Justin is younger than Hassan. Their ages are consecutive integers. Find Justin's age if the product of their ages is 210.
Answers
Justin is 14 years old, and Hassan is 15 years old.
What are integers?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let's assume that Justin's age is x. Then, Hassan's age is x + 1, since their ages are consecutive integers and Hassan is older than Justin.
We are given that the product of their ages is 210:
x(x + 1) = 210
Expanding the left-hand side and simplifying, we get:
x² + x - 210 = 0
This is a quadratic equation in standard form. We can solve for x by using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -210.
Plugging these values into the formula, we get:
x = (-1 ± √(1² - 4(1)(-210))) / 2(1)
x = (-1 ± √(1 + 840)) / 2
x = (-1 ± √(841)) / 2
We take the positive root because x represents Justin's age, which is a positive integer. Therefore:
x = (-1 + 29) / 2 = 14
So, Justin is 14 years old, and Hassan is 15 years old.
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Related Questions
What is the answer to this problem
IMMEDIATE HELP
Answers
A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit. The given expression when simplification is equal to (-30 - 8i)/(7 + 6i³).
What is a complex number?A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit, and satisfies the equation i² = -1; every complex number may be represented as a + bi, where a and b are real numbers.
The given expression can be simplified as shown below.
\(\dfrac{\sqrt{-3}\cdot\sqrt{-3}\ \ - \sqrt{-64}+\ \ \sqrt{-9}\cdot\sqrt{-9}\cdot\sqrt{9}}{7+6i^3}\)
\(=\dfrac{(\sqrt{-3})^2\ - \sqrt{-64}+\ \ (\sqrt{-9})^2\cdot\sqrt{9}}{7+6i^3}\)
= [(-3) - 8i + (-9 · 3)] / (7+6i³)
= (-3 - 8i - 27 ) / (7+6i³)
= (-30 - 8i) / (7 + 6i³)
Hence, the given expression when simplification is equal to (-30 - 8i)/(7 + 6i³).
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The next model of a sports car will cost 12.1% less than the current model the current model cost $52,000 how much will the price decrease in dollars what will be what will be the price of the next model
Answers
In order to find the decrease in price, we need to multiply the cost of the current model ($52000) by 12.1%.
First, let's remember that:
12.1% = 12.1/100 = 0.121
So, we have:
Decrease in price = $52000 * 0.121
=$52 * 1000 * 0.121
= $52 * 121
= $6292
Now, the price of the next model will be the price of the current one minus the decrease:
Price of next model = $52000 - $6292
= $45708
Therefore, the answers are:
Decrease in price: $6,292
Price of next model: $45,708
1. A playground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters added to its outside. If the sides of the rectangle are 38 m and 28 m, find the perimeter and the area of the playground T(ake π = 27/7).
Answers
Given l=36m,b=24.5m
⇒ Area of a rectangle =l×b=36×24.5=882m
2
⇒ Radius of a semi circle =
2
24.5
=12.25m
⇒ Area of a semicircle =
2
πr
2
=
7×2
22×(12.25)
2
=235.812m
2
⇒ Area of two semi-circle =2×235.812=471.624m
2
∴ Area of playground = Area of rectangle + Area of two semi-circle
∴ Area of the playground =(882+471.624)m
2
=1353.624m
2
Please Look At The Attach File!
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calculate the pay for the following day of a weekly time card given a wage $13/hr
HELP PLEASE
Answers
Answer:
$130
Step-by-step explanation:
The person gets $13 and hour and works for 10 hours 15 minutes. You round down to 10 hours and 10x13=130.
Hope this helps.
The required wage or pay for the day of the weekly time card is $113.75.
Given that,
A table has been shown,
Describing the working hours,
pay per hour = $13/hr.
Daily wage to be determined
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
Here are the total working hour,
= 4:00 + 4:45
= 8:45 hours or (8 + 3/4) hours
Wage per hour = $13/hour
= 13 * 35/4
= $113.75
thus, the required wage or pay for the day of the weekly time card is $113.75.
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help plsssss ayuda pls
Answers
Answer:
PERDON POR HACER ESTO
Step-by-step explanation:
NO ENTIENDO
What is the arc measure of major arc AC on circle P in degrees
Answers
An arc is a segment of a circle. An arc measure is the measure of an angle that the arc creates in the center of a circle, while an arc length is the span of the arc. This measure can be given in degrees or radians. We can easily convert between the two using the fact that pi radians = 180 degrees.
Integer rules:
When adding Integers with the same sign you
Add,subtract,multiply
them and keep the sign.
When adding integers with different signs you
Add,subtract,multiply
them and keep the sign of the bigger number.
To make subtracting integers easler, you can change all subtraction problems to
Word,multiplication,addition
problems.
Answers
For each pair of funcation f and g below find f
Answers
(a)
Given
\(\begin{gathered} f(x)=2x+3 \\ \text{and} \\ g(x)=\frac{x-3}{2} \end{gathered}\)Then,
\(\begin{gathered} \Rightarrow f(g(x))=f(\frac{x-3}{2})=2(\frac{x-3}{2})+3=x-3+3=x \\ \Rightarrow f(g(x))=x \\ \text{and} \\ \Rightarrow g(f(x))=g(2x+3)=\frac{(2x+3)-3}{2}=\frac{2x}{2}=x \\ \Rightarrow g(f(x))=x \end{gathered}\)f(g(x))=x, and g(f(x))=x
Therefore, f and g are inverses of each other.
(b)
Given
\(\begin{gathered} f(x)=2x \\ \text{and} \\ g(x)=2x \end{gathered}\)Then,
\(\begin{gathered} f(g(x))=f(2x)=2(2x)=4x \\ \Rightarrow f(g(x))=4x \\ \text{and} \\ g(f(x))=g(2x)=2(2x)=4x \\ \Rightarrow g(f(x))=4x \end{gathered}\)Therefore, f(g(x))=4x, and g(f(x))=4x
f and g are not inverses of each other.
GED/HISET Social Studies Test 2023 at PASS the TEST!! small country in a recent
1. Total income for the population: 24 billion U.S. dollars
2. Per capita income: 7,000 U.S. dollars
3. 90% of the total income was received by 5% of the population
Which of the following conclusions about
incomes in the country is best supported by these
statements?
A. The total income is evenly distributed among
the population.
B. 95% of the population have relatively low
incomes.
C. 25% of the population have relatively high
incomes.
D. 5% of the population have incomes less than
$7.0009
19:35 / 21:40
Answers
The best supported conclusion about incomes in the country is: B. 95% of the population have relatively low incomes.
What is percent?Percent is a way of expressing a number as a fraction of 100, often used to indicate a portion or rate out of 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.
Here,
This is because even though the total income for the population is high at 24 billion U.S. dollars, the fact that 90% of it is received by only 5% of the population means that the remaining 95% of the population must share the remaining 10% of the total income. Additionally, the per capita income of 7,000 U.S. dollars is relatively low compared to the total income, further supporting the conclusion that the vast majority of the population has relatively low incomes.
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Is each statement true for parallelogram DEFG? Drag each statement into the correct box.
DF=EG
EF=DG
∠DEG ≅ ∠FGE
Answers
The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.
What is Quadrilateral?a quadrilateral is a four-sided polygon, having four edges and four corners.
DEFG is a parallelogram.
A parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
DF=FG is a true statement.
The diagonal passing through a parallelogram are equal in length.
EF=DG is a true statement
The opposite sides of a parallelogram are equal.
∠DEG ≅ ∠FGE are congruent angles.
Because the opposite angles of a triangle are equal in meausure.
Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.
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Determine whether the statement is true or false:
A linear equation has ONE solution when both sides of the equation are equivalent.
Group of answer choices
True
False
Answers
Answer:
True
Two equations are said to be equivalent when they have the same solution set.
i will mark you. i need help fast thank you!
Answers
Answer:
If I'm correct it should be the second one
Step-by-step explanation:
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what is √ − 3 ⋅ √ − 27 =
Answers
We are given the expression:
√-3 * √-27
__________________________________________________________
Explaining the concept:
We know that:
√ab = √a * √b
Using this concept, we will simplify the given expression and solve it
__________________________________________________________
Simplifying the expression:
√-3 * √-27
√(-1*3) * √[(-1)*(3)(3)(3)]
√-1 * √3 * √-1 * √3 * √3 * √3
(√-1 * √-1) * (√3 * √3 * √3 * √3)
(√-1)² * (√3)² * (√3)²
-1 * 3 * 3
-9
Hence, after simplifying the given expression, we get -9
someone please help me with this.
Answers
Answer:
17
Step-by-step explanation:
What we have to realize is that RS + ST = RT. Since we know the value of all, let's substitute inside the equation.
\(23 - 2x + 9x - 5 = 39\)
Now let's try and solve for x by isolating the variable on one side.
Combine like terms:
\(7x + 18 = 39\)
Subtract 18 from both sides:
\(7x = 21\)
Divide both sides by 7:
\(x = 3\)
Now that we know the value of x, we can substitute it back into the equation for RS, \(23-2x\).
\(23-2(3)\\\\23-6\\17\)
Hope this helped!
I need help with this quickly, it would be very much appreciated.
Answers
Answer:
complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)
Step-by-step explanation:
90=46+5x-1
45=5x
x=9
Answer:
x = 9 Complementary
Step-by-step explanation:
The angles are compplementary cause the angle add up to 90°
Well to find x we need to make the following equation,
46 + (5x - 1) = 90
We need to simplify and combine like terms,
46 - 1 = 45
45 + 5x = 90
-45 to both sides
5x = 45
Divide 5 by both sides
x = 9
Thus,
x is 9.
Hope this helps :)
Maria's grandmother gave her a gift of $2,000 for her birthday in November 2015. She deposited this into a savings account on January 2, 2016, after the holidays. The savings bank offered 0.725% interest at the time. Over the next year, the inflation rate averaged 1.3%. Now consider the following statements:
Statement I: In 2016, the buying power of Maria's gift decreased by about 0.6%.
Statement II: Maria's gift earned around $14.50 in interest during 2016, but this amount did not keep up with inflation.
Statement III: Maria's savings account had less than $2000 in it by the end of 2016.
Statements I and II are correct, but not Statement III.
None of the statements are correct.
All the statements are correct.
Statements I and III are correct, but not Statements II.
Statements II and III are correct, but not Statements I.
Answers
According to the given question we can conclude that statement I and statement II are correct but not statement III.
Define interest?Interest is the cost incurred when lending and borrowing a specific amount of money from a financial standpoint. It is crucial to note that interest is calculated as a percentage.
given,
Statement I is correct because the inflation rate averaged 1.3%, and Maria's savings account earned interest at a rate of 0.725%, which is lower than the inflation rate. This means that the buying power of her gift decreased by approximately 1.3% - 0.725% = 0.575% or 0.6% (rounded).
Statement II is also correct because Maria's savings account earned interest on the deposit of $2,000 for one year at a rate of 0.725%. The interest earned can be calculated as:
Interest = Principal x Rate x Time
Interest = $2,000 x 0.00725 x 1 year
Interest = $14.50
However, statement III is not correct. Since Maria deposited the entire gift of $2,000 into the savings account and did not make any withdrawals during the year, the balance in the account at the end of 2016 would be the sum of the initial deposit and the interest earned, which is $2,000 + $14.50 = $2,014.50. Therefore, the correct option is:
Statement III is incorrect, however Statements I as well as II are true.
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A new cell phone has a purchase price of $225. With the extended warranty, the total cost comes to $289. What percent of the purchase price is the price of the warranty?
Answers
Answer:
28.45%
Step-by-step explanation:
The price of a new cell phone = $225
With the extended warranty, the total cost comes to $289.
We need to find the percent of the purchase price is the price of the warranty. It can be calculated as follows :
\(\%=\dfrac{|\text{purchase price-extended warrenty price}|}{\text{purchase price}}\times 100\\\\=\dfrac{|225-289|}{225}\times 100\\\\=28.45\%\)
So, the percent of the purchase price is 28.45%.
Answer:
a) EDGE 2021
Step-by-step explanation:
One jar of spaghetti sauce is made with 1/4 of a cup of tomatoes. How many full jars of spaghetti sauce can be made with 3 cups of tomatoes?
Answers
Answer:
you can make 12 cans of them
1.Use the Pythagorean Theorem to find AD and DC. Then find AC using addition. Show your calculations.
Answers
Answer:
c=a2+b2=102+172≈19.72308
Step-by-step explanation:
a calculator bro its easy
how do you find answer to 9/35 - 1/5?
Answers
Answer:
2/35
Step-by-step explanation:
\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)
A skyscraper casts a shadow 200 ft long. If the angle of elevation of the Sun is 38 degrees, then the height of the skyscraper is approximately _____.
A. 200 ft
B. 173.34 ft
D. 156.26 ft
Answers
The height of the skyscraper is D. 156.26 ft
How to determine the valueTo determine the height of the skyscraper, we need to consider the following trigonometric identities listed thus;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Angle, θ = 38 degrees
The shadow casted is the adjacent side of the angle and is 200 ft
The height off the skyscraper is the opposite side
Now, using the tangent identity, we have that;
tan θ = opposite/adjacent
tan 38 = h/200
cross multiply the values, we get;
h = 200(0.7812)
Multiply the values
h = 156. 26 ft
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Select all the irrational numbers
Answers
Determine the probability that it will not rain for the next two weeks. Express your answer as a decimal precise to two decimal places.
Answers
Answer:
Probability of not raining in next two weeks is 0.696
Step-by-step explanation:
Let us calculate -
Probability diagram is attached below .
Probability of not raining in next week is 0.8
Probability of not raining in second week is 0.87
Therefore, Probability of not raining in next two weeks = \(0.8\times 0.87\)
= 0.696
Thus , the probability is 0.696
Lesson 3: Linear Equations in x
Classwork
Exercises
1. Is the equation a true statement when x = -3? In other words, is-3 a solution to the equation
6x + 5 = 5x +8+2x? Explain.
2. Does x = 12 satisfy the equation 16-x=x+1? Explain.
Answers
The first statement is correct whereas the second statement is wrong. This can be obtained by solving the algebraic equation for the value of x.
Is the equations a true statement?Here in the question it is given that the statements,
1) 6x + 5 = 5x + 8 + 2x, the solution x = -3
2) 16 - x = x + 1, the solution x = 12
We have to find the solution to each algebraic equation by solving for the value of x.
1) 6x + 5 = 5x + 8 + 2x
Add like terms,
6x + 5 = 7x + 8
Add -6x on both sides of the equation,
6x - 6x + 5 = 7x - 6x + 8
5 = x + 8
Add -8 on both sides of the equation,
5 - 8 = x + 8 - 8
x = - 3
Thus the given statement is true.
2) 16 - x = x + 1
Add x on both sides of the equation,
16 - x + x = x + x + 1
16 = 2x + 1
Add -1 on both sides on the equation,
16 - 1 = 2x + 1 - 1
15 = 2x
x = 15/2
Thus the given statement is not true.
Hence the first statement is correct whereas the second statement is wrong.
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Find the common factor for 24and 18
Answers
⦁ Avery noticed that 9/10 of the apples in a basket are red. There are 45 red apples in the basket. ⦁ Represent the situation with an equation. Use a for the variable. ⦁ Solve the equation in Part (a). Show your work. ⦁ What does the solution of the equation represent in the situation? ⦁
Answers
We want to write and solve an equation that represents the given situation. The equation we will find is (9/10)*a = 45, and its solution is a = 50.
So we know that 9/10 of the apples in the basket are red, and we know that there are 45 red apples.
Then, if we define a as the total number of apples, we know that (9/10) times a must be equal to 45, we can write this as:
(9/10)*a = 45
This is the equation that we must solve.
We can solve this if we multiply both sides by (10/9), it gives;
(10/9)*(9/10)*a = (10/9)*45
a = (10/9)*45 = 50
This means that there are 50 apples in the basket.
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Simplify using the order of operations. 2+6*8=
Answers
Answer:
The answer is 50.
Step-by-step explanation:
Use MDAS
Multiplication, Division, Addition and Subtraction
2 + 6 * 8 =
Multiply first then add
2 + 6*8 = ?
= 2 + 48
= 50
solve the quadratic equations
x^2 -8x + 35 = 0
x^2 +8x + 25 = 0
Answers
Answer:
x^2=8x-35
Step-by-step explanation:
1.1 Factoring x2-8x+35
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is +35
Step-1 : Multiply the coefficient of the first term by the constant 1 • 35 = 35
Step-2 : Find two factors of 35 whose sum equals the coefficient of the middle term, which is -8 .
-35 + -1 = -36
-7 + -5 = -12
-5 + -7 = -12
-1 + -35 = -36
1 + 35 = 36
5 + 7 = 12
7 + 5 = 12
35 + 1 = 36
I bought a loaf of bread and gave 7/12 of it to my brother, what fraction of the bread remain?
(
Answers
12 x 25 + 2-10 what’s is the answer bishesss
Answers
Answer:
292
Step-by-step explanation:
Answer:
292
Step-by-step explanation:
12X25=300
300+2=302
302-10=292
PEMDAS
also used calculator
look it up on internet