Answer:
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Step-by-step explanation:
Evaluate:
[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]
When a=-4, b=2, c=-3, and d =4
Solution:
Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Ryan’s heart beats 9 times per 10 seconds while Ryan is resting. About how many times would Ryan’s heat beat during 3 minutes of rest.
WILL MAKE BRAINLEST!! Which equation best represents the line??
A. Y=1/3X-1
B. Y=3X-1
C. Y= -X+ 1/3
D. Y= 3X+1
Answer:
B is the answer. ........
Answer:
B
Step-by-step explanation:
it intercepts the y line at -1 and the rise over run is 3
I NEED HELP ASAP!!!!
1. if x and y are both even whole numbers. what is a possible solution for x + y?
a. 5
b. 9
c. 4.6
d. 8
2. assume n and m are both even whole numbers and m > n. what is a possible solution for m - n?
a. 16
b. 1/2
c. 0
d. -2
1. The possible solution for x + y is 8 ⇒ d
2. The possible solution for m - n is 16 ⇒ a
Step-by-step explanation:
Lets explain some notes about the even numbers
Their sum is evenTheir difference is evenTheir product is even1.
∵ x and y are both even whole numbers
∴ Their sum is even whole number
∵ 5 and 9 are odd numbers ⇒ impossible
∵ 4.6 is not a whole number ⇒ impossible
∵ 8 is an even whole number ⇒ possible
∴ x + y could be 8
The possible solution for x + y is 8
2.
∵ n and m are both even whole numbers
∵ m > n
∴ m - n must be positive even whole number
∵ 1/2 is not a whole number ⇒ impossible
∵ 0 is not a positive number ⇒ impossible
(zero is not positive nor negative)
∵ -2 is not a positive number ⇒ impossible
∵ 16 is a positive even whole number ⇒ possible
∴ m - n could be 16
The possible solution for m - n is 16
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f(x)=−x+2, find f(-5)f(−5).
To calculate f(-5) for the function f(x)=-x+2, we substitute -5 in place of x, which gives us f(-5) = 7.
Explanation:To find the value of f(-5) for the function f(x)=−x+2, we simply substitute x with -5:
f(-5) = −(-5) + 2
Now, we perform the operations:
f(-5) = 5 + 2
f(-5) = 7
Therefore, the answer is 7.
Help me with the highlighted ones
Colin invests £3500 into his bank account.
He receives 5% per year compound interest.
How much will Colin have after 6 years?
Give your answer to the nearest penny where appropriate.
Answer: 4,690.33
Step-by-step explanation:
The formula for calculating amount is given by :
A = P [tex](1+r)^{n}[/tex]
Where :
A = amount = ?
P = Principal = 3500
r = rate = 0.05
n = number of years = 6
substituting the given values into the formula , we have
A = 3500[tex](1+0.05)^{6}[/tex]
A = 3500 [tex](1.05)^{6}[/tex]
A = 3500 (1.340095640625)
A = 4690.3347421875
A = 4,690.33
Final answer:
To calculate Colin's investment with compound interest after 6 years, we use the formula for compound interest and determine that he will have £4690.33 to the nearest penny.
Explanation:
To calculate how much Colin will have after 6 years with compound interest, we use the formula for compound interest:
A = P(1 + r/n)nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In Colin's case, we have:
P = £3500
r = 5% or 0.05
n is not mentioned, so we assume it is compounded once per year, thus n = 1
t = 6 years
Plugging these values into the formula:
A = £3500(1 + 0.05/1)1×6 = £3500(1 + 0.05)6
A = £3500 × (1.05)6 = £3500 × 1.340095
A = £4690.3325
To the nearest penny, Colin will have
£4690.33 after 6 years.
Determine whether the random variable described is discrete or continuous.
The height of a randomly chosen basketball player.
The height of a randomly chosen basketball player is a continuous random variable since height is measured and can take on an infinite range of values.
The random variable described, the height of a randomly chosen basketball player, is a continuous random variable. This is because height can take an infinite number of possible values within a range and is measured rather than counted. Unlike discrete random variables, which have countable values such as the number of heads in a coin toss, continuous random variables like height are measured and can include values such as 6'1" or 6'1.5". The values are on a continuous scale, and therefore the probability distribution of a continuous random variable is concerned with the probability of the variable falling within a certain range, rather than taking specific countable values.
Simplify: (5x^6y^-4)^3(2x^8y^3)
Answer:
250x^26/y^9
Step-by-step explanation:
What is the expression for triple 9 then multiply 8
Answer:
3R
Step-by-step explanation:
when x-y=3 work out the value of 2x-2y
Answer:
6
Step-by-step explanation:
Given
2x - 2y ← factor out 2 from each term
= 2(x - y) ← substitute x - y = 3 into the expression
= 2(3)
= 6
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
x - y = 3
2x - 2y
The value of 2x - 2y is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x - y = 3 _____(1)
The value of 2x-2y.
= 2x - 2y
Taking 2 as common.
= 2 (x - y)
From (1) we get,
= 2 x 3
= 6
Thus,
The value of 2x - 2y is 6.
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What is a real world situation for the problem 42.48 Divided by 25
Answer:
At the donut shop, Karley and 24 of her co-workers have split the tip jar. There is $42.48 in the tip jar. How much money does each worker get from the jar?
Darcy’s house is 6 times as far from school as her friend’s house. If her friend’s house is 3/4 mile from school, how many miles from school is Darcy’s house?
A coffee shop served hot and cold coffee to a total of 340 people. 45% of the people chose cold coffee.
How many people chose hot coffee?
Answer:
187 people
Step-by-step explanation:
340 people multiplied by 0.45 or 45% is 153. Subtract 153 from 340 and you get 187 people.
Answer:
187 people
Step-by-step explanation:
340 people multiplied by 0.45 or 45% is 153. Subtract 153 from 340 and you get 187 people.
Trevin puts 8 gallons of gas in his car and pays $22, ate this rate what is the cost for 9 gallon of gas
Answer:
$24.75
Step-by-step explanation:
Find the unit rate for 1 gallon, to dothis divide $22 by the 8 gallons of gas. 22/8 is $2.75. now that we know the unit rate, multiply it by 9 for our answer. 2.75*9=24.75,the cost for 9 gallons.
Trevin puts 8 gallons of gas in his car and pays $22. The cost of 9 gallons of gas at this rate is $24.75
Word problems in mathematics involve a careful understanding of the question. It is usually written or expressed in one or more sentences and it requires pupils to apply their arithmetic skills to a real-life issue.
From the information given:
Trevin put 8 gallons of gas in his car and pays $22 for iti.e
8 gallons = $22We are to determine the rate he will pay for 9 gallons. i.e.
9 gallons = xFrom the above two expressions, by cross multiplying, we have:
[tex]\mathbf{x = \dfrac{9 \ gallons \times \$22 }{8 \ gallons}}[/tex]
x = $24.75
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In order to find the height of a cliff, you stand at the bottom of the cliff, walk 60 feet
from the base, and place a mirror on the ground. Then you face the cliff and step back
5 feet so that can see the top of the cliff in the mirror. Assuming your eyes are 6 feet
above the ground, explain how to use this information to find the height of the cliff.
(The angles marked congruent are congruent because of the nature of the reflection of
light in a mirror.)
Q5ft
60 ft
K
Mirror
Answer: 72 ft
Step-by-step explanation:
We can solve this problem using geometry, if we draw two righ triangles (figure attached):
-One formed by you, assuming you are 6 ft tall, and the ground
-The other formed by the height of the cliff, the bottom of the cliff and the ground.
Both triangles are congruent, having the mirror as a common vertex, hence we can use the following relation to find :
[tex]\frac{6 ft}{y}=\frac{5 ft}{60 ft}[/tex]
Isolating :
[tex]y=\frac{(60 ft)(6 ft)}{5 ft}=72 ft[/tex] This is the height of the cliff
The calculated height of the cliff is 72 feet.
To determine the height of the cliff, we use a mirror and the property of the reflection of light. Here are the steps to solve the problem:
Place the mirror 60 feet from the base of the cliff and stand back 5 feet from the mirror.Since your eyes are 6 feet above the ground, the light reflecting from the mirror at the point where you see the top of the cliff will create similar triangles based on the reflection.The triangles formed involve your height of 6 feet over the 5 feet back from the mirror and the unknown height of the cliff over the 60 feet from the mirror.Set up the proportion from the similar triangles:height of cliff / 60 feet = 6 feet / 5 feet.
5. Solve for the height of the cliff:
height of cliff = (6 feet / 5 feet) * 60 feet = 72 feet.
Thus, the height of the cliff is 72 feet.
-3х + 40 = 10
I don’t know how to solve
Answer:
Step-by-step explanation:
NEED HELP NOW
Shawn got a haircut at the barber shop. It cost $11, and he left a $3 tip.
What percent tip did he leave the barber?
Answer: He left a 27.27272727% tip
The difference between the solutions of the equation 5x2−x−k=0 is 1.8. Find the solutions.
The solutions are - 0.8 and 1
Step-by-step explanation:
In the quadratic equation ax² + bx + c = 0
The sum of the two solutions of the equation is [tex]\frac{-b}{a}[/tex] The product of the two solutions is [tex]\frac{c}{a}[/tex]Assume that the solutions of the equations are m and n
∵ 5x² - x - k = 0
- By comparing it by the form above
∴ a = 5, b = -1 , c = -k
- Use the rule of the sum of the two solutions above
∵ The sum of the two solutions = [tex]\frac{-b}{a}[/tex]
∴ The sum of the two solutions = [tex]\frac{-(-1)}{5}=0.2[/tex]
∵ The two solutions are m and n
∴ m + n = 0.2 ⇒ (1)
∵ The difference of the two solutions is 1.8
∴ m - n = 1.8 ⇒ (2)
Now we have a system of equations to solve
Add Equations (1) and (2) to eliminate n
∴ 2m = 2
- Divide both sides by 2
∴ m = 1
- Substitute the value of m in equation (1) to find n
∴ 1 + n = 0.2
- Subtract 1 from both sides
∴ n = -0.8
The solutions are - 0.8 and 1
If you want to find the value of k
∵ The product of the solutions is [tex]\frac{c}{a}[/tex]
∴ The product of the solutions = [tex]\frac{-k}{5}[/tex]
∵ m × n = 1 × (-0.8) = - 0.8
- Equate [tex]\frac{-k}{5}[/tex] by - 0.8
∴ [tex]\frac{-k}{5}=-0.8[/tex]
- Multiply both sides by -5
∴ k = 4
∴ The equation is 5x² - x - 4 = 0
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Answer:
x = 1; x = -0.8
Step-by-step explanation:
Here is a simpler approach if needed for future students:
5x^2-x-k = 0,
System of Equations: x1 - x2 = 1.8 & x1 + x2 = 1/5 = 0.2 (if x1 and x2 are roots)
Now let's add the two:
x1 - x2 = 1.8
+ x1 + x2 = 0.2
----------------------
2x1 = 2,
x1 = 2/2 = 1
- x2 = 1.8 - 1 = 0.8 => x2 = -0.8
What is the change in temperature from 15 degrees to -9 degrees? -6, 6, -24, 25
Answer:
24 degrees
Step-by-step explanation:
The distance from 15 degrees to 0 degrees is 15, and the distance from 0 degrees to -9 degrees is 9, so then the total distance from 15 degrees to -9 degrees is (15+9 degrees) which adds up to be 24 degrees
a dragonfly can beat its wings 30 times per second. write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times that dragonfly beats its wings
Please help ASAP will give BRAINLIEST ANSWER!!!!!!!
Answer:A $35 decrease followed by a $25 increase is less than the original.
A 50% decrease then 33.333% increase is the same.
A 30% increase then 15% decrease is more.
A 50% decrease then 100% increase is the same.
A 70% increase then 50%decrease is less.
Step-by-step explanation:
Find the circumcenter of the triangle ABC.
A( - 4,3), B(5,7), C(-4,7).
Answer:
Circumcenter O (0.5 , 5)
Step-by-step explanation:
Circumcenter O (x , y)
OA = OB = OC
OA² = (x + 4)² + (y - 3)²
OB² = (x - 5)² + (y - 7)²
OC² = ( x + 4)² + (y - 7)²
OA² = OC² : (x + 4)² + (y - 3)² = ( x + 4)² + (y - 7)²
(y - 3)² = (y - 7)² y² - 6y + 9 = y² -14y + 49
8y = 40
y = 5
OB² = OC² : (x - 5)² + (y - 7)² = ( x + 4)² + (y - 7)²
x² - 10x + 25 = x² + 8x + 16
18x = 9
x = 0.5
Circumcenter O (0.5 , 5)
Emily has a total of 20 dimes and nickels. If the dimes were nickels and nickels were dimes she would have 20 cents less than she has now.
Write a system of equations that represents the problem(2 pts)
How many of each coin does she have(2 pts)?
The system of equation is:
x + y = 20
x - y = 4
She has 12 dimes and 8 nickels
Step-by-step explanation:
The given is:
Emily has a total of 20 dimes and nickelsIf the dimes were nickels and nickels were dimes she would have 20 cents less than she has nowWe need to write a system of equations that represents the problem and how
many of each coin she has
Assume that she has now x dimes and y nickels
∵ She has x dimes and y nickels
∵ She has a total of 20 coins
- Add x and y, then equate the sum by 20
∴ x + y = 20 ⇒ (1)
∵ One dime = 10 cents
∵ One nickels = 5 cents
- Multiply x by 10 and y by 5 to find how many cents she has now
∵ She has now (10x + 5y) cents
∵ The dimes were nickels and the nickels were dimes
- Multiply x by 5 and y by 10 to find how many cents she has
after the change
∴ She had after the change (5x + 10y) cents
∵ The value after the change is less than the value now by
20 cents
- Subtract (5x + 10y) from (10x + 5y) and equate the difference
by 20
∴ (10x + 5y) - (5x + 10y) = 20
- Add the like terms in the left hand side
∴ (10x - 5x) + (5y - 10y) = 20
∴ 5x - 5y = 20
- Divide both sides by 5
∴ x - y = 4 ⇒ (2)
The system of equation is:
x + y = 20
x - y = 4
Now we have a system of equations to solve it
Add equations (1) and (2) to eliminate y
∴ 2x = 24
- Divide both sides by 2
∴ x = 12
- Substitute the value of x in equation (1) to find y
∵ 12 + y = 20
- Subtract 12 from both sides
∴ y = 8
She has 12 dimes and 8 nickels
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Alexis and 3 friends are at the mall.each person buys a pretzel for 4$, sauce for $1, and a drink for $2. write and expression for the total and find the total cost.
Answer:
(4+1+2)3= 21
Step-by-step explanation:
you add the cost of snacks then multiply by 3 because there are 3 people to get total cost.
4+1+2=7 7*3=21Answer:
4+4+4+1+1+1+2+2+2=25
What is gcf of 24, 60, and 36
Answer:
12
Step-by-step explanation:
the average number 1 0 1 5 6 3 4
Answer: 2
Step-by-step explanation: Edge 2023
Final answer:
To find the average number from a list of numbers, add up all the numbers and then divide the sum by the total number of numbers.
Explanation:
The question asks for the average number from a given list of numbers. To find the average, you add up all the numbers in the list and then divide the sum by the total number of numbers in the list.
In this case, the average of the numbers 1, 0, 1, 5, 6, 3, and 4 can be found by adding those numbers together (1 + 0 + 1 + 5 + 6 + 3 + 4) and then dividing the sum by 7 (the total number of numbers in the list). So, the average is 4.
2. Tickets to a play cost $8 each. Write an
expression that gives the ticket cost in dollars
for a group of g girls and b boys.
Expression that gives the ticket cost in dollars for a group of g girls and b boys is (8g + 8b) dollars
Solution:
Given that tickets to play cost $ 8 each
To find: Expression that gives the ticket cost in dollars for a group of g girls and b boys
From given,
cost of 1 ticket = $ 8
Number of girls = g
Number of boys = b
Thus the expression can be framed for total cost as:
Total cost = (number of girls + number of boys)(cost of 1 ticket)
[tex]Total\ Cost = (g + b) \times 8\\\\Total\ Cost = 8g + 8b[/tex]
Thus the expression that gives total cost is (8g + 8b) dollars
How Do You Write The Expression For Triple 9 Then Multiply 8
Helppppppp let’s get to 100!!!!
Answer: 3
Step-by-step explanation:
10 had sprinkles and 2 did not which mean there are 12.
So would it be 3 that not have a sprinkles?
I think so.