Answer:
See the expressions and the answers below
Step-by-step explanation:
Given data
The first expression is given as
x^2+169 .-> we can not factorize the expression anymore
The second expression
5x^2-50x+125
5(x^2-10x+25)
The third expression
100x^2-25y2
25(4x^2-y^2)
URGENT 100 POINTS AND BRAINIEST
Question 9 (Essay Worth 10 points)
(04.01, 04.02 HC)
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Part B: How much time does Ted spend practicing the breaststroke every day? Show your work. (3 points)
Part C: Is it possible for Ted to have spent 45 minutes practicing the butterfly stroke if he practices for a total of exactly 50 minutes and practices the breaststroke for 20 minutes longer than he practices the butterfly stroke? Explain your reasoning. (2 points)
Answer:
Part A:
x + y = 50
y = x + 20
Part B:
Ted spends 35 minutes practicing the breaststroke every day.
Part C: It is not possible, as 45 + 65 isn't 50.
Step-by-step explanation:
what is 32⋅(12)x+1=2x−14?
Answer:
[tex]x=-\frac{15}{382}[/tex]
Step-by-step explanation:
32 × 12x + 1 = 2x - 14
384x + 1 = 2x - 14
384x + 1 - 1 = 2x - 14 - 1
384x = 2x - 15
384x - 2x = 2x - 2x - 15
382x = - 15
382x ÷ 382 = - 15 ÷ 382
[tex]x=-\frac{15}{382}[/tex]
Make a T-chart with 5 points and Graph the function below on the graph paper you have been provided with. Identify the Key features. AOS, DOMAIN, and RANGE. Make sure I can easily identify your answers on your paper. Also, answer the question below.
Answer:
look this up ok
Step-by-step explanation:
Graph axis of symmetry vertex and max and min, domain and range
Can someone help me thank youuu!!!
Answer:
D.
Step-by-step explanation:
cos is positive and sin is negative
=>
it must be in quadrant IV.
you remember, 1 = sin² + cos²
1 = sin² + (3/5)² = sin² + 9/25
25/25 = sin² + 9/25
16/25 = sin²
sin = 4/5 or -4/5
and as sin of this angle is < 0, our solution is -4/5
Flying with a tailwind, a flight crew flew 500 km in 4 hours. Flying against the tailwind, the crew flew 468 km in 4 hours. Find the speed of the plane in calm air and the speed of the wind, both in km per hour.
Answer:
spped of the plane in calm air=121 km/h
speed of the wind= 4km/h
Step-by-step explanation:
Let say V the speed of the plane in calm air
and v the speed of the wind
Flying with a tailwind, a flight crew flew 500 km in 4 hours ==> 500= (V+v)*4
Flying against the tailwind, the crew flew 468 km in 4 hours ==> 468 = (V-v)*4
We divide the 2 equations by 4 and then add the 2 results equations:
(500+468)/4=2V ==> V=121 (km/h)
We replace that value in the first equation:
V+v=500/4=125
v=125-121=4 (km/h)
A die is rolled five times and a 5 or 6 is considered a success. Find the probability of
(i) at least 2 successes,
(ii) at least one but no more than 3 successes.
Answer:
(i) The probability of at least 2 successes is 0.2093.
(ii) The probability of at least one but no more than 3 successes is 0.9548.
Step-by-step explanation:
Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.
Favourable cases = {1, 6} = 2.
[tex]p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = \frac{2}{3} \\\\n=5[/tex]
i) at least 2 successes,
[tex]P(X\geq 2) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\geq 2) = 0.2093[/tex]
ii) at least one but no more than 3 successes,
[tex]P(X\leq 3) = (^{n}C_{x} )\times p^{x} \times (1-p)^{n-x}\\\\P(X\leq 3)= 0.9548[/tex]
88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95
Find the Mean, Median, Mode, Range and Outlier of the data set above?
Answer:
Mean = 83.15
Median = 90
Mode = 88
Range = 110
Outlier = 5
Step-by-step explanation:
Mean - (88+92+76+42+88+90+100+110+115+5+88+92+95)/2 = 83.15
Median - 5, 42, 76, 88, 88, 88, 90, 92, 92, 95, 100, 110, 115 = 90
Mode - 88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95 = 88
Range - 115 - 5 = 110.
Outlier - 88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95 = 5
hope it helps :)
please mark brainliest!!! (took a lot effort!)
Answer:
Step-by-step explanation:
Arrange the data from the lowest to the highest value ( after you rearrange them count to see if you still have the same amount of values -13 numbers)
5, 42, 76, 88, 88, 88, 90, 92, 92, 95, 100, 110, 115
Mean: sum up all the values /number of values
mean = (5+42+76+88+88+88+90+92+92+95+100+110+115)/13 ≅83.15
Median: is the number in the middle (or if you have an even amount of numbers you do the average of the 2 middle numbers)
median = 90
Mode: is the number that appears the most (a data set can have more than one mode if different numbers appear with the same frequency )
mode= 88
Range: is the difference between the biggest and smallest value
range = 115-5 = 110
Outlier: is a value that is significantly different than the rest of the values
outlier = 5
What is the simplified form of the following expression?
Answer:
-( cube root of 2x)-6(cube root of x)
Find the value of x. Show your work with proper statements and notation
Answer: x = 14
====================================================
Explanation:
For any triangle, the three inside or interior angles always add to 180
M+N+P = 180
32+64+6x = 180
6x+96 = 180
6x = 180-96
6x = 84
x = 84/6
x = 14
A shopkeeper bought a second-hand car for Rs 1,50,000. He spent Rs 10,000
on its painting and repair and then sold it for Rs 2,00,000. Find his profit or loss.
Please Help me and don't report this
8 < x < 8.5 is your answer
other sides has to always be less than the hypotenuse
9514 1404 393
Answer:
0.5 < x < 16.5
Step-by-step explanation:
The sum of the two shortest sides of a triangle must always exceed the length of the longest side.
If x and 8.0 are the short sides, then ...
x + 8.0 > 8.5
x > 0.5
If 8.0 and 8.5 are the short sides, then ...
8.0 +8.5 > x
16.5 > x
So, for the given triangle to exist, we must have ...
0.5 < x < 16.5
_____
Additional comment
You will notice that the value 0.5 is the difference of the given sides, and 16.5 is their sum. This will always be the case for a problem like this. The third side length always lies between the difference and the sum of the other two sides.
easy! please help :( The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.
Choosing which 2 books describes a pair of dependent events?
Answer:
D: one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf
Step-by-step explanation:
A pair of 2 dependent events are simply those in which the choice of the second item depends on taking the first item such that the probability changes.
Because when the first item is taken without replacement, the sample size would have reduced and as such picking the exact same item will reduce the probability.
Now, what this means in relation to the question is that for 2 of the events to be independent, they must be on the same shelf and of same type of book such that the second book can't be selected until the first one has been selected.
The only option that fits this definition is option D where both books are on the same shelf and they are same type of books.
Answer:
one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf
Step-by-step explanation:
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Total People=5+7+4=16
Women=7We know
[tex]\boxed{\sf P(W)=\dfrac{No.\:of\:women}{Total\:People}}[/tex]
[tex] \\ \sf \longmapsto \: p(w) = \frac{7}{16} [/tex]
Here is the picture of the problem I need help with.
Answer:
-5
Step-by-step explanation:
We need to find a number less than -3
-1 is greater than -3
0 is greater than -3
2 is greater than -3
-5 is less than -3
Answer:
option A
Step-by-step explanation:
Because its colder than negative 3 degrees F.
Please help!!!! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answers Below:
Answer:
B) 13+14 (n - 1)
Step-by-step explanation:
this is an arithmetic sequence
13 represent the first term
14 is a constant difference
Answer:
The answer is B
Step-by-step explanation:
substitute the value of n in the equation.
How do i solve this quesiton 6(x − 2) > 15
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \!\!6(x-2)>15 \\\\6x-12>15 \\\\6x>27\\\\ \boldsymbol{x>4,5 \ \ or \ \ x\in(4,5\ ; \infty)}[/tex]
A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280πcm3. Find the radius of the can if the height is 16cm16cm. Keep your answers in simplified radical form.
Answer:
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Radius of the can:
The radius of the can is given by:
[tex]r^2 = \frac{V}{h\pi}[/tex]
In which V is the volume and h is the height.
In this question:
[tex]V = 1280\pi, h = 16[/tex]
Thus
[tex]r^2 = \frac{V}{h\pi}[/tex]
[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]
[tex]r^2 = 80[/tex]
[tex]r = \sqrt{80}[/tex]
[tex]r = \sqrt{5*16}[/tex]
[tex]r = \sqrt{5}\sqrt{16}[/tex]
[tex]r = 4\sqrt{5}[/tex]
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES
Answer:
A
Step-by-step explanation:
Slope = term that multiply x
y intercept = the number without a variable
Charles spent 1/4 of his allowance on a shirt, and 2/5 of the remainder on a book. A.What fraction of his allowance did he have left? B.If he spent $18 on the book, how much did he have at first?
Answer:
18.65
Step-by-step explanation:
1/4+2/5+18=18.65
18.65
hope it helps you good luck
Solve for x.
A. 1
B. 4
C. 7
D. 9
9514 1404 393
Answer:
B. 4
Step-by-step explanation:
The product of segment lengths to the near and far circle intercepts is the same for both secants.
5(5 +(x-1)) = 4(4 +(x+2))
5(x +4) = 4(x +6) . . . . . simplify inside parentheses
5x +20 = 4x +24 . . . eliminate parentheses
x = 4 . . . . . . . . . . . . subtract 20+4x
A barbecue grill is a circle with a diameter of 2.2 feet. What is the circumference of the grill (in feet)? (R
decimal places.)
Step-by-step explanation:
circumference =pi × diameter
=(22/7)×2.2
=6.914ft
Answer:
6.91 feet
Step-by-step explanation:
Suppose a rumor is going around a group of 210 people. Initially, only 34 members of the group have heard the rumor, but 3 days later 69 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)
Answer:
116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.
Step-by-step explanation:
Logistic function:
The logistic function is given by:
[tex]P(t) = \frac{K}{1 + Ae^{-kt}}[/tex]
In which:
[tex]A = \frac{K - P(0)}{P(0)}[/tex]
Considering that K is the carrying capacity, k is the growth/decay rate and P(0) is the initial population.
Suppose a rumor is going around a group of 210 people.
This means that [tex]K = 210[/tex]
Initially, only 34 members of the group have heard the rumor:
This means that [tex]P(0) = 34[/tex] and:
[tex]A = \frac{210 - 34}{34} = 5.1765[/tex]
So
[tex]P(t) = \frac{210}{1 + 5.1765e^{-kt}}[/tex]
3 days later 69 people have heard it.
This means that [tex]P(3) = 69[/tex], and we use this to find k.
[tex]69 = \frac{210}{1 + 5.1765e^{-3k}}[/tex]
[tex]69 + 357.1785 e^{-3k} = 210[/tex]
[tex]357.1785 e^{-3k} = 141[/tex]
[tex]e^{-3k} = \frac{141}{357.1785}[/tex]
[tex]\ln{e^{-3k}} = \ln{\frac{141}{357.1785}}[/tex]
[tex]-3k = \ln{\frac{141}{357.1785}}[/tex]
[tex]k = -\frac{\ln{\frac{141}{357.1785}}}{3}[/tex]
[tex]k = 0.3098[/tex]
So
[tex]P(t) = \frac{210}{1 + 5.1765e^{-0.3098t}}[/tex]
How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?
This is P(6), so:
[tex]P(6) = \frac{210}{1 + 5.1765e^{-0.3098*6}} = 116[/tex]
116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.
If it's possible to tell, decide if a and b are positive or negative: a-3>b-3 and b>4
PLEASE HELP NEED ASAPPPPPPP
Answer:
a and b are positive
Step-by-step explanation:
We are given that
[tex]a-3>b-3[/tex]
[tex]b>4[/tex]
We have to find that a and b are positive or negative.
We have
[tex]b>4[/tex]
It means b is positive and greater than 4.
[tex]a-3>b-3[/tex]
Adding 3 on both sides
[tex]a-3+3>b-3+3[/tex]
[tex]a>b>4[/tex]
[tex]\implies a>4[/tex]
Hence, a is positive and greater than 4.
Therefore, a and b are positive
1/2-5(2/3x + 6)+4/5x?
Answer:
[tex]-29.5-\frac{38}{15}x[/tex]
Step-by-step explanation:
First, we must expand out the -5.
-5 times 2/3x is equal to -10/3x, and -5 times 6 is equal to -30. 1/2 minus 30 is equal to -29.5, and 4/5x minus 10/3x is equal to -38/15x.
the area for this shape.
Answer:
Step-by-step explanation:
Clear parentheses by applying the distributive property.
-(-4s + 9t + 7)
Answer:
4s-9t-7
Step-by-step explanation:
multiply the negative one with all terms inside the bracket, since they are all unlike terms the answer remains the same
Solve the right triangle given that mZA= 30°, mZC = 90°, anda = 15. Round your result to one decimal place.
Answer:
[tex]\angle B = 60^o[/tex]
[tex]b =17.3[/tex]
[tex]c = 20[/tex]
Step-by-step explanation:
Given
[tex]a= 15[/tex]
[tex]\angle A = 30^o[/tex]
[tex]\angle C = 90^o[/tex]
See attachment for illustration
Required
Solve the triangle
First, we calculate the measure of B
[tex]\angle A + \angle B + \angle C = 180^o[/tex] --- angles in a triangle
[tex]30^o + \angle B + 90^o = 180^o[/tex]
Collect like terms
[tex]\angle B = 180^o-90^o-30^o[/tex]
[tex]\angle B = 60^o[/tex]
Solve for (c) using sine function
[tex]\sin(30) = \frac{a}{c}[/tex]
Make c the subject
[tex]c = \frac{a}{\sin(30)}[/tex]
Substitute known values
[tex]c = \frac{10}{0.5}[/tex]
[tex]c = 20[/tex]
Solve for (b) using Pythagoras
[tex]c^2 = a^2 + b^2[/tex]
This gives:
[tex]20^2 = 10^2 + b^2[/tex]
[tex]400 = 100 + b^2[/tex]
Collect like terms
[tex]b^2 =400 - 100[/tex]
[tex]b^2 =300[/tex]
Take square roots
[tex]b =17.3[/tex]
Camilla and Aisha are sisters and go to the same school. This morning, Camilla decided to bike to school, and Aisha decided to walk. They left home at the same time. Camilla’s speed was 6.5 miles per hour, and Aisha’s speed was 2 mph. When Camilla reached the school, Aisha was 1.5 miles behind. How far away from their house is the school?
Answer:
2 1/6
Step-by-step explanation:
6.5x=2x+1.6=1/3
1/3*6.5=2 1/6
Help please so lost!!!!!!!!!!!!
Answer:
hmmmmm please send the pic again
Write an equation for a line containing (–2,8) that is perpendicular to the line containing the points (3,–4)and (–7,1).
Answer and I will give you brainiliest
Answer:
y = 2x + 12
Step-by-step explanation:
the formula for a line is typically
y = ax + b
a is the slope of the line (expressed as y/x ratio describing how many units y changes, when x changes a certain amount of units).
b is the offset of the line in y direction (for x=0).
we have the points (3, -4) and (-7, 1).
to get the slope of the line let's wander from left to right (x direction).
to go from -7 to 3 x changes by 10 units.
at the same time y changes from 1 to -4, so it decreases by 5 units.
so, the slope is -5/10 = -1/2
and the line equation looks like
y = -1/2 x + b
to get b we simply use a point like (3, -4)
-4 = -1/2 × 3 + b
-4 = -3/2 + b
-5/2 = b
so, the full line equation is
y = -1/2 x - 5/2
now, for a perpendicular line the slope exchanges x and y and flips the sign.
in our case this means +2/1 or simply 2.
so, the line equation for the perpendicular line looks like
y = 2x + b
and to get b we use the point we know (-2, 8)
8 = 2×-2 + b
8 = -4 +b
12 = b
so, the full equation for the line is
y = 2x + 12
Answer:
2x-y+12= 0 or y = 2x+12 is the answer
Step-by-step explanation:
slope of the line joining (3,-4) and (-7,1) is 1-(-4)/-7-3
= -5/10
= - 1/2
slope of the line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) = 2
Equation of the line line containing (-2,8) and that is perpendicular to the line containing (3,-4) and (-7,1) is y-8 = 2(x-(-2))
y-8 = 2(x+2)
y- 8 = 2x+4
y=2x+12 (slope- intercept form) or 2x-y+12= 0 (point slope form)
