Answer:
A = 286 episodes
B = 284 episodes
Step-by-step explanation:
Let n = the [tex]\text{number of episodes}[/tex] of show B
n + 2 = the [tex]\text{number of episodes}[/tex] of show A
Therefore, according to the question,
The sum of the number of the episodes of each show are consecutive even integers = 570
Therefore,
n + n + 2 = 570
2n + 2 = 570
2n = 568
n = 284
Therefore, the number of episodes for B = 284
The number of episodes for A = n + 2 = 284 + 2
= 286
ВС
2. In ATVW if VW is three meters longer than TV, TW
is 19 meters shorter than the sum of VW and TV,
and the perimeter of ATVW is 62 meters, find the length of VW.
20.75 m
15.75 m
25.5 m
21.75 m
None of the above
9514 1404 393
Answer:
21.75 m
Step-by-step explanation:
The given relations tell us that ...
VW = TV +3
TW = VW +TV -19
VW +TW +TV = 62
__
Solving the first equation for TW gives ...
TV = VW -3
Substituting that into the second equation gives ...
TW = 2VW -22
And using these expressions in the third equation, we have ...
VW +(2VW -22) +(VW -3) = 62
4VW = 87 . . . . . . . . collect terms
VW = 21.75 . . . . . . divide by 4
The length of VW is 21.75 meters.
A brick staircase has a total of 17 steps The bottom step requires 131 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?
Answer: 1547 bricks are required to build the staircase.
Step-by-step explanation:
We are given:
Number of bricks in the first step, [tex]a_1[/tex] = 131
Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126
Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121
Sequence become:
131, 126, 121, .....
These are in arithmetic progression where a = 131 and d (common difference) = -5
To calculate the sum of an AP, we use the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
where,
n = number of terms = 17
Putting values in above equation, we get:
[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]
Hence, 1547 bricks are required to build the staircase.
can someone tell me what the diffrence of 8 through 5 is
Answer:
The answer is 3.
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
Answer:
3
Step-by-step explanation:
What is the difference between 8 and 5? In mathematics, the difference between two numbers usually means to subtract them. So if you want to find the difference, you take the bigger one minus the smaller one. So, the difference between 8 and 5 is 3.
PLEASE HELP MEEEEEEE EMERGENCY :(
Answer:
Ok ☺️✌️✌️✌️Ok ok ok ok
The price of a 5-minute phone call is $1.75. What is the price of a 19-minute phone call?
Answer:
$6.65
Step-by-step explanation:
You could start by seeing the price of a 1 minute phone call. if you divide 1.75 by 5 it is 0.35. that means 1 minute costs $0.35. so the equation would be 0.35 times 19. which is 6.65 dollars.
5 minutes call = $1.75
1 minute call = $1.75/5 = $0.35
19 minutes call = $0.35 × 19 = $6.65
x^3y+2x^2y^2+xy^3 and 2x^3+4x^2y+2xy^2 Find the HCF.
Answer:
[tex]x(x+y)^2[/tex]
Step-by-step explanation:
We are given that
[tex]x^3y+2x^2y^2+xy^3[/tex] and [tex]2x^3+4x^2y+2xy^2[/tex]
We have to find HCF.
[tex]x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)[/tex]
=[tex]xy(x+y)^2[/tex]
By using the formula
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex]xy(x+y)^2=x\times y\times (x+y)^2[/tex]
[tex]2x^3+4x^2y+2xy^2=2x(x^2+2xy+y^2)[/tex]
[tex]=2x(x+y)^2[/tex]
[tex]2x(x+y)^2=2\times x\times (x+y)^2[/tex]
HCF of ([tex]x^3y+2x^2y^2+xy^3,2x^3+4x^2y+2xy^2[/tex])
[tex]=x(x+y)^2[/tex]
Solve the system x-2y+2z=9 y+2z=5 z=3
Enter the answer as an ordered triple, (X,Y,Z)
The last equation says z = 3, so that in the second equation we get
y + 2z = y + 6 = 5 ==> y = -1
and in turn, the first equation tells us
x - 2y + 2z = x + 2 + 6 = x + 8 = 9 ==> x = 1
So the solution to the system is (x, y, z) = (1, -1, 3).
PLEASE HELP WKLL MARK IF YOU HELP ME !!!
Answer :
Let in Triangle abc,
a=90,
b = (we have to find)
c = (we have to find)
c + 144=180 (linear pair)
c = 180 - 144
c = 36
a + b + c = 180 (Angle sum property)
90 + b + 36 = 180
126 + b = 180
b = 180-126
b = 54
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.
a) dy/dx = (x − y)/x
b) (x + 1)dy/dx = −y + 20
c) dy/dx = 1/(x(x − y2))
d) dy/dx =(y^2 + y)/(x^2 + x)
e) dy/dx = 5y + y^2
f) y dx = (y − xy^2) dy
g) x dy/dx = ye^(xy) − x
h) 2xyy' + y^2 = 2x^2
i) y dx + x dy = 0
k) (x^2 + 2y/x) dx = (3 − ln x^2) dy
l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0
Here, we have to classify each differential equation based on their characteristics:
a) dy/dx = (x − y)/xThis is a separable differential equation because the variables can be separated on different sides of the equation.
It's of the form dy/dx = g(x) - f(y)/h(y), where g(x) = x/x and h(y) = 1.
b) (x + 1)dy/dx = −y + 20This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/(x + 1) and Q(x) = 20/(x + 1).
c) [tex]dy/dx = 1/(x(x - y^2))[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
d) [tex]dy/dx = (y^2 + y)/(x^2 + x)[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
e)[tex]dy/dx = 5y + y^2[/tex]This is a Bernoulli differential equation because it is of the form [tex]dy/dx = p(x)y + q(x)y^n[/tex], where p(x) = 0 and q(x) = 5x, n = 2.
f) [tex]y dx = (y - xy^2) dy[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
g) [tex]x dy/dx = ye^{(xy)} - x[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/x and [tex]Q(x) = e^{(xy)} - x^{(-1)[/tex].
h) [tex]2xyy' + y^2 = 2x^2[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -2/x and Q(x) = 2x.
i) y dx + x dy = 0This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
k) [tex](x^2 + 2y/x) dx = (3 - \text ln x^2) dy[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), although it's not immediately obvious what P(x) and Q(x) are.
l) [tex](y/x^2) dy/dx + e^{(2x^3)} + y^2 = 0[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where [tex]P(x) = -1/x^2[/tex] and [tex]Q(x) = -e^{(2x^3)} - y^2[/tex].
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It costs $100 to join a fitness center plus a monthly fee you spent $700 last year at the fitness center how much was the monthly fee
Answer:
58.3
Step-by-step explanation:
divide 700 by 12
Answer:
$50
Step-by-step explanation:
The equation for this is:
700 = 12m + 100, where $700 is the total cost, m is the monthly fee, 12 is the number of months in a year, and $100 is the starting fee
Solve the equation:
700 = 12m + 100
12m = 600
m = 50
consider the polygon shown. Determine the value of y. PLEASE HELP
Answer:
y = 64°
Step-by-step explanation:
From the picture attached,
m(∠E) = 90°
m(∠E) = m(∠D)
m(∠B) + 67° = 180° [pair of linear angles]
m(∠B) = 113°
m(∠C) + 75° = 180°
m(∠C) = 180° - 75°
= 105°
Since, sum of interior angles of a polygon = (n - 2) × 180°
Here, n = number of sides
For n = 5,
Sum of interior angles = (5 - 2) × 180°
= 540°
m(∠A) + m(∠B) + m(∠C) + m(∠D) + m(∠E) = 540°
m(∠A) + 113° + 105° + m(∠D) + 90° = 540°
(m∠D) + m(∠D) = 540 - 308 [Since, m(∠A) = m(∠D)]
2(m∠D) = 232
m(∠D) = 116°
m(∠D) + y° = 180° [Linear pair of angles]
116 + y = 180
y = 64°
The length of a rectangle is four times its width.
If the area of the rectangle is 100 yd”, find its perimeter.
Answer: 50yd
Step-by-step explanation:
We know that the area of any rectangle is length times width. The perimeter is the sum of twice the length and twice the width.
Let width = x
Let length = 4x
Area = 100m2
Next, we can write an equation using these variables and formula for area.
4x2 = 100
x2 = 25
x = -5 and x = 5
Since the dimensions cannot be negative, we accept the positive value:
x = 5
Next, we can substitute this value of x into the variables.
width = 5 m
length = 20 m
Finally, we can find the perimeter by plugging in these dimensions into the perimeter formula,
Perimeter = 2(5 m) + 2(20 m)
= 10 m + 40 m
= 50 m
a and b are complementary angles and a and c are supplementary angles. If a=xº, (a) express b and c in terms of x
(b) find c - b.
Step-by-step explanation:
a + b = 90
a + c = 180
a) If a = x, the. we can write
x + b = 90 and x + c = 180
or
b = 90 - x
c = 180 - x
b) c - b = (180 - x) - (90 - x)
= 180 - x - 90 + x
= 90
The absolute value of -7
Answer:
7
Step-by-step explanation:
|-7| means find the distance from 0
We take the non negative value
|-7| = 7
What’s the range of the given function?
I marked that answer by accident btw
The range of the given function is - 2
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F. 2084
G. 2044
H. 2043
J. 2086
Answer: (f)
Step-by-step explanation:
Given
The growth equation is [tex]y=50(1.05)^x[/tex]
When population becomes 1500
[tex]\Rightarrow 1500=50(1.05)^x\\\Rightarrow 30=(1.05)^x\\\text{Taking log both sides}\\\Rightarrow \ln (30)=x\ln (1.05)\\\\\Rightarrow x=\dfrac{\ln (30)}{\ln (1.05)}\\\\\Rightarrow x=69.71[/tex]
Thus, after 69.71 years of year 2015 i.e. [tex]2015+69.71=2084.71[/tex]. In year 2084, it becomes 1500.
option (f) is correct.
4(x+9)=2x-6
Solve for x
Answer:
-21
Step-by-step explanation:
4(x+9) = 4x+36
4x+36 = 2x-6
-36 -36
minus 36 from both sides
4x = 2x-42
2x = -42
-42/2 = -21
x = -21
Hi there!
We are given the equation below:
[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]
1. Expand 4 in the expression.
When expand in the expression, it is like multiply everything in the expression. So when we expand 4 in x+9, it becomes 4(x)+9(4).[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]
Cancel the brackets.
[tex] \large{4x + 36 = 2x - 6}[/tex]
2. Isolate x-term and solve for the variable.
Think it easy. If you want to isolate x-term then what should you do? Well simply swap sides, and change the operator/sign.[tex] \large{4x - 2x = - 6 - 36}[/tex]
Finally, combine like terms.
[tex] \large{2x = - 42}[/tex]
Then divide both sides by 2 so we can finally leave only x-term.
[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]
3. Check the solution if it is right or wrong.
This step is optional but if you are not confident on your answer, this step is recommended.To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,
[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]
Since both sides are equal when substitute in x = -21.
4. Answer
Hence, the answer for this equation is x = -21.I hope this helps and let me know if you have any doubts!
Raj is travelling to another country.
He flies for 5 hours at an average speed of 950 km/h on one plane.
He then flies for 6 hours 30 minutes at an average speed of 830 km/h on a second plane.
What is the total distance, in km, he travelled by plane?
Answer:
10145
Step-by-step explanation:
5 times 950 equals 4750
and 6.5 times 830 equals 5395
add first and second value
4750 + 5395 equals 10145
there is no arguing
Answer:
10145 km
Step-by-step explanation:
Time x speed = Distance
5 x 950 = 4750
6.5 x 830 = 5395
add together = 10145
Use a calculator to find the mean of the data. {217, 253, 214, 247, 217, 253, 232, 246, 223, 227, 229, 247, 206, 241, 239, 223, 222, 216, 252, 209, 236, 256}
Answer:
[tex]\frac{5105}{22}[/tex]
Step-by-step explanation:
Used Python function to get all the numbers and add them, then I divided it by 22, which is the number of numbers in the array.
The mean of the data is 232.045.
To find the mean of the data.
What is mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations). Mean is the most commonly used measure of central tendency. There are different types of mean, viz. arithmetic mean, weighted mean, geometric mean (GM) and harmonic mean (HM).
Given that:
The data are:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
=5105 / 22 = 232.045
So, the mean of the data is 232.045.
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The option is missing:
A. 230.811
B. 231.045
C. 232.045
D. 232.811
Please answer my question step be step
9514 1404 393
Answer:
z = 20
m∠A = 70°
Step-by-step explanation:
Step 0: read and understand the question. Identify the given information and the information requested.
Step 1: consult your knowledge of inscribed quadrilaterals to determine that opposite angles are supplementary.
Step 2: identify angles A and C as being marked with expressions in z.
Step 3: use those expressions and the relation in Step 1 to write an equation.
A + C = 180°
(4z -10)° +(10 +5z)°= 180°
Step 4: solve for z.
9z = 180 . . . . simplify, divide by °
z = 20 . . . . . . divide by 9
Step 5: use the relation between z and the measure of angle A to answer the question.
m∠A = (4z -10)° = (4·20 -10)°
m∠A = 70°
Step 6: check your answer. This can be done by making sure that angle C is supplementary to angle A.
C = (10 +5z)° = (10 +5·10)° = 110° = 180° -70° ∴ answer checks OK
x( 3x - 2y + 4z)x = -2, y = 4, and z = -3
PLS HELPP MEE !!
Use a calculator to find the r-value of these data. Round the value to three decimal places.
The Answer is -0.985
I just took the test.
The shoes still have a marginal cost of 25$. You want to earn a profit, so you bathe a price of what
Answer:
12
Step-by-step explanation:
Find r, if 6r7 = 511 8
Answer:
121.857
Step-by-step explanation:
6×7r = 5118
42r = 5118
r = 121.857
Answer:
121.8571428571429
Step-by-step explanation:
r= 5118/42
A triangle has sides measuring 2 inches and 7 inches. If x represents the
length in inches of the third side, which inequality gives the range of possible
values for x?
O A. 5sxs 9
O B. 2 sxs7
O C. 2
OD. 5
Answer is
5 gives the range of possible values for x.
The product of ______________ and (-1) is -35.
Answer:
35Step-by-step explanation:
The product of 35 and (-1) is -35.
As,
35 × (-1) = -35
Solve this asap for me
Answer:
by using middle term break method
Step-by-step explanation:
9x^2 + 12x + 4
9x^2+ (6 + 6)x + 4
9x^2 + 6x + 6x + 4
3x(3x + 2) + 2(3x + 2)
(3x + 2)(3x + 2)
(3x + 2)^2
length 21cm area 315cm2 find the breath
Answer:
Breadth = 15 cm
Step-by-step explanation:
Area = length x breadth
315 = 21 x breadth
[tex]\frac{315}{21} = \frac{21}{21} \times breadth[/tex] [ dividing both sides by 21 ]
[tex]15 = 1 \times breadth\\\\breadth = 15 \ cm[/tex]
___________________________________
Symbols of:[tex]\quad\quad\quad\quad\tt{A = A rea}[/tex]
[tex]\quad\quad\quad\quad\tt{ l = length} [/tex]
[tex]\quad\quad\quad\quad\tt{ b \: = breadth} [/tex]
Given that:[tex]\quad\quad\quad\quad\tt{A = 315 {cm}^{2} }[/tex]
[tex]\quad\quad\quad\quad\tt{l = 21cm}[/tex]
[tex]\quad\quad\quad\quad\tt{b = \: ? }[/tex]
Formula for breadth (b):[tex]\quad\quad\quad\quad\tt{breadth = \frac{Area}{length} }[/tex]
Solution:[tex]\quad\quad\quad\quad\tt{b = \frac{315 {cm}^{2} }{21cm} }[/tex]
[tex]\quad\quad\quad\tt{\:\:b = {15cm}}[/tex]So, the breadth (b) is:[tex]\quad\quad\quad\quad\tt \boxed{ \boxed{ \color{magenta}{b = 15cm }}}[/tex]
___________________________________
#CarryOnLearning
✍︎ C.Rose❀
Given that abcd ~Jklm. Find the value of x, y, and z
Answer:
x = 7.2
y = 10
z = 6
Step-by-step explanation:
Since ABCD ~ JKLM, therefore, the ratio of their corresponding sides would be equal. Thus:
JK/AB = KL/BC = LM/CD = JM/AD
Substitute
12/x = y/6 = 15/9 = 10/z
✔️Find x:
12/x = 15/9
12/x = 5/3
Cross multiply
x*5 = 3*12
5x = 36
x = 36/5
x = 7.2
✔️Find y:
y/6 = 15/9
y/6 = 5/3
Cross multiply
y*3 = 5*6
3y = 30
y = 30/3
y = 10
✔️Find z:
15/9 = 10/z
5/3 = 10/z
Cross multiply
5*z = 10*3
5z = 30
z = 30/5
z = 6
A book store had 30816 exercise books which were paclced in cartons each carton contained 24 exercise books the mass of an empty carton was 2kg and a full carton 12kg
30,816 books would go into 1,284 containers which would weigh 15,408kg with all the books in them or 2,568kg with the books not in them.
