You can add and subtract radicals by ensuring that they have same radical parts.
What's radical?It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.
The necessary steps to add or subtract radicals include:
Identify the radical parts.
Add them together.
If there's unlike radical parts, one will manipulate the parts involved before solving.
Example: Add ✓63 + 5✓7
It should be noted that ✓63 = ✓9 × ✓7 = 3✓7
Therefore, ✓63 + 5✓7 will be:
= 3✓7 + 5✓7
= 8✓7.
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Simplify this expression
12g+9g
Answer:
21g
Step-by-step explanation:
12 + 9 = 21 then add the variable.
After Simplify this expression 12 g + 9 g. We get, 21g.
To simplify this expression
12 g + 9 g,
Add ( 12 + 9) ,which is 21
So, 12 g + 9 g = 21 g.
Therefore, the final answer is 12 g + 9 g = 21 g.
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HELP EASY LOOKING FOR ANSWERS TO NUMBER FOUR
Answer:
Step-by-step explanation:
it should be Venus
hmmm. im thinking its venus
please help i’m literally so stressed out
Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $209.67.
•He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.
•He plans to spend some or all of the money he has left to buy new biking outfits
for $37.16 each.
Which inequality can be used to determine x, the maximum number of outfits Luis
can purchase while staying within his budget?
The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
How to solve inequality?Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
He buys a new bicycle for $209.67.He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.He plans to spend some or all of the money he has left to buy new biking outfits for $37.16 each.Therefore,
x = maximum number of outfits Luis can purchase while staying within his budget.
Hence, the inequality that can be used to represent the situation is as follows;
209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420
235.44 + 12.08 + 37.16x ≤ 420
247.52 + 37.16x ≤ 420
37.16x ≤ 420 - 247.52
37.16x ≤ 172.48
divide both sides by 37.16
x ≤ 4.64155005382
x ≤ 4
Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
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3. The graph below shows the number of points that Lebron scored in each of his first
four games of a season.
On average, how many more points per game did Lebron score in the last two games than the
first two games?
Which fractions are equivalent to 0.4? Select all that apply.
Answer:
Step-by-step explanation:
2/5 or 4/10 or 8/20 or 16/40
4x-10=-6x-2 the value of x
Answer:
x = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
4x - 10 = - 6x - 2 ( add 6x to both sides )
10x - 10 = - 2 ( add 10 to both sides )
10x = 8 ( divide both sides by 10 )
x = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]
1. Jake reads the following problem: If the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches, what is the length on the new scale drawing if the scale factor of the new scale drawing length to actual length is 1/144? He works out the problem: 8 inches ÷ 1/90 = 720 inches 720 inches× 1/144 = 5 inches Is he correct? Explain why or why not.
Yes Jake is correct we the scales are accurately represented.
How to calculate the value?From the information, the original scale factor for a scale drawing of a square swimming pool is 1/90, and the length of the original drawing is measured to be 8 inches.
Therefore, the original length will be:
= 8 ÷ 1/90
= 8 × 90
= 720 inches
Therefore, Jack is correct.
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PLEASE HELP ME
TEMPERATURE The hottest temperature recorded in Key West, Florida, was 98°F. This was 25°F colder than 3 times the coldest temperature
recorded in Key West. Which equation can be used to find the coldest temperature recorded in Key West? What is the coldest temperature
recorded in Key West?
A) 3T + 2598; 24.3°
O B) T+25=98; 73°
O C) 3T98; 32.7"
OD) 3T-25= 98; 41°
The equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.
What is an equation?The equation represents the relationship of two expressions on either side of the sign.
We have,
The hottest temperature = 98°F.
And that this was 25°F colder than 3 times the coldest temperature.
If we let the coldest temperature be denoted by T
We can write an equation as:
98°F + 25°F = 3T
Subtracting 25° on both sides.
98°F = 3T - 25°F
3T - 25°F = 98°F
The coldest temperature recorded in key west:
3°T - 25°T = 98°F
3°T = 123°F
T = 103°F / 3
T = 41°F
Thus the equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.
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Please help me I’m very confused!!
first off let's keep in mind that an absolute value is really a ± equation in disguise, so |5x -4| can pretty much be rewritten as ±(5x - 4), so is a dual equation, let's solve both for "x".
[tex]|5x-4|\leqslant 3x\implies \pm(5x-4)\leqslant 3x \\\\[-0.35em] ~\dotfill\\\\ +(5x-4)\leqslant 3x\implies 5x-4\leqslant 3x\implies 2x-4\leqslant 0\implies 2x\leqslant 4 \\\\\\ x\leqslant \cfrac{4}{2}\implies {\LARGE \begin{array}{llll} x\leqslant 2 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-(5x-4)\leqslant 3x\implies (5x-4)\stackrel{\stackrel{notice}{\downarrow }}{\geqslant} -3x\implies 8x-4\geqslant 0 \\\\\\ 8x\geqslant 4\implies x\geqslant \cfrac{4}{8}\implies {\LARGE \begin{array}{llll} x\geqslant \cfrac{1}{2} \end{array}}[/tex]
Check the picture below.
What is the slope of the line that passes through the points(−4,2) and (−5,0)?
Step-by-step explanation:
the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.
the direction does not matter, but it is essential that once a direction is picked for one coordinate, we use the same one then also for the other.
I prefer to go from left to right, so (-5, 0) to (-4, 2) :
x changes by +1 (from -5 to -4).
y changes by +2 (from 0 to 2).
so, the slope is +2/+1 = 2/1 = 2.
find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continuesm8, 0, 8, 0,
The formula for the general term and of the sequence is ±8.
What do we mean by sequence?A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not is numbered to another set of elements.To find the formula for the given sequence:
Given sequence: 8, 0, 8, 0, So, the formula cen be ±8.+8 to get the terms of odd numbers and -8 to get the terms of even numbers.Therefore, the formula for the general term and of the sequence is ±8.
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Do the points (15, -12), (28,14), and (32,21) all lie on the same line? Be sure you can explain why or why not.
Choosing different pairs of points we got different slopes, then we conclude that the 3 points don't lie on the same line.
Do the points lie on the same line?Remember that if a line contains two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
a = (y₂ - y₁)/(x₂ - x₁)
Here the 3 points are on the same line if we get the same slope for any pair that we choose.
If we use the first two; (15, -12) and (28, 14), the slope is:
a = (14 - (-12))(28 - 15) = 8.67
If we use the second and third point (28, 14) and (32, 21), we get:
a = (21 - 14)/(32 - 28) = 6.125
We got different slopes, then we conclude that the 3 points don't lie on the same line.
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If tanθ= 3/4, find sin θ
P= 3
b=4
By using pythagorus therom,
h^2=p^2+b^2
=3^2+4^2
=9+16
=25
h =5
now,
sin(theta)= p÷h
=3÷5
Select the correct answer.
Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have?
A. x + 1/2x + 2/3x = 30 - 4, which has no solution
B. x + 1/2x + 2/3x = 30, which has infinitely many solutions
C. x + 1/3x + 2/3x - 4 = 30, which has one solution
D. x + 1/2x + 2/3x +4 = 30, which has one solution
E. 1/2x + 2/3x = x - 4, which has no solution
Answer: C, I think is correct
PLEASE SOLVE THIS FOR MEEEE<333
please help with 7, 9 and 11!! i am stuck on problems
7) (x, TU, TB) = (4, 8, 13)
9) (x, RS, MN) = (8, 41, 41)
11) (AB, BC, AC) = (42, 42, 84)
What are the values of the variable x and the lengths of the line segments?
In this question we have three cases of colinear line segments, each of them can be solved by using definitions from Euclidean geometry and algebraic handling:
Case 7 - TU = 2 · x, UB = 3 · x + 1, TB = 21
TB = TU + UB
21 = 2 · x + 3 · x + 1
21 = 5 · x + 1
5 · x = 20
x = 4
Then, the lengths of each line segment are:
TB = 21
TU = 2 · 4
TU = 8
UB = 3 · 4 + 1
UB = 13
The solutions are (x, TU, TB) = (4, 8, 13).
Case 9 - RS = 3 · x + 17, MN = 7 · x - 15
RS = MN
3 · x + 17 = 7 · x - 15
4 · x = 32
x = 8
And the lengths of each line segment are:
RS = MN = 41
The solutions are (x, RS, MN) = (8, 41, 41).
Case 11 - AB = 2 · x - 8, BC = x + 17
AB + BC = AC
AB = BC
2 · x - 8 = x + 17
x = 25
And the lengths of each line segment are:
AB = 2 · 25 - 8
AB = 42
BC = AB
BC = 42
AC = 42 + 42
AC = 84
The solutions are (AB, BC, AC) = (42, 42, 84).
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I need answer please. I don’t know how to divide and what to divide by.. could someone give me answers to these questions?
Answer:
1) 60 miles per hour (60.00, if rounded)
2) 152 customers per day (150, if rounded)
3) 3.5 meters per second (3.50, if rounded)
4) 1.48 dollars per pound (1.48, if rounded)
5) 0.4825 dollars per pair (0.48, if rounded)
( shown work in screenshots, 1-5; magnify it to see better :D )
Grandma has one cup of sugar. How many dozen cookies will she be able to make?
Givien f(x) = 5x+4, solve for x when f(x) = -6.
Answer: -26
Step-by-step explanation:
5 x -6 = -30
-30 + 4 = -26
5(-6) + 4 = -26
.chris p. bacon worked 44 hours last week and gets double time pay for overtime. his regular pay is $14 per hour. how much was his paycheck for the week?
The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week, regular pay $14 per hour and double time pay for overtime.
As given,
Regular pay per hour = $14
Overtime work payment= 2 × ($14)
Total hours work done last week = 44hours
Let regular timing be 8 hours per day 5 days a week
Total regular working hours = 8 × 5
= 40 hours
Over time = 44-40
= 4 hours
Payment check = (40 × 14)+ (4 × 28)
= $672
Therefore, The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week.
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YALL IS ANYONE WILLING TO SOLVE MATH?
Answer:
A = 1160
B = 1160 is already in standard form.
C = 1200
7x + 3x + x⁴ divided by x-2 using long division
Answer:
10x + x^4/x-2
Step-by-step explanation:
Combine like terms
(10x + x^4)/(x-2)
PLss answer
Given f(x) = 2x − 3 and g(x) = f(3x), which table represents g(x)?
The table which represents the function g(x) is: answer option A.
x g(x)
1 -3
2 3
3 9
What is a function?In Mathematics, a function can be defined as a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.
This ultimately implies that, a function typically shows the relationship between input values and output values of a data set, as well as showing how the elements in a table are paired (mapped).
When x = 1, the function f(x) is given by:
f(x) = 2x − 3
f(1) = 2(1) − 3
f(1) = 2 - 3
f(1) = -1.
Therefore, the function g(x) = f(3x) = 3 × -1 = -3.
When x = 2, the function f(x) is given by:
f(x) = 2x − 3
f(2) = 2(2) − 3
f(2) = 4 - 3
f(2) = 1.
Therefore, the function g(x) = f(3x) = 3 × 1 = 3.
When x = 3, the function f(x) is given by:
f(x) = 2x − 3
f(3) = 2(3) − 3
f(3) = 6 - 3
f(3) = 3.
Therefore, the function g(x) = f(3x) = 3 × 3 = 9.
In conclusion, the table which represents the function g(x) is as follows:
x g(x)
1 -3
2 3
3 9
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Answer: A
Step-by-step explanation:
rxl ontop
A truck enters a highway driving 60 mph. A car enter the highway at the same place 14 minutes later and drives 67 mph in the same direction . From the time the car enters the highway, how long will it take the car to pass the truck
Time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.
As given in the question,
Speed of a truck=60mph
⇒60 minutes = 60miles
⇒14 minutes = (60/60)×14
= 14 miles
Car speed =67mph
67 miles=60minutes
⇒1miles = (60/67) minutes
⇒14miles = (60/67)×14
≈12.54 minutes (approximately)
Therefore, time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.
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which of the following situations best descrbies a student engaged in active learing 1. A student uses only one of the resources provided by the teacher 2. A student skips parts of lessons that she find difficult 3. A student records questions to ask the teacher about a concept 4. A student does not discuss math outside of lessons.
Answer:1.c 2.b 3.a
Step-by-step explanation:
A printing service charges a set-up fee of $10.00 for each order and 8 cents more for each copy. The total cost, C (in dollars), for an order of x copies is given
by the following function.
C(x) = 10.00 +0.08x
What is the total cost for an order of 50 copies?
Answer:
$14 for 50 copies.
Step-by-step explanation:
Given that,
→ C(x) = 10.00 + 0.08x
Then the cost for 50 copies will be,
→ C(50) = 10.00 + (0.08 × 50)
→ C(50) = 10.00 + 4
→ [ C(50) = $14 ]
Hence, the total cost of $14.
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' y'-4x-4y=e^-t x' y' 2x y=e^4t
It looks like the system of ODEs is
[tex]\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}[/tex]
Differentiate both sides of both equations with respect to [tex]t[/tex].
[tex]\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}[/tex]
Eliminating the exponential terms, we have
[tex](2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0[/tex]
[tex](x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0[/tex]
Now we can eliminate [tex]y[/tex] and it derivatives.
[tex]\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0[/tex]
Solve for [tex]x[/tex]. The characteristic equation is [tex]r^2 + 4 = 0[/tex] with roots at [tex]r=\pm2i[/tex], hence the characteristic solution is
[tex]\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}[/tex]
Solve for [tex]y[/tex]. Substituting [tex]x[/tex] into the second ODE gives
[tex]x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)[/tex]
The characteristic equation this time is [tex]r + 1 = 0[/tex] with a root at [tex]r=-1[/tex], hence the characteristic solution is
[tex]y(t) = C_3 e^{-t}[/tex]
Assume a particular solution with unknown coefficients [tex]a,b,c[/tex] of the form
[tex]y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)[/tex]
Substituting into the ODE gives
[tex]5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5[/tex]
so that the general solution is
[tex]\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}[/tex]
help please
15 points
1) d - c is calculated as; -4
2) Simplifying ³/₄ - ²/₅ gives; 7/20
What is the solution to basic arithmetic?
1) We are given;
c = 12 and d = 8. Thus;
d - c is calculated as;
8 - 12 = -4
2) We want to simplify ³/₄ - ²/₅
Factoring out 1/20 gives;
1/20(15 - 8) = 7/20
3) Number of pencils purchased = 888 pencils
Number of pencils in a box = 12
Thus;
Number of boxes purchased = 888/12 = 74 boxes
4) An integer is a whole number (not a fractional number) that can be positive, negative, or zero. The only one that is not an integer here is; 20/6
5) √64 = 8
6) (30 - 4 * 2)/(2 * 2²)
= (30 - 8)/8
= 22/8 = 11/4
7) 11 = x + 19
x = 11 - 19
x = -8
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Sheila put $350 in a savings account for 1 year. The annual interest rate was 3% per year.
a) How much simple interest did the money earn her in 1 year?
b) How much money was in the account after 1 year?
Please answer fast and show how u got the answer step by step thank u
The simple interest was $10.5 and the amount after 1 year would be $360.5 in her account.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as
Principal amount (P) = $350
Time (T) = 1 year
The rate of interest (R) = 3%
Simple interest= P × R × T
Simple interest = 350 × 3/100 × 1
Simple interest = $10.5
So the amount after 1 year would be P + S.I. = 350 + 10.5 = $360.5
Therefore, the simple interest would be $10.5 and the amount after 1 year would be $360.5.
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The following is a list of P/E ratios (current stock price divided by company's earnings per share) for 17 companies. 57, 53, 50, 46, 42, 35, 31, 56, 52, 34, 34, 34, 30, 30, 55, 55, 51. Draw the histogram for these data using an initial class boundary of 29.5, an ending class boundary of 59.5, and 5 classes of equal width. Note that you can add or remove classes. Label each class with its endpoints.
The histogram for these data is given at the end of the answer.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
For this problem, there are 5 classes with a range of 30, as 59.5 - 29.5 = 30, hence the class width is of:
30/5 = 6.
From the data-set, we have that:
There are 7 values between 29.5 and 35.5.There are 0 values between 35.5 and 41.5.There are 2 values between 41.5 and 47.5.There are 4 values between 47.5 and 53.5.There are 4 values between 53.5 and 59.5.Considering this, the histogram is given at the end of the answer.
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