Answer: x is anything from the set {2, 3, 5, 7, 11}
This is the list of primes between 1 and 11. The value 1 is not prime.
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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The sharks are fed three times a day. During the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning. if the total weight of the fish fed in a day is 1/2 of a ton, how much is fed during the feeding at night?
The shark is fed during the feeding at night is 1/6 tons.
What is a proper fraction?
A proper fraction is one that doesn't contain any whole numbers and has a smaller numerator than a denominator. A fraction that represents a number greater than one and has a larger numerator than the denominator is said to be improper.
Given that during the morning feeding, 2/15 of a ton of fish is fed. During the afternoon feeding the weight of the fish fed will be 1/15 of a ton more than the fish fed during the morning.
The shark fed (2/15 + 1/15) ton during the afternoon.
Assume that the shark fed x tons at night.
Therefore, the total fed is 2/15 + (2/15 + 1/15) + x
The equation is:
2/15 + (2/15 + 1/15) + x = 1/2
Add like terms:
5/15 + x = 1/2
1/3 + x = 1/2
Subtract 1/3 from both sides:
x = 1/2 - 1/3
x = (3-2)/6
x = 1/6
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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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how many significant figures do each of the following measurements contain? type a number (i.e., 1, 2, 3, etc) for each of your responses, not the written word for the number.
Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2 significant figures.
Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.
Below are the key figures for each value reported.
(a) 2- 1significant digits
(b) 81.640 - 4 significant digits;
(c) 7.03 - 3 Significant Figures
(d) 0.003 - 1significant digits
(e) 0.0086 to 2 significant digits
(f) 3236 - 4 significant digits
(g) 8700 - 2 significant digits
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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]
39. Tugboat A and Tugboat B are pulling a barge. Each tugboat is connected to the barge via a cable. If the length of the cables are 63 meters and 68 meters and the tugboats are 35 meters apart, find the angle formed between the cables.
The angle formed between the cables is 48.7°.
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
Given: Tugboat A and Tugboat B are pulling a barge. Each tugboat is connected to the barge via a cable. If the length of the cables is 63 meters and 68 meters and the tugboats are 35 meters apart.
a = 68 m
b = 63 m
c = Distance between the tugboats = 35 m
m∠C = Angle between the cables
c² = a² + b² - 2abcosC
m∠C = cos⁻¹(c² - a² - b²)/(-2ab)
m∠C = cos⁻¹(35² - 68² - 63²)/(-2(68)(63))
m∠C = 48.7°
Hence, the angle formed between the cables is 48.7°.
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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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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
what is the measure of the angle of one slice of pizza if the length of the crust (arc) is 4.9 in and the length of one side of the slice is 6.2 in?
The correct answer is 45.28°
In order to get that answer, you must set up the arc length formula.
l = m/360 • 2πr
4.9 = m/360 • 12.4π
We are trying to find the angle measure; therefore, we are going to divide.
4.9 = 0.10821m
Flip the equation
0.10821m = 4.9
0.10821m/0.10821 = 4.9/0.10821
m = 45.28°
We can use the formula angle = (arc length / radius) or an online calculator to find the angle of the slice, which is approximately 47 degrees in this case.
To find the measure of the angle of one slice of pizza, we can use the formula:
angle = (arc length / radius)
However, we are not given the radius of the pizza, so we first need to find it. One way to do this is to use the length of one side of the slice and the central angle of the slice. We know that the central angle of the slice is twice the angle at the center of the pizza that the slice occupies, so we can find this angle by:
angle at center = (angle of slice) / 2
We can then use the law of cosines to find the length of the radius:
radius² = (side length / 2)^2 + (side length / 2)² - 2 * (side length / 2) * (side length / 2) * cos(angle at center)
Once we have the radius, we can use the formula above to find the angle of the slice. However, since this calculation can be quite involved, it may be simpler to use an online pizza slice angle calculator. Using this tool with the given values, we find that the angle of one slice of pizza is approximately 47 degrees.
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PLEASE HELP !!
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A university has 32,370 students. In a random sample of 180 students, 12 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is ___________ .
The institution anticipates having 2158 students who can speak three or more languages.
Describe proportion in simple terms.The two ratios given are equivalent to one another, as demonstrated by the proportional equation. The percentage expresses the equality of something like the two ratios as well as fractions.
How do you teach pupils about proportion?Comparing two integers that each stand for a component of a whole results in a percentage. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.
[tex]\frac{x}{32370}=\frac{12}{180}[/tex]
[tex]{x} = \frac{12}{180}\times32370\\{x}=2158[/tex]
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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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A pet store has 80
geckos and anole lizards altogether.
The ratio of geckos to anole lizards is 1:3
.
How many geckos does the pet store have?
Answer:
About 54 geckos
PLEASE HELP A WHOPPING 100 POINTS!!! AND BRAINLY NO LINKS
Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer: 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The 30-60-90 triangle rule states that the hypotenuse is twice the length of the shortest leg (which would be 5) and the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg.
Since we are trying to find x we would use the rule for the longer leg
so 5 * [tex]\sqrt{3}[/tex] would just be 5[tex]\sqrt{3}[/tex]
The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
What is Triangle theorem?The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.
here, we have,
Using this theorem, we can write:
y = hypotenuse
Opposite of 30° angle = 5 = hypotenuse/2
Opposite of 60° angle = x = hypotenuse × (√(3)/2)
Solving for the hypotenuse in terms of y from the first equation, we get:
hypotenuse = 5×2 = 10
Substituting this value into the third equation, we get:
x = 10 × (√(3)/2) = 5 × √(3)
Hence, The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
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(1 point) The expression 4^65536g³y² √√/65536g³y² equals kg³y³
where r, the exponent of g, is:
and s, the exponent of y, is:
and k, the leading coefficient is:
The 4 is the square root
The exponent of g, r, is -65536.
The exponent of y, s, is 1.
The leading coefficient, k, is 4.
Note: The expression 4^65536g³y² √√/65536g³y² is not equal to kg³y³, but instead represents the value of 4 raised to the power of 65536 times g raised to the power of -65536, divided by the square root of 65536 times g raised to the power of -65536 times y squared. The square root symbol is used twice, which is equivalent to taking the square root of the square root, or the fourth root.
Boat
Boat A
Boat B
Cost
$2400
$2800
< Previous
Miles Per Gallon
(MPG)
15
18
Estimated Repairs
$600
$250
Stephanie wants to compare the total cost of buying and using these boats on her local lake.
Stephanie estimates she will drive the boat at least 40 miles per month.
The average cost of gasoline per gallon in her city is $3.89.
• Stephanie plans on owning the boat for 3 years.
Which boat will cost Stephanie the least to buy and use? How much will the difference in cost be?
Boat A will cost less for Stephanie. The difference in cost will be $400.
Boat B will cost less for Stephanie. The difference in cost will be $12.24
Boat A will cost less for Stephanie. The difference in cost will be $12.24.
O Boat B will cost less for Stephanie. The difference in cost will be $400.
The boat that will cost Stephanie less to buy and use is boat B, and the difference between the cost is $11.7.
How much will each boat cost?Let's calculate first the cost of each boat:
Boat A
cost + repairs + gasoline for 3 years= total cost
2400 + 600 + gasoline cost
gasoline cost = 40 / 15 = 2.66 gallons per month x 36 = 95.76 X 3.89 = 372.5
2400 + 600 + 372.5 = 3,372.5
Boat B
cost + repairs + gasoline for 3 years= total cost
2800 + 250 + gasoline cost
gasoline cost = 40 / 18 = 2.22 gallons per month x 36 = 79.92 X 3.89 = 310.88
2800 + 250 + 310.88 = 3,360.88
Difference: 3,372.5 - 3, 360.88 = 11.7
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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?
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!
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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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?
multivariate data set contains 25 subjects and 7 variables (5 numerical and 2 categorical). what is the correct size of the distance matrix? question 15 options: 25 x 25 25 x 7 25 x 2 7 x 7
The correct size of the distance matrix for a multivariate data set with 25 subjects and 7 variables is 25 x 25.
Understanding the many objectives and histories of the various types of multivariate analysis, as well as how they connect to one another, is the focus of multivariate statistics.
The distance matrix contains the pairwise distances between all pairs of subjects in the dataset, and therefore has the same number of rows and columns as the number of subjects in the dataset. Since there are 25 subjects in this dataset, the distance matrix will have 25 rows and 25 columns.
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Rewrite x(t)=(1.45)^t/2 in the form y=a(1+r)^t or y=a(1-r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.
The given function represents exponential growth, the value of a is 1 and the value of r is 0.45.
What is the exponential growth?The quantity increases slowly after which the rate of change and the rate of growth increases over a period of time rapidly. This increase in growth is calculated by using the exponential growth formula.
The exponential growth formula is [tex]Amount = Initial value(1+\frac{r}{100} )^{\frac{t}{n}}[/tex].
The given exponential function is [tex]x(t)=(1.45)^{\frac{t}{2} }[/tex].
Now, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex]
Compare, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex] with [tex]y=a(1+r)^t[/tex], we get
a=1 and r=0.45
Therefore, the value of a is 1 and the value of r is 0.45.
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While shopping for clothes, Tracy spent $38 less than 3 times what Daniel spent. Write and solve an equation to find how much Daniel spent. Let x represent how much Daniel spent.
This is 7th grade math lol and i have no idea how to do it
On solving the provided question, we can say that equation for getting amount spent by Daniel is y + 38 / 3 = x
What is equation?A mathematical equatiοn is a formula that joins two statements and uses the equal symbοl (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equatiοn in algebra.
For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.
equatiοn for getting amοunt spent by Daniel -
x = y+38 / 3
Tracy then spent (in dοllars) accοrding to the provided descriptiοn (we don't write symbols like $ when writing equations because it is clear from the cοntext what the quantity stands fοr).
y = 3x - 38
y + 3x8 = 3x
y + 38 / 3 = x
equation for getting amοunt spent by Daniel is
y + 38 / 3 = x
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The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. How many gears does the bike have
The bike has 21 gears, 3 on the front and 7 on the rear cogset, giving a total of 21 average possible gear combinations.
The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. This combination of 3 sprockets on the front and 7 on the rear creates a total of 21 possible gear combinations. This is calculated by multiplying the number of sprockets on the front by the number of sprockets on the rear. When you change the gear on the bike, you are changing the combination of the front and rear sprockets. By doing this, you can adjust the gearing of the bike to make it easier or harder to pedal depending on the terrain. Having a wide range of gears helps you to climb hills, accelerate and maintain speed on flat roads, as well as descend hills. Having 21 gears gives you a lot of options to make your ride as comfortable and efficient as possible.
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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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Robin and 2 friends each were able to jump rope for 4/5 minute. How long did they jump rope for altogether?
Answer:
[tex]p(3and7)andq(1and9)[/tex]
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.
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:
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
Yousuff deposits $2,500 into a savings account that has a simple interest rate of 3.8%.
5A) How much interest will Yousuff make in one year? Show your work!
5B) How much interest will Yousuff make after 8 years? Show your work!
5C) After 8 years, how much money will Yousuff have in his account? Remember to include both the original principal money AND the interest she made.
Step-by-step explanation:
Principal = $2,500
Rate = 3.8%
5A). The interest Yousuff make in one year
Therefore Time = 1 year.
Simple interest
[tex] = \frac{pincipal \times time \times rate}{100 \\ } \\ = \frac{2500 \times 1 \times 3.8}{100} \\ = 25 \times 1 \times 3.8 \\ = 95 .[/tex]
Therefore the interest Yousuff make in one year = $95.
5B). Interest Yousuff make in after 8 years
the time = 8 years
the interest
[tex] = \frac{pincipal \times time \times rate}{100} \\ = \frac{2500 \times 8 \times 3.8}{100} \\ = 25 \times 8 \times 3.8 \\ = 200 \times 3.8 \\ = 760 [/tex]
Therefore the interest Yousuff make after 8 years = $760.
5C). Principal - interest that Yousuff made after 8 years.
$2500 - $ 760
= $ 1,740.
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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