With the exception of x=4/5, the domain of s(x) over t(x) is all real numbers. Except when x=-3/2, all real numbers fall within the domain of w(x).
Given,
The value of the independent variable, often x, for which the supplied function is specified is the domain of a function.
When the value of the denominator falls to zero, a function that is composed of the fraction of two polynomials is not defined.
The numerator of t(x) should not be zero since the domain of s(x) over t(x) will be all real integers except the numerator of zero.
t(x) = 0
5x + 4 = 0
5x = -4
x = -4/5
With the exception of x=-4/5, all real numbers fall into the domain of s(x) over t(x).
Similar to w(x), s(x) should not be zero because the domain of w(x) will be all real numbers except for the one that makes the denominator equal to zero.
s(x) = 0
2x - 3 = 0
2x = 3
x = 3/2
With the exception of x=-3/2, all real numbers fall within the domain of w(x).
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A plane is 141 mi north and 162 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree.
The value of x = 41.02°
Trigonometric Ratios:The ratios of lengths of a right-angled triangle's sides are known as trigonometric ratios. These trigonometric ratios connect the ratio of a right triangle's sides to each angle.
The basic trigonometric ratios:sin = (Opposite side/ Hypotenuse)
cos = (Adjacent side/ Hypotenuse)
tan = (Opposite side/ Adjacent side)
Here we have
A plane is 141 m north and 162 m east of an airport.
x is an angle that the pilot should turn in order to fly directly to the airport.
[ The picture that can represent the above information is given below ]
From given figure
ABC is a right-angled triangle with a right angle at A
As we know from trigonometric ratios
Tan θ = Opposite side/Adjacent side
⇒ Tan x = 141/162
⇒ Tan x = 141/162
⇒ Tan x = 47/54
⇒ Tan x = 0.870
⇒ x = Tan⁻'(0.870)
⇒ x = 41.02°
Therefore,
The value of x = 41.02°
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Select the transformation
the pre-image FISH onto its image F'I'S'H'.
[₁
S'
H
F₁ H'
FL
rule that correctly maps
S
T
The vertices have been shifted toward the left by 1 unit and also 3 units up to form the image F'I'S'H'.
What is graph transformation?
The process of altering a graph to produce a different version of the preceding graph is known as graph transformation. The graphs can be moved about the x-y plane or translated. They can also be stretched, or they can undergo a combination of these changes. We discuss the various graph transformations in this post.Graph stretching
A function's graph can be stretched by adding a constant factor to it or to one of its independent variables. The stretch could be horizontal or vertical. Let's talk about stretching horizontally and vertically.Observing each of the vertices of the square, we can say that the vertices have been shifted toward the left by 1 unit and also 3 units up to form the image F'I'S'H'. So, the transformation involved in moving the preimage FISH to form F'I'S'H' the image is translation.
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Graph the inequality on the axes below.
x + 3y ≥ 9
how do you find the measure of each angel indicated??
Answer:
by knowing the sum of the shape represented
PLEASE HELP ME I REALLY NEED IT
Answer:
-1/2
Step-by-step explanation:
Ignore the (2,2) just use (-2,1) and (-4,2)
Write a verbal expression or word problem that could be represented by the following equation.
2x + 7 = 35
The required verbal expression : Twice of a variable x when added with 7 will give a constant equal to 35
What is a variable ?An unknown numerical value in an equation or algebraic expression is represented by a symbol (typically a letter) in algebra. A variable is, to put it simply, a quantity that is changeable and not fixed and is frequently represented by an alphabet.
What is a verbal expression ?A verbal statement is a mathematical problem. Algebraic 8 + 6 is an example of using numbers and numeric variables. It is necessary to be familiar with the words used to describe mathematical operations in order to translate between verbal statements and algebraic expressions.
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3. The table below shows the temperature of an oven, in degrees Fahrenheit, t minutes
after it is turned on.
Oven Temperature
Time, t
(in minutes)
0
3
5
Temperature, F
(in °F)
70
160
220
10
370
An equation for a line of best fit for these data is F = 30t + 70. What is the slope of this
line, and what does it represent?
The slope of this line, and what it represent is: The slope is 30, and it represents the increase in temperature, in degrees Fahrenheit, each minute the oven is on.
How to identify and interpret the slope?Mathematically, the standard form of the equation of a line can be calculated by using this equation:
y = mx + c .......equation 1.
Where:
m represents the slope.x and y represent the variables.c represents the y-intercept.From the information provided, we have the following equation of line:
F = 30t + 70 ..........equation 2.
Comparing equation 1 and equation 2, we have:
Slope, m = 30, which is the increase in temperature of the oven in degrees Fahrenheit.
y-intercept, c = 70, which also represents the initial temperature of the oven in degrees Fahrenheit.
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Complete Question:
The table below shows the temperature of an oven, in degrees Fahrenheit, t minutes after it is turned on. An equation for a line of best fit for these data is F = 30t + 70. What is the slope of this line, and what does it represent?
answer choices
The slope is 30, and it represents the initial temperature, in degrees Fahrenheit, of the oven.
The slope is 70, and it represents the initial temperature, in degrees Fahrenheit, of the oven.
The slope is 30, and it represents the increase in temperature, in degrees Fahrenheit, each minute the oven is on.
The slope is 70, and it represents the increase in temperature, in degrees Fahrenheit, each minute the oven is on.
simplify 4x5 - 25x³/ 2x-5
Help me and I'll reward you.
Answer:
i don't understand
Step-by-step explanation:
the question is 11 divided 2and2over 3
[tex]=\frac{x^{3}(4x^{2} -25) }{2x-5} \\=\frac{x^{3} (2x+5)(2x-5)}{2x-5} \\=x^{3} (2x+5)\\=2x^{4}+5x^{3}[/tex]
⇒Note there was a 2x-5 in the numerator and a 2x-5 in the denominator so they canceled each other. Leaving the above expression.
Given ∠RUY=90° and ∠RST=90°
Find YT=
Answer:
YT= 23
We know that:
line RU is 32 and US is 16
line RY is 46
In other words, RU = 32, US = 16, and RY = 46
so we use the triangle proportionality theorem to state that:
[tex]\frac{RU}{US}=\frac{RY}{YT}[/tex]
Input your values
[tex]\frac{32}{16} =\frac{46}{YT}[/tex]
Use cross products :
[tex]32YT=(16)(46)[/tex]
Simplify:
[tex]32YT=736[/tex]
[tex]\frac{32YT}{32} =\frac{736}{32}[/tex]
[tex]YT=23[/tex]
I hope this answers you question :)
What was the winner's speed during last year's race? (3 points for speed, 2 points for conversion to knots).
Given: 6076 feet/nautical mile.
The winner's time was 16.5 minutes.
(distance unknown)
Part VIII of 2.11.2 Project: Performance Task: The Parrallax Problem apex
The speed of the winner based on the information is 368.24 mile per minutes
How to calculate the speed ?It should be noted that speed is calculated as the distance divided by the time given.
The following can be deduced from the information given:.
Distance = 6076 feet/nautical mile.
Time =16.5 minutes.
Speed = Distance / Time
Speed = 6076 / 16.5
Speed = 368.24 mile per minutes
The speed is 368.24 mile per minutes.
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What is the sum of (3x + 4) + (9x – 10)?
Step-by-step explanation:
(3x+4)+(9x-10)
= 3x+4+9x-10
=3x+9x+4-10
=12x-6
ANSWER IS 12X-6
Answer:
The solution is 12x-6
Step-by-step explanation:
(3x+4)+(9x-10)
We remove the brackets
= 3x+4+9x-10
= 3x+9x+4-10
= 12x-16
33 is what percent of 132?
- Solution for 33 is what percent of 132:
- Percentage solution with steps:
Step 1: We make the assumption that 132 is 100% since it is our output value.
Step 2: We next represent the value we seek with "x".
Step 3: From step 1, it follows that 100%=132
Step 4: In the same vein, x%=33
Step 5: This gives us a pair of simple equations:
100%=132(1)
x%=33(2)
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left-hand side) of both equations have the same unit (%); we have
100%/x% = 132/33
Step 7: Taking the inverse (or reciprocal) of both sides yields
x%/100%=33/132
x=25%
Therefore, 33 is 25% of 132
Please help me it’s due.
Answer:
A = Research question
B = Hypothesis
C = Analysis of data
D = Reflecting on the results
Step-by-step explanation:
Im 85% sure
The area of a rectangle and its length, if its width is 2cm
Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged. Estimate N, the total number of fish in the entire sampling area.
The total number of fish in the entire sampling area is 600
Sampling:
The process of selecting the group that you will actually collect data from in your research is called sampling.
Given,
Consider a case where 400 fish are tagged and released during a first outing. During a second outing in the same area, 400 fish are again caught and released, of which half are already tagged.
Here we need to find the total number of fish in the entire sampling area.
Let us consider N be the number of fish in the entire sampling area.
While looking through the given question,
We have identified the following,
Number of fish tagged = 400
Next time number of fish caught = 400
We know the half of them are tagged, so the untagged fishes are
=> 400/2
=> 200
Therefore, the total number of fishes is
=> 400 + 200
=> 600
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Mario purchased a storage cube with a volume of 27 cubic feet. he wants to sit it on a shelf that is 4 feet wide wide. volume: 27ft³ Will the cube fit on the shelf? Explain how you know
Answer:
No, the cube will not fit on the shelf because it is too big. The shelf is only 4 feet wide, but the cube is 27 cubic feet, which is much bigger.
Aslam invested rs 210000part at 8% per annum and the rest at 6%per annum. if the annual incomes from both investment were the same, find the amount invested at each rate.
a = amount invested at 8%
how much is 8% of "a"? (8/100) * "a", namely 0.08a.
b = amount invested at 6%
how much is 6% of "b"? (6/100) * "b", namely 0.06b.
we know the total amount invested is 210000, so whatever "a" and "b" might be, we know that a + b = 210000.
we also know that the yielded amount in interest is the same for both, so whatever 0.08a and 0.06b are, we know they're the same.
[tex]\begin{cases} a+b=210000\\\\ 0.08a=0.06b \end{cases}\hspace{5em}a+b=210000\implies b=210000-a \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.08a~~ = ~~0.06(210000-a)}\implies 0.08a=12600-0.06a\implies 0.14a=12600 \\\\\\ a=\cfrac{12600}{0.14}\implies \boxed{a=90000}\hspace{9em}\boxed{\stackrel{210000~~ - ~~90000}{b=120000}}[/tex]
Using only a compass and a straightedge, you are constructing a line perpendicular to AB and passing through a given point, M, on AB. With a
compass of set width, you have drawn arcs that intersect AB on each side of M and marked the two intersection points as P and Q.
The next step in this construction is to place the compass needle on
P (or Q) and mark an arc roughly where M's reflection across AB is located.
How to use a compass?One tool for drawing circles is a compass. According to the circle's radius, which is drawn with a compass, the sizes of the circles vary.
A compass's handle is held in place by our thumb and forefinger. A circle is typically drawn using just one hand. Between the forefinger and thumb, the compass is turned.
Around this point, the pencil tip is rotated. The circle's radius is determined by the distance between the pencil tip and the compass needle. A ruler is used to set it. The gap can be adjusted by adjusting the angle between the compass's arms.
At that point of reflection (M'), arcs drawn from P and Q in M's approximate location across AB will intersect. As desired, the line passing through point M and perpendicular to AB will connect M and M'.
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Kelly drank .86 of her Gatorade and John drank 7/8 of his Ginger Ale. Who drank less?
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
That's a lot of exclamation marks :DDDDD
Rate of change, Δ often said as "delta" or also known as slope of a line. Rate of change is much easier when it's a line
it's just the slope of the line.
I see that the line in the picture... so the graph of the line.... is going down 1 after it goes over 4... so rate of change is rise over run..
-1 / 4
see how I got that?
so B) looks good
a landscaping company ordered 17 plants and 8 trees for a total $ 964. if plants are $ 12 each, write and solve a linear equation to find the cost for each tree
Answer:
$95
Step-by-step explanation:
If 1 plant is $12 each, 17 plants will be
= 17($12)
= $204
Substitute the number of trees for x
The total cost of both is $964
Hence,
17($12) + 8(x) = $964
$204 + 8x = $964
Collect like terms
8x = $964 - $204
8x = $760
Divide both sides by 8
8x/8 = 760/8
x = $95
what does the graph do if “a” is a number between zero and one compared to greater than one?
For any given graph when "a" is a number between zero and one then graph of the function get horizontal stretch.
And when "a" is a number greater than one then graph of a function get horizontal compress.
As given in the question,
For any graph of a function,
When "a" is a number between zero and one than the graph of the function get horizontal stretch.
f(x) = ax²
let a = 1/2 , 0 < 1/2 < 1 so satisfied the condition of "a" between zero and one.
f(x) = x²/2
In this case , graph of the given function get horizontal stretch compare to original graph.
When a = 2 , 2 > 1 satisfied the condition of "a" greater than one.
f(x) = 2x²
In this case , graph of the given function get horizontal compress compare to original graph.
Therefore, for any given graph when "a" is a number between zero and one then graph of the function get horizontal stretch.
And when "a" is a number greater than one then graph of a function get horizontal compress.
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a spherical balloon is inflated so that its volume is increasing at the rate of 3.7 ft3/min. how rapidly is the diameter of the balloon increasing when the diameter is 1.5 feet?
Using Sphere geometry formulas , 2.45 ft/min is increasing rate of spherical ballon when the diameter is 1.5 feet.
Sphere is a three dimensional form of circle .
let V and D be volume and diameter of the sphere. we have given that ,
Volume increasing rate of spherical ballon (dV/dt)
= 3.7 ft³/min
diameter of sphere at time of increasing = 1.5 feet
the increasing rate of spherical ballon is dD/dt.
Now, Volume of sphere (V) = 4/3π³ ft³
or we know that D = r/2 so,
V = 4/3 π (D)³×8 ft³
differentating both sides we get ,
dV/dt = 32/8π 3D³dD/dt
=> 3.7 = 32/3 (3.14)(1.5)²dD/dt
=> dD/dt= 2.45 feet/min
Hence, 2.45 ft/min is the rate of the diameter of the balloon increasing when the diameter is 1.5 feet.
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Use properties to rewrite the given equation. Which equations have the same solution as 2. 3p – 10. 1 = 6. 5p – 4 – 0. 01p? select two options. 2. 3p – 10. 1 = 6. 4p – 4 2. 3p – 10. 1 = 6. 49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2. 3p – 14. 1 = 6. 4p – 4.
The equations 2.3p - 101 = 6.49p -4 and 23p - 101 = 65p - 40 - p are the equation that has the same solution:
The given equation is:
2.3p - 10.1 = 6.5p - 4 - 0.1p
The first option is:
2.3p - 10.1 = 6.4p - 4
which is equal to the given equation.
The second option:
230p - 1010 = 650p - 400 - p
which is not equal to the given equation
The third option:
23p - 101 = 65p - 40 - p
which is equal to the given option.
The last option:
2.3p - 14.1 = 6.4p -4
which is not equal to the given option.
Therefore equations 2.3p - 10.1 = 6.4p - 4 and 23p - 101 = 65p - 40 -p are the correct option.
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f(n)=-3n+7; find f(-8)
Answer:
f(-8) = 31
Step-by-step explanation:
f(-8) = -3(-8) + 7
= 24 + 7
= 31
The average daily attendance at the Lincoln School was 348 students during the month of March. If the month had 21 school days, what was the total attendance?
The total attendance for Lincoln school for month of March is 7308.
What is average attendance?
Divided by the total number of days in the ordinary school year, is the total number of days that students were present. One ADA(Avg. Daily attendance) would be the number of students who attend every day. The number of kids enrolled in each school and district, known as enrollment, is not the same as ADA.
Main Body:
So according to formula ,
Average daily attendance = Total attendance / total days of school
348 = total attendance/ 21
total attendance = 348* 21
= 7308
Hence total attendance is 7308.
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if you had to serve six persons equally from a standard 750-ml. bottle of champagne, how many oz. could you serve each of them?
If you were serving a metric standard 750 ml bottle of champagne to 6 people equally, you would need to pour 4.2 fl oz to each one of them to get 6 equal serving.
A bottle of champagne with a metric unit of volume of 750 ml divided equally among 6 people will give each of them a 125 ml serving of champagne by volume.
750/6=125
Converting metric system to imperial unit of volume of US fluid ounce, with 1 fl oz = 29.57 ml, you will get:
125/29.57=4.23
Hence you will be pouring each one of them 4.2 fl oz serving of champagne.
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show all work
An employee receives a 4% raise once per year. If the employee’s initial salary is $40,000, what will the employee’s salary be after 8 years?
(2 points –1 writing the exponential equation, 1 salary after 8 years)
Exponential equation S is 40,000(1.04)^8, and Salary after 8 years: S is $64,735.20.
What is Exponential equation?An exponential equation is an equation that contains a variable in the form of an exponent. It is used to solve problems involving exponential growth and decay. The equation has the form y = a × b^x, where "a" is the initial value, "b" is the base of the exponent, and "x" is the exponent. This equation can be used to find the value of y, given a value for x. Exponential equations are commonly used in fields such as mathematics, physics, economics, and biology.
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Reduce -34/87 to the lowest terms.
The value of the fraction -34/87 to the lowest term is still -34/87 as there's no common factor.
How to reduce to lowest term?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
To reduce to lowest term, divide the numerator and denominator by the greatest common factor to reduce a fraction to its simplest terms.
The steps involved are:
Divide the numerator (top number) and the denominator (bottom number) into prime factors.Remove any commonalities.Multiply the remaining numbers to get the numerator and denominator with the reduced numerator and denominator.In this case, there is no common factor and the value is still the same as -34/87.
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Use the value of the discriminant to determine whether the quadratic equation has two rational solutions, two irrational solutions, one repeated real solution, or two complex solutions that are not real.
3z² +3z +10=0
Choose the correct answer below.
O A. one repeated real solution
OB. two irrational solutions
OC. two rational solutions
OD. two complex solutions that are not real
Answer:
D
Step-by-step explanation:
discriminant = 9 - 4(10 * 3)
9 - 4 * 30
9 - 120 = -111
Is negative so the equation has two complex solutions