4 written as a percent

Answers

1/4 written as a percent is 25%. To get this answer, divide 1 into 4. 1/4=0.25. Now, multiply 0.25 by 100 to get 25. :) 
Hope this helps! 
Tue answer is 1/4 written as a percent is 25% hope this helps you

What is the volume of the pyramid?

Answers

volume of pyramid = 1/3 (B) (h)
B is the area of base length.

V=1/3(121)(12)
V=484 cm^2
the base of the "square" pyramid is an 11x11 square, and its height is 12, therefore

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\quad \begin{cases} B=\textit{area of its base}\\ h=height\\ ---------\\ B=\stackrel{11\times 11}{121}\\ h=12 \end{cases}\implies V=\cfrac{(121)(12)}{3}[/tex]

PLEASE HELP WILL GIVE BRAINLIEST ******* Lucy made tables of values to approximate the solution to a system of equations.

Answers

When you look at the data, the value is between 1.6 and 1.5 since that is where the y-values cross at.  So my best answer would be (1.6,1.3) since it closely matches the values of intersection on the table

Answer:(1.6,1.3)

Step-by-step explanation:

In the diagram, what is the value of x?

Answers

The answer is option C (98°)

x is a supplementary angle to the angle labelled as measuring 82° (that is, the sum of x and 82° is 180°) because together, they make a straight line.

Mathematically,
x + 82° = 180°
x = 180° - 82°
x = 98°

Let us take as a given that x is normally distributed with a mean of 8.5 and a standard deviation of 2, what is p(x ≤ 6)? note: round your answer, if necessary, to two places after the decimal. please express your answer with two places after the decimal.

Answers

/ncvmbae,vnk.sdb,mfð v>Kjdbg,jrnvlnkjfnvkj,sbdkjvnkrjlhbvilabfns

Yi and Sue play a game. They start with the number $42000$. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way.

For example, Yi could start by dividing $42000$ by $3$. In this case, he would pass Sue the number $14000$. Then Sue could divide by $7$ and pass Yi the number $2000$, and so on.

The players are not allowed to produce a quotient that isn't an integer. Eventually, someone is forced to produce a quotient of $1$, and that player loses. For example, if a player receives the number $3$, then the only prime number (s)he can possibly divide by is $3$, and this forces that player to lose.

Who must win this game, and why? Explain your reasoning in complete sentences. (Don't just show one example of how the game could go. Instead, explain why the same player must always win, no matter what strategy either player tries to use!)

Answers

42000 = 2^4*3*5^3*7, so has 9 prime factors

The player who plays 9th will lose. If only 2 people are playing, that is the person who takes the first turn. The second player in a 2-person game with this starting number will always win.

A science teacher needs up to 15 female and male students for a competition. The science teacher needs at least 6 male volunteers. Let x represent the number of male volunteers and y represent the number of female volunteers. Which inequalities model the situation? Select each correct answer.
a. x+y≤15
b. y≥0
c. x+y<15
d. x>6
e. x≥6

Answers

e and c but don't quote me on that one haha
E and c I think hope it helped if not sorry

Johan takes out a 20-year mortgage at 4% to buy a house. When he looks at investing in 20-year, fixed-rate Treasuries, which of the following rates is most likely closest to the coupons on the Treasuries? Select the best answer from the choices provided. 2.2% 7.8% 3.9% 9.2%

Answers

Given that Johan takes-out a 20 year mortgage at 4% to buy a house. If he looks at investing in 20-year, fixed rate Treasuries, the most likely closest to the coupons of the treasuries is 3.8%, this is because any other rates apart from this will lead to an arbitrage opportunity. This means that if the percentage of the coupons are high, Johan may invest his proceeds from mortgage to treasuries and earn risk free interest. The right rate is 3.9%

Answer:

3.9%

Step-by-step explanation:

Investing in treasuries is often seeing as a risk free investment since it is sure that they will pay, but the rates are too low, when banks and other finnance corporations set up their mortages and other kinds of large loans interests rates they set them up higher than the fixed rate treasuries since otherwise it´d just be a better deal to put that money on treasuries than lending it to people.

What is the correct expression of 34,000 x 96,000 using scientific notation?

Answers

3.264 x 109 i got taught this in 5th grade

For this case we have the following product:

[tex] 34000 * 96000
[/tex]

We can rewrite both numbers using scientific notation.

We have then:

[tex] (3,4 * 10 ^ 4) * (9,6 * 10 ^ 4)
[/tex]

Then, we can rewrite the expression as follows:

[tex] (3,4 * 9,6) * (10 ^ 4 * 10 ^ 4)
[/tex]

Same basis, the exponents are added:

[tex] (3,4 * 9,6) * 10 ^ 8
[/tex]

Multiplying the expression within the parenthesis we have:

[tex] (32.64) * 10 ^ 8
[/tex]

Rewriting the left term as scientific notation we have:

[tex] (3,264 * 10 ^ 1) * 10 ^ 8
[/tex]

Finally we have:

[tex] 3,264 * 10 ^ 9 [/tex]

Answer:

the correct expression of 34,000 x 96,000 using scientific notation is:

[tex] 3,264 * 10 ^ 9 [/tex]

Helppppppppppppppppppppp

Answers

The composition of a function and its inverse is x. So an easy approach to solve this question is to find the composition of a function with itself. If the composition results in an answer "x", then this will mean that function and its inverse are the same.

Finding the composition for 1st option:
[tex](fof)(x) = f(f(x))= \frac{ \frac{x-1}{x+5}-1 }{ \frac{x-1}{x+5}+5 } \\ \\ = \frac{ \frac{x-1-x-5}{x+5} }{ \frac{x-1+5x+25}{x+5} } \\ \\ = \frac{-6}{6x+24} \\ \\ = \frac{1}{x+4} [/tex]

Since the composition of the function with itself is not x, the function and its inverse are not the same.

Similarly, we can find the compositions of next 3 functions with themselves. The results of compositions are listed below:

(gog)(x)=g(g(x)) = x

(hoh)(x)=h(h(x))=[tex] \frac{4x-3}{7-x} [/tex]

(kok)(x)=k(k(x))= x

Thus the option 2 and 4 are the correct answers i.e. these functions are the same as their inverse functions. 

Ratio Question solving with algebra need help must finish soon

Answers

Consider this option.
Note, that the answers are marked by green colour.

Is Sylvia buys 5 shirts for $75 a unit rate?

Answers

I believe you are finding the total cost of 5 shirts given the unit rate. To compute for the total cost, you have to multiply the unit rate to the number of shirts bought:

5 shirts x $75 unit rate = $375

Therefore, Sylvia will spend $375 to buy 5 shirts.

No is Sylvia buys 5 shirts for $75 one shirt would be $15 .

What is the diameter of a circle with a circumference of 176 feet use for 22 over for pie

Answers

Formula for Diameter: 2 x radius
Formula for Radius:  R= C/2(pi)
R= 176/2(22/7)
R=28.01
2(28.01)=56.02

Answer= 56.02


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