Answer:
x = 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
6x + 2 = 2(x + 4) - 2
Step 2: Solve for x
Distribute 2: 6x + 2 = 2x + 8 - 2Combine like terms: 6x + 2 = 2x + 6Subtract 2x on both sides: 4x + 2 = 6Subtract 2 on both sides; 4x = 4Divide 4 on both sides: x = 1Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 6(1) + 2 = 2(1 + 4) - 2Multiply: 6 + 2 = 2(1 + 4) - 2Add: 8 = 2(5) - 2Multiply: 8 = 10 - 2Subtract: 8 = 8Here we see that 8 does indeed equal 8.
∴ x = 1 is the solution to the equation.
22 is 55% of what number ?
Answer:
40
Step-by-step explanation:
55% of n is equal to 22.
First, let's make an equation:
(55/100)*n = 22
(11/20)*n = 22 (reduced the fraction)
n = 22/(11/20) (divide both sides by 11/20)
n = 40
Hope this helps!
Please help!!
The options for both of these is right here!
Card A:
16
6
90
9
Card B: Card B *
QR
TU
RS
ST
Given:
Triangle ABC is similar to triangle EFG.
Pentagon ABCDE is similar to pentagon QRSTU.
To find:
The length of segment FG.
The missing value in [tex]\dfrac{D}{EA}=\dfrac{?}{UQ}[/tex].
Solution:
In card A,
AC = 15 in.
BC = 9 in.
EG = 10 in.
Triangle ABC is similar to triangle EFG. So, the corresponding sides are proportional.
[tex]\dfrac{AC}{BC}=\dfrac{EG}{FG}[/tex]
Putting the values, we get
[tex]\dfrac{15}{9}=\dfrac{10}{FG}[/tex]
[tex]\dfrac{5}{3}=\dfrac{10}{FG}[/tex]
[tex]5\times FG=3\times 10[/tex]
[tex]5FG=30[/tex]
Divide both sides by 5.
[tex]FG=6[/tex]
Therefore, the length of segment FG is 6 in.
In card B, pentagon ABCDE is similar to pentagon QRSTU.
The corresponding sides of similar figure are proportional. So,
[tex]\dfrac{AB}{QR}=\dfrac{BC}{RS}=\dfrac{CD}{ST}=\dfrac{DE}{TU}=\dfrac{EA}{UQ}[/tex]
Now,
[tex]\dfrac{CD}{ST}=\dfrac{EA}{UQ}[/tex]
It can be written as
[tex]\dfrac{CD}{EA}=\dfrac{ST}{UQ}[/tex]
Therefore, the missing side is ST.
Differentiate Vx(x + 2) with respect to x.
Answer:
[tex]y'= \frac{3x+2}{2\sqrt{x} }[/tex]
General Formulas and Concepts:
Calculus
The derivative of a constant is equal to 0
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Product Rule: [tex]\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]y=\sqrt{x} (x+2)[/tex]
Step 2: Rewrite
[tex]y=x^{\frac{1}{2} } (x+2)[/tex]
Step 3: Differentiate
Product Rule [Basic Power/Chain Rule]: [tex]y'= \frac{1}{2} x^{\frac{1}{2} -1}(x+2)+x^{\frac{1}{2} }(1)[/tex]Simplify: [tex]y'= \frac{1}{2} x^{\frac{-1}{2}}(x+2)+x^{\frac{1}{2}}[/tex]Rewrite: [tex]y'= \frac{x+2}{2\sqrt{x} } + \sqrt{x}[/tex]Add: [tex]y'= \frac{3x+2}{2\sqrt{x} }[/tex]Gladys scored 42 points in a basketball game. She only took 2-point shots and 3-point shots. She made a total of 18 shots. Write a system of equations to find the number of 2-point shots and 3-point shots Gladys made. Let LaTeX: xx represent the number of 2-point shots and LaTeX: yy represent the number of 3-point shots that Gladys made.
Answer:
[tex]x+y=18 \\2x+3y=42[/tex]
Number of 2-point shots taken = 12
Number of 3-point shots taken = 6
Step-by-step explanation:
Total number of points scored by Gladys = 42
Only 2-point and 3-point shots are taken by Gladys.
Let number of 2-point shots taken = [tex]x[/tex]
Let number of 3-point shots taken = [tex]y[/tex]
Total number of shots taken = 18
Therefore, first equation can be written as:
[tex]x+y=18[/tex]
Total points scored = 42
Therefore, second equation can be written as:
[tex]2x+3y=42[/tex]
System of equations is:
[tex]x+y=18 .... (1)\\2x+3y=42 .... (2)[/tex]
Using elimination method to solve the system of equations.
Multiplying equation by 2 then subtracting it from equation (2):
[tex]3y - 2y = 42 - 36\\\Rightarrow y = 6[/tex]
By equation (1):
[tex]x+6=18\\\Rightarrow x = 12[/tex]
Therefore, Number of 2-point shots taken = 12
Number of 3-point shots taken = 6
pls helppp
math work
bleh
Answer:
m = -10
Step-by-step explanation:
>:)
Answer:
m= -10
Step-by-step explanation:
2< -7 - (-10)
2< -7 + 10
2< 3
I will give multiple brainlist to people who help me with these slides!
Answer:
A)6
B)ST
Step-by-step explanation:
A if u turn it, 15 is equal to the 10
15/9=10/x
x=90/15
x=6
B) Turn it so #2 is facing up.
ST is the same.
Hope this helps plz hit the crown :D
Step-by-step explanation:
—MathA. BC/FG = AC/EG
9/FG = 15/10
FG = (9 x 10) / 15
FG = 6
B. CD/EA= ST/UQ
Follow my account^^
f(x) = -x^2 – 10x find f(-5)
Answer:
f(-5)=-(-5)^2 - 10(-5) = 25
Step-by-step explanation:
The value of f(-5) is 25 when x = -5
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 12 -2 = 10
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
Given that
⇒ f(x) = -x² – 10x
To determine the value of f(-5)
Substitute the value x = -5
⇒f(-5 ) = -(-5)² - 10(-5)
⇒f(-5 ) = 25
Hence, the value of f(-5) is 25 when x = -5
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
PLS HELP ME ASAP I DONT HAVE TIME IT ALSO DETECTS IF ITS RIGHT OR WRONG
Answer
3.2
Step-by-step explanation
8% of 40 is 3.2
so it would be 40- 3.2 and that = 36.8
mrs. page needed two types of paper for her art class. the premium color paper costs $40 per case and the plain white paper costs $30 per case. if she bought 20 cases all together and spent $720 total, how many cases of plain white paper did she buy?
Mrs. Page bought 8 cases of plain white paper.
To solve for the number of cases of plain white paper Mrs. Page bought, we will use algebraic expressions.
Algebraic expression is an expression consisting variables ad coefficient.
We will designate a variable for the unknown and solve it using the algebraic expressions made.
The number of cases of plain white paper and premium color paper is unknown.
Let x = number of cases of plain white paper
and y = number of cases of premium color paper
If Mrs. Page bought 20 cases altogether, then
x + y = 20
If Mrs. Page spent a total of $720 for the 20 cases, and the premium color paper costs $40 per case and the plain white paper costs $30 per case, then:
30x + 40y = 720
Multiplying the first equation by 30, we get:
30x + 30y = 600
Subtracting it to the 2nd equation,
30x + 40y = 720
- 30x + 30y = 600
10y = 120
y = 12
Recall that x + y = 20. Then,
x + 12 = 20
x = 8
Hence, Mrs. Page bought 8 cases of plain white paper and 12 cases of premium color paper.
To learn more about solving word problems using algebraic expressions: https://brainly.com/question/12470265
#SPJ4
twice the difference of a number and 3 is 5.
Answer:
2(3-n)=5
Step-by-step explanation:
The function f(t) = 750t + 20,000 models the number of movie theaters in the United States t years after 1985. Use this equation to predict the year in which the United States will have 35,000 movie theaters.
Given:
The function models the number of movie theaters in the United States t years after 1985.
[tex]f(t)=750t+20,000[/tex]
To find:
The year in which the United States will have 35,000 movie theaters.
Solution:
We have,
[tex]f(t)=750t+20,000[/tex]
Putting f(t)=35000, we get
[tex]35,000=750t+20,000[/tex]
[tex]35,000-20,000=750t[/tex]
[tex]15,000=750t[/tex]
Divide both sides by 750.
[tex]\dfrac{15,000}{750}=t[/tex]
[tex]20=t[/tex]
It means, United States will have 35,000 movie theaters 20 years after 1985.
[tex]1985+20=2005[/tex]
Therefore, United States will have 35,000 movie theaters is 2005.
A bucket contains 15 white, 8 pink, 3 yellow, and 10 black golf balls. What is the probability of selecting a yellow ball, keeping it, then selecting a white ball? Write your answer as a fraction in simplest form.
Answer:
5/144
Step-by-step explanation:
Step one:
given data
sample space
15 white,
8 pink,
3 yellow, and
10 black golf balls
Sample size= 15+8+3+10= 36 golf balls
Step two:
1. first event
selecting a yellow ball= 3/36= 1/12
2. second event with a replacement on the first event
selecting a white ball= 15/36= 5/12
hence for the two events, the probability is
1/12*5/12
= 5/144
The mean of 30 numbers is 18. What will be the new mean, if each observation is
increased by 2.
Answer:
The new mean will be 20.
Step-by-step explanation:
The Mean Value of a Data Set
The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:
[tex]\displaystyle \bar x=\frac{\sum x_i}{n}[/tex]
Where xi is the value of each data and n is the total number of values.
The mean of n=30 numbers is [tex]\bar x=18[/tex]. If each observation is increased by 2, then xi'=xi+2 and the new mean value will be:
[tex]\displaystyle \bar x'=\frac{\sum x'_i}{30}[/tex]
[tex]\displaystyle \bar x'=\frac{\sum x_i+2}{30}[/tex]
[tex]\displaystyle \bar x'=\frac{\sum x_i}{30}+\frac{\sum 2}{30}[/tex]
The sum of 30 times 2 is 60, thus:
[tex]\displaystyle \bar x'=18+\frac{60}{30}=18+2=20[/tex]
The new mean will be 20.
Pls I need help plsssss
Answer:
The first option!
Step-by-step explanation:
2 2/3 but brainliest? Thanks!
The surface area of a solid is 4500 square inches. Is the surface area greater than 3 square yards
If the surface area of the solid is 4500 square inches, then the surface area of the solid is greater than 3 square yards
What are areas?The area of a shape is the amount of space on the shape.
For most regular quadrilaterals, the area is the product of the length and the width of the quadrilateral
Is the surface area greater than 3 square yards?The surface area of the solid is given as
Surface area = 4500 square inches
As a general rule of unit conversion
1 square inches = 1/1296 square yards
Next, we multiply both sides of the equation by 4500
So, we have
4500 * 1 square inches = 4500 * 1/1296 square yards
Evaluate the products in the above equation
4500 square inches = 3.5 square yards
3.5 square yards is greater than 3 square yards
Hence, the surface area of the solid is greater than 3 square yards
Read more about surface area at
https://brainly.com/question/22744289
#SPJ1
help! what is the equation of the line??!
Answer: y=-1/3-2
Step-by-step explanation:
slope=-1/3
y intercept=-2
What is 5×10+4×1+8×110+6×1100+1×11,000 ?
Answer:
18534 is the answer of this question
Find NX. PLs help with this problem !
Answer:
It i 5.Because it is Equlitrial triangle
determine the rate of change for the graph from 2014 to 2015:____ students per year
Answer:
The answer would be 9
Step-by-step explanation:
-3(x+5) - (2x+3) equals
-5x,-18
i hope im right im not quite sure bout this one
Use the distributive property to rewrite each expression in its equivalent form.
1. 4(x + 3)
2. -7(4 - y)
3. 6(3x + 5y -4)
4. 9a-3/3
Rewrite each linear expression by factoring out the greatest common factor.
5. 64x + 24
6. -5y -35
HELPP I NEED TO SUMBIT SOON
Help me PLEASEEEE I’m on a time limit
Answer:
C. 20/52
Step-by-step explanation:
Find the value of x.
Answer:
x=102
Step-by-step explanation:
Plainfield Community Center is buying new seating for their building. They want to purchase a combination of stools and chairs. Stools cost $50 and chairs cost $65. The center cannot spend more than $3000.
Which inequality represents all possible combinations of s stools and c chairs?
50s+65c≤3000
50c+65s≥3000
50s+65c<3000
50c+65s≤3000
Answer:
D) 50s + 65c ≤ 3000
Step-by-step explanation:
50s represents the stools and 65c represents the chairs
you can't go over 3000 and so this is the only answer that makes sense.
Answer:
The answer is D) 50s + 65c ≤ 3000!
Step-by-step explanation:
I just took the test and i got 100%. Hope this helps! :]
Which statements are true? Select the two correct answers.
The square root of a positive number greater than 1 is less than the number,
The square root of a positive number is always less than half of the number itself.
The square root of a positive number less than 1 is less than the number.
The square root of a perfect square is not a whole number.
The square root of a positive number less than 1 is between 0 and 1.
the person ontop is wrong its a and e
Step-by-step explanation:
:)
16 - 3x = 4 + x
solve please
Answer:
x = 3
Step-by-step explanation:
Solution for 16-3x=4+x equation:
Simplifying
16 + -3x = 4 + x
Solving
16 + -3x = 4 + x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1x' to each side of the equation.
16 + -3x + -1x = 4 + x + -1x
Combine like terms: -3x + -1x = -4x
16 + -4x = 4 + x + -1x
Combine like terms: x + -1x = 0
16 + -4x = 4 + 0
16 + -4x = 4
Add '-16' to each side of the equation.
16 + -16 + -4x = 4 + -16
Combine like terms: 16 + -16 = 0
0 + -4x = 4 + -16
-4x = 4 + -16
Combine like terms: 4 + -16 = -12
-4x = -12
Divide each side by '-4'.
x = 3
Simplifying
x = 3Solution for 16-3x=4+x equation:
Simplifying
16 + -3x = 4 + x
Solving
16 + -3x = 4 + x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1x' to each side of the equation.
16 + -3x + -1x = 4 + x + -1x
Combine like terms: -3x + -1x = -4x
16 + -4x = 4 + x + -1x
Combine like terms: x + -1x = 0
16 + -4x = 4 + 0
16 + -4x = 4
Add '-16' to each side of the equation.
16 + -16 + -4x = 4 + -16
Combine like terms: 16 + -16 = 0
0 + -4x = 4 + -16
-4x = 4 + -16
Combine like terms: 4 + -16 = -12
-4x = -12
Divide each side by '-4'.
x = 3
Simplifying
x = 3Solution for 16-3x=4+x equation:
Simplifying
16 + -3x = 4 + x
Solving
16 + -3x = 4 + x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1x' to each side of the equation.
16 + -3x + -1x = 4 + x + -1x
Combine like terms: -3x + -1x = -4x
16 + -4x = 4 + x + -1x
Combine like terms: x + -1x = 0
16 + -4x = 4 + 0
16 + -4x = 4
Add '-16' to each side of the equation.
16 + -16 + -4x = 4 + -16
Combine like terms: 16 + -16 = 0
0 + -4x = 4 + -16
-4x = 4 + -16
Combine like terms: 4 + -16 = -12
-4x = -12
Divide each side by '-4'.
x = 3
Simplifying
x = 3
find the value of x so that f(x)= 7
Answer: f (x) =7
Step-by-step explanation:
Which statement describes the graph of f(x) = –x4 + 3x3 + 10x2?
Answer:
The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = -2.
Step-by-step explanation:
please help! (will give brainlist!)
37: given the line y=3/4x-2
a: find the parallel slope.
b: find the perpendicular slope.
38: determine if the lines are parallel or perpendicular:
a: -2x+5y=9 and 5x+2y=-6
b: 4y=8x+12 and -12x+6y=24
39: write an equation of a line that passes through (-4,-6) and is parallel to y=3x-8
40: write an equation of a line that passes through (2,5) and is perpendicular to y=1/4x-12
Step-by-step explanation:
Two lines are parallel if they have the same slope and are perpendicular if the product of their slopes is -1
37.a.Parallel slope=¾
b.Perpendicular slope =-1/¾=-4/3
38.a. -2x+5y=9 and 5x+2y=-6
For the first line,5y=2x+9,y=2/5x+9/5
For the second line,2y=-6-5x,y=-3-5/2x
Compare the slopes
2/5 vs -5/2 we see that -5/2 is the negative reciprocal of 2/5 therefore they are perpendicular
39. If both lines are parallel then their slopes are equal. The slope of y=3x-8 is 3
Using the point-slope form, y-y1=m(x-x1)
y--6=3(x--4)
y+6=3(x+4)
y+6=3x+12
y=3x+12-6
y=3x+6
40.The slope of y=¼x-12 is ¼
The negative reciprocal of it is the slope of it's perpendicular that is -1/¼=-4
Using the point slope form, y-y1=m(x-x1)
y-5=-4(x-2)
y-5=-4x+8
y=-4x+8+5
y=-4x+13
if you answer correct you get brainliest!
Answer:
The correct answer is D.) y = -2x-3
Step-by-step explanation:
You can solve the given equation y - 5 = -2(x + 4):
y - 5 = -2(x + 4) simplify the right side
y - 5 = -2x - 8 add 5 to both sides
y = -2x - 3
Hope it helps! have a great day! :)
Answer:
D
Step-by-step explanation:
solve whats in ( ) first y-5= -2x -8
move the constant to the right y = -2x - 8+5
(5 is the constant )
add the sums y= -2x -3
This is actually the slope intercept form