Need help with number 8 please
Answer:
B
Step-by-step explanation:
5x+2x=7x
4-1=3
The answer is 7x + 3
chris runs 2.3 miles every day of the week, except sunday. on sunday he only runs 2 miles. how many miles will he run in 2 weeks?
Answer:
He will run 31.6 miles in two weeks.
Step-by-step explanation:
6 days a week = 2.3 miles
6 days · 2 weeks = 12 days total running 2.3 miles
1 day a week = 2 miles
1 day · 2 weeks = 2 days total running 2 miles
(12 · 2.3) + (2 · 2)
27.6 + 4
31.6 miles
What rotation was applied to triangle DEF to create D’E’F’?
Answer:
90 degree Clockwise Rotation
Step-by-step explanation:
Look at the figure and its points. When you rotate the paper clockwise, you will see that D'E'F is in the same position as DEF.
Answer:
90 degree anti-clockwise rotation
Step-by-step explanation:
if you turn the paper anti-clockwise, u can see that DEF is turned into D'E'F.
A man 1.5 metres tall standing on top of a mountain 298.5m high observes the angles of depressions of two flying boats D and C to be 28 and 34 degrees respectively. Calculate the distance between the boats.
Pls I need urgent answer plss
Answer:
119.45 meters
Step-by-step explanation:
This question can be solved using one of the three trigonometric ratios. The height mentioned is 298.5 + 1.5 = 300 m and the angle of depression is 28 degrees for Boat D and 34 degrees for Boat C. It can be seen that the required distance is given by x feet, which is the distance between the two boats. This forms two right angled triangle, as it can be seen in the diagram. The perpendicular is given by 300 m, the base is the unknown, and the angles 28 degrees for boat A and 34 degrees for boat B is is given, as shown in the attached diagram. Therefore, the formula to be used is:
tan θ = Perpendicular/Base (For the distance between the mountain and Boat D)
Plugging in the values give:
tan 28 degrees = 300/d.
d = 300/tan 28.
d = 564.22 m (to the nearest hundredth).
tan θ = Perpendicular/Base (For the distance between the mountain and Boat C)
Plugging in the values give:
tan 34 degrees = 300/c.
c = 300/tan 34.
c = 444.77 m (to the nearest hundredth).
The difference between d and c will be x, i.e. that distance between the boats. So 564.22 - 444.77 = 119.45 meters (to the nearest hundredth).
Therefore, the boats are 119.45 meters apart from each other!!!
To calculate the distance between the two boats, we can use the concept of angles of depression and trigonometry. The distance to boat D is calculated using the tangent function with the angle of depression and the height of the observer. The same process is used to find the distance to boat C. The distance between the boats is then the difference between these two distances.
Explanation:To calculate the distance between the two boats, we can use the concept of angles of depression. Let's consider the boat D first. The angle of depression is the angle that the line of sight makes with the horizontal when looking down. In this case, the angle of depression for boat D is 28 degrees. Similarly, the angle of depression for boat C is 34 degrees.
Now, let's use trigonometry to find the distances. We can use the tangent function, which is the opposite side divided by the adjacent side. The opposite side represents the height difference between the observer and the boat, while the adjacent side represents the distance between the observer and the boat.
For boat D, we have:
tan(28 degrees) = opposite/adjacent
opposite = 1.5 m (height of the observer)
adjacent = distance between the observer and boat D
distance between the observer and boat D = 1.5 m / tan(28 degrees)
We can use the same process to find the distance between the observer and boat C:
distance between the observer and boat C = 1.5 m / tan(34 degrees)
Therefore, the distance between the boats is the difference between the distance to boat D and the distance to boat C.
One of the sides of a rectangle has length 7. Which of the following points, paired with (6,5), will make a side of this length?
Answer:
B (6,12)
Step-by-step explanation:
The distance from point A (6,5) to point B should be 7.
A- (6,5)-> (7,5) is 1 unit right
B- (6,5)-> (6,12) is 7 units up
C- (6,5)-> (6,7) is 2 units up
D- (6,5)-> (12,5) is 6 units up
A city that had 40,000 trees started losing them at a rate of 10 percent per year because of urbanization.
In approximately years, the number of trees in the city reduced to a quarter of the original amount. Hint: Model the situation as P = P0(1 − r)t.
Answer:
t = 13.1576 years
Step-by-step explanation:
The situation can be modeled as
P = Po.(1-r)^t
Where
t is the years transcurred
Po is the initial amount
r is the rate of change
Po = 40000
r = 10% equivalent to 0.1
Now
A quarter of the original amount
(1/4)*Po = Po.(1-r)^t
(1/4) = (0.9)^t
t = 13.1576
Please, see attached picture
Will give brainiest and 10 Points, NEED ANSWER ASAP!
Find the total area of the Regular Pyramid.
L.A=
Answer:
The total area is [tex]16\sqrt{3}\ units^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the regular pyramid is equal to the area of its four triangular faces
Each face is an equilateral triangle
so
Applying the law of sines
The surface area is equal to
[tex]SA=4[\frac{1}{2}b^{2}sin(60\°)][/tex]
we have
[tex]b=4\ units[/tex]
[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]
[tex]SA=4[\frac{1}{2}(4)^{2}\frac{\sqrt{3}}{2}][/tex]
[tex]SA=16\sqrt{3}\ units^{2}[/tex]
Answer:
16 sqrt 3
Step-by-step explanation:
Simplify 3 (x+2)- x + 8
Answer:
The answer is x = 7
Step-by-step explanation:
3(x+2) - x + 8
Open the bracket
3(x + 2) distribute
3x + 6
3x + 6 - x + 8
combine the like terms
3x - x + 8 + 6
2x + 14
Please mark me as brainliest
First you must distribute the 3 to the numbers inside the parentheses, which would be x and 2...
(3 * x) + (3 * 2) - x + 8
3x + 6 - x + 8
Now you must combine like terms. This means that first numbers with no variables go together. Then the numbers with the same variables must be combined...
no variable combination:
3x + 6 -x + 8
6 + 8 = 14
3x - x + 14
same variable combination:
3x - x + 14
3x - x = 2x
2x + 14
Hope this helped!
~Just a girl in love with Shawn Mendes
Determine if each number is a whole number, integer, or rational
number. Include all sets to which each number belongs.
4. -12.
5. 7/8
Final answer:
The number -12 is both an integer and a rational number, but not a whole number. The number 7/8 is a rational number but neither a whole number nor an integer.
Explanation:
We need to determine if each provided number belongs to the sets of whole numbers, integers, or rational numbers.
-12
-12 is an integer because it is a whole number that can be positive or negative, including zero. Since all integers are also rational numbers (they can be written as a ratio of integers, for example, -12 can be written as -12/1), -12 is also a rational number. However, it is not a whole number because whole numbers are non-negative integers (0, 1, 2, 3,...).
7/8
7/8 is a rational number because it is expressed as the ratio of two integers (7 and 8). It is not an integer nor a whole number because it is not a whole number without a fractional or decimal component.
A soccer ball kicked from the ground with an initial velocity of 32 ft/s is given by the function
h(t) = -16 + 321. When is the soccer ball moving through the air?
Answer:
In words the answer is between t=0 and t=2.
In interval notation the answer is (0,2)
In inequality notation the answer is 0<t<2
Big note: You should make sure the function I use what you meant.
Step-by-step explanation:
I hope the function is h(t)=-16t^2+32t because that is how I'm going to interpret it.
So if we can find when the ball is on the ground or has hit the ground (this is when h=0) then we can find when it is in the air which is between those 2 numbers.
0=-16t^2+32t
0=-16t(t-2)
So at t=0 and t=2
So the ball is in the air between t=0 and t=2
Interval notation (0,2)
Inequality notation 0<t<2
According to the question:
Make sure the function I use is what you intended, please.I'm going to interpret it as h(t)=-16t^2+32t, so I'm hoping that's the function.The ball is in the air between those two numbers, therefore if we can determine when it is on the ground or has hit the ground (when h=0), we can determine when it is in the air.0 = -16t^2+32t.
0 = -16t(t-2).
So, at t=0 and t=2.
Thus, between t=0 and t=2, the ball is in the air.
Periodic notation (0,2).
Inequality notation 0<t<2.
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Consider the two points A(9.7) and B(5,2).
What is the ratio of the vertical change from A to B to the horizontal change from A to B? In other words, what is the
slope?
What the answer
Answer:
The slope is [tex]m=\frac{5}{4}[/tex] or [tex]m=1.25[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(9,7)\ B(5,2)[/tex]
Substitute the values
[tex]m=\frac{2-7}{5-9}[/tex]
[tex]m=\frac{-5}{-4}[/tex]
[tex]m=\frac{5}{4}=1.25[/tex]
A solution of the equation f(x)=g(x) is the same as
Answer:
The solution of the equation f (x) = g (x) is the same as the coordinates of the intersection.
Exaple in the attachment.
f(x) = g(x) → x = -2, y = -1 or x = -1 and y = 0 or x = 1 and y = 2.
find the volume of a trianglular prism that has a triangular base of 14 and and a height of 17 with a prism height of 5 leave your answer in a0 cubic units WILL GIVE BRAINLIEST!
Answer:
Exact Form:
1190/ 3
Decimal Form:
396. 6
Mixed Number Form:
396 2 /3
Step-by-step explanation:
Final answer:
The volume of the triangular prism with a triangle base of 14 units and height of 17 units and a prism height of 5 units is 595 cubic units.
Explanation:
To find the volume of a triangular prism, we need to first find the area of the base triangle and then multiply it by the height of the prism. The formula for the volume of a triangular prism is given by V = (base area) imes (prism height). However, we need to be clear about what the given 14 and 17 represent. Assuming they stand for base and height of the triangle, respectively, the area of the base triangle is A = (1/2) imes base imes height = (1/2) imes 14 imes 17. Multiplying this area by the prism height of 5 units gives us the volume of the prism.
Calculating the base area: A = (1/2) imes 14 imes 17 = 119 square units. The volume is then V = 119 imes 5 = 595 cubic units. Therefore, the volume of the triangular prism is 595 cubic units.
Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3 x + 5. 1. k(x) = (3g + 5h)(x) 2. k(x) = (h - g)(x) 3. k(x) = (g + h)(x) 4. k(x) = (5g + 3h)(x) 5. k(x) = (3h - 5g)(x) 6. k(x) = (5h - 3g)(x)
Answer:
1. k(x) = (3g + 5h)(x) = -24x+40
2. k(x) = (h - g)(x) = 0
3. k(x) = (g + h)(x) = -6x+10
4. k(x) = (5g + 3h)(x) = -24x+40
5. k(x) = (3h - 5g)(x) = 6x-10
6. k(x) = (5h - 3g)(x) = 10-6x
Step-by-step explanation:
Given
h(x) = 5 - 3x
and
g(x) = -3 x + 5
1. k(x) = (3g + 5h)(x)
3*g(x) = 3(-3 x + 5)
=> -9x+15
5*h(x) = 5(5 - 3x)
=>25-15x
(3g + 5h)(x)=3*g(x)+5*h(x)
= -9x+15+25-15x
=-9x-15x+15+25
=-24x+40
2. k(x) = (h - g)(x)
(h - g)(x) = h(x) - g(x)
= 5 - 3x -(-3 x + 5)
=5-3x+3x-5
= 0
3. k(x) = (g + h)(x)
(g+h)x = g(x) + h(x)
= -3 x + 5 + 5 - 3x
= -6x+10
4. k(x) = (5g + 3h)(x)
5*g(x) = 5(-3 x + 5)
=-15x+25
3*h(x) = 3(5 - 3x)
=15-9x
(5g + 3h)(x) = 5*g(x) + 3*h(x)
= -15x+25+15-9x
= -15x-9x+25+15
=-24x+40
5. k(x) = (3h - 5g)(x)
(3h - 5g)(x) = 3*h(x)-5*g(x)
=15-9x-(-15x+25)
=15-9x+15x-25
=-9x+15x+15-25
=6x-10
6. k(x) = (5h - 3g)(x)
5*h(x)-3*g(x) = 25-15x - (-9x+15)
= 25-15x+9x-15
= 25-15-15x+9x
=10-6x
Answer:
1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x
2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10
3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x
4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x
5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x
6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x
The expression 2(1 + w) is used to calculate the perimeter of a rectangle, where I is length and w is width. If the length is ⅔ unit
and the width is ⅓
unit, what is the perimeter of the rectangle in units?
A: ⅔ unit
B: 1 unit
C: 1 ⅔ units
D: 2 units
PLEEEASEEEE HELLLPPPP FASTTTTT!!!!!
Answer: D: 2 units
Step-by-step explanation:
You may have mistaken the formula, as it's 2(l + w), not 1.
If we use this formula, we can say:
2([tex]\frac{2}{3} + \frac{1}{3}[/tex]) = 2(1) = 2
Therefore, the answer is 2 units.
Hope this helps! :^)
compute the probability of tossing a six-sided die and getting a 7
A triangular city lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420
feet on the third. Find the approximate measure of the largest angle formed by these streets.
Answer:
The approximate measure of the largest angle formed by these streets is [tex]99.2\°[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2}+b^{2} -2(a)(b)cos(C)[/tex]
In this problem we have
[tex]a=300\ ft[/tex]
[tex]b=250\ ft[/tex]
[tex]c=420\ ft[/tex] ----> is the greater side
substitute and solve for angle C
[tex]420^{2}=300^{2}+250^{2} -2(300)(250)cos(C)[/tex]
[tex]176,400=152,500 -150,000cos(C)[/tex]
[tex]cos(C)=[152,500-176,400]/150,000[/tex]
[tex]cos(C)=-0.1593[/tex]
[tex]C=arccos(-0.1593)=99.2\°[/tex]
The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? Amplitude = 1 foot; period = 12 hours; midline: y = 5 Amplitude = 2 feet; period = 6 hours; midline: y = 1 Amplitude = 2 feet; period = 12 hours; midline: y = 5
Answer:
The correct option is 1.
Step-by-step explanation:
The general cosine function is
[tex]y=A\cos (Bx+C)+D[/tex]
where, A is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, C is phase shift and D is midline.
It is given that the Chesapeake Bay tides vary between 4 feet and 6 feet. it means the minimum value is 4 and maximum value is 6.
Amplitude of the function is
[tex]Amplitude=\frac{Maximum-Minimum}{2}[/tex]
[tex]Amplitude=\frac{6-4}{2}[/tex]
[tex]Amplitude=1[/tex]
Therefore the amplitude of the function is y=5.
Midline of the function is
[tex]Mid line=\frac{Maximum+Minimum}{2}[/tex]
[tex]Mid line=\frac{6+4}{2}=5[/tex]
Therefore the midline of the function is y=5.
It completes a full cycle in 12 hours.
[tex]Period=12[/tex] hours
[tex]\frac{2\pi}{B}=12[/tex]
Period of the function is 12 hours. Therefore the correct option is 1.
Answer:
A. Amplitude = 1 foot; period = 12 hours; midline: y = 5
cube root of b to the 12 power
[tex]\sqrt[3]{b^{12}}=\sqrt[3]{(b^4)^3}=b^4[/tex]
The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people. The town's tax status will change once the population is below 6,000 people. Create an inequality that can be used to determine after how many years, t, the town's tax status will change, and use it to answer the question below.
Answer:
After 2.9 years the town's tax status will change
The towns tax status change within the next 3 years
Step-by-step explanation:
The question below is
Will the towns tax status change within the next 3 years ?
Let
y -----> the population of a small town
t ----> the number of years
we have a exponential function of the form
[tex]y=a(b)^{t}[/tex]
where
a is the initial value
b is the base
In this problem
[tex]a=9,400\ people[/tex]
[tex]b=100\%-14.3\%=85.7\%=85.7/100=0.857[/tex]
substitute
[tex]y=9,400(0.857)^{t}[/tex]
Remember that
The town's tax status will change once the population is below 6,000 people
so
The inequality that represent this situation is
[tex]9,400(0.857)^{t}< 6,000[/tex]
Solve for t
[tex](0.857)^{t}< 6,000/9,400[/tex]
Apply log both sides
[tex](t)log(0.857)< log(6,000/9,400)[/tex]
[tex]-0.067t< -0.1950[/tex]
Multiply by -1 both sides
[tex]0.067t > 0.1950[/tex]
[tex]t > 2.9\ years[/tex]
so
After 2.9 years the town's tax status will change
therefore
The answer is
Yes, the towns tax status change within the next 3 years
the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.
To find out after how many years the population of the town would decrease to below 6,000 people, we start with the current population and apply the annual exponential decrease. The population decreases at a rate of 14.3% each year, which means the remaining population each year is 85.7% (100% - 14.3%) of the previous year. Starting with a population of 9,400 people, we need to solve for t in the inequality 9400 × (0.857)^t < 6000. We take the natural logarithm of both sides to solve for t:
ln(9400 × (0.857)^t) < ln(6000)
t × ln(0.857) < ln(6000) - ln(9400)
t > (ln(6000)-ln(9400)) / ln(0.857)
Using a calculator, we find that:
t > 7.17
Therefore, the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.
17. In 2014, 16,674 earthquakes occurred world wide. Of these,
89.6% were minor tremors with magnitudes of 4.9 or less on
the Richter scale. How many minor earthquakes occurred in
the world in 2014? Round to the nearest whole. (Source: U.S.
Geological Survey National Earthquake Information Center)
Answer:
15836
Step-by-step explanation:
Formula
Minor Earthquakes = (%) * Total Earthquakes.
Givens
Minor Earthquakes = ??
% = 89.6
Total Earthquakes = 17674
Solution
Minor Earthquakes = 89.6 / 100 * 17674
Minor Earthquakes = 1583590.4/100
Minor Earthquakes = 15836
Answer: There are 14940 minor earthquakes occurred in the world in 2014.
Step-by-step explanation:
Since we have given that
Number of earthquakes occurred world wide = 16674
Percentage of minor tremors with magnitude of 4.9 or less = 89.6%
So, Number of minor earthquakes occurred in the world in 2014 is given by
[tex]\dfrac{89.6}{100}\times 16674\\\\=0.896\times 16674\\\\=14939.90[/tex]
Hence, there are 14940 minor earthquakes occurred in the world in 2014.
Write a general formula to describe the variation: x varies directly with y
Answer:
x veries directly to y means that
x=ky. k is solved for which is substituted into the equation.
Final answer:
To describe the situation where x varies directly with y, one uses the equation y = kx, where k is the proportionality constant signifying the ratio between y and x.
Explanation:
The student is asking for a general formula to describe the situation where x varies directly with y. When two quantities vary directly, as one increases, the other increases as well, and the relationship between them can be described by a directly proportional relationship. This can be expressed with the equation y = kx, where k is the proportionality constant. The value of k remains constant within any given relationship, indicating how much y changes in response to a change in x. If y is plotted against x on a graph, you would obtain a straight line that passes through the origin, reflecting the direct proportionality.
You decide to practice your soccer goal-scoring skills by drawing the outline of a soccer goal for players up to 12 years old(21 by 7 feet) on a wall that measure 36 by 9 feet. Unfortunately, you are a soccer rookie so your shots tend to bounce off the wall randomly. The probability that you actually hit the target goal is
Heyyyyyyyyyyyy
12 is to 7 is the answer
Idlkkk
The probability of hitting the soccer goal drawn onto the wall is approximately 45%, given that the soccer shots are completely random.
Explanation:The subject of this question is probability, which is part of mathematics. The scenario describes a soccer training drill where the aim is to hit a goal that has been drawn onto a wall. The goal's dimensions are 21 feet by 7 feet, and the wall's dimensions are 36 feet by 9 feet.
In order to calculate the probability of hitting the target goal, we first need to calculate the area of the goal and the area of the wall. The area of the goal is obtained by multiplying the length by the height (21ft x 7ft = 147ft^2). Similarly, the area of the wall is 36ft x 9ft = 324ft^2.
Now that we have the areas, the probability of hitting the goal can be calculated by dividing the area of the goal by the area of the wall. That is, 147ft^2/324ft^2 = 0.4537, or approximately 0.45 or 45% when converted into a percentage.
Therefore, given that the shots are completely random, there is a 45% probability that the soccer ball will hit the drawn goal on the wall.
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Which are harder in geometry? Theorems or proofs? Explain why
The difficulty between theorems and proofs in geometry is subjective. Theorems are proven true statements, while proofs are the logical processes used to establish the truth of theorems. Students may find one harder than the other depending on their individual abilities and understanding.
In the study of geometry, students often ask which are harder: theorems or proofs. To address this, it's important to understand the nature of both. A theorem is a statement that has been proven to be true through a logical sequence of statements, starting from agreed-upon assumptions, known as axioms. The Pythagorean Theorem, for instance, states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem provides a consistent and reliable outcome as long as the arithmetic is carried out correctly.
On the other hand, a proof is the process by which a theorem is shown to be true. Proofs involve a series of logical deductions from accepted principles and previously proven theorems. They are essentially the 'work' or argument that establishes the truth of a theorem. In any proof, each step must logically follow from the previous ones based on established geometric postulates and existing theorems. Therefore, a proof can be viewed as a bridge that connects the basic assumptions of geometry to the theorem being proven.
Whether theorems or proofs are harder is subjective and depends on the student's strengths. Some students find memorizing theorems challenging, while others may struggle with the logical sequence and creativity required to craft proofs. Nonetheless, the study of geometry contributes valuable reasoning skills and knowledge that connects fundamental truths of mathematics to practical applications in the real world, like engineering and physics.
Can sumone plzhelp..Apply the distributive property to factor out the greatest common factor of all three terms .
9a-18b+21c=
Answer:
3(3a - 6b + 7c )
Step-by-step explanation:
The greatest common factor of 9, 18 and 21 is 3
Factor out 3 from each term
9a - 18b + 21c
= 3(3a - 6b + 7c) ← in factored form
Answer:
3(3a - 6b + 7c)
Step-by-step explanation:
Write each term as a multiplication of its factors. Then see which factors are in common to all terms.
9a - 18b + 21c =
= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c
The common factors are shown below in bold:
= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c
The only common factor is 3.
Now use the distributive property to factor out a 3.
= 3(3 * a - 2 * 3 * b + 7 * c)
Now multiply each term in parentheses again.
= 3(3a - 6b + 7c)
What is the remainder in the synthetic division problem below?
Answer: 9
Step-by-step explanation:
Answer:
the remainder is 9
Step-by-step explanation:
find the remainder in the synthetic division
1 4 6 -1
Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder
1 4 6 -1
0 4 10
--------------------------------
4 10 9 -> Remainder
So the remainder is 9
HELP PLEASEEEEEEEEEEEEEEEEEEE
Answer:
counterclockwise rotationclockwise rotation90 degrees rotation270 degrees rotationValue A rent a car a luxury car at a daily rate of $36.09 plus 5 cents per mile. A business person is allotted $120 for a car rental each day. How many miles can the business person travel on the $120?
Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x as the independent variable?
Answer:
f(x) = 6x + 9
Step-by-step explanation:
Given
y - 6x - 9 = 0
Express the equation with y as the subject
Add 6x + 9 to both sides
y = 6x + 9
To express in functional notation let y = f(x), hence
f(x) = 6x + 9
Answer:
A. [tex]f(x)=6x+9[/tex]
Step-by-step explanation:
We have been given an equation [tex]y-6x-9=0[/tex]. We are asked to write our given equation in function notation with x as the independent variable.
First of all, we will convert our given equation in slope-intercept form by separating y on one side of equation.
[tex]y-6x-9=0[/tex]
[tex]y-6x+6x-9=0+6x[/tex]
[tex]y-9=6x[/tex]
[tex]y-9+9=6x+9[/tex]
[tex]y=6x+9[/tex]
Now, we will replace [tex]y[/tex] with [tex]f(x)[/tex].
[tex]f(x)=6x+9[/tex]
Therefore, our required function would be [tex]f(x)=6x+9[/tex] and option A is the correct choice.
question 2-5 please
Answer:
1. [tex]m=1\frac{1}{14}[/tex]
2. undefined
3. [tex]-6[/tex].
4. [tex]2\frac{1}{3}[/tex].
5. [tex]2[/tex].
6. [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
1. The required line passes through [tex](3,0),(-11,-15)[/tex]. The slope of the line joining the points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]
Either of them yields the same result.
Substitute [tex]x_1=3,y_1=0,x_2=-11,y_2=-15[/tex] into the first formula to get,
[tex]m=\frac{-15-0}{-11-3}[/tex] [tex]\implies m=\frac{-15}{-14}=\frac{15}{14}[/tex]
You can write this as a mixed number to obtain:
[tex]\implies m=1\frac{1}{14}[/tex]
2. The given line passes through [tex](4,-8),(4,13)[/tex].
Observe that the first coordinates are the same for both points. This implies that, the line is vertical.
The slope of all vertical lines are undefined.
3. The average rate of change of the function [tex]y=f(x)[/tex] on the interval [tex][a,b]\:\:or\:\:a\le x\le b[/tex] is given by:
[tex]ARC=\frac{f(b)-f(a)}{b-a}[/tex].
The given function is [tex]f(x)=x^2-4x[/tex]
[tex]f(-2)=(-2)^2-4(-2)=12[/tex]
[tex]f(4)=(4)^2-4(4)=0[/tex]
[tex]ARC=\frac{f(4)-f(-2)}{4--2}[/tex].
[tex]ARC=\frac{0-12}{6}=-6[/tex].
4. The given function is [tex]f(x)=2^x-1[/tex]
[tex]f(0)=2^0-1=0[/tex]
[tex]f(3)=2^3-1=7[/tex]
[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].
[tex]ARC=\frac{7-0}{3}=2\frac{1}{3}[/tex].
5. From the graph
[tex]f(3)=7,f(0)=1[/tex]
[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].
[tex]ARC=\frac{7-1}{3}[/tex].
[tex]ARC=\frac{6}{3}=2[/tex].
6. The given equation is :
[tex]2y-7x=-4[/tex]
Add [tex]7x[/tex] to both sides.
[tex]2y=7x-4[/tex]
Divide through by 2.
[tex]y=\frac{7}{2}x-2[/tex]
Compare this function to [tex]y=mx+b[/tex]
The slope is [tex]m=\frac{7}{2}[/tex]