Answer:
Infinite amount of solutions.
Step-by-step explanation:
Step 1: Write equation
2x - x + 7 = x + 3 + 4
Step 2: Solve for x
Combine like terms: x + 7 = x + 7Subtract 7 on both sides: x = xHere, we see that x is infinite amount of solution. We can plug in any number x and it will render the equation true.
Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or −1. There may be more than one correct answer.
The y-intercept is
(0, 9).
The x-intercepts are
(−3, 0), (3, 0).
Degree is 2.
End behavior: as
x → −[infinity],
f(x) → −[infinity],
as
x → [infinity],
f(x) → −[infinity].
polynomial function is as follows:
we get: f(x) = -3/4x² + 27/4
Given the information about the graph of a polynomial function is as follows:
y-intercept is (0,9)
The x-intercepts are (-3, 0), (3,0)
Degree is 2
End behavior: as x → -∞, f(x) → -∞, as x → ∞, f(x) → -∞The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.
The degree of the function is given to be 2, which means that the leading coefficient is a quadratic polynomial, and it has at least one x-intercept.
The leading coefficient is assumed to be 1 or -1 since it is not given.
Let's determine the quadratic function using the given intercepts:
When x = 0, y = 9. Therefore, the constant term in the quadratic function is c = 9.
The x-intercepts are (-3, 0) and (3, 0).
Thus, (x + 3) and (x - 3) are factors of the quadratic function.
Therefore, the quadratic function is in the form off
(x) = a(x + 3)(x - 3) + 9
We can substitute one of the points to determine the value of the leading coefficient.
Substituting the point (3, 0), we have: 0 = a(3 + 3)(3 - 3) + 9
Simplifying the equation, we get: 0 = 12a + 9a = -3/4
The quadratic function is:
f(x) = -3/4(x + 3)(x - 3) + 9
Multiplying the terms and collecting like terms, we get:
f(x) = -3/4x² + 27/4
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Find an equation for the plane that passes through (1, -1, -1) and is parallel to the plane 5x - y - z = 6 .
The equation of the plane parallel to 5x - y - z = 6 and passing through (1, -1, -1) is 5x - y - z = 7.
The equation of the plane that passes through (1, -1, -1) and is parallel to the plane 5x - y - z = 6 can be written as 5x + y + z = k, where k is a fixed number or constant.
To find the value of k, we substitute the coordinates of the given point (1, -1, -1) into the equation of the plane:
5(1) - (-1) - (-1) = k
5 + 1 + 1 = k
7 = k
Therefore, the equation of the plane parallel to 5x - y - z = 6 and passing through (1, -1, -1) is 5x - y - z = 7.
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What is the range of the function shown in the table?
2 3
4 4
6 5
8 6
A. (2, 3), (4, 4), (6, 5), (8, 6,)
B. {2, 3, 4, 5, 6, 8}
C. {3, 4, 5, 6}
D. {2, 4, 6, 8}
Answer:
C
Step-by-step explanation:
The range of a function is going to be the output of the table. 3, 4, 5, and 6 are all outputs in the table. C is the correct answer.
Hope this helps you.
Have a nice day.
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion. Let BBB represent the number of paintballs that Carolina buys.
This question is incomplete
Complete Question
Carolina goes to a paintball field that charges an entrance fee of $18 and $0.08per ball. The field has a promotion that says, "Get $10 soff if you spend $75more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let B represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
(Choice A)
A
18+0.08B≤75
(Choice B)
B
18+0.08B≥75
(Choice C)
C
18+0.08B≤10
(Choice D)
D
18+0.08B≥10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs
Answer:
a
1) The correct equation is:
Option B) 18+0.08B≥75
2)Carolina needs to buy at least 712 paintballs
Step-by-step explanation:
We are told in the question that:
Carolina goes to a paintball field that charges an entrance fee of $18 and $0.08per ball. The field has a promotion that says, "Get $10 soff if you spend $75more!"
Hence, our inequality equation is:
Let us represent the number of balls as B
$18 +0.08 × B ≥$75
18 +0.08B ≥75
0.08 ≥ 75 - 18
0.08B ≥57
B ≥ 57/0.08
B≥ 712.5
Therefore, Carolina needs to buy at least 712 paintballs.
Answer:
1. b 2. 713
Step-by-step explanation:
b)Suppose that the linear equation for consumption in a hypothetical economy is C = $40 + 0.8Y. Also suppose that income (Y) is $400. Determine (i) the marginal propensity to consume, (ii) the marginal propensity to save, (iii) the level of consumption, (iv) the average propensity to consume and (v) the level of savings. [5 marks]
(i) The marginal propensity to consume (MPC) is 0.8.
(ii) The marginal propensity to save (MPS) is 0.2.
(iii) The level of consumption is $360.
(iv) The average propensity to consume (APC) is 0.9 or 90%.
(v) The level of savings is $40.
The given linear equation for consumption, C = $40 + 0.8Y, and the income (Y) is $400, let's calculate the following:
(i) The marginal propensity to consume (MPC):
The marginal propensity to consume represents the change in consumption resulting from a change in income. It is the coefficient of the income term in the consumption function.
MPC = ∆C / ∆Y = 0.8
(ii) The marginal propensity to save (MPS):
The marginal propensity to save represents the change in savings resulting from a change in income. It is equal to 1 minus the marginal propensity to consume.
MPS = 1 - MPC = 1 - 0.8 = 0.2
(iii) The level of consumption when income (Y) is $400:
Plug the given income value into the consumption function.
C = $40 + 0.8Y = $40 + 0.8 * $400 = $40 + $320 = $360
Therefore, the level of consumption when income is $400 is $360.
(iv) The average propensity to consume (APC):
The average propensity to consume represents the proportion of income that is spent on consumption. It is calculated by dividing consumption by income.
APC = C / Y = $360 / $400 = 0.9
Therefore, the average propensity to consume is 0.9 or 90%.
(v) The level of savings:
Savings (S) is the difference between income (Y) and consumption (C).
S = Y - C = $400 - $360 = $40
Therefore, the level of savings is $40.
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Why do the friends decide to drive to
the radio station?
Answer:
Because they want a better signal or they just want to
Step-by-step explanation:
If there were no units in beginning work in process, 75,000 units completed and transferred, and 10,000 units in the ending work in process that were 50% complete as to materials and conversion costs, what were the equivalent units of production for the period? a. 70,000 b. 75,000 c. 80,000 d. 85,000
The equivalent units of production for the period is 80,000
The equivalent units of production for the period can be calculated by considering the units that were completed and transferred, as well as the units in the ending work in process. In this case, 75,000 units were completed and transferred, and there were 10,000 units in the ending work in process that were 50% complete as to materials and conversion costs.
To determine the equivalent units of production, we need to account for the work done on the units in the ending work in process. Since these units are 50% complete as to both materials and conversion costs, we can treat them as half complete units. Therefore, the equivalent units for the ending work in process would be 10,000 units multiplied by 0.5, which equals 5,000 equivalent units for both materials and conversion costs.
Adding the equivalent units from completed and transferred units (75,000) to the equivalent units from the ending work in process (5,000) gives us a total of 80,000 equivalent units of production for the period.
In summary, the equivalent units of production for the period is 80,000. This includes 75,000 equivalent units from completed and transferred units and 5,000 equivalent units from the ending work in process that were 50% complete as to materials and conversion costs. Therefore, the correct answer is option c. 80,000.
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0.00078 to scientific notation
Answer:
7.8×10^4
Step-by-step explanation:
move the decmial right til you have a number that is greater than one and less than 10.
count how many you put to the right and put ×10^etc
but it would be opposite if you were trying to reverse it
Doug consumes two goods, X and Y. His utility function is given
by
u(X, Y)= X+lnY
The price of X is $1 and the price of Y is $2. He has income of
$150 to spend. What is his optimal amount of Y?
Doug's optimal amount of Y is 75 units found using the utility function.
The optimal amount of Y for Doug is 75 units as per his utility function, u(X, Y) = X + ln Y.
The price of good X is $1 and the price of good Y is $2 and Doug has an income of $150 to spend.
Doug's aim is to maximize his utility subject to his budget constraint.
Let X and Y be the number of units of goods X and Y that Doug purchases respectively.
Then we can write Doug's utility function as:u(X, Y) = X + ln Y
The total amount that Doug spends is:
PₓX + PᵧY = $150
where Pₓ and Pᵧ are the prices of X and Y respectively.
Substituting Pₓ = $1, Pᵧ = $2 and solving for X, we get:
X = $150 - 2Y
Since we want to maximize Doug's utility function, we differentiate it with respect to Y and set it equal to zero, i.e.,
du(X, Y)/dY = 0
Differentiating u(X, Y) = X + ln Y with respect to Y gives:
du(X, Y)/dY = 1/Y
Therefore, at the optimal level of Y, we have:
1/Y = 0
Solving for Y, we get:
Y = 1/0 which is undefined.However, we know that Doug's budget constraint has to hold, i.e.,
PₓX + PᵧY = $150.
Substituting Pₓ = $1 and Pᵧ = $2, we get:
X + 2Y = 150
Substituting X = $150 - 2Y in the above equation and solving for Y gives:
150 - 2Y + 2Y
= 150Y
= 150/2Y
= 75
Therefore, Doug's optimal amount of Y is 75 units.
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how do I solve for X?
Answer:
x = -9
Step-by-step explanation:
The top angle would be 90 degrees due to the square.
The angles of a triangle add up to 180 degrees.
Set up the equation:
90 + 45 + x + 54 = 180
189 + x = 180
Subtract 189 from both sides:
x = -9
Now, if you need to solve for the angle, just plug x in:
-9 + 54 = 45 degrees
(In your case it is just looking for x so it would be x = -9)
Which of the following functions describes the sequence 4, −2, 1, −1 41
The function that describes the sequence 4, −2, 1, −1, ... , 41 is given by:an = 10 - 6n.
The sequence 4, −2, 1, −1, ... , 41 is an arithmetic sequence, which means that the difference between each consecutive term is constant. To find the common difference,
we can subtract any two consecutive terms in the sequence. Let's use the first two terms as an example: −2 − 4 = −6. We can see that the common difference is −6.
Thus, the nth term of the sequence can be expressed as follows:an = a1 + (n - 1)dwhere an represents the nth term of the sequence, a1 represents the first term of the sequence, and d represents the common difference.
Using the values given in the problem, we can plug them into the formula and simplify:an = 4 + (n - 1)(-6)an = 4 - 6n + 6an = 10 - 6n
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Guys i rlly need help im getting an F on this can someone please help me :(
Answer:
THE SLOPE OF THE GRAPH
Step-by-step explanation:
Answer:
the slope of the graph of y = mx+b
Step-by-step explanation
The equation of any straight line can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.
Help.ASAP............
Answer:
Step-by-step explanation:
density = mass/volume
density = 3g/0.5cm^3 = 3x2g/cm^3=6g/cm^3
Answer:
6g/cm^3
Step-by-step explanation:
P = m/v
P = density
m = mass = 3g
v = volume = 0.5cm^3
3/0.5 = 6
Find the area under the standard normal curve for the following using the z-table.
Between z=0 and z=.68
Between z= -0.46 and z=0
Between z= -0.34 and z=0.68
1. The area between z=0 and z=0.68 is: 0.7517 - 0.5000 = 0.2517.
2. The area between z=-0.46 and z=0 is: 0.5000 - 0.3222 = 0.1778.
3. The area between z=-0.34 and z=0.68 is: 0.7517 - 0.3669 = 0.3848.
To find the area under the standard normal curve using the z-table, you need to locate the corresponding z-scores and subtract the areas.
Between z=0 and z=0.68:
From the z-table, the area to the left of z=0 is 0.5000, and the area to the left of z=0.68 is 0.7517.
Therefore, the area between z=0 and z=0.68 is: 0.7517 - 0.5000 = 0.2517.
Between z=-0.46 and z=0:
From the z-table, the area to the left of z=-0.46 is 0.3222, and the area to the left of z=0 is 0.5000.
Therefore, the area between z=-0.46 and z=0 is: 0.5000 - 0.3222 = 0.1778.
Between z=-0.34 and z=0.68:
From the z-table, the area to the left of z=-0.34 is 0.3669, and the area to the left of z=0.68 is 0.7517.
Therefore, the area between z=-0.34 and z=0.68 is: 0.7517 - 0.3669 = 0.3848.
Note: The z-table provides the area to the left of the given z-score. To find the area between two z-scores, you need to subtract the areas corresponding to those z-scores.
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Explanation Page O LINES AND ANGLES Proofs involving segment congruence ? QUESTION Use the given information to prove that EG=HJ. E J Given: EF = FJ FG = HF Prove: EG HJ H F
To prove that EG = HJ, we are given the information that EF = FJ and FG = HF.
To prove the congruence EG = HJ, we can use the transitive property of congruence.
From the given information, we have EF = FJ and FG = HF. By adding these two equations together, we obtain EF + FG = FJ + HF.
Now, using the transitive property, we can substitute EG for EF + FG and HJ for FJ + HF in the equation above. This gives us EG = HJ, which proves the desired congruence.
In summary, by using the given information and applying the transitive property of congruence, we have shown that EG = HJ.
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A line passes through the point (10, 1) and (-8, 5). What is the slope of a line that is parallel to that line?
Calculate the length of segment RS with midpoint M when RM= 2x and MS= x+5.
The length of the line segment RS =120 having midpoint M
Given :
Line segment RS with midpoint M when RM= 2x and MS= x+5.
Midpoint M divides the line equally
So length of RM=MS
Substitute the expressions RM and MS and solve for x
[tex]RM=MS\\2x=x+5\\Subtract \; x \; on \; both \; sides\\x=5[/tex]
Now find out RS using the x value
[tex]RS= RM+MS\\RS=2x+x+5\\RS=3x+5\\RS=3(5)+5\\RS=20[/tex]
The length of the line segment RS =120 having midpoint M
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One car alarm is set to go off every 10 seconds another car long is it to go every five seconds and a good car alarm is set to go off every four seconds if they all start to go off at the same time due to a loud clap of thunder how long will it take to all sound at the same time again
Answer:
20 seconds
Step-by-step explanation:
Given the following :
Alarm 1 (goes off every 10 seconds)
Alarm 2 (goes off every 5 seconds)
Alarm 3 (goes off every 4 seconds)
If they all go off now, how long will it take all to go off at the same time again.
Obtain the multiples of the time in seconds in which each alarm goes off and select the lowest multiple common to all three;
Multiples of 10 : 10, 20, 30, 40, 50,...
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40,...
Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36,....
Hence, the lowest multiple common to all three alarm times is 20.
Hence, all three alarms will go off at the same time again after 20 seconds
Seven baseball players are trying out for a team and the coach wants to see who can throw the baseball the farthest. The distance each player threw the baseball is recorded in the list below.
74 yards, 88 yards, 94 yards, 80 yards, 95 yards, 102 yards, 91 yards.
Part 1:
Determine the median and the mean for 7 throws, to the nearest yard. Show or explain how you got your answers.
The coach allowed two additional players to try out for the team, and each player threw the ball a distance of 91 yards.
Part 2:
What effect will these two additional distances have on the median and mean you calculated? Show or explain your work and justify your answers.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data below :
74 yards, 88 yards, 94 yards, 80 yards, 95 yards, 102 yards, 91 yards.
Rearranging the data in ascending order :
74, 80, 88, 91, 94, 95, 102
The median :
1/2(n+1)th term
n = number observations = 7
1/2(7 + 1)th term
8/2 = 4th term
= 91 yards
Mean:
Σ(74 + 80 + 88 + 91 + 94 + 95 + 102) / n
= 624 / 7
= 89.14
The coach allowed two additional players to try out for the team, and each player threw the ball a distance of 91 yards.
New data :
74, 80, 88, 91, 91, 91, 94, 95, 102
n = 9
The median :
1/2(n+1)th term
n = number observations = 7
1/2(9 + 1)th term
10/2 = 5th term
= 91 yards
Mean:
Σ(74 + 80 + 88 + 91 + 91 + 91 + 94 + 95 + 102) / n
= 806 / 9
= 89.56
solve the equation f/4-5= -9
Answer:
f = -16
Step-by-step explanation:
f/4-5= -9
Add 5 to each side
f/4-5+5= -9+5
f/4 = -4
Multiply each side by 4
f/4 *4 = -4 *4
f = -16
Answer:
f= -16
Step-by-step explanation:
[tex]f/4-5= -9\\\\\frac{f}{4}-5=-9\\\\\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\\\\\frac{f}{4}-5+5=-9+5\\\\Simplify\\\\\frac{f}{4}=-4\\\\\mathrm{Multiply\:both\:sides\:by\:}4\\\frac{4f}{4}=4\left(-4\right)\\\\Simplify\\f=-16[/tex]
1) Which expression is equivalent to 45^-3/45^3
A 45^-1
B 45^0
C 1/45^6
D 45^6
Answer:
C. [tex]\frac{1}{45^{6}}[/tex]
Step-by-step explanation:
Concepts Used:
ExponentsThe rule of Negative exponentsPower of a Product RuleSimplifying the given expression:
We are given the expression:
[tex]\frac{45^{-3}}{45^{3}}[/tex]
According to the rule of negative exponents, 45⁻³ = 1/45³
[tex]\frac{1}{45^{3}}*\frac{1}{45^{3}}[/tex]
[tex]\frac{1}{45^{3}*45^{3}}[/tex]
According to the Power of a Product rule: aⁿ X aᵇ = aⁿ⁺ᵇ
Using the Power rule to further simplify our expression:
[tex]\frac{1}{45^{6}}[/tex]
Hence, Option C is correct
julia spent $50 on a book. the cost of the book was $16 less than twice what she spent on a backpack. how much did the backpack cost?
Mrs. Metcalfe bought 2 bags of cookies for her 3 dogs. Each bag contains 6 cookies. The dogs shared the cookies equally among themselves. How many cookies did each dog get? Write an expression to show the priority of the operations you used.
Answer:
Each dog got 4 cookies.
Tammy has a rectangular poster. The poster is 1.2 meters long and 0.9 meters wide. What is the area of the poster in square centimeters? Do not round your answer. Be sure to include the correct unit in your answer.
Answer:
HOI
Step-by-step explanation:
Question 5( 11 marks) a. Consider the triangle PQR i. Find the length QR to one decimal place R P ھے 6 Q 10 I ii. Find the size of angle QRP to the nearest degree. Mar [2] [2]
In triangle PQR, with PQ = 6, PR = 10, and angle PQR = 90°, we need to find the length of QR rounded to one decimal place which is approximately 11.7 units.
To find the length of QR, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, PQ and PR are the two sides, and QR is the hypotenuse. Given that PQ = 6 and PR = 10, we can calculate the length of QR.
Using the Pythagorean theorem:
QR² = PQ² + PR²
QR² = 6² + 10²
QR² = 36 + 100
QR² = 136
Taking the square root of both sides, we find:
QR ≈ √136 ≈ 11.66
Rounded to one decimal place, the length of QR is approximately 11.7.
Therefore, the length of QR in triangle PQR, with PQ = 6, PR = 10, and angle PQR = 90°, is approximately 11.7 units.
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the complete question is:
Question 5( 11 marks) a. Consider the triangle PQR i. Find the length QR to one decimal place
PQ=6, PR=10, angle PQR=90°
Bob drafts his favorite race car on a scale drawing. The drawing scale is 2 inches for each foot. If the drawing is 30 inches long, how long is the actual race car?
Answer:
15 feet: 30 divided by 2 is 15
Step-by-step explanation:
HURRY!!!
A line goes through points (-3,1) and (-2,4)
(A) what is the slope of the line
(B) write the equation of the line in point slope form
(C) write the equation of the line in slope intercept form
SHOW ALL WORK!! WILL GIVE BRAILEST.
A) m = (y2-y1)/(x2-x1)
m = (4-1)/(-2-(-3))
m = 3/1
m = 3
B) point slope equation : y-y1=m(x-x1)
y - 4 = 3 ( x + 2 )
C) slope intercept equation: y = mx + c
4 = 3(-2) + c
4 = -6 +c
c = 10
Thus, the equation is y= 3x + 10
Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,350 down and $200 each month. At another dealer, she would pay $3,250 down and $175 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be? (Im giving all my points for this some1 please answer 58 points and will give brainliest)
Answer:
36 months$9550Step-by-step explanation:
Let the number of month be x
Expression to show amounts
2350 + 200x = 3250 + 175x200x - 175x = 3250 - 235025x = 900x = 900/25x = 36Amount
2350 + 200*36 = 2350 + 7200 = 9550Time is 36 months
Amount is $9550
I will try solve these ok na neo
A hair dresser is placing an order for a new shampoo. Company A charges $4.00 per
bottle plus $10.00 handling fee per order. Company B charges $3.00 per bottle plus a 25
handling fee per order . How many bottles, x, must the hairdresser buy for Company A to cost more than Company B?*
A the answer is a your welcome
A lion runs 50 mph and a cheetah runs 74 mph. How far does the cheetah run in the time it takes the lion to run 75 miles?
To anyone who needed an explanation- I GOTCHU
Answer:
111 miles
Step-by-step explanation:
First, we need to find out how far the cheetah goes if the lion goes 1 mile.
74/50=1.48
So, if the lion goes 1 mile, the cheetah goes 1.48 miles. If the lion goes 75 miles, we must multiply it by how far the cheetah goes.
75*1.48=111 miles
I hopw this helped! Tell me if you have any questions about this :)
Sighe speed - distance relation, the cheetah will cover a distance of 111 miles in the same time.
Lion :
Speed = 50 mph
Time taken to cover 75 miles
Time taken = Distance / speed
Time taken = 75 / 50 = 1.5 hours
CHEETAH :
Speed = 74 mph
Time taken = 1.5 hours
Distance covered in 1.5 hours
Distance = speed × time
Distance covered = 1.5 × 74 mph = 111 miles
Therefore, the cheetah will cover a distance of 111 miles in the same time.
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