Through algebra, we found that Xavier's current age is 61, which makes Yolanda 65. Subtracting the 40 years of marriage from their current ages, we determined that Yolanda was 25 years old when they got married.
Explanation:The question given by the student is a problem that can be solved with simple algebra. To find out how old Yolanda was when they married, we first need to establish the current ages of Xavier and Yolanda based on the information given.
Let's denote Xavier's current age as x years. Consequently, Yolanda's current age will be x + 4 years (since she is 4 years older than Xavier). According to the problem, the sum of their ages now is 126 years. We can set up the following equation based on this information:
x + (x + 4) = 126
By solving the equation:
Combine like terms: 2x + 4 = 126
Subtract 4 from both sides: 2x = 122
Divide both sides by 2: x = 61
This means that Xavier is now 61 years old, and Yolanda is x + 4, which is 65 years old. Since they have been married for 40 years, we subtract 40 from their current ages to get their ages at the time they got married. So, Yolanda was 25 years old when she got married.
Sharif and jose share money in the ratio 2:7 bose gets #49 work out how much Sharif gets
Answer:
$14
Step-by-step explanation:
given
Sharif : Jose ---> 2:7
this means that:
Fraction of total that Sharif gets = 2 / (2+7) = 2/9
Fraction of total that Jose gets = 7 / (2+7) = 7/9
we are given that Jose gets $49, hence
jose's fraction = 7/9 , represents $49
i.e
7/9 -----> $49
1/9 -----> $49 ÷ 7 = $7
Sharif's fraction = 2/9 -----> $7 x 2 = $14
Graph the system of equations to determine the solution. In your final answer, include your graph and the solution.
x = y + 4
y = x - 4
Answer:
Infinitely many solution.
Step-by-step explanation:
The given system is
x = y + 4
y = x - 4
To graph the first equation, we write it in slope-intercept form to get: to
x=y+4
This implies y=x-4.
This has a slope of 1 and a y-intercept of -4.
The graph of this function is shown in the attachment.
The second equation is y=x-4.
This equation is identical to first equation, so its graph coincides with the first one.
The system has infinitely many solution.
The system of equations has infinitely many solutions.
The system of equations:
1. [tex]\( x = y + 4 \)[/tex]
2. [tex]\( y = x - 4 \)[/tex]
can be rearranged to show that they represent the same line:
1. [tex]\( y = x - 4 \)[/tex] (Rearranged from [tex]\( x = y + 4 \)[/tex])
2. [tex]\( y = x - 4 \)[/tex]
Graphing these equations shows that they are the same line, meaning every point on the line [tex]\( y = x - 4 \)[/tex] is a solution to the system.
Thus, the solution to the system of equations is all points [tex]\((x, y)\)[/tex] that satisfy [tex]\( y = x - 4 \)[/tex]. This means the lines intersect everywhere along [tex]\( y = x - 4 \)[/tex].
There is no single intersection point because they overlap completely.
Mindy bought10 grapefruits at the rate of $6.00 per dozen. How much did she pay for the fruit?
Answer 5
Step-by-step explanation:
6/12=.5
.5*10=5
Final answer:
Mindy bought 10 grapefruits at a rate of $6.00 per dozen. By calculating the cost per grapefruit at 50 cents and multiplying by 10, we find that she paid a total of $5.00 for the grapefruits.
Explanation:
Calculating the Cost of Grapefruits
Mindy bought 10 grapefruits at the rate of $6.00 per dozen. To find out how much she paid for the grapefruits, we need to calculate the cost per grapefruit and then multiply by the number she bought.
A dozen grapefruits cost $6.00, so each grapefruit costs $6.00 divided by 12, which is 50 cents per grapefruit. Since Mindy bought 10 grapefruits, the total cost will be 10 grapefruits multiplied by 50 cents each.
Performing the multiplication, we get:
10 grapefruits × 50 cents per grapefruit = 500 cents
Since there are 100 cents in a dollar, 500 cents is the same as $5.00.
Therefore, Mindy paid $5.00 for the grapefruits.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A teacher brings 3 gallons of juice on a field trip. there are 36 students on the trip. A. how many fluid ounces of juice does the teacher bring? show your work. B. does the teacher have enough juice to give each student a 12-fluid ounce glass of juice? explain.
Answer:
A) The teacher brought 384 fluid ounces of juice
B)NO, the teacher doesn't have enough juice to give each student a 12-fluid ounce glass of juice
Step-by-step explanation:
Given:
The total quantity of juice brought by the teacher for the field trip = 3 gallons of juice
The number of students in the field trip = 36
A)fluid ounces of juice
We know that
1 gallon = 128 fluid ounce
So we have to convert the given 3 gallons of juice to fluid ounces
3 gallons of fruit juice [tex]= 3 \times 128[/tex] fluid ounces
3 gallons of fruit juice = 384 fluid ounces
The teacher had 384 fluid ounces of fruit juice
B. enough juice to give each student a 12-fluid ounce glass of juice
The teacher wants to give 12 fluid ounce of juice to one student
So, to give 36 students
the teacher will need
=> [tex]36 \times 12[/tex]
=> 432 fluid ounces of juice
but the teacher has only 384 fluid ounces of juice .
Thus the teacher still needs 48 fluid ounces of juice
Solve 7x + 3 = 3 + 7x. Show all work
Answer:
Infinitely many solutions.
Step-by-step explanation:
7x+3=3+7x
7x-7x+3=3
3=3
If f(7)=22, then f^-1(f(7))=?
Please help!!
Answer:
7
Step-by-step explanation:
In general, the point of an inverse function is to show you the value that gives a particular function value. That is, ...
[tex]f^{-1}(22)=7\\\\f^{-1}(f(x))=x\\\\f^{-1}(f(7))=7[/tex]
The inverse function [tex]f^{-1}[/tex]essentially 'undoes' the operation of the function f. Given that f(7) is 22, applying the inverse function [tex]f^{-1}(f(7))[/tex] will return us to the original input, which is 7.
Explanation:The question is discussing the concept of inverse functions in mathematics. A function has an inverse if it can be 'undone' or 'reversed'. In the notation [tex]f^{-1}[/tex], it signifies the inverse function of f. The value of [tex]f^{-1}(f(7))[/tex] indicates that we have first applied the function f to the input 7 and then applied the inverse function [tex]f^{-1}[/tex] The result would be the original input before function f was applied.
Given that f(7) is equal to 22, applying the inverse function f^-1 to this result will return us to the original input. Hence, [tex]f^{-1}(f(7))[/tex]equals 7.
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find the average rate of change of f(x) = 3(2)* between x = 1 and x = 4
Find the average rate of change of f(x) = 3(2)^x between x = 1 and x = 4
Answer:The average rate of change is 14
Solution:The rate of change is given by formula:
[tex]\text { Average Rate }=\frac{f(b)-f(a)}{b-a}[/tex]
Here the given interval is x = 1 and x = 4
Therefore, the formula becomes,
[tex]\text { Average Rate }=\frac{f(4)-f(1)}{4-1}\\\\\text { Average Rate }=\frac{f(4)-f(1)}{3}[/tex]
Let us find f(4) and f(1)
Given function is:
[tex]f(x)=3(2)^x[/tex]
Substitute x = 4 in function
[tex]f(4)=3(2)^4\\\\f(4) = 3 \times 16 = 48[/tex]
Thus f(4) = 48
Substitute x = 1 in function
[tex]f(1) = 3(2)^1\\\\f(1) = 6[/tex]
Now substitute the values back into formula
[tex]\text { Average Rate }=\frac{f(4)-f(1)}{3}\\\\\text { Average Rate }= \frac{48-6}{3}\\\\\text { Average Rate }= 14[/tex]
Thus average rate of change is 14
I need help please and thank you
Answer:
58 degrees
Step-by-step explanation:
180-87-35= 58
Write 51% as a fraction in simplest form
Howard is saving to buy a mountain bike that costs $245, excluding tax. he has already saved $28. what is the least amount of money Howard must save each week so that at the end of the 9th week. he has enough money to buy the bike? round your answer to the nearest dollar.
Answer: 24
Step-by-step explanation:
245-28= 217
217÷9= 24.1
The equation can be set up as 245 = ?(9) + 28
Solving for the ?, we subtract 28 from the entire equation: 217 = ?(9)
Divide by 9: 24.11111 or, rounded, $24 each week.
Solve 12=0.9a '''''''''''''''''''''''''''''''
Answer:
13.3
Step-by-step explanation:
Because in order to get the a separated from the 0.9, you must divide the 0.9a by 0.9 to cancel the 0.9 out of the equation. That way, you are left with A. but in order to do that, you must divide both sides of the equation.
Ultimately, it ends up being 12 divided by 0.9, which is 13.3
What is 15.06 rounded to the nearest tenth?
15.0
15.1
15.6
16.1
Answer:
15.1
Step-by-step explanation:
Answer:
15.1
Step-by-step explanation:
Since the digit in hundredths place is greater than 5, hence after removing the digit 6 we will add 1 in the tenth place. So the answer will become 15.1
If one-third of a number, x, is greater than five less than twice the number, which of the following is true?
If one-third of a number, x, is greater than five less than twice the number, which of the following is true? x < 3, x > -3, x > -3/5, x < 3/5
Answer:Option A
The true inequality is x < 3
Solution:Let the number be "x"
One third of number means that,
[tex]\rightarrow \frac{1}{3} \text{ of number } = \frac{1}{3} \times x = \frac{x}{3}[/tex]
Thus from given statement,
one-third of a number x is greater than five less than twice the number
[tex]\text{ one-third of a number x } > \text{ five less than twice the number x }[/tex]
[tex]\frac{x}{3} > 2x - 5[/tex]
Solve the above inequality
Multiply both sides of inequality by 3
[tex]\frac{x}{3} \times 3 > (2x - 5) \times 3[/tex]
[tex]x > 3(2x-5)[/tex]
Solve for brackets in R.H.S
[tex]x > 6x - 15[/tex]
Add -6x on both sides of inequality
[tex]x - 6x > 6x - 15 -6x\\\\-5x>-15[/tex]
Multiply both sides of inequality by -1
Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign
[tex]5x < 15[/tex]
Divide both sides of inequality by 5
[tex]x < 3[/tex]
Thus the true inequality is x < 3
Final answer:
The inequality one-third of a number x being greater than five less than twice the number translates to x < 3 after solving the inequality properly.
Explanation:
If one-third of a number, x, is greater than five less than twice the number, we can write this as an inequality. To solve for x, we can set up the following expression:
1/3 * x > 2x - 5Now, we need to solve for x. First, we'll get all the x terms on one side and the constants on the other:
(1/3)x - 2x > -5To combine like terms, we convert 2x to 6/3x:(1/3)x - (6/3)x > -5-5/3x > -5Multiplying through by -3/5 to isolate x reverses the inequality:x < 3The statement that is true is that x is less than 3. This means all solutions for x are numbers that are less than 3.
What is the value of the expression below 81^1/4
Answer:
3
Step-by-step explanation:
recall that 81 = 3 x 3 x 3 x 3 = 3⁴
given
[tex]81^{\frac{1}{4} }[/tex]
= ( 3⁴) ^ (1/4)
= [tex]3^{(4)(1/4)}[/tex]
= 3
Answer:
Step-by-step explanation:
81^1/4
And 81 = 3⁴
:- 81^1/4 = 3^(4×1/4)
= 3¹ = 3
5. PLEASE HELP
What is the potential energy of the ball as it is half way through the fall, 20 meters high? Answer:
Answer:
The potential energy of the ball having 2kg mass would be [tex]392[/tex] J
Step-by-step explanation:
I am assuming the ball has a mass of 2 kg, as you have not mentioned the mass of a ball.
Considering the formula for calculating the gravitational potential energy
[tex]G.P.E\:=\:m.g.h[/tex]
As
[tex]m = 2[/tex] kg
Acceleration of gravity = g = 9.8 [tex]ms^{-2}[/tex]
As the ball is on the height = h = 20 meters
So,
[tex]G.P.E\:=\:(2)(9.8)(20)[/tex]
[tex]G.P.E\:=392[/tex] J
Therefore, the potential energy of the ball = [tex]392[/tex] J
Keywords: potential energy, Gravitation potential energy
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Answer:
i agree
Step-by-step explanation:
Dimensions of a rectangle whose length is 8 more than twice it’s width and has a perimeter of 40 cm.
Answer:
Width = 4 cm
Length = 16 cm
Step-by-step explanation:
We are given;
Perimeter = 40 cm Assuming the width is x Then, length is 2x + 8 ( 8 more than twice the width)We are required to determine the dimensions of the rectangle;
We need to know that the perimeter of the rectangle is given by;Perimeter = 2 (length + width)In this case;
2 ( 2x + 8 + x) = 40
2 ( 3x + 8 ) = 40
6x + 16 = 40
6x = 24
x = 4
Thus; the dimensions of the rectangle are;
Width = 4 cm, and
Length = 16 cm
You're trying to enlarge an image that is 4 centimeters tall and 10 centimeters wide onto a billboard that is 3 meters tall and 8 meters wide.
What is the height scale?
Answer: Its pretty basic
Step-by-step explanation:
Compare 4 centimeters to 300 centimeters.
is there any smart people here who ACTUALLY answer questions? everytime i ask questions, people just ignore them, or troll me. its so annoying. im asking to find at leat ONE person that can do stuff. anyone???????
Answer:
I will answer any question you ask me! You can call me by my nickname- Dark. If you have any questions, just ask me!
Step-by-step explanation:
Answer: At your service. I don't troll. I think it's pointless to troll because people on brainly are here for HELP not for Jokes.
how many solutions are there to the following system of equations? 3x-9y=0 -x+3y=-3
Answer:
no solution
Step-by-step explanation:
if you graph both equation the lines are parallel.
parallel = no solution
overlap = infinite solution
intersect = one solution
Amanda drove her car 81 km and use 9 L of fuel. She wants to know how many kilometers she can drive on 22 L of fuel. She assumes her car will continue consuming for you at the same rate. How far can a man to drive on 22 L of fuel?
If 81km = 9L, then 9km = 1L.
So ?km = 22L.
With 22L, Amanda can drive 198km.
An ice-cream factory makes 100 quarts of ice cream in 5 hours. How many quarts could be made in 36 hours? What was that rate per day?
Answer: the answer would be 720
Step-by-step explanation:
Answer:
Step-by-step explanation:
direct proportion
100:5 = x : 36
Product of mean = 5*x
Product of extremes = 100*36
Product of mean = Product of extremes
5*x=100*36
x = 100*36/5
= 20*36 = 720
720 quarts could be made in 36 hours.
Evaluate the expression when c=-5 and x= 3.
-6x+c
ALEKS
At eagle bay, it cost $12 per hour to rent a canoe. Nate and his friends rented a canoe for 4 hours and paid $68. Write and solve a linear equation to find the cost of the canoe for 7 hours
To find the cost of renting a canoe for 7 hours, we can set up a linear equation using the given information. Using the point-slope form, we can find the equation of the line. Substituting x = 7 into the equation gives us the cost for 7 hours. The cost of renting a canoe for 7 hours is $100.25.
Explanation:To find the cost of renting a canoe for 7 hours, we can set up a linear equation using the given information. Let's define the variables:
x = number of hours
y = cost of renting a canoe for x hours
From the given information, we know that it cost $12 per hour to rent a canoe. Nate and his friends rented a canoe for 4 hours and paid $68. This gives us the first point on the line: (4, 68).
To find the equation, we can use the point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using the slope formula, we can find the slope: m = (y2 - y1) / (x2 - x1) = (68 - 25) / (4 - 0) = 43 / 4 = 10.75.
Now we can plug in the values into the point-slope form: y - 68 = 10.75(x - 4).
To find the cost for 7 hours, we substitute x = 7 into the equation and solve for y: y - 68 = 10.75(7 - 4), y - 68 = 10.75 * 3, y - 68 = 32.25, y = 32.25 + 68, y = 100.25.
Therefore, the cost of renting a canoe for 7 hours is $100.25.
Final answer:
To calculate the cost of renting a canoe for 7 hours, first find the fixed cost by using the known rental time and cost. The equation is y = 12x + 20, where y is the total cost and x is the number of hours. For 7 hours, the cost is $104.
Explanation:
We are given that the cost to rent a canoe at Eagle Bay is $12 per hour. Nate and his friends rented the canoe for 4 hours, and they paid a total of $68. To find the equation, we need to consider that there might be a fixed cost in addition to the hourly charge. First, let's define our variables: let x be the number of hours the canoe is rented, and let y be the total cost.
Based on the information provided, we can create the equation y = 12x + b, where b is the possible fixed cost.
To find the fixed cost, we use the information that renting the canoe for 4 hours cost $68: 68 = 12(4) + b. Solving for b, we find:
68 = 48 + b
b = 68 - 48
b = 20
So, the fixed cost is $20, and the equation becomes y = 12x + 20. To find the cost of renting the canoe for 7 hours, we substitute 7 for x in our equation:
y = 12(7) + 20
y = 84 + 20
y = $104
The cost to rent the canoe for 7 hours would be $104.
Gretchen made a paper cone to hold a gift for a friend. The paper cone was 16 inches high and had a radius of 4 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
Answer:
268.0 in²
Step-by-step explanation:
refer to attached graphic as reference
volume of cone, V = (1/3) πr²h
in our case, we are given r = 4" and h = 16"
substituting this into equation:
V = (1/3) πr²h
= (1/3) ·(3.14) · (4)²· (16)
= 267.94667 in²
= 268.0 in² (nearest tenth)
The volume of the paper cone to the nearest tenth = 268.0 in².
Volume of coneVolume of cone, V = (1/3) πr²h
Where, h= height of the cone
r = radius of the cone
V= volume of the cone
In our case, we are given r = 4" and h = 16"
substituting this into the equation:
V = (1/3) πr²h
Substitute into the formula we have
The value of π = 3.14
V = (1/3) ·(3.14) · (4)²· (16)
= 267.94667 in²
= 268.0 in² (nearest tenth)
Therefore, the volume of the cone = 268.0 in² (nearest tenth)
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Give me 10 cash amounts that total up to 16,100.00.
Answer:
Ten amounts:
$ 13,979 $1,000 $100 $2 $10 $300 $4 $5 $200 $500
Step-by-step explanation:
Choose any numbers you want for the first 9 cash amounts. Then, find out the difference between the 9 cash amounts and 16,100. That will be the tenth amount.
Example:
I choose $1,000 $100 $2 $10 $300 $4 $5 $200 $500.
If I add them together, I get $2,121.
Remember that was 9 amounts, and we need 10.
To get the last amount, subtract what you have ($2,121) from what you need ($16,100).
16,100 - 2,121 = $13,979
The last amount will be $13,979.
Check your answer:
Add all of the ten amounts to get 16,100.
1,000 + 100 + 2 + 10 + 300 + 4 + 5 + 200 + 500 + 13,979
= 16,100
Therefore this answer is correct.
the length of a rectangular window is 5 feet more than its width, w. The area of the window is 36 square feet. Which equation could be used to find the dimensions of the window?
Answer:
36 = (w+5)w = w^2 + 5w
Step-by-step explanation:
The equation to find the dimensions of the window is w*(w + 5) = 36, where w represents the width of the window.
Explanation:The subject of this question is Mathematics. This problem is a classic example of a quadratic equation in algebra, where you are given the area of a rectangle and a relationship between its length and width. In this case, the length of the rectangle is 5 feet more than its width (w). So, the length can be represented as w + 5. The area of a rectangle is calculated as length times width, so we can set up the following equation where the area is 36 square feet: w*(w + 5) = 36.
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the velocity v of an object rolled down an inclined plane is given by the formula v equals 26d square-rooted, where d is the distance the object has rolled. solve for d
Answer: d = v/26
Step-by-step explanation:
What is the answer too -4(3a-5b-7)
Hope it will help u.........
Please do 13 ive been trying for 3 hour pls solve x
Answer:
x = 3
Step-by-step explanation:
We should know that:
A straight segment joining the middle of two sides in a triangle is parallel to the third side and equal to half of it.
So,
3x + 1 = (1/2) * 20 = 10
3x = 10 - 1 = 9
x = 9/3 = 3
So, the value of x = 3
Please help me figure out
Answer:
The equation of line will be [tex]y=x+2.75[/tex]
Step-by-step explanation:
Given admission and [tex]6[/tex] sample costs $[tex]8.75[/tex]
And admission and [tex]9[/tex] samples costs $[tex]11.75[/tex]
Let cost of the sample is [tex]y[/tex] and number of sample is [tex]x[/tex]
Now, we will find the slope of line
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{11.75-8.75}{9-6}\\\\m=\frac{3}{3}\\\\m=1[/tex]
Plug slope as [tex]1[/tex] and point [tex](6,8.75)[/tex] in the equation we get,
[tex](y-y_1)=m(x-x_1)\\y-8.75=1(x-6)\\y-8.75=x-6\\y=x-6+8.75\\y=x+2.75[/tex]
The equation of line will be [tex]y=x+2.75[/tex]