the difference between any two consecutive numbers in the list a,b,c,d,e is the same . If b = 5.5 and e = 10, what is the value of a
Answer:
a = 4
Step-by-step explanation:
You are given an arithmetic sequence with second term 5.5 and fifth term 10. You want to know the first term.
Common differenceThe 2nd term will have 3 times the common difference added to it to make the 5th term. Then that difference can be found from ...
5.5 +3d = 10 . . . . using 'd' for the common difference
3d = 4.5
d = 1.5
First termThe second term (a2) is obtained by adding the common difference (d) to the first term (a1):
a2 = a1 +d
5.5 = a1 + 1.5
4.0 = a1
The value of 'a' is 4.
__
Additional comment
The 'd' we're using here to represent the common difference is not to be confused with the 'd' in the problem statement that represents the fourth term of the list.
The fact that adjacent list members have the same difference is what tells you this is an arithmetic sequence. In terms of the problem statement, you have ...
{a, b, c, d, e} = {4, 5.5, 7, 8.5, 10}
Here, we have used the more common notation for elements of an arithmetic sequence.
The length of a rectangle is four less than twice its width. If the perimeter of the rectangle is 76 units, what is its width?
a
13
b
14
c
20
d
26
e
28
The width of the rectangle is 14 units and the right option is b 14
What is perimter?Perimeter can be defined as the total distance around an object.
To calculate the width of the rectangle, we use the formula of perimeter.
Formula:
P = 2(l+w).................... Equation 1Where:
P = Perimter of the rectanglel = Length of the rectanglew = Width of the rectangle.From the question,
Given:
P = 76 unitsl = 2w-4Substitute these values into equation 1
76 = 2[w+(2w-4)]76 = 6w-86w = 76+86w = 84w = 84/6w = 14unitsHence, the width of the rectangle is 14 units and the right option is b 14
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(100 points) HELP ME NOW!!!! NOOOOW!!!!! OR ELSE UR GONNA BE SUPER DUPER SORRY >:)
unit 2: equations and inequalities/ homework 11: compound inequalities
Jerry can do 34 push ups in 2 minutes. how many can he do in 11 minutes?
Answer: 187 push ups
Step-by-step explanation:
34/2=17 push ups per minute
11 minutes * 17 push ups/1 minute =187 push ups
A car is traveling at 55 miles per hour. Use dimensional analysis to convert
the car's speed to feet per minute.
5,280 feet in 1 mile?
The car's speed to feet per minute is 80.67ft per second.
What is speed?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.Speed is a way to gauge how rapidly something is happening, moving, or moving swiftly. The speed of a car being driven at 45 mph serves as an illustration. A person cleaning a room in 10 minutes is an illustration of speed. Speed can be compared to how swiftly a jaguar moves.1 mile = 5280 feet
so 55 miles = 55*5280 = 290,400ft
there are 60 seconds in 1 minute and 60 minutes in 1 hour
so 1 hour = 60*60 = 3600 seconds
55mile/1hour = 290400ft/3600 seconds = 80.67ft per second
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Which is a correct way to evaluate the expression 3(53+100)−12
3
(
53
+
100
)
-
12
?
Answer:
by using BADMAS rule
Step-by-step explanation:
3(53+100)-12
3×153-12
459-12
447answer
Answer:
447
Step-by-step explanation:
i think the bodmas rule applies first so brackets first which means 53+100 then you times the by 3 and finally that answer you minus it by 12 and even if you put the whole expression on the calculator thats the same answer you will get.
25.
9
E
Which statement about AABC and ADEF is true?
9
12,
A
B
A
12
16
12
They are similar because they are both isosceles triangles.
They are similar because AB is four more than ED, AC is three more than DF
BC is three more than EF.
201
Answer:
C. They are similar because corresponding sides are proportional.
Step-by-step explanation:
A and B are not are not how you would find similar triangles, so you can rule those answers out. We can also rule out D since the triangles aren't congruent - we can see they have different lengths. This leaves option C.
Here's how to check:
We'll take the ratio of FD:DE, which is 9:12.
9 ÷ 12 = 0.75
The corresponding sides on the second triange are CA:AB, which is 12:16
12 ÷ 16 = 0.75
9:12 = 12:16
The two traingles are similar & have proportional corresponding sides
Question 3
The first five triangular numbers are shown, where n represents the number of dots in the base of the figure, and d (n)
represents the total number of dots in the figure.
1 3 6
15
When n = 1, there is 1 dot. When n = 2, there are 3 dots. When n = 3, there are 6 dots. Notice that the total number of dots
d (n) increases by n each time.
Use induction to prove that d (n) = n(n+1)
10
Part A
Prove the statement is true for n = 1.
On a math test, Ana writes 9 as the solution to 327.
a. Find the correct solution.
b. What error did Ana likely make on the test?
Considering the cube root of 27, we have that:
a) The correct solution is of 3.
b) The error that Ana likely made is that she considered the cube root as the number that is multiplied by 3 to get a result of 27, not the number that is elevated to three.
What is the problem?
The question is that Ana wrote 9 as a solution to the cube root of 27.
The cube root of a number is the number that is elevated by 3 to reach the number, for example:
1³ = 1, hence the cube root of 1 is of 1.2³ = 8, hence the cube root of 8 is of 2.3³ = 27, hence the cube root of 27 is of 3.From the last bullet point, we get the correct answer for item a.
For item b, we have that 9 x 3 = 27, hence the error that Ana likely made is that she considered the cube root as the number that is multiplied by 3 to get a result of 27, not the number that is elevated to three.
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Solve for x: 4- (x + 2) < −3(x + 4)
X <-7
X>=7
X<-9
X>-9
Answer:
x<-7
Step-by-step explanation:
4-x-2<-3(x+4)
if the lesser of two consecutive even integers is tripled, the result is 20 more than twice the greater integer. find the two integers.
Answer: 24, 26
Step-by-step explanation:
a=first even number. b=second even number
a=b-2
a*3=b*2+20
(b-2)*3=2b+20
3(b-2)=2b+20
3b-6=2b+20
b-6=20
b=26
a=b-2
a=26-2
a=24
24, 26
Answer:
mark me please
Explanation:
If the lesser of two consecutive even integers is tripled, the result is 20 more than twice the grater integer. find the two integers
let the numbers be x & x+2
3x=20+2(x+2)
3x=20+2x+4
3x-2x=24
x=24
The integers are 24 & 26
Add 7 x 10−6 and 2.1 x 10−5.
Answer:
Step-by-step explanation:
84.5
Note: Your teacher will grade your response to ensure that you receive proper credit for your answers.
6. A
field has an area of 479 ft². What is the approximate length of a side of the field?
Give your answer to the nearest foot. Explain your response.
Answer:
Step-by-step explanation:
The number of square units required to fill a square is the area.
Area of a square = side × side
Area of a square = side2 square units
Area of a square field = 479 ft2 [Given]
So the side can be determined by:
Length of a side of the field = √479 = 21.9 feet
Therefore, the length of a side of the field is 21.9 feet.
At a local drive-thru restaurant, 3 out of every 8 drinks sold are diet drinks. If the restaurant sells 4,200 drinks in one month, how many would be diet drinks?
Answer:
1575
Step-by-step explanation:
3/8 as a decimal is .375. Multiply 4200 by .375 to get your answer.
what is 2 1/3+ 5 5/16+ 2/7
Answer: 7.93
Step-by-step explanation: I am not sure if this is correct but I really hope it helps.
What is the equation solve it
Answer:
1/4
Step-by-step explanation:
First u subtract both sides by 9
12x + 9-9= 4x + 7-9 = 12x = 4x + 2
Then u subtract
12x= 4x - 2
12x - 4x =4x - 2 - 4x=
and this will get u 1/8 but then u simplify and get 1/4
Can someone help me I will make u brilliant
Answer: R'=(6, -2)
S=(-6,9) ==> S'=(6, -9)
T=(-5,9) ==> T'=(5, -9)
U=(-5,2) ==> U'=(5, -2)
Step-by-step explanation:
When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.
R=(-6, 2) ==> R'=(6, -2)
S=(-6,9) ==> S'=(6, -9)
T=(-5,9) ==> T'=(5, -9)
U=(-5,2) ==> U'=(5, -2)
Please help me i need this badly show work if you could
Answer:
a: 4
b: 5 is alone, p, -4p and 5p are in the same group, and 7q is alone
c: 2uv squared and -uv squared are in the same group. Everything else is alone.
Step-by-step explanation:
4 is multiplied by y. Kinda self explanatory.
Even though p doesnt have a number before it, it still does. Variables always have coefficients, and if you can't see it, that means it's one.
uv squared is one of the terms, so any number before it makes it part of the group. Everything else is not similar, so you got your answer.
I don't know what grade you are in, but I'm guessing your in a low grade, so sorry if I was unclear.
Solve the inequality 3/4q - 2/3q < 5/12q - 1/12 and write the solution in interval notation?
Solution of the inequality is q> 1/4 and in interval notation is (1/4 , ∞ ).
According to the question we have been given the inequality that is
3/4q - 2/3q < 5/12q - 1/12
Solving the equation step by step we get
First simplifying 3/4q - 2/3q which will get q/12
Therefore, q/12 < 5/12q - 1/12
moving all the terms with q on the left hand side we get
q/12 - 5/12q < -1/12
(q-5q)/12 < -1/12
-4q/12 < -1/12
multiplying both sides by 12 we get
-4q/12 * 12 < -1/12*12
-4q < -1
multiplying -1 both sides we get
4q>1
q >1/4
Hence solution of the inequality we get
(1/4 , ∞ )
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Pete worked 51 hours and 30 minutes on his new job. He makes $11.55 per/hour. For each hour of overtime, he earns time and a half. How much will he earn for one week?
Pete will earn $594.83 for one week that he worked for 51 hours
What is the normal hours of work per week?
The number of hours that Pete works normally in any week is 40 hours, beyond the 40 hours, it is regarded as overtime and the overtime hours are paid at one and a half of the normal hourly rate of $11.55
overtime=51.50-40
overtime=11.50
normal earnings=40*$11.55
normal earnings=$462.00
overtime pay=11.50*$11.55
overtime pay=$132.83
total weekly earnings=$462.00+$132.83
total weekly earnings=$594.83
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For DEF, e=52, f=41 and M
For ΔDEF, Where e=52, f=41 and ∠F=48°. Find all the possible ∠E to the nearest degree.
The possible ∠E to the nearest degree is ∠E=70°
Given that,
ΔDEF with e=52 and f=41 sides of the triangle.
Angle ∠F=48°.
We have to find ∠E=?
By using the Law of sine
The relationship between the sides and angles of non-right (oblique) triangles is known as the Law of Sines. It simply states that for all sides and angles of a given triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same.
If triangle ABC are there with sides a, b, and c then Law of sine is
[tex]\frac{a}{SinA} =\frac{b}{SinB} =\frac{c}{SinC}[/tex]
Now, in the given triangle we have e and f sides so we take
[tex]\frac{SinE}{e}=\frac{SinF}{f}\\[/tex]
Substituting the values of e, f and F
We get,
[tex]\frac{SinE}{52}=\frac{Sin48^\circ}{41}\\ SinE=\frac{Sin48^\circ}{41}\times52\\SinE=\frac{52}{41} \times Sin48^\circ\\SinE=1.268\times 0.743\\SinE=0.942\\E=Sin^{-1}(0.942)\\[/tex]
∠E=70°
Therefore, The possible ∠E to the nearest degree ∠E=70°.
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The average amount of money spent by students in the cafeteria last week was $2.75. The actual amount spent varied by no more than $0.50. Write and solve an absolute value inequality to represent the range of possible amounts.
Answer:
Step-by-step explanation:
Last week, the typical amount of money spent by kids in the cafeteria ranged from $2.25 to $3.25.
What is Equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.
A mathematical equation can have many different components, such as coefficients, variables, operators, constants, terms, expressions, and an equal sign. An "=" symbol, as well as terms on both sides, are required when writing an equation.
Given:
Average amount spend = $2.75
Let x be the average dollar amount that students spend.
Then, the equation can be
|x - 2.75| = 0.5
Now, we have two values one is positive and another is negative
x - 2.75 = 0.5 or -(x - 2.75) = 0.5
x = 3.25 or x = 2.25
Hence, Last week, the typical amount of money spent by kids in the cafeteria ranged from $2.25 to $3.25.
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What is the equation of the parabola with focus (0,7) and directrix y = 1?
The equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).
What is the equation of the parabola with the given focus and directrix?Since the directrix y = 1, it shows it is vertical, so we use the equation of the parabola that opens up or down.
( x - h )² = 4p( y - k )
Given the data in the question;
Focus: (0,7)directrix y = 1First, we determine the vertex.
The vertex ( h,k ) is half way between the directrix and the focus.
Find the y-coordinate of the vertex using;
y = ( y-coordinate of focus + directrix )/2
y = (7+1)/2 = 8/2 = 4
The x-coordinate of the vertex is the same as that of the focus 0
Hence, the vertex is ( 0,4 )
Next, we determine the distance p from the focus to the vertex.
p = y-coordinate of focus - y-coordinate of vertex
p = 7 - 4
p = 3
Now, plug the known values into the equation and simplify
( x - h )² = 4p( y - k )
( x - 0 )² = 4(3)( y - 4 )
x² = 12( y - 4 )
Therefore, the equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).
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From the London Summer Olympics 2012 to the Rio Summer Olympics 2016, the number of medals awarded increased by 118.5%. If 962 medals were awarded in London, how many were awarded four years later in Rio?
Answer:
1,440
Step-by-step explanation:
London 962
Rio +118.5%
One percent of 962 is 9.62 you get that by moving the decimal place over one place, multiply by 118.5 to get 1,139.97 there is no partial medals so round to the nearest whole number and you get 1,140.
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Write a multiplication expression and a
division expression that would havе
result.
a)-8
b) -15
help please
Step-by-step explanation:
a. 8 × -1 = -8 or -2 × 4 = -8
8 ÷ -1 = -8 or 32 ÷ -4 = -8
b. -3 × 5 = 15 or 15 ×(-1) = -15
45 ÷ -3 = -15 or 225 ÷ -15 = -15
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You invested $25,000 in two
accounts paying 9% and 8%
annual interest. If the total interest
earned for the year is $2100 how
much was invested of each rate?
let x be the capital invested in the 9% account
let y be the capital invested in the 8% account
let j be the interest earned from the 9% account
let k be the interest earned from the 8% account
[tex]j = xi_{1}n \: \: \: (n = 1 \: year)\\ j = x( \frac{9}{100})(1) = 0.09x[/tex]
[tex]k =yi_{2}n \: \: \: \: (n = 1 \: year) \\ k = y( \frac{8}{100} )(1) = 0.08y[/tex]
But the total interest made is 2100 $, hence:
[tex] \: \: \: \: \: \: \: j + k = 2100 \\ 0.09x + 0.08y = 2100[/tex]
And the total capital invested is 25000 $
[tex]x + y = 25000[/tex]
System of 2 equations and two unknowns:
[tex]0.09x + 0.08y = 2100 \\ x + y = 25000 \\ \\ \: \: \: \: (x,y)=(10000,15000)[/tex]
7 3/4 as a improper fraction
Answer:
31/4
Step-by-step explanation:
The Mixed Number 7 3/4 can be changed into the improper fraction 31/4.
step 1: The denominator of the improper fraction will be 4, since the denominator of the original fraction is 4.
to find the improper fraction, multiply the denominator of the original fraction (4) by the whole number (7). 4x7=28 then add the numerator of the original fraction: 28+3=31. This tells you the numerator of the improper fraction will be 31.
The improper fraction is 31/4.
Given g(x) = 2x + 4, find g(-6).
2x+4
substitute x as -6
-12+4= -8
g(-6)=-8
Is this correct, if not whats the right answer.
Answer:
Answer is x=11
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(x−8)+11=17
(2)(x)+(2)(−8)+11=17(Distribute)
2x+−16+11=17
(2x)+(−16+11)=17(Combine Like Terms)
2x+−5=17
2x−5=17
Step 2: Add 5 to both sides.
2x−5+5=17+5
2x=22
Step 3: Divide both sides by 2.
2x/2=22/2
x=11
Rochelle and Irene do some fundraising for their sporting team. Together they raised $741.
If Irene raised $p, and Rochelle raised $199 more than Irene:
Solve for the value of P
Answer:
$271
Step-by-step explanation:
$741-$199= $542
$542/2= $271
271=p
Irenes $271+ Rochelles $271+199 more than Irene= $741
Irene only raised $271 and rochelle raised 470$