we have
[tex]0.5-\left|x-12\right|=-0.25[/tex]
we know that
The absolute value has two solutions
Subtract [tex]0.5[/tex] both sides
[tex]-\left|x-12\right|=-0.25-0.5[/tex]
[tex]-\left|x-12\right|=-0.75[/tex]
Step 1
Find the first solution (Case positive)
[tex]-[+(x-12)]=-0.75[/tex]
[tex]-x+12=-0.75[/tex]
Subtract [tex]12[/tex] both sides
[tex]-x+12-12=-0.75-12[/tex]
[tex]-x=-12.75[/tex]
Multiply by [tex]-1[/tex] both sides
[tex]x=12.75[/tex]
Step 2
Find the second solution (Case negative)
[tex]-[-(x-12)]=-0.75[/tex]
[tex]x-12=-0.75[/tex]
Adds [tex]12[/tex] both sides
[tex]x=-0.75+12[/tex]
[tex]x=11.25[/tex]
Statements
case A) The equation will have no solutions
The statement is False
Because the equation has two solutions------> See the procedure
case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation
The statement is True -----> See the procedure
case C) A good first step for solving the equation is to split it into a positive case and a negative case
The statement is False -----> See the procedure
case D) The positive case of this equation is 0.5 – |x – 12| = 0.25
The statement is False
Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure
case E) The negative case of this equation is x – 12 = –0.75
The statement is True -----> see the procedure
case F) The equation will have only 1 solution
The statement is False
Because The equation has two solutions------> See the procedure
The equation 0.5 - |x - 12| = -0.25 has no solutions because an absolute value cannot be negative. Attempting to split the equation into positive and negative cases or solving for x is fruitless because the left side of the equation will always be at least 0.5.
Explanation:When solving the equation 0.5 - |x - 12| = -0.25, we can immediately notice that it will have no solutions because the absolute value is always non-negative, and therefore the left-hand side cannot be less than 0.5. Hence, subtracting 0.5 from both sides is not a good first step. Instead, you would typically isolate the absolute value on one side, but given that the equation equals a negative number, we know it has no solutions without additional steps.
Additionally, splitting the equation into a positive case and a negative case isn't useful here, because no matter what's inside the absolute value, the output cannot lead to a negative result, thus making both cases moot.
The statements that say "The positive case of this equation is 0.5 - |x - 12| = 0.25" and "The negative case of this equation is x - 12 = -0.75" are incorrect as they misinterpret how the absolute value works. Lastly, the equation does not have any solution, so it cannot have only one solution.
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Convert the following using dimensional analysis:
13.2 cm to ft & in
Can someone help me with this math problem, please? Thanks!
How would you represent 4 eighth notes as a fraction?
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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what are the domain and range of the following functions? write your answer using inequality symbols if possible
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.
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%
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
Final answer:
To convert 28.7251 degrees to degrees, minutes, and seconds, take the whole number of degrees (28) and multiply the decimals (.7251) by 60 to get the minutes (43). Then multiply the remaining decimal of the minutes (.506) by 60 to get the seconds (30), resulting in 28 degrees, 43 minutes, and 30 seconds (28° 43' 30").
Explanation:
To convert 28.7251 degrees to degrees, minutes, and seconds, you follow a multi-step process which involves converting the decimal part of the degrees into minutes and then into seconds. First, identify the whole number of degrees, which is 28 in this case.
To convert the decimal part (.7251) to minutes, multiply by 60. Using the operation provided in the reference, with 0.7251 × 60, you get 43.506 minutes. The whole number part, 43, is the minutes.
To convert the remaining decimal part of minutes (.506) into seconds, again multiply by 60. This gives you (.506 imes 60) 30.36 seconds, which when rounded to the nearest second is 30 seconds.
Therefore, 28.7251 degrees is equal to 28 degrees, 43 minutes and 30 seconds (28° 43' 30").
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.
simplify each expression by destributing. math problem> 3(2y-7)
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?
If the x-axis is Quantity and the y-axis is Price, which of the following is the best summarization of the supply shift from S1 to S2?
A)The supply decreased.
B) The supply stayed the same.
C) The supply increased.
D) The supply outweighed demand.
Answer:
Option B is correct.
Step-by-step explanation:
We have been given x-axis representing quantity
And y-axis representing price
S1 and S2 are supply
So, these two supply have parallel lines which means they will never intersect they will remain same throughout the domain.
Therefore, the supply stayed the same.
Option B is correct.
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 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 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
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 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).
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
ind the area of an octagon with a radius of 6 meters. Round your answer to the nearest tenth.
Which kinematics equation is a quadratic equation?
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.
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
Which expression represents the area of triangle ABC in square meters?
Answer:
the correct answer is A. 1/2 x 14 x 57
Step-by-step explanation:
i got it right on my test
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 ?
△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′?
True or false
Two points determine a plane
Find the missing number in the proportion. 8/56 = ?/49
(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.