The value of the greatest integer is -9.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the sum of an integer and 4 times the next consecutive integer is -46.
Assume that the integer is x. Then, its consecutive integer will be (x + 1).
Then we can write -
x + 4(x + 1) = - 46
x + 4x + 4 = - 46
5x + 4 = - 46
5x = - 50
x = - 10
Then -
x + 1 = - 9, which is also greater than -10
Therefore, the value of the greatest integer is -9.
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PLEASE HELP ILL MARK BRAINEST.
1) The value of x that would make m║n is; x = 13
2) The value of x that would make m║n is; x = 14
3)a) The angles are congruent by alternate interior angles postulate.
b) The angles are congruent by linear pairs postulate.
c) The angles are congruent by corresponding angles postulate.
How to find corresponding angles?When two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
1) From definition of corresponding angles, line m is parallel to line n and as such, we can say that;
2x + 12 = 38
2x = 38 - 12
2x = 26
x = 13
2) From definition of corresponding angles, line m is parallel to line n and as such, we can say that;
3x + 41 = 8x - 29
8x - 3x = 41 + 29
5x = 70
x = 14
3) a) From definition of alternate interior angles, we can say that yes the angles are congruent by alternate interior angles postulate.
b) Linear pair of angles are formed when two lines intersect each other at a single point. Thus, the angles are supplementary and add up to 180° and they are congruent by linear pairs postulate.
c) The angles are congruent by corresponding angles postulate.
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PLS HELP i’m stuck on this question
Answer:
I djdhdhdh47747
Step-by-step explanation:
jrhrhdhrhdbdndbdbdjdjdjfjfjfjfjfjfjfjffuufufurtuhrbrbrnrntjrjfjfjdjfufufjfjfjfjffiitiririfiififig
Find the value of x and y
Answer:
a
Step-by-step explanation:
Vertical angles are congruent, so:
[tex]7x+7=112 \\ \\ 7x=105 \\ \\ x=15[/tex]
Using linear pairs,
[tex]112+4y=180 \\ \\ 4y=68 \\ \\ y=17[/tex]
The area of a rectangle whose length is 7ft is 14ft squared. Use the equation 14=7w, where w represents the width of the rectangle, and these values for w: 2, 4, 98. Determine the width of the rectangle.
The most appropriate choice for area of rectangle will be given by:
Width of rectangle is 2 ft
What is area of rectangle?
Area of rectangle is the total space taken by the rectangle.
If the length of rectangle be [tex]l[/tex] ft and breadth of rectangle be [tex]b[/tex] ft, area of rectangle [tex]l \times b[/tex] [tex]ft^2[/tex]
Here,
Let the width of the rectangle be w ft
Length = 7ft
Area = 7 x w [tex]ft^2[/tex]
By the problem,
7 x w = 14
w = [tex]\frac{14}{7}[/tex]
w = 2 ft
Width of rectangle is 2 ft
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7x-3y=13
9x+10y=-11
help me
Answer:
Step-by-step explanation:
it's below
Answer:
(1, - 2 )
Step-by-step explanation:
7x - 3y = 13 → (1)
9x + 10y = - 11 → (2)
multiplying (1) by 10 and (2) by 3 and adding will eliminate y
70x - 30y = 130 → (3)
27x + 30y = - 33 → (4)
add (3) and (4) term by term to eliminate y
97x + 0 = 97
97x = 97 ( divide both sides by 97 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (2)
9(1) + 10y = - 11
9 + 10y = - 11 ( subtract 9 from both sides )
10y = - 20 ( divide both sides by 10 )
y = - 2
solution is (1, - 2 )
Division in Base Three: 22011/12
Answer: 1122
Step-by-step explanation:
if 7(n-m) = 3m, what is m/n
Answer:
10m/7n
Step-by-step explanation:
distribute the
7n-7m=3m
7n=
Exit Ticket
Donnie earns extra money as a lifeguard. He earns $52.50 for
5 hours. Identify the constant of proportionality, and write an
equation for the proportional relationship.
Answer:
10.5
10.5x = 52.50
Step-by-step explanation:
To identify the constant of proportionality, divide money by hours.
52.50 ÷ 5 = 10.5
Use the constant of proportionality to write the equation.
10.5x = 52.50
3. John and Savanah are saving money to go on a trip to Mexico. They need at least $2,545 in order to go. John tutors English and Savanah works as a babysitter to raise money. John charges $15 per hour and Savanah charges $20 per hour. The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hours.. Write a set of constraints to model the problem, with x representing the number of hours John tutors and y representing the number of hours Savanah babysits.
The set of constraints to model the problem include
y < 5x and y ≥ 40 hoursHow to write a set of constraints to model the problemThe following is data given in the problem
They need at least $2,545 x representing the number of hours John tutorsy representing the number of hours Savanah babysitsThe number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hoursThe constraints to model the problem is as follows:
The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled.
no more than means it is not greater that which implies it is less thany < 5xSavanah will babysit at least 40 hours
at least 40 hours means a minimum of 40 hours this is 40 hours and above simplified further to greater than or equal to 40 hoursy ≥ 40 hoursThe two constraints required is modelled using inequalities and represented as follows y < 5x and y ≥ 40 hours
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Find the distance between each pair of points
Answer: [tex]\sqrt{82}[/tex]
Step-by-step explanation:
Points are (4,-4) and (3,5)
We find the difference between the numbers
5- - 4 = -9
3 - 4 = -1
Then find the length between them using a triangle [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]\sqrt{-9^{2} +-1^{2} } =\sqrt{82}[/tex]
5a-b=7 for a
Help please
what is the answer 67+2=?
Answer:This is 69
Step by step explanation:67 +2 is 69
13) Three adjacent angles are at a point. The first angle is represented by x, the second angle is 20° more than the
first, and the third angle is 20° more than the second angle. Find the measurements of all three angles.
Answer:
x=40 degrees
Step-by-step explanation:
adjacent angles add up to 180 degrees
First angle=x
second angles=x+20
third angle =x+40
add all and equate to 180 degrees i.e.
x+x+20+x+40=180
3x=180-60
x=40 degrees
x+20=40+20=60 degrees
x+40=40+40=80 degrees
Solve the equation for x.
1=0.4x - 0.8x - 35
What does x equal
Answer:
x = - 90
Step-by-step explanation:
1 = 0.4x - 0.8x - 35 ( add 35 to both sides )
36 = - 0.4x ( divide both sides by - 0.4 )
- 90 = x
What is the average rate of change between the points (3, 9) and (5, 15)?
The average rate of change between the given points (3, 9) and (5, 15) is: 3.
What is the Average Rate of Change between two Points?To find the average rate of change between two points on a coordinate plane, the formula below is used:
Average rate of change = change of y over the change of x = (y2 - y1)/(x2 - x1).
Given the following points on a coordinate plane:
(3, 9)
(5, 15)
Let:
(3, 9) be represented as (x1, y1)
(5, 15) be represented as (x2, y2)
Substitute the values into the average rate of change formula:
Average rate of change = (15 - 9)/(5 - 3)
Average rate of change = 6/2
Average rate of change = 3
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Shelby bought a painting for d dollars. She was charged a 7% sales tax for the painting. Which expression correctly shows the total price that Shelby paid for the painting?
Answer:
The expression is 1.07d.
Find the value is cos W rounded to the nearest hundredth, if necessary
cosine = adj/hypt.
inverse of cosine = arccosine
arccosine(6/22) = 74.34
HELPP ME ASAP
Which point is located on the y axis iready
Answer: The first option (0,-3)
A train leaves city A at 0800 h and travels at a uniform speed of 60 kmh¹ towards city B. Another train leaves city B at the same instance and travels at a uniform speed of 40 kmh¹ towards city A. If the distance between the two cities A and B is 100 km, calculate the time at which the two trains pass each other.
The 100 km difference between the two cities takes two trains to pass each other in 5 hours.
What do time, distance, and speed mean?The relationship between speed, distance, and time is described using the formula of speed, distance and time.
That is speed = distance/time.
What is relative speed?The velocity of an object in relation to another observer is referred to as the relative speed.
Given:
A train departs from city A and moves toward city B at a constant speed of 60 km/h and time taken is 8 hours.
At the same time, a second train departs city B and heads toward city A at a constant speed of 40 km/h.
The relative speed of first train with respect to the second train = 60-40
= 20 km/h
It is given that the two cities A and B are located 100 kilometers apart from one another.
So, distance between both cities = 100 km
By using the speed formula,
Speed = Distance/Time
Time = Distance/Speed
Time = 100/20
∴ Time = 5 hours
Consequently, it takes 5 hours for the two trains to pass one another with 100 km distance between two cities.
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3(x-2)+2x=1/2(10x-12)
Answer:
this equation is always true
Step-by-step explanation:
3(x-2)+2x=1/2(10x-12)
3x - 6 + 2x = 5x - 6
5x - 6 = 5x -6
5x - 5x = 6 - 6
0 = 0
this equation is always true
Answer:
Infinitely many solutions
Step-by-step explanation:
[tex]\sf 3(x - 2) + 2x = \dfrac{1}{2}*(10x - 12)\\\\ 3x - 3*2 + 2x = \dfrac{1}{2}*10x - \dfrac{1}{2}*12 \ [\bf distributive \ property]\\\\ 3x - 6 + 2x = 5x - 6[/tex]
Combine like terms,
3x + 2x - 6 = 5x - 6
5x - 6 = 5x - 6
There are infinitely many solutions for this equation.
triangle ABC has vertices A(-2,-1), B (1,2) and C (2,-4), if triangle A'B'C' is a dilation of triangle ABC with a scale factor of 2,5 and center of dilation (0,0), give the coordinates of the vertices of triangle A'B'C'
After a dilation with a scale factor of 2.5 and center of dilation (0, 0), the coordinates of the vertices of triangle A'B'C' are A' (-5, -2.5), B' (2.5, 5), and C' (5, -10).
What is dilation?Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
What is scale factor?A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as triangles.
For the given coordinates, the dilation with a scale factor of 2.5 and center of dilation (0, 0) should be calculated as follows:
Point A (-2, -1) → Point A' (-2 × 2.5, -1 × 2.5) = Point A' (-5, -2.5).
Point B (1, 2) → Point B' (1 × 2.5, 2 × 2.5) = Point B' (2.5, 5).
Point C (2, -4) → Point C' (2 × 2.5, -4 × 2.5) = Point C' (5, -10).
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The distinct lines ABC and deer in the same place tell how Line A. And line B. related to each other justify your answer a ll b,b ll c,c | d
Line A is perpendicular to D because a is parallel to c and c is perpendicular to d.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.
WE have been given that a ll b,b ll c,c is perpendicular to d.
Here the line a is parallel to b and b is parallel to c so a must be parallel to c.
As we know that c is perpendicular to d since, a is parallel to c.
Therefore, Line A is perpendicular to D because a is parallel to c and c is perpendicular to d.
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Which of the following are characteristics of the graph of the linear parent
function?
Check all that apply.
A. It is a straight line.
B. It goes through the origin.
C. It is a parabola.
D. It has a slope of 1.
You have saved $24 towards the purchase of your own laptop. you get a job at the corner store cleaning after hours on sundays that pays $40 per week. the laptop you want costs $850 and includes everything you'll need to start college.
The number of weeks needed to get $850 is 21 weeks.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
Let the number of weeks be represented by w
Amount saved = $24
Amount needed = $850
Number of weeks = w.
This will be illustrated as:
24 + 40w = 850
Collect like terms
40w = 850 - 24
40w = 826
Divide
w = 826 / 40
w = 20.65 = 21 approximately
There'll be 21 weeks.
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You have saved $24 towards the purchase of your own laptop. you get a job at the corner store cleaning after hours on sundays that pays $40 per week. the laptop you want costs $850 and includes everything you'll need to start college. How may weeks are needed?
Lucy earns $15.75 per hour. Last week she worked 25 hours. What is her gross pay:
Lance has a yearly salary of $52,300 and pays 21% in taxes. Answer the following
a. How much does he pay in taxes?
b. What is his net pay?
c. If he receives two paychecks a month, how much will each paycheck be?
Lucy's gross pay per week is $393.75.
Lance's tax payment amount is $10983.
Lance's net pay is $41,317.
Lance's every paycheck of two will be around $2179 per month.
How find the pay?1) Lucy earns $15.75 per hour.
Last week she worked 25 hours.
Solution:
Lucy's gross pay per week is $15.75 * 25 hours.
Lucy's gross pay per week = 15.75 * 25 = $393.75
2) Lance has a yearly salary of $52,300
He pays 21% as taxes.
Solution:
a) Lance tax pay amount = 21/100*52,300 = $10983
b) Lance's net pay = $52,300 - $10983 = $41,317
c) Per month salary = $52,300/12 = $4358
Each paycheck will be 4358/2 = $2179
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Determine the degree measure measure of One angle of a 30 sided regular polygon.
5400°
5040°
180°
168°
The degree measure of one angle of a 30 sided regular polygon is 168°
What is a regular polygon?A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.
The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.
We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is
(Side - 2) × 180°
(30 - 2) × 180°
= 5040°
Measure of each angle of 30-gon
= 5040°/30
= 168°
Thus, the degree measure measure of One angle of a 30 sided regular polygon is 168°
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Answer: 168
Step-by-step explanation: did the test
A property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance if the distance between two points on the map is 4.9cm
A property map is drawn at a scale of 1:1000, if the distance between two points on the map is 4.9cm. then the actual distance is = 4.9 * [tex]10^{3}[/tex]
A property map is drawn at a scale of 1:1000
The distance between two points on the map is 4.9cm
Based on the given conditions, formulate :
= 4.9 * 1000/1
= 4.9 * 1000
Calculate the product or quotient,
= 4900
This alternative forms is,
= 4.9 * [tex]10^{3}[/tex]
Therefore,
The actual distance is = 4.9 * [tex]10^{3}[/tex], if the distance between two points on the map is 4.9cm.
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what will be the value of k so that the equation [tex]kx^{2} -4x+1[/tex] has two equal roots (same roots)
The value of k so that the equation has two equal roots is 4
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the value of k in the equation?The quadratic equation is given as
kx^2 - 4x + 1
A quadratic equation is represented as
ax^2 + bx + c
This means that
a = k, b = -4 and c = 1
When the equation has equal roots, we have
b^2 = 4ac
So, we have
(-4)^2 = 4 * k * 1
Evaluate
k = 4
Hence, the value of k is 4
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Kevin and Randy Muise have a jar containing 69 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.25 How many of each type of coin do they have?
Taking into account the definition of a system of linear equations, Kevin and Randy Muise have 19 quarters and 50 nickels.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In this way, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of quarters and nickelsIn this case, a system of linear equations must be proposed taking into account that
"q" is the amount of quarters."n" is the amount of nickels.You know that:
Kevin and Randy Muise have a jar containing 69 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.25The system of equations to be solved is
q + n= 69
0.25q + 0.05n= 7.25
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "q" from the first equation:
q= 69-n
Replacing this expression in the second equation:
0.25(69 - n) + 0.05n= 7.25
Solving:
0.25×69 - 0.25n + 0.05n= 7.25
17.25 - 0.25n + 0.05n= 7.25
- 0.25n + 0.05n= 7.25 - 17.25
-0.2n= -10
n= (-10)÷ (-0.2)
n= 50
Remembering that q= 69 -n, you get:
q=69 - 50
q= 19
Finally, there are 19 quarters and 50 nickels.
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PLEASE HELP AGAIN PLS
Answer:
(5,0)
Step-by-step explanation:
Let y=0. Then, x=5.