Answer:
daughter = 9yrs
mother = 27yrs
Step-by-step explanation:
let age of daughter be x
age of mother = 3x
by qsn,
three yrs ago,
4 (x-3) = 3x-3
4x-12 = 3x-3
4x-3x = -3+12
× = 9 yrs (age of daughter )
3x = 3×9 = 27 yrs ( age of mother)
The profit function, P(x), revenue function, R(x), and cost function, C(x), are related by the equation P(x)=R(x)−C(x). Andrew has determined that the revenue and cost functions for a new product line at his business are given by these functions.
R(x)=5x
C(x)=1200+3x
What is the profit function for Andrew’s new product line?
P(x)=2x−1200
P(x)=2x+1200
P(x)=8x−1200
P(x)=8x+1200
Answer:
The answer is P(x)8x-1200
Step-by-step explanation:
The profit function for Andrew’s new product line will be P(x) = 2x - 1200. Then the correct option is A.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.
The profit is given as,
Profit = Revenue function - Cost function
Andrew has determined that the revenue and cost functions for a new product line at his business are given by these functions.
R(x) = 5x
C(x) = 1200 + 3x
Then the profit function for Andrew’s new product line will be
P(x) = R(x) - C(x)
P(x) = 5x - 1200 - 3x
P(x) = 2x - 1200
The profit function for Andrew’s new product line will be P(x) = 2x - 1200. Then the correct option is A.
More about the profit is given below.
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What value belongs next to the 1 in the table? What does it mean in this context?
Answer:
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
Step-by-step explanation:
The value next to 1 in the table above = number of dimes we have in 1 quarter.
Let the value next to 1 be "x".
That is:
1 quarter = x dimes
If 4 quarters = 10 dimes, then,
Cross multiply to find, how many dimes, x is equal to.
Thus:
1*10 = 4*x (cross multiplication)
10/4 = 4x/4 (dividing both sides by 4)
2.5 = x
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
Which products result in a difference of squares? check all that apply. (5z 3)(–5z – 3) (w – 2.5)(w 2.5) (8g 1)(8g 1) (–4v – 9)(–4v 9) (6y 7)(7y – 6) (p – 5)(p – 5)
Option second [tex]\rm (w-2.5)(w+2.5)[/tex] and option fourth [tex]\rm (-4v-9)(-4v+9)[/tex] are the products that result in a difference in squares
It is required to identify which products result in a difference of squares.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We know that:
[tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]
In option first:
[tex]\\\rm= (5z+3)(-5z-3)\\\rm =-(5z+3)(5z+3)\\\rm =-(5z+3)^2[/tex]
It is not the difference between squares.
In option second:
[tex]\rm = (w-2.5)(w+2.5)\\\rm = (w^2-2.5^2)[/tex] By using [tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]
It is the difference between squares.
Similarly, in option third:
[tex]\rm = (8g+1)(8g+1)\\\rm = (8g+1)^2[/tex]
It is not the difference between squares.
Similarly, in option forth:
[tex]\rm = (-4v-9)(-4v+9)\\\rm = (4v+9)(4v-9)\\\rm = (4v)^2-9^2[/tex]
It is the difference between squares.
Similarly, in option fifth:
[tex]\rm = (6y+7)(7y-6)\\\rm = 42y^2+13y-42[/tex]
It is not the difference between squares.
Similarly, in option sixth:
[tex]\rm = (p-5)(p-5)\\\rm = (p-5)^2[/tex]
It is also not the difference between squares.
Thus, option 2 and option 4 are correct.
Learn more about polynomial here:
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Alice was having a conversation with her friend Trina, who had a discovery to share:
Pick any two integers. Look at the sum of their squares, the difference of their squares,
and twice the product of the two integers you chose. Those three numbers are the
sides of a right triangle.
a. Write an equation that models this conjecture using the variables x and y.
b. Investigate this conjecture for at least three pairs of integers. Does her trick
appear to work in all cases, or only in some cases? Explain.
c. Use Trina’s trick to find an example of a right triangle in which all of the sides
have integer length, all three sides are longer than 100 units, and the three side
lengths do not have common factors.
BONUS: If Trina’s conjecture is true, use the equation found in part a to prove the
conjecture. If it is not true, modify it so it is a true statement, and prove the new
statement
Answer:
a. (x² + y²)² = (x² - y²)² + (2xy)²
b. The conjecture works in all cases.
c. Sides of 119, 120, and 169
Step-by-step explanation:
a. Equation that models this conjecture
x² + y² = sum of squares
x² - y² = difference of square
2xy = twice the product of the integers
If these are the sides of a right triangle then
(x² + y²)² = (x² - y²)² + (2xy)²
b. Test the conjecture
(i) Try x = 2, y = 1
(2² + 1²)² = (2² - 1²)² + (2×2×1)²
5² = 3² + 4²
25 = 9 + 16
(ii) Try x = 3, y = 1
(3² + 1²)² = (3² - 1²)² + (2×3×1)²
10² = 8² + 6²
100 = 64 + 36
(iii) Try x = 3, y = 2
(3² + 2²)² = (3² - 2²)² + (2×3×2)²
13² = 5² + 12²
169 = 25 + 144
The conjecture appears to work in all cases.
c. A possible triangle
We must have one side greater than 100. That means,
x² > 100 or x >1 0.
Let x = 12
One side = 12² + y²
The second side = 12² - y²
The third side must have 2xy > 100
24y > 100
y > 4.2
Try y = 5
(12² + 5²)² = (12² - 5²)² + (2 × 12 × 5)²
169² = 119² + 120²
So, one right triangle could have sides of 119, 120, and 169.
Furthermore, these sides have no common factors.
Check:
169² = 119² + 120²
28561 = 14161 + 14400
28561 = 28561
difference between mass and weight
Mass is how much "matter" something is. Weight is this with respect to gravity. Therefore, if you took a ball to the moon, its mass would not change because the amount of matter is unaffected but the weight will change because the Earth and the Moon have different gravitational pulls.
Hope this helps!!
Carpet Plus installs carpet for $100 plus $8 per square yard of carpet. Carpet World charges $75 for installation and $10 per square yard of carpet. Find the number of square yards of carpet for which the cost including carpet and installation is the same.
Answer:
12.5 square yards.
Step-by-step explanation:
Let a square yard of carpet = x
The cost of installing a carpet is given by;
100 + 8x
The charge for installation
75 + 10x
The number of square yards of carpet for which the cost including carpet and installation is the same is given by;
100 + 8x = 75 + 10x
100 - 75 = 10x - 8x
25 = 2x
x = 25 / 2
x = 12.5 square yards.
Answer:
old post so answering for points
Step-by-step explanation:
Please help!!
Find the equivalent rate:
300 miles in 20 seconds to miles per minute.
30 miles per min
15 miles per min
3 miles per min
Step-by-step explanation:
300/20 × 3/3 = 900/60
* 60 sec is 1 min therefore you want to get 60 secs in the denominator. In order to get that, you need to multiply.
900/60 divided by 60/60 is 15/1.
So 300m/20sec = 900m/60sec = 900mpm
If we're to do the same for all then it would be:
30m/20sec = 90m/60sec = 90mpm
15m/20sec = 45m/60sec = 45mpm
3m/20sec = 9m/60sec = 9mpm
The distance between slits on a diffraction grating is 0. 60 mm, and one of the angles of diffraction is 0. 30°. The light forms a second-order bright band. How large is the path difference? 1047 nm 1571 nm 3142 nm 6284 nm.
The path difference will be 1571 nm
What will be the path difference?Now for the constructive interference, the formula is given
[tex]\rm dsin\theta==n\lambda[/tex]
here,
d = is the distance between slits.=060mm
θ = is the angle of diffraction=0.30 Degree
n = is the order of fringe=2
λ = is the path difference.
[tex]\lambda=\dfrac{(dsin\theta)}{n}[/tex] [tex]\lambda=\dfrac{(0.60\times10^{-3}\times sin(0.30)}{2} = 1.57\times10^{-6}[/tex]
Thus path difference will be 1571 nm
To know more about the Diffraction of light follow
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The answer is C. 3142
Tucker deposited $20,000 in a savings account with simple interest. Five years later, he had earned $14,000 in interest. What was the interest rate? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
the interest rate should be 14%
how do i do 21 divided by 18
Answer:
Hello~Step-by-step explanation:
[tex]21 \div 18[/tex]
if you will use calculator you'll simply get the answer 1.16666667but simply you can put 1.1666Friday’s temperature was 40 degrees and the temperature increased by 130% by Sunday evening. What was the temperature on Sunday evening?
Answer:
By Sunday evening the temperature would be 92 degrees
Step-by-step explanation:
Find 130% of 40
40 × 1.3 = 52
Add the product to your original temperature (40)
40 + 52 = 92
What is the value of x in the equation -5/8x=-160
Answer:
x=256
Step-by-step explanation:
Answer:
x=256
Step-by-step explanation:
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We know that:
[tex]x - 11 \space\ and \space\ 2x + 8 \space\ are \space\ a \space\ linear \space\ pair. \space\ (Refer \space\ to \space\ attachment.)[/tex]This means that:
[tex](x - 11) + (2x + 8) = 180[/tex]Step-by step calculations:
Open the parenthesis:
[tex](x - 11) + (2x + 8) = 180[/tex]=> [tex]x - 11 + 2x + 8 = 180[/tex]Combine like terms:
=> [tex]x - 11 + 2x + 8 = 180[/tex]=> [tex](x + 2x) + (-11 + 8) = 180[/tex]Simplify the LHS:
=> [tex]3x - 3 = 180[/tex]Add 3 both sides:
=> [tex]3x - 3 = 180[/tex]=> [tex]3x - 3 + 3 = 180 + 3[/tex]=> [tex]3x = 183[/tex]Divide 3 both sides:
=> [tex]\frac{3x}{3} = \frac{183}{3}[/tex]=> [tex]x = 61[/tex]Same side exterior angles are linear pair and have sum 180°
[tex]\\ \rm\Rrightarrow x-11+2x+8=180[/tex]
[tex]\\ \rm\Rrightarrow 3x-3=180[/tex]
[tex]\\ \rm\Rrightarrow 3x=183[/tex]
[tex]\\ \rm\Rrightarrow x=61[/tex]
A baby is b weeks old. How old will it be in five weeks time
Answer:
b(5)
Step-by-step explanation:
pls I am not sure
pls I really don't want any bad comment I already feeling bad
What is the domain of the given function?
Answer:
b or c
Step-by-step explanation:
need this asap so if you know it please let me know quickly
Answer:
Step-by-step explanation:
-20d + 12
4(d + 9) - 8(-3d - 3)
4d + 36 - 24d - 24
4d - 24d + 36 - 24
-20d + 12
Sammy scored an 80% on her math quiz. She answered 12 correctly. How many questions were on her quiz?
Answer:
15 questions
Step-by-step explanation:
If Sammy got 80%, we can see that 12/15=0.8, and 0.8 as a percentage is 80%.
Hope it helps!!
The table of values below represents a linear function and shows the weight of a kitten as it has grown. What is the output for the initial value?
Weight of a Kitten
Kitten’s Age (weeks)
2
4
6
8
10
Weight (pounds)
0.8
1.4
2.0
2.6
3.2
a.0.2 pounds
b.0.3 pounds
c.0.6 pounds
d.0.8 pounds
Answer:
A. 0.2 pounds
Step-by-step explanation:
I just did it on edge.
Answer:
a 0.2
Step-by-step explanation:
The perimeter of a rectangular pool is 246 m.
If the width of the pool is 52 m, what is its length?
please answer this
9²+5x2+ 1³
Answer: your answer would be 92 .
Step-by-step explanation: all you have to do is add . hope this helped <3 .
Write down the equation of a straight line with a gradient m= 1/2 which passes through the point (0,7)
Answer:
y=mX+c
7=(1/2)(0)+c
c=7
y = 1/2 X + 7
Step-by-step explanation:
Please brainleist
║
∨
°ω°
To get an A, you need more than 200 points on a two-part test. You score 109 points on the
first part. How many more points do you need?
Answer:
91 more points are needed
Step-by-step explanation:
Answer:91
Step-by-step explanation:
Mr. Campbell decides that too many students are getting a pass on homework. He adds 10 yellow marbles to the jar. Tell whether each part of the probability model does or does not change.
The sample space change.
Each event within the sample space change. The probability of each event
change.
Answer:
The new probability of drawing a red marble is ()=.
Step-by-step explanation:
The sample space change. Each event within the sample space change. The probability of each event changes.
What is a plane? Please help! Answer ASAP
Answer: A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.
Step-by-step explanation:
Hope this helps
A plane is eather a airplane or plane a flat surface of land that is very big
Vickie conducts a survey of home builders to determine the average cost of building a new home. She samples 10 home builders who are building in the town in which she lives. Under which conditions will her sample be a representative sample? Select two options.
Complete question is;
Vickie conducts a survey of home builders to determine the average cost of building a new home. She samples 10 home builders who are building in the town in which she lives. Under which conditions will her sample be a representative sample? Select two options:
A) The builders were chosen at random.
B) The population included only builders who build in Vicki’s town.
C) The population included builders who build homes in any town.
D) The population included builders who do not build homes in Vicki’s town.
E) The builders were referred to Vicki by the realtor who will be selling the houses.
Answer:
Options A & B are correct.
A) The builders were chosen at random.
B) The population included only builders who build in Vicki’s town.
Step-by-step explanation:
Looking at the question, we see that Vickie wanted to determine the cost of building a new home in the town in which she lived. Now, she sampled builders who are building in the town in which she lives and thus, it makes the sample more representative.
However, the random method of choosing the builders would help to remove any lingering biases that may arise.
Thus, we can conclude that the builders were chosen at random and that it included only those who build in her town.
Thus, options A & B are correct.
Answer:
A)The builders were chosen at random., B)The population included only builders who build in Vicki’s town.
Step-by-step explanation:
due today
please help
Answer:
Hiking
Step-by-step explanation:
Given: Kayaking burns 4.5 calories per minute
The slope of the graph is 5
You can use rise over run to figure out the slope. Or you may have noticed the order pair (1,5)
This means hiking burns 5 calories per minute, which is greater than 4.5
3. In Figure 5.37 below, O is the centre of the circle PA and PB are tangents to the circle at A and B, respectively. If m(ZACB)=1150 ,then find: a. m(AB) b. m(ACB) . A o С P B Figure 5.37
Please assist!!!! No links
Answer:
The choice C.
Step-by-step explanation:
[tex] {( \frac{ {2}^{ - 10} }{ {4}^{2} } )}^{7} = \frac{ {(2}^{ - 10}) ^{7} }{ {( {4}^{2}) }^{7} } = \frac{ {2}^{ - 10 \times 7} }{ {4}^{2 \times 7} } = \frac{ {2}^{ - 70} }{ {4}^{14} } \\ \\ = \frac{1}{ {2}^{70} \times {4}^{14} } [/tex]
You randomly draw a marble from a bag, record its color, and then replace it. You draw a red marble 3 out of 20 times. What is the experimental probability that the next marble will be red? Write your answer as a fraction, decimal, or percent. The experimental probability that the next marble will be red is
Answer:
3/20 or 0.15 or 15%
Step-by-step explanation:
Since 3 red marbles were drawn out of 20 outcomes, the probability the next marble will be red is 3/20. If you convert it to a decimal it will be 0.15, and if you convert it to a percent it will be 15%.
what the midpoint between the point 2,6 and "-4,6
Answer: (-1, 6)
Step-by-step explanation:
Use the midpoint formula:
(Xm, Ym) = ([x1 + x2]/2, [y2 + y1]/2)
(Xm, Ym) = ([2 + -4]/2, [6 + 6]/2)
(Xm, Ym) = (-2/2, 12/2)
(Xm, Ym) = (-1, 6)
The midpoint is (-1, 6)