Given the functions f(x) = –4ˣ + 5 and g(x) = x³ + x² – 4x + 5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
Answers
Answer:
f(x) is an exponential functiong(x) is a polynomial function of degree 3Key common features: same domain, both have one x-intercept and one y-intercept.Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]
Function f(x)This is an exponential function.
An exponential function includes a real number with an exponent containing a variable.
x-intercept (when y = 0):
[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]
Therefore, the x-intercept of f(x) is (1.16, 0).
y-intercept (when x = 0):
[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]
Therefore, the y-intercept of f(x) is (0, 6).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]
Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it. Therefore:
Domain: (-∞, ∞)Range: (-∞, 5)Function g(x)This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).
A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.
x-intercept (when y = 0):
There is only one x-intercept of function g(x). It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.
From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.
y-intercept (when x = 0):
[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]
Therefore, the y-intercept of g(x) is (0, 5).
End behavior
[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]
[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]
Therefore:
Domain: (-∞, ∞)Range: (-∞, ∞)Conclusion
Key features both functions have in common:
One x-intercept (though not the same)One y-intercept (though not the same)Same unrestricted domain: (-∞, ∞)
Related Questions
Rewrit using factored form solve using zero product property
Answers
Answer:
Step-by-step explanation:
a. d^2 - 7d + 6 = 0
(d - 1)(d - 6) = 0
d - 1 = 0, d - 6 = 0 therefore:
d = 1, 6.
b, x^2 + 18x + 81 = 0
(x + 9)(x + 9) = 0
x = -9 multiplicity 2.
c u^2 + 7u - 60 = 0
(u + 12)(u - 5) = 0
u = -12, 5.
If two cards are drawn from a deck, what is the probability that exactly one of the cards will be a face card?
Answers
The probability of getting exactly one face card is 0.72.
According to the questions two cards are drawn from a deck.
Since, we know that
Total number of cards in a deck = 52
Total number of face cards = 3 × 4 = 12
So, the number of ways of selecting 2 cards from a deck = [tex]^{52} C_{2}[/tex]
And, the total number of ways of getting exactly one face cards
= [tex]^{12} C_{1} \times ^{40} C_{1}[/tex] + [tex]^{40} C_{1} \times ^{12} C_{1}[/tex]
= 2[tex]^{40} C_{1} \times ^{12} C_{1}[/tex]
Therefore, the probability of getting exactly one face card
= [tex]\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }[/tex]
[tex]= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }[/tex]
[tex]= \frac{2(40\times 12)}{26\times 51}[/tex]
[tex]=\frac{2\times 480}{1326}[/tex]
= 0.72
Hence, the probability of getting exactly one face card is 0.72.
Find out more information about probability here:
https://brainly.com/question/13293035
#SPJ4
2. G.CO.9 Look at the diagram below showing two parallel lines being cut
by two transversals. If m24 = 70 and m412 = 130, which of the following
statements are true? SELECT ALL THAT APPLY.
Answers
The statements that are true regarding the angles formed by the transversal and parallel lines are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
How to Find the Angles Formed by a Transversal and Parallel Lines?Given the following angle measures formed when two parallel lines ( being cut by two transversals:
m∠4 = 70° m∠12 = 130°Using relevant theorems, let's determine which of the statements are true:
Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.
m∠4 = m∠1
m∠1 = 70°.
m∠2 = 180 - m∠4 [linear angles theorem]
m∠2 = 180 - 70
m∠2 = 110°
m∠6 = m∠4 [base on the alternate interior angles theorem]
m∠6 = 70°.
m∠9 = 180 - m∠12 [based on the linear angles theorem]
m∠9 = 180 - 130
m∠9 = 50°
m∠16 = m∠12 [based on the corresponding angles theorem]
m∠16 = 130°
The statements that are true are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
Learn more about transversal and parallel lines on:
https://brainly.com/question/24607467
#SPJ1
A set of eight cards were labeled as M, U, L, T, I, P, L, Y. What is the sample space for choosing one card?
S = {I, U, Y}
S = {M, L, T, P}
S = {I, L, M, P, T, U, Y}
S = {I, L, L, M, P, T, U, Y}
Question 2(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. List the sample space when choosing one marble.
S = {1, 2, 3, 4, 5}
S = {red, blue, green, yellow}
S = (g, r, b, y, o}
S = (green, blue, yellow, orange}
Question 3(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A four-part spinner is spun once.
spinner with four parts labeled W, X, Y, and Z
List the sample space for the experiment.
S = {X, Y, Z}
S = {W, Z, Z}
S = {W, Y, Y, Z}
S = {W, X, Y, Z}
Question 4(Multiple Choice Worth 2 points)
(Sample Spaces LC)
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces MC)
Julia had a bag filled with gumballs. There were 2 lemon-lime, 3 watermelon, and 5 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = 2, 3, 5
Sample space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
Question 6 (Essay Worth 4 points)
(Sample Spaces HC)
Part A: Create your own experiment with 5 or more possible outcomes. (2 points)
Part B: Create a sample space for a single experiment and explain how you determined the sample space. (2 points)
Answers
The correct answers to the sample space illustrated will be:
S = {I, L, L, M, P, T, U, Y}.
S = {g, r, b, y, o}.
S = {W, X, Y, Z}.
Flipping a fair, two-sided coin.
Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.
S = {Joy, Bob, Ben, Peter, John}
How to explain the probability?A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. The sample space when choosing one marble will be S = {g, r, b, y, o}.
A four-part spinner is spun once and the spinner with four parts labeled W, X, Y, and Z. The sample space for the experiment is S = {W, X, Y, Z}.
The event will have a sample space of S = {h, t} is the flipping a fair, two-sided coin.
The correct sample space for the gumballs in her bag will be sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.
My experiment with 5 or more possible outcomes will be that a teacher wants to randomly give one of his give students a pack of chocolate.
The sample space for the experiment will be based on their names. This will be S = (Joy, Bob, Ben, Peter, John).
Learn more about sample space on:
brainly.com/question/10558496
#SPJ1
Which point is a solution to the system of inequalities graphed here? y ≤ 2x 2 y ≥ -5x 4
Answers
The point that is a solution to the system of inequalities is (5, 0)
How to determine the points on the solution?The system of inequalities is given as:
y ≤ 2x + 2
y ≥ -5x + 4
Next, we test the given options.
From the list of options, we have
(x, y) = (5, 0)
Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4
y ≤ 2x + 2
0 ≤ 2 * 5 + 2
0 ≤ 12 -- this is true
y ≥ -5x + 4
0 ≥ -5 * 5 + 4
0 ≥ -21 -- this is true
Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)
Read more about system of inequalities at:
https://brainly.com/question/24372553
#SPJ1
Complete question
Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2
y ≥ -5x + 4
A. (1,6)
B. (-6,0)
C. (0,5)
D. (5,0)
A legend says that a tower of hanoi puzzle with 64 discs is being solved, one move per
second. how long will it take to solve this puzzle? explain how you know.
Answers
It will take 585 billion years to solve the puzzle tower of Hanoi puzzle.
What is hanoi of tower?
The Tower of Hanoi is a mathematical game or puzzle that uses three rods and a number of disks that can slide onto any rod. It is also known as The Problem of the Benares Temple, the Tower of Brahma, Lucas' Tower, or simply the pyramid puzzle. The disks are stacked on one rod at the start of the problem, the smallest at the top and roughly forming a conical shape.
Using the Tower of Hanoi as little as possible
In one version of the problem, 64 golden disks are being used by Brahmin priests to solve it.
Minimum moves required if you had 64 golden disks [tex]=2^{64}-1[/tex]
The problem would take around 585 billion years to solve if every move took a single second.
To know more about the tower of Hanoi
https://brainly.com/question/13045854
#SPJ4
Suppose we want to choose 5 letters, without replacement, from 16 distinct letters.
(a) If the order of the choices is taken into consideration, how many ways can this be done?
(b) If the order of the choices is not taken into consideration, how many ways can this be done?
Answers
Answer: Your answers are
A. 1, 287 ways
B. 154,440 ways
Hope this helped :D
Please mark me brainliest
(n - 1)!, where n = 4
Answers
Answer:
6
Step-by-step explanation:
Original Equation
(n-1)!
Plug in 4 as n
(4-1)!
Subtract
(3)!
Rewrite using definition of factorial: [tex]a! = a*(a-1)*(a-2)....*1[/tex]
3! = 3*2*1
You don't really have to write the 1, since it doesn't change the value
6
Find an equation for the conic that satisfies the given conditions. parabola, focus (−8, 0), directrix x = 2
Answers
The equation of the given parabola is y2=−20(x+3)
A parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
In general in a parabola, if we have
(y−n)2=4p(x−m),
then the vertex is (m,n)
The axis of symmetry is y=m
The focus is (p+m,n)
The directrix is x=m−p.
Hence, for the given case
p+m=−8
n=0
m−p=2
⇒n=0
m=−3
p=−5
So, the answer will be y2=−20(x+3)
For more information about parabola, visit
https://brainly.com/question/4061870
#SPJ4
How do I rewrite 1/4 book 1/3 hour as a unit rate?
Answers
The unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.
Unit rateUnit rate is the rate of a quantity in terms of another quantity per unit.
Number of books = 1/4Number of hours = 1/3Unit rate(books per hour) = Number of books / Number of hours
= 1/4 ÷ 1/3
= 1/4 × 3/1
= (1×3) / (4×1)
= 3/4 books per hour
Therefore, the unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.
Learn more about unit rate:
https://brainly.com/question/4895463
#SPJ1
What is the value of x?
w
t
105°
80°
Answers
Answer:
x = 75°Step-by-step explanation:
Opposite angles in a cyclic quadrilateral are supplementary.
Applicationx° = 180° -105°
x° = 75°
__
The value of the other angle is similarly found:
w° = 180° -80°
w° = 100°
__
Additional comment
This result comes from the inscribed angle theorem. That theorem tells you the measure of the inscribed angle is half the measure of the intercepted arc.
The opposite angles of a cyclic quadrilateral intercept the circle at the same two points, dividing the total 360° circle into two parts. Each angle has a measure equal to half its corresponding arc, so the total of the two angles is half the total of the two arcs: 360°/2 = 180°. The angles are supplementary.
Find an equation for the conic that satisfies the given conditions. ellipse, foci (±2, 0), vertices (±5, 0)
Answers
The equation of the ellipse having foci (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].
Given the foci of ellipse is (±2,0) and vertices (±5,0).
We are required to find the equation of ellipse having foci (±2,0) and vertices (±5,0).
Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables looks like ax+by=c.
Equation of ellipse is as under:
[tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex],where a is the semi major axis.
We have been given that a=5, c=2.
We know that [tex]c^{2} =a^{2} -b^{2}[/tex]
We have to find the value of b.
b=[tex]\sqrt{a^{2} -c^{2} }[/tex]
=[tex]\sqrt{5^{2} -2^{2} }[/tex]
=[tex]\sqrt{25-4}[/tex]
=[tex]\sqrt{21}[/tex]
Using the values of a and b in the equation [tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex]
[tex]x^{2} /(2)^{2} +y^{2}/\sqrt{21} ^{2} =1[/tex]
[tex]x^{2} /4+y^{2} /21=1[/tex]
Hence the equation of the ellipse having foci (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].
Learn more about ellipse at https://brainly.com/question/16904744
#SPJ4
What is the quotient of the rational expression below?
3x+1 x-7
x+8 5x
O A.
O B.
O C.
O D.
3x² + x
x²+x-56
15x² +5x
x² +15x-56
15x² +5x
x²+x-56
15x² +1
x²+x-56
Answers
Answer: C
Step-by-step explanation:
[tex]\frac{3x+1}{x+8} \div \frac{x-7}{5x}\\\\=\frac{3x+1}{x+8} \times \frac{5x}{x-7}\\\\=\frac{5x(3x+1)}{(x+8)(x-7)}\\\\=\frac{15x^2 +5x}{x^2 +x-56}[/tex]
5x-2y=10
4y+20=10x
Solving systemd
Answers
Answer:
The answer is x=2 and y=0.
Step-by-step explanation:
The given Equations are:
5x-2y=10 ----------------- (i)
4y+20=10x ----------------- (ii)
From equation find the value of x, that is:
5x=10+2y (Obtained By adding 2y on both side of Equation (i))
Next divide with 5 on both side to get x:
x=(10+2y)/5 ------------------ (iii)
Put this value of x in equation (ii):
4y+20=10((10+2y)/5)
Simplifying the above equation:
4y+20=2(10+2y)
4y+20=20+4y
From the above equation the solution of y is not possible.
We can make it 0. So,
y=0
Put this value of y in equation (iii), to get value of x:
x=(10+2(0))/5
x=(10+0)/5
x=10/5
x=2
Hey help mee if you solve it you are intelligent // what number is car park
Answers
Answer: The answer is 87. when you look at the picture each number is one number apart from each other like look at
86, 87, 88, 89, 90, 91
85 + 1 = 86
86 + 1 = 87
87 + 1 = 88
89 + 1 = 90
90 + 1 = 91
Step-by-step explanation:
Enter the correct answer in the box. in triangle abc, the side lengths are ab = 13, ac = 21, and bc = x. write a compound inequality that represents the range of possible values for x.
Answers
The range of possible values should be (7,34), i.e 7 < x < 34.
The answer must be more noteworthy than 7, else the two sides are less than or rise to to the third. That triangle is outlandish. The reply must moreover be less than 34, since at that point the two other sides would rise to the third, making an impossible triangle.
By the property of triangle, Sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
To prove above propert, let us assume a ΔABC
extend AB to D in such a way that AD=AC.
In ΔDBC, as the angles opposite to equal sides are always equal, so,
∠ADC=∠ACD
so,
∠BCD>∠BDC
As the sides opposite to the greater angle is longer, so,
BD>BC
AB+AD>BC
Since AD=AC, then,
AB+AC>BC
Hence, sum of two sides of a triangle is always greater than the third side.
To learn more about triangles from the given link
https://brainly.com/question/2644832
#SPJ4
Answer:
7 < x < 34
Step-by-step explanation:
A 3.0-kg ball moving eastward at 4.0 m/s suddenly collides with and sticks to a 5.0-kg ball moving northward at 3.0 m/s. what is the magnitude of the momentum of this system just after the collision?
Answers
Magnitude of the momentum of this system just after the collision = 19.2Kgm/s
What is law of conservation of momentum?Law of conservation of momentum states that the total momentum after the collision must be equal to the total momentum before the collision.
The momentum of each ball is given by:
p = mv
where m is the mass of the ball and v its velocity.
The momentum of ball 1 is:
p = mv
= (3.0 kg)(4.0 m/s)
= 12.0 kg m/s in the eastward direction
The momentum of ball 2 is:
p = mv
= (5.0 kg)(3.0 m/s)
= 15.0 kg m/s in the northward direction
The two momenta are in perpendicular directions, so the magnitude of the total momentum can be found as:
[tex]p = \sqrt{p1^{2} +p2^{2} }[/tex]
[tex]p = \sqrt{12^{2} +15^{2} }\\p = \sqrt{144 + 225} \\p = \sqrt{369}\\ p = 19.2 kgm/s[/tex]
and due to the law of conservation of the momentum, this is also equal to the total momentum after the collision.
To learn more about law of conservation of momentum from the given link
https://brainly.com/question/12773641
#SPJ4
Use theorem 9. 11 to determine the convergence or divergence of the p-series. 1 1 6 32 1 6 243 1 6 1024 1 6 3125. .
Answers
The given series is diverges according to the P Test.
According to the statement
we have given that the a series and we have to find that the those series is a converges or diverges.
So, For this purpose, we know that the
P-series test to say whether or not the series converges.
So, The given series is
[tex]1 + 1/\sqrt{32} + 1/\sqrt[3]{243 } + 1/\sqrt[4]{1024} + 1/\sqrt[5]{3125}[/tex]
And then
The value of P becomes P = 5/6 < 1 when we find it using the p series test.
Hence, the p-series diverges
Because according to the p series test, The series converges if, and only if, the power satisfies p>1.
And diverges if, and only if, the power satisfies p<1.
So, The given series is diverges according to the P Test.
Learn more about Convergence and Divergence here
https://brainly.com/question/4730059
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5.
#SPJ4
What is the equation for the line of best fit on the scatter plot below?
Answers
We've got a negative slope, but it doesn't look steep enough to go through 6 on the y-axis.
So, it's the last option:
y = - 1.25x + 5.75
Hope this helps!
Towns A, B, and C lie on a straight line, as shown below. Jack and Arthur start at Town B and drive for an hour from Town B to Town C, where they stop for an hour to eat lunch. Which of the following graphs could represent their distance from Town A during these two hours?
Answers
The situation described by the distance from Town A is the first graph.
Given that cities A,B and C are on straight line.
We are required to find the graph appropriate the given situation.
Distance is basically the measurement of how far two things,places are located.It can be measurement from one point to another .
On the first hour,they leave town B to town C moving farther from Town A,hence the distance is increasing on the first hour.
On the second hour they stop for lunch,meaning that the distance remains constant at the point, it was at the end of the first hour.
Hence if towns A,B C lie on a straight line and Jack and Arthur start at town B and drive for an hour from Town B to Town C then the distance shown from Town A during these two hours is first graph.
Learn more about distance at https://brainly.com/question/2854969
#SPJ1
Consider the exponential function g(x) = 1,296 x .
Find the output values for x-values x = –1.75, –1, –0.25, 0, 0.25, 0.50, 0.75, and 1.
Answers
The values associated to the exponential function are listed below:
g(- 1.75) = 3.572 × 10⁻⁶g(- 1) = 7.716 × 10⁻⁴g(- 0.25) = 0.167g(0) = 1g(0.25) = 6g(0.50) = 36g(0.75) = 216g(1) = 1 296How to evaluate an exponential function
Herein we have the exponential function [tex]g(x) = 1\,296^{x}[/tex], which has to be evaluated, that is, replacing the variable x by constants and make use of algebra properties until result is found.
g(- 1.75) = 3.572 × 10⁻⁶
g(- 1) = 7.716 × 10⁻⁴
g(- 0.25) = 0.167
g(0) = 1
g(0.25) = 6
g(0.50) = 36
g(0.75) = 216
g(1) = 1 296
To learn more on exponential functions: https://brainly.com/question/11487261
#SPJ1
Assuming brokerage fees of $6000, calculate the amount of cash needed to retire baldwin's 12. 4s2028 bond early
Answers
The amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.
How to calculate the cash?It should be noted that from the information given, we are to calculate the amount of cash needed to retire baldwin's bond early based on the brokerage.
This will be:
= 6000 + (5756951 × 94.18/100)
= 6000 + 5421896.45
= 5427896
Therefore, the amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.
Learn more about brokerage on:
brainly.com/question/14898119
#SPJ1
If the store has only 12 red balloons and only 8 blue balloons but at least 29 of each other color of balloon, how many combinations of balloons can be chosen?
Answers
The number of combinations of balloons that can be chosen is 1716.
Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them.
Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.
Number of red balloons = 12
Number of blue balloons = 8
First, we figure out how to choose from 13 red and 9 blue balloons.
There are 7 balloons left out of the 29 total (i.e. 29 - 13 - 9)
So, n = 7+7-1
n = 13
r = 7
Number of combinations of balloons = [tex]_{13} C_{7}[/tex]
= 13!/(13-7)!7!
= 13!/6!7!
= 1716
Learn more about combinations here:
https://brainly.com/question/11732255
#SPJ1
On a certain day, the temperature in Bismarck, North Dakota, was below 4∘F. Write an inequality to describe the possible temperatures. Let t represent the temperature.
Answers
The inequality to describe the possible temperature in Bismarck, North Dakota given that t represent temperature is t < 4°F
InequalityThe inequality signs are;
Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤Let
Temperature = tTemperature in Bismarck, North Dakota, was below 4∘F.Below in inequality sign means less than <So
t < 4°F in Bismarck, North Dakota
This means, temperature in Bismarck, North Dakota is less than 4°F
Therefore, t < 4°F is the inequality to represent temperature in Bismarck, North Dakota.
Learn more about inequality:
https://brainly.com/question/25275758
#SPJ1
A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.
65% of the 800 students at North High School ride the bus. How many students ride the bus?
Answers
Answer:
800÷100 = 8
65×8=520
[tex]\frac{520}{800}[/tex]
another way:
100%-65%=35%
35% = 0.35
800×0.35= 280
800-280=520
another way:
65% = 0.65
0.65×800=520
Hope it helped! :)
Louise, Tammy, Delores, and Sheryl score 78 points total in the tennis matches they play. They score a consecutive number of points from smallest to greatest in respect to the order of the names mentioned. How many points does Louise score?
Answers
[tex]\huge\boxed{18\ \text{points}}[/tex]
We'll represent Louise's, Tammy's, Delores's, and Sheryl's point values with [tex]x[/tex], [tex]x+1[/tex], [tex]x+2[/tex], and [tex]x+3[/tex] respectively since each one is 1 point more than the last.
Add all of these values up and set it all equal to [tex]78[/tex].
[tex]x+x+1+x+2+x+3=78[/tex]
Now, simplify.
[tex]4x+6=78[/tex]
Subtract [tex]6[/tex] on both sides.
[tex]\begin{aligned}4x+6-6&=78-6\\4x&=72\end{aligned}[/tex]
Divide both sides by [tex]4[/tex].
[tex]\begin{aligned}\frac{4x}{4}&=\frac{72}{4}\\x&=\boxed{18}\end{aligned}[/tex]
Since Louise's score is [tex]x[/tex], the answer is [tex]18[/tex].
Double-checkingTo verify our answer, add the point totals [tex]18[/tex], [tex]19[/tex], [tex]20[/tex], and [tex]21[/tex].
This equals [tex]78[/tex], so we can be sure the answer is correct.
Solve each pair of simultaneous equations by elimination method.
a) 2x+3y-1=0
5x+2y+3=0
Answers
2x = -3y + 1
5x = -2y -3
now times the answers to get the lcd
(2x = -3y + 1) x 5
10x = -15y + 5
(5x = -2y -3) 2
10x = -4y -6
now that they are equal to the same number:
-15y + 5 = -4y -6
-15y + 4y = -6 -5
-11y = -11
y = 1
now to find x we substitute y
2x = -3y + 1
2x = -3(1) + 1
2x = -3 + 1
2x = -2
x = -1
Answer:
x = -1
y = 1
Step-by-step explanation:
PART I: Find the y-valueGiven expressions
1) 2x + 3y - 1 = 0
2) 5x + 2y + 3 = 0
Add 1 on both sides of the 1) equation:
2x + 3y - 1 + 1 = 0 + 1
2x + 3y = 1
Subtract 3 on both sides of the 2) equation:
5x + 2y + 3 - 3 = 0 - 3
5x + 2y = -3
Current System
1) 2x + 3y = 1
2) 5x + 2y = -3
Multiply 2.5 on both sides of the 1) equation
(2.5) 2x + (2.5) 3y = (2.5) 1
5x + 7.5y = 2.5
Current System
1) 5x + 7.5y = 2.5
2) 5x + 2y = -3
Subtract 2) equation from 1) equation
(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)
Get rid of the parenthesis
5x + 7.5y - 5x - 2y = 2.5 + 3
Combine like terms
5x - 5x + 7.5y - 2y = 5.5
0 + 5.5y = 5.5
5.5y = 5.5
Divide 5.5 on both sides
5.5y / 5.5 = 5.5 / 5.5
[tex]\boxed{y=1}[/tex]
PART II: Find the x-valueSubstitute the y-value back to one of the equations to find the x-value
2x + 3y - 1 = 0
2x + 3(1) - 1 = 0
Combine like terms
2x + 3 - 1 = 0
2x + 2 = 0
Subtract 2 on both sides
2x + 2 - 2 = 0 - 2
2x = -2
Divide 2 on both sides
2x / 2 = -2 / 2
[tex]\boxed{x=-1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Point C is at (-9, -2) and point M is at (-1, 4). Point M
is the midpoint of the line segment whose endpoints
are C and D.
What are the coordinates of endpoint D?
Answers
Answer:
The coordinates of D is (7, 10)
Explanation:
Let the coordinates of endpoint D be (x, y)
Mid-point formula:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Applying formula:
[tex]\sf (-1, \:4) = (\dfrac{-9+ x}{2},\: \dfrac{-2+y}{2} )[/tex]
Comparing found:
[tex]\sf -1 =\dfrac{-9+ x}{2} \quad and \quad \: 4 = \dfrac{-2+y}{2}[/tex]
[tex]\sf 2(-1)+9 =x \quad and \quad \: 2(4)+2 =y[/tex]
[tex]\sf x = 7 \quad and \quad \: y = 10[/tex]
So, coordinates of D is (7, 10)
The answer is (7, 10).
Remember the midpoint formula : [tex]\boxed {M = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})}[/tex]
Finding the x coordinate of D
x = (x₁ + x₂) ÷ 2-1 = (-9 + x₂) ÷ 2-2 = -9 + x₂x₂ = 7Finding the y coordinate at D
y = (y₁ + y₂) ÷ 24 = (-2 + y₂) ÷ 28 = -2 + y₂y₂ = 10A map has a scale of 1cm:4km the actual distance between the two cities is 52km. What is the distance between the two cities on the map
Answers
Answer:
13cm
Step-by-step explanation:
Given the map scale:
1cm on the map : 4km actual distance
4km actual distance : 1cm on the map
1km actual distance : [tex]\frac{1}{4} =0.25cm[/tex] on the map
Therefore,
52km actual distance = 0.25 * 52 = 13cm
Simplify the expression to a single numerical value. a. 144 b. 432 c. 900 d. 5,184
Answers
The correct option is: (b)
=432.
What is simplification?By employing multiple processes, simplification refers to reducing the expression to a simpler form. Approximation is the process of making something less complicated and hence easier to accomplish or understand, or the object that arises from this process. The mathematical formula is simplified to its nearest value but is not exactly correct.
What is the simplified equation?Therefore, we must follow the order listed above when simplifying expressions. In the example before, we divide 8 by 4 and then add the result to 12 because, according to BODMAS, division (D) comes before multiples (M).
[tex]$3 \cdot 2^{3} \cdot 2 \cdot 3^{2}Calculate exponents $2^{3}: 8$$$=3 \cdot 8 \cdot 2 \cdot 3^{2}$$Calculate exponents $3^{2}: 9$$$=3 \cdot 8 \cdot 2 \cdot 9$$ $3 \cdot 8 \cdot 2 \cdot 9= 432$$$=432$$[/tex]
So. the value will be = 432
To know more about simplification visit:
https://brainly.com/question/1511685
#SPJ4
I understand that the question you are looking for is :
Simplify the expression to a single numerical value.
3*2^3*2*3^2
(a)144
(b)432
(c)900
(d)5,184
