Step-by-step explanation:
Solution: Let the current ages of the father be F and that of the son, S.
Three years ago their ages were (F-3) and (S-3) and the sum was 48, or
F+S = 48+3+3 = 54, or
F = 54-S …(1)
(F+3) : (S+3) = 3:1, or
F+3 = 3S+9, or
F = 3S+6 …(2)
Equate (1) and (2): 54-S = 3S+6, or
4S=48, or S = 12 and So F = 42.
The father is 42 years and the son 12 years,
Answer:
+3 year after now Dad = 45; Son = 15 ====> 30 years old
now Dad = 42; Son = 12 ====> 30 years old
-3 year after now Dad = 39; Son = 9 =====> 30 years old
Step-by-step explanation:
Before 3 year is 48 so after 3 year is + 6 right???
so ==> 48 + 6(father and son so it's 2) + 6(same same) ==> 60
the ratio is 3:1 so son gets 1 dad gets 3 right?
==> 4 is the sum
So son is 60/4x1 = 15
Dad is 60/4x3(dad have three remember?) = 45
so now dad and son will be:
Dad = 45 -3 (only dad ok?) = 42
Son = 15-3(only son) = 12
so you can find the before to by minus 3 again ok??
Thanks for seeing
Tell me if it's wrong or right :P | XD | (❁´◡`❁)
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
1/5
12
1/12
Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15), the scale factor used is: A. 5.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Scale factor = -15/-3
Scale factor = 5.
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Answer: its 5
Step-by-step explanation: I did it in a test and got it right
Solve this equation 20 POINTS
Eight years after opening her savings account, Macy had $7,880 in the account which earns annual simple interest. If Macy started with $5,000 in her account and did not make any additional deposits or withdrawals, what was the approximate annual interest rate on the savings account?
The principal amount of $5,000 deposited for 8 years with simple interest gives amount $7,880 at the annual interest of 7.2%.
Total amount 'A' in the Macy account after 8 years = $7,880
Time 't' = 8 years
Principal amount 'P' = $5,000
Let 'r' be the rate of interest given in saving account with annual simple interest.
Simple interest = Amount - Principal
= $7,880 - $5,000
= $2,880
Simple interest = ( P × r × t ) / 100
Substitute the value we get,
⇒ $2,880 = ( 5,000 × r × 8 ) / 100
⇒ r = ( 2,880 × 100 ) / ( 5,000 × 8 )
⇒ r = 7.2%
Therefore, the annual interest rate for the given amount as per simple interest is equal to 7.2%.
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Damari wants to sell laptops and smartphones. Each laptop is sold for the same amount of money, and each smartphone is sold for the same amount of money. She wants to sell at least 12 total devices and make at least $4500 to cover expenses and turn a profit. Laptops sell for $425 and smartphones sell for $125.
Answer:
12000
Step-by-step explanation:
4500:12=470
425:125=100
1000×12=12000
Use substitution to solve the system of equations.
y=3x−34
y=2x−5
The solution for this equation system is x= 29, y=53, (29, 53).
Step-by-step explanation:1. Write the equations.[tex](1)y=3x-34\\ \\(2)y=2x-5[/tex]
2. Substitute "y" in equation "1" by the expression on equation "2".[tex](2x-5)=3x-34\\\\2x-5=3x-34[/tex]
3. Add "5" on both sides of the equation.[tex]2x-5+5=3x-34+5\\ \\2x=3x-29[/tex]
4. Subtract "3x" from both sides of the equation.[tex]2x-3x=3x-29-3x\\ \\-1x=-29\\ \\-x=-29[/tex]
5. Multiply both sides by "-1".[tex]-x(-1)=-29(-1)\\ \\x=29[/tex]
6. Find a value of "y".To find a value of "y", use the calculated value of "x" (29), and substitute in any of the two equations to find the value of "y". For this solution, we're going to use equation 2.
[tex]y=2(29)-5\\ \\y=58-5\\ \\y=53[/tex]
7. Verify the answer.On step 6 we proved that the value of "x=29" returns a value of "53" when evaluating with equation 2. Now, if equation 1 returns the same "y" value when evaluating "x=29", then the calculated values of both "x" and "y" are correct. Let's verify!
[tex]y=3(29)-34\\ \\y=87-34\\ \\y=53[/tex]
8. Conclude.Both of the equations return the same value of "y" (53) when evaluated with "x=29". Therefore, the solution for this equation system is x= 29, y=53, (29, 53).
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8t+1+(−4t)+(−6) ?????????????
3.1 The solutions of a quadratic equation are given by x of m will this equation have? a) Two equal solutions? -2 ±√2m+5 For which value(s)of m will the equation have? two equal solution
The value of m for which the equation will have two equal solutions is given as follows:
m = -2.5.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution = two equal real solutions.Δ < 0: two complex solutions.For this problem, the discriminant is given as follows:
Δ = 2m + 5 (it is the term that goes inside the root during the solution).
Hence, to have two equal solutions, the condition is:
Δ = 0.
Hence:
2m + 5 = 0
2m = -5
m = -5/2
m = -2.5.
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A plane is traveling Northeast. If the eastern component of it's velocity is 300 mph, how fast is the plane traveling?
The plane is travelling at a speed of 424.26 mph.
What is Velocity?Velocity of an object is the speed of the object with a given direction. Therefore velocity is a vector quantity and speed is a scalar quantity.
Given that,
A plane is traveling Northeast.
If the plane is travelling northeast, then the angle that the plane makes with the horizontal component will be 45°.
The eastern component of it's velocity is 300 mph.
Vector v can be represented as v cos (θ) i + v sin(θ) j.
Here v cos (θ) is the eastern component and v sin(θ) is the northern component.
v cos (θ) = 300
v cos(45°) = 300
v = 300 / cos(45°)
= 300 / (1/√2)
= 424.26 mph
Hence the speed of the plane is 424.26 mph.
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A local bike race is broken into 12 parts. Each stage is 14 1/2 miles. What is the total distance of the bike race?
Answer: 174 miles
Step-by-step explanation: 14.5 (14 1/2) times 12 is 174
Easy but still help QvQ
The length of a rectangle is 5 cm longer than its width.
If the perimeter of the rectangle is 74 cm, find its length and width.
The length and the width are 21cm and 16cm respectively.
How to determine the length and widthThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l +w)
Given that;
P is the perimeterl is the length of the rectanglew is the width of the rectangleBut we have that;
Length = 5 + w
Substitute the value
74 = 2(5 + w + w)
collect like terms
74=2 (5 + 2w)
expand the bracket
64 = 4w
Make 'w' the subject of formula
w = 16cm
Then, length = 5 + 16 = 21cm
Hence, the values are 16cm and 21cm
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pls help me if ur able to thanks
Write the quadratic function f(x)=-3x^2-3x-46
in the form f(x)=a•(x-h)^2+k
Answer:
-3(x+0.5)^2-181/4 (if I calculated correctly)
Step-by-step explanation:
f(x)=-3x^2-3x-46
=-3(x^2+x+46/3)
=-3(x+0.5)^2-(0.5)^2+46/3
=-3(x+0.5)^2+181/12
=-3(x+0.5)^2-181/4
The bacteria population in a small pond is decreasing because of pesticides. Each month, the
population of bacteria decreases. Initially, there were 60,000 bacteria in the pond. Fill in the
blanks for the table and the equation. Please do not use commas.
The number of bacteria after 3 months is 7500.
The equation is y = 60,000 x [tex]0.5^3[/tex].
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
Number of bacteria initially = 60,000
After one month,
The number of bacteria = 30,000
This means,
60,000 - 30,000 = 30,000
The percentage decreased.
= 30,000 / 60,000 x 100
= 1/2 x 100
= 50%
Now,
The equation for the number of bacteria after x months.
y = 60,000 x [tex]0.5^x[/tex]
For x = 3,
y = 60,000 x [tex]0.5^3[/tex]
y = 60,000 x 0.125
y = 7500
Thus,
The number of bacteria after 3 months is 7500.
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Ed runs 1/6 mile in 7/9 minutes, what is his speed in miles per minute?
Answer:
Let's first convert 1/6 mile into minutes by multiplying the distance by the number of minutes per mile:
1/6 mile * (1 minute/1/6 mile) = 6 minutes/mile
Next, let's convert the 7/9 minutes into miles:
7/9 minutes * (1/6 mile/minute) = 7/9 * 1/6 mile = 7/54 miles
Now that we have the distance and time in the same units, we can calculate Ed's speed as:
Speed = Distance / Time = 7/54 miles / 7/9 minutes = 7/54 miles / (7/9 * 1 minute) = 7/54 miles / (7/9) minutes = 7/54 miles / (7/9) = 54/7 miles/minute
So, Ed's speed is 54/7 miles per minute.
Step-by-step explanation:
place the numbers 2 , 6 , 7 , 8 , and 9 in the circles so that the sums across (horizontally) and down (vertically) are equal. which number will you place in the middle?
The number 7 will be placed in the middle circle.
To place the numbers 2, 6, 7, 8, and 9 in the circles so that the sums across and down are equal, you can use the following method:
1. Place the median number (7) in the middle circle.
2. Place the two smallest numbers (2 and 6) on either side of the median number.
3. Place the two largest numbers (8 and 9) in the top and bottom circles.
Here is a list of them. Each group of three numbers makes up a side of the triangle. Of course, within a side you can replace round numbers that are not on a corner, but that does not really give any new solutions.
So, the final arrangement would be:
6 2 7
9 8 7
6 2 7
Therefore, the number 7 will be placed in the middle circle.
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What is the product of and ? Write your answer in standard form.
(a) Show your work.
(b) Is the product of and equal to the product of and ? Explain your answer.
In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Multiplication is often referred to as repeated addition because what the multiplication problem is telling you is that you have a certain number of groups of something, all containing a specific number. Confused yet? Here's an example.
You have 3 bags of candy, and each bag contains 5 pieces of candy. How many pieces of candy do you have?
There are two ways to solve this problem. The first is by adding up the pieces of candy:
5 + 5 + 5 = 15
The other way to solve this problem is to use multiplication, because you have 3 groups of candy with 5 pieces of candy in each bag.
3 * 5 = 15
The answer to this multiplication problem is the product, which in this case is 15.
Here's another example. The classroom has 8 rows of chairs and each row has 7 chairs in it. How many chairs are there?
Again, you could add:
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56
Or, you can find the product by multiplying:
7 * 8 = 56
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CORRECT QUESTION FORMAT IS GIVEN BELOW -----
Q. What is the Product in Math?
A 2-column table titled f (x + 1) = 4 (f (x)) has 5 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5. Column 2 is labeled f (x) with entries 4, A, B, C, 1,024.
What are the missing values in the table representing the recursively defined geometric sequence?
A =
B =
C =
The chart fits the functional equation for all values of x, according to the claim made.
The meaning of the term "geometric"?The Geometric Mean (GM) in mathematics is the average or mean that, by calculating the product of the values of the collection of numbers, denotes the central trend of the numbers. In essence, we combine the numbers collectively and calculate their nth root, in which n is the entire amount of data values.
We can use the given functional equation f(x+1) = 4(f(x)) to find the values of f(x) for each value of x, given that we know f(1) = 4. We start by computing:
f(2) = 4(f(1)) = 4(4) = 16
f(3) = 4(f(2)) = 4(16) = 64
f(4) = 4(f(3)) = 4(64) = 256
f(5) = 4(f(4)) = 4(256) = 1024
Now, we have determined all the values of f(x) for x=1 to 5. Since the table has 5 rows, we can write:
x f(x)
1 4
2 16
3 64
4 256
5 1024
We can check that the table satisfies the given functional equation f(x+1) = 4(f(x)). For example, when x = 3, we have:
f(x+1) = f(4) = 256
4(f(x)) = 4(f(3)) = 4(64) = 256
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-3x^5+x^3/2-x^2+8
3.1.1) How many terms are in this expression?
3.1.2) Determine the coefficient of x^3
3.1.3) Give the value of the constant term?
3.1.4) Find the degree of the expression.
Answer:
3.1.1) There are four terms in this expression.
3.1.2) The coefficient of x^3 is 0.5.
3.1.3) The constant term is 8.
3.1.4) The degree of the expression is 5.
the adjoining figure shows a racing track consisting of two parallel stretches which is 119 M long and 10 metre wide its other two end are semicircular the inner distance between the two parallel Streches is 70 m evaluate and also find the distance around the track along its outer edge and the area of the track
The distance around the track along its outer edge is 238 + 100 x π metres and the area of the track is 1250 x π + 2380 square metres.
The racetrack is divided by two parallel sections and two semi-circular endpoints. The two parallel segments are 119 metres long, and the track is 10 metres wide. The inner length of the two parallel sections is 70 metres.
To calculate the distance around the track's outer edge, multiply the lengths of the two parallel segments by the diameter of the two semi-circular ends. C = 2 x π x r, where r is the radius of the semi-circle, may be used to compute the circumference of each semi-circular end.
The radius of each semi-circle is calculated by subtracting the track width (10 metres) from half the inner distance between the two parallel sections (70 metres / 2 = 35 metres). So, the radius of each semi-circle is 35 metres - 10 metres = 25 metres.
As a result, the circumference of each semi-circle is 2 x π x 25 = 50 x π metres. As a result, the circumference of the track along its outside border is 119 metres + 119 metres + 50 x π metres + 50 x π metres = 238 + 100 x π metres.
To calculate the area of the track, first calculate the areas of the two semi-circular ends and the two parallel segments, then add them. A = π[tex]r^{2}[/tex], where r is the radius of the semi-circle, may be used to compute the area of each semi-circular end.
Each semi-circle has an area of π x [tex]25^2[/tex] = 625 x π square metres. The size of the two parallel lengths is 1190 square metres (119 metres x 10 metres). The track's total area(A) = 625 x π + 625 x π + 1190 + 1190
A= 1250 x π + 2380 square metres.
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can somebody help me solve this?
Simultaneous equation is a finite set of equations for which common solutions are soughtThe equivalent expression is 5x + 7y = 37
Solving simultaneous equationA finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
Given the simultaneous equation below:
-2x - y = -4
7x + 8y = 41
In order to compress the equation into 1, we need to add the equation or subtract the equation
On adding, we will have:
(-2x + 7x) + (-y + 8y) = -4 + 41
5x + 7y = 37
Hence the equivalent expression is 5x + 7y = 37
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5. What is the value of x if the
side length of Terrarium A is
four times the side length of
Terrarium B? Terrarium A V=2^x m^3 Terrarium B V= 2 m^3
The required value of x, if the side length of Terrarium A is four times the side length of Terrarium B is 3.63.
What is Terrarium?A terrarium is a glass container with soil and plants inside of it that can be opened for maintenance purposes. Terraria, however, can be exposed to the atmosphere rather than being sealed. Terraria are usually kept as decorative or ornamental items.
According to question:The volume of Terrarium B is 2 m³, so its side length is the cube root of 2, which is approximately 1.26.
The side length of Terrarium A is 4 times that, or approximately 5.04. The volume of Terrarium A is [tex]2^x[/tex] cubic meters, so we can set up the equation:
(5.04)³ = [tex]2^x[/tex]
Taking the cube of both sides, we get:
125.7376 = [tex]8^x[/tex]
Taking the log base 8 of both sides:
x = log(125.7376) / log(8)
x is approximately 3.63.
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5. What is Carnival?
A public event or celebration, typically held outdoors and involving stalls, entertainment, and processions.
The ratio of boys to girls Ms. Garcia’s class is 4:5.
b. If she randomly selects a student from the class to present their solution to a math problem, what is the probability the student will be a girl?
The probability of randomly selecting a girl from Ms. Garcia's class is 5/9.
The ratio of boys to girls in Ms. Garcia's class is 4:5Which means that for every 5 students in the class, 4 of them are boys and 5 of them are girls.
To calculate the probability of selecting a girl from the class, we need to divide the number of girls by the total number of students:
Number of girls: 5 students
Total number of students: 4 students + 5 students = 9 students
Probability of selecting a girl: 5 students / 9 students = 5/9
So the probability of randomly selecting a girl from Ms. Garcia's class is 5/9.
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Translate the sentence into an equation. Four more than the product of a number and 8 is 6. Use the variable b for the unknown number.
Answer:
8b + 4 = 6
Step-by-step explanation:
8b + 4 = 6
It didn't say you have to solve for b, but just in case...
8b = 6 - 4 = 2
b = 2/8 = 1/4
i need help pls
schoology
Answer:
b=95; c=85
Step-by-step explanation:
B is equivalent to 85 degrees because of the vertical angle theorem. B is equivalent to 95 degrees because b and c lie along a straight line; a straight line is 180 degrees, so 180-85=95.
Hope this helps! If you found my answer helpful, please consider marking brainliest! If you have any questions, feel free to ask me in the comments!
Answer:
b equals 95 c equals 85 that's what I think and I have straight A's so I think I'm right
Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places.
r = 10.26 inches, θ = 240°
A) 42.98 inches B) 43.08 inches C) 43.28 inches D) 43.18 inches
The length of the arc is 42.98 inches, so the correct option is A.
How to find the length of the arc?For an arc defined by an angle θ on a circle of radius r the length of the arc is given by:
L = (θ/360°)*2*pi*r
Where pi = 3.1416
Here we know that:
r = 10.26 inches
θ = 240°
Then we can replace that in the formula above, we will get:
L = (240°/360°)*2*3.1416*10.26 in
L = 42.98 inches
The correct option is A.
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I need help so please help guys!
Step-by-step explanation:
So to start
Perpendicular lines are lines that form 90 degree angles when they meet.
Parallel lines will never touch, no matter how far they go.
So
Top left
A vertical line and a horizontal line
This would be perpendicular
Lines that intersect to form right angles
As mentioned above this would be perpendicular
Two nonvertical lines that have a product of -1 for their slopes.
Parallel lines always have the same slope, so this goes for parallel.
Equations that can be written in slope intercept form
This would be both as all lines can be written in this form
Non vertical lines that have the same slope and different y-intercepts
As they have the same slope this would make it parallel
You can determine the relationship between two lines by comparing their slopes and y-intercepts.
This is both as this is a way to compare all lines
Lines in the same plane never intersect
This would be parallel
Slopes are opposite reciprocals
This is perpendicular as the slopes of perpendicular lines are reciprocals
Vertical lines that have different x-intercepts
This would be parallel
Sorry this is a lot
Hope this helped though :)
which of theses inequalities best represents this situation? (only answer the first question)
Please help me with this math problem!! Will give brainliest!! :D 15 POINTS!!!
Step-by-step explanation:
For the first question, let's add the %'s
37% + 13% + 25% + 25% = 100%
So it looks like you have a 100% chance to win a prize.
-------------
For the second question
It cost $2 to play
Soda - $1
Candy Bar - $1
Toy - $3
Mega Win - $40
It looks like 2 out of 4 (50%) cost more than the price to play.
So we add the % of the Toy and Mega since those are the ones more than $2
25% + 13% = 38% chance to win a prize more than the cost to play
every matrix transformation is a linear transformation . t/f
"Every linear transformation is a matrix transformation." This is false. Not all linear transformations are matrix transformations, even if all matrix transformations are linear transformations.
A point, line, or geometric object can be changed in four different ways that are all referred to as transformations. The Pre-Image refers to the object's initial shape, and the Image, after transformation, refers to the object's ultimate shape and location.
Bring out the pattern blocks, tangrams, and geoboards for another low-prep, high-engagement method of teaching geometric transformations. Students can produce an original design and then hand it off to a partner so that they can add a reflection, rotation, or translation to it.
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