The 205th term of the sequence is 768 with a common difference of 4.
What is the common difference?In an arithmetic series, a common difference is one between any term and its predecessor, and it is typically denoted by the letter "d."To find the common difference in an arithmetic sequence, subtract the first term from the second term, the second term from the third term, and so on.The difference that exists between every pair of phrases that follow one another in a series is a common difference.For example, the number 3 is a frequent difference in the series 4, 7, 10, 13, and so on. A series of differences constitute an arithmetic progression.The common difference is so named because it is both the difference between each number in the sequence and the same, or common, to all of them.So, the sequence is:
-48, -44, -40, -36, -32,... +4
The common difference is: -48 + 4 = - 44 ⇒ 4
Formula: aₙ = a + (n - 1)d
Now calculate as follows:
aₙ = a + (n - 1)d
aₙ = -48 + (205 - 1)4
aₙ = -48 + (204)4
aₙ = -48 + 816
aₙ = 768
Therefore, the 205th term of the sequence is 768 with a common difference of 4.
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please help with this (percentages)
2. Amy was asked to find mABC in the picture. Her work is shown below.
The alternate interior angles are congruent when the lines
are paralled so
mLABC-3(27)-47
-81-47
-34°
30-47-n+7
-47
+47
3n-+54
-n-h
20-54
2
n=27
Explain Amy's mistake
A
(3n-47)
(n+7)
B
D
Show all work to find the correct mABC.
Amy's mistake was she took the angles as alternate interior angles, rather they form supplementary angles. The measure of both angles are 118 and 62.
What are alternate interior angles?The alternate interior angles theorem states that if a transversal connects two parallel lines, the alternate interior angles are identical in size. If we know the measure of the corresponding alternate interior angle, we may use this theorem to determine the measure of the alternate interior angle.
As per the given question,
both angles are not alternate interior angles,
rather both of the angles are supplementary angles.
This means that both form the sum of 180
⇒ 3n - 47 + n + 7 = 180
⇒ 4n - 40 = 180
⇒ 4n = 220
⇒ n = 55
∴ The measure of both angles will be 3n - 47 = 118 and n + 7 = 62
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The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $11 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a
a. Let x represent the number of monthly calls. The answer is
(Type an inequality.)
Plan 1 is more economical than plan 2. 0.04y + 11 > 30
What is inequality?A statement of an order relationship between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to). The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity. This means that the left part, 5x 4, is greater than the right part, 2x + 3. In mathematics, an inequality depicts the relationship between two non-equal values in an algebraic expression. Inequality signs can indicate that one of the two variables is greater than, greater than or equal to, less than, or less than or equal to another value.Therefore,
We can point to the digit of calls as "y"
From plan 1, the Total monthly charge is $30
From plan 2, the Fix charge is $11 with $0.04 per call
We can express the cost of the "y" call as( $0.04y)
From plan2, The monthly charge can be expressed as (0.04x + 11)
a) Use an imbalance to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
Here, Plan 1 is more economical than plan 2.
0.04y + 11 > 30
Multiply both sides by 100
0.04y . 100 + 11.100 > 30.100
Refine
4 y+1100>3000$
Subtract 1100 from both sides
4 y+1100-1100>3000-1100
Simplify
4 y>1900
Divide both sides by 4
[tex]$\frac{4 y}{4} > \frac{1900}{4}[/tex]
Simplify
y>475
b) in case, more than 375 calls are made, then the economical plan is plan 1
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Please help me
Thank you ;)
Explanation:
SAS = side angle side
The tickmarks tell us which sides are congruent to one another. This forms one S of SAS.
The other S would be the shared overlapping sides between the triangles. We're using the reflexive property here.
The marked angles in red are congruent to one another, which refers to the 'A' in SAS. We have two pairs of congruent sides, and a pair of congruent angles between those sides. This allows us to use the SAS rule.
SSS can't be used since we don't know anything about the third pair of sides.
9
Marisa needs to hire at least 10 staff members for an
upcoming project. The staff members will be made
up of junior directors, who will be paid $640 per
week, and senior directors, who will be paid $880 per
week. Her budget for paying the staff members is no
more than $9,700 per week. She must hire at least
3 junior directors and at least 1 senior director.
Which of the following systems of inequalities
represents the conditions described if x is the
number of junior directors and y is the number of
senior directors?
A) 640x+8800700
Answer:
$9,700=640x+880y+100 let me know if it is set up in a different way because I can only see a's answerStep-by-step explanation:
first we find out how much the required directors will take out of our budgetwe need 3 Jr and 1 SrJr get paid$640 a week and a Sr gets paid$880so we do 640×3=1,920now we add the Jrs and the Sr1,920+880=2,800so we are gonna subtract them from our total9,700-2,800=6,900we have $6,900 left we need at least 7 more employees so we need to figure out how much money we can spend for the next 7 employees6,900÷7= $985.7142857now we know how much we can spend at least $985 per employee we can hire 7 more Sr directors7×880= $6,160now we take that off the left over to see what we get6,900-6,160=740we can afford one more Jr director then we will have $100 remainingin total we can afford 8 Sr directors and 4 Jr directors with $100 remainingto put that in an equation it would be$9,700=640x+880y+100The width of stamp M is 43 inches, and the length is 75 inches. The dimensions of stamp M are 76 times the dimensions of stamp P. What is the length of stamp P, in inches? A:6/5 B:8/7 C:14/9 D:49/3
If the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.
Given that the width of stamp M is 43 inches, length is 75 inches and the dimensions of stamp M are 76 times the dimensions of stamp P.
We are required to find the length of stamp P in inches.
Suppose the length of stamp P be x.
According to question, the length of stamp will be 76x.So,
75=76x
x=75/76
Hence if the dimensions of stamp M are 76 times the dimensions of stamp P then the length of stamp P in inches will be 75/76.
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Answer:
the answer is A, 6/5
how many hundreds multiplied by 4 will fit into 2018
We need to know numbers that multiplied by 4 are not greater than 2018.
For example, the number 100 (one hundred), when multiplied by 4 gives 400.
It obviously fits into 2018.
The number 900 by 4 gives 3600
are the ratios 19:20 and 3:4 equivalent?
Answer:
no
Step-by-step explanation:
The ratios 19:20 and 3:4 are not equivalent. Both of them are in their simplest form.
Here is a recipe for cupcakes.
• Terrance has cup of flour and eggs.
• Duri has cups of flour and grams of butter.
• Habib has cups of milk and cups of sugar.
• Anika has cup of sugar and cups of milk.
If each person has enough of all the other ingredients,
The number of cupcakes made by each person based on the limiting ingredients are;
Terrance → 6 cupcakes
Duri → 12 cupcakes
Habib → 12 cupcakes
Anika → 12 cupcakes
What is a limiting factor of a process or experiment?A limiting factor of a process is one that is used up completely upon completion of the process
The possible missing parts of the question are;
Recipe for making 12 cupcakes;
2 cups of flour
3/4 cups of sugar
2 eggs
3/4 cups of milk
125 g of butter
The ingredients each person has
Terrance; 1 cup of flour + 6 eggs
Duri; 12 cups of flour + 1,000 grams of butter
Habib; 3 cups of milk + 6 cups of sugar
Anika; 1 cup of sugar+ 4 cups of milk
Required;
The number of cupcakes each person can make on their own if each person has enough of the other ingredients.
Solution;
The question is with regards to the limiting variable or factor to making of the cakes
Terrance;
2 cups of flour bakes 12 cupcakes;
The number of cupcakes the 1 cup of flour Terrance has can bake is therefore;
(2 cups of flour)/2 = 1 cup of flour
(2 cups of flour)/2 bakes (12 cupcakes)/2 or 6 cupcakes
1 cup of flour bakes 6 cupcakes
Terrance can bake only 6 cupcakesDuri;
Duri has both more than the required number of cups of flour and grams of butter to make 12 cupcakes, therefore;
The number of cupcakes Duri can make given that he only has sufficient amounts of the other ingredients to make 12 cupcakes is therefore;
12 cupcakesHabib;
Habib also has more than the required amount of milk and sugar, but is limited by the other ingredients of which he only has enough to make 12 cupcakes, therefore;
The number of cupcakes Habib makes is 12Anika;
Anika also has more than the prerequisite amounts of sugar and milk to make 12 cupcakes, therefore;
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Jan uses 7/8
yard of fabric for one quilt square and 1/7
yard in another. How much fabric has Jan used?
ASAP!!!
Jan used the total amount for fabric 57/56 yard.
The amount of fabric used by Jan can be calculated by performing addition of the individual values.
Total amount of fabric used = Amount used in one square + amount used in another square
Keep the values in formula to find the total amount of fabric used.
Total amount of fabric used = 7/8 + 1/7
Taking LCM, we get 56
Total amount of fabric used = (7×7 + 1×8)/56
Total amount of fabric used = (49 + 8)/56
Performing addition on Right Hand Side
Total amount of fabric used = 57/56
Thus, Jan used 57/56 yard of fabric.
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Help find the value of x due today
Answer:if that is 68 get should be 68 degrees too
Step-by-step explanation:
Step-by-step explanation:
68+68+y=180
136+y=180
y=180-136
y=44°
T°=90-44
T°=46°
x+x+46=180
2x=180-46
2x=136
x=136÷2
x=38°
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-7,-2); y= -3x + 1
the equation of line which passes through point (-7,-2) and is parallel to the graph of the given equation is y = -3x +23.
What is Algebraic expression ?
Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables..
Here, the given equation is :
y = -3x + 1
which passes through point (-7,-2)
Let us first find the slope of line m which is parallel to the liney = -3x + 1 using point-intercept equation of line that is given by :
y = mx + c....(1)
y = -3x + 1
comparing above equation with equation (1) we get
m = -3
Now, the slope of line parallel to line y = -3x + 1 will have same slope that is m = -3
Now, Let us find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-(-2)) = -3(x-(-7))
(y+2) = -3x-21
y = -3x -21 -2
y = -3x +23
Therefore, the equation of line which passes through point (-7,-2) is y = -3x +23.
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if AB = 7x, CB = 5x + 8, and BD ⊥ AC, what is the length of CB?
Answer: 28
Step-by-step explanation:
Because BD ⊥ AC we can conclude that AB is equal to CB so we can set them equal to each other in an equation.
7x = 5x + 8
2x = 8
x = 4
Because X is 4 we can fill it into CB's expression.
5(4) + 8
20 + 8
28
Solve and show your work
The most appropriate choice for factorization will be given by-
[tex](x - 6)(x - 3)[/tex] is the required factorization
What is factorization?
At first, it is necessary to know about algebraic expression.
Algebraic expressions consists of variables, numbers connected with operations like addition, subtraction, multiplication and division.
Factorization is the process of breaking an algebraic expression into a product of smaller expressions. Each smaller expression is known as factors of the algebraic expression
One of the technique of factorization is to do middle term breaking.
Factorization is a very important tool in mathematics
Here,
Middle term technique will be used.
[tex]2x^2 - 9x -18\\2x^2 - 12x + 3x -18\\2x(x-6)+3(x-6)\\(x-6)(2x + 3)[/tex]
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Minh borrowed $30,000 from a bank for a car loan. if the length of the car loan is 7 years and the intrest rate is 18%, what is the total amount he owes the bank at the end of the loan.
Including interest on the principal the total loan amount is $67800
A loan occurs when one or more individuals, businesses, or other entities lend money to additional individuals, businesses, or other entities.
A loan is obtained, and the recipient, or borrower, is typically liable for both the principal borrowed as well as interest payments until the debt is repaid.The principle amount borrowed, the interest rate the lender is charging, and the due date for repayment are often disclosed in the promissory note used to demonstrate the obligation. The subject asset(s) are temporarily divided between the borrower and the lender when a loan is issued.Interest on the loan = 30000 × 0.18 × 7 = $37800
Total amount to be paid = $ 30000 + $ 37800 = $67800
Hence he owes a total of $67800 to the bank.
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what is the slope intercept form for x+3y=0
Answer:
y = -1/3 x
Step-by-step explanation:
what is the slope intercept form for x+3y=0
Slope intercept form solves for y:
x + 3y = 0
subtract x from both sides:
x + 3y - x = 0 - x
3y = -x
divide both sides by 3:
3y/3 = -x/3
y = -1/3 x
Two parrel lines cut by a transversal find each angle mesure
The angles formed between the parallel lines and the common transversal are;
7. [tex] \displaystyle{m \angle ABC = 92^{ \circ} }[/tex]
8. [tex] \displaystyle{m \angle MPQ = 125^{ \circ} }[/tex]
9. [tex] \displaystyle{m \angle MNP = 56^{\circ} }[/tex]
10. [tex] \displaystyle{m \angle WXZ = 130^{ \circ} }[/tex]
Corresponding angles
1 and 5, 2 and 6, 4 and 8, 3 and 7
Alternate interior angles
4 and 6, 3 and 5
Alternate exterior angles
1 and 7, 2 and 8
Same side exterior angles
1 and 8, 2 and 7
Same side interior angles
4 and 5, 6 and 3
What are parallel lines on a coordinate plane?Parallel lines on a coordinate plane are lines that have the same slope.
7. According to corresponding angle theorem, we have;
4•x° = (3•x + 23)°
Which gives;
4•x = (3•x + 23)
4•x - 3•x = 23
x = 23
[tex] \displaystyle{m \angle ABC = 4 \cdot x^{ \circ} = (4 \times 23)^{ \circ} = 92^{ \circ} }[/tex]
8. 5•x° = (3•x + 50)°
5•x - 3•x = 50
2•x = 50
x = 50 ÷ 2 = 25
[tex] \displaystyle{m \angle MPQ = (3 \cdot x + 50)^{ \circ} = (3 \times 25 + 50)^{ \circ} = 125^{ \circ} }[/tex]
9. According to alternate interior angles theorem we have;
2•a° = (a + 28)°
2•a° - a° = 28°
a = 28
[tex] \displaystyle{m \angle MNP = (a + 28)^{\circ} = (28 + 28)^{ \circ} = 56^{\circ} }[/tex]
10. 5•y = 2•y + 78°
5•y - 2•y = 78°
3•y = 78°
y = 78° ÷ 3 = 26°
y = 26°
[tex] \displaystyle{m \angle WXZ = 5•y = 5 \times 26^{\circ} = 130^{ \circ} }[/tex]
Corresponding angles
The corresponding angles are;
1 and 5, 2 and 6, 4 and 8, 3 and 7
Alternate interior angles
The alternate interior angles are;
4 and 6, 3 and 5
Alternate exterior angles
The alternate exterior angles are;
1 and 7, 2 and 8
Same side exterior angles
The same side exterior angles are;
1 and 8, 2 and 7
Same side interior angles
The same side interior angles are;
4 and 5, 6 and 3
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if A,B and C are three collinear points such that AB=10 units and AC=15, units what could be the length of BC?
The answer should be 25 unites
There are 6 triangles and 2 squares. What is the simplest ratio of squares to total shapes?
Answer:
1:4
Step-by-step explanation:
6 triangles
2 squares
total number of shapes = 6 + 2 = 8
ratio of squares to total = 2/8 = 1/4
Answer: 1:4
Find the missing side of the triangle.A. 19−−√ miB. 22–√ miC. 11−−√ miD. 1 mi
From the right angled triangle given,
To find the missing side, x, of the triangle, Pythagorean theorem is applied
The Pythagorean theorem formula is
[tex]\begin{gathered} (\text{Hyp)}^2=(\text{Opp)}^2+(\text{Adj)}^2 \\ \text{Hyp is the hypotenuse} \\ \text{Opp is the opposite } \\ \text{Adj is the adjacent} \end{gathered}[/tex]The dimensions of the triangle are
[tex]\begin{gathered} \text{Hyp}=\sqrt[]{10}mi \\ \text{Opp}=xmi \\ \text{Adj}=3mi \end{gathered}[/tex]Substituting the values into the Pythagorean theorem formula above,
[tex]\begin{gathered} (\sqrt[]{10})^2=x^2+3^2 \\ 10=x^2+9^{} \\ \text{Collect like terms} \\ x^2=10-9 \\ x^2=1 \\ \text{Square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{1} \\ x=1 \end{gathered}[/tex]The missing side, x is 1mi
Answer is D
Evan's parents budget 15% of their monthly disposable income of $5,200 for clothes. They budget 25% of the 15% budget amount for Evan's clothing, Evan buys his ownclothes above the budgeted amount. Evan had the following estimated totals for the six-month period from March through August: clothes = $1,278; repairs and alterations =$75; and dry cleaning = $70. How much will Evan have to pay out of his own pocket?$253.00$250.25$245,50$241.75None of these choices are correct.
First find the 15% of $5,200 to know how money they spend on clothing.
(15*5,200)/ 100 = $780
They budget 25% of the 15% budget amount for Evan's clothing
(25*780)/100 = 195 for each month
195*6 = $1,170 for the six-month period
The estimated totals for the six-month period is
$1,278 + $75 +$70 = $1,423
Make the subtraction between the six month period and the estimated totals for the six-month period:
$1,170 - $1,423 =-253
$253.00 is the amount that Evan have to paoy out of his own pocket.
.Solve the multistep equation using distributive property.
2 (3x - 5) = 4x + 2
2(3x - 5) = 4x + 2
Using distributive property, we can write the equation as:
2(3x) - 2(5) = 4x + 2
⇒ 6x - 10 = 4x + 2
⇒ 6x - 4x = 10 + 2
⇒ 2x = 12
⇒ x = 12/2
⇒ x = 6
The value of x is 6
What is Distributive property?This property states that multiplying the total of two or more addends by a number will produce the very same result as multiplying each addend by the number separately and then adding the results together. The distributive property is the distributive law of multiplication over operations on basic arithmetic, such as addition and subtraction.Among the axioms for rings and fields are the distributive laws, such as the ring of integers (like the field of rational numbers). In this situation, multiplication has a distributive advantage over addition, while addition does not. Boolean algebras much like the algebra of sets or the switching algebra are two instances of structures with two operations that are each distributive over the other.To learn more about Distributive Property, refer to:
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A virus is spreading around Kingwood. At the moment, 368 people are infected. If the virus is spreading at a rate of 6% each day, how many people in all will have caught the virus in 5 days?
Answer:
478 / 479
Step-by-step explanation:
6% of 368 is 22.08.
5 days = 6% x 5 = 30%.
30% of 368 = 110.4
110.4 + 368 = 478.4
492 people will be infected with the virus in 5 days.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
We have,
Number of people infected = 368
Rate of spreading = 6%
We can make an equation for the number of people infected in x days.
y = 368 x [tex](106/100)^x[/tex]
y = 368 x [tex]1.06^x[/tex]
Substitute x = 5
y = 368 x [tex]1.06^5[/tex]
y = 492.467
y = 492
Thus,
492 people will be infected with the virus in 5 days.
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\frac{5}{8}-\frac{1}{8} 8 5 − 8 1
After solving the given fractions, the resultant fraction is 1/2.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The terms with a numerator and a denominator are called fractions.So, 5/8 - 1/8:
Now, solve as follows:
5/8 - 1/8(5 - 1)/84/81/2
Therefore, after solving the given fractions, the resultant fraction is 1/2.
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The correct question is given below:
Solve: 5/8 - 1/8
Conrad has 6 more marbles than Rory has. Let r represent the number of marbles that Rory has. Select the expression that represents the number of marbles that Conrad has.
Answer:
Conrad = r + 6
Step-by-step explanation:
I need help will give brainlist
Answer:
area of Δ K = 160 units²
Step-by-step explanation:
given scale factor of sides a , then
scale factor of areas = a²
here scale factor = 4 so factor of areas = 4² = 16
area of Δ J = [tex]\frac{1}{2}[/tex] × 5 × 4 = 10 units² , then
area of Δ K = 16 × 10 = 160 units²
4 3/20 as a simplified common fraction
Answer:[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Please help with assignment (Due today)
Calculate the area of the shaded region in each figure. Use 3.14 for pi and round to the nearest hundredth, if necessary.
Answer:to question 1:55
Step-by-step explanation: area of purple 10 * 8=80 and then we subtract the area of the circle which is 25 so 80 minus 25=55
I did this like 3 weeks ago in 7 grade advance maths.
if i had 90 days and i did two months how many days do i have with the school breaks in it to ???
Answer:
Nothing cause your an special and you should know
Step-by-step explanation:
duh
I have been trying for a long time and I’m still stuck on it
Answer:
I'm not quite sure what you're trying to get but if you wanted it simplified the answer is 8^32 and if you needed to rewrite the expression the answer is 2^96
Answer:
[tex]8^{32}[/tex] They are looking for the exponent k = 32
Step-by-step explanation:
[tex](8^{8}) ^{^{4} }[/tex] this means that we have
[tex]8^{8}[/tex] four times
[tex]8^{8}[/tex] x [tex]8^{8}[/tex] x [tex]8^{8}[/tex] x [tex]8^{8}[/tex] Each one of these is 8 8's
(8x8x8x8x8x8x8x8)x(8x8x8x8x8x8x8x8)x(8x8x8x8x8x8x8x8)x(8x8x8x8x8x8x8x8)
How many 8s is that? 32.
The power or powers principal tells us that we can just multiply the exponents. (8 x 4) = 32
