Answer:
16/15 or 1 1/15
Step-by-step explanation:
2/6/8=8/3
1/5/8=8/5
----------------
8/3-8/5=40/15-24/15=16/15=1 1/15
. In an encyclopedia of language, the author presents five sentences that make a reasonable paragraph regardless of their order. The sentences are listed below. Mark had told him about the foxes. John looked out of the window. Could it be a fox? However, nobody had seen one for months. He thought he saw a shape in the bushes. In how many different orders can the five sentences be arranged?
Answer:
the 1st & last paras are fixed.
that leaves 3 to be put in any order
there are 3 choices for the 1st,
2 choices left for the 2nd
and just 1 choice for the last
multiply to get
3*2*1
= 6 ways
We want to find the total number of orders in which we can order the given sentences.
We will see that there are 120 different orders.
There are 5 sentences, let's define them as:
s₁ = Mark had told him about the foxes.s₂ = John looked out of the window.s₃ = Could it be a fox? s₄ = However, nobody had seen one for months.s₅ = He thought he saw a shape in the bushes.We know that we can order these in any order, so we can think of the situation as 5 empty slots, in each slot, we can put one of the previous statements.
Let's count the number of options for each one of these slots.
On the first one, we have 5 options (5 sentences)
On the second one we have 4, because we already used one on the first slot.
On the third, we have 3 options.
On the fourth, we have 2 options.
On the fifth, we have 1 option.
The total number of combinations is given by the product of these numbers of options.
Combinations = 5*4*3*2*1 = 120
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If lines m and n are parallel, and the measure of
angle 1 is 130°, what is the measure of angle 8?
Answer:
18.55, lines m and n are parallel and t is the transversal. If ∠1 = 130o, find the measures of the other angles and give reasons.
Step-by-step explanation:
The measure of angle 8 will be 130° since it corresponds to angle 1, and their measures are equal because lines m and n are parallel.
Explanation:To find the measure of angle 8 when lines m and n are parallel, and the measure of angle 1 is 130°, it's important to understand the concept of corresponding angles in the context of parallel lines. Corresponding angles are equal when two lines are parallel. Given that angle 1 is 130°, and assuming that angle 1 and angle 8 are corresponding angles (since the question does not specify their positions), the measure of angle 8 is also 130°.
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Amit built a sand castle that measured 600 centimeters by 600 centimeters, and dug a moat around it.
Afterward, he decided to change the castle size, making it 8 meters by 6 meters.
How much longer will the new moat be than the old one?
Answer:
4 meters longer.
Step-by-step explanation:
Amit built a sandcastle that measured 600 cm by 600 cm i.e. 6 meters by 6 meters.
Therefore, its perimeter is 2(6 + 6) = 24 meters
Now, afterward, he decided to change the castle size, making it 8 meters by 6 meters.
Therefore, its perimeter is 2(6 + 8) = 28 meters
Therefore, the perimeter of the new castle is increased by (28 - 24) = 4 meters.
If Amit dug a moat around his castle then the new moat will be 4 meters longer than the old one. (Answer)
As the moat is dug around the castle, its length will be the same as the perimeter of the castle.
Help me please with question 4 b
Answer:
see explanation
Step-by-step explanation:
The second term of sequence P is 2a + b
The third term of sequence Q is 3b + a
Equating gives
2a + b = 3b + a ( subtract a from both sides )
a + b = 3b ( subtract b from both sides )
a = 2b ← as required
Good evening ,
Step-by-step explanation:
4 (b)
The 2nd term of sequence P is 2a+b
The 3rd term of sequence Q is 3b+a
2a+b=3b+a ⇌ (2a-a) = (3b-b) ⇌ a=2b.
:)
Five tenths in standard and expanded form
Answer:
Standard form: 5 x 10^-1
Expanded form: 0.5
Step-by-step explanation:
hope this helps
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...} Show all your work please:)
The recursive formula for given sequence is:
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
-16, 4, -1, ...
First of all, we have to find the common ratio. common ratio is the ratio between two consecutive terms of a geometric sequence
Here
[tex]a_1 = -16\\a_2 = 4\\a_3 = -1\\Now\\r = \frac{a_2}{a_1} = \frac{4}{-16} = -\frac{1}{4}\\r = \frac{a_3}{a_2} = \frac{-1}{4} = -\frac{1}{4}[/tex]
The recursive of geometric sequence is:
[tex]a_n = r * a_{n-1}[/tex]
Putting the value of r
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Hence,
The recursive formula for given sequence is:
[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]
Keywords: Geometric sequence, Recursive formula
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Determine the next three terms in the following sequence:
1, 2, 5, 10,
a 17, 26, 37
b. 19, 30, 43
c50, 500, 25,000
d. 15, 25, 40
The correct sequence is a. 17, 26, 37.
To determine the next three terms in the sequence, we must first identify the pattern governing the sequence. Let's examine the differences between consecutive terms:
- The difference between the second term (2) and the first term (1) is 1.
- The difference between the third term (5) and the second term (2) is 3.
- The difference between the fourth term (10) and the third term (5) is 5.
- The difference between the fifth term (17) and the fourth term (10) is 7.
We can see that the differences between consecutive terms are increasing by 2 each time. This suggests that the sequence is generated by adding consecutive odd numbers to the previous term. To find the next terms, we continue this pattern:
- The sixth term will be the fifth term (17) plus the next odd number (9), which is 17 + 9 = 26.
- The seventh term will be the sixth term (26) plus the next odd number (11), which is 26 + 11 = 37.
- The eighth term will be the seventh term (37) plus the next odd number (13), which is 37 + 13 = 50.
Therefore, the next three terms of the sequence are 26, 37, and 50, confirming option a as the correct answer.
14) What is the graph of the function rule ?
y= |2x|-1
Because the equation contains an absolute value, the shape of the graph would be a V,.
The Y intercept is -1, so this would be the lowest point on the graph.
Replace X with 1 and solve:
y = 2(1) -1 = 2-1 = 1, so another point would be (1,1) and another point would be (-1,1) ( Absolute value would use both -1 and 1 as the same).
Make 3 points on the graph:
(-1,1) (1,1) ans (0,-1) and draw lines through them.
See attached picture:
What is the exact volume of the cone?
108π cm3
162π cm3
18π cm3
486π cm3
V = π·r²·h/3 = π·81·6/3 = 2·81·π = 162π cm³
-2+4(-x+4)=10 using distributive property and collecting like terms
Answer:
x = 1Step-by-step explanation:
[tex]-2+4(-x+4)=10\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\-2+(4)(-x)+(4)(4)=10\\\\-2-4x+16=10\qquad\text{combine like terms}\\\\-4x+(-2+16)=10\\\\-4x+14=10\qquad\text{subtract 14 from both sides}\\\\-4x+14-14=10-14\\\\-4x=-4\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-4}{-4}\\\\x=1[/tex]
Find the value of each expression.
10. |-41|
12. -|1.5|
Step-by-step explanation:
10. |-41|= 41
12. -|1.5|= -1.5
Answer:
A.) 41
B.) -1.5
Step-by-step explanation:
Absolute value means to make whatever that is inside positive
10.) The absolute value of negative 41 would simply be positive 41
11.) Since the negative sign is on the outside of the absolute value, you do the absolute value of everything inside then apply a negative sign. Absolute value of 1.5 is just 1.5 because it's already positive. Then apply the negative sign, which would make it -1.5
What is the value of the expression if m=3 and n=2?
2(m3) + (6-n)n
Be sure to explain all of the steps you used in solving this problem.
Step-by-step explanation:
So fill it in
2(3 times 3)+(6-2)2
so
2(9)+(4)2
then
18+8=26
Answer: 26
hope that is right
Answer:
First plug in for m and n
2(3)(3) +(6-2)(2)
Next solve
18 + 8
Answer= 10
Step-by-step explanation:
Simultaneous equations !
Who can help
The cost of glass is: £4
The cost of mug = £2
Step-by-step explanation:
Let g be the number of glasses and
m be the number of mugs
[tex]3g+3m = 18\ \ \ \ \ Eqn\ 1\\6g+4m=32\ \ \ \ \ Eqn\ 2[/tex]
Multiplying equation 1 by 2
[tex]6g+6m=36\ \ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex]6g+6m - (6g+4m) = 36-32\\6g+6m-6g-4m=4\\2m=4[/tex]
Dividing both sides by 2
[tex]\frac{2m}{2} = \frac{4}{2}\\m = 2[/tex]
Putting m=2 in eqn 1
[tex]3g+3(2) = 18\\3g+6 = 18\\3g = 18-6\\3g = 12[/tex]
Dividing both sides by 3
[tex]\frac{3g}{3} = \frac{12}{3}\\g = 4[/tex]
Hence,
The cost of glass is: £4
The cost of mug = £2
Keywords: Linear Equation, simultaneous equations
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plz help me plz I will mark brainlest for the person who answer first
Answer:
[tex] \frac{16}{20} [/tex]
Step-by-step explanation:
he sold 16 and he was supposed to sell 20. therefore it's 16/20. not relevant, but he sold 80% of the tickets
Answer:
I don't know why but I personally think its 1/4 I'm probably wrong but I'm trying my best well I hope dis helps and stay safe :3
What is the final step in solving the inequality -2(5 - 4x)
Step 1: -10 + 8x < 6x - 4
Step 2: -10 <-2x - 4
Step 3: -6<-2x
Step 4
AVA
Step-by-step explanation:
[tex]-2(5-4x)<6x-4\qquad\text{use the distributive property}\\\\(-2)(5)+(-2)(-4x)<6x-4\\\\-10+8x<6x-4\qquad\text{subtract}\ 8x\ \text{from both sides}\\\\-10+8x-8x<6x-8x-4\\\\-10<-2x-4\qquad\text{add 4 to both sides}\\\\-10+4<-2x-4+4\\\\-6<-2x\qquad\text{divide both sides by (-2)}\\_{\text{by dividing by a negative number, flip the inequality sign}}\\\\3>x[/tex]
A textbook costs $65.49 before tax. The tax on the textbook is 6.5%.
What is the total cost of the textbook?
Round your answer to the nearest cent.
Enter your answer in the box.
Answer:
$69.75
Step-by-step explanation:
Given: Cost of textbook before tax=$65.49
The tax on the textbook = 6.5%
The tax amount = 6.5% of $65.49
=\frac{65}{1000}\times65.49=4.25685\approx4.26
⇒The tax amount = $4.26
The total cost of the textbook=Cost of textbook before tax+tax amount
=$65.49+$4.26
=$69.75
The total cost of the textbook is $69.75.
Credit goes to @JeanaShupp
Answer:
Answer is69.75
Step-by-step explanation:
Please help solve with steps: Order of operation with integers.
6 (divide by ) (-3) - (-9)
Answer:
7Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents
MD Multiplication and Division
AS Addition and Subtraction
[tex]6:(-3)-(-9)[/tex] first - division
[tex]=-2+9[/tex] use commutative property a + b = b + a
[tex]=9+(-2)=9-2=7[/tex]
Karen bought a coat for 20% more than the price she wanted to pay. If she paid $150, how much was she looking to pay?
The first one to get both correct will be brainiest!!!!!!!
120% = $150
divide both sides by 6
20% = $25
We want the regular price, so 100%.
multiply both sides by 5
100% = $125
Answer:125
Step-by-step explanation:
150/1.20
=125
Please help me I need help quick
!!!!
Jim’s new car has 150 miles on the odometer. He takes a trip and drives an average of m miles each day for three weeks. Which expression represents the mileage on Jim’s car after his trip?
Answer:
[tex](150+21m)\ miles[/tex]
Step-by-step explanation:
we know that
[tex]1\ week=7\ days[/tex]
Remember that the speed is equal to divide the distance by the time
Let
s ---> the speed in miles per day
d ---> the distance in miles
t ---> the time in days
[tex]s=\frac{d}{t}[/tex]
[tex]d=st[/tex]
we have
[tex]s=m\ miles/day[/tex]
[tex]t=3\ weeks[/tex]
Convert to days
[tex]t=3(7)=21\ days[/tex]
Find the distance covered in the trip
[tex]d=st[/tex] ----> [tex]d=m(21)=21m\ miles[/tex]
To find out the mileage on Jim’s car after his trip, sum the mileage before his trip (150 miles) plus the mileage of the trip
[tex](150+21m)\ miles[/tex]
2. Use the linear combination method to solve the system of equations. Explain each step of your solution
3x - By = 7
x +2y = -7
x = - 3
y = -2
Step-by-step explanation:
3x - 8y = 7
x +2y = -7
We standardize the coefficient of one variable such that it addition will result to zero;
3x - 8y = 7
(x +2y = -7)4
Then multiply the one equation with a constant (this case 4) to get;
3x – 8y = 7
4x + 8y = - 28
We add the two equations;
3x – 8y = 7
+
4x + 8y = - 28
=
7x = - 21
x = -21 / 7
x = - 3
Now we evaluate y by replacing the value of x with -4 in one of the equation;
x +2y = -7
-3 +2y = -7
2y = -7 + 3
2y = - 4
y = -2
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A restaurant manager can spend at most $400 a day for operating costs and payroll. It costs $100 each day to operate the bank and $50 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most: 50x + 100 ≤ 600
Answer:
The restaurant Manager can afford 6 employees for the day.
Step-by-step explanation:
Manager can spend at most of $400.
Total Money ≤ $400
Cost to operate bank = $100
Cost for each employee = $50
Let number of employees for the day be[tex]x[/tex]
Hence the equation will become;
[tex]50x + 100 \leq 400[/tex]
Solving this equation we get;
[tex]50x + 100 \leq 400\\50x \leq 400-100\\50x \leq 300\\x\leq \frac{300}{50}\\\\x\leq 6[/tex]
Hence, The restaurant Manager can afford 6 employees for the day.
Answer:
x < = 10
Step-by-step explanation:
i did it on photo math so yah
3х – 2 y = 0
I need some help idk why but I just can’t remember how to do this one
Answer:
y=3x/2
Step-by-step explanation:
first you want to get the -2y alone so you move the 3x. since it's adding now the opposite of addition is subtraction. now your left with -2y= -3x. since your trying to solve for y now you divide -2 on both sides and your gonna be left with y= -3x/-2. since their both negatives it turns to postive. that's why the answer would be y= 3x/2.
Step-by-step explanation:
this line will cross the origin
to help I'm just going to explain something real quick.
make it into y intercept form (y=mx+b)
-2y=0-3x
y=3/2x +0
the m (3/2) is the slope
and b (0) is the y intercept
if you want to check it then imput a point on the line into the x and y variables
find the slope and the y-intercept of y=9x-2
Answer:
The Slope is 9 and the y-intercept is -2
Step-by-step explanation:
Answer: slope=9
Y-intercept=-2
Step-by-step explanation:
Use y=mx+b where m equals slope and b equals y-intercept
For apples 2 lb for $3.38 unite rate___ cost___
Answer:
1.69
Step-by-step explanation:
well to find out the unit rate that would be a pound now we need to find out how much it would cost for 1 lb which would be 3.38 / 2 which would be 1.69 as your answer
Answer:
$1.69 per pound
Step-by-step explanation:
3.38/2=1.69
If 6 + 2 = 8, does 6+2 +3= 8+3? Why or
why not?
Answer:
yes
Step-by-step explanation:
Because 6+ 2 equals 8 then plus 3 equals 11 and 11 equals 8+3
The graphs below have the same shape. What is the equation of the blue graph?
Answer:
Option C. [tex]g(x)=(x+5)^{2}[/tex]
Step-by-step explanation:
we know that
The equation of the parent function f(x) (red graph) is
[tex]f(x)=x^{2}[/tex]
This is a vertical parabola open upward
The vertex is the point (0,0) (the origin)
The function g(x) (blue graph) is a vertical parabola open upward
The vertex is the point (-5,0)
The transformation of f(x) to g(x) has the following rule
f(x) -----> g(x)
(0,0) ----> (-5,0)
(x,y) ----> (x-5,y)
That means----> The transformation is a translation of 5 units at left
therefore
The equation of g(x) is
[tex]g(x)=(x+5)^{2}[/tex]
What is 8.4 x 10^12/4.2 x 10^6
Answer:
2 × [tex]10^{6}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
Split the fraction into a product, that is
= [tex]\frac{8.4}{4.2}[/tex] × [tex]\frac{10^{12} }{10^{6} }[/tex]
= 2 × [tex]10^{(12-6)}[/tex]
= 2 × [tex]10^{6}[/tex]
The black graph is the graph of y=f(x). Choose the equation for the red graph.
Please help!!!
Answer:
C
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x) by c units
• If c > 0 then shift c units up
• If c < 0 then shift c units down
The red graph is a vertical translation f(x) of 3 units down
Thus
y = f(x) - 3 ( add 3 to both sides )
y + 3 = f(x) ← equation of red graph
There's 5 trees fill with apples. Alex wants 2 off each tree. How much apples do she have?
Answer:
10
Step-by-step explanation:
5 trees * 2 from each = 10 apples
Answer:
10
Step-by-step explanation:
5*2=10
35 is 51% of what number?
Answer:
68.627
Step-by-step explanation:
51%=0.51
35/0.51=68.627
Answer:
68.627 is the answer!
Step-by-step explanation: I just took a test on it like 5 minutes ago!PLEASE MARK BRAINLIEST!!!! PLEASE!!! HAVE A NICE DAY!!!!