The two equations combined is
3x + y = 2010x + y = 55Eliminating one variable gives
7x = 35the variables are
x = 5y = 5How to eliminate one variable in the equation formedThe equation formed is a consistent independent set of equation with two variables solved by elimination method as follows
Elimination of one of the variable
3x + y = 20 (1)
10x + y = 55 (2)
subtracting (1) from (2)
10x - 3x + y - y = 55 - 20
7x + 0 = 35
7x = 35
x = 5
substituting to find y
3x + y = 20
3 * 5 + y = 20
15 + y = 20
y = 20 - 15
y = 5
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attachment above please
Two people are jogging around a circular track in the same direction one person can go to completely around the track in 21 minutes the second person takes 18th if they both start running in the same direction at the same time how long will it take them to be together at this place if they continue to run
Answer:
n * 21 = m * 18 one runs n laps and one runs m laps to again be together at the same place
7 n = 6 m divide by 3
one runs 7 * 18 = 126 min
the other runs 6 * 21 = 126 min
After 126 min they will be together at the start
Which of the following equations does the graph below represent?
A. 3x + 7y = 21
B. -3x + 7y = 21
C. x + 7y = 21
D. -3x + y = 21
Answer:
B
Step-by-step explanation:
if x = 0 ; y = 3
if x = -7 ; y = 0
A 0 + 7(3) = 21
0 + 21 = 21
21 = 21 (ok)
3(-7) + 0 = 21
-21 = 21 (false)
B
0 + 21 = 21
21 = 21 (ok)
(-3)(-7) + 0 = 21
21 = 21 (ok)
Given CB || ED,;CB=ED prove CBF= EDF using isometric ridged transformation outline the necessary transformation to prove CBF = EDF using a paragraph proof. Be sure to name specific sides or angles used in the transformation and any congruency statements
The given triangle is rotated about 180 degrees and as such, we can say that the triangle CBF is congruent to the triangle EDF.
How to prove congruent angles?
From the attached image, we see that CB is parallel to ED. We also see that the transversal lines are BD and CE.
The point E will become the image of point C by a rotation of 180° around the point F.
Now, the point D will be the image of point B by a rotation of 180° around the point F.
Rotation is a type of transformation and as such ΔEDF will be the image of ΔCBF.
Therefore we can conclude that ΔCBF ≅ ΔEDF
The second way to prove this congruency is as follows;
∠B = ∠D (Due to the fact that alternate angles are congruent)
∠C = ∠E (Due to the fact that alternate angles are congruent)
Now, since CB ≅ ED , then it means that ΔCBF ≅ ΔEDF by SAS congruency postulate
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10. Chelsea had completed 2/3 ofa 5-mile race when
her shoelace came untied. How many miles had
Chelsea completed at that point?
Answer:
3.3 miles with a bar notation on decimal 3
Step-by-step explanation:
convert 2/3 to decimal (2 divided by 3)
multiply 5 by decimal of 2/3
add bar notation on repeating decimal
12) m/GOP = 80°, m/ROP
and m/ROG= 32x + 4. Find x.
R
Q
= 3 +59x,
G
By using linear pair, we have found that the value of x is 3.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
Given that Angle QGP = 80°, Angle ROP = 3 + 59x and Angle ROG= 32x + 4. Find x.
Therefore, we can see that Angle ROG and Angle QGP lie in a straight line.
Thus, by linear pair
Angle ROG + Angle QGP = 180
80° + 32x + 4 = 180
32x = 100 - 4
x = 96/32
x = 3
Hence, the value of x is 3.
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16 2/3-15 1/6+1.3/2.5x1.56x0.4
HELP ASAP
Answer:
Step-by-step explanation:
The answer would be 1.82448
A Calculator salesman’s monthly income is $1500 salary plus a commission of 7% of his sales over $5000 what was his income the month that he sold $11,470 in calculators
$142428 income earned. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services.
What is commission?A type of variable-pay compensation for goods or services sold are commissions. Salespeople are frequently encouraged and rewarded with commissions. Additionally, commissions can be created to promote particular sales habits. For instance, commissions may be decreased while providing significant discounts.
Let X be the sales for a man
so7% of sales=7x/100
Total that needs to be earned=$11470
So,
Total needs to be earned= salary +commission on sale
11470=1500+7x/100
11470-1500=7x/100
9970=0.7x
X=9970/0.7
X=142428
Therefore $142428 income earned .
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Children at nutrition are either playing or sitting down resting. The ratio of kids playing to resting is 3:1. If there are 8 children resting, then how many are playing?
Answer: 24 kids playing
Step-by-step explanation: Since the ratio of the kids playing and resting is 3:1, and there are 8 kids resting, replace the 1 with 8, and multiply the 3 with 8 to make the equation balanced. 24:8!
95 POINTS
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answer: 33577
Step-by-step explanation:
3x3x5x7x7 = 2205
Martha's employee benefits include family health-care coverage. She contributes 18% of the
cost. Martha gets paid biweekly and $108.00 is taken out of each paycheck for family health-care
coverage. How much does her employer contribute annually for the family coverage?
use dollar sign, decimal and comma
The family coverage paid by Martha's employer for health care coverage is $2592.
What is a health care coverage?
Health insurance is a sort of insurance that pays for unexpected medical costs brought on by a disease. These expenditures may be associated with the price of hospitalisation, or the cost of medical visits.
Main body:
Let the total biweekly salary of Martha be x.
Therefore according to question :
18% of x =$108
(18/100)*x =108
x= 600
Martha earns $600 biweekly.
monthly earning of Martha be 600*2 =$1200
Therefore total coverage annually = 108*total salary day
=108*24
=$2592
Hence the answer is $2592.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height $h$, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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Which two operations are needed to write the expression that represents "five less than the quotient of a number and
three"?
The two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.
What is the quotient?
A result is obtained by dividing two amounts.
The quotient is the result of a division.
The term "less than" represents subtraction.
So, the two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.
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Swimming, Manufacturing, and Painting
Problem
Variables to use
Equation
Tyler swims at a constant speed, 5 meters every 4 seconds.
A factory produces 3 bottles of sparkling water for every 8 bottles of plain water.
A certain shade of light blue paint is made by mixing 1 ½ quarts of blue paint with 5 quarts of white paint.
For each of the previous three situations, write an equation to represent the proportional relationship.
The equations that represent the proportional relationships between the variables are as follows:
Problem Variables to use Equation
1. Tyler swimming Time / Distance D = 1.25t
2. Factory production Total quantity, Q, Q = 3s + 8p
and Sparkling / Plain
3. Paint mixture Blue / White Paints 6q = 1.5b + 5w
What is an equation?An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).
Tyler:Speed = 5 m/4s
= 1.25 m/s (5/4)
Swimming equation: D = 1.25t
Where D = distance and t = time spent.
Given the speed and time, we can find the swimming distance covered by Tyler.
Factory:
Bottles of sparkling water = 3
Bottles of plain water = 8
Ratio = 3:8
Production equation, Q = 3s + 8p
Where Q = total quantity, s = sparkling water, and p = plain water
Paint:Blue paint = 1 ½ quarts
White paint = 5 quarts
Ratio = 1.5:5
Production equation, 6q = 1.5b + 5w
Where 6q = 6 quarts, b = blue paint, and w = white paint
Thus, using the equations, we can use the known variables to find the unknown variables.
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Evergreen Landscaping bought 7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270. The next week the firm bought 5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015. Pea gravel costs $28 less per ton than topsoil. Find the cost per ton for each item.
The cost of topsoil per ton would be $48.
The cost of pea gravel per ton is $20.
The cost of mulch per ton is $479.
What is the linear equations in two variable?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.
We have,
7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.
5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.
Let,
cost of topsoil per ton = x
cost of pea gravel per ton = x - 28
cost of mulch per ton = m
7x + 6m + 3(x - 28) = 3270
7x + 6m + 3x - 84 = 3270
10x + 6m = 3270 + 84
10x + 6m = 3354 -------------(i)
5x + 5m + 5(x - 28) = 3015
5x + 5m + 5(x - 28) = 3015
10x + 5m = 3015 - 140
10x + 5m = 2875 -----------(II)
Subtracting equation (II) from (I), we get
10x + 6m = 3354
- 10x + 5m = 2875
Solving we get
m = 479
Put m = 479 in equation(I), we get
10x + 6m = 3354
10x + 6(479) = 3354
10x = 480
x = 480/10
x = 48
Hence,
The cost of topsoil per ton would be = x = $48.
The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.
The cost of mulch per ton = m = $479.
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A patient is using a bicycle as part of their physiotherapy routine. The diameter of the bicycle’s wheel is 590 mm. While in session, the wheel is rotating at a speed of 82 rpm (revolutions per minute). If the patient is riding the bicycle for 1 h and 10 minutes, determine the number of kilometres the patient has travelled. Round to the nearest tenth.
The total distance traveled by the patient in 1 hour and 10 minutes is 10.6 kilometers.
What is the distance?The distance is the length from one point to the end.
For our purpose, distance represents the product of speed and time.
Diameter of the bicycle's wheel = 590 mm
Speed (Revolutions) per minute = 82 rpm
Time riding the bicycle = 1 hr and 10 minutes = 70 minutes
1 Kilometer = 1,000,000 Millimeters
Distance per rotation = pi x diameter
= 3.14 x 590
= 1,852.6 mm/minute
Total distance traveled in kilometers = (1,852.6 x 82 x 70) ÷ 1,000,000
= 10,633,924 ÷ 1,000,000
= 10.6 kilometers
Thus, we can conclude that the patient traveled 10.6 kilometers by bicycling for one hour and 10 minutes.
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How did you compute sums of dollar amounts that were not whole numbers? For example, how did you compute the sum of $5.89 and $1.45? Use this example to explain your strategy.
The Sum of dollars in decimal is not a whole number.
Whole numbers are made up of natural numbers plus the number zero. In mathematics, the set of whole numbers is symbolized by the symbol W and is given as W = {0, 1, 2, 3, 4, …}.
To calculate a number of dollars that is not a whole number.
As an example, consider the sum of $5.89 and $1.45:
$5.89 + $1.45
Taking the whole numbers first:
$5 + $1 = $6
Take the sum of the decimals :
$0.89 + $0.45 = $1.34
sum of original whole + sum of decimal whole
$6 + $1 = $7
Remaining decimal: $1.34 - $1 = $0.34
$7 + $0.34 = $7.34
Therefore $7.34 is not a whole number
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Find the GCF of 21 and 28.
Answer: 7
Step-by-step explanation:
Answer:
7 is the GCF of 21 and 28
Step-by-step explanation:
The GCF of 21 and 28 is 7. To calculate the greatest common factor (GCF) of 21 and 28, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 21 and 28, i.e., 7.
round square root of 4004 to the nearest integer
It takes Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Assuming Abby doesn't stop, what is her average speed from Ashdown to Carton to 1 dp?
The average speed for the given situation is 56 mph.
Given that, Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Now, distance = Speed × Time
= 60 × 3
= 180 miles
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Now, Time = 30/40
= 0.75 hours
Total time =3+0.75=3.75 and total distance =180+30=210
Then average speed = 210/3.75
= 56 mph
Therefore, the average speed for the given situation is 56 mph.
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1/3a^2+a=0
It's rather urgent, please or else I will fail my semester...
The solution of the equation given as 1/3a² + a=0 is a = 3
How to determine the solution to the equation?From the question, we have the following equation that can be used in our computation:
1/3a^2+a=0
Rewrite the equation properly
So, we have
1/3a² + a=0
Multiply through the above equation by 3
So, we have the following equation
3 * (1/3a² + a) =0 * 3
Evaluate the products
So, the equation becomes
a² + 3a = 0
Next, we divide through the equation by the variable a
This gives
a + 3 = 0
Subtract 3 from both sides of the equation
i.e. Add -3 to both sides of the equation
a = -3
The above equation cannot be solved further.
So, we leave it like that and stop solving
Hence, the solution to the equation is a = -3
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The doubling period of a bacterial population is 20 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0?
Find the size of the bacterial population after 3 hours.
The initial population of the bacterial population at time t = 0, can be found to be 1,406.25.
The size of the bacterial population after 3 hours is 720,000.
How to find the bacterial population?The doubling period of the bacterial population is said to be 20 minutes. The number of doubling periods in 120 minutes is:
= 120 / 20
= 6 doubling periods
The initial population is:
= Population at 120 minutes / 2 ^ number of doubling periods
= 90,000 / 2⁶
= 1,406.25
The bacterial population at 3 hours is:
= Bacterial population at t = 0 x 2 ^ number of doubling periods in 3 hours
= 1,406.25 x 2 ^ (180 minutes in 3 hours / 20)
= 1,406.25 x 2⁹
= 720,000
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Classify the polynomial by its degree: 4m³-9x² + 10
A) 0
B) 1st
C) 2nd
D) 3rd
E) 4th
In 5-10, match each expression with the correct value
Trignometric equation can be used to answer this:
What is trignometric equation?A trigonometric equation is any equation that contains a trigonometric function. Up until now we have introduced trigonometric functions, but not fully explore them. In the lessons within this SparkNote on trigonometric equations, we'll learn exactly how to solve trigonometric equations.As mentioned in Trigonometric Identities, a trigonometric equation that holds true for any angle is called a trigonometric identity. There are other equations, though, that only are true for certain angles. They are generally known as conditional equations, but in this text we'll just call them equations. We'll learn some techniques for solving general equations, as well as how to derive an infinite number of solutions to an equation based on a single solution to that equation.acc to our question-
5. cos(75)= 2-√3
6. tan(22/7)= 1+√2
7. sin 3π/6= √2-√√2/2
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What line is perpendicular to the line y= -1/2x + 8
Answer: y=2x+8
Step-by-step explanation:
you take the reverse of the slope being 2 including the negative.
What is the equation of the line that passes through the point (6, 4) and has a slope 2/3
The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x
Given,
The points which the line passes through = (6, 4)
Slope = 2/3
We have to find the equation of line;
Linear equation;
Y = mx + b is one way to represent a linear equation.
A point's coordinates are x and y.The slope is m.The position of the point where the line crosses the y axis is represented by the integer b, which is the ordinate to the origin.Here,
x is 6 and y is 4
Slope, m is 2/3
Then,
Substitute the values in y = mx + b
Here,
y = mx + b
4 = 2/3 (6) + b
4 = 12/3 + b
4 = 4 + b
b = 4 -4
b = 0
Then,
The equation of line is, y = 2/3x + 0
That is,
The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x
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One spring day, Harper noted the time of day and the temperature, in degrees
Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 58° F. For the
next 3 hours, the temperature rose 4° per hour. For the next 5 hours, it rose 1° per
hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the
temperature was 70° at midnight. On the set of axes below, graph Harper's data.
The graph that shows Harper's data about temperature and time is shown below .
The graph is a relation that represents the relationship between two variables on the x and y axis .
In the question ,
Harper's data of time of day and the temperature, in degrees Fahrenheit is given,
the temperature at 6 a.m. = 58° F
for the next 3 hours the temperature rose 4° each hour means
in 3 hours it will rise 12°
So , the temperature at 9 a.m. = 70° F
For the next 5 hours, it rose 1° per hour which means
in 5 hours it will rise 5°
So , the temperature at 2 p.m. = 75° F
The temperature then stayed steady until 6 p.m. which means
temperature at 6 p.m. = 75° F
For the next 2 hours, the temperature dropped 1° per hour , which means
temperature at 8 p.m. = 73° F
the temperature at midnight = 70° F
So , from the above data the graph is shown below .
Therefore , The graph that shows Harper's data about temperature and time is shown below .
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The function C(x)=−21x+2025 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $24?
The least number of items that can be produced so that the average cost is no more than $24 is 95.
According to the question,
We have the following information:
The function C(x)=−21x+2025 represents the cost to produce x items.
Cost should be no more than $24.
So, we have the following inequality to find the number of items:
-21x+2025 ≤24
Subtracting 2025 from both sides:
-21x≤24-2025
-21x ≤ -2001
Dividing both sides by -21:
x ≤ 2001/21
x ≤95.28
Hence, the least number of items that can be produced so that the average cost is no more than $24 is 95.
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1/3 divide by 4 3/4 simplest form
Step-by-step explanation:
first put 4 3/4 into a improper fraction ---> 19/4
you get 19/4 because 4 is equal to 16/3 plus the 3/4
then you will do keep, flip change so it becomes multiplication
so instead of 1/3 divided by 19/4 it will be 1/3 x 4/19 then
multiply it out to get 19/12
Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present.
How many yards does he have left?
Step-by-step explanation:
Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present. How many yards does he have left?
5/6 - 2/6 = 3/6
3/6 reduces to 1/2 yards left