Part A: the functions are written and evaluated
f(x) = 2x + 1, f(2) = 5f(x) = (3x + 1)/4, f⁻¹(4) = 53y - 6 = 2(y - 1), y = 4Part B statement 1 and statement 2 has same result
How to evaluate the functionsThe statement are written as equation then evaluated
Statement 1 reads f of 2 when function f of x equals two times x plus one,
f(x) = 2x + 1
f(2) = 2 * 2 + 1 = 5
Statement two reads f inverse of four when function f of x equals quantity three times x plus one all divided by four,
f(x) = (3x + 1)/4
let f(x) = y and solving for the inverse
4y = 3x + 1
4y - 1 = 3x
x = (4y - 1)/3
hence f⁻¹(x) = (4y - 1)/3 interchanging y to x i the inverse equation
f⁻¹(x) = (4x - 1)/3
f⁻¹(4) = (4 * 4 - 1)/3 = 5
Statement three reads three times y minus six equals two times y minus 1
3y - 6 = 2(y - 1)
3y - 6 = 2y - 2
3y - 2y = 6 - 2
y = 4
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3. Step 1: Complete the table for y ≥ -x + 3.
Equations are relationships between two or more variables that are used to determine an unknown variable's value based on the values of other variables that are known.
How to find the calculation?y = −x − 3
Calculate the slope and y-intercept using the slope-intercept form.
In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.
y = m x + b
With the use of the formula y = m x + b, determine the values of m and b.
m = − 1 b = − 3
M represents the line's slope, while B represents the y-intercept.
Slope is 1 and the y-intercept is (0, 3).
Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.
Less steps by tapping...
Assign the x and y values to a table.
x y
0 − 3
1 − 4
The slope and y-intercept, or the points, should be used to graph the line.
Slope: 1 y-intercept: (0, 3 )
x y
0 3
1 4.
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(Look at picture) and ty btw <3
What’s the value of x solve the equation
-3x+4=2x-6
Answer: x=2
Step-by-step explanation:
−3x+4=2x−6
Subtract 2x from both sides.
−3x+4−2x=−6
Combine −3x and −2x to get −5x.
−5x+4=−6
Subtract 4 from both sides.
−5x=−6−4
Subtract 4 from −6 to get −10.
−5x=−10
Divide both sides by −5.x=−5−10
Divide −10 by −5 to get 2
x=2
One force is 4kn and resultant is 8kn included at 60 degree find other force
The way I view this problem is the resultant R is making a 60 degree angle from one of the forces, The two forces are at right angle from each other and they are the x-component Rx and the y- component Ry of the resultant. If the magnitude of Rx = 4N then the angle opposite the side is 30 degrees. The Ry component can be solved using the Pythagorean theorem.
How to find the other force?Step 1
one force=4kn
resultant=8kn
degree=60
it can be solved using the Pythagorean theorem.
Step 2
R^2 = Rx^2 + Ry^2
8^2 = 4^2 + Ry^2
64 = 16 + Ry^2
Ry^2 = 64 - 16
Ry^2 = 48
Ry = 6.9282 N
Solving for the direction of Ry
Ry is 90 degrees from Rx
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The angle of depression from an airplane to the top of an air traffic control tower is 56°. If the tower is 320 feet tall and the airplane is flying at an altitude of 7,450 feet, how far away is the airplane from the control tower?
Answer:
There are two possible answers depending on how you interpret the question. Please read the explanation below carefully and in full
Diagonal distance from top of tower to plane :
[tex]\boxed{d= 12,571\;feet}[/tex]
Horizontal distance from control tower to plane:
[tex]\boxed{h = 10571\;feet}[/tex]
Step-by-step explanation:
Before explanation, I must say the question is confusing. Are they asking for the distance from the top of the tower or the horizontal distance from the location of the tower?
I am giving answers for both. You can ask your professor about this and answer with the right one.
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This question and explanation can best be understood by drawing a diagram with given information
First, look at the attached Image
A is the top of the control tower 320 feet above the ground
B is the location of the plane 7450' above ground level.
The point C which lies on the vertical line is at the same height from the ground as the top of the control tower i.e. 320 feet
So B
Points ABC form a right triangle with m∠ACB = 90°
m∠ABC = 56° (given)
Since the 3 angles of a triangle add up to 180°, we have
m∠BAC + 56 + 90 = 180°
m∠BAC = 180 - (56 + 90) = 34°
Diagonal distance from top of tower(d)
The objective is to find d.
Use the law of sines which states:
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
[tex]\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]
Looking at the various side lengths and angles and applying this law we get
[tex]\dfrac{7130}{\sin 34^\circ} = \dfrac{d}{\sin 90^\circ}\\\\\textrm{Since }\sin 90^\circ } = 1\\\\\dfrac{7130}{\sin 34^\circ} = d\\\\d = 12,750.5194 = 12,751 \textrm{ feet rounded to nearest foot}\\\\[/tex]
Horizontal distance from tower
Use the law of sines again.
Without calculating d first, we can use
[tex]\dfrac{h}{\sin 56^\circ} = \dfrac{7130}{\sin 34^\circ}\\\\[/tex]
[tex]h = \dfrac{7130 (\sin 56^\circ)}{\sin 34^\circ} = 10,570.659 = 10,571 \;feet[/tex]
Therefore the possible answers are
Diagonal distance from top of tower to plane :
[tex]\boxed{d= 12,571\;feet}[/tex]
Horizontal distance from control tower to plane:
[tex]\boxed{h = 10571\;feet}[/tex]
It is highly likely that they are looking for the horizontal distance but check with your prof or include both answers
1.5[3(14.5+7)-3]-7.4
the answer to this math equation is 84.85
The length of the drawing is 13 inches the actual length of the bridge is about 1599 feet. What is the scale factor
Your estimated closing cost for your $450,000 home were $11,500, the actual closing cost were 4.5% of
the cost of the home. Were the closing costs higher or lower than the estimate?
The 4.5% of cost of home is $20250 which is higher than the estimated.
What is percentage ?
percentage can be defined as the product of ratio of given value, total value and hundred.
Given,
Your estimated closing cost for your $450,000 home were $11,500,
the actual closing cost were 4.5% of the cost of the home.
So,
the 4.5% of cost of home is
= 4.5% of 450,000
= (4.5 / 100) * 450,000
= 45*450
= 20250
Hence, The 4.5% of cost of home is $20250 which is higher than the estimated.
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Zhen and Ryder work as tutors at two different test-prep companies. In one week, Zhen earns 45% of the $2400 collected from the pupils tutors. earns % of the $ collected from the pupils she tutors the same week. Who earns more money in a week? Explain.
The tutor that will earn more money in a week would be Zhen with the total income of =$1,080.
How to calculate the earnings of each tutor?The total amount collected from pupils tutor by Zhen company = $2400
The 45% of $2400 = 45/100 × 2400
= 108000/100
= $1,080
The total amount collected from pupils Ryder tutored would be = $1080
The 45% of $1080 = 45/100 × 1080
= 48600/100
= $486
Therefore, the tutor that earned higher income is Zhen with an income of $1,080.
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Complete question:
Zhen and Ryder work as tutors at two different test-prep companies. In one week, Zhen earns 45% of the $2400 collected from the pupils tutors. Ryder earns 45% of the $1080 collected from the pupils she tutors the same week. Who earns more money in a week? Explain.
(1.2 x 10^8) divided by (3 x 10^2). Give your answer in standard index form
Step-by-step explanation:
(1.2 x 10^8) =120000000
(3 x 10^2). =300
120000000÷300=400000
4×10 in the power of 6