Answer:
2.35 x 10^11
Step-by-step explanation:
The formula for finding the nth term in a geometric sequence is ar^n-1.
a = 3, r = 23, and n = 9:
3(23)^9-1 = 3(23)^8 = 2.35 x 10^11.
Please Help. Will Mark Brainliest Answer. A container of juice is taken from the refrigerator and poured into a pitcher. The temperature of the juice will warm to room temperature over time. The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator. Use the drop-down menus to complete the explanation of how the function models the juice warming over time. Dropdown possible answers: When t = 0, the temperature of the juice is -0.06, 0, 2.718, 32, 40, 72 degrees. As time increases, -32(2.718)^-0.06t gets close and closer to -0.06, 0, 2.718, 32, 40, 72. So, f(t) gets close and closer to -0.06, 0, 2.718, 32, 40, 72.
Answer:
When t= 0
f(t)= 40 degrees
The value of −32(2.718)^−0.06t approach 0 as t increases
If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72
Step-by-step explanation:
The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator.
f(t)=72−32(2.718)^−0.06t
When t= 0
f(t)=72−32(2.718)^−0.06(0)
f(t)=72−32(2.718)^(0)
f(t)=72−32(1)
f(t)=72−32
f(t)= 40 degrees
As t increases −32(2.718)^−0.06t
Let t= 1
=−32(2.718)^−0.06(1)
= −32(2.718)^−0.06
= -30.14
Let t = 2
=−32(2.718)^−0.06(2)
=−32(2.718)^−0.12
=−32(0.8869)
= -28.38
The value of −32(2.718)^−0.06t approach 0 as t increases
If −32(2.718)^−0.06t approach 0 as t increases then f(t)=72−32(2.718)−0.06t approach 72
When t = 0, the temperature of the juice is 40°.
As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.
So, f(t) gets close to 72°
Function representing the temperature of of the juice at any time 't' is,
[tex]f(t)=72-32(2.718)^{-0.06t}[/tex]
1). If t = 0,
[tex]f(0)=72-32(2.718)^{-0.06\times 0}[/tex]
[tex]=72-32(1)[/tex]
[tex]=40[/tex] degrees
2). If [tex]t\rightarrow \infty[/tex],
[tex]-\frac{1}{32(2.718)^{0.06t}} \rightarrow 0[/tex]
[As denominator of the fraction becomes larger and larger with the increase in the value of t, value of fraction gets smaller and smaller]
3). if [tex]t\rightarrow \infty[/tex], [tex]f(t)\rightarrow 72[/tex]
Therefore, when t = 0, the temperature of the juice is 40°.
As time increases, [tex]-32(2.718)^{-0.06\times 0}[/tex] gets closer and closer to 0.
So, f(t) gets close to 72°.
Learn more,
https://brainly.com/question/10283950
Can someone help me with this please it’s algebra 2
Answer:
7 8 9
Step-by-step explanation:
Let P be a non zero polynomial such that P(1+x)=P(1−x) for all real x, and P(1)=0. Let m be the largest integer such that (x−1) m divides P(x) for all such P(x). Then m equals
Answer:
m = 0, P(3)/2, P(4)/6, P(5)/12 ..........
Step-by-step explanation:
For non zero polynomial, that is all real x as follows:
x = 1, 2, 3, 4 ............
Using, P(1 + x) = P(1 - x)
For x = 1: P(2) = P(0) = 1
For x = 2: P(3) = P(-1) = 2
Hence, P(x)/m(x - 1) can be solved as follows:
When = 1
P(2)/0 = 1
∴ m = 0
When x = 2
P(3)/m = 2
∴ m = P(3)/2
When x = 3
P(4)/2m = 3
∴ m = P(4)/6
When x = 4
P(5)/3m = 4
∴ m = P(5)/12
Hence, m = 0, P(3)/2, P(4)/6, P(5)/12......
determine the image of the point p[-3,10) under the translation [5,-7]
[tex](-3+5,10-7)=(2,3)[/tex]
5x+4(-x-2) = -5x + 2(x-1)+12 solve for x
Hello!
Answer:
[tex]\huge\boxed{x = 4.5}[/tex]
Starting with:
5x + 4(-x - 2) = -5x + 2(x - 1) + 12
Distribute terms outside of the parenthesis:
5x + 4(-x) + 4(-2) = -5x + 2(x) + 2(-1) + 12
5x - 4x - 8 = -5x + 2x - 2 + 12
Combine like terms:
x - 8 = -3x + 10
Isolate for the "x" variable by adding 3x for both sides:
4x - 8 = 10
Add 8 to both sides:
4x = 18
Divide both sides by 4:
x = 18/4
x = 4.5
Hope this helped! :)
Answer:
[tex] \boxed{x = 4.5}[/tex]
Step-by-step explanation:
[tex] \mathrm{5x + 4( - x - 2) = - 5x + 2(x - 1) + 12}[/tex]
Distribute 4 through the parentheses
Similarly, Distribute 2 through the parentheses
[tex] \mathsf{ 5x - 4x - 8 = - 5x + 2x - 2 + 12}[/tex]
Collect like terms
[tex] \mathsf{ x - 8 = - 3x - 2 + 12}[/tex]
Calculate the sum
[tex] \mathsf{x - 8 = - 3x + 10}[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] \mathsf{ x + 3x = 10 + 8}[/tex]
Collect like terms
[tex] \mathsf{4x = 10 + 8}[/tex]
Calculate the sum
[tex] \mathsf{4x = 18}[/tex]
Divide both sides of the equation by 4
[tex] \mathsf{ \frac{4x}{4} = \frac{18}{4}} [/tex]
Calculate
[tex] \mathsf{x = 4.5}[/tex]
Hope I helped!
Best regards!
Please answer this question now in two minutes
Answer:
m∠C = 102°
Step-by-step explanation:
This diagram is a Quadrilateral inscribed in a circle
The first step is to determine what m∠B
is
The sum of opposite angles in an inscribed quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
Second step is we proceed to determine the exterior angles of the circle
m∠ADC = 2 × m∠B
m∠ADC = 2 × 100°
m∠ADC = 200°
m∠ADC = m∠CD + m∠AD
m∠AD = m∠ADC - m∠CD
m∠AD = 200° - 116°
m∠AD = 84°
The third step is to determine m∠BAD
m∠BAD = m∠AD + m∠AB
m∠BAD = 84° + 120°
m∠BAD = 204°
The final step Is to determine what m∠C is
It is important to note that:
m∠BAD is Opposite m∠C
Hence
m∠C = 1/2 × m∠BAD
m∠C = 1/2 × 204
m∠C = 102°
If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA
Answer:
Step-by-step explanation:
Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA
Starting with the expression
4sinB= 3sin(2A+B)
Let us re write angle B = (A + B) - A
and 2A + B = (A + B) + A
Substituting the derived expression back into the original expression ww will have;
4Sin{(A + B) - A } = 3Sin{(A + B)+ A}
From trigonometry identity;
Sin(D+E) = SinDcosE + CosDSinE
Sin(D-E) = SinDcosE - CosDSinE
Applying this in the expression above;
4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}
Open the bracket
4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA
Collecting like terms
4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA
Sin(A+B)CosA = 7Cos(A+B)sinA
Divide both sides by sinA
Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA
Since cosA/sinA = cotA, the expression becomes;
Sin(A+B)cotA = 7Cos(A+B)
Finally, divide both sides of the resulting equation by sin(A+B)
Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)
CotA = 7cot(A+B) Proved!
I need help factoring this question, Factor 4(20) + 84.
Answer:
164
Step-by-step explanation:
B for brackets
O for of
D for division
M for multiplication
A for addition
S for subtraction
You first start with the brackets (20) and multiply with 4 which is equal to 80 and then add it to 84 which makes 164
I hope this helps
70000000000x50000000000000
Answer:
Step-by-step explanation: Multiply
70000000000*50000000000000=3.5e+24
This rectangular wall is to be painted. Paint is sold in tins. How much does it cost to paint the wall?
Answer:
£23.96
Step-by-step explanation:
Area to be painted:
3.6 m * 8.3 m = 29.88 m^2
The area to be painted is 29.88 m^2.
A tin of paint covers 8 m^2. We divide to find the number of tins needed.
29.88/8 = 3.735
Since full tins must be bought, the smallest number of tins needed is 4.
Now we find the price of 4 tins. 1 tin costs £5.99, so 4 tins cost:
4 * £5.99 = £23.96
Solve the equation 7b-27=8(6+4b)
Answer:
b = -3
Step-by-step explanation:
7b-27=8(6+4b)
Distribute
7b -27 = 48 + 32b
Subtract 7b from each side
7b-7b-27=48+32b-7b
-27 = 48+25b
Subtract 48 from each side
-27-48 = 48+25b -47
-75 = 25b
Divide each side by 25
-75/-25 =25b/25
-3 =b
Answer: b= -3
Step-by-step explanation:
[tex]7b-27=8\left(6+4b\right)[/tex]
distribute
[tex]7b-27=48+32b[/tex]
add 27 to both sides
[tex]7b-27+27=48+32b+27[/tex]
[tex]7b=32b+75[/tex]
subtract 32b on both sides
[tex]7b-32b=32b+75-32b[/tex]
divide -25 on both sides
[tex]-25b=75[/tex]
[tex]b=-3[/tex]
. Over the next two days, Clinton Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of 2. On the second day, the agency will interview clients in groups of 4. If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day?
Answer:
4
Step-by-step explanation:
Given that :
Clients are interviewed in groups of 2 on the first day; meaning two persons at a time
Second day, clients are interviewed in groups of 4; meaning 4 persons at a time.
Therefore, if the same number of clients are to be interviewed on each day, the smallest number of clients that could be interviewed each day could be obtained by getting the Least Common Multiple of both numbers: 2 and 4
- - - - 2 - - - 4
2 - - - 1 - - - 2
2 - - - 1 - - - 1
Therefore, the Least common multiple is (2 * 2) = 4
Therefore, the smallest number of clients that could be interviewed each day is 4.
The height of a building model is 2% of its actual height. If the building
model is 3 feet tall, how tall is the actual building?
Answer:
x = 150 feets
Step-by-step explanation:
Given that,
The height of a building model is 2% of its actual height.
The building model is 3 feet tall, h = 3 feet
We need to find the height of the actual building. Let it is x.
According to question,
h = 2% of x
We have, h = 3 feet
So,
[tex]x=\dfrac{h}{2\%}\\\\x=\dfrac{3}{2/100}\\\\x=150\ \text{feet}[/tex]
So, the actual height of the building is 150 feets.
Help me with this please :)
Answer:
Hey there!
X+Y=0.
For example, two numbers that are equally far from the 0 on a number line are -2 and 2.
-2+2=0
Hope this helps :)
Answer:
x + y = 0
Step-by-step explanation:
Since the two values are the same distance from zero on the number line (i.e., they are equivalent in distance) and one is in the negative direction, and the other is in the positive direction, then the sum of both will be zero.
Since they are the same distance, just opposite in direction, it requires the same amount of "hops" for both values to reach zero, hence they will cancel each other out when added together.
Consider, -1 and 1. Both are the same distance from 0; however, if you add them together (-1 + 1) you'll get the sum to be 0.
Cheers.
solve this equation -2x+9=-5x-15
Answer:
x = -8
I hope this helps!
The graph of f(x) = StartRoot x EndRoot is reflected over the y-axis. Use the graphing calculator to graph this reflection. Which list contains three points that lie on the graph of the reflection? (–81, 9), (–36, 6), (–1, 1) (1, –1), (16, –4), (36, –6) (–49, 7), (–18, 9), (–1, 1) (1, –1), (4, –16), (5, –25)
Answer:
(–81, 9), (–36, 6), (–1, 1) are the correct three points.
Step-by-step explanation:
Given the function:
[tex]f(x) =\sqrt x[/tex]
Please refer to the attached image.
The green line shows the graph of actual function.
It is reflected over y axis.
The reflected graph is shown in black color in attached image.
When reflected over y axis, the sign of variable [tex]x[/tex] changes from Positive to Negative.
So, the resultant function becomes:
[tex]f(x)=\sqrt{-x}[/tex]
i.e. we will have to give the values of x as negative now.
so, the options in which value of x is negative are the possible answers only.
The possible answers are:
(–81, 9), (–36, 6), (–1, 1) and
(–49, 7), (–18, 9), (–1, 1)
Now, we will check the square root function condition.
In the 2nd option, (–18, 9) does not satisfy the condition.
So, the correct answer is:
(–81, 9), (–36, 6), (–1, 1)
Answer:
A on E2020
Step-by-step explanation:
:)
A bag of chocolates weighs 70 grams. If the weight of the bag increases by 25% find the new weight of the bag.
A ship drops its anchor into the water and creates a circular ripple. The radius of the ripple increases at
a rate of 50 cm/s. If the origin is used as the location where the anchor was dropped into the water.
Find the equation for the circle 12 seconds after the anchor is dropped
Please write all the steps it’s for my summer school test and I need it done quick as possible thanks.
Answer:
The equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000
Step-by-step explanation:
To find the equation for the circle 12 seconds when the radius of the ripple increases at a rate of 50 cm/s, the circle radius will be;
50 * 12 = 600 cm
Then place the equation inform of Pythagoras equation which is;
x^2 + y^2 = r^2
Where r is the radius
x^2 + y^2 = 600^2
x^2 + y^2 = 360,000
Then, the equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000
You double the radius of a circle. Predict what will happen tothe circle’s circumference and what will happen to its area. Test yourprediction for a few circles. Use a different radius for each circle. Thenpredict how doubling a circle’s diameter will affect its circumferenceand area. Test your prediction for a few circles with different diameters.
Answer:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
Step-by-step explanation:
Given that
Radius of a circle is doubled.
Diameter of circle is doubled.
To study:
The effect on circumference and area on doubling the radius and diameter.
Solution/explanation:
Let us discuss about the formula for circumference and area.
Formula for Circumference of a circle in form of radius:
[tex]C =2\pi r[/tex]
It is a linear equation in 'r'. So by doubling the radius will double the circumference.
Formula for Area of a circle in form of radius:
[tex]A =\pi r^2[/tex]
It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.
Testing using example:
Let the initial radius of a circle = 7 cm
Initial circumference = [tex]2 \times \frac{22}{7} \times 7 = 44 cm[/tex]
Initial area = [tex]\frac{22}{7} \times 7 \times 7 =154 cm^2[/tex]
After doubling:
Radius = 14 cm
circumference = [tex]2 \times \frac{22}{7} \times 14 = 88 cm[/tex] (Twice the initial circumference)
area = [tex]\frac{22}{7} \times 14 \times 14 =616 cm^2[/tex] (4 times the initial area)
------------------------------------
Formula for Circumference of a circle in form of Diameter:
[tex]C =\pi D[/tex]
It is a linear equation in 'D'. So by doubling the diameter will double the circumference.
Formula for Area of a circle in form of diameter:
[tex]A =\dfrac{1}{4}\pi D^2[/tex]
It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.
Testing using example:
Let the initial diameter of a circle = 28 cm
Initial circumference = [tex]\frac{22}{7} \times 28 = 88 cm[/tex]
Initial area = [tex]\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2[/tex]
After doubling:
Diameter = 56 cm
circumference = [tex]\frac{22}{7} \times 56= 176 cm[/tex] (Twice the initial circumference)
area = [tex]\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2[/tex] (4 times the initial area)
So, the answer is justified:
When radius is doubled:
Circumference becomes double.
Area becomes four times.
When diameter is doubled:
Circumference becomes double.
Area becomes four times.
Help.. ~Probability
7. Find the probability of choosing a red counter if a counter is chosen from a box that contains the following counters.
A. 3 red and 3 yellow
B. 3 red and 5 yellow
C. 1 red, 1 yellow and 2 blue
D. 5 red, 12 green and 7 orange
E. 10 red only
F. 6 blue and 4 green
A.
[tex]|\Omega|=6\\|A|=3\\\\P(A)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]
B.
[tex]|\Omega|=8\\|A|=3\\\\P(A)=\dfrac{3}{8}[/tex]
C.
[tex]|\Omega|=4\\|A|=1\\\\P(A)=\dfrac{1}{4}[/tex]
D.
[tex]|\Omega|=24\\|A|=5\\\\P(A)=\dfrac{5}{24}[/tex]
E.
[tex]|\Omega|=10\\|A|=10\\\\P(A)=\dfrac{10}{10}=1[/tex]
F.
[tex]|\Omega|=10\\|A|=0\\\\P(A)=\dfrac{0}{10}=0[/tex]
A combination lock uses three numbers between 1 and 46 with repetition, and they must be selected in the correct sequence. Is the name of "combination lock" appropriate? Why or why not? Choose the correct answer below. A. No, because the multiplication counting rule would be used to determine the total number of combinations. B. Yes, because the combinations rule would be used to determine the total number of combinations. C. No, because factorials would be used to determine the total number of combinations. D. No, because the permutations rule would be used to determine the total number of combinations.
The correct answer is D. No because the permutations rule would be used to determine the total number of combinations.
Explanation:
The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.
A holiday company charters an aircraft to fly to Malta at
a cost of $22 000. It then sells 150 seats at $185 each and a
futher 35 seats at a 20% discount. Calculate the profit made
per seat if the plane has 200 seats.
Answer:
$54.65 profit per seat
Step-by-step explanation:
150(185) + 35(185)(.8) = 27,750 + 5,180 = 32,930 - 22,000 = 10,930
10,930/200 = $54.65 profit per seat
Answer:
$54.65
Step-by-step explanation:
First, we find the total amount made. This is easy:
(150 x 185) + (35 x .8(185)) =
27750 + 5180 =
32930
We then subtract the $22000, so the company makes a profit of 10930. There are 200 seats, so the profit made per seat is $54.65
True or false? If false give counterexample The product of a rational number and an integer is not an integer
Answer:
False
Step-by-step explanation:
Required
State if the product of rational numbers and integer is an integer
The statement is false and the proof is as follows
Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;
Take for instance: 0.2, 0.5, 2.25, etc.
When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;
1. It can result to an integer:
For instance;
[tex]0.2 * 5 = 1[/tex]
[tex]0.5 * 4 = 2[/tex]
[tex]2.25 * 8 = 18[/tex]
2. It can result in a decimal number
For instance;
[tex]0.2 * 3 = 0.6[/tex]
[tex]0.5 * 5 = 2.5[/tex]
[tex]2.25 * 7 = 15.75[/tex]
From (1) above, we understand that the product can result in an integer.
Hence, the statement is false
Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet. A triangle is created from point Bird Watcher, point First Bird, and point Second Bird. Angle First Bird is a right angle, and angle Second Bird measures x degrees. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth. 35.4° 44.7° 45.3° 54.6°
Answer:
Step-by-step explanation:
When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:
[tex]sin(x)=\frac{32}{45}[/tex] and
sin(x) = .711111111
Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:
[tex]sin^{-1}([/tex]
and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.
Angle of depression = 90 - angle x and
Angle of depression = 90 - 45.325 so
Angle of depression = 44.67 or 44.7 degrees.
Answer:
Its 45.3!!!
Step-by-step explanation:
Someone pleaseeee help me!!!! I’m stuck
Answer:
Hey there!
1/2 can also be written as 8/16.
Thus, starting from 0, count 8 tick marks, and place a point there.
3/16 is just 3/16.
Thus, starting from the 8th tick mark (where you left off in the first part) count three more tick marks to the 11th tick mark.
This shows us that 8/16+3/16=11/16.
Hope this helps :)
Answer:
so 1/2+3/16 is 11/16
Step-by-step explanation:
count the lines until u get to 11 and thts where u put the point.
hope this helps.have a good day
Graph the image of H(-8,5) after a reflection over the x-axis.
Answer ?
Answer: plot a point at (-8, -5)
The y coordinate flips from positive to negative, or vice versa, when we reflect over the horizontal x axis. The x coordinate stays the same.
The rule can be written as [tex](x,y) \to (x,-y)[/tex]
A zoo train ride costs $4 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who took the ride was 27, and the total money collected was $60. What was the number of children and the number of adults who took the train ride that day, and which pair of equations can be solved to find the numbers? 1) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 2) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a + c = 60 3) 11 children and 16 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60 4) 16 children and 11 adults Equation 1: a + c = 27 Equation 2: 4a − c = 60
Answer:
11 adults and 16 children
Step-by-step explanation:
a + c = 27 and 4a + c = 60
3a = 60 - 27 = 33
a= 11
so c = 16
Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-2, 4, 2)
Where x = -2, y = 4, and z = 2.
Step-by-step explanation:
We are given the system of three equations:
[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]
And we want to find the value of each variable.
Note that both the second and third equations have an x.
Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.
Solve the second equation for z:
[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]
Likewise, solve the third equation for y:
[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]
Substitute the above equations into the first:
[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]
Hence, x = -2.
Find z and y using their respective equations:
Second equation:
[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]
Third equation:
[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]
In conclusion, the solution is (-2, 4, -2)
Answer:
x = -2
y =4
z=-2
Step-by-step explanation:
4x−y−2z=−8
−2x+4z=−4
x+2y=6
Solve the second equation for x
x = 6 -2y
Substitute into the first two equations
4x−y−2z=−8
4(6-2y) -y -2 = 8
24 -8y-y -2z = 8
-9y -2z = -32
−2(6-2y)+4z=−4
-12 +4y +4z = -4
4y+4z = 8
Divide by 4
y+z = 2
z =2-y
Substitute this into -9y -2z = -32
-9y -2(2-y) = -32
-9y -4 +2y = -32
-7y -4 = -32
-7y =-28
y =4
Now find z
z = 2-y
z = 2-4
z = -2
Now find x
x = 6 -2y
x = 6 -2(4)
x =6-8
x = -2
solve for k k + (2 - 5k)(6) = k + 12
Answer:
k=0
Step-by-step explanation:
[tex]k+(2-5k)(6)=k+12\\k-30k+12=k+12\\12-12=29k+k\\0=30k\\k=0[/tex]
Answer:
k=0
Step-by-step explanation:
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 4x+4\leq9x+84x+4≤9x+8
Answer:
x ≥ -4/5
Step-by-step explanation:
Maybe you want to solve ...
4x+4 ≤ 9x +8
0 ≤ 5x +4 . . . . . subtract 4x+4
0 ≤ x +4/5 . . . . . divide by 5
-4/5 ≤ x . . . . . . . subtract 4/5
Answer:
x ≥−4/5
Step-by-step explanation:
