Select the correct inequality for the graph below: A solid line passing through points (1, 2) and (2, 5) has shading below. y < 3x − 1 y ≤ 3x − 1 y ≥ 3x − 1 y > 3x − 1
Answers
Here is your answer:
Solving the equation:
[tex] (5-2)\div(2-1)= 3 [/tex][tex] \frac{y - y1}{(x - x1) } [/tex][tex] y-5=3(x-2) [/tex][tex] y= 3x- 6+ 5 [/tex]" [tex] y= 3x-1 [/tex] " or option B.Hope this helps!
Step 1
Find the equation of the line that passes through points [tex](1, 2)[/tex] and [tex](2, 5)[/tex]
Find the slope of the line
The formula to calculate the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{5-2}{2-1}[/tex]
[tex]m=\frac{3}{1}[/tex]
[tex]m=3[/tex]
Find the equation of the line
The equation of the line into slope-point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3[/tex]
[tex](1, 2)[/tex]
substitutes
[tex]y-2=3(x-1)[/tex]
[tex]y=3x-3+2[/tex]
[tex]y=3x-1[/tex]
Step 2
Find the equation of the inequality
we know that
The solution is the shaded area below the solid line
therefore
the inequality is
[tex]y\leq 3x-1[/tex]
the answer is
[tex]y\leq 3x-1[/tex]
see the attached figure to better understand the problem
Related Questions
Rewrite the expression x^2-12x as a(x-h)^2+k
Answers
EASY 5 POINTS!!!! A new park in the shape of a hexagon will have 66 sides of equal length. On a scale drawing, the coordinates of the vertices of the park are: (6.5,5)6.5,5, (18.5,0)18.5,0, (6.5,-5)6.5,-5,
(-6.5,-5)-6.5,-5, (-18.5,0)-18.5,0, and (-6.5,5)-6.5,5. How long is each side of the park?
Answers
To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.
The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.
The distance formula given two points is:
d^2 = (x2 – x1)^2 + (y^2 – y^1)^2
Now we calculate the distance between 2 points:
d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2
d^2 = 169
d = 13
Therefore the length of each side of the park is 13 units.
Answer:
13 units
To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.
Explanation:To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:
Take the coordinates of two adjacent vertices of the hexagon.Use the distance formula, which is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.Plug in the coordinates and calculate the distance.Repeat the process for different pairs of adjacent vertices to make sure all sides have the same length.By following these steps, you should be able to determine the length of each side of the hexagon.
P(1+r)t Using the expression above, choose the correct answers for the new balance and the amount of interest earned in the following compound interest problem. $950 at 7% for 8 years, compounded annually. Total Amount = $ Interest Amount = $
Answers
Future value = accumulated amount, F = P(1+r)^t
P=principal
r=annual interest rate [compounded annually]
t=number of years of loan
Given:
P=950
r=0.07
t=8
F=950(1.07)^8
= 1632.28 (total amount)
Interest = total amount - principal
=1632.28 - 950
=682.28
Final answer:
The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.
Explanation:
The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.
First, we calculate the new balance:
Total Amount = $950(1 + 0.07)^8
Total Amount = $950(1.07)^8
Total Amount = $950 * 1.718186
Total Amount = $1632.77 (rounded to two decimal places)
Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:
Interest Amount = Total Amount - Original Principal
Interest Amount = $1632.77 - $950
Interest Amount = $682.77
Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.
Harland just got his second major credit card, so his credit score rose from 671 to 711. According to the following table for a $150,000 mortgage, how much less per year would Harland have to pay on a $150,000 mortgage with the new credit score?
Answers
Answer:
2004
Step-by-step explanation:
how to prove a polygon is a rectangle?
Answers
arman needs 4 1/2 inches of cable to make A,3 3/4 inches to make B, and 5 1/8 inches to make C. He used a 12 inch piece of cable to make A and B.
Answers
He used 12 inches of cable...
12 - 8 1/4 = 11 4/4 - 8 1/4 = 3 3/4....length left after A and B are made
he doesn't have enough to make the last one...
5 1/8 - 3 3/4 = 41/8 - 15/4 = 41/8 - 30/8 = 11/8 = 1 3/8....he is short by 1 3/8 inches
Answer:
8 1/4
Step-by-step explanation:
Evaluate x 1 - x -1 + x 0 for x = 2
a) 0
b)1/2
c)1 1/2
d)2 1/2
Answers
(2)^1 - (2) - 1 + 2^0 = 0.
The answer would be a)
The solution of expression is, 7/2.
What is an expression?A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
We have to give that,
An expression is,
⇒ x¹ + x⁻¹ + x⁰
Now, Substitute x = 2 in the above expression and find the value,
⇒ x¹ + x⁻¹ + x⁰
⇒ 2¹ + 2⁻¹ + 2⁰
⇒ 2 + 1/2 + 1
⇒ 3 + 1/2
⇒ (6 + 1)/2
⇒ 7/2
Therefore, The solution is, 7/2
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Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14?
Answers
Starting at vertex V going until vertex S, we make our calculations.
VR = 14
Rx = x
therefore, xS = VR – Rx
xS = 14 – x ---> 1
Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R
VR = 14 - x
at UV = 15 – (14 – x)
at UV = 1 + x
at TU = 7 – (1 + x)
at TU = 6 – x
at ST = 9 – (6 – x)
at ST = 3 + x ---> 2
Equate 1 and 2:
14 – x = 3 + x
2 x = 11
x = 5.5
To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.
Pentagon RSTUV and the Value of x
Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,
where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.
For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:
RS + TU + x = ST + UV + VR
Substituting the given values:
6 + 7 + x = 9 + 15 + 14
Simplifying the right-hand side:
6 + 7 + x = 3813 + x = 38x = 38 - 13x = 25Thus, the value of x is 25.
Given m || n, find X....PLEASE HELP ASAP....SOS...SUCK AT MATH PLEASE HELP ME!!
Answers
3x + 3 + 2x + 22 = 180
Combining like terms,
(3x + 2x) + (3 + 22) = 180
Simplifying,
5x + 25 = 180
Transpose the constants to only one side of the equation,
5x = 155
Divide the equation by 5.
x = 31
ANSWER: x = 31
Complete parts (a) and (b) using the probability distribution below.
The number of overtime hours worked in one week per employee
Overtime hours
0 1 2 3 4 5 6
Probability
0.026 0.072 0.154 0.303 0.215 0.164 0.066
(a) Find the mean, variance, and standard deviation of the probability distribution.
Find the mean of the probability distribution.
μ = 3.4
σ2 = 2.0
σ = 1.4
Choose the correct answer below.
A.
An employee works an average of 2.0 overtime hours per week with a standard deviation of approximately 1.4 hours.
B.
An employee works an average 3.4 of overtime hours per week with a standard deviation of approximately 4 hours.
C.
An employee works an average of 1.4 overtime hours per week with a standard deviation of approximately 3.4 hours.
D.
An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
Answers
μ = 0 + 0.072 + 0.304 + 0.909 + 0.86 + 0.82 + 0.396
μ = 3.361 ≈ 3.4
We need the value of ∑X² to work out the variance
∑X² = (0²×0.026) + (1²×0.072) + (2²×0.152) + (3²×0.303) + (4²×0.215) + (5²×0.164) + (6²×0.066)
∑X² = 0+0.072+0.608+2.727+3.44+4.1+2.376
∑X² = 13.323
Variance = ∑X² - μ²
Variance = 13.323 - (3.4)² = 1.763 ≈ 2
Standard Deviation = √Variance = √1.8 = 1.3416... ≈ 1.4
The correct answer related to the value of mean and standard deviation is the option D
An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.
Explanation:The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:
μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4
The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:
σ2 = Σ [(x - μ)2 * P(x)] = 2.0
And the standard deviation (σ) is simply the square root of the variance:
σ = √σ2 = 1.4
the circle is centered at the origin and the length of its radius is 4. what is
the circles equation
Answers
Answer: [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
The general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given: Radius of the circle : r= 4 units
The center of the circle : (h,k)=(0,0)
Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-
[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]
Answer:
X²+Y²=16
Step-by-step explanation:
A p e x
Which number produces an irrational number when multiplied by 0.4?
Answers
If CD is the perpendicular bisector of AB, then the value of x is:
10.
5.
22.
11.
Answers
CD = CD [ Common side ]
AD = BD [ CD is the perpendicular "bisector" of AB ]
∠CDA = ∠CDB [ CD is the "perpendicular" bisector of AB ]
Thus, ΔCAD and ΔCBD are congruent triangles. [ SAS congruency ]
If these triangles are congruent, then AC = BC.
2x = 3x -10
x = 10.
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Use the position equation
s = −16t^2 + v0t + s0
as the model for the problem.
A cargo plane flying at 6000 feet over level terrain drops a 700-pound supply package.
(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.)
(b) The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
Answers
A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:
s = −16 t^2 + v0 t + s0
Where,
s = distance of the plane from the ground = - 6000 ft (negative since the package moves from top to bottom)
t = time for it to strike the ground = unknown
v0 = 0 since the package starts from rest
s0 = 0 since we take the plane as the reference point
Substituting the given values:
- 6000 = -16 t^2 + 0 * t + 0
16 t^2 = 6000
t^2 = 375
t = 19.36 s
B. s = v * t
where v = 600 miles / hr = 0.17 miles / s
s = (0.17 miles / s) * 19.36 s
s = 3.23 miles = 17,054 ft
A manufacturing machine has a 10% defect rate. if 4 items are chosen at random, what is the probability that at least one will have a defect?
Answers
The probability that at least one of the four randomly chosen items will be defective is 34.39%. This is calculated by subtracting the probability that all items are not defective from 1.
Explanation:The subject of the question relates to the field of Probability. This problem pertains to the concept known as 'probability of at least one' event. In this case, we are considering the probability that at least one item will have a defect.
To calculate this, it's easier to find the probability that none of the items have a defect and then subtract that from 1. Since the machine has a 10% defect rate, it means there's a 90% chance that any item chosen will NOT be defective. If we choose 4 items, the probability that all are good is 0.9 * 0.9 * 0.9 * 0.9 = 0.6561.
So, the probability that at least one defective item will be chosen is 1 - 0.6561 = 0.3439 or 34.39%.
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lim θ→π/4 1 - tan θ / sin θ - cos θ
Answers
Indicate in standard form the equation of the line through the given points.
P(0, -4), Q(5, 1)
Answers
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-4)=1(x-0)\implies y+4=x\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}[/tex]
now, the so-called standard form, is moving the variables to the left-hand-side, sort them in descending order according to their exponents, and usually alphabetically some, so the "x" is left of the "y" and so on
-x+y=-4
An employee earned $3,300 working for an employer in the current year. the current rate for fica social security is 6.2% payable on earnings up to $117,000 maximum per year and the rate for fica medicare 1.45%. the employer's total fica payroll tax for this employee is:
Answers
3y^2-16y+16
could someone help me walk through this?
Answers
3y^2-16y+16
Multiply a by c value and replace as shown below
y^2-16y+48
Factor normally
(y-12)(y-4)
Divide both numbers by the previous a value
(y-12/3)(y-4/3)
(y-4)(y-4/3)
Because -4/3 does not become a whole number change the three to become the coefficient of y
(y-4)(3y-4)
Check by foiling
Final answer: (3y-4)(y-4)
there is a cafe at the park it is 13 meters long and 8 meters wide. what is the area of the cafe
Answers
The answer should be 104 meters cubed
A maintenance man has 12 keys on his key ring. if he tries the keys at random on a storage room door, discarding those that do not work, what is the probability that he will get the door open on his 4th try?
Answers
P(Failure on second try) = 10/11
P(Failure on third try)= 9/10
P(success on fourth try) = 1/9
P(success exactly on fourth try) = 11/12*10/11*9/10*1/9 = 1/12
Final answer:
The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.
Explanation:
The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.
To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.
Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:
(11/12) * (10/11) * (9/10) * (1/9) = 1/12.
Graph y=3x^2 -5 and it's inverse
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward
Find the inverse function
Exchange variables x for y and y for x
[tex]x=3y^{2}-5[/tex]
Isolate the variable y
[tex]3y^{2}=x+5[/tex] -----> inverse function (horizontal parabola open to the right)
or
[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]
using a graphing tool
see the attached figure
The graph of function and it's inverse of the graph is shown in image.
We have to given that,
To graph the function y = 3x² - 5 and it's inverse.
Here, The equation is,
y = 3x² - 5
So, We can find it's inverse as,
y = 3x² - 5
y + 5 = 3x²
(y + 5) / 3 = x²
x² = (y + 5)/3
x = √(y + 5)/3
Hence, the inverse of function is,
f ⁻¹ (x) = √ (x + 5)/3
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If one calendar year had two consecutive months with Friday the thirteenth, which months would they be?
Answers
In a leap year, no 2 months in a row would have that.
A person in a casino decides to play blackjack until he loses a game, but he will not play more than 3 games. let l denote a loss and w denote a win. what is the sample space for this random experiment
Answers
The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.
Explanation:The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.
Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.
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The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 42 inches, how long is each spoke? Round your answer to the nearest hundredth.
Answers
Ahmed is working at the burger joint. His boss pays him $6.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages in dollars, starting with his current wage?
Answers
Answer:
Sequence will be $6.50, $6.75, $7.0, $7.25.......
Step-by-step explanation:
Ahmed is working at the burger joint and he was paid by his boss $6.50 per hour.
His boss promised him to raise $0.25 per hour every six months.
So we have to find the sequence which describes Ahmed's expected hourly wages starting with his current wage.
As at every 6 months increase in wages is $0.25 so the sequence formed will be an arithmetic sequence with common difference of 0.25 and first term 6.50
Sequence will be $6.50, $6.75, $7.0, $7.25,.........
Convert 85°to radians
Answers
1 degree = 0.0174533 radians
85* 0.0174533 = 1.4835305 radians
Round answer as needed
Answer:
17pi/36 (PLATO answer)
Step-by-step explanation:
The value of the given digits in the numbers 7s in 775 823 159
Answers
BE is the midsegment of triangle ACD. The value of x is:
5.
20.
35.
40.
Answers
Verify that the divergence theorem is true for the vector field f on the region
e. give the flux. f(x, y, z) = 3xi + xyj + 4xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.
Answers
[tex]\implies\nabla\cdot\mathbf f(x,y,z)=3+x+4x=3+5x[/tex]
[tex]\displaystyle\iint_{\partial E}\mathbf f(x,y,z)\,\mathrm dS=\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_{z=0}^{z=3}\int_{y=0}^{y=3}\int_{x=0}^{x=3}(3+5x)\,\mathrm dx\,\mathrm dy\,\mathrm dz[/tex]
[tex]=\displaystyle9\int_0^3(3+5x)\,\mathrm dx[/tex]
[tex]=\dfrac{567}2[/tex]
To verify the divergence theorem, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
Explanation:To verify the divergence theorem for the given vector field f(x, y, z) = 3xi + xyj + 4xzk on the region e, which is a cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
The flux, Ƭ, can be calculated using the surface integral of the vector field over each face of the cube. According to the divergence theorem, this should be equal to the volume integral of the divergence of the vector field over the entire volume of the cube.
By calculating both sides of the equation, we can verify that the divergence theorem holds true for the given vector field on the specified region.
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