The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 34.5, [tex]a_{5}[/tex] =12.5 are d = 47 and a = -106.5.
What is sequence?[tex]a_{4}[/tex] = 34.5
34.5 = a +3d.............1
[tex]a_{5}[/tex] =12.5
-12.5 = a + 4d...........2
equating equation 1 and 2
34.5 = a +3d
-12.5 = a + 4d
d = 47
d = 47 ..............3
from equation 3
a = -106.5
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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A small bag of fries at a quick service restaurant weighs 80 grams and costs $1.39, while a large bag of fries weighs 114 grams and costs $1.69. which bag of fries has the lower cost per gram and what is its cost per gram?
Comparing the unit price of each bag of fries, the large bag of fries, which costs $0.014825 per gram, has the lower cost per gram than the other bag.
Unit price is defined as the price or the cost per unit of the item. The importance of the unit price is that it allows the buyer to understand how the total price has been calculated. Unit price can be solved by dividing the total cost to the total amount of the item.
unit price = total cost/total amount
Solving for the unit price of each bag of fries:
small bag : unit price = $1.39/80 grams = $0.017375/gram
large bag : unit price = $1.69/114 grams = $0.014825/gram
$0.014825 < $0.017375
large bag < small bag
Hence, the large bag which costs $0.014825 per gram has the lower cost per gram.
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Solve |2x - 3| ≤7.
OA.
2-2 and x ≤ 4
OB.
2-3 or x ≤ 2
OC. 2-2 and x ≤ 6
OD. 2-2 and x < 5
The solution of the inequality expression is -2 ≤ x ≤ 5
How to solve the inequality expression?The inequality expression is given as
|2x - 3| ≤7
Remove the absolute bracket
So, we have
2x - 3 ≤ 7 and 2x - 3 ≥ -7
Add 3 to both sides of the inequalities
2x ≤ 10 and 2x ≥ -4
Divide to both sides of the inequalities by 2
x ≤ 5 and x ≥ -2
Rewrite as
-2 ≤ x ≤ 5
Hence, the solution of the inequality expression is -2 ≤ x ≤ 5
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.65 and the cost of a large greeting card is $5.40. How much would it cost to get 3 small greeting cards and 2 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The cost to get 3 small greeting cards and 2 large greeting cards is $15.75 and the it cost to get xx small greeting cards and yy large greeting cards is equals to $1.65(xx) + $5.40(yy)
To find out the cost of three small greeting card we need to multiply the cost of one small greeting card with 3 which equals to $4.95
To find out the cost of two large greeting card we need to multiply the cost of large greeting card with two which equals to $10.80
To find out the cost to get 3 small greeting cards and 2 large greeting cards we need to add $4.95 and $10.80 which equals to $15.75
As explained above to find the cost to get xx small greeting cards and yy large greeting cards we need to multiply with their respective unit price which equals to $1.65(xx) + $5.40(yy)
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A clearance rack is marked as 35% off the regular price. a shirt on the clearance rack has a regular price of $45.99. if there is 7.25% sales tax, what will the shirt ring up for at the register? a. $17.26 b. $21.67 c. $29.89 d. $32.06 please select the best answer from the choices provided a b c d
According to the question, the given data for the clearance rack is as written below:
Regular price of the clearance rack = $[tex]$ 45.99[/tex]
Sales tax = [tex]7.25[/tex] percent
As per the question, multiply the given marked percentage with the regular price to get the exact value.
Therefore, Marked price(in $) = [tex]45.99X0.35 = 16.10[/tex]
Now, subtract the calculated price from the regular price:(in $)[tex]45.99-16.10 = 29.89[/tex]
Multiply the regular price with the sales tax: [tex]29.89X0.0725 = 2.17[/tex]
Add the tax price with the calculated regular price to know the register price: [tex]29.89+2.17=32.06[/tex]
Therefore, [tex]32.06[/tex] is the amount for the shirt ring up for at the register.
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I need help with this asap
A classmate says that the system consisting of x=0, y=0 , and z=0 has no solution. Explain the student's error.
So, the statement we are provided with is that,
A classmate says that the systems consisting of
x = 0, y = 0 and, z = 0 has no solution.
This statement is clearly wrong, and we look at the points/ conditions that make this statement completely invalid.
Firstly, a system cannot have only zeros like here. In this case, we have zeros for all three terms (x, y, and z).
Secondly, there will be only one answer for this system, which will be a non-zero value or no answer.
Hence one variable is at least not equal to zero for a proper system.
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HURRY!! Right triangles ABC and PQR are shown below, where ∠A ≅ ∠P. What is the area, in square inches, of triangle PQR?
The area in square inches of triangle is 36.75.
Given,
∠A ≅ ∠P
Tan A = tan P
6/8 = x/14
X= 21/2
Area = 1/2 * 7*21/2
= 36.75 square
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base. Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides.
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
Hence, the area in square inches of triangle will be 36.75
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Write an equation of each line in standard form with integer coefficients.
(2/3)x+3=6 y-15
The equation of the line in standard form of (2/3)x + 3 = 6y - 15 is 2x - 18y = -54.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given the equation (2/3)x + 3 = 6y - 15, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
(2/3)x + 3 = 6y - 15
(2/3)x - 6y = -15 - 3
(2/3)x - 6y = -18
Multiplying both sides by 3 to have integer coefficients.
3[(2/3)x - 6y] = 3(-18)
2x - 18y = -54
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WILL GIVE BRAINLIEST :3 !
1.) 64 dollars
2.) 145 dollars
3.) -110 dollars?
4.) -50 solldars
54 + 10 = 64
60+85=145
-180+70=-110
37-87=-50
Answer:
Step-by-step explanation:
Okay so the first question you need to add because the store is giving a refund to Clare of $10. The second question you need to subtract $60 from $85. The third one you need to add again 180+ 70. The final problem you need to subtract 87 from 37 (Just know you will get a negative number) I hope this helps you! :D
Three competing subcontractors are reporting their average work output to a large project leader for a new housing development.
Rosk Construction provided an equation, where w represents the number of full weeks of work and a represents the estimated area of vinyl siding that can be installed in 100 ft2 units.
Equation from Rosk Construction: a = 62w
Fosbert’s Contracting provided a table indicating similar data from two jobs that had recently been completed by its crew.
Durable B Construction provided a graph showing the results of three of its recently completed jobs.
The unit rate for Rosk Construction is
The unit rate for Fosbert's Contracting is
The unit rate for Durable B Construction is
Based on the construction information, the unit rates will be 62, 65, and 63.
What do we mean by unit rates?A unit rate is a price for one unit of something. This is written as a ratio with a denominator of one.For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.So, Rosk Construction's unit rate is 62. This is due to a=62w.
Fosbert's Construction has a unit rate of 65 because:
130/2 = 65260/4 = 65390/6 = 65Therefore the unit rate is 65
Then,
Durable B Construction will have a unit price of 63.
This is due to:
63/1 = 63126/2=63189/3=63Therefore, based on the construction information, the unit rates will be 62, 65, and 63.
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The correct question is given below:
Three competing subcontractors are reporting their average work output to a large project leader for a new housing development. Rosk Construction provided an equation, where w represents the number of full weeks of work and a represents the estimated area of vinyl siding that can be installed in 100 ft2 units. Equation from Rosk Construction: a=62w Fosbert’s Contracting provided a table indicating similar data from two jobs that had recently been completed by its crew. Forsbert's contracting Number of Full Weeks, w 2 4 6 Area (square feet), a 130 260 390
4 and 1/2 minus 1 and 1/3
Answer:
3 1/6
Step-by-step explanation:
Hope this helps you :)
Answer:
3 1/6.
Step-by-step explanation:
4 1/2 - 1 1/3
= 9/2 - 4/3
= 27/6 - 8/6
= 19/6
= 3 1/6.
c. Elena's bed measures 4 cm by 3 cm on the scale drawing. What are the actual
measurements of her bed?
Based on the ratio and the measurement on the scale drawing, Elena's bed's actual measurements are 200 cm by 150cm.
What are the actual measurements?The scale is given as 1 is to 50.
This means that every centimeter on the drawing is 50 actual centimeters for the bed.
The dimensions are:
= 4 x 50 = 200 cm
= 3 x 50 = 150 cm
Remaining part of the question:
The ratio is 1 to 50
In conclusion, the actual measurements are 200 cm by 150 cm.
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Evaluate each expression 14^3
Line q has an equation of y = -10/9x+ 2. Line r includes the point (9, -3) and is parallel to
line q. What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
pro
fractiong imn
-fractions or intogoro
The equation of the line r is y = ₋(10/9)x ₊ 7.
Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form
equation of line q is y = ₋10/9x ₊ 2
it's already in slope intercept form.
hence slope is:
m = (₋10/9) from the above the equation.
we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.
y = mx ₊ b
₋3 = ₋10/9 (9) ₊ b
₋3 = ₋10 ₊ b
b = 7
plug the y intercept back into the equation to get our final answer.
y = ₋(10/9)x ₊ 7
hence we get the equation of the line r as y = ₋(10/9)x ₊ 7.
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Work out the value of the question mark in
the function machine below.
Input
-2→ ×?
Output
X-3-18
Answer:
output = -23
Step-by-step explanation:
if x = -2
output = x - 3 - 18 = -2 - 3 - 18 = -23
Find the coordinates of the midpoint of the line segment with endpoints (6, -2) and (-3, -2).
Answer: (3/2, -2)
Step-by-step explanation:
basically average of the x's and y's
6+-3/2 and -2+-2/2
which gives
(3/2, -2)
Djhsjsjakamakamsdgzhjshsbzjsjsn
please help it’s urgent thank you!
this is a proportional relationship that can be written as:
P = 5,184*S
Could there be a realtionship?Top see this, just take the quotient between the number of pixels and the number of square inches of each screen, and let's see if we get the same value for the given rows.
31,104/6 = 5,184
For the next row we have:
373,248/72 = 5,184
And so on, you will get the same quotient for the 3 rows, then we can conclude that yes, this is a proportional relationship that can be written as:
P = 5,184*S
Where P is the number of pixels and S is the number of square inches.
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Solve 0.203 ÷ 7.
1.421
0.290
0.029
−6.797
Answer:
0.029
Step-by-step explanation:
The answer
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
also show regular work
Answer:
The value of x is 9Step-by-step explanation:
Perimeter of rectangle = 2(Length+Breadth)
Length= (2+x)ft
Breadth= 3ft
Perimeter= 28ft
P=2(L+B)
[tex]28 = 2((2 + x) + 3) \\ 28 = 2(2 + x + 3) \\ 28 = 2(5 + x) \\ 28 = (2 \times 5) + (2 \times x) \\ 28 = 10 + 2x \\ [/tex]
Collect like terms
[tex]28 - 10 = 2x \\ 18 = 2x \\ \\ \frac{18}{2} = \frac{2x}{2 } \\ \\ 9 = x \\ x = 9[/tex]
Checking
P= 2(L+B)
[tex]28 = 2((x + 2) + 3) \\ 28 = 2((9 + 2) + 3) \\ 28 = 2(9 + 2 + 3) \\ 28 = 2(14) \\ 28 = 2 \times 14 \\ 28 = 28[/tex]
Confirmed
I just need these two done, please!
3. Both triangles are congruent by ASA congruence theorem.
4. There is no enough information to prove that the triangles are congruent by neither ASA nor AAS.
What is the ASA and AAS Congruence Theorem?If two triangles have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent by ASA congruence theorem.
If two triangles have two pairs of corresponding congruent angles and a pair of corresponding non-included congruent sides, then both triangles are congruent by AAS congruence theorem.
3. Both triangles are congruent by ASA congruence theorem.
4. There is no enough information to prove that the triangles are congruent by neither ASA nor AAS.
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Solve each system.
5x + y = 0 , 5x + 2y = 30
After solving each system, 5x + y = 0, 5x + 2y = 30, the values of x and y are calculated to be -6 and 30 respectively.
The given equations are considered linear equations as the highest power of the variables in these equations is one.
By rearranging the first equation, the value of y can be found to be,
5x + y = 0
y = -5x
Putting the calculated value of y in the second equation,
5x + 2y = 30
5x + 2(-5x) = 30
5x - 10x = 30
-5x = 30
x = 30 / -5
x = -6
To solve for y, put x = -6 in the first equation as follows,
5x + y = 0
5(-6) + y = 0
-30 + y = 0
y = 30
Hence, the values of x and y in these systems are calculated to be -6 and 30 respectively.
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What is the length of AB with endpoints A (-1,0) and B (4,-3)
Answer:
√34
Step-by-step explanation:
it would be radical 34.
Find x. x² + 5² = 13²
The value of the unknown variable x in the equation x² + 5² = 13² is 12.
The use of numbers and words in the same mathematical equation is considered as an algebraic expression.
We can calculate the square of a number by multiplying the number by itself.
Therefore, the square of 5 is equal to 5 multiplied by 5 which is equal to 25.
While the square of 13 is equal to 13 multiplied by 13 which is equal to 169.
So to find the value of x, we can rearrange the given equation as:
x² = 13² - 5 ²
x² = 169 - 25
x² = 144
As x² is equal to 144, we can calculate the value of x by taking the square root of the value of 144.
Therefore,
x= √144
x= 12
Hence, the value of the unknown variable x in this equation is 12.
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10 less than 5 times a number is equal to 15.
05(2-n) = 15
5-10n = 15
10-5n = 15
5n-10 15
Answer:
5n - 10 = 15.
Step-by-step explanation:
If the number is n then 5 times it is 5n.
10 less than this is 5n - 10.
So, the equation is
5n - 10 = 15.
Find the value of c that completes the square.
r^2+21r+c
Answer: c=110.25
Step-by-step explanation:
[tex]r^2+21r+c\\r^2+(2)(r)(10.5)+(10.5)^2=\\(r+10,5)^2\\Hence,\\c=(10.5)^2\\c=(10.5)(10.5)\\c=110.25[/tex]
what is the answear for 12c-9d-4c+d
Step-by-step explanation:
12c-4c-9d+d
8c-8d..........
Answer:
8c - 8d
Step-by-step explanation:
Combine like terms..
12c-9d-4c+d
8c - 9d + d
then combine the other like terms then you will get
8c - 8d
Ilya was using the properties to rewrite expressions. This time, his work is all correct. Fill in the blanks to explain the properties he used or to answer the questions.
First, he convert the terms into a positive sign, then he replaces the terms, then he used additive and division property for equality.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Ilya was rewriting expressions using the parameters. His work is flawless this time around.
The steps of the solution are given below.
1) 3x - 12 + 7 - 5x = 91
2) 3x + -(12) + 7 + (-5x) = 91
In the 2nd step, he converts all the terms with a positive sign.
3) 3x + (-5x) + (-12) + 7 = 91
In the 3rd step, he places the like terms closer.
4) (3+-5)x + (-12) + 7 = 91
In the 4th step, he took common from the first two terms.
5) -2x + (-5) = 91
6) -2x + 5 + (-5) = 91 +5
In the 6th step, he used the additive property for equality.
7) -2x = 96
8) (-1/2) × (-2x) = 96 × (-1/2)
And in the 8th step, he used division property for equality.
9) x = - 96/2
10) x = - 48
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What is the product of 4\sqrt{21}4
21
and 9\sqrt{6}9
6
in simplest radical form?
The product of the irrational numbers 4√21 and 9√6 in simplest radical form is 108√14.
What is the product of two radical expressions?In this problem we must find the product of two radical numbers, whose procedure has to be done by radical properties and other properties:
4√21 × 9√6 Given
4√(3 × 7) × 9√(2 × 3) Definition of multiplication
(4√7 × √3) × (9√2 × √3) Root square of a product
(4√7 × 9√2) × (√3 × √3) Associative property
36√14 × 3 Definition of power / Root square of a product
108√14 Associative property / Definition of multiplication / Result
RemarkThe statement is poorly formatted. The correct form is shown below:
What is the product of 4√21 and 9√6 in simplest radical form?
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The midpoint of AB
is M(-3, 0)M(−3,0). If the coordinates of AA are (1, -4)(1,−4), what are the coordinates of BB?
The required coordinate of b is given as (-7, 4 ).
Given that,
To determine the coordinate of b if M is the midpoint of AB. A(1, -4) and M(-3 ,0).
What is the midpoint?The midpoint is that point the line whose distance from both the ends of the line is equal.
Here,
We have given two coordinates one of the endpoints of AB and the other is midpoint M i.e. A(1, -4) and M(-3, 0).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 1, x = -3 , y₁ = -4, y = 0
now,
-3 = [1 + x₂] / 2 ; 0 = [-4 + y₂] / 2
x₂ = -6 - 1 ; y₂ = 0 + 4
x₂ = -7 : y₂ = 4
Thus, the required coordinate of b is given as (-7, 4 ).
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