Answers
Answer:
Part a) The solution is the ordered pair (6,10)
Part b) The solutions are the ordered pairs (7,3) and (15,1.4)
Step-by-step explanation:
Part a) we have
[tex]\frac{x}{2}-\frac{y}{5}=1[/tex] ----> equation A
[tex]y-\frac{x}{3}=8[/tex] ----> equation B
Multiply equation A by 10 both sides to remove the fractions
[tex]5x-2y=10[/tex] ----> equation C
isolate the variable y in equation B
[tex]y=\frac{x}{3}+8[/tex] ----> equation D
we have the system of equations
[tex]5x-2y=10[/tex] ----> equation C
[tex]y=\frac{x}{3}+8[/tex] ----> equation D
Solve the system by substitution
substitute equation D in equation C
[tex]5x-2(\frac{x}{3}+8)=10[/tex]
solve for x
[tex]5x-\frac{2x}{3}-16=10[/tex]
Multiply by 3 both sides
[tex]15x-2x-48=30[/tex]
[tex]15x-2x=48+30[/tex]
Combine like terms
[tex]13x=78[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=\frac{x}{3}+8[/tex]
[tex]y=\frac{6}{3}+8[/tex]
[tex]y=10[/tex]
The solution is the ordered pair (6,10)
Part b) we have
[tex]xy=21[/tex] ---> equation A
[tex]x+5y=22[/tex] ----> equation B
isolate the variable x in the equation B
[tex]x=22-5y[/tex] ----> equation C
substitute equation C in equation A
[tex](22-5y)y=21[/tex]
solve for y
[tex]22y-5y^2=21[/tex]
[tex]5y^2-22y+21=0[/tex]
Solve the quadratic equation by graphing
The solutions are y=1.4, y=3
see the attached figure
Find the values of x
For y=1.4
[tex]x=22-5(1.4)=15[/tex]
For y=3
[tex]x=22-5(3)=7[/tex]
therefore
The solutions are the ordered pairs (7,3) and (15,1.4)
Related Questions
I need the answer I tried to do the work but my work is wrong so can you help me
Answers
Answer:
$545
Step-by-step explanation:
Let the total cost per year be y.
He spent a flat amount of $125 per year.
Then he spend an additional $35 per months. There are 12 months in a year so that's a total of 35*12=$420.
Add up the cost
y = 125 + 420 = $545
While looking at some reports, a store manager notes that carousel horses that retail for $620 end up costing customers $651 once the sales tax is added. What is the sales tax percentage?
Answers
Answer:
[tex]\large \boxed{5.0 \, \% }[/tex]
Step-by-step explanation:
1. Calculate the amount of tax
Total cost = selling price + sales tax
Sales tax = total cost - selling price
Total cost = $651
-Selling price = - 620
Sales tax = $ 31
2. Calculate the percent tax
[tex]\text{\% Tax} = \dfrac{\text{\$31}}{\text{\$620}} \times 100 \, \% = \mathbf{5.0 \, \%}\\\\ \text{The sales tax percentage is $\large \boxed{\mathbf{5.0 \, \% }}$}[/tex]
I
10
11
12
13
Miguel bought 6 cos that were each the same price. Including sales tax, he paid a total of $99.60. Each CD had a tax of $1.30. What was the price of each CD
before tax?
*
5
?
Continue
Submit Assignment
2019 McGraw-Hill Education All Rights Reserved. Terms of Use
Pry
9 N > EO
Sign out
Us
Answers
Answer:
The price of each CD before tax was $15.30.
Step-by-step explanation:
Given:
Miguel bought 6 CDs that were each the same price.
Including sales tax, he paid a total of $99.60.
Each CD had a tax of $1.30.
Now, to find the price of each CD before tax:
So, to get the price of 1 CD including tax by using unitary method:
Total price of 6 CDs including tax = $99.60.
So, the price of 1 CD including the sales tax = $99.60 ÷ 6 = $16.60.
Thus, the price of each CD including tax = $16.60.
Tax on each CD = $1.30.
Now, by subtracting we get the price of each CD before tax:
[tex]\$16.60-\$1.30[/tex]
[tex]=\$15.30.[/tex]
Therefore, the price of each CD before tax was $15.30.
To write the explicit rule, we need some information about the following series:
3, 6, 12, 24, 48, ...
In Blank 1: a1 =
In Blank 2: r =
Answers
Answer:
see explanation
Step-by-step explanation:
Note the common ratio r between consecutive terms of the sequence
r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
The explicit rule for a geometric sequence is
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 3 and r = 2, thus
[tex]a_{n}[/tex] = 3[tex](2)^{n-1}[/tex] ← explicit rule
Farrah bought a new car in 2016 one year later the car had depreciated in value by 2300 and was worth $20,140 find the value of her car when she purchased it in 2016
Answers
Answer:
Farrah purchased the car in 2016 at the price of $22,440.
Step-by-step explanation:
Given:
Cost of the car in 2017 = $20,140
Depreciation in the cost after 2016 was = $2300
To find cost of the car in 2016.
Solution:
Let cost of the car in dollars in 2016 be = [tex]x[/tex]
Depreciation in value after a year was by = $2300
Thus, cost of car in dollars in 2017 will be = [tex]Original\ cost-Depreciation\ =x-2300[/tex]
Given cost of car in 2017 = $20,140
So, we have:
[tex]x-2300=20140[/tex]
Solving for [tex]x[/tex]
Adding 2300 both sides.
[tex]x-2300+2300=20140+2300[/tex]
∴ [tex]x=22440[/tex]
Thus, cost of the car in 2016 was = $22,440
Find X.
pls & thank you :)
Answers
Answer:
The correct answer is D. 69
Step-by-step explanation:
Let's recall that if an exterior angle has its vertex where two rays share an endpoint outside a circle, the measure of that exterior angle is found by dividing the difference between the measures of the intercepted arcs by two.
Therefore, we have:
x = (Measure of arch CD - Measure of arch BD)/2
Replacing with the real values:
x = (210 - 72)/2
x = 138/2 = 69°
The correct answer is D. 69
∫x(x-6)³dx by using substitution u=x-6
Answers
Answer:
[tex]\large\boxed{\int\bigg(x(x-6)^3\bigg)dx=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C}[/tex]
Step-by-step explanation:
[tex]\int\bigg(x(x-6)^3\bigg)dx\Rightarrow\left[\begin{array}{ccc}x-6=u\\x=u+6\\dx=du\end{array}\right]\Rightarrow\int\bigg((u+6)u^3\bigg)du\\\\=\int(u^4+6u^3)du=\dfrac{1}{5}u^5+\dfrac{6}{4}u^4+C=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C[/tex]
Which of the following will help you reach long term goals?
A.Breaking big goals into smaller ones
B.Writing down your goals
C.Taking care of your physical and mental health
D.All of the above
Answers
Answer:
D
Step-by-step explanation:
If you Break the bigger ones into smaller ones they will seem more attainable. Writing down your goals will help you remember. Taking care of resell will help you attain your goals faster and easier
CAN ANYONE HELP PIZZ FAST
Answers
The figure/drawing isn't needed to answer this question.
The question tells us ABCD ~ WXYZ, which means trapezoid ABCD is similar to WXYZ.
Point A corresponds to point W, B corresponds with X, C corresponds with Y, and D corresponds with Z (first, second, third, and last letters correspond with each other according to the similarity statement).
Now let's check each answer choice and see which applies to these similar trapezoids:
Since point B corresponds with point X and the trapezoids are similar, they must be congruent angles. Thus, the first choice is correct.Point Y does not correspond with point A. Thus, it is possible the angles are not congruent. The second choice is incorrect.Point A corresponds with W and B corresponds with X. Thus, line segment AB will be similar to line segment WX. However, they are not equal. Thus, the third choice is incorrect.There's an equal sign in this choice, too, just like the last, and the two segments are corresponding line segments. Thus, the fourth choice is incorrect.This looks like the third choice, but with a similarity symbol instead of an equal sign. Now, the statement is true and the fifth choice is correct.This looks like the fourth choice but with a similarity instead of an equal sign. Now, the statement is true and the sixth choice is correct.Let me know if you need any clarifications, thanks!
Answer:
c kd kjdkwj
Step-by-step explanation:
jc kjkd ndjfhcajhd,cm sdnfj vkdshf vndc jdsfhbv
When two of the three numbers are added at a time, the possible sums are 32, 39, 23. What is the sum of all three numbers?
Please explain.
Answers
Answer:
47
Step-by-step explanation:
Let a, b, and c be those three numbers.
When two of the three numbers are added at a time, the possible sums are 32, 39, 23. Let
[tex]a+b=32\\ \\a+c=39\\ \\b+c=23[/tex]
Add these three equations:
[tex]a+b+a+c+b+c=32+39+23\\ \\2a+2b+2c=94[/tex]
Divide this equation by 2:
[tex]a+b+c=47[/tex]
The sum of all three numbers is 47.
Emily Runs 10 ft./s Jake runs 334 feet and 26 seconds Katie runs 1 mile in 596 seconds and Stephanie runs 580 feet in one minute who runs the fastest
Answers
Jake runs fastest
Step-by-step explanation:
The given is:
Emily Runs 10 ft./sJake runs 334 feet in 26 secondsKatie runs 1 mile in 596 secondsStephanie runs 580 feet in one minuteWe need to find who runs fastest
To solve the problem we must to find the unit rate of each one in feet per second
∵ Jake runs 334 feet and 26 seconds
- To find the unite rate divide 334 feet by 26 seconds
∴ Jake's rate = 334 ÷ 26 = 12.85 ft./s
∵ Katie runs 1 mile in 596 seconds
- Change the mile to feet
∵ 1 mile = 5280 feet
∴ Katie runs 5280 feet in 596 seconds
- To find the unite rate divide 5280 feet by 596 seconds
∴ Katie's rate = 5280 ÷ 596 = 8.86 ft./s
∵ Stephanie runs 580 feet in one minute
- Change the minute to seconds
∵ 1 minute = 60 second
∴ Stephanie runs 580 feet in 60 seconds
- To find the unite rate divide 580 feet by 60 seconds
∴ Stephanie's rate = 580 ÷ 60 = 9.67 ft./s
∵ Emily's rate is 10 ft./s
∵ Jake's rate is 12.85 ft./s
∵ Katie's rate is 8.86 ft./s
∵ Stephanie's rate is 9.67 ft./s
- The fastest one who has the greatest rate
∵ Jake's rate is the greatest
∴ Jake runs the fastest
Jake runs fastest
Learn more:
You can learn more about the word problems in brainly.com/question/1634276
#LearnwithBrainly
To find the quotient of 8 divided by 1/3, multiply 8 by?
Answers
Answer:
Multiplying 8 by 3 will give the same quotient.
Step-by-step explanation:
We have to find the quotient of 8 divided by [tex]\frac{1}{3}[/tex], so, we have to follow the following steps.
[tex]8 \div \frac{1}{3} = \frac{8}{\frac{1}{3}} = 8 \times 3 = 24[/tex]
So, it is clear from the above steps that dividing 8 by [tex]\frac{1}{3}[/tex] is equivalent to multiplying 8 by 3.
Therefore, multiplying 8 by 3 will give the same quotient. (Answer)
Answer:
3/4 divied by 8 im sorry if it wrong im not to smart cuz my mom or dad doesnt help me :( and im homeschooled
Step-by-step explanation:
The Neolithic Revolution
led people to lead lives based on hunting and gathering
allowed people to live in permanent settlements
reduced people’s need for food and resources
prevented the advance of civilization
i wel give the branlist to howe answers it carect
Answers
The Neolithic Revolution allowed people to live in permanent settlements.
Explanation:
The Neolithic Revolution is the phase of transition in which many of the human cultures in the world shifted their lifestyle to permanent settlement and agriculture from hunting and gathering.
This era is also named as First Agricultural Revolution or Neolithic Demographic Transition. The agricultural practices led the cultures to develop the knowledge of domestication of animals and they began to observe and experiment with the plants (to learn or know how they grow and develop).
Neolithic period is named as revolution because this period changed the way of life of most of the communities. This first occurred in so-called "Fertile Crescent" or Mesopotamia (modern Iraq).
The Neolithic Revolution allowed people to live in permanent settlements.
Answer: Option B
Step-by-step explanation:
This phase 'Neolithic Revolution' witnessed the change in the behavior of the people, notably the development of habits like hunting and gathering of animals and fruits.Although it is a development of habits, people refer to it as a revolution because it changed the lifestyle of the communities.It dates back to prehistoric times which is said to have happened almost nine thousand years ago. Thereby concluding that, the Neolithic revolution allowed people to live in permanent settlements.15 more than twice a number
Answers
Answer:
15×2x
Step-by-step explanation:
Answer:
15 more than twice a number if it is a certain number u would multiply 15 times what ever number u chose
Step-by-step explanation:
A recipe for 8 apple dash cinnamon muffins calls for 1 cup of flour. The number of muffins that can be made varies directly with the amount of flour used. There are 1 and three fourths cups of flour available. How many muffins can be made?
Answers
Answer:
you can make 14 muffins
Step-by-step explanation:
To get this answer you first need to know that 1 cup makes 8 muffins. Next know that there's 1 3/4 cups of flour. Because you know that 1 cup makes 8 muffins you need to figure out how many muffins 3/4 a cup of flour can make. To do this you divide 8 by 4. Hence 8 divided by 4 is 2. So know you know that for every 1/4 cup you can make 2 muffins. Now since there's 3/4 cup of flour you then multiply 2 by 3 which is 6. Now you have to add 1 cup ( 8 muffins) to 3/4 cup ( 6 muffins ) of flour which then equals 14. You then get the answer , 1 3/4 cups of flour can make 14 muffins. Hope this helped ;)
One number is 10 times as large as another and their difference is 81. Find the numbers.
Answers
Answer:
one number is 90 and the other one 9
Step-by-step explanation:
Let's refer to the larger number as "x", and the smaller as "y", so we can create equations with those unknowns and solve them algebraically.
Now let's write the first phrase we are given in mathematical form:
"One number is 10 times as large as another one"
Remember that our larger number is "x", so the first equation out of this phrase is:
x = 10 * y
Now for the second phrase:
"Their difference is 81"
Here we need to make the difference setting the larger number first (x), minus the smaller number (y), so as to get a positive difference of 81 units:
x - y =81
now we solve this system by substituting "x" in the second equation with "10 * y" according to what our first equation states:
10 y - y = 81
9 y = 81
y = 81/9
y = 9
and therefore now that we know the value of number y (9) we can go back to the first equation to find what number "x" is:
x = 10 * (9)
x = 90
Finally: x = 90, and y = 9
There were 16 sandwiches on a tray for a lunch meeting. After the meeting, 3 were left. How many sandwiches were eaten?
Answers
Answer:
13
Step-by-step explanation:
16-3+= 13
Which describes the amount of product a seller is able to make?
A. Market
B. Demand
C. Supply
D. Can’t tell
Answers
Answer:
c) supply
Step-by-step explanation:
Answer:
supply
Step-by-step explanation:
What is the probability of drawing a king or a queen?
Answers
Answer:
2/13
Step-by-step explanation:
There are 4 kings and 4 queens in a standard deck of 52 cards. So the probability is:
P = 8/52
P = 2/13
Let f(x)=7^x and g(x)=7^x+2-4. Which transformations are needed to transform f(x) to the graph g(x)?
Answer ASAP
Answers
Answer:
4. vertical translation 4 units down
6. horizontal translation 2 units to the right
Step-by-step explanation:
Given [tex]f(x)=7^x[/tex] and [tex]g(x)=7^{x+2}-4[/tex]
1. Adding 2 to x means horizontal translation 2 units to the right.
2. Subtracting 4 from the function [tex]7^{x+2}[/tex] means vertical translation 4 units down.
So, to transform the graph of the function f(x) to the graph of the function g(x), you need to translate the graph of the function f(x) horizontally 2 units to the right and vertically 4 units down.
Answer:the answers are “ horizontal translation 2 units left” and “ vertical translation 4 units down” :)
Step-by-step explanation:
Please help me out this kind of confused me thank you in advance!
Answers
Answer:
In the quotient [tex]x^4+2x^3+x^2+5x+10=0[/tex] , the coefficient of x is 5.
Step-by-step explanation:
Given rational expression is [tex]\frac{-x^5+3x^3-3x^2+20}{x-2}[/tex]
Nicolette used synthetic division to solve the given rational expression.
Nicolette's work is given below:
Given that x-2 is a zero of given rational expression
By using synthetic division for the given rational expression.
2_| -1 0 3 -3 0 20
0 -2 -4 -2 -10 -20
____________________________
-1 -2 -1 -5 -10 | 0
Therefore the simplified expression can be written as below
[tex]-x^4-2x^3-x^2-5x-10=0[/tex]
Taking negative sign outside.
[tex]-(x^4+2x^3+x^2+5x+10)=0[/tex]
Multiply negative sign with "0" we get "0"
Therefore [tex]x^4+2x^3+x^2+5x+10=0[/tex]
In the quotient [tex]x^4+2x^3+x^2+5x+10=0[/tex], the coefficient of x is 5.
Monica built a porch that contained 2 different colors of bricks to create a pattern. She purchased the red bricks for $7 each and the gray bricks for $4 each.
Write a system to find how many red bricks did Monica purchase if she spent $193 on 40 bricks?
What is the system that models this situation? Equation #1: Equation #2:
How many red bricks did Monica purchase?
Answers
Equation #1: x+y=40
Equation #2: 7x+4y=193
Monica bought 11 red bricks.
Step-by-step explanation:
Given,
Cost of one red brick = $7
Cost of one gray brick = $4
Total spent on bricks = $193
Total bricks bought = 40
Let,
x represents the number of red bricks bought.
y represents the number of gray bricks bought.
What is the system that models this situation?
Equation #1: x+y=40
Equation #2: 7x+4y=193
How many red bricks did Monica purchase?
Multiplying Eqn 1 by 4
[tex]4(x+y=40)\\4x+4y=160\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](7x+4y)-(4x+4y)=193-160\\7x+4y-4x-4y=33\\3x=33[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{33}{3}\\x=11[/tex]
Monica bought 11 red bricks.
Keywords: linear equation, elimination method
Learn more about elimination method at:
brainly.com/question/6108628brainly.com/question/6112033#LearnwithBrainly
BRAINLIEST!!! 10 POINTS!!
Make a list of the possible outcomes from the table.
Answers
Answer: The answer is A my friend.
Step-by-step explanation:
All possible outcomes:
Yellow shirt, white trouser
Yellow shirt, black trouser
Green shirt, white trouser
Green shirt, black trouser
Hope this helps. Please hit the thanks button if it is right. I would appreciate it. :)
Please help me guys I really need it
Answers
The figure is a 4 sided pyramid, so it has 4 triangles and the base is square.
The net would be the lower left one.
Answer:
C
Step-by-step explanation:
PLZ HELP 5 QUESTIONS FOR 50 POINTS
Answers
Answer:
3. 113.04
4. 137.1
5. $9.24
Answer:
3. 113.04
4. 137.1
5. $9.24
The difference between two numbers is 2 and their product is 120.
What are the numbers?
Answers
Answer:
x=12,y=10
Step-by-step explanation:
let two nos are x and y
so x-y=2.............(1)
xy=120................(2)
(x+y)^2=(x-y)^2+4xy
(x+y)^2=2^2+4(120)
(x+y)^2=4+480=484
x+y=[tex]\sqrt{484}[/tex]
x+y=22.................(3)
adding (1) and (3),
x+y=22
x-y=2
2x=24
x=12,y=10 answer
Answer:
yo m om s u c k c o c k
Step-by-step explanation:
What is solution to equation ? 4x + 5 = -3
Answers
Answer:
x=-2
Step-by-step explanation:
Solve for x:4x (+ 5-5) = -3-5
4x = -8
4x/4 = -8/4
x=-2
Checking Answer:4(-2) + 5= -3
-8 + 5 = -3
-3 = -3
Answer is Correct.
Answer:
[tex] \: \: \: \: \: \: 4x + 5 = - 3 \\ = > 4x = -3 - 5 \\ = > 4x = - 8 \\ = > x = \frac{ - 8}{4} \\ = > x > - 2[/tex]
what's 20 times 2 and add 4?
Answers
Answer:
20*2 is 40
add 4?
its 44
Answer:
44
Step-by-step explanation:
20 * 2 = 40
40 + 4 = 44
Hope this helps :)
The base of a triangle is shrinking at a rate of 1cm/min and the height if the triangle is increasing at a rate of 5cm/min. Find the rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm.
Answers
The rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm is 14 cm²/min.
Using the formula for a triangle's area, A = (1/2) × base × height, we can determine rate of the triangle's area changes.
We can describe the rate of change of the base as db/dt = -1 cm/min (negative because it is shrinking) given that the base is shrinking at a rate of 1 cm/min.
The height is increasing at a rate of 5 cm/min, so the rate of change of the height can be expressed as dh/dt = 5 cm/min.
We must determine dA/dt for h = 22 cm and b = 10 cm in order to determine the rate at which the triangle's area changes at these two points.
We can start by differentiating the area formula with respect to time (t):
dA/dt = (1/2) × (db/dt × h + b × dh/dt)
Substituting the given values:
dA/dt = (1/2) × (-1 cm/min × 22 cm + 10 cm × 5 cm/min)
Simplifying:
dA/dt = (1/2) × (-22 cm/min + 50 cm/min)
= (1/2) × 28 cm/min
= 14 cm/min
Therefore, the rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm is 14 cm/min.
Learn more about rate of change click;
https://brainly.com/question/29181688
#SPJ12
The rate at which the area of the triangle changes is 2 cm²/min. This is found by applying the chain rule of differentiation to the triangle area formula, substituting the given values and rates, and simplifying.
Explanation:The subject of this question is rate of change in context of the Triangle Area Formula: 1/2 * base * height. Given that the base is shrinking at a rate of 1cm per minute (1 cm/min) and the height is increasing at a rate of 5 cm/min, we can express this rate of change in the formula. A negative sign is used for the base because the base length is decreasing.
To find the rate of change in the area, use the chain rule of differentiation, leading to the formula (-1/2 * height * db/dt) + (1/2 * base * dh/dt). When the height is 22 cm and the base is 10 cm, substituting these values along with the rates at which the base and height are changing, the formula becomes (-1/2 * 22cm * 1 cm/min) + (1/2 * 10cm * 5 cm/min). Simplify to find that the area of the triangle is changing at 2 cm²/min.
Learn more about Rate of Change here:https://brainly.com/question/29181502
#SPJ11
how do you find if these are similar solids?
Answers
Step-by-step explanation:
Compare the ratios of their heights, widths, and lengths. If they're the same, then the solids are similar.
10/5 = 2
6/3 = 2
6/3 = 2
The ratios are the same, so the solids are similar.