Answer:
[tex]x = \frac{k + c}{4}[/tex]
Step-by-step explanation:
Given:
[tex]4x - c = k[/tex]
Solve for:
[tex]x[/tex]
Solution:
(1) Let's move all of components that do not contain [tex]x[/tex] (our target) to the right side (notice the change of sign of [tex]c[/tex] from negative to positive):
[tex]4x = k + c[/tex]
(2) Let's divide both sides of equation by 4:
[tex]\frac{4x}{4} = \frac{k + c}{4}[/tex]
(3) Now, we simplify the left side:
[tex]x = \frac{k + c}{4}[/tex]
This is the solution.
Hope this helps!
:)
a) Expand and simplify (4x + 3)(2x - 5)
(2)
+
b) Factorise x2 + 5x + 6
(2)
Total marks: 4
Answer:
a. [tex]8x^{2} -14x-15[/tex]
b. [tex](x+3)(x+2)[/tex]
Step-by-step explanation:
A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)
For F, take the first terms of the 2 and multiply
[tex]4x*2x=8x^{2}[/tex]
For O, take the outer terms and multiply
[tex]4x*-5=-20x[/tex]
For I, take the inner terms and multiply
[tex]3*2x=6x[/tex]
For L, take the last terms and multiply
[tex]3*-5=-15[/tex]
After that, add all of them up
[tex]8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15[/tex]
B. Since the equation is in the form x^2+bx+c,
[tex](x+?)(x+?)[/tex]
Now we need to find 2 numbers that will add up to 5 and multiply to 6.
Here are some of the combinations of numbers that multiply to 6
3*2
1*6
-3*-2
-1*-6
3 and 2 add up to 5 so:
[tex](x+3)(x+2)[/tex]
PLEASE HELP ASAP, BRAINLEST
Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5.
Enter your answer into the blank equation box.
Answer:
equation in standard form is -3x + 5y = -26
Step-by-step explanation:
standard form of equation of line is
Ax + By = C
where A,B and C are integers.
such line has slope -A/B
Another form of line equation is slope intercept form, which can be written as
y = mx+ c
since in problem m = 3/5
thus, equation is
y = 3/5 x + c
Given that (2,-4) passes through this line, this point will satisfy the above equation
-4 = 3/5 *2 + c
=> - 4 = 6/5 + c
=> c = -4 -6/5 = (-4*5 - 6)/5
=> c = (-20 - 6)/5 = -26/5
Thus, equation in slope intercept form is
y = 3/5 x -26/5
lets rewrite this equation in Ax + By = C
Multiplying LHS and RHS by 5 we have
5y =( 3/5 x)* 5 - (26/5 * 5)
=> 5y = 3x - 26
we have to bring 3x on LHS for that
we subtract 3x from both side
5y -3x = 3x - 26 -3x
=> 5y -3x = - 26
rearranging the equation
-3x + 5y = -26
Thus, equation in standard form is -3x + 5y = -26
A large cooler contains 15 liters of iced tea and A small cooler contains 5 liters of iced tea how many more milliliters of iced tea does the large cooler contain than the small cooler?
Answer:
10000 ml
Step-by-step explanation:
1 liter =1000 ml
15 -5 = 10
10 * 1000= 10000
PLEASE HELP ME SHOW ME HOW U GOT YOUR ANSWER PLZ AND THANK U
Answer:
2/3
Step-by-step explanation:
There are 6 marbles in the jar
4 are not purple
P(not purple) = marbles that are not purple/ total marbles
= 4/6 = 2/3
Answer:
2/3
Step-by-step explanation:
since there are 6 total marbles and 4 of them are colors other than purple, there is a 4/6 chance of drawing a marble that is not purple which can be simplified to 2/3.
Please help! Correct answer only!
You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 20. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is even, you win $34. If the number the ball lands on is odd, you win nothing. If you play the game, what is the expected payoff?
Answer:
" Expected Payoff " - 17 Dollars ; Type in 17
Step-by-step explanation:
Consider the probability of landing in an odd section;
[tex]Sections of the Wheel - 20 Sections,\\Numbers Numbered On the Wheel - 1 To 20,\\\\Odd Numbers = Even Numbers,\\Odd Numbers = 20 / 2 = 10,\\Even Numbers = Odd Numbers = 10,\\\\Probability of Spinning Even - 10 / 20 = ( Simplified ) 1 / 2,\\Money Won = 34 Dollars,\\\\Proportionality - 1 / 2 = x / 34, Where, x = " Expected Payoff "\\1 / 2 = x / 34,\\2x = 34,\\x = 17 Dollars,\\\\Conclusion ; " Expected Payoff " = 17 Dollars[/tex]
Solution ; Provided Directly Above
What is the slope? will mark brain
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
The slope is 3.
Step-by-step explanation:
The answer is 3( slope ) because
6÷2=3.
Improper fraction = 3/1
Which quadratic equation is equivalent to (x + 2)^2 + 5(x + 2) – 6 = 0? A. (u + 2)^2 + 5(u + 2) – 6 = 0 where u = (x – 2) B. u^2 + 4 + 5u – 6 = 0 where u = (x – 2) C. u^2 + 5u – 6 = 0 where u = (x + 2) D. u^2 + u – 6 = 0 where u = (x + 2) (This is a question from Edg by the way)
Answer:
C. u^2 + 5u – 6 = 0 where u = (x + 2)
Step-by-step explanation:
(x + 2)^2 + 5(x + 2) – 6 = 0
Let u = x+2
(u)^2 + 5(u) – 6 = 0
Answer:
C.u^2+5u-6=0
Step-by-step explanation:
By comparing (x+2)^2+5(x+2)-6=0 to answer C,that is u^2+5u-6=0,u=(x+2).
By sustituting (x+2)into answer C,we get;
(x+2)^2+5(x+2)-6=0 which is the same as the quadriatic equation given in the question.
Line JK passes through points J(-4,-5) and K(-6, 3). If the equation of the line is written in slope-intercept form, y = mx + b,
what is the value of b?
-21
-4
11
27
Mark this and retum
Save and Exit
Nex
Answer:
A
Step-by-step explanation:
If the equation of the line is written in slope-intercept form, y = mx + b then the value of b will be -21; the correct answer is option A.
What is the slope of a straight line?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. That is why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.
Formula for slope, thus, is;
Slope = (y₂ - y₁) / (x₂ - x₁)
Parameters;
J(-4, -5) and K(-6, 3)
= (3 - (-5)) / (-6 - (-4))
= (3 + 5) / (-6 + 4)
= 8 / -2
= -4
Substitute one of the coordinates into the formula to solve for b
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
b = - 21
Read more about Slope of a line here
brainly.com/question/20848
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URGENT!!! A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points) A: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 B: No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 C: Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 D: Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answer:
A: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Step-by-step explanation:
c for child
a for adult
4c+ 6a ≤ 120 for build
4c +4a ≤ 100 for test
We want 20 child and 6 adult
4(20)+ 6*6 ≤ 120
80+36 ≤ 120
116 ≤ 120 true for build
4*20 +4*6 ≤ 100
80+24 ≤ 100
104 ≤ 100
False for test
Answer:
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Step-by-step explanation:
Convert the angle radians to degrees
Answer:
160 degrees
Step-by-step explanation:
To change from radians to degrees, multiply by 180 / pi
8 pi/9 * 180/pi
160 degrees
How long would it take you to reach 100 for the number of times you did your activity from this graph?
PLEASE HELP NOW
ILL GIVE YOU BRAINLIEST
Answer:
33 1/3 minutes
Step-by-step explanation:
I note x- number of sentences
y=time
when x=3, y=1
x=6, y= 2
I observe that for every 3 sentences I have one more minute ( y increases by 1) so y= x/3
when x=99 i have y=99/3=33 minutes
for x= 100 I have y=100/3minutes= 33 1/3 minutes
What is the slope of a line perpendicular to the line whose equation is
12x + 9y = 162.
Fully reduce your answer.
Answer:
3/4
Step-by-step explanation:
HELP!!!! Identify the volume of the composite figure rounded to the nearest tenth.
Answer:
4618.1 ft³
Step-by-step explanation:
Volume of the cone:
[tex]V_{cone} = \frac13 \pi r^2 h[/tex]
[tex]V_{cone} = \frac13 \cdot \pi \cdot 49 \cdot 12 = 196\pi[/tex]
Volume of the cilinder:
[tex]V_{cilinder} = \pi r^2 h[/tex]
[tex]V_{cilinder} = \pi \cdot 49 \cdot 22 = 1078\pi[/tex]
Total volume is 2*Vcone + Vcilinder = 1470π ≈ 4618.1 ft³
Dada la función cuadrática () = + + . Determinar: a. Si la gráfica se abre hacia arriba o hacia abajo b. Las coordenadas del vértice c. El punto de corte con el eje de las y d. Los puntos de corte con el eje de las x e. El eje de simetría
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remaining eggs were white in color. Which equation can be used to solve for w, the number of white eggs used last week?
46+w=231
w=185
# brown eggs (46) + # white eggs (w) = total # of eggs (231)
Answer:
231 - 46 = 185
Step-by-step explanation:
We know that the restaurant used 231 eggs last week. (That's a lot!)
That is out starting point. It doesn't change.
Then, it says 46 are brown eggs.
To find the number of white eggs, we know it must equal to 231 when added to the 46 brown eggs. Or, 46 + ? = 231.
So, we do the opposite operation of addition; subtraction.
Like this:
231 eggs - 46 brown = ? white eggs.
That equals 185 white eggs.
Keep up the EGGcellent work! ;)
-Bella,
BrainlyBluebell
1/3 of 6 1/2 multiply 3/4 (56 divide by 7) pls help me
Answer:
13
Step-by-step explanation:
1/3 of 6 1/2 multiply by 3/4 (56 divided by 7)
1/3* 13/2 * 3/4 * 56/7= 1*13*3*56/3*2*4*7= 13*3*56/3*56= 13
What is the value of the expression below?
7-2-4.5x3-8
Answer:
6.5
Step-by-step explanation:
7-2=5-4.5=0.5
0.5ₓ3=1.5
8-1.5=6.5
How much is one gram into ounces?
Answer:
1 gram is 0.035274 in ounces
Answer:
It would be about 0.035274
Step-by-step explanation:
For an approximate result, divide the mass value by 28.35
Hope this helps
1. X-3.3< 16.2 *
O x<19.5
O x> 19.5
O x< 12.9
O
X > 12.9
Answer:
x <19.5
Step-by-step explanation:
X-3.3< 16.2
Add 3.3 to each side
X-3.3+3.3< 16.2+3.3
x <19.5
There are three types of tickets to enter the amusement park of a particular city. The normal ticket costs R $ 52.00, the child ticket costs R $ 20.00 and the elderly ticket costs R $ 28.00. A group of friends went to the park and paid in total R $ 480.00. In this group, each adult (normal or senior) took two children. How many normal tickets purchased?
Answer:
3 normal tickets were sold, 3 tickets were sold for the elderly, and 12 tickets were sold for children
Step-by-step explanation:
Let x = normal ticket number
Let y = child ticket number
Let z = elderly ticket number
The total amount spent is 480, so we can create this equation:
52 * x + 20 * y + 28 * z = 480
They also tell us that each adult took two children, so:
y = 2 * (x + z)
We have two equations and three unknowns, therefore we must simplify and do trial and error. First, let's substitute "y" in terms of "x" and "z" in the first equation, then simplify:
52 * x + 20 * y + 28 * z = 480
52 * x + 20 * 2 * (x + z) + 28 * z = 480
52 * x + 40 * (x + z) + 28 * z = 480
52 * x + 40 * x + 40 * z + 28 * z = 480
92 * x + 68 * z = 480
23 * x + 17 * z = 120
Let's solve for x in terms of e:
23 * x = 120-17 * z
x = (120-17 * z) / 23
We know that (120 - 17 * z) has to be a multiple of 23 for "x" to be an integer. So let's look at testing some values of "z" to make valid values for "x":
120-17 (0) = 120 (not multiple of 23)
120-17 (1) = 103 (not multiple of 23)
120-17 (2) = 86 (not multiple of 23)
120-17 (3) = 69 (multiple of 23)
120-17 (4) = 52 (not multiple of 23)
120-17 (5) = 35 (not multiple of 23)
120-17 (6) = 18 (not multiple of 23)
120-17 (7) = 1 (not multiple of 23)
After that, we get negative values for "x", so here there is only one possible value for "x", so we know that z = 3:
Now we can solve for "x" and "y":
x = (120-17 * 3) / 23
x = (120-51) / 23
x = 69/23
x = 3
Now for and:
y = 2 * (x + y)
y = 2 (3 + 3)
y = 12
Therefore, 3 normal tickets were sold, 3 tickets were sold for the elderly, and 12 tickets were sold for children.
The bar graph shows the results of rolling a number cube (die) 50times. What is the experimental probability of rolling each of the number on the number cube?
Column A Column B
1. a. 18%
2. b. 8%
3. c. 22%
4. d. 16%
5. e. 20%
6.
c. 22%
Step-by-step explanation:
sorry for no explanation
Solve 3x - 3 =27 - 2x pls answer
Answer:
[tex]\fbox{\begin{minipage}{3em}x = 6\end{minipage}}[/tex]
Step-by-step explanation:
Given:
Equation: [tex]3x - 3 = 27 - 2x[/tex]
Solve for:
[tex]x[/tex]
Solution:
Step 1: Select relevant approach:
Let's move all the components containing x to the left side and other components to the right side (notice the change of sign of each one from + to - or - to +), then calculate [tex]x[/tex]
Step 2: Perform the calculation:
[tex]3x -3 = 27 - 2x[/tex]
Moving components:
<=> [tex]3x + 2x = 27 + 3[/tex]
Adding up components:
<=> [tex]5x = 30[/tex]
Dividing both sides by 5 (coefficient of component containing [tex]x[/tex]:
<=> [tex]\frac{5}{5} x = \frac{30}{5}[/tex]
Simplifying to work out [tex]x[/tex]:
<=>[tex]x = 6[/tex]
Hope this helps!
:)
Answer:
x = 6
Step-by-step explanation:
3x - 3= 27 - 2x
First we put all the x terms to on side, making it 3x + 2x - 3= 27.
Remeber that when we move a term to the other side of the equals sign (=), we change its sign to be the opposite of what it currently is.
Then, we move all the numberics to the other side, so we derieve 3x + 2x = 27 +3. Again, the sign changes when we move it across.
What is left to do is add up the quantities. So 3x + 2x = 5x and 27 +3 = 30.
We are left with 5x = 30. If 5 x's is 30, how much is one? Sinply divide it to get the answer of 30 / 5 which is six!
To make sure the answer is correct substituite 6 in the equation as x and see if its accurate: 3(6) -3 = 7 - 2 (6). And it is!
So x is equal to six.
If the slope if the line a is -4 and line a is perpendicular to line b. Which statement must be true?
Answer:1/4
Step-by-step explanation:
The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.
HELP PLS I WILL MARK BRAINLIEST!!!!!!!!!!!!
a
because it has the highest values from all the options from all the above
Help please will give brainliest!
Answer:
C
Step-by-step explanation:
x4(x4-5)+5(x4-5)
=x8-5x4+5x4-25
x8-25
please help i put a picture on top
Answer:
1/8÷7
Step-by-step explanation:
I think
If you're reproducing a 4 cm x 4 cm picture on a 3 m x 3 m wall, what ratio should you use?
Answer:
So you can divide by 2 for the picture. 4/2 = 2
So you can get 2 x 2 picture. The ratio would be 1
if you have a variable it would always be
x by x.
If you want to cover whole wall multiply by 4/3 on the 4 x 4 picture
The original needs to be scaled up by a factor of 75.
Given that, reproducing a 4 cm × 4 cm picture on a 3 m × 3 m wall.
We need to find what ratio we should use.
What is the ratio?Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.
We know that 1 m=100cm, then 3 m=300 cm.
The picture on the wall is (300 cm)/(4 cm) = 75 times as large in each dimension as the original.
Therefore, the original needs to be scaled up by a factor of 75.
To learn more about the ratio visit:
https://brainly.com/question/13419413.
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Enter the equation for the graph.
Answer:
y = cos x
Step-by-step explanation:
The graph begins at (0, 1) and completes its first period at (2π, 1) Thus the period of this function is 2π. The amplitude is 1; this is the value that y takes on when x = 0.
Thus the equation of this graph is y = 1cos x, or y = cos x.
Carmen is dividing her rectangular garden with a diagonal fence. The length of the garden is 11 feet and the diagonal is 19 feet. Write an equation that can be used to find the width of the garden. Then find the width of the garden. Round to the nearest tenth, if needed.
Answer:
Equation: 19^2 - 11^2 = width
Step-by-step explanation:
use Pythagorean theorem to find the width.
so, 19^2 - 11^2 = 361-121= 240.
so width = square root of 240
Answer:
19^2 - 11^2 = width
Step-by-step explanation:
I need help finding the surface area, can someone help
Answer:
1). Surface area of the prism = 112 cm²
2). Area of the sphere = 615.8 cm²
Step-by-step explanation:
1). Surface area of the triangular prism = Area of the triangular bases + Area of three lateral (rectangular) sides
Area of a triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(3)(7)[/tex]
= 10.5 cm²
Area of a rectangle = Length × width
Area of the rectangular lateral sides = (3 × 5) + (8 × 5) + (7 × 5)
= 15 + 40 + 35
= 90 cm²
Surface area of the prism = (2 × 10.5) + 90
= 21 + 90
= 112 cm²
2). Surface area of the sphere = 4πr²
= 4π(7)²
= 615.75
≈ 615.8 cm²
