Option (c) represents an inconsistent system of equations, as the constant terms are not proportional, while the coefficients of x are. This system (y=4x-3, y=4x+3) has no solutions.
Explanation:In mathematics, specifically in algebra, an inconsistent system is a system of equations that has no solutions. To check which system is inconsistent from the options you've given, we need to compare the coefficients of each equation within a system. An inconsistent system will have proportional coefficients of x and y between the two equations, but the constant terms will not be proportional.
Looking at each option:
Option (a): y=x+4 and y=2x+4
Option (b): y=x and y=−x
Option (c): y=4x−3 and y=4x+3
Option (d): y=2x−3 and 2y=4x−6
From here, we can see that option (c): y=4x-3, y=4x+3 is inconsistent. In this system, the coefficients of x are proportional (4), but the constant terms (-3 and +3) are not proportional.
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A cylindrical tank standing upright (with one circular base on the ground) has a radius of 1212 cm for the base. how fast does the water level in the tank drop when the water is being drained at 2323 cm33/sec? note that the volume of a cylinder is v=πr2hv=πr2h where rr is the radius of the base and hh is the height of the cylinder.
To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.
We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).
Substituting the values, we get:
dh/dt = 23 cm³/sec / (π * (12 cm)²)
Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.
How can 3.7=x+(-5) be solved for x in one step?Add 3.7 to both sides .Add 5 to both sides. Subtract 3.7 from both sides Subtract 5 from both sides
The first step to solve for x in the given algebra using properties of equality is; Add 5 to both sides.
How to Simplify Algebra?We want to simplify the algebraic expression;
3.7 = x + (-5)
When dealing with algebra like this, what we have to first do is to balance both sides of the equation.
To solve this particular algebra problem, we will use additional property of equality by adding 5 to both sides to get;
3.7 + 5 = x + (-5) + 5
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The first step to solving the expression 3.7 = x + (- 5) is,
''Add 5 to both sides''
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to give that,
An algebraic expression to simplify,
⇒ 3.7 = x + (- 5)
Now, Simplify the expression by combining like terms as,
⇒ 3.7 = x + (- 5)
⇒ 3.7 = x - 5
Use the additional property of equality by adding 5 to both sides to get;
3.7 + 5 = x + (-5) + 5
8.7 = x
x = 8.7
So, the first step is, ''Add 5 to both sides''.
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Which kinematics equation is a quadratic equation?
The figure consists of a tangent and a secant to the circle. Solve for x.
A. 9.2
B. 7.7
C. 14.3
D. 85
Answer:
9.2
Step-by-step explanation:
We are given that a figure in which a tangent and a secant to the circle.
We have to find the value of x.
Length of tangent segment=x
Length of secant segment=12 +5=17 units
Length of external segment=5 units
We know that secant-tangent theorem
It states that product of length of secant segment and its external segment is equal to square of length of tangent segment.
[tex]x^2=17\times 5=85 [/tex]
[tex]x=\sqrt{85}=9.2 units[/tex]
Hence, the value of x=9.2
A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. find the height of the tree to the nearest meter.
Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.
Explanation:The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.
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True or false
Two points determine a plane
simplify each expression by destributing. math problem> 3(2y-7)
Julio has started his very own floral business. He sells centerpieces for $19.50 each. His fixed costs are $500 per month, and each centerpiece cost $8 to produce. What is your break-even point? a. Julio must sell approximately 18 centerpieces to break even. b. Julio must sell approximately 23 centerpieces to break even. c. Julio must sell approximately 44 centerpieces to break even. d. Julio must sell approximately 55 centerpieces to break even.
500= (19.50-8.00)x
500 = 11.50x
x=500/11.50=43.48
so he needs to sell approximately 44 centerpieces to break even
Write the equations in graphing form, then state the vertex of the parabola or the center and radius of the circle.
x^2+y^2+y+2=8
Jenna surveyed the students at her dance class to find out if they like salsa and/or ballet. The results of her survey are shown in the two-way table below:
Like Salsa
Do Not Like Salsa
Total
Like Ballet
32
42
74
Do Not Like Ballet
22
4
26
Total
54
46
100
If a student does not like ballet, what is the probability that student also does not like salsa?
8.7%
15.4%
18.2%
84.6%
Tom is showing his work in simplifying (5.2 – 8.5) – 0.5 + 6.8. In which step did Tom make an error? Step 1:: (5.2 – 8.5) – 0.5 + 6.8 Step 2: 5.2 + (–8.5 – 0.5) + 6.8 (distributive property) Step 3: 5.2 – 9 + 6.8 Step 4: 5.2 + 6.8 – 9 (commutative property) Step 5: 12 – 9 = 3 Step 2; he wrote distributive instead of commutative Step 2; he wrote distributive instead of associative Step 4; he wrote commutative instead of associative Step 4; he wrote commutative instead of distributive
Answer:
B
Step-by-step explanation:
Step 2 he wrote distributive instead of associative
what are the domain and range of the following functions? write your answer using inequality symbols if possible
Transform both equations in each system of equations so that each coefficient is an integer.
***I also need it to be solved using substitution method.
The roof of a house is being reconstructed to accommodate heavy snows. the current 32 foot roofline makes an 18.2° angle with the horizontal. the owner has decided to construct the new roof so that it makes a 50° with the horizontal as shown below. what will be the length of the new roofline?
To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.
Explanation:To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:
tan(50°) = 32/x
To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:
x = 32/tan(50°)
Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:
x ≈ 32/1.1917
By calculating this, we find that the length of the new roofline is approximately 26.9 feet.
The absolute value function g(x) = |x + 7| − 4 is translated 5 units right and 2 units up to become g′(x). The quadratic function f(x), graphed below, is also moved 5 units right and 2 units up to become f′(x). Which of these two transformed functions has a range of y ≤ −2 and what is the vertex of this transformed function?
g′(x) has a range of y ≤ −2 and its vertex is at (−2, −2).
g′(x) has a range of y ≤ −2 and its vertex is at (2, −2).
f′(x) has a range of y ≤ −2 and its vertex is at (3, −2).
f′(x) has a range of y ≤ −2 and its vertex is at (−7, −6).
what is the solution to 2sin^(2)x+sinx+1=0
a. 30 deg
b.150 deg
c.240 deg
d. 270 deg
e. 330 deg
give and example of a line that is parrallel to 9x+6y= -6
Can someone help me with this math problem, please? Thanks!
A sixteen-sided number cube has the numbers 1 through 16 on each face. each face is equally likely to show after a roll. what is the probability that you will roll an even number or an odd prime number? round to the nearest thousandth.
a. 0.063
b. 0.813
c. 0.219
d. 0.875
Answer:
B. 0.813
Step-by-step explanation:
A sixteen-sided number cube has the numbers 1 through 16 on each face.
So, [tex]|\ S\ |=16[/tex]
Let us assume that, A be the event that the number will be an even number. So,
[tex]A=\left \{ 2,4,6,8,10,12,14,16 \right \}[/tex] and [tex]|\ A\ |=8[/tex]
Then,
[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]
Let us assume that, B be the event that the number will be an odd prime number.
[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]
Then,
[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]
So the probability that you will roll an even number or an odd prime number will be,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)
[tex]=\dfrac{13}{16}[/tex]
[tex]=0.813[/tex]
What is the intersection of this sphere with the yz-plane? find an equation of the sphere with center (−3, 2, 9) and radius 6?
The equation of the sphere with center (-3, 2, 9) and radius 6 is (x + 3)² + (y - 2)² + (z - 9)² = 6². The intersection of this sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.
Explanation:The equation of a sphere with center (-3, 2, 9) and radius 6 is given by:
(x + 3)² + (y - 2)²+ (z - 9)² = 6²
To find the intersection of this sphere with the yz-plane, we need to set x = 0 in the equation:
(0 + 3)² + (y - 2)² + (z - 9)² = 6²
Simplifying this equation gives:
(y - 2)² + (z - 9)² = 27
So, the intersection of the sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.
Frank borrowed $400 from his neighbor. He made 3 payments of $65 each and another payment of $95. How much does Frank still owe?
The mean of a set of credit scores is u=690 and o=14. Which credit score is within z-score of 3.3?
A)634
B)640
C)720
D)750
I think it is C
BMK ><
Answer:
c)720
Step-by-step explanation:
The mean of a set of credit scores is u=690 and o=14.
mean = 690 and standard deviation SD = 14
We use z- score formula
[tex]z=\frac{x-mean}{SD}[/tex]
z= 3.3 given
Plug in the values and find out x
[tex]3.3=\frac{x-690}{14}[/tex]
Multiply 14 on both sides
46.2 = x- 690
Now add 690 on both sides
x= 736.2
Credit score is 720 that comes under 736.2
So answer is 720
An airplane pilot over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?
A. 403 m
B. 405 m
C. 4611 m
D. 4647 m
Rounded to the nearest meter, the height of the plane is approximately 405 meters.
So, the correct answer is B. 405 m.
To find the height of the plane, we can use trigonometry, specifically the tangent function.
Let's denote the height of the plane as h (in meters).
From the information given, we know that the angle of depression from the airplane to the atoll is 5 degrees, and the horizontal distance from the airplane to the atoll is 4629 meters.
Using the tangent function, we have:
tan(angle of depression) = height / horizontal distance
tan(5 degrees) = h / 4629
To find the value of h, we can rearrange the equation:
h = 4629 * tan(5 degrees)
Now, let's calculate the height of the plane:
h ≈ 4629 * 0.0874886635 ≈ 404.773 meters
Rounded to the nearest meter, the height of the plane is approximately 405 meters.
So, the correct answer is B. 405 m.
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Write a point-slope equation for the line that has slope 5 and passes through the point (6, 22). Do not use parenthesis on the y side.
Choose a number. add 5. multiply by -4. subtract 3. for each starting number what is your ending number ?
What is the value of 3yx +2x when x=4 and y=-2
A.-28
B.-16
C.8
D.56
If one u.s. dollars equals 5.76 egyptian pounds and one u.s. dollar equals 0.56 british pound, how many egyptian pound equal one british pound?
FIND THE MISSING VALUE. SHOW YOUR WORK.
c:
to find x multiply the side (24) by the tangent of the angle(13)
so 24 * tan(13) = 5.5408
D:
to find x
divide the side (10) by the sin of the angle (20)
10/sin(20) = 29.238
Round the answers as needed.
△LMN, with vertices L(2,2), M(3,5), and N(6,1), is rotated 90° about the origin. What is the location of M′?
(HELP ASAP) Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides.
The area of EFGH is 35 square units. What is the value of x?
4 units
5 units
6 units
7 units
The answer is 5 units on e2020.