20 - 6 + 4k = 2 - 2k
14 + 4k = 2 - 2k added like terms (20 and -6)
+2k +2k
14 + 6k = 2
-14 -14
6k = -12
[tex]\frac{6k}{6} = \frac{-12}{6}[/tex]
k = -2
Answer: k = -2
The solution to the equation is k = -2.
To solve for k in the equation 20 - 6 + 4k = 2 - 2k, we can start by simplifying both sides of the equation.
Combining like terms on each side:
14 + 4k = 2 - 2k
Next, we can isolate the variable k by moving all terms containing k to one side of the equation.
Adding 2k to both sides:
14 + 4k + 2k = 2 - 2k + 2k
14 + 6k = 2
Now, we'll isolate the variable k by subtracting 14 from both sides:
14 + 6k - 14 = 2 - 14
6k = -12
To solve for k, we'll divide both sides by 6:
(6k)/6 = (-12)/6
k = -2
Therefore, the solution to the equation is k = -2.
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What roles did African American men take on during the war? Check all of the boxes that apply They worked as cooks. They enlisted in the Union Army. They served as generals in the army.
All except generals
Union supported African Americans as soldiers
They worked as slaves so obviously cooks
Answer:
They worked as cooks.They enlisted in the Union Army.Step-by-step explanation:
The emancipation proclamation allowed the African American men to serve in the Union army.
They worked as cooks. Enslaved blacks were sometimes used for camp labor also.
But they did not served as generals in the army.
Hence, the answer is :
They worked as cooks.They enlisted in the Union Army.For which values of x is the inequality 2(1 + x) > x + 8 true?
A) 3 & 2
B) 4 & 3
C) 6 & 5
D) 7 & 8
he work shows how to use long division to find (x2 + 3x –9) ÷ (x – 2). What will be the remainder over the divisor?
Explanation of how to find the remainder using long division with a polynomial expression.
Explanation:Long Division Example:
We are given (x² + 3x – 9) ÷ (x – 2). To find the remainder using long division, we need to divide x² + 3x - 9 by x - 2 step by step.
Start by dividing x² by x, which gives x. Multiply x by (x - 2) to get x² - 2x.
Subtract x² - 2x from x² + 3x to get 5x. Bring down the -9.
Repeat the process: divide 5x by x to get 5. Multiply 5 by (x - 2) to get 5x - 10.
Subtract 5x - 10 from 5x - 9. The remainder is 1, which is the value over the divisor x - 2.
A person travels to a destination at a rate of 50m/h and returns the next day at a rate of 40m/h. If the time returning is 1hour more than the time going, how many miles are traveled in all?
the time returning=x h,
the time going=(x-1) h,
s=t*v
s=(x-1)*50,
s=x*40,
(x-1)*50=x*40
x=5h,
s=t*v=5*50=250 miles
Verify the equation below with each of the values listed for x to find a solution.
5 = 3x + 4
Answer:
123123131231231312312
Step-by-step exp13123123123lanation:
jkbbhivbyuiiyu1312312
Solve for x. 14+x>18 Enter your answer, as an inequality, in the box.
x > 4 is your answer
What is the known and unknown in 6 multiple by 2 are are 12 devided by 6
What is the sum of the angle measures in a decagon?
1,800°
1,440°
1,260°
210°
Use the formula (n - 2) * 180 to find the sum of the interior measures of a polygon.
n stands for the number of sides that the polygon has, so substitute 10 for n since a decagon has 10 sides.
(10 - 2) * 180, start by solving inside the parentheses and subtracting 10 and 2.
(8) * 180, multiply.
B. 1,440 is your answer.
If you finish one year of collage does it raise your income for the rest of your life?
5 quarts of water are needed for every 2 pounds of chicken, how much water do you need per pound
Which of the following equations represents the line with a slope of negative 8/7 and a y-intercept of negative 3?
y = 8/7x - 3
y = 8/7x + 3
y = -8/7x - 3
y = -8/7x + 3
Answer:
y = -8/7x - 3
Step-by-step explanation:
A line represents a linear relationship between x and y with constant slope and defined for all values of x and y.
Any line equation in slope intercept form would be of the form
y =mx+c where
m = slope of line
and c = y intercept
In our quesion we are given that slope of line = -8/7
and intercept = negative 3 = -3
Hence equation is
y =-8x/7-3
Sten had some apples in his basket. He ate 3 and then put 3 in each of 4 bags. How many apples did Sten start with in his basket?
3 * 4 + 3 = 12 + 3 = 15
Answer: He had 15 apples.
If f(x) = 2x + 7 and g(x) = x2 2, what is [f o g](3)?
Answer:
The value [fog](3) is 29.
Step-by-step explanation:
The given functions are
[tex]f(x)=2x+7[/tex]
[tex]g(x)=x^2+2[/tex]
We have to find [fog](3).
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(3)=f(g(3))[/tex]
[tex](f\circ g)(3)=f(3^2+2)[/tex] [tex][\because g(x)=x^2+2][/tex]
[tex](f\circ g)(3)=f(11)[/tex]
[tex](f\circ g)(3)=2(11)+7[/tex] [tex][\because f(x)=2x+7][/tex]
[tex](f\circ g)(3)=22+7[/tex]
[tex](f\circ g)(3)=29[/tex]
Therefore the value [fog](3) is 29.
Find f(6) if f(x) = x2 ÷ 3 + x.
4
10
18
f(x) = x2 ÷ 3 + x
f(6)
Replace X with 6 then follow order of operations.
6^2 / 3 + 6
6^2 = 36:
36 / 3 + 6
36 /3 = 12:
Add:
12 + 6 = 18
The answer is 18
The question is in the attached below , thank you for helping me .
JKLM is a parallelogram. - Given
JM is a parallel to KL. - Definition of bisect
Given - LN bisects <KLP.
<2 ~= <3 - Definition of bisect
<1 ~= <3 - Transitive Property of Congruence
Given a line segment with end points A (0,0) and B (6,8), find point C (x,y) that the triangle vertices A, B and C has an area of 25 square units?
Answer:
C(6.25 , 0)
Step-by-step explanation:
Draw the diagram
A is at (0,0)
B is at (6,8)
Draw a line from A to B.
Put a large dot where (0,6) is. Call this D
Draw BD
Draw another line from (0,0) to just beyond (6,0) Call this C. Draw in BC
What You Have Drawn
The height of the triangle is BD and it is 8. That comes from B which is (6,8)
Solve
Formula
Area = 1/2 * B * H
Area = 25
H = 8
Area = 1/2 B * H
25 = 1/2 * B * 8 Switch sides
1/2 * B * 8 = 25 Combine factors on the left.
4 B = 25 Divide both sides by 4
4B/4 = 25/4
B = 6.25
What that means is that AC is 6.25 units long and is on the x axis
C is C(6.25,0)
Can someone please help me?
Which of the sets of ordered pairs represents a function?
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
In the inequality, what are all the possible values of x? 2 − 3(2x + 1) < 6x(2 − 4) A) x ≥ 1 6 B) x ≤ 1 6 C) x ≥ − 1 6 D) x ≤ − 1 6
2 - 3(2x + 1) < 6x(2 - 4)
2 - 6x - 3 < 12x - 24x
-1 - 6x < -12x
-1 < -6x
Dividing by -6 both sides gives you;
1/6 < x or;
Final answer is x > 1/6
Answer:
A) x ≥ 1 6
: )
What is the solution of the equation when solved over the complex numbers? X2+24=0.
Answer:
[tex]x=+-2i\sqrt{6}[/tex]
Step-by-step explanation:
[tex]x^2+24=0[/tex]
To solve for x we need to get x alone
Subtract 24 from both sides
[tex]x^2+24=0[/tex]
[tex]x^2=-24[/tex]
Now take square root on both sides to remove the square
[tex]x^2=-24[/tex]
[tex]\sqrt{x^2} =\sqrt{-24}[/tex]
[tex]x=+-2\sqrt{-6}[/tex]
square root of -1 is 'i'
[tex]x=+-2i\sqrt{6}[/tex]
Answer:
Step-by-step explanation:
2i√6 and -2i√6 :))
Jules reads that 1 pint is equivalent to 0.473 liters. He asks his teacher how many liters are in a pint . His teachers responds that there about 0.47 liters on a pint. He asks his parents they say they are about 0.5 liters in a pint. Jules says they are both correct . How can that be true explain your answer
There are about 25.4 millimeters in one inch. Write this number in scientific notation.
Answer:
I inch = 25.4mm
Step-by-step explanation:
i inch =25.4mm
= 2.54×10^1
25.4 millimeters in scientific notation can be written as [tex]2.54 \times 10^1 \text {milimeters}[/tex]
The value "25.4 millimeters" must be expressed as a decimal number between 1 and 10, multiplied by a power of 10, in order to be written in scientific notation.
We may write the given number, 25, as follows:
[tex]2.54 \times 10^1[/tex]
In scientific notation, the decimal point is placed after the first non-zero digit, and in this case it is 2. The exponent 1 indicates that we move the decimal point one place to the right to get the original value.
Therefore, 25.4 millimeters in scientific notation is [tex]2.54 \times 10^1\text{millimeters }[/tex]
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Suppose each square on the grids below is 1 cm by 1 cm. Estimate the area of the figure.
about 30 cm2
about 40 cm2
about 20 cm2
about 10 cm2
Answer:
About [tex]20cm^2[/tex]
Step-by-step explanation:
In the given image each of the square has side 1 cm by 1 cm.
If we could count the whole squares in the image we can see that there are about 14 whole squares, then there are 6 squares which are nearly half occupied so that makes about 3 whole squares. And then there are almost 12 squares whose quarter area is enclosed by the lines so that makes about 3 whole squares.
So the total area of the given figure is about [tex]20 cm^2[/tex].
Answer:
Option "C" would be the correct answer
please help asap 30 pts
[tex]-18-5y\geq52\qquad|\text{add 18 to both sides}\\\\-5y\geq70\qquad|\text{change the signs}\\\\5y\leq-70\qquad|\text{divide both sides by 5}\\\\y\leq-14\\\\Answer:\ \boxed{d.\ y\leq-14}[/tex]
y=–3x + 6y=9 What is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)
ANSWER
The solution is [tex](-1,9)[/tex]
EXPLANATION
We want to solve the simultaneous equations
[tex]y=-3x+6---(1)[/tex]
and
[tex]y=9--(2)[/tex].
We substitute equation (2) in to equation (1), to obtain
[tex]9=-3x+6[/tex]
This has now become a linear equation in a single variable [tex]x[/tex].
We solve for x by grouping like terms.
[tex]9-6=-3x[/tex]
[tex]3=-3x[/tex]
We divide through by negative 3 to get;
[tex]-1=x[/tex].
Hence, the solution is [tex](-1,9)[/tex]
A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
slope = - 2, midpoint = (2, - 2 )
the slope m is calculated using the ' gradient formula '
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 6 ) and (x₂, y₂ ) = (0, 2 )
m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2
calculate midpoint using midpoint formula
{[tex]\frac{1}{2}[/tex] (4 + 0 ), [tex]\frac{1}{2}[/tex] (- 6 + 2 )] = (2, - 2 )
gradient of perpendicular bisector = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
equation in slope-intercept form is
y = mx + c ( m is slope and c the y-intercept )
partial equation is y = [tex]\frac{1}{2}[/tex] x + c
to find c substitute ( 2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 in slope-intercept form
Answer:
-2
(2,-2)
1/2
y=(1/2)x-3
Step-by-step explanation:
It’s correct on edge.
The expression below is the factorization of what trinomial? -1(x - 6)(x + 8) apex question
Final answer:
The trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.
Explanation:
The trinomial factorization you are asking about is -1(x - 6)(x + 8). To find out the trinomial it factors from, you need to multiply the two binomials together and then multiply by -1. Let's do this step by step:
Multiply the binomials using the FOIL method, which stands for First, Outer, Inner, Last. This gives us the following intermediate step: (x - 6)(x + 8) = x(x) + x(8) - 6(x) - 6(8)
Simplify the intermediate step: x² + 8x - 6x - 48
Combine like terms: x² + 2x - 48
Finally, multiply the entire expression by -1 to give the final trinomial: -x² - 2x + 48.
Thus, the trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.
Find the prime factorization of 210
A.) 2 X 3 X 5 X 7
B.) 2 X 3 X 35
C.) 2 X 7 X 15
To prime factorization would be A: 2 X 3 X 5 X 7
Because if your do 2 X 3 it would be 6
Then you do 5 X 7 it would be 35
And 6 X 35 would be 210
AND THAT IS FACTORING THE PROBLEM
[tex]210:2=105\\\\105:5=21\\\\21:3=7\\\\7:7=1\\\\210=2\cdot3\cdot5\cdot7[/tex]
The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use x to represent the number of ride tickets and y to represent the total cost.
Find the cost of admission to the fair. Explain how you found the cost of admission.
Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
Explain what the coefficient of x and the constant of your linear equation represents.
Answer:
Admission to the fair = $ 18
[tex]y = 2.50x +18[/tex].
Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.
Step-by-step explanation:
The total money Henry spent was $ 55.50
If Henry only spent the money on the tickets for the rides and at the entrance to the fair, then we know that:
Bought 15 tickets at 2.5 $
Therefore the price of the admission to the fair is the total expense ($ 55.50) minus the expense in the tickets for the rides ($ 2.50 * 15)
55.50 - 15 * 2.50 = 18
So:
Admission to the fair = $ 18
Ticket for the rides = $ 2.50
So if we call y at the total cost and x the number of tickets for the rides:
[tex]y = 2.50x +18[/tex].
This is a linear equation that represents the total cost.
Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.
To find the cost of admission to the fair, set up a linear equation using the given information: 2.5x + y = 55.50. The coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.
Explanation:To find the cost of admission to the fair, we can set up a linear equation based on the given information. Let's denote the cost of the admission as y and the number of ride tickets as x. We are given that the county fair charges $2.50 per ticket, so the cost of the ride tickets would be 2.5x. Additionally, we know that Henry bought 15 ride tickets and spent a total of $55.50, so we have the equation 2.5x + y = 55.50.
The linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission is 2.5x + y = 55.50.
In this equation, the coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.
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Which integer is closest to 0 on the number line?
A.
–12
B.
–8
C.
10
D.
14
An integer is close to zero if it is "small".
By small, we mean that it is small in absolute value. In fact, for any given distance [tex] d [/tex], there are two integers that are [tex] d [/tex] units away from zero: [tex]d [/tex] and [tex] -d [/tex].
So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.
So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.
A train leaves Roseville heading east at 6:00 am at 40 miles per hour. Another eastbound train leaves on a parallel track at 7:00 am at 50 miles per hour. What times will it be when the two trains are at the same distance away from Roseville?
Answer:
At 11:00 am the both trains will be at same distance away from Roseville
Step-by-step explanation:
The first train was 40 miles away from Roseville at 7:00 am
After some time t the both trains will be at the same distance away from Roseville.
We will make equation for that situation
d- distance v1= 40mph and v2= 50mph - velocity
d = v1*t + 40 = v2*t => v2*t - v1*t = 40 => t (v2-v1) = 40 -> t = 40/ (v2-v1)
t = 40/(50-40) = 40/10= 4h t = 4h
7:00 am * 4h = 11:00 am
Good luck!!!