The domain of the function f(x) = (x - 5) / (2x - 3) is all real numbers except for x = 3/2 because this value would cause the denominator of the function to be zero, which is undefined.
Explanation:The domain of a function refers to all possible values that can be inputted into the function, or 'x' values. For a rational function, such as f(x) = (x - 5) / (2x - 3), it is important to note that the function is undefined for values of x that would make the denominator equal zero. Because functions cannot have a denominator of zero, these values should be excluded from the domain.
To find these values, you would set the denominator equal to zero and solve. Thus, 2x - 3 = 0. Solving this, x = 3/2. Therefore, all real numbers except for x=3/2 are in the domain for this rational function.
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The window frame is a regular octagon. It is made from eight pieces of wood shaped like congruent isosceles trapezoids . What are m angle A , m angle B.m angle C and m angle D ?
Answer:
∠A= 112.5°, ∠B=67.5°, ∠C is 67.5° and ∠D 112.5°.
Step-by-step explanation:
Consider the provided information.
The sum of all interior angle of a polygon is: [tex](n-2)180[/tex]
Substitute n = 8.
[tex](8-2)180=1080[/tex]
Thus, the measure of each angle is: [tex]\frac{1080}{8}=135[/tex]
∠B and ∠C are congruent and their sum is 135°
∠B+∠C=135°
∠B=67.5°
Hence, the m angle B and m angle C is 67.5°.
The sum of all angles of a quadrilateral is 360°.
∠A+∠D+∠B+∠C=360°
∠A+∠D=360°-135°
∠A+∠D=225°
∠A and ∠D are congruent and their sum is 225°
∠A+∠D=225°
∠A=∠D=112.5°
Hence, the m angle A and m angle D is 112.5°.
Complete the proof of the exterior angle theorem.
Given: angle ACD is an exterior angle of triangle BCD.
Prove: angle B + angle C = angle ADC
Statements:
1. angle ADC is an exterior angle of triangle BCD
2.
3. angle ADC and angle BCD form a linear pair
4.
5.
6.
7. angle ADC = angle B + angle C
Reasons:
1. Given
2. Triangle Sum Theorem
3.
4.
5.
6.
7. Subtraction Property of Equality
(i need the blanks filled in)
Answer
Step-by-step explanation:
From the attached diagram below,
< ADC + <D = 180° (sum of linear angle) ------------(1)
<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)
Since the two equations are equal to 180°, We equate the two equation
i.e
(1) = (2)
< ADC + <D = <B + <C + <D
<D from the left hand side will cancel <D on the right hand side
We are now left with
<ADC = <B + <C
The Exterior Angle Theorem is proven by using the Triangle Sum Theorem, the Linear Pair Postulate, and the Subtraction Property of Equality to show that the sum of the interior opposite angles of a triangle equals the exterior angle.
Explanation:To complete the proof of the Exterior Angle Theorem using the fact that angle ACD is an exterior angle of triangle BCD and prove that angle B + angle C = angle ACD, follow the steps below:
Angle ACD is an exterior angle of triangle BCD.Angles B, C, and BCD sum to 180° (Triangle Sum Theorem).Angle ACD and angle BCD form a linear pair.Angles forming a linear pair sum to 180° (Linear Pair Postulate).Angle ACD + angle BCD = 180° (from statements 3 and 4).Angles B + C + angle BCD = 180° (from statement 2).Angle ACD = angle B + angle C (from statements 5 and 6 and by the Subtraction Property of Equality).Choose a system of equations with the same solution as the following system:
6x+2y=-6
3x-4y=-18
Answer:
x + 2 = 0 and y - 3 = 0
Step-by-step explanation:
We have to find the solution of the system of equations
6x + 2y = - 6 ........... (1)
⇒ 12x + 4y = - 12 .......... (2) and
3x - 4y = - 18 ........... (3)
Now, solving equations (2) and (3) we get,
15x = - 30
⇒ x = - 2
Hence, from equation (1) we get, 2y = - 6 - 6x = - 6 - 6(- 2) = 6
⇒ y = 3
Therefore, the solution of the given system of equations is (-2,3).
Now, x + 2 = 0 and y - 3 = 0 are another system of equations that have the same solutions. (Answer)
Evaluate 3/5 mod 6 please help me
Answer:
3/5 0r 0.6
Step-by-step explanation:
A mod B = R
3/5 mod 6, because 3/5 < 6
so (3/5) / 6 = 0 ... R 3/5
Which expression is equivalent to 7a-8-12a+4
Answer:
-5a - 4 is the expression equivalent
Following are the calculation to the given expression:
Given:
[tex]\bold{7a-8-12a+4}[/tex]
To find:
solve the expression=?
Solution:
[tex]\to \bold{7a-8-12a+4}\\\\\to \bold{-5a-4}\\\\[/tex]
Therefore, the final answer is "[tex]\bold{-5a-4}[/tex]".
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Please help me ASAP I will mark branlist just explain
Answer:
Measure of Angle 5 = 150 degree.
Step-by-step explanation:
Given line g and h are parallel lines.
Let angle measuring [tex]30\ degree[/tex] be a.
From figure we can see that [tex]\angle a\ and\ \angle 3[/tex] both are Linear Pair Postulate,
i.e. [tex]\angle\ a+\angle 3 =180\ degree[/tex]
So,
[tex]30\ degree +\angle 3 =180\ degree[/tex]
[tex]\angle 3 = 180-30[/tex]
[tex]\Therefore \angle 3=150\ degree[/tex] ------------(equation 1)
Now, [tex]\angle\ a\ and\ \angle\ 4[/tex] are alternate interior angles, and alternate interior angles are equal.
i.e. [tex]\angle\ a = \angle 4[/tex]
Therefore [tex]\angle\ 4 =30\ degree[/tex] ------------(equation 2)
Now, [tex]\angle 4\ and\ \angle 7[/tex] both are Linear Pair Postulate,
i.e. [tex]\angle\ 4 +\angle\ 7 = 180\ degree[/tex]
[tex]30+\angle\ 7=180[/tex] ------------------(from equation 2)
[tex]\angle\ 7 =180-30[/tex]
[tex]\therefore\ \angle\ 7 = 150\ degree[/tex] ---------(equation 3)
Now, [tex]\angle\ 7\ and \angle\ 5[/tex] are vertically opposite angles, and vertically opposite angles are equal.
So,
[tex]\angle 7=\angle 5[/tex]
[tex]\therefore\ \angle 5=150\ \ degree[/tex] -----------------(from equation 3)
7/9 as an improper fraction
Answer:
Step-by-step explanation:its not a improper fraction
Answer:
1 and 2/9
Step-by-step explanation:
7 goes into 9 1 time and there are 2 left over so that 2 would be 2/9 so it's 1 whole and 2/9
Cars are made in a factory at a rate of 39 cars every 3hours at this rate, how many cars can be made on the factory in 7 hours
Answer:
Step-by-step explanation:
39 cars every 3 hrs.......that means (39/3) = 13 cars every hr
and if its 13 cars every hr....in 7 hrs, there will be (7 * 13) = 91 cars <==
you can either do it that way....the unit rate way...OR
you can set it up as a proportion...
39 cars to 3 hrs = x cars to 7 hrs...
39 / 3 = x / 7....cross multiply
(3)(x)= (39)(7)
3x = 273
x = 273/3
x = 91 <====
either way, u get the correct answer
UGRENT 8TH GRADE MATH QUESTION! Write the equation 4x + 2y - 6 = 0 in the slope-intercept form (y = mx + b).
Answer:
y = -2x + 3
Step-by-step explanation:
4x + 2y - 6 = 0
2y - 6 = -4x
2y = -4x + 6
y = -2x + 3
Answer:
The slope-intercept form is,
y = -2x + 3
Step-by-step explanation:
The given equation of the line is,
4x + 2y - 6 = 0
Subtracting "(4x- 6)" from both sides of the above equation, we get
4x + 2y - 6 - (4x - 6) = 0 - (4x - 6)
⇒ 4x + 2y - 6 - 4x + 6 = 0 - 4x + 6
⇒ 2y = -4x + 6
Now, dividing both sides by '2' of the above equation, we get
2y ÷ 2 = (-4x + 6) ÷ 2
⇒y = -2x + 3
This is the required slope-intercept form of the given line.
It took 48 minutes to drive downtown. An app estimated it would be less than that. If the error was 20%, what was the app’s estimate?
Answer:
40 min
Step-by-step explanation:
1 x 48 + .20 .48
(1.20) (48)= 40 min
y-x+3
please help solve with points not graphs
Answer:
(0,3) (3,0)
Step-by-step explanation:
if your asking for y=-x+3
or y=x+3 is (0,3) (0,-3
PLEASE PLEASE HELP ME PLEASE
Select the system of linear inequalities whose solution is graphed.
A:y < 3x – 2, x + 2y ≤ 4
B:y ≤ 3x – 2, x + 2y ≤ 4
C:y ≥ 3x – 2, x + 2y ≤ 4
D:y > 3x – 2, x + 2y < 4
Answer:
C
Step-by-step explanation:
They're solid lines and overlap at that point
If a_1=6a1=6 and a_n=a_{n-1}+3an=an−1+3 then find the value of a_4a4
Answer:
The value of [tex]a_{4}=15[/tex]
Step-by-step explanation:
Given that [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]
Given sequence is of the form arithmetic sequence
For arithmetic sequence the sequence is [tex]a_{1},a_{2},a_{3},...[/tex]
The nth term is of the form [tex]a_{n}=a_{n-1}+d[/tex]
Here [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]
from this the common differnce is 3.
Therefore d=3
To find [tex]a_{2}[/tex], [tex]a_{3}[/tex] , [tex]a_{4}[/tex]
[tex]a_{n}=a_{n-1}+d[/tex]
put n=2 and d=3 we get
[tex]a_{2}=a_{2-1}+3[/tex]
[tex]a_{2}=a_{1}+3[/tex]
[tex]a_{2}=6+3[/tex] (here [tex]a_{1}=6[/tex] )
Therefore [tex]a_{2}=9[/tex]
[tex]a_{n}=a_{n-1}+d[/tex]
put n=3 and d=3 we get
[tex]a_{3}=a_{3-1}+3[/tex]
[tex]a_{3}=a_{2}+3[/tex]
[tex]a_{3}=9+3[/tex] (here [tex]a_{2}=9[/tex] )
Therefore [tex]a_{3}=12[/tex]
[tex]a_{n}=a_{n-1}+d[/tex]
put n=4 and d=3 we get
[tex]a_{4}=a_{4-1}+3[/tex]
[tex]a_{4}=a_{3}+3[/tex]
[tex]a_{4}=12+3[/tex] (here [tex]a_{3}=12[/tex] )
Therefore [tex]a_{4}=15[/tex]
Therefore the sequence is 6,9,12,15,...
Therefore the value of [tex]a_{4}=15[/tex]
Which of the following correctly simplifies the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared.? (5 points)
Group of answer choices
3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 1 squared over 4 squared. = 1 over 6.
3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 0 over 4 squared. = 0
3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 0 over 4 squared. = 0
3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 1 squared over 4 squared. = 81 over 16.
Answer: 21
Step-by-step explanation:
9 + 10 = 21
The expression simplifies to 81 over 16 by applying the exponent rules, particularly recognizing that any number to the power of 0 is 1 and when raising a power to a power, we multiply the exponents.
The student's question is asking to simplify the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared. To simplify this expression, we should apply the exponent rules.
Let's simplify step-by-step:
First, recognize that any number raised to the power of 0 is 1.
The expression now simplifies to square of three, since anything multiplied by 1 remains unchanged.
Now, take the entire expression over 4 and square it as indicated.
Thus, the correct answer is 3 to the power of 4 multiplied by 1 squared over 4 squared equals 81 over 16.
The length of a rectangle is 7 feet more than twice the width, and the area of the rectangle is 99 ft.² Find the dimensions of the rectangle
Answer:
Step-by-step explanation:
A = L * W
A = 99
L = 2w + 7
now we sub
99 = (2w + 7)(w)
99 = 2w^2 + 7w
2w^2 + 7w - 99 = 0
(2w - 11)(w + 9) = 0
2w - 11 = 0
2w = 11
w = 11/2
w = 5 1/2 ft (or 5.5 ft) <==== width is 5 1/2 ft)
L = 2w + 7
L = 2(5.5) + 7
L = 11 + 7
L = 18 ft <====== length is 18 ft
Your round-trip drive to work is 4310 miles. How many miles do you drive to and from work in 3 days?
Final answer:
To find the total distance driven to and from work over 3 days, multiply the daily round-trip distance of 4310 miles by 3, resulting in 12,930 miles.
Explanation:
The question asks how many miles you would drive to and from work in 3 days if your round-trip to work is 4310 miles. To calculate this, you just need to multiply the daily round-trip distance by the number of days you travel. In this case, you travel to and from work for 3 days.
Determine the daily round-trip distance. (Already provided as 4310 miles)
Multiply the daily round-trip distance by the number of days traveled: 4310 miles × 3 days.
The calculation would be 4310 miles × 3 which equals 12,930 miles. This is the total distance driven to and from work over the 3 day period.
Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour; the other is headed west at a constant speed of 40 miles per hour. What is the distance between the cars in 30 minutes?
13.23 miles
Step-by-step explanation:
The vector creates an inverted right-angled triangle. The westbound car will have covered 20 miles while the southbound car will ahve covered 15 miles in 30 mins;
40 miles /hr * ½ hr = 20 miles
30 miles/ hr * ½ hr = 15 miles
To find the hypotenuse (distance between the two cars), we shall use the formulae;
a² + b² = c²
20² + 15² = c²
c² = 20² – 15²
c² = 175
c = 13.23
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Which function is the inverse of f(x)=2x+3?
Answer:
B) y=1/2x-3/2
Step-by-step explanation:
y=2x+3
x=2y+3
2y=x-3
y=1/2x-3/2
Answer:
B
Step-by-step explanation:
EDGE 2020
is 144 a perfect square or not
Answer: Yes
Step-by-step explanation: 144 is a perfect square. In other words, it's possible to find a whole number that can be multiplied by itself that gives us 144.
In this case, we multiply 12 by 12 or 12² to get 144 which means 144 is a perfect square. Also, it's on our perfect square list which I will attach below.
SOMEONE HELP IM TIMED !!!!!
PLZ HELP !!
Graph the line for y+1=−3/5(x−4) on the coordinate plane.
Answer:
The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.
Step-by-step explanation:
As the linear equation y + 1 = −3/5 (x − 4) is given.
Since y-y₁ = m (x - x₁) is the Point-slope form is the general form y-y₁=m(x-x₁) for linear equations.
Hence, from the linear equation we can determine the slop which is m = -3/5
Also, when we put x = 0 in the linear equation, we determine the y-intercept as follows:
y + 1 = −3/5 (x − 4)
y + 1 = -3/5(-4) ∵x = 0
y = 12/5 - 1
y = 7/5
y-intercept: 7/5
Hence,
Table for some points can be made for x and values as:
x y0 7/5
1 4/5
The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.
Keywords: graph, straight line
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Help me plz
find the soultion to the system of linear equation using the elimination method.
1. 2x – 3y = -2
2x + y = 14
2. x = -6y - 3
8x + 8y = -24
3. 5x + 5y = 20
-3x + 5y =4
Answer:
I could do 1 and 3
1) 2x-3y=-2 ....1
-
2x+y=14......2
=-4y=-16
y=4
Substitute (y=4) into equation 1
2x-3 (4)=-2
2x-12=-2
2x=-2+12
2x=10
×=5
3) 5x+5y=20....1
-
-3x+5y=4......2
=8x=16
x=2
Substitute (x=2) into equation 1
5 (2)+5y=20
10+5y=20
5y=20-10
5y=10
y=2
Answer: (1) x = 5 , y = 4
(2) x = -3 and y = 0
(3) x = 2 and y = 2
Step-by-step explanation:
(1) 2x - 3y = -2 ................... equation 1
2x + y = 14 ................ equation 2
solving the system of linear equation by elimination method. We need to decide the variable to eliminate first , in this case , since the coefficient of x are the same and they have the same signs (+), we can eliminate the variable x first by subtracting equation 1 from equation 2, so we have
2x - 2x + y - (-3y ) = 14 - ( - 2)
4y = 16
divide through by 4
y = 4
substitute y = 4 into equation 1 , we have
2x - 3 (4) = -2
2x - 12 = -2
2x = -2 + 12
2x = 10
x = 5
Therefore :
x = 5 and y = 4
(2) x = -6y - 3 ....................... equation 1
8x + 8y = -24 ....................... equation 2
Solving the system of linear equation by substitution method , substitute x = -6y - 3 into equation 2 , equation 2 becomes
8(-6y - 3 ) + 8y = -24
expanding , we have
-48y - 24 + 8y = -24
-40y - 24 = -24
Add 24 to both sides , we have
- 40y = -24 + 24
-40y = 0
divide through by -40
y = 0/-40
y = 0
substitute y = 0 into equation 1 , equation 1 then becomes
x = -6(0) - 3
x = -3
Therefore : x = -3 and y = 0
(3) 5x + 5y = 20 ........................ equation 1
-3x + 5y = 4 ............................ equation 2
solving the system of linear equation by elimination method , we have to decide the variable to eliminate first , since the coefficient of y are the same and are both positive, we will eliminate y by subtracting equation 2 from equation 1 , we have
5x - (-3x) + 5y - 5y = 20 - 4
5x + 3x + 0 = 16
8x = 16
x = 2
substitute x = 2 into equation 1 , equation becomes
5(2) + 5y = 20
10 + 5y = 20
5y = 20 - 10
5y = 10
y = 2
Therefore : x = 2 and y = 2
Which of the following equations have exactly one
solution?
Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.
To determine which of the given equations have exactly one solution, we will analyze each equation to see if it can be simplified or rearranged to form an identity (true for all values of [tex]\( x \))[/tex] or a contradiction (false for all values of [tex]\( x \))[/tex], or if it remains a valid equation with a unique solution for [tex]\( x \).[/tex]
An equation has exactly one solution if it can be simplified to the form [tex]\( ax = b \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( a \)[/tex] is not zero.
Let's analyze each option step by step:
Option A: [tex]\( -5x + 12 = -12x - 12 \)[/tex]
1. Add [tex]\( 12x \)[/tex] to both sides: [tex]\( -5x + 12x + 12 = -12 + 12x \).[/tex]
2. This simplifies to [tex]\( 7x + 12 = -12 \).[/tex]
3. Subtract [tex]\( 12 \)[/tex] from both sides: [tex]\( 7x = -24 \).[/tex]
4. Divide by
This equation has exactly one solution, [tex]\( x = -\frac{24}{7} \).[/tex]
Option B: [tex]\( -5x + 12 = 5x + 12 \)[/tex]
1. Add [tex]\( 5x \)[/tex] to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x + 12 \).[/tex]
2. This simplifies to [tex]\( 12 = 10x + 12 \).[/tex]
3. Subtract \( 12 \) from both sides: [tex]\( 0 = 10x \).[/tex]
4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = 0 \).[/tex]
This equation has exactly one solution, [tex]\( x = 0 \).[/tex]
Option C: [tex]\( -5x + 12 = -5x - 12 \)[/tex]
1. Subtract \( -5x \) from both sides: [tex]\( 12 = -12 \).[/tex]
This simplifies to a contradiction since [tex]\( 12 \)[/tex] does not equal [tex]\( -12 \).[/tex]
Therefore, this equation has no solution.
Option D: [tex]\( -5x + 12 = 5x - 5 \)[/tex]
1. Add \( 5x \) to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x - 5 \)[/tex].
2. This simplifies to [tex]\( 12 = 10x - 5 \)[/tex].
3. Add [tex]\( 5 \)[/tex] to both sides: [tex]\( 17 = 10x \).[/tex]
4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = \frac{17}{10} \)[/tex].
This equation has exactly one solution, [tex]\( x = \frac{17}{10} \)[/tex].
Based on this analysis, Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.
Anyone able to help?
Answer:
Step-by-step explanation:
The domain on all x-squared parabolas is all real numbers.
The range of an x-squared parabola is always found at the y coordinate of its vertex, and then is determined by whether it opens upwards or downwards. Our vertex has a y coordinate of -1 and opens downwards, so the range is all real numbers less than or equal to -1.
There are no x-intercepts (aka places on the graph that go through the x-axis), but the y-intercept is also the vertex, which is (0, -1).
Because this is an upside down parabola, it has a max point, again at the vertex. It has no min point.
It increases from negative infinity to its max point and is notated as follows: (-∞, 0]
and decreases from its max point to negative infinity: [0, -∞)
Plz help me it is very important i beg of you
1. Let x represent the missing angle.
The sum of angles in a triangle is 180°
65° + 57° +x =180
122° +x=180°
x=180-122
x=68°
2. Let y represent the missing angle.
Then
y+90°+40°=180°
y+130°=180°
y=180°-130°
y=50°
3. Let the missing angle be t, then
t+20°+130°=180°
t+150° =180°
t=180°-150°
t=30°
4. Let the missing angle be m, then
m+85°+50°=180°
m=180°-50°-85°
m=180-135°
m=45°
5. Let the missing angle be e, then by the exterior remote angle theorem:
137°=102° +e
137-102=e
e=35°
6. Let the unknown angle p, be the missing angle.
Then by vertical angle property and exterior angle property:
p=35° +100°
p=135°
7. Let g be the missing angle, then
g+20°+30°=180°
g+50°=180°
g=180°-50°
g=130°
8)
Let v be the missing angle:
By angle on straight line, and exterior angle theorem property,
g=(180-155)+60°
g=25°+60°
g=85°
A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36
legs. How many of each animal are there?
Answer:
there are 8 pigs because each pig has 4 legs. meanwhile, ducks technically by definition, only have 2 legs,wings do not count as legs.
Step-by-step explanation:
so 1 pig=4 legs.
8 pigs =32 legs
so 32+2x=36
To solve the problem, set up a system of equations using the number of pigs and ducks. Solve the system of equations to find the values of 'p' and 'd'. There are 8 pigs and 2 ducks in the farmhouse.
Explanation:Let's assume the number of pigs is 'p' and the number of ducks is 'd'. Since each pig has 4 legs and each duck has 2 legs, we can set up the equation: 4p + 2d = 36 (since there are 36 legs in total). We also know that there are 10 animals in total, so we can set up another equation: p + d = 10. Now we have a system of equations which we can solve to find the values of 'p' and 'd'.
Multiplying the second equation by 2, we get 2p + 2d = 20. Subtracting this equation from the first equation, we get 4p + 2d - (2p + 2d) = 36 - 20, which simplifies to 2p = 16. Dividing both sides of the equation by 2, we find that p = 8. Substituting this value back into the second equation, we get 8 + d = 10, which means d = 2.
Therefore, there are 8 pigs and 2 ducks in the farmhouse.
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The one below find the angle how do you do that one
-2(-5)q + (-72) (-q)
7grade
Answer:
82q
Step-by-step explanation:
-2(-5)q+(-72)(-q)
10q+72q
82q
Hey there! :)
-2(-5)q + (-72)(-q)
Simplify!
10q + (72q)
Since both terms contain "q," we know that we can add them together.
Simply look at it this way: 10+72 , then add the q at the end of your answer.
10 + 72 = 82 --> add the q! Therefore, your final answer is 82q.
~Hope I helped! :)
Lincoln works for a recreational vehicle company that sells ATVs, dirt bikes, and motorcycles. His boss pays me $500 for the week, plus a 5% commission on each vehicle he sells. What is the minimum amount of dollars lincoln needs to make in sales to earn more than $1500?
Answer:
$20,001
Step-by-step explanation:
Let $x be the amount of dollars Lincoln needs to make in sales to earn more than $1500.
His boss pays him $500 for the week, plus a 5% commission on each vehicle he sells.
5% of $x is $0.05x, the Lincoln earns
[tex]\$(500+0.05x)[/tex] in total.
Hence,
[tex]500+0.05x>1,500[/tex]
Solve this inequality:
[tex]0.05x>1,500-500\\ \\0.05x>1,000\\ \\5x>100,000\\ \\x>20,000[/tex]
Lincoln needs to make in sales more than $20,000, so the minimum amount of dollars Lincoln needs to make in sales is $20,001
Linley rode her scooter for 1/3 hour and traveled 2 1/6 kilometers. What is her average speed in kilometers per hour
To find kilometers per hour, we need to multiply 2 1/6 by 3, because it took Linley 1/3 hour to ride that far.
2 1/6 * 3 = 6 1/2
So, her average speed in kilometers per hour is 6 1/2 kph
Calculate the distance between (3 + i) and (3 − i).
Answer:
2 units
Question:
Calculate the distance between (3 + i) and (3 − i).
Step-by-step explanation:
This problem is equivalent to the problem:
"Calculate the distance between the points (3,1) and (3,-1)."
Since the [tex]x[/tex]-coordinates are the same, this is a vertical distance.
A vertical distance be be found by computing the positive difference of the [tex]y[/tex]-coordinates. In other words, we need only the find the distance between the numbers [tex]y=1[/tex] and [tex]y=-1[/tex] on a number line.
This distance is 1-(-1)=1+1=2 units.