Answer:
So the solution to the system of equations is (x,y) = (3,-2).
Step-by-step explanation:
To solve for x and y using substitution, we can first substitute y=-2 into the second equation to find the value of x, and then use that to find y.
Starting with the second equation:
4x - 3(-2) = 18
Expanding the -3(-2) using the distributive property:
4x + 6 = 18
Subtracting 6 from both sides:
4x = 12
Dividing both sides by 4:
x = 3
Now that we have x = 3, we can substitute that back into the first equation to find y:
y = -2
So the solution to the system of equations is (x,y) = (3,-2).
In the diagram below,
ABCE is a trapezium,
AD is parallel to BC,
DE=4cm
Area of ABCE=60cm^2
Area of ABCD=48cm^2
Work out the values of f and g.
You must show all your working.
The values of f and g based on the given diagram ABCE is 6cm and 8cm respectively.
What is the values of f and g?Area of ABCE = 60cm²
Area of ABCD = 48cm²
Area of ADE = Area of ABCE - Area of ABCD
= 60 cm² - 48 cm²
= 12 cm²
Area of ADE = 1/2 × base × height
12 = 1/2 × 4 × h
12 = 4/2h
12 = 2h
divide both sides by 2
h = 12/2
h = 6 cm
AD = height = BC = 6 cm
Area of ABCD = length × width
48 = l × 6
48 = 6l
l = 48/6
l = 8 cm
In conclusion, f and g are 6cm and 8cm respectively.
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Which of the following shows measurements ordered from smallest to largest? answers: 60,000 mg, 1.5 kg, 3,000 g 3,000 g, 1.5 kg, 60,000 mg 1.5 kg, 3,000 g, 60,000 mg 60,000 mg, 3,000 g, 1.5 kg who ever help me get 100 brainy.
Answer:
60000 mg, 1.5 kg, 3000 g-----------------------
Given measurements:
60000 mg, 1.5 kg, 3000 gBring all to same unit, grams, then compare;
60000 mg = 60 g,1.5 kg = 1500 g,3000 gOrder them from smallest to largest:
60 g < 1500 g < 3000 g or 60000 mg < 1.5 kg < 3000 gAnswer:
The order of the measurements from smallest to largest is:
60,000 mg, 1.5 kg, 3,000 gStep-by-step explanation:
The three given measurements of mass are:
60,000 mg1.5 kg3,000 gDefinitions"g" means grams."mg" means milligrams. "Milli" means a thousandth.Therefore, to be able to order the three given measurements from smallest to largest, first convert them to the same unit of mass (grams):
⇒ 3,000 g = 3,000 g
⇒ 60,000 mg = 60,000 × 0.001 = 60 g
⇒ 1.5 kg = 1.5 × 1000 = 1,500 g
Therefore, the order of the measurements in grams from smallest to largest is:
60 g < 1,500 g < 3,000 gSo, the order of the measurements in their original units from smallest to largest is:
60,000 mg, 1.5 kg, 3,000 gFind the polynomial function k(x) of lowest degree in standard form if it has roots:
x=1,3,2i
Answer:
So the polynomial function is
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
Step-by-step explanation:
A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),
From the above data we can get,
k(x) = (x - 1)(x - 3)(x - 2i)
After expanding the equation ,
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
So the polynomial function is
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
10.a) Which numbers less than 100 have exactly 3 factors (including 1 and the number itself)?
b) Which two numbers less than 100 have exactly 5 factors?
c) Which number less than 100 has exactly 7 factors?
Step-by-step explanation:
a)
any prime number has only 2 (1 and the number itself).
almost every even number has 1, 2, a factor of 2 and the number itself. so that did not work either.
following that line of thought, the only possible solutions are square numbers of prime numbers :
4, 9, 25, 49
they have only 1, its square root and the number itself as factors.
b)
in the same line of thinking it must be powers of 4 of prime numbers :
2⁴ = 16
with the factors 1, 2, 4, 8, 16
3⁴ = 81
with the factors 1, 3, 9, 27, 81
c)
and so, it must be a power of 6 of a prime number.
the only one possible is
2⁶ = 64
with the factors 1, 2, 4, 8, 16, 32, 64
Use factoring to find the x-intercept(s)
of the function below.
Enter the smaller value first.
0 = 2x² + 5x - 3
Answer: x = -3, 1/2
Step-by-step explanation:
the number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete
The number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete are not directly related. The time it takes for a person to complete a jigsaw puzzle depends on several factors, including the person's experience with puzzles, the level of difficulty of the puzzle, the size of the puzzle pieces, and the person's level of concentration.
For example, a 500-piece puzzle might take one person several hours to complete, while another person might be able to finish it in just a few hours. Similarly, a 1000-piece puzzle might take one person a full day to complete, while another person might be able to finish it in just a few hours.
In general, the larger the number of pieces in a puzzle, the more time it will take to complete. However, the actual time required can vary greatly depending on the individual and the specific puzzle.
Mrs. Jacobson is shopping for school supplies with her children. Isabelle selected 4 one-inch binders and 5 two-inch binders, which cost a total of $24. Bill selected 1 one-inch binder and 2 two-inch binders, which cost a total of $9. How much does each size of binder cost?
ANSWER is one- incher=1 while two inch binder=2.By using simultaneous equation.
FIND THE PERIMETER AND AREA OF THE RECTANGLE
Answer:
Area = 15a^3b^6
Perimeter: 10a^2b^4+6ab^2
Step-by-step explanation:
Formula For Area: L*W
Input The Numbers: 5a^2b^4 * 3ab^2
5a^2b^4 * 3ab^2 = 15a^3b^6
Area = 15a^3b^6
Formula for perimeter: P=2(l+w)
Input the Numbers: P = 2(5a^2b^4 + 3ab^2)
2(5a^2b^4 + 3ab^2) = 10a^2b^4+6ab^2
Perimeter: 10a^2b^4+6ab^2
Hope this helped!
If 4 is added to twice the number n, the result is the same as if n were increased by 7. What is the value of n?
Answer:
n = 3
Step-by-step explanation:
Starting equation:
2n + 4 = n + 7
Subtract by n on both sides:
n + 4 = 7
Subtract 4 on both sides
n = 3
Check to see if the answer works:
2(3) + 4 = 3 + 7
6 + 4 = 3 + 7
10 = 10
The solution works
n = 3
In a rectangular dog pen, a temporary fence is constructed from D to Y to enclose
an area for a new puppy to play, away from the more energetic older dogs. OY= 12
feet, DY= 31 feet, and mOYD= 65°. What is the area of the triangular puppy
pen, to the nearest tenth of a square foot?
The area of the right triangular puppy pen found using the formula 1/2(b.h²) is 4900.90 feet².
What is a triangle?
A polygon with three edges and three vertices is called a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A right triangle is a specific kind of triangle that has one angle that is exactly 90 degrees.
Given,
The length of OY = 12 feet
The length of DY = 31 feet
m∠OYD = 65°
Since SDOG is a rectangle, m∠DOY = 90°.
So the ΔDOY is a right triangle.
Area of right triangle = 1/2 * b * h²
where b = base length
h = height
From the given figure,
b = OY = 12
h = OD
h can be found using Pythagoras' theorem.
DY² = OD² + OY²
OD² = DY² - OY² = 31² - 12² = 817
OD = √817 = 28.58 feet = h
Therefore the area of the right triangle ΔDOY is
area = 1/2 * b * h² = 0.5 * 12 *28.58² = 4900.90 feet².
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Graph the inequality on the axes.
y < 3x - 7
Answer:
Step-by-step explanation:
make the inequality y=3x-7 to get the linear line then find x=0 with is -7 and anything below that line or on the line is not part of the inequality therefore remember to graph with a dotted line instead of a solid.
Based on this graph, what is the solution to the system of equations?
Answers:
1. There are an infinite number of solutions.
2. There is no solution.
3. (1, 3)
4. (2, 3)
5. (3, 2)
One solution exists for the following system of equations. In this question, correct answer is option (5) which states the solution is point
(3 , 2).
What is Equation ?There are many various ways to define an equation. The definition of an equation in algebra is a mathematical statement that illustrates the equality of two mathematical expressions.
As we know that when the system of equations are given in graph form ,
then the solution to them is the number of points they intersect each other.
one solution - if graph of equations intersects at one pointtwo solution - if graph of equations intersects at two pointsno solution - if graph of equations do not intersect at any pointmany (infinite) solutions - if graph of equations intersects at many points or coincide each other.Now in the given question,
In the given graph it can be clearly seen that graphs of equations meet at one point. The point at which the graph meets is (3 , 2).
We can see that option (5) is correct.
So the given system of equations have one solution.
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Situation
ion below. Then wr
1.
A rectangle is 4 times as long as it is wide. The
perimeter of a rectangle is 50 cm. What are the
dimensions of the rectangle?
Identify what you are looking
for and assign variables..
Write equations to model the
situation described in the
problem.
The dimensions will be as follows;
width is 5cm while the length is 20cm.
Let width = w
Let length = 4w (according to question)
Perimeter = 50cm
Perimeter formula for a rectangle = 2 (l +w)
Substituting in the variables (width and length)
2(w + 4w) = 50
2(5w) = 50
10w = 50
w = 5
Remember that length = 4w
length = 4w
length = 4(5)
length = 20cm
Therefore, the dimensions of the rectangle are 5cm by 20 cm.
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Find the perimeter and area of the rectangle
Answer:
Step-by-step explanation:
The perimeter of the rectangle: We know that the frame is equal to 2(L+B)
therefore, the edge of a rectangle is 2[5a^2b^4 + 3ab^2]
= 2[ab^2(5ab^2 + 3)]
The area of a rectangle is L * B
= (5a^2b^4) * (3ab^2)
= 15a^3b^6
at the city museum, child admission is and adult admission is . on wednesday, tickets were sold for a total sales of . how many child tickets were sold that day?
Number of child tickets were sold on Wednesday is 33 if three times as many adult tickets as child tickets were sold.
According to the question
At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10
Number of Child admission = x
Number of Adult admission = y
On Wednesday ;
y = 3x
9.80y + 6.30x = 1178.10
9.80(3x) + 6.30x = 1178.10
29.40x + 6.30x = 1178.10
35.70x = 1178.10
x = 1178.10 / 35.70
x = 33
So, 33 child tickets were sold on Wednesday.
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The complete question is
At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10 . How many child tickets were sold that day?
What is an equation of the line that passes through the points (-1,6) and (4,-4)
The linear equation that passes through the two given points is:
y = -2x + 4
How to write the equation of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, 6) and (4, -4), then the slope is:
a = (-4 - 6)/(4 + 1) = -2
y = -2x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-1, 6) we will get:
6 = -2*-1 + b
6 = 2 + b
6 - 2 = b = 4
The linear equation is y = -2x + 4
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Zendaya was comparing the price of grapefruit juice at two stores. The equation
y = 0.97x represents what Zendaya would pay in dollars and cents, y, for x bottles
of grapefruit juice at store A. Zendaya can buy 4 bottles of grapefruit juice at Store b
for a total cost of $6.80.
How much more is a bottle of grapefruit juice at Store B than
at Store A?
5x-5=3x+15
it’s confusing someone help
Answer:
x=10
Step-by-step explanation:
First, add 5 to both sides of the equation, getting rid of the -5 on the left side but still making them equal.
5x=3x+20
Then, do the same with 3x, Subtract from both sides.
2x=20
Lastly, Divide both sides by 2 and you'll get your answer
x=10
Answer:
[tex] \sf \: x = 10[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x - 5 = 3x + 15
Then the value of x will be,
→ 5x - 5 = 3x + 15
→ 5x - 3x = 15 + 5
→ 2x = 20
→ x = 20 ÷ 2
→ [ x = 10 ]
Hence, the value of x is 10.
10. If the opposite angle of the parallelogram is 22 less, than thrice the other angle. Find the other angle (a) 24° (c) 22° (d) 32° (b) 34°
The measure of the other angle of the parallelogram is 22 degrees.
What is the other angle of the parallelogram?Opposite angles of a parallelogram are equal (or congruent).
Let the missing angle be represented by x.
First angle = xOpposite angle = 2x - 22Since the opposite angles of a parallelogram are equal (or congruent).
x = 2x - 22
Solve for x
2x - 22 = x
2x = 22 + x
2x - x = 22
x = 22°
Therefore, 22 degrees is the measure of the other angle.
Option C) 22° is the correct answer.
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HELP PLS! ITS DUE IN 30 MIN!!!!!!!
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending:
y = -10x + 300
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending:
y = -10x + 300
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
Using the given linear equation, we found the altitude of the plane at different time periods and the altitude of airplane at 5 and 30 minutes is found to be 250 feet and 0 feet respectively.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.
The linear equation which shows the altitude of an airplane is as follows,
y = -10x + 300
where y = altitude (in feet)
x = time of descend ( minutes)
a) when x = 0
y = 300 feet
when x = 5 minutes
y = -10 * 5 + 300 = 250 feet
when x = 8 minutes
y = -10 * 8 + 300 = 220 feet
when x = 10 minutes
y = -10 * 10 + 300 = 200 feet
when x = 30 minutes
y = -10 * 30 + 300 = 0 feet.
the table is as follows:
x (minutes) 0 5 8 10 30
y(feet) 300 250 220 200 0
b) From the above table, we can see that at 5 minutes the altitude is 250 feet and at 30 minutes, the altitude is 0 feet. There is a decrease in altitude, which suggests the plane is descending and finally landed when the time was 30 minutes.
Therefore using the given linear equation, we found the altitude of the plane at different time periods and discussed the altitude of airplane at 5 and 30 minutes.
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The point (1/6,0) is on the curve. Find the value of (y^-1)' (0)
The value of the inverse relation is y'(0) = 1/6
How to determine the value of the inverse functionFrom the question, we have the following parameters that can be used in our computation:
The point (1/6,0) is on the curve
The notation (y^-1)' (0) is an inverse notation
Using the above as a guide, we have the following:
(1/6,0) means y(1/6) = 0
This also means that
y'(0) = 1/6
Hence, the solution is 1/6
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When factoring a tricky trinomial, a > 1, and you have more than one pair of factors for a term, which pair should you always try first?
When factoring a tricky trinomial with a leading coefficient greater than 1, and you have more than one pair of factors for a term, it is usually best to try the pair of factors that multiplies to give the constant term first.
This is because when factoring a trinomial with a leading coefficient greater than 1, the first term will always have fewer factors than the last term, and it can be easier to find the correct pair of factors for the constant term than for the first term.
If the correct pair of factors for the constant term is found first, it can be easier to use that information to deduce the correct pair of factors for the first term.
In addition, once you have found one pair of factors for the trinomial, you can use the factoring by grouping technique to factor the trinomial completely. This involves grouping the terms of the trinomial in pairs, factoring out the greatest common factor of each pair, and then factoring out the greatest common factor of the resulting expressions.
Overall, when factoring a tricky trinomial with a leading coefficient greater than 1, it can be helpful to start by trying the pair of factors that multiplies to give the constant term first, and then using the factoring by grouping technique to factor the trinomial completely.
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Find Integral 0 to 1 f’(x)dx if f(5) = -7.8.
Answer:
[tex]-22.8[/tex]
Step-by-step explanation:
[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]
30 minutes twice a day for 184 days how many gallons of water will be used in each hole
30 minutes twice a day for 184 days, total 368 gallons of water will be used in each hole.
Assuming that each hole uses one gallon of water per 30 minutes.
1 hole = 1 gallon of water
The total amount of water used in each hole over 184 days would be 184 gallons.
So, in 184 days = 184 gallons of water
This is because each hole would be watered twice a day for 184 days, which comes out to 368 separate waterings.
= 184 × 2
= 368 gallons
The total amount of water used would be 368 gallons.
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The complete question is:
How many gallons of water will be used in each hole if 30 minutes is spent twice a day for 184 days?
It takes Andre 4 min to swim 5 laps how many laps per min?
Answer:
1.25 laps per minute
Step-by-step explanation:
5 laps in 4 minutes so distance over time is equal to rate so
5/4=1.25
the number of people living in baltimore is 183,000. the number of new active cases of tb occurring between january 1 and june 30, 2012 was 26. the number of active tb cases according to the city register on june 30, 2012 was 264. the incidence rate of active cases of tb for the 6-month period was:
The incidence rate of active cases of tb for the 6-month period was 0.00014
An incidence rate describes how quickly disease occurs in a population.
Incidence rate is the rate of new occurrence of a particular disease divided by the population of people at risk of the disease.
So for this question
The number of new active cases of tb occurring between January 1 and June 30, 2012 was 26
Population at risk in Baltimore is 183,000
Incidence rate = 26/183,000
The incidence rate of active cases of tb for the 6-month period was 0.00014 or 14 per 100,000 population.
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Evelyn bought 8.4 gallons of gas for $23.94. Which equation can be used to determine the price of each gallon of gas?
8.4x = 23.94
StartFraction x over 8.4 EndFraction = 23.94
23.94 x = 8.4
StartFraction x over 23.94 EndFraction = 8.4
Answer:
Step-by-step explanation:
The required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.here,Let the cost of gas per gallon be x,Now according to the question,Cost of 8.4 gallons of fuel = 8.4xfrom the question,8.4x = 23.94Thus, the required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.
The graph shows f(x)and its transformation g(x). Enter the equation for g(x) in the box. g(x) =
The function g(x) can be written as -
g(x) = f(x - 1)
What is graph translation?Graph translation is a process of moving the graph over the dimensional plane either vertically, horizontally or both.
A translation can take place either horizontally or vertically as -
Vertical translation → Upward (y + k) & Downward (y - k).Horizontal translation → Upward (x + k) & Downward (x - k).Given are the graphs of exponential functions f(x) and g(x).
We can write the exponential function g(x) as -
g(x) = f(x - 1)
Therefore, the exponential function g(x) can be written as -
g(x) = f(x - 1).
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A helium tank shaped like a cylinder has 2,401π in3 of space inside the tank. If the diameter of the helium tank is 14 inches, what is its height?
49 inches
28 inches
12.25 inches
7 inches
A helium tank shaped like a cylinder has 2,401π in³ of space inside the tank. If the diameter of the helium tank is 14 inches, its height is 1 inch.
What is Volume?
Volume is a measure of the amount of space occupied by a three-dimensional object or a region of space. It is usually measured in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or liters (L).
For a solid object, such as a cube, cylinder, or sphere, volume is calculated by measuring the length, width, and height of the object and using a formula that is specific to that shape. For irregularly shaped objects, such as rocks or trees, volume can be determined by using techniques such as water displacement.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, we are given the diameter of the cylinder, which is 14 inches. The radius of the cylinder is half of the diameter, so r = 7 inches.
We are also given the volume of the cylinder, which is 2,401π cubic inches.
Using the formula for the volume of a cylinder, we can set up the following equation:
2,401π = π(7)²h
Simplifying this equation, we get:
2,401 = 49h
Dividing both sides by 49, we get:
h = 49/49 = 1
Therefore, the height of the helium tank is 1 inch.
However, this answer seems unlikely since the height of the tank should be greater than its radius. Therefore, there may be an error in the given volume or diameter of the tank.
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the answer is A its height is 49
put numbers in order smallest to largest: 0.5, 0.03, 0.42, 0.3, 0.243
Answer: 0.03, 0.243, 0.3, 0.42, 0.5
Step-by-step explanation:
Hope this helps you!
Answer:
Step-by-step explanation:
0.243, 0.03, 0.3, 0.42, 0.5
