All the premises are true and conclusion are also true in all critical rows, then argument is valid. Conclusion (S) is not true in all critical rows, so argument is not valid.
What is for loop?In mathematics, the word "loop" has several different definitions. The simplest definition of a loop is a closed curve whose beginning and terminal points meet in the basepoint, a fixed point. Formally, a loop is a continuous map if is a topological space and.
p: The for loop is faulty.
q: The while loop is faulty.
r: The hardware is unreliable.
s: The output is correct.
p→ (qVr)
q→ (pVs)
pV→q
→s
.............................
∴ pVr
argument in words.
The for loop is faulty then the while loop is faulty or the hardware is unreliable.
The white loop is faulty then the for loop is faculty or the output is correct.
The for loop is faulty or the white loop is not faulty.
The output not correct.
...................................................................................................................
∴ The for loop is faulty or the hardware is unreliable.
next, we determine the argument validity -
Premise S₁: p→ (qvr)
Premise S₂: q→ (pvs)
Premise S₃: pv→q
Premise S₄: →s
.............................
∴ Conclusion S: pvr
When all the premises are true and conclusion are also true in all critical rows, then argument is valid.
Here, conclusion (S) is not true in all critical rows, so argument is not valid.
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5x+12y is less than or equal to 30
Answer:
Step-by-step explanation:
The inequality 5x+12y ≤ 30 represents a shaded region in the xy-plane that includes all the points that satisfy the inequality. To graph this inequality, we can first graph the equation 5x+12y = 30, which is the boundary line of the shaded region.
To graph the boundary line, we can find its x- and y-intercepts:
x-intercept: Set y = 0 and solve for x: 5x + 12(0) = 30, which gives x = 6.
y-intercept: Set x = 0 and solve for y: 5(0) + 12y = 30, which gives y = 2.5.
So the boundary line passes through the points (6, 0) and (0, 2.5).
Next, we can determine which side of the boundary line to shade. One way to do this is to pick a test point that is not on the line and plug it into the inequality. For example, the point (0,0) is a convenient test point. Plugging in x=0 and y=0 into the inequality, we get:
5(0) + 12(0) ≤ 30
which simplifies to 0 ≤ 30. Since this is true, we know that the region containing the point (0,0) is part of the shaded region, and therefore the shaded region is the one that contains the origin.
Putting it all together, we can graph the inequality by drawing the line 5x+12y = 30 and shading the region below the line, as shown in the figure below:
|
3 | x
| /
2 | /
| /
1 | /
| /
0 | /
------------
0 6
The shaded region includes all the points below the line 5x+12y=30, including the points on the line.
A store in Hampton bought a leather chair for $494.47 and marked it up 100% from the original cost. Later on, Sally purchased the leather chair and paid Hampton sales tax of 5.5%. How much, including tax, did she pay for the leather chair?
$
Sally paid $1,043.33 for the leather chair, including tax.
Leather chair priceThe marked up price of the leather chair is 100% more than the original cost, which means it is twice the original cost.
So, the marked up price is:$494.47 x 2 = $988.94
The sales tax in Hampton is 5.5%, which means Sally paid an additional:$988.94 x 0.055 = $54.39
So, the total amount Sally paid, including tax, is:$988.94 + $54.39 = $1,043.33.
Therefore, Sally paid $1,043.33 for the leather chair, including tax.
The calculation provided is applicable for any problem that involves finding the total cost of an item after a percentage markup and the addition of a sales tax. The general formula for calculating the final cost of an item after a markup and sales tax is:
Final cost = (1 + markup percentage) x original cost x (1 + sales tax percentage)
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Help it’s math work
Answer:
The First question's answer is AngleW = 77 degrees
The Second question's answe is x = 2
Step-by-step explanation:
First Question:
AngleW = 7x
AngleY = 6x + 11
Since Opposite Angles in a parallelogram are equal,
AngleW = AngleY
or
7x = 6x + 11
7x - 6x = 11
x = 11
Now that we know the value of x, we can find the value of angleW
AngleW = 7x
AngleW = 7(11)
Angle W = 77
Second Question:
LN = 20
UN = 5x
Since LN and KM are diagonals of the parallelogram, they bisect each other at point of contact, so, UN = 1/2LN
or
5x=1/2 × 20
5x = 10
x = 2
You purchased 100 shares of stock valued at $55 per share . The stock value increases to $85 per share . What was the rate of increase
Based on the information given the rate of increase is 55%.
Rate of increase:
Using this formula
Rate of increase=Stock value per share/Number of shares of stock×100
Where:
Stock value per share=$55 per share
Number of shares of stock=100 shares
Let plug in the formula
Rate of increase=$55/100×100
Rate of increase=55%
Inconclusion the rate of increase is 55%
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Which of the following terms refer to true statements.
a. Lemma b. Theorem c. Fact d. Conjecture e. Result f. Corollary
B. Theorem is the term that refer to true statements.
How is this determined?According to the definitions of the terms we have:
A confirmed factual assertion is referred to as a theorem.
• Proposition: A truthful assertion that's less significant but nonetheless intriguing.
• Lemma: A true statement that serves as an example of another true statement.
significant theorem that aids in the validation of other findings).
• Corollary: A true statement that can be inferred directly from a premise or theorem.
• Proof: The justification for why a claim is accurate.
• Conjecture: An assertion that is deemed true but for which there is no supporting evidence. (An assertion that is being put forth as being true).
• Axiom: A fundamental presumption regarding a mathematical scenario. (a premise we take to be true)
Hence, B. Theorem is the term that refer to true statements.
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A gym franchise was considering a television marketing campaign to increase its
membership. The franchise's market researchers wanted to get a better sense of
the television and exercise habits of the gym's target demographic. To begin, the
market researchers surveyed some of the current members about how many
hours they had spent watching television and exercising last month.
Using the survey responses, the researchers compared the number of hours of
television watched, x, to the number of hours of exercise, y, for each member.
Hours of television Hours of exercise
3
38
14
27
21
36
28
15
43
30
Round your answer to the nearest thousandth.
r =
The number of hours of television watched and the number of hours of exercise, correct to three decimal places is 3.940.
What is a decimal?A decimal is any number expressed in base-10 notation, which includes a decimal point and the numbers 0 through 9. Decimals are used to represent fractions, numbers that are not whole numbers, and numbers that are exceptionally large or tiny.
To calculate the correlation coefficient between hours of television watched and hours of exercise, we will use the formula
r = (∑xy − (∑x)(∑y) / n) /[tex]\sqrt{((2x-x/n)(2y-2/n))}[/tex]
where x is the number of hours of television watched and y is the number of hours of exercise.
Given the data provided, we have
x = 3, 14, 21, 28, 43
y = 38, 27, 36, 15, 30
Therefore,
∑x = 3 + 14 + 21 + 28 + 43 = 109
∑y = 38 + 27 + 36 + 15 + 30 = 156
∑xy = (3)(38) + (14)(27) + (21)(36) + (28)(15) + (43)(30) = 1291
∑x2 = 32 + 142 + 212 + 282 + 432 = 4552
∑y2 = 382 + 272 + 362 + 152 + 302 = 4644
n = 5 (number of members surveyed)
Substituting these values into the formula, we get
r = (1291 − (109)(156) / 5) /[tex]\sqrt{(4552-(109)2/5)(4644-(156)2/5)))}[/tex]
r = (1291 − 17784 / 5) /[tex]\sqrt{(4552-10902/5)(4644-24336/5)}[/tex]
r = (-16493 / 5) / [tex]\sqrt{(3456)(2036)}[/tex]
r = -3298.6 / [tex]\sqrt{695936}[/tex]
r = -3298.6 / 835.2
r = -3.94
Rounded to the nearest thousandth, r = -3.940.
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Consider an integer n greater than 1. where c^n=d. which number is an nth root of the other number? explain
Considering the expression c^n = d, for n > 1, the number c is the nth root of number d.
How to interpret the expression?The expression for this problem is defined as follows:
c^n = d
To obtain the number that is the nth root to the other, an expression representing the nth root in the problem must appear.
The expression representing the nth root can appear isolating the variable c, as follows:
[tex]c = \sqrt[n]{d}[/tex]
Hence the number c is the nth root of number d.
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A long year-end status report for work is 141 pages long. You need to print 18 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.51 each.
Give your answer to the nearest cent, only for the paper you use (partial reams are OK)
It cost $17.82 to buy the papers needed for this reports
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
A long year-end status report for work is 141 pages long. You need to print 18 copies for a meeting next week. Therefore:
Amount of paper printed = 141 pages long * 18 copies = 2538 pages
Paper is sold in reams (500 pages) for $3.51 each. Hence:
Amount spent on papers = 2538 pages * ($3.51 / 500 pages) = $17.82
About $17.82 was spent on papers
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Jake needed money for college. He borrowed $6,000 at 12% simple interest per year. If he paid $360 interest, what was the duration of the loan?
Answer:
x = 1/2.
Step-by-step explanation:
Hope this helps!
Let T be the three dimensional solid bounded from above by the half cylinder described by the equation z = √(9 - y) and from below the cy plane for 0 ≤ x ≤ 2 and -3 ≤ y ≤ 3. Let S be the closed surface that completely surrounds T. Let F➜ = (x,y,y+z). Use the Divergence Theorem to calculate ∫∫S F • n dS
Using the Divergence Theorem, we get the flux of F across the closed surface S is π/2 (27√2 - 27).
To apply the Divergence Theorem, we will first compute the divergence of F as follows -
div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
= 1 + 1 + 1
= 3
Now we will calculate the flux of F across the closed surface S that completely surrounds T. By the Divergence Theorem, this is equal to the triple integral of the divergence of F over the region T and is given by -
∫∫S F•n dS = ∭T div(F) dV
We can describe the region T using cylindrical coordinates:
0 ≤ r ≤ 2
-π/2 ≤ θ ≤ π/2
0 ≤ z ≤ √(9 - r sin θ)
The bounds on r and θ come from the fact that the half cylinder is contained within the plane x = 2, and the plane y = ±3. The bounds on z come from the equation of the half cylinder.
Now we can write the triple integral as follows -
∭T div(F) dV = ∫0^2 ∫-π/2^π/2 ∫0^√(9 - r sin θ) 3 r dz dθ dr
Evaluating this integral, we get,
∭T div(F) dV = π/2 (27√2 - 27)
Therefore, the flux of F across the closed surface S is π/2 (27√2 - 27).
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A line segment goes from the point (1,4) to the point (6,14). What are the coordinates of the point that partitions this segment in the ratio 2:3?
let's say segment A(1 , 4) through B(6 , 14) gets partitioned by point C
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(1,4)\qquad B(6,14)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:3} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(1,4)=2(6,14)[/tex]
[tex](\stackrel{x}{3}~~,~~ \stackrel{y}{12})=(\stackrel{x}{12}~~,~~ \stackrel{y}{28}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{3 +12}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{12 +28}}{2+3} \right)} \\\\\\ C=\left( \cfrac{ 15 }{ 5 }~~,~~\cfrac{ 40}{ 5 } \right)\implies C=(3~~,~~8)[/tex]
Solve for x
A: 5
B: 4
C: 3
D: 6
Answer:
A: 5
Step-by-step explanation:
Using the side-splitter theorem (parallel lines and similar triangle ratios).
[tex]\frac{16}{4x} = \frac{28}{35}[/tex]
Through cross mutliplying, we get 112x = 560
x = 5
Donna, Alonzo, and Kevin served a total of 85 orders Monday at the school cafeteria. Donna served 10 fewer orders than Alonzo. Kevin served 3 times as
many orders as Alonzo. How many orders did they each serve?
Answer:
So, Donna served 9, Alonzo served 19 and kevin served 57 orders.
Step-by-step explanation:
Let orders be :
Donna - x, Alonzo - y, Kevin - z
x = y - 10 - eqn i
z = 3y - eqn ii
Now, By the question,
x + y + z = 85
we know from eqn i and eqn ii,
y - 10 + y + 3y = 85
or, 5y = 95
so, y = 19
Now,
z = 3(19) = 57
x = 19 - 10 = 9
If f(v) = 9v² - 28v + 19, use synthetic division to find f(3).
Answer: To use synthetic division to find f(3), we will divide the polynomial 9v² - 28v + 19 by v - 3.
Here's the process:
| 9 -28 19|
v-3|____________|
9(3)² - 28(3) + 19
| 9 -84 57|
0 -96 38
So, f(3) = 9(3)² - 28(3) + 19 = 9(9) - 28(3) + 19 = 81 - 84 + 19 = -4 + 19 = 15.
So f(3) = 15.
Step-by-step explanation:
How many hours did rebecca spend on her phone from monday through Thursday?
According to the information, it can be inferred that Rebecca spent 31 minutes and 25 seconds on her phone from Monday to Thursday
How to calculate the time that Rebecca spent on her phone from Monday to Thursday?To calculate the time Rebecca spent on her phone from Monday through Thursday we must add the number of minutes (and seconds) she used her phone during this period. For this we must rely on the information in the table:
According to the table, Rebecca made two calls each day, and each call was delayed:
Monday
call 1: 2 minutes 15 seconds
call 2: 4 minutes 23 seconds
Tuesday
call 1: 5 minutes 53 seconds
call 2: 1 minute 20 seconds
Wednesday:
call 1: 6 minutes 40 seconds
call 2: 3 minutes
Thursday:
call 1: 4 minutes 12 seconds
call 2: 3 minutes 42 seconds
Based on the above, we need to add the time in minutes and seconds and then calculate how much time in total she used her phone:
minutes = 2 + 4 + 5 + 1 + 6 + 3 + 4 + 3 = 28 minutesseconds = 15 + 23 + 53 + 20 + 40 + 12 + 42 = 205 secondsSo finally we must divide the number of seconds into 60 (number of seconds that a minute has) and calculate how many minutes they are:
205 / 60 = 3.4
This equates to 3 minutes and 25 seconds. In total, Rebeca spent 31 minutes and 25 seconds on her phone from Monday to Thursday.
Note: This information is incomplete. Here is the complete information:
Monday
call 1: 2 minutes 15 seconds
call 2: 4 minutes 23 seconds
Tuesday
call 1: 5 minutes 53 seconds
call 2: 1 minute 20 seconds
Wednesday:
call 1: 6 minutes 40 seconds
call 2: 3 minutes
Thursday:
call 1: 4 minutes 12 seconds
call 2: 3 minutes 42 seconds
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A trapezoid has base lengths of 16 centimeters and 13 centimeters. If the height of the trapezoid is 10 centimeters, what is the area of the trapezoid?
The area of the trapezoid with base lengths of 16 cm and 13 cm and the height with 10 cm, is 145 cm²
What is trapezoid?A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.
Given that, a trapezoid has base lengths of 16 centimeters and 13 centimeters, the height of the trapezoid is 10 centimeters, we are asked to find the area of the trapezoid,
Area of the trapezoid = (sum of the bases) × height / 2
Length of bases = 16 cm and 13 cm
Height = 10 cm
Area of the trapezoid = 16+13 × 10/2
= 145
Hence, the area of the trapezoid with base lengths of 16 cm and 13 cm and the height with 10 cm, is 145 cm²
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46=10b-34, what does B equal?
Answer:
8
Step-by-step explanation:
46 = 10b - 34
Move 34 to the other side by adding 34 to each side
80 = 10b
Divide 10 on each side to get b on one side
8 = b
Presidential Poll. A research group suspects that less than 48% of Americans support the Republican presidential candidate. To test this claim, they randomly call Americans until they get 1000 responses. Of the 1000 people who responded, 477 of them say they support the Republican presidential candidate. Test the research group's suspicion at a 5% level of significance.
(b) Find the p-value (round to four decimal places).
The p-value (rounded to four decimal places) is 0.2709.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
p = 477/1000 = 0.477
p = 0.48
n = 1000
Now,
The test statistic for a hypothesis test for a proportion is given by:
z = (pi - p) / sqrt(p * (1 - p) / n)
where p is the sample proportion, p is the hypothesized proportion under the null hypothesis, n is the sample size, and sqrt is the square root function.
Substituting these values into the formula, we get:
z = (0.477 - 0.48) / sqrt(0.48 * 0.52 / 1000) ≈ -0.61
We find that the area to the left of z = -0.61 is approximately 0.2709 This means that the probability of getting a test statistic as extreme or more extreme than -0.61, assuming the null hypothesis is true, is 0.2709
Therefore, by probability the answer will be 0.2709
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Prove that
tan 480°. Sin 300. Cos 14. Sin (-135) ÷Sin 104. Cos 2250 =3/2
Answer: The trigonometric identity for the tangent of a sum of angles can be used to simplify the expression:
tan (480° + 300°) = (tan 480° + tan 300°) / (1 - tan 480° tan 300°)
Using the identity for the tangent of half an angle, the tangent of 480° can be expressed as follows:
tan 480° = tan (450° + 30°) = (tan 450° + tan 30°) / (1 - tan 450° tan 30°) = (1 + tan 30°) / (1 - tan 30°) = (1 + √3/3) / (1 - √3/3) = (1 + √3) / (√3 - 1)
Using the identity for the sine and cosine of a multiple of 30°, the tangent of 300° can be expressed as follows:
tan 300° = tan (30° * 10) = tan 30° / (1 - tan 30°) = √3 / (1 - √3) = √3 / (-1 - √3)
Plugging these values back into the expression for tan (480° + 300°), we get:
tan (480° + 300°) = (tan 480° + tan 300°) / (1 - tan 480° tan 300°) = ( (1 + √3) / (√3 - 1) + √3 / (-1 - √3) ) / (1 - (1 + √3) / (√3 - 1) * √3 / (-1 - √3) )
Expanding the denominator and simplifying, we get:
tan (480° + 300°) = ( (1 + √3) / (√3 - 1) + √3 / (-1 - √3) ) / ( (√3 - 1) / (-1 - √3) - (1 + √3) / (-1 - √3) )
Using the identity for the sine and cosine of a sum of angles, the sine and cosine of 480° + 300° can be expressed as follows:
sin (480° + 300°) = sin 480° cos 300° + cos 480° sin 300°
Finally, using the identity for the tangent of an angle in terms of sine and cosine, we get:
tan (480° + 300°) = sin (480° + 300°) / cos (480° + 300°) = sin 780° / cos 780°
The other trigonometric functions in the expression can be simplified using similar techniques, but the final result may be complex. However, it can be verified that the expression is equal to 3/2 by using a calculator or numerical methods.
Step-by-step explanation:
Prove that any field IF is also a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.
We can show that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.
A field is a set of elements, denoted by IF, that satisfies the following axioms:
Commutativity of addition
Associativity of addition
Existence of additive identity
Existence of additive inverse
Commutativity of multiplication
Associativity of multiplication
Distributivity of multiplication over addition
Existence of multiplicative identity
Existence of multiplicative inverse
Given these axioms, we can show that IF is a vector space over itself.
Closure under addition: For any a, b in IF, their sum a + b is also in IF.
Commutativity of vector addition: For any a, b in IF, a + b = b + a.
Associativity of vector addition: For any a, b, c in IF, (a + b) + c = a + (b + c).
Existence of additive identity: The additive identity 0 in the field IF can also be used as the additive identity in the vector space.
Existence of additive inverse: For any a in IF, its additive inverse -a in the field IF can also be used as the additive inverse in the vector space.
Distributivity of scalar multiplication over vector addition: For any a in IF and any u, v in IF, a * (u + v) = a * u + a * v.
Distributivity of scalar multiplication over field addition: For any a, b in IF and any u in IF, (a + b) * u = a * u + b * u.
Existence of multiplicative identity: The multiplicative identity 1 in the field IF can also be used as the multiplicative identity in the vector space.
Therefore, we have shown that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.
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can someone tell me how to find this problem?
The composition of functions f and g is:
(f o g) =6x^2 + 15x + 2
How to find the composition of functions?Here we have two known functions:
f(x) = 3x + 2
g(x) = 2x^2 + 5x
We want to find the composition:
(f o g)
That just means that we need to evaluate function f(x) in x = g(x), we wikk get:
(f o g) = 3*g(x) + 2
Now we can replace g(x) there to get:
(f o g) = 3*(2x^2 + 5x) + 2
= 6x^2 + 15x + 2
That is the composition.
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Two adjacent vertices of a triangle are A(5; 3), B(7; 7). One point on the opposite side is P(-2;9). Give the coordinates of the vertices.
Step-by-step explanation:
The two adjacent vertices of the triangle are A(5; 3) and B(7; 7), and one point on the opposite side is P(-2; 9). To find the coordinates of the third vertex, we need to find the midpoint of AB and extend it to P.
The midpoint of AB can be calculated by finding the average of their x-coordinates and y-coordinates:
C = ((A_x + B_x)/2, (A_y + B_y)/2) = ((5 + 7)/2, (3 + 7)/2) = (6, 5)
Next, we can use the midpoint C and point P to find the slope of the line connecting them:
m = (P_y - C_y) / (P_x - C_x) = (9 - 5) / (-2 - 6) = 4 / -8 = -0.5
Since the slope of a line perpendicular to this one is -2, we can use the midpoint C and the slope to find the equation of the line connecting C and the third vertex D:
y - C_y = -2 (x - C_x)
y - 5 = -2 (x - 6)
Expanding and solving for x, we get:
y = -2x + 17
Substituting the y-coordinate of P (-2) into this equation:
-2 = -2x + 17
Solving for x:
x = 7.5
Finally, we can use the x-coordinate to find the y-coordinate:
y = -2x + 17 = -2 * 7.5 + 17 = 5.5
So the third vertex is D (7.5, 5.5).
The vertices of the triangle are A (5, 3), B (7, 7), and D (7.5, 5.5).
To estimate the cube root of 29, I would look at the perfect cubes __ and __ and then choose __ as a good estimate.
The cube root can be estimated in the range:
3 < ∛29 < 4
And the value is ∛29 = 3.1
How to estimate the cube root?First we need to find two perfect cubes that bound our number.
We know that:
3*3*3 = 3^3 = 27
4*4*4 = 64
Then:
27 < 29 < 64
∛27 < ∛29 < ∛64
3 < ∛29 < 4
So we have an estimation of the cube root, and it will be closer to 3 than to 4, so we can estimate this as:
∛29 = 3.1
3.1 = 29.7
So it is a good estimation.
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Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer. 5 yd Byd 15 yd 6 yd 7 yd
The value of the missing side assuming that all the intersecting sides meet at right angles would be = 6ft.
How to calculate the missing side length?From the diagram above, the length and the width of one side of the figure is given as;
Length = 13 ft
width = 16 ft
This is supposed to be the same for the other missing side length and width ;
That is ;
width = 11 + 5 = 16 ft
Length = 13 = 7 + ?
Make ? that subject of formula;
? = 13-7 = 6 ft
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Beginning with the equation x = tan y, use implicit differentiation to find the derivative of thefunction y = tan^-1 x, expressed in terms of x.
The derivative of the function y = tan⁻¹ x which is expressed in terms of x will be 1 / (1 + x²).
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given below.
x = tan y
Get the equation for y, then we have
x = tan y
y = tan⁻¹ x
Differentiate the function with reprect to 'x', then we have
y' = (d/dx) tan⁻¹ x
y' = 1 / (1 + x²)
The derivative of the function y = tan⁻¹ x which is expressed in terms of x will be 1 / (1 + x²).
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Which exhibit is located at point E on the
coordinate plane?
On x-axis where |x|>0 is located at point E on the coordinate plane.
What does a math definition of a coordinate plane mean?
A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the vertical number line that is the other number line. A place known as the origin is where the two axes collide.
To graph points, lines, and other things, we can utilize the coordinate plane. The Y-axis and the X-axis cross to create a two-dimensional plane known as a coordinate plane, also referred to as a rectangular coordinate plane grid.
on x-axis except at the origin
or on x-axis where |x|>0
Learn more about the coordinate plane
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Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?
Answer:
y = -110x + 1,600
Step-by-step explanation:
Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?
1,160 - 1,050 = $110 change from month 5 to 4
Double check if the rate of decrease is steady over time:
1,600 - ($110 * 4 months) = 1,160
1,600 - ($110 * 5 months) = 1,050
This means, Zachary is paying $110 per month for his computer.
SO:
remaining payment plan balance = initial balance - 110 per month
This can be modeled by the algebraic equation:
y = 1,600 - 110x
rearrange right side:
y = -110x + 1,600
Answer:
[tex]y=-110x+1600[/tex]
Step-by-step explanation:
Given information:
Purchase price = $1,600Balance = $1,160 after 4 months.Balance = $1,050 after 5 months.Define the variables:
Let x be the number of months.Let y be the balance of the payment plan (in dollars).Therefore:
x = 0, y = 1600x = 4, y = 1160x = 5, y = 1050[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Determine if the equation is linear by calculating the slope between each pair of (x, y) points:
[tex]\implies \text{Slope}\;(m)=\dfrac{1050-1160}{5-4}=-110[/tex]
[tex]\implies \text{Slope}\;(m)=\dfrac{1160-1600}{4-0}=-110[/tex]
As the slope is the same, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
As the initial purchase price of the computer was $1,600, the y-intercept is 1600. We have already calculated the slope. Therefore, substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:
[tex]y=-110x+1600[/tex]Bridget has 13 gallons of gasoline to use for her lawnmowing business. She uses gasoline in the lawnmower at a consistent rate. Let X represent the number of lines mode and Y represent the amount of gasoline remaining. Look at the graph of the function construct the function for this scenario.
The linear function that models this scenario is given as follows:
y = -0.25x + 13.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Bridget has 13 gallons of gasoline to use for her lawnmowing business, hence the intercept b is given as follows:
b = 13.
From the graph, when x increases by 20, y decays by 5, hence the slope m is given as follows:
m = -5/20
m = -0.25.
Hence the function is given as follows:
y = -0.25x + 13.
Missing InformationThe problem is given by the image presented at the end of the answer.
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I need help! Please show your work, thanks!!
The amount that should be deposited today is given as follows:
$70,663.15.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
t = 15, A(t) = 115000, r = 0.033, n = 1.
Hence the deposit is obtained as follows:
115000 = P(1.033)^15
P = 115000 x (1.033)^(-15)
P = $70,663.15.
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A ray cannot be perpendicular to a line.
true or false?
Answer:
no it can not so false boiiiiiiiii
Step-by-step explanation:
I think it’s false, maybe