Add 6 on both sides, canceling out that -6
3x = 21
Divide both sides by 3 to isolate that variable and get your answer
x = 7.
Answer:
x=7
Step-by-step explanation:
3x-6+6=15+6
3x=21
3x/3=21/3
x=7
When you isolate the variable, the goal is to get the variable
A
to equal 1.
B
on both sides of the equal sign to show they are equal.
C
by itself on one side of the equal sign and a value on the other.
D
by itself on one side of the equal sign and zero on the other side.
Answer:
C
Step-by-step explanation:
For example
[tex]y = 77 \\[/tex]
The answer is C: by itself on one side of the equal sign and a value on the other.
Let's go through the detailed steps of isolating the variable with each option in mind.
Option: C - by itself on one side of the equal sign and a value on the other.
Given equation:[tex]\(3x + 7 = 16\)[/tex]
Step 1: Identify the Variable
The variable in the equation is [tex]\(x\).[/tex] We want to isolate [tex]\(x\)[/tex] to find its value.
Step 2: Isolate Terms with the Variable
Move terms containing the variable to one side of the equation. Here, we'll move [tex]\(3x\)[/tex] to the left side by subtracting [tex]\(7\)[/tex] from both sides:
[tex]\[3x + 7 - 7 = 16 - 7\][/tex]
This simplifies to:
[tex]\[3x = 9\][/tex]
Now, the term [tex]\(3x\)[/tex] is isolated on the left side of the equation.
Step 3: Perform Inverse Operations to Isolate the Variable
Since [tex]\(x\)[/tex] is being multiplied by [tex]\(3\),[/tex] to isolate [tex]\(x\),[/tex] we divide both sides by [tex]\(3\):[/tex]
[tex]\[\frac{3x}{3} = \frac{9}{3}\][/tex]
This simplifies to:
[tex]\[x = 3\][/tex]
Now, the variable [tex]\(x\)[/tex] is isolated on the left side of the equation, and its value is [tex]\(3\).[/tex]
By following these detailed steps, we have successfully isolated the variable [tex]\(x\)[/tex] on one side of the equal sign and a specific value (option C) on the other side, demonstrating equality between the two sides of the equation.
For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations. If she has 22 travelers checks in all, how many of each denomination does she have?
Let x represent the number of $10 traveler's checks she has. Which expression represents the value of the $20 traveler's checks she has?
20 x
20(22 - x)
20(22)
Answer:
20(22-x)
Step-by-step explanation:
find the area and perimeter of the rectangle with vertices (4, -7), (-3, -7), (-3, 3), and (4, 3).
Answer:
Area: 42
Perimeter = 26
Step-by-step explanation:
Distance from (4,-7) to (-3,-7) = 7
Distance from (-3,-7) to (-3,3) = 6
These are the length and width of the rectangle.
Area: 7 * 6 = 42
Perimeter = 2*(7+6) = 26
The perimeter of a semicircle is 35.98 meters. What is the semicircle's diameter?
To find the diameter of the semicircle, divide the circumference of the whole circle by 2. Given that the perimeter of the semicircle is 35.98 meters, the diameter would be approximately 22.87 meters.
Explanation:To find the diameter of the semicircle, we first need to find the circumference of the entire circle and then divide it by 2. The formula for the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.
Given that the perimeter of the semicircle is 35.98 meters, the circumference of the whole circle will be twice that value. So, 2 * 35.98 = 71.96 meters.
Now we can use the formula C = π * d to solve for the diameter: 71.96 = π * d. Dividing both sides of the equation by π gives us d = 71.96 / π.
Using a calculator, we can approximate π to 3.14. So, d = 71.96 / 3.14 = 22.87 meters.
How did the gulf of Tonkin resolutions affect US involvement in the Vietnam war?
Answer:
I don't know how this is math but...
The Gulf of Tonkin Resolution authorized President Lyndon Johnson to “take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression” by the communist government of North Vietnam. Hope I helped! ☺
Answer:
It gave the president the ability to send troops without congressional approval.
Step-by-step explanation:
4p+10=p-14 what is the solution and how do you check the solution
Answer:
p=-8
Step-by-step explanation:
Its on the picture
$4,000 invested in Fund A returned 5% profit. Amount invested in Fund B returned a 2% profit. How much was invested in Fund B if both funds returned 4%?
as I read it, what I get is that
x = returned profits or yielded interest from investment in A
y = returned profits or yielded interest from investment in B
T = total amount invested or namely A + B.
4000 were invested in A, and it yielded 5%, what's 5% of 4000? (5/100)(4000) = 200 = x.
we know the total amount is T, since A get 4000, B must have gotten T - 4000, or the slack. We also know that B yielded a 2% profit, well, what's 2% of T - 4000? (2/100)(T-4000) = y.
we also know that, whatever "x" and "y" are, their sum total yielded a 4% returns from T, or the total principal, what's 4% of T? (4/100)T = 0.04T.
[tex]\bf \begin{cases} T=\textit{total principal}\\[-0.5em] \hrulefill\\ A=4000\\ x = \stackrel{\textit{5\% of A}}{200}\\[-0.5em] \hrulefill\\ B=T-4000\\ y=\stackrel{\textit{2\% of B}}{0.02(T-4000)} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{5\% of A}}{200}+\stackrel{\textit{2\% of B}}{0.02(T-4000)}~~=~~\stackrel{\textit{4\% of T}}{0.04T} \\\\\\ 200+0.02T-80=0.04T\implies 120+0.02T=0.04T\implies 120=0.02T \\\\\\ \cfrac{120}{0.02}=T\implies 6000=T~\hfill \stackrel{~\hfill \textit{invested in B}}{6000-4000\implies 2000}[/tex]
-3x+3y=9 2x−7y=−14
Researchers wanted to learn more about people who rent apartments and who have pets. They
began a study of 971 renters. The researchers found that 216 of the renters in their study
reported that they owned pets. Of the renters who owned pets, 2/3 of the renters owned a dog.
What percentage of all renters in the study owned a dog?
9 lb 4 oz − 2 lb 12 oz
Answer: 6 LB 12 OZ
16 OZ in a LB
9 LB - 2 LB = 7 LB
4 OZ - 12 OZ difference of 8 OZ
4 - 4 = 0 then 16 OZ in a LB
4 remaining - 16 = 12 dropping the 7 LB to 6 LB
Step-by-step explanation:
First, turn into just ounces (1lb. = 16oz.)
9 lb 4 oz = 148 oz
2 lb 12 oz = 44 oz
Second, subtract.
148 - 44 = 104 oz
Third, turn into pounds and ounces.
104 oz = 6 lb 8 oz
______
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Solve the system of equations:
3x + 2y = 4
3x + 6y = -24
I'm really confused on how to solve these types of problems! I was wondering if you can explain this to me.
The solution of the system of equations is (6 , -7)
Step-by-step explanation:
There are two method to solve the system of equations
Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variableSubstitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variableLet us use the elimination method with your problem
∵ 3x + 2y = 4 ⇒ (1)
∵ 3x + 6y = -24 ⇒ (2)
- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs
∵ -3x - 2y = -4 ⇒ (3)
- Add equations (2) and (3)
∴ 4y = -28
- Divide both sides by 4
∴ y = -7
Substitute value of y in equations (1) OR (2) to find x
∵ 3x + 2(-7) = 4
∴ 3x - 14 = 4
- Add 14 for both sides
∴ 3x = 18
- Divide both sides by 3
∴ x = 6
The solution of the system of equations is (6 , -7)
I hope this explanation help you
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What are the factor paira of 48
Answer:
1 x 48 = 48
2 x 24 = 48
3 x 16 = 48
4 x 12 = 48
6 x 8 = 48
8 x 6 = 48
12 x 4 = 48
16 x 3 = 48
24 x 2 = 48
48 x 1 = 48
Step-by-step explanation:
Answer:
The factor pair for 48 is 1,2,3,4,6,8,12,16,24 and 48
Your welcome!
A ball is thrown vertically upward from the ground with an initial velocity of 122 ft/sec. Use the quadratic function
h(t) = -16t2 + 122t +0 to find how long it will take for the ball to reach its maximum height, and then find the
maximum height. Round your answers to the nearest tenth.
Answer:
232.6 metres after 3.8 seconds.
Step-by-step explanation:
h(t) = -16t² + 122t
a = -16 b = 122 c = 0
Substitute into the quadratic formula
(Ignore the Â)
[tex]x = \frac{-b±\sqrt{b^{2}-4ac}}{2a} [/tex]
[tex]x = \frac{-122±\sqrt{122^{2}-4(-16)(0)}}{2(-16)} [/tex]
[tex]x = \frac{-122±122}{-32} [/tex]
Split the equation at the ±
[tex]x = \frac{-122+122}{-32}[/tex] [tex]x = \frac{-122-122}{-32} [/tex]
[tex]x = \frac{0}{-32}[/tex] [tex]x = \frac{-244}{-32} [/tex]
[tex]x = 0[/tex] [tex]x = \frac{61}{8}[/tex]
The two x-intercepts at 0 and 61/8. The midpoint of the x-intercepts is the axis of symmetry, which is the x-coordinate of the vertex.
Midpoint = [0 + (61/8)] / 2
Midpoint = 61/16 <= This is the time for maximum height
t = 61/16
t = 3.8125 => Round to t = 3.8
To find the maximum height, substitute t=61/16 into the equation
h(t) = -16t² + 122t
h(61/16) = -16(61/16)² + 122(61/16)
h(61/16) = 232.5625 => Round to h = 232.6
Therefore, the ball will reach the maximum height of 232.6 metres after 3.8 seconds.
21. A postal carrier can deliver to 130 houses in
2.5 hour period. At this rate, how many hours will
it take to deliver to 234 houses?
Answer:
4.5 hours
Step-by-step explanation:
we know that
A postal carrier can deliver to 130 houses in 2.5 hour
so
using proportion
Find out how many hours will it take to deliver to 234 houses
[tex]\frac{130}{2.5}\ \frac{houses}{hours} =\frac{234}{x}\ \frac{houses}{hours} \\\\x=234(2.5)/130\\\\x=4.5\ hours[/tex]
there are 50 jelly beans in a jar. 32 percent are black, 52 percent are green, and 16 percent are purple. how many green jelly beans are in the jar?
HELP ASAP! A store clerk is unpacking a box of cameras. The line plot displays the weight of each camera. How much do all the cameras in the box weigh?
Answer:
3\8 I think is the answer
Step-by-step explanation:
I know because I know!
Answer:
8 3/8
Step-by-step explanation:
I have study island too
simplify -3w-5(4x-4w)-4x
-3w-5(4x-4w)-4x
multiply the bracket by -5
(-5)(4x)=-20x
(-5)(-4w)=20w
-3w-20x+20w-4x
-3w+20w-20x-4x ( combine like terms)
answer:
17w-24x or -24x+17w
An item on sale costs 70% of the original price. If the original price was $30, what is the sale price
Answer:
$21
Step-by-step explanation:
70%=0.7
30*0.7=21
Answer:
$9.00
Step-by-step explanation:
Subtract 70 percent from 30 dollars
the size of the largest angle in a triangle is 3 times the size of the smallest angle.
the third angle is 10° more than the smallest angle
work out the size, in degrees, of each angle in the triangle.
You must show your working (let X be the smallest angle).
The sizes of the angles are 34° , 44° , 102°
Step-by-step explanation:
The given is:
The size of the largest angle in a triangle is 3 times the size of the smallest angleThe third angle is 10° more than the smallest angleThe size of the third angle is xWe need to find the size of each angle in the triangle
∵ The size of the smallest angle = x°
∵ The size of the largest angle is 3 times the size of the smallest angle
∴ The size of the largest angle = x × 3 = (3x)°
∵ The third angle is 10° more than the smallest angle
∴ The size of the third angle = (x + 10)°
Add the size of the three angles and equate the sum by 180°
∵ The sum of the sizes of the interior angles of a Δ is 180°
∴ x + (3x) + (x + 10) = 180
∴ x + 3x + x + 10 = 180
- Add like terms
∴ 5x + 10 = 180
- Subtract 10 from both sides
∴ 5x = 170
- Divide both sides by 5
∴ x = 34
∵ x is the size of the smallest angle
∴ The size of the smallest angle is 34°
∵ 3x is the size of the largest angle
∴ The size of the largest angle = 3(34) = 102°
∵ x + 10 is the size of the third angle
∴ The size of the third angle = 34 + 10 = 44°
The sizes of the angles are 34° , 44° , 102°
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What is the sum of the solutions of x2 + 9x + 20 = 0?
What is the product (or multiplication) of the solutions of 6x2 + 7x = 3?
Answer:
Sum of the solutions of [tex]x^2+9x+20=0[/tex] is -9.
Product of the solutions of [tex]6x^2+7x=3[/tex] is [tex]-0.50[/tex]
Step-by-step explanation:
1. [tex]x^2+9x+20=0[/tex]
Given:
The expression whose sum of the solution is required is given as:
[tex]x^{2} +9x+20=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the sum of the solutions is given as:
Sum = [tex]\frac{-b}{a}[/tex]
Here, [tex]a=1,b=9,c=20[/tex]
Therefore, the sum of the solutions = [tex]-\frac{9}{1}=-9[/tex]
2. [tex]6x^2+7x=3[/tex]
Rewriting the above equation in a standard quadratic equation, we get:
[tex]6x^2+7x-3=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the product of the solutions is given as:
Product = [tex]\frac{c}{a}[/tex]
Here, [tex]a=6,b=7,c=-3[/tex]
Therefore, the product of the solutions = [tex]\frac{-3}{6}=-0.50[/tex]
Through (-1,4) and a perpendicular to 4y-2x=12
Answer:
y = -2x + 2 → 2x + y = 2Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2[/tex]
[tex]\text{We have the equation of a line in the standard form:}\ Ax+By=C.\\\\\text{Convert to the slope-intercept form:}\\\\4y-2x=12\qquad\text{add}\ 2x\ \text{to the both sides}\\\\4y-2x+2x=2x+12\\\\4y=2x+12\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{2x}{4}+\dfrac{12}{4}\\\\y=\dfrac{1}{2}x+3\to\boxed{m_1=\dfrac{1}{2}}[/tex]
[tex]\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{Put the value of the slope and the coordinates of the given point (-1, 4)}\\\text{to the equation of a line:}\\\\4=-2(-1)+b\\\\4=2+b\qquad\text{subtract 2 from the both sides}\\\\4-2=2-2+b\\\\2=b\to b=2\\\\\bold{FINALLY:}\ y=-2x+2[/tex]
[tex]\text{Convert to the standard form:}\\\\y=-2x+2\qquad\text{add}\ 2x\ \text{to the both sides}\\\\y+2x=-2x+2x+2\\\\2x+y=2[/tex]
Which of the following best represents the average rate at which a person can
quickly walk?
01) 3 steps per hour
O2) 3 steps per second
03) 30 steps per minute
O4) 30 steps per second
Which triangles are congruent in the diagram?
A softball team is ordering pizza to eat after their tournament. They plan to order cheese pizzas that cost $6
each and four-topping pizzas that cost $10 each. They order c cheese pizzas and f four-topping pizzas.
Which expression represents the total cost of all the pizzas they order?
The total cost of all the pizzas that the softball team order can be calculated as 6c + 10f, where c represents the number of cheese pizzas ordered, and f represents the number of four-topping pizzas ordered.
Explanation:To determine how much the softball team is spending on pizzas, we need to multiply the cost of each type of pizza by the number of each type they are ordering. For the cheese pizzas, that cost $6 each, the cost will be:
6c (where 'c' is the number of cheese pizzas).
For the four-topping pizzas, that cost $10 each:
The cost will be 10f (where 'f' is the number of four-topping pizzas).
Now, to calculate the total cost, we add up the cost of the cheese pizzas and the four-topping pizzas:
Total cost = 6c + 10f
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One side of a triangle is 2 times the second side. The third side is 5 ft longer than the second side. The perimeter of a triangle is 81 ft. Find the length of each side.
Answer:
The length of each side of triangle are 19 ft, 24 ft and 38 ft.
Step-by-step explanation:
Let the length of second side be x.
Now given:
Length of first side is 2 times length of second side.
Length of first side = 2x
Also, Length of third side is 5 ft longer than the second side.
Length of third side = 5+x
Perimeter of triangle = 81 ft.
We need to find the length of each side.
Now perimeter of triangle is sum of all three sides of triangle.
Therefore;
Perimeter of triangle = Length of first side + length of second side + Length of third side.
[tex]2x+x+5+x=81 ft\\4x+5=81ft\\4x= 81 -5 ft\\4x = 76ft\\x= \frac{76}{4} = 19 ft[/tex]
Length of Second Side = 19 ft.
Length of First side = [tex]2x= 2\times19 = 38 ft[/tex]
Length of Third side = [tex]5+x= 5+19=24ft[/tex]
Hence the Length of triangles are 19 ft,38 ft,24 ft.
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 6
A. log(2) + log(1/6)
B. log 2
C. log(1/3)
D. log 3
Answer:
C. log(1/3)
Step-by-step explanation:
Remember the quotient/subtraction rule for logs:
log2 - log6 can be written as log(2/6)
Hence, it's equal to C. log(1/3)
Hope this helps!
Mark brainliest if you think I helped! Would really appreciate!
The expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.
The correct option is (A&C).
To solve [tex]\( \log 2 - \log 6 \)[/tex], we can use the property of logarithms that states:
[tex]\[ \log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right) \][/tex]
Given [tex]\( \log 2 - \log 6 \)[/tex], applying the above property:
[tex]\[ \log 2 - \log 6 = \log\left(\frac{2}{6}\right) = \log\left(\frac{1}{3}\right) \][/tex]
So, the expression \[tex]( \log 2 - \log 6 \)[/tex] is equivalent to [tex]\( \log\left(\frac{1}{3}\right) \)[/tex], which matches option C.
Now, let's check the other options:
A. [tex]\( \log(2) + \log\left(\frac{1}{6}\right) \)[/tex]
This expression can be simplified using the properties of logarithms to [tex]\( \log\left(2 \times \frac{1}{6}\right) = \log(1/3) \),[/tex] which is equivalent to the original expression. So, option A is also correct.
B. [tex]\( \log 2 \)[/tex]
This option is not equivalent to the original expression. It only represents [tex]\( \log 2 \),[/tex] not the difference of [tex]\( \log 2 \) and \( \log 6 \).[/tex]
D. [tex]\( \log 3 \)[/tex]
This option is not equivalent to the original expression. It only represents [tex]\( \log 3 \)[/tex], which is unrelated to the expression [tex]\( \log 2 - \log 6 \).[/tex]
So, the expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.
David did not have time to wait for the elevator on the first floor of the building so he decided to go up the stairs. If it took him 2 minutes to get to the third floor, how long will it take him to get to the ninth floor?
Answer:
8 minutes
Step-by-step explanation:
It takes 2 minutes every 2 floors, and Floor 9 is 8 floors away from Floor 1, so 2x4=8.
HELP ME PLEASE!!!!!!!!!!!! Correct answer only, just don't write or guess or you will get reported!
A plumber charges a flat fee of $45 to answer a service call in addition to an hourly rate of $30.50. The plumber has estimated he will earn at least $197.50 from his next repair job. Which inequality can be used to determine the number of hours, h, that the plumber will work on his next job?
Group of answer choices
$30.50h + 45 > $197.50, with a solution of h>6
$30.50h + 45 < $197.50, with a solution of h<6
$30.50h + 45 ≤ $197.50, with a solution of h≤6
$30.50h + 45 > $197.50, with a solution of h>6
Answer: The second one is correct I believe
Step-by-step explanation:
To find the value of the following expression, what operation should you do first? 20-(7+4) x5
Answer:
Distributive Property.
Answer:
-35
Step-by-step explanation:
20-(7+4)*5
20-(11)(5)
20-55
-35
Choose the answer that best translates
the algebraic expression below.
9a
9 more than a number
9 less than a number
9 times a number
9 divided by a number
Answer:
9 times a number
Step-by-step explanation:
If a number and a variable are next to each other, you multiply.