- - - - - - - - - - - - - - - - - - - - - - - -
Find common denominators :)
6/9
Divide by 4 (the common factor of 9 and 12)
2/3
Multiply by 4
8/12
8/12 = 8/12
Now, simplify.
2/3
- - - - - - - - - - - - - - - - - - - - - - - -
Have a great day/night! :)
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~pinetreee
2(
5
1
m−
5
2
)+
5
3 =
Answer:
102m-51
Step-by-step explanation:
2(51m-52)+53
= 102m - 104+53
102m-51
Factorize the expression:
[tex]2(51m-52)+53[/tex]
[tex]102m-104 +53[/tex]
[tex]102m-51[/tex]
[tex]51(2m-51)[/tex]
⬆️
Simplify the expression:
[tex]2(51m-52)+53[/tex]
[tex]2*51m-2*52+53[/tex]
[tex]102m-2*52+53[/tex]
[tex]102m-104+53[/tex]
[tex]102m(-104+53)[/tex]
[tex]102m-51[/tex]
⬆️
1. Give an example of a radical inequality that would not need restrictions. Explain your reasoning.
Step-by-step explanation:
a restricting is only necessary, if we need to limit the x values or the y values for various reasons.
the limit for the x values are to eliminate any values that would create an invalid or otherwise undefined result.
otherwise the inequality itself establishes a restriction already.
e.g. sqrt(x) + 3 >= 1 would need an additional restriction
x >= 0 to know we can't even try small negative x to find out verify the solution.
something like
sqrt(x² + 3) >= 1 does not need any further restrictions, because we can use any value for x, from - infinity to +infinity. and the inequality will always be valid.
also consider, that the left side can never get smaller than sqrt(3) which is larger than 1. so, really everything goes.
we could say something like
sqrt(x² + 16) >= 5
we still don't need to give any additional restrictions, but the inequality itself rules out all x that are
-3 < x < 3.
-2x - 8y = 14, 2x + 8y = - 14
Directions: Write the following algebraic expressions and equations as verbal expressions and sentences. 9 - 6x
Verbal expression or sentence of algebraic expression of 9 - 6x are Six times x is substracted from nine and Nine is substracting six times x.
It is given that algebraic expressions = 9 - 6x
There are many ways to write 9 - 6x as verbal expression, but today we will learn to the given algebraic expression in two ways.
First way :
Here we can see that 6 is multiplied by x, so
we can specify 9 - 6x as
Six times x is substracted from nine.
Second way :
Nine is substracting six times x.
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$21,023 is invested, part at 13% and the rest at 11%. If the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 11% by $1045.31, how much is invested at each rate?
The amount invested at 11% by $1045.31 and investment rate is -
amount invested at 13%. is $13991
amount invested at 11%. is $7032
Let x represent the amount invested at 13%.
Let y represent the amount invested at 11%.
$21,023 is invested, part at 13 % and the rest at 11%. This means that
x + y = 21023
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the amount invested at 13%,
P = x
R = 13%
T =1 year
I = (x × 13 × 1)/100 = 0.13x
Considering the amount invested at 11%,
P = y
R =11%
T = 1 year
I = (x × 11 × 1)/100 = 0.11y
If the interest earned from the amount invested at
13% exceeds the interest earned from the amount invested at
5% by $1045.31, it means that
0.13x - 0.11y = 1045.31 - - -- - - - - -1
Substituting x = 21023 - y into equation 1, it becomes
0.13(121023 - y) - 0.11y = 1045.31
y = 7032
x = 21023 - y = 21023-7032
x = 13991
amount invested at 13%. is $13991
amount invested at 11%. is $7032
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Investing for college, Jake originally put $5000 into a savings account that paid 3.5%. There is now $6400 in the account. How long did Jake have the money in the savings account?
Jake put the money in the savings account for about 17.5 years.
Simply explained, a savings account is a place where you can deposit funds and earn interest.
Most people won't pay any tax on their savings interest because it is paid tax-free. Only people with extremely big sums of savings would need to be concerned about this, which is less than 5% of us as basic-rate taxpayers can earn £1,000/year tax-free and higher-rate taxpayers £500.
The interest calculated in a savings account is compound interest:
So let us now calculate the savings rate of interest at 3.5% for the whole time
We know that
[tex]A=P(1+r)^n[/tex]
Where A is the amount , P is the principal , r is the rate and n is the time.
Substituting the values we calculate the value of x.
6400 = 3500 ( 1+0.035 )ⁿ
or, n = 17.54..
So the time required will be about 17.5 years in the savings account.
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Algebra 1 honors (9th grade) I NEED HELP ASAP I BEG YOU
Answer:
3.5
Step-by-step explanation:
cross multiply
5/0.50 35/x
35 times 0.50 = 17.5
17.5/5 = 3.5
Please answer this my grade depends on it, also I have other problems like these so please feel free to answer them if you would like.
Answer:
-4,-3 and 4,5
Step-by-step explanation:
Given 7(x, y) = (x + 5, y + 4) and the point P (2, 3), what is 7(P)? please show work so sorry
Answer:
(7, 7)
Step-by-step explanation:
We are given the formula 7(x, y) = (x+5, y+4) for a pair of coordinates (x,y).
P is given as the coordinates: (2, 3), therefore if we substitute P into the equation, we can replace x and y in the given equation for the coordinates of P (2,3).
P is given as (2,3), so 7(P) = 7(2,3).
Using the given formula:
7(2,3) = (2+5, 3+4)
2+5 = 7, 3+4 = 7
Therefore 7(P) = (7, 7)
Hope this helped!
Find the domain of the following function and show your work
The domain of the given function [tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex] is x < -4096 or x > - 4096.
What do we mean by domain?The set of possible inputs into a function, or the set of input values for which the function is defined, is known as the domain of the function. The set of objects that the machine will accept as inputs are known as the domain in the function machine metaphor. Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, [tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex]:
[tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex][tex]\left[\begin{array}{cc}\text { Solution: } & x < -4096 \text { or } \quad x > -4096 \\\text { Interval Notation: } & (-\infty,-4096) \cup(-4096, \infty)\end{array}\right][/tex]Therefore, the domain of the given function is x < -4096 or x > - 4096.
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Write inequalities to represent the situations below.
To qualify for the championship, a runner must complete the race in no more than 55 minutes.
Use t to represent the time (in minutes) of a runner who qualifies for the championship.
To be eligible for financial aid, a student must earn less than $20,000 per year.
Use s to represent the yearly earnings (in dollars) of a student eligible for financial aid.
The inequalities which represent the situations as described in the task content are as follows;
t <= 55 minutes.s < $20,000 per year.What inequalities correctly represents the given situations as in the task content?It follows from the task content that the inequalities which correctly represents the situations as described in the task content be determined.
On this note, since the time, t in minutes of a runner who qualifies for the championship must be no more than 55 minutes, it follows that t can be less or at most, equal to 55.
t <= 55.Also, since the yearly earnings of a student must be less than $20,000 per year, it follows that the inequality which represents the situation is;
s < $20,000.Read more on inequalities;
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URGENT
The area of rectangle abcd is 28cm^2
What is answer to a and b
Answer:
The answer should be a=10 and b= 4
Step-by-step explanation:
(x+6)(x+4)=28
x^2 +10x + 24 =28
x^2 + 10x= 28-24
x^2 +10x =4
same as
x^2 + ax = b
Pls Help
Find the Least Common Denominator of 5/6 and 3/8, show all of your work:
Answer:
24
Step-by-step explanation:
A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per poundBut at the end of the month the peanuts had not sold well, so, in order to sell 60 pounds of peanuts, the manager decided to mix the 60 pounds of peanuts with some cashews and sell the mixture for $2.50 per poundHow many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue? The manager should mix pounds of cashews with the peanuts
In a nut store the required quantity of the cashews in the mix = x / 4 = 3 / 4 pound.
Here,
Cost of 1 pound of cashew = $4.00
Cost of 1 pound of peanut = $1.50
Total cost = 5.50
The average cost of per pound = 5.50 / 2 = 2.75
Now, peanut and cashews mixes,
quantity of the cashews in the mix = x / 4.00
quantity of the peanuts in the mix = x / 1.50
x/4.00 + x/1.50 = 2.75
x = 3
Now,
The required quantity of the cashews in the mix = x / 4 = 3 / 4 pound
and the mix of the peanut in the mix x / 1.50 = 3 / 1.50 = 2 pounds
Thus, The required quantity of the cashews in the mix = x / 4 = 3 / 4 pound
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Alejandro is taking a multiple choice test with a total of 80 points available. Each question is worth exactly 5 points. What would be Alejandro's test score (out of 80) if he got 7 questions wrong? What would be his score if he got x questions wrong?
Answer:
The answer is 45points
100-5x
Step-by-step explanation:
80/5=16questions
16-7=9questions
9x5=45points
Answers and Explanation:
- Total of 80 point available.
- Each question is worth 5 points.
If he gets 7 questions wrong --> he loses 7 x 5 points = 35 points.
100 - 35 = 65 --> So, his score would be 65.
If he got x questions wrong --> he would lose 5x points.
So, his score would be 100 - 5x.
--
Have a nice day!
Answer for this problem please
Answer:
f(2) = -9, and f(-2) = 19
Step-by-step explanation:
Just plug it in.
If [tex]f(x) =2x^{2} -3x+5[/tex], and you have f(2), and f(- 2), you can do, [tex]f(2) = -2(2^{2} )-3(2)+5[/tex], and [tex]f(-2)=-2(-2^{2} )-3(-2)+5[/tex].
Once you do all the math, you get f(2) = -9, and f(-2) = 19.
Which has a value between −13 and −14 ?
Answer:
numbers between -13.001 and -13.999
-2 3/4 divided by 1/2
Answer:
-11/2
Step-by-step explanation:
Calvin bikes to school and back home. When Calvin rides his bike to school, he bikes 10.54 miles round trip in one day. this week, Calvin rode his bike to school and back Monday through Thursday. on Friday, he rode his bike to school but received a car ride home from his friend. how many total miles did Calvin bike this week.
A: 42.16 miles
b: 57.97 miles
c: 52.7 miles
d: 47.43 miles
please help me:(
Answer:
What digital/technological features will your futuristic bath/shower time utilize?
PLEASE HELP ASAP 30 POINTS!
Answer:
-4/3
Step-by-step explanation:
Answer:-4/3
Step-by-step explanation:
According to the graph below, what is y when x is 4?
y-axis
10
9
8
2
2
3
x-axis
4
5 6
The numeric value of the function when x = 4 is of: y = 5.
What is the missing information?The graph is not given, but researching the problem on a search engine, it is found that a graph that passes through these following points is given by:
(1,10), (2,8), (3,6), (4,5), (5,2), (6,1).
How to find the numeric value of a function given it's graph?The numeric value of a function is the value of y for the given value of x, hence, we have to look at the value of x on the horizontal axis, and verify the equivalent value of y on the vertical axis.
From the given points in the graph, that we listed in the missing information subsection, we have that the function passes through point(4,5), hence:
The horizontal axis is of x = 4.The vertical axis is of y = 5.Hence:
The numeric value of the function when x = 4 is of: y = 5.
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help pls i need this as one and will give 20 points
delta math question
what are the coordinates
Question
Graph the image of the given triangle, translated 4 units to the right and 5 units down.
Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Polygon with coordinates: (-5, -3), (-1, 3), (2, -1), (-5, -3).
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Cans of soup are stocked in 1,250 sq. ft. of warehouse space. If each can requires 2 1/2 sq. ft. of space, how many cans of soup can be stored in this space?
Answer:
500 cans
Step-by-step explanation:
Let c be the number of cans.
2.5c = 1,250
c = 500 cans
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction? m = –4 m = –2 m = 2 m = 4
The solution to the equation is mathematically given as
m=-2
This is further explained below.
What is the solution to the equation?Generally, the equation is mathematically given as
[tex]\frac{m}{m+4}+\frac{1}{4-m}=\frac{m^2}{m^2-16}[/tex]
Where
The LCM of the denominators are
m^2-16=(m+4)(m-4)
Hence
[tex](m+4)(m-4)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=(m+4)(m-4) \cdot \frac{m^2}{m^2-16} \\[/tex]
m(m-4)-4(m+4)=m^2
m^2-4 m-4 m-16=m^2
8 m=-16
m=-2
In conclusion, the solution to the equation is
m=-2
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Answer:m=-2
Step-by-step explanation:
just answered
Wendi got 15 out of 20 questions correct on her English quiz and 9 out of 10 question correct on her math quiz which quiz did she do better on
Answer:
she did better on her math quiz
Step-by-step explanation:
15/20<9/10
15/20<18/20
Simple but effective
Let me know if this helps
Part 1: Identify each pair of angles adjacent vertical complementary supplementary and/or a linear pair
Part 2: use the figure at the right to answer each question
Answer:
1. adjacent
2. vertical
3. adjacent
Step-by-step explanation:
adjacent angles: angles next to each other with one common side
vertical angles: 2 non-adjacent angles formed by the intersection of 2 lines
complementary angles: two angles whose measures add to 90 deg
supplementary angles: two angles whose measures add to 180 deg
linear pair: 2 adjacent angles whose non-common side lie on a single line
Part 1
1 Adjacent
2. Vertical
3. Adjacent
4. Linear pair
5. Adjacent
6. Linear pair
7. Vertical
8. Complementary angles
9.Supplementary angles
Part 2
10. <BGC and <CGD
11. <AGD and <CGF
12. <BGC and <CGD
13. <AGF and <AGD
14. <AGB and <BGC
15. <FGC
What are Adjacent angles?This term refers to angles sitting side by side, like next to each other.
What are Vertical Opposite angles?This term refers to angles sitting in the face of the each other or opposite to each other.
What are Complementary angles?This term refers to angles that sum up to 90 degrees.
What are Supplementary angles?This term refers to angles that sum up to 180 degrees. When the angles are formed by a single point of intersection in a straight line it is called Linear pair.
What are Linear pair angles?This term refers to a form of supplementary angles where the angles are formed from a single point of intersection. The angles formed in linear pair are adjacent to each other
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Select an equivalent form of this equation:
X/12-7= X/4
A. X-84 = 3X
B. X-74= 12X
C. X-7=3X
step by step solution for 4(x-3)=0.5x+2
Answer:
x = 4
Step-by-step explanation:
4(x-3) = 0.5x +2
Multiply both sides by 10
40(x-3) + 5x + 20
Simplify (multiply 40 by x-3)
40x - 120 = 5x + 20
Add 120 to both sides
40x = 5x + 140
Subtract 5x from both sides
35x = 140
Divide 35 on both sides
x = 4
The nearest star to us, Alpha Centauri, is 4.3 light years away. A light year is 5, 865,696,000,000 miles. How far away is Alpha Centauri in miles? Express your a swer in scientific notation?
Answer:
2.52224885 x [tex]10^{13}[/tex]
Step-by-step explanation:
4.3 x 5.865695 x [tex]10^{12}[/tex]
25.2224885 x [tex]10^{12}[/tex]
2.52224885 x [tex]10^{13}[/tex]