Answer:
7 + 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
Given
(2 + [tex]\sqrt{3}[/tex] )² = (2 + [tex]\sqrt{3}[/tex] )(2 + [tex]\sqrt{3}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
2(2 + [tex]\sqrt{3}[/tex] ) + [tex]\sqrt{3}[/tex](2 + [tex]\sqrt{3}[/tex] ) ← distribute both parenthesis
= 4 + 2[tex]\sqrt{3}[/tex] + 2[tex]\sqrt{3}[/tex] + 3 ← collect like terms
= 7 + 4[tex]\sqrt{3}[/tex]
Solve the system using elimination
Answer:
(3, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
2x + 5y = 16
3x - 5y = -1
Step 2: Solve for x
Eliminate y (add equations): 5x = 15Divide 5 on both sides: x = 3Step 3: Solve for y
Define equation: 2x + 5y = 16Substitute in x: 2(3) + 5y = 16Multiply: 6 + 5y = 16Subtract 6 on both sides: 5y = 10Divide 5 on both sides: y = 2Answer:
(3, 2)
Step-by-step explanation:
2x + 5y = 16 ........ (1)
3x - 5y = - 1 ......... (2)
(1) + (2)
( 2x + 3x ) + [ 5y + ( - 5y)] = 16 + (- 1)
5x = 15 ⇒ x = 3
2(3) + 5y = 16 ⇒ y = 2
(3, 2)
Cynthia is training to run the 100 yard dash. The first week she ran it is 14.0 seconds. The third week she ran it in 13.1 seconds. What is the percent change from week 1 to week 3 rounded to the nearest tenth of a percent?
Answer:
We assign the older value to variable A and the newer value to variable B. Units, in this case the dollars, are always stripped or canceled out in percent change problems since we’re looking for increases or decreases in percentage.
Step-by-step explanation:
Write the equation in slope intercept form from the graph below
Answer:
y=[tex]-\frac{1}{3}[/tex]+2
Step-by-step explanation: m=slope, b= y-intercept
y=mx+b how to find the slope= [tex]\frac{3-0}{1-2}[/tex]
y=m(x)+b
1=m(3)+b
1=[tex]-\frac{1}{3}(3)[/tex]+2
can someone make my day and explain this to me
Answer:
Step-by-step explanation:
Remark
The first step is the critical one. Take the base and raise it to x. Then take the log of the base and the number whose log you need. x (the power)is brought down and the logs divided.
2^x = 1024
log 2^x = log(1024)
x log(2) = log(1024)
x * 0.30102 = 3.0102
x = 30102/0.30102
x = 10
You could use the e system to solve this as well
2^x = 1024
ln(2^x) = ln(1024)
x * ln(2) = ln(1024)
x 0.6931 = 6.9315
x = 6.9315/0.69315
x = 9.999959
x = 10
4 divided by 2/9 in fraction form( whoever sees this I hope you have a wonderful day! )
Answer:
4x9/2
4x9/2
36/2
18
UwU
18 is your answer
Algebra
S.4 Find the slope from two points M05
Learn with an example
Find the slope of the line that passes through (5, 6) and (7, 7).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Submit
Is the answer right?
Answer:
yes I think...........
find the missing value in the ratio table
PLEASE HELP ILL MARK BRAINLIEST !!!
The following tables describe arithmetic sequences
(a) what is the common difference of the sequence xn?
(b) what is x8? what is x12?
(c) what is the common difference of the sequence am?
(d) what is a12? what is a15?
Answer:
a) the common difference is 20
b) [tex]x_8=115 , x_{12}=195[/tex]
c) the common difference is -13
d) [tex]a_{12}=52, a_{15}=13[/tex]
Step-by-step explanation:
a) what is the common difference of the sequence xn
Looking at the table, we get x_3=16, x_4=36 and x_5= 56
Deterring the common difference by subtracting x_4 from x_3 we get
36-16 =20
So, the common difference is 20
b) what is x_8? what is x_12
The formula used is: [tex]x_n=x_1+(n-1)d[/tex]
We know common difference d= 20, we need to find [tex]x_1[/tex]
Using [tex]x_3=16[/tex] we can find [tex]x_1[/tex]
[tex]x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25[/tex]
So, We have [tex]x_1 = -25[/tex]
Now finding [tex]x_8[/tex]
[tex]x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115[/tex]
So, [tex]\mathbf{x_8=115}[/tex]
Now finding [tex]x_{12}[/tex]
[tex]x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195[/tex]
So, [tex]\mathbf{x_{12}=195}[/tex]
c) what is the common difference of the sequence [tex]a_m[/tex]
Looking at the table, we get a_7=104, a_8=91 and a_9= 78
Deterring the common difference by subtracting a_7 from a_8 we get
91-104 =-13
So, the common difference is -13
d) what is a_12? what is a_15?
The formula used is: [tex]a_n=a_1+(n-1)d[/tex]
We know common difference d= -13, we need to find [tex]a_1[/tex]
Using [tex]a_7=104[/tex] we can find [tex]x_1[/tex]
[tex]a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195[/tex]
So, We have [tex]a_1 = 195[/tex]
Now finding [tex]a_{12}[/tex] , put n=12
[tex]a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52[/tex]
So, [tex]\mathbf{a_{12}=52}[/tex]
Now finding [tex]a_{15}[/tex] , put n=15
[tex]a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13[/tex]
So, [tex]\mathbf{a_{15}=13}[/tex]
What is an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4
Answer:
The equation of required line is: [tex]\mathbf{x+y=5}[/tex]
Step-by-step explanation:
We need to find an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4
For finding an equation of line, we need to find slope and y-intercept of the line.
Finding slope:
If the lines are parallel their slope is same
We are given: x+y=4
Writing in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
[tex]x+y=4\\y=-x+4[/tex]
Comparing [tex]y=-x+4[/tex] with [tex]y=mx+b[/tex] the slope m is -1
So, slope of given line is -1
It is parallel with required line, so they have same slope.
The slope of required line is m=-1
Finding y-intercept
Using slope m=-1 and point(2,3) we can find y-intercept
Using slope-intercept form: [tex]y=mx+b[/tex]
[tex]y=mx+b\\3=-1(2)+b\\3=-2+b\\b=3+2\\b=5[/tex]
So, y-intercept is: b=5
The equation of required line having slope m=-1 and y-intercept b = 5 is
[tex]y=mx+b\\y=-1x+5\\y=-x+5\\x+y=5[/tex]
So, equation of required line is: [tex]\mathbf{x+y=5}[/tex]
The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y = -x + 5
Two equations are parallel if they have equal slope
For the equation x + y = 4
Rewrite the equation in the form y = mx + c
y = -x + 4
Compare y = -x + 4 with y = mx + c
The slope, m = -1
The equation parallel to x + y = 4 will also have a slope, m = -1
The line passes through the point (2, 3)
That is, x₁ = 2, y₁ = 3
The point-slope form of the equation of a line is:
y - y₁ = m(x - x₁)
Substitute x₁ = 2, y₁ = 3 into y - y₁ = m(x - x₁)
y - 3 = -1(x - 2)
y - 3 = -x + 2
y = -x + 2 + 3
y = -x + 5
The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y = -x + 5
Learn more here: https://brainly.com/question/19484034
solve the equation by taking square roots
(x-3)^2 +8 = -10
Answer:
x = 3 ± 3i√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Vertex Form: f(x) = a(bx - c)ⁿ + dCompleting the SquareSolving rootsAlgebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define equation
(x - 3)² + 8 = -10
Step 2: Solve for x
Subtract 8 on both sides: (x - 3)² = -18Square root both sides: x - 3 = ±√-18Factor: x - 3 = √-1 · ±√18Simplify: x - 3 = ±3i√2Add 3 to both sides: x = 3 ± 3i√2solve for w and simplify this fraction 3/2w=-20
Answer:
4 2/3
Step-by-step explanation:
Answer:
w = -1.3 (.3 repeating)
Step-by-step explanation:
3/2w = -20
3/2w time 2/3 (flip to get rid of fraction)
- 20 time 2/3 (what you do to one side, you must do to the other side)
w = 1.3 (.3 repeating)
1.3 as a fraction is 4/3
which function describes -1,1,3,5,7,9,11,13
Answer:
+2
Step-by-step explanation:
I NEED THIS ANSWER ASAP THIS IS WORTH A LOT OF POINTS PLEASE
Answer:
Step-by-step explanation:
the slope is 1/1
Choose one answer is math
the answer is d which is x=.5x=-4
First person to get it right gets brainliest
Answer:
4
Step-by-step explanation:
Mai has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy?
Answer: 8
Step-by-step explanation: 36/4.50
Answer:
8tickets
Step-by-step explanation:
she has $36
1rickeet costs $4.50
hence,
$36/$4.50
=$8.0
=8tickets.
hope was helpful!
Geometry! Find the length of a-b. Give answer in simplest radical form.
Answer:
Length of AB is [tex]\sqrt{106}[/tex]
Step-by-step explanation:
Let us use the rule of the distance To find the length of AB
∵ A = (9, -3)
∵ B = (0, 2)
∴ x1 = 9 and y1 = -3
∴ x2 = 0 and y2 = 2
∵ AB = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
→ Substitute the values of x1, x2, y1, and y2 in the rule to find AB
∴ AB = [tex]\sqrt{(0-9)^{2}+(2--3)^{2}}[/tex]
∴ AB = [tex]\sqrt{(-9)^{2}+(2+3)^{2}}[/tex]
∴ AB = [tex]\sqrt{81+(5)^{2}}[/tex]
∴ AB = [tex]\sqrt{81+25}[/tex]
∴ AB = [tex]\sqrt{106}[/tex]
→ The square root of 106 is the simplest radical form
∴ Length of AB is [tex]\sqrt{106}[/tex]
Item 5 Which list shows the absolute values in order from least to greatest? Select each correct answer. |−17.12| , |−17.08| , ∣∣17.06∣∣ ∣∣21.95∣∣ , |−22.02| , |−22.11| |−7.38| , ∣∣7.39∣∣ , |−7.41| |−3.07| , ∣∣−3.25∣∣ , |3.31|
Lets go over some stuff before we answer this absolute values make anything positive or make you count down from zero so then just imagine those numbers as positive.
ill put them as positives and then sort them here
3.07 3.25 3.31 |3.07 3.25 3.31 (Correct)
7.38, 7.39 , 7.41 | 7.38, 7.39 , 7.41 (Correct)
17.12, 17.08 17.06 | 17.06 ,17.08 ,17.12 (Wrong)
21.95 , 22.02 , 22.11 | 21.96 , 22.02 , 22.11 (Correct)
Answer:
|−17.12| , |−17.08| , ∣∣17.06∣wrong∣ ∣∣21.95∣∣ , |−22.02| , |−22.11| correct |−7.38| , ∣∣7.39∣∣ , |−7.41|correct |−3.07| , ∣∣−3.25∣∣ , |3.31|:correct
write the slope-intercept form of the equation
6x-3y-12=0
Answer:
y=2x-4
Step-by-step explanation:
HELPP ✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨
Brad already has $50 but needs a total of at least $250 per day for delivering
papers. What is the least number of days he must work to get enough money for
his vacation? Write the inequality an solve
Answer:
he needs to work 3 more days in order to make 250 dollars for his vacation
Step-by-step explanation:
Identify the parent function that can be used to graph the function f(x) =4|x|-3
c. F(x) = x
b. F(x) = [x]
d. f(x) = |x|
Answer:
d
Step-by-step explanation:
f(x) = |x| will always be parent function unless told otherwise.
URGENT! WILL MARK BRANLIEST
Draw the shape made by slicing the CUBE (THINK: A CUBE HAS 6 SIDES THAT ARE THE SAME MEASURE) parallel to its bases.
A) Square
B) Rectangle
C) Trapezoid
D) Rhombus
Answer:
B. Ractangle
Step-by-step explanation:
Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.
q + d = 19
0.25q + 0.1d = 4
How many quarters does she have?
4
5
14
15
Answer:
I'm terrible at explaining so here's a screenshot
- Ripper
Step-by-step explanation:
The number of the quarters coins are 14. Then the correct option is C.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
Kat has 19 coins, all quarters and dimes, that are worth a total of $4.
The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.
q + d = 19
d = 19 – q ...1
0.25q + 0.1d = 4 ...2
Solve the equation, we have
0.25q + 0.1(19 – q) = 4
0.25q – 0.1q + 1.9 = 4
0.15q = 2.1
q = 14
Then the correct option is C.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Will each student get more than or less than 1 cup of broth? Explain.
Answer:
1
Step-by-step explanation:
because every cup has to be equal and if is not then every cup will be less then a cup eather way it will be the same
what fraction is equal to 0.2
Answer:
Fraction Decimal Percent
2/3 0.666… 66.666…%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
Will the answer to this expression be POSITIVE or NEGATIVE?
12 - 22
Answer:
the answer is -10
Step-by-step explanation:
the steps are in the picture
Answer:
The answer to this expression would be negative.
Step-by-step explanation:
-10
Will give Brainliest!!!
Ella is going to drive from her house to City A without stopping. Ella's house is 100 miles from City A and after driving for 3 hours, she will be 25 miles away from City A. Write an equation for D,D, in terms of t,t, representing Ella's distance from City A tt hours after leaving her house.
Answer:
d = 100 - 25t
Step-by-step explanation:
The cost of a vacation package is 249$ per person for the Smith family. If there are 6 family members, what is the total cost of the vacation package?
Answer:
$1,494
Step-by-step explanation:
the total cost multiplied by the number of family members
xoxo,your highness...Step-by-step explanation:
249 x 6 = 1,494
Answer: $1,494
Please help with geometry!
Find x
Answer:6x-5+2x+5+3x+22 and u get your answer
Step-by-step explanation: