The family has 3 sons and 3 daughters, for a total of 6 children.
Explanation:
The question is a problem in basic algebra which can be solved using simple logical reasoning. We are given that each daughter in the family has as many brothers as sisters, and each son has three times as many sisters as brothers.
Let's start by saying that the number of daughters is D and the number of sons is S.
If each daughter has the same number of brothers as sisters, that means D = S. But, each son has three times as many sisters as brothers, which we can express as S = 3*(D - 1), because the number of sisters for each son is the number of daughters minus one (each son doesn't count himself as a sister).
By substituting D from the first equation into the second, we get S = 3 * (S - 1), which simplifies to S = 3, and thus D = 3 as well.
So, the family has 3 sons and 3 daughters, for a total of 6 children.
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please help me with my math homework??
-3(m-2n) = 5m
solve for m
Answer:
n=3n/4
Step-by-step explanation:
Find the value of x, please
4 inside angles = 360 degrees
131 + 75 + 105 = 311
360 - 311 = 49
x^2 = 49
x = sqrt(49) = 7
x = 7
Brandon has 7/1/2gallon of paint. He plans on using 1/1/2 gallon on each room. How many rooms will he be able to paint.
Pqr is a right angle. If pq=8 what is equivalent
does the set of numbers form a pythagorean triple explain 24 , 10 ,26
Suppose you drop a ball from a window 10 meters above the ground. The ball bounces to 80% of its previous height with each bounce. What is the total number of meters (rounded to the nearest tenth) the ball travels between the time it is dropped and the 10th bounce?
79.3 meters
73.2 meters
89.3 meters
77.5 meters
In sakura's garden for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How maNY red flowers are in sakura'sgarden?
Answer:
25 red flowers
Step-by-step explanation:
yeah
Consider the equation below. f(x) = 4x3 + 6x2 − 24x + 3 (a) find the intervals on which f is increasing. (enter your answer using interval notation.)
The function f(x) = 4x^3 + 6x^2 - 24x + 3 is increasing on the interval (-2/3, 1.5), where the derivative of the function is positive.
Explanation:To find the intervals on which the function f(x) = 4x^3 + 6x^2 − 24x + 3 is increasing, we first need to calculate its derivative, which will give us the slope of the tangent line to the function at any point x. The function is increasing wherever its derivative is positive.
The derivative of f with respect to x is:
f'(x) = 12x^2 + 12x - 24.
To find where the function is increasing, set the derivative greater than zero:
12x^2 + 12x - 24 > 0
Solve this inequality to find the intervals for x. Factoring the quadratic, we get:
(2x - 3)(6x + 4) > 0
The zeros of this equation are x = 1.5 and x = -2/3. These values divide the real number line into intervals. Test a value from each interval to see where the function is increasing:
If x < -2/3, for example x = -1, the derivative becomes negative, indicating the function is decreasing.If -2/3 < x < 1.5, for example x = 0, the derivative is positive, indicating the function is increasing.If x > 1.5, for example x = 2, the derivative is again negative, indicating the function is decreasing.Thus, the function f(x) is increasing in the interval (-2/3, 1.5).
If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 4, what is the equation of the new function?
A. g(x) =1/4 x2
B. g(x) = (1/4x)2
C. g(x) = 4x2
D. g(x) = (4x)2
Answer:
B is your answer
Step-by-step explanation:
g(x)=(1/4x)^2
Really need help with this GeoMETry qUIz
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ. :
(picture attached)
According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are _____________ angles, they are congruent according to the ____________ Angles Postulate. Finally, angle VQT is congruent to angle WRS by the Transitive Property of Equality.
Which term accurately completes the proof?
1Same-side interior
2Corresponding
3Alternate interior
4Vertical
Find the absolute value and the opposite of the integer.
–989,006
In a triangle, the measure of the first angle is three timesthree times the measure of the second angle. the measure of the third angle is 80 degrees80° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
The price of a bookcase, including 8% sales tax, is $378. What is the price of the bookcase, before sales tax?
Can someone help me with this question?
A car travels 95 miles on 5 gallons of gas. give the ratio of miles to gallons as a rate in miles per gallon.
The parent function of a graph is f(x) = x2. The graph shifts a units to the left and down b units. Which function models the transformed function?
A) y = x2 - a + b
B) y = (x - a)2 - b
C) y = (x + a)2 - b
D) y = (x - b)2 - a
Answer:
Option c
Step-by-step explanation:
A parent function is given by f(x) = x²
If the graph of the parent quadratic function is shifted a units to the left then new function will become
f'(x) = (x+a)²
Now the new function f'(n) is shifted b units down then the shifted function will be
f" (x) = (x + a)² - b
Therefore, Option c. is the answer.
A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell
2500 t-shirts for $10. They consider raising the t-shirt price in order to earn more
profit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent the
number of $1 increases.
a. Write a function,
Write a function, c(x), to represent the cost of one t-shirt based on the number
of increases.
b. Write a function, t(x), to represent the number of t-shirts sold based on the
number of increases.
c. Write a revenue function, r(x), for the t-shirt sell that could be used to maximize
a. Let us say that c(x) is the cost of one t shirt based on the number of increases therefore:
c = 10 + x
b. Say that t(x) is the number of t shirts sold based on the number of increases so:
t = 2500 – 100 x
b. The revenue is simply the product:
r(x) = (10 + x) (2500 – 100 x)
Combining:
r(x) = 25000 – 1000 x + 2500 x – 100 x^2
r(x) = 25000 + 1500 x – 100 x^2
Taking the 1st derivative and setting dr / dx = 0 to get the maxima:
dr / dx = 1500 – 200 x
1500 = 200 x
x = 7.5
t = 2500 – 100 x = 2500 – 100 (7.5) = 1750
Hence 1750 shirts should be sold.
I made a clay snake 9 5/8 inches long, but a section 1 7/8 inches long broke off. How long is the snake now?
A hockey team played 81 games in a season. they won one fewer games than three times the number of ties, and lost eight fewer games than they won. how many games did they win? lose? tie?
Final answer:
The hockey team won 38 games, lost 30 games, and tied 13 games in the season.
Explanation:
Let's define the variables for the different outcomes in the hockey team's season:
T = number of games tiedW = number of games won = 3T - 1L = number of games lost = W - 8The total number of games is the sum of wins, losses, and ties, and we know this number is 81. This gives us the equation:
W + L + T = 81
Substituting W and L gives:
(3T - 1) + (3T - 1 - 8) + T = 81
Combining like terms and solving for T:
7T - 10 = 81
7T = 91
T = 13 (number of ties)
We then calculate W and L as:
W = 3T - 1 = 3(13) - 1 = 38 (number of wins)
L = W - 8 = 38 - 8 = 30 (number of losses)
A rectangle has a length of n units its width is 6 unit less its length what is the area of the rectangle
Answer:
Step-by-step explanation:
The sum of 4 consecutive even integers is 36, what is the 3rd largest integer in the set?
The sum of four consecutive even integers that equal 36 is broken down to find the smallest integer. Once the smallest integer is found (6), we can determine that the third largest integer in the sequence is 8.
Explanation:To solve for the third largest integer in a set of four consecutive even integers that sum to 36, we can define the smallest integer as x. The next integers would be x + 2, x + 4, and x + 6. Setting up the equation:
x + (x + 2) + (x + 4) + (x + 6) = 36
Combining like terms, we get:
4x + 12 = 36
Subtracting 12 from both sides:
4x = 24
Dividing by 4:
x = 6
Now we have our integers: 6, 8, 10, 12. The third largest integer, which is the second smallest, is 8.
What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?
3,−6,12,−24,...
You can rewrite this as:
(−1)n3⋅(1,2,4,8,...)
If we focus on 1,2,4,8...
an+1=2an
with a0=1.
This can be written out as a nice sum:
N∑n=02n=20+21+22+23+...
=1+2+4+8+...
Thus, now we can recombine everything to get:
3N∑n=0(−1)n2n
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. time (hours) 4, 6, 8, 10 distance (miles) 212, 318, 424, 530
Answer:
The car travels 53 miles per hour.
Step-by-step explanation:
time (hours) 4 6 8 10
distance (miles) 212 318 424 530
The rate of change can be given as:
[tex]\frac{318-212}{6-4}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph
[tex]\frac{424-318}{8-6}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph
Hence, the rate of change is 53 mph or we can say the car travels 53 miles per hour.
Two numbers are between 20 and 30. their greatest common factor is 4.Which two numbers could they be?
A car travels 100 meters in 5 seconds. What is the speed of the car/7281023/14f0e74f?utm_source=registration
The steps to do it. It says "solve for x. Each figure is a parallelogram. Show your work.
The value of x is 4.
To solve for x, we'll use the property of parallelograms that opposite angles are supplementary.
Given that one angle is [tex]\(140^\circ\)[/tex], we can set up the equation:
140 + 10x = 180
Now let's solve for x:
10x = 180 - 140
10x = 40
[tex]x = \frac{40}{10}[/tex]
x = 4
Therefore, the value of x is 4. Adjacent angles in a parallelogram are indeed supplementary.
Rectangle EFGH is graphed on a coordinate plane with vertices at E(-3,5), F(6,2), G(4,-4), and H(-5,-1). Find the slopes of each side. What do you notice about the slopes of opposite sides? What do you notice about the slopes of adjacent sides?
Find the GCF of the given polynomial.
16a⁴b⁴ + 32a³b⁵ - 48a²b⁶
Write the ratio as a fraction in simplest form a/b. What is the ratio of baseballs to basketballs?
Answer: 5/8 im pretty sure i hope it helps :) i took it on freckle so i know but i think this is right
11/12+(−7/12). Write your answer as a fraction in simplest form.
The result of the operation 11/12 + (-7/12) simplifies to 1/3, because the sum of the numerators is 4, and we keep the same denominator of 12, giving us 4/12. In simplest form, this fraction is 1/3.
Explanation:The question is asking us to perform an addition operation on two fractions. Specifically, we are asked to add 11/12 and -7/12. When adding or subtracting fractions, the most important thing is that they have the same denominator, which our fractions do. Here's how you perform the operation:
Add the numerators of the fractions: 11 + (-7) = 4.
You keep the same denominator: 12.
So, 11/12 + (-7/12) = 4/12.
To simplify this fraction, we find the greatest common divisor of 4 and 12, which is 4, and divide both the numerator and denominator by it. So, 4/12 simplifies to 1/3.
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