The required two numbers are 6 and 8.
Let us denote the required numbers by c and d.
Given that the difference between two natural numbers is 2.
If we assume d > c, then d – c = 2
⇒ d = 2 + c → equation 1.
Also given that the sum of their squares is 100.
⇒ c² + d² = 100
⇒ c² + (2 + c)² = 100 (using the value of d from equation 1)
⇒ 2c² + 4c + 4 = 100
⇒ 2c² + 4c = 96
⇒ 2c(c+2) = 96
⇒ c(c+2) = 48
Using the factorization for 48, we get 6 × 8 = 48
⇒ c = 6
⇒ c+2 = 8
⇒ d = 8
Therefore, the required two numbers are 6 and 8.
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how can you Introduce and Represent a ratio
A ratio can be introduced as an ordered pair of numbers, and it can be represented as x:y.
What is a ratio?A ratio can be introduced or described as an ordered pair of numbers.
For example, given two numbers x and y, where y is not equal to 0, the ratio can be represented as follows:
x:y
For example, let x represent the number of plates and equal to 2, and y represents the number of spoons and equal to 5, we will have the ratio as follows:
2:5
The ratio 2:5 implies that for every 2 plated there are 5 spoons.
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The Drama Club sold 900 tickets to the school play. They charged $5.50 for students and $8.00 for non-students.
If they took in $5700, how many non-student tickets were sold?
Answer:
300 non student tickets were sold
Step-by-step explanation:
Let's solve the equation step by step,
In order to solve for how many non student tickets were sold, let's make an equation
5.50x + 8.00y = 5700 --------(equation 1)
x + y = 900 ---------------(equation 2)
Let's solve for x and y
5.5x+8y=5700;x+y=900
Rewrite equations:
x+y=900;5.5x+8y=5700
Step: Solve x+y=900 for x:
x+y=900
x+y+−y=900+−y(Add -y to both sides)
x=−y+900
Step: Substitute−y+900forxin5.5x+8y=5700:
5.5x+8y=5700
5.5(−y+900)+8y=5700
2.5y+4950=5700(Simplify both sides of the equation)
2.5y+4950+−4950=5700+−4950(Add -4950 to both sides)
2.5y=750
2.5y/2.5 = 750/2.5
(Divide both sides by 2.5)
y=300
Step: Substitute300foryinx=−y+900:
x=−y+900
x=−300+900
x=600(Simplify both sides of the equation)
Since y = 300 then 300 non student tickets were soldDanae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day workec second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to after how many days, d, Danae would make the same amount of money regardless of the job she choose
Answer: 120d + 1,500 = 110d + 2,500
Step-by-step explanation:
Answer:
$1,500 + 120d = $2,500 + 110d
Step-by-step explanation:
Just in case you want the solution as well:
10d = 1000
d = 100
The workers at Antonio's pizza shop can make 18 pizzas for every hour. They have already made 40 pizzas. Write a function rule that can be used to determine the number of pizzas at Antonio's pizza shop f(p) at p hours.
Answer:
f(p) = 18p + 40
Step-by-step explanation:
Since they can make 18 pizzas per hour, number of pizzas made in p hours = 18p
They already have 40 pizzas
So total number of pizzas at any time p is f(p) = 18p + 40
Please help me with this question I'm so confused
Answer:
x is equal to 15.
Step-by-step explanation:
In this problem, it is said that ΔABC ~ ΔXYZ. This means that the shapes are the same, however they are not the same size. Here the problem is asking for the value of x when the triangle is scaled up.
Look on the triangles for where there are values on both ABC and XYZ. Notice that the hypotenuse for both triangles have a value.
The hypotenuse of triangle XYZ is 10, while the hypotenuse of triangle ABC is 25. Dividing both of those results by 10 results in a 1:2.5 ratio, meaning that the values of triangle ABC are 2.5 times larger than the values of triangle XYZ.
Knowing this, take the value of XZ on triangle XYZ, and multiply it by 2.5 to get the value of AC on triangle ABC, or x.
6 * 2.5 = 15
The value of x is 15.
Answer:
x = 15
Step-by-step explanation:
Since the triangles are similar that means that the sides are proportional. There are a couple of ways to find x. One way is to find the scale factor. We can use the two corresponding sides that we know. 25 and 10 are corresponding sides. They are both the hypotenuse of their triangles or you can say that they are both the side across from the 90 degree angle.
There is some number that I can multiple 10 by to get 25. This is my scale factor. This is how I can find it.
Let s = the scale factor.
10s = 25 Divide both sides of the equation by 10
s = 2.5 This means that each side of the larger triangle is 2.5 times longer than each side of the original triangle.
To find x. Find is corresponding side on the right and take that length and multiple it by 2.5
6 x 2.5 = 15
Another way is to set up a proportion.
[tex]\frac{10}{6}[/tex] = [tex]\frac{25}{x}[/tex] I could cross multiply and solve for x
10x = (6)(25)
10x = 150 Divide both sides by 10
x = 15
21x21 I need real help with this.Really struggling ;)
Answer: Human calculator says 21 x 21 = 441!
Good Luck!
Approximately how much fencing is needed to enclose a circular pond with a diameter of 12. 5 feet?.
Approximately 39.26 feet is needed to enclose a circular pond with a diameter of 12. 5 feet.
What is the circumference of a circle?The circumference (from Latin circumference, meaning "carrying around") is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were finally opened and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure. The circumference can also refer to the circle itself, i.e. the locus corresponding to a disk's edge. A sphere's circumference is the circumference, or length, of any of its great circles.To fin the circumference:
Formula: C = 2πrRadius = Diameter/2 = 12.5/2 = 6.25So,
C = 2πr= 2 · π · 6.25≈ 39.26991Therefore, approximately 39.26 feet is needed to enclose a circular pond with a diameter of 12. 5 feet.
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-1/2 is equivalent to 1/2
Answer: No
Step-by-step explanation:
No because its off by 1 point, -1/2, 0, 1/2
Use the distributive property to write an equivalent expression.
4(w-2x+4)
A cell phone provider charges a monthly fee of $20 dollars and also charges customers $0.05 per text message. The function C (t) = 0.05t+ 20 represents the cost C, per month based on t text messages in a month.
Which best describes the domain of the function?
- All real numbers
-All real numbers that are multiples of 0.05.
-all whole numbers
-all whole numbers from 0 to 20
The best description of the domain of the function is (c) all whole numbers
How to determine which best describes the domain of the function?The function is given as
C(t) = 0.05t + 20
The input variable of the above function is t
t represents the number of text messages
The number of text messages cannot be negative
Hence, the best description of the domain of the function is (c) all whole numbers
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2/3 of the students in class are male. If 18 of the students are male, how many students are in the class
Answer:
27 students
Step-by-step explanation:
Split 18 into 2 to find 1/3. 18/2= 9
9= 1/3
18= 2/3
27= 3/3 or 1
Answer:
There are 27 students.
Step-by-step explanation:
Given that,
→ 2/3
→ 18 ÷ 2
→ 9 = 1/3
Now the number of students are,
→ x = (2/3) + (1/3)
→ x = 18 + 9
→ [ x = 27 ]
Hence, there are 27 students.
8w-6(w-4)=2(w+9)
please help asap
Answer:
w = -7.04 and 1.705
Step-by-step explanation:
First lets distribute.
We have 8w-6w(w-4), so let's distribute the -6w to w and -4
8w-6w^2+24w = 2(w+9)
Now for the other side we distribute 2 to w and 9
8w-6w^2+24w = 2w +18
Now we combine like terms
6w^2+32w = 2w +18
Carry both 2w and 18 to the other side
6w^2 +30w -18 = 0
Now we can factor the equation, i used the quadratic method which is x= -b+- the square root of b^2-4ac /2a (in this case x would be w)
Plugging that in:
x= -32 +- square root of 32^2 -4(6 * -18) / 2(6)
-32 +- square root of 1024 +1728 / 12
-32 +- square root of 2752 /12
-32 +- 52.46 /12
x = -32 - 52.46/12 and -32 + 52.46/12
x= -84.46/12 and 20.46/12
x= -7.04 and 1.705
so w = -7.04 and 1.705
Sorry this was so complicated, but I hope this helps
Find the value of x please.
Answer: To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Answer:
85 degrees
Step-by-step explanation:
a line equals 180 degrees.
so 180-140= 40 degrees one of the missing angles in the triangle.
180 degrees is the full amount of degrees the angles of a triangle can equal.
So we have to add up the angles we know...
55+40=95 degrees
and subtract them from 180...
180-95=85 degrees
x=85
simplify. -2(7-n) +4
Answer:
-2(7+2n) +4 = 5
step by step explantation:
-2(7-n) +4
-2×7 =-14
-2x-n = 2n
14+2n = 4
2n = 14 - 4
2n/ 2= 10/2
n= 5
What is the product of (−3)(18) • (−5)?
Answer:
The product of (-3)(18) * (-5) is 270.
Step-by-step explanation:
(-3)(18) * (-5)
Multiply -3 and 18.
(-54) * (-5)
Multiply -54 and -5. When multiplying 2 negative numbers, the result will become positive.
270.
Answer:
270
Step-by-step explanation:
BODMAS
Brackets, Order, Division, Multiplication, Addition, Subtraction.
(-3)(18) is basically (-3) • (18)
No more expressions within brackets so we go by order from left to right of the equation.
(-3) • (18) = (-54)
(-54) • (-5) = 270
Hope this helps! ^^
there are 24 baseball teams in a league. each team plays two matches against each of the other teams, work out the total number of matches played
Answer:
I need this question too... HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The total number of matches played is 552
How to determine the total number of matches played?The given parameters are
Teams = 24
Matches against each other = 2
So, the total number of matches played is
Total = Teams * (Teams - 1)
This gives
Total = 24 * (24 - 1)
Evaluate
Total = 552
Hence, the total number of matches played is 552
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PLS ILL GIVE U A LOT OF POINTS
Step-by-step explanation:
(3.5q³k^4)³ (2q²k³)²
(42.875 q^9 k^12) (4 q^4 k^6)
171.5 q^13 k^18
The answer is C.
Saeed plans to run 10 km. On the first day, he runs 2 km. What percent of the total distance does he run the first day?
Answer:
He runs 20% or 1/5 of the total distance the first day
Step-by-step explanation:
We know this due to the fact that 2km / 10km is equal to 1/5 and we then know that 1/5 equates to the percentage equivalence value of 20%
Please help! Find the value of FG. The drawing is not to scale. EF=11 and EG=21
The value of FG is 32.
The drawing is attached with this.
Given that,
Value of EF = 11
Value of EG = 21
From the above given data we can assume that F and G be the corner points.
E is the point lie between F and G.
We have to find the value of FG. It may be a straight line.
So,
Value of FG = Value of EF + Value of EG
FG = 11 + 21
FG = 32
That is, the value of FG is 32.
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As treasurer of her school's 4H club, Carol wants to buy gifts for all
11 members. She can buy t-shirts for $5 and sweatshirts for $12.
The club has $118 to spend and Carol wants to spend all of the
money. How many of each type of gift should she buy?
Using algebraic expressions and equations, Carol should buy 2 t-shirts and 9 sweatshirts.
We can set up an algebraic expressions and equations to determine how many of each type of gift should Carol buy.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
1. Write an equation for the total number of members.
x + y = 11 (equation 1)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
2. If each t-shirt costs $5 and each sweatshirt costs $12, write an equation for the total amount spent buying the gift.
$5(x) + $12(y) = $118 (equation 2)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
3. Rewrite equation 1 as an equation of y in terms of x.
x + y = 11 (equation 1)
y = 11 - x
4 . Plug in the expression for y in equation 2 and solve for x.
$5(x) + $12(y) = $118 (equation 2)
5x + 12(11 - x) = 118
5x + 132 - 12x = 118
-7x = -14
x = 2
5. Substitute the value of x in either equation 1 or 2 and solve for x.
x + y = 11 (equation 1)
2 + y = 11
y = 11 - 2
y = 9
Hence, Carol should buy 2 t-shirts and 9 sweatshirts.
Checking,
2 + 9 = 11
Each member will receive a gift.
2($5) + 9($12) =$118
Carol will be spending $118 for the gifts.
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Determine whether or not the function is one-to-one, and if it is, determine its inverse function
Determine the conditions for when a function has an inverse. Use the horizontal line test to recognize when a function is one-to-one. Find the inverse of a given function.
What is a horizontal line test?It is simple to establish whether the inverse of a function is also a function using the horizontal line test.
Because it fails the vertical line test, a function's inverse might not actually be a function.
Graph of the line
f\left( x \right) = - x + 2
f(x)=−x+2.
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What is a situation that can be represented as 4(-2)?
Thanks.
Suppose a vector y is orthogonal to vectors u and v. show that y is orthogonal to the vector u v.
Using Dot product
Two vectors x and y are said to be orthogonal if their dot product is zero
⇒ x.y = 0
This is because orthogonal vectors are make an angle of 90° with each other and therefore θ becomes 90°
Dot product is given by :
x.y = x*y*cosθ = xycos90°
∵cos90° is zero , x.y=0 for orthogonal vectors.
Let u,v,y be vectors in R
y is orthogonal to u and v
⇒ y.u = 0 and y.v=0
Now, we have to prove that y is orthogonal to (u+v)
The dot product of these vectors is given by:
y.(u+v) = y.u + y.v (Dot product is distributive) = 0 + 0 = 0
∵The dot product is zero , vector y and (u+v) are orthogonal
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there are twenty four hours in a day. jack worked for two-fourths of the day. how much time will jack spend working?
Answer: 12 hours
Step-by-step explanation: divided 24 by 4, which equals to 6, if Jack worked 2/4 of the day, he would have worked half the day, which is 12 hours.
4. Jennifer spent $153.36 at the mall. Sally spent $85.20.
How many
times greater is the amount that Jennifer spent than the amount that
Sally spent?
A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is $3/2$ times the probability that a freshman is elected. Everyone on the junior varsity swim team is either a freshman or sophomore. What fraction of the swim team are sophomores?
Using the probability concept, it is found that 60% of the swim team are sophomores.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The sum of the probabilities of all outcomes of an event is of 1, hence:
P(freshman) + P(sophomore) = 1.
The probability that a sophomore is elected is $3/2$ times the probability that a freshman is elected, hence:
x + 3/2x = 1.
5/2x = 1
5x = 2
x = 0.4.
Thus:
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CH#6 LINES & ANGLES
I. In fig. the values of x and y are equal to:
(a) 130⁰
(b) 150⁰
c) 160⁰
(d) 135⁰
2. The dimensions of a desk are 36in long and 24in wide. What is the aspect ratio of the desk?
The aspect ratio of the desk is 3:2
How to calculate the aspect ratio ?
Aspect ratio can be described as the ration of the width to the height of an object
The desk is 36 inches long
The width is 24 inches
The aspect ratio can be calculated as follows
= 36/24
= 6/4
= 3/2
Hence the aspect ratio is 3:2
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List from least to the greatest: 7/4, 1.5, √2, √4 – 0.1
Answer: 0.1, 1.5, 7/4, 2, 4
Step-by-step explanation:
A pair of cars, 70 miles apart, begin at the same time to run toward each other. If car A
from city A runs at a rate that is 5 mph faster than car B from city B, and if they meet 2
hours later, how far is the place they meet away from city A?
Answer: car a must be meet to cannot be so your aner is a
Step-by-step explanation:
