⇒Given that the general rule to find the nth term is
[tex]T_{n} =-2+6(n-1)[/tex]
⇒To find the 11th term this means that they need a term which is in the position 11
⇒To get the number we plug in the 11 which is the position in the place of n and simplify.
[tex]T_{11} =-2+6(11-1)\\T_{11} =-2+6(10)\\T_{11} =-2+60\\T_{11} =58[/tex]
The 11th term is 58
Goodluck!!!
Which of the following represents the dimensions of the room
Given:
The length of the rectangular room is 6 more than the width.
The area of the room, A = 27 square units.
Required:
We need to find the dimensions of the given rectangular room.
Explanation:
Let w be the width of the rectangle.
6 more than means add 6.
The length of the rectangle, l= w+6.
Consider the area of the rectangle formula.
[tex]A=lw[/tex]Substitute A = 27, and l=w+6 in the formula.
[tex]27=(w+6)w[/tex][tex]27=w^2+6w[/tex]Subtract 27 from both sides of the equation.
[tex]27-27=w^2+6w-27[/tex][tex]0=w^2+6w-27[/tex][tex]w^2+6w-27=0[/tex][tex]Use\text{ }6w=9w-3w.[/tex][tex]w^2+9w-3w-27=0[/tex]Take out the common multiple.
[tex]w(w+9)-3(w+9)=0[/tex][tex](w+9)(w-3)=0[/tex][tex](w+9)=0,(w-3)=0[/tex][tex]w=-9,3[/tex]The measure is always positive.
[tex]w=3\text{ units,}[/tex]Substitute w =3 in the equation l =w+6.
[tex]l=3+6=9\text{ units.}[/tex]We get l =9 units and w =3 units.
Final answer:
The dimensions of the room are 3 and 9.
Write the equation of the line that passes through
the given point and is parallel to the given line.
SEE EXAMPLE 1
15. (5, −4); y = ≤⁄x − 4
17. (-3, 2); y=-4
16. (2, 7); 3x - y = 5
18. (6, 4); 2x + 3y = 18
Answer:
I'll do #17 as an example of how to do the others. #15 doesn't make sense. What is "= ≤⁄x?"
Step-by-step explanation:
17. (-3, 2); y=-4
y=4 is a horizontal line, where all values of y are 4, regardless of x. A horizontal line has a slope of 0. [Y does not depend on x].
That leaves us with y =0x + b
For this line to go through point (-3,2), it would have to have a y-intercept (b) of 2 [b is the value of y when x=0]. Since y=0 regardless of x, b must be 2.
The parallel line that goes through (-3,2) is:
y = 0*x + 2, or
y = 2
5 people can claim joint ownership of an item and intend to divide it by the method of sealed bids. The winner offers a bid of $8,000, how much will that bidder need to put into a kitty for the other bidders to be compensated?
Step-by-step explanation:
there is one item and it cannot be split.
the winning bid was $8,000.
that means the fair share for each one of the 5 participants is
8000/5 = $1,600
the winner is getting one item with a value greater than his fair share.
so, he has to pay the difference into the kitty :
8000 - 1600 = $6,400
Use the information provided to answer questions 2 - 5. Leah would like to earn at least $ 120 per month. She babysits for $ 5 per hour and works at an ice cream shop for $ 8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;
[tex]\begin{gathered} 5x+8y\ge120---(1) \\ x+y\leq20---(2) \\ Solve\text{ these on a graph and you'll have;} \end{gathered}[/tex]The red graph represents x + y =<20
The blue graph represents 5x +8y =>120
Observe that the region where the blue and red are "mixed" together represent the solution region.
Option A (4, 15)
Option B (5, 12) and
Option C (10, 9) are possible solutions
consider the following basket of goods: 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes. suppose that in 1999, each lollipop was 10 cents, each bar of chocolate was $1.50, each jar of peanut butter was $2.50, and each ice-cream cake was $7.99. in 2018, each lollipop was 80 cents, each bar of chocolate was $3.75, each jar of peanut butter was $4.25, and each ice-cream cake was 12.99. what was the value of the basket in 2018?
The value of the basket in 2018 was $92.48 if the basket contains 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes.
The value of the basket in 2018 can be calculated by using multiplication and addition.
First, we multiply the cost of each good in 2018 by the number of that good in the basket to calculate their total cost.
Lollipop: $0.80 × 15 = $12
Chocolate: $3.75 × 10 = $37.5
Peanut butter: $4.25 × 4 = $17
Ice-cream cake: $12.99 × 2 = $25.98
Now the value of the basket in 2018 can be calculated by adding these amounts of each good. Therefore;
Value of basket = $12 + $37.5 + $17 + $25.98
Value of basket = $92.48
Hence the value of the basket in 2018 is $92.48
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In an examination, Sarah obtained 87.5% by gaining 105 marks. How
many marks did she lose?
Answer: 14
Step-by-step explanation:
87.5% of 105 is 91.875 (91)
105-91=14
12x^2(y^8)/3xy^7 solve
The value of the expression given as 12x^2(y^8)/3xy^7 is 4xy
How to solve the expression?From the question, the expression is given as
12x^2(y^8)/3xy^7
Start by removing the bracket in the above expression
So, we have the following equation
12x^2(y^8)/3xy^7 = 12x^2y^8/3xy^7
Divide 12 by 3 in the above equation
So, we have the following equation
12x^2(y^8)/3xy^7 = 4x^2y^8/xy^7
Divide x^2 by x
So, we have the following equation
12x^2(y^8)/3xy^7 = 4xy^8/y^7
Divide y^8 by y^7
So, we have the following equation
12x^2(y^8)/3xy^7 = 4xy
Hence, the expression is 4xy
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3x3 determinant of -2, 3, 8 6, 7, 1 4, 5, 9
Lena purchased a prepaid phone card for 30.50 . calls cost 15 cents a minute using this card. the credit, c (in dollars), left on the card after it is used for minutes of calls is given by the following. how much credit is left on the card after lena uses it for 15 minutes of calls?
Only $28.25 are available. After Lena uses the card for 15 minutes of calls, there are still 28.25 credits left.
Given that,
Lena spent $30.50 on a prepaid phone card. With this card, calls cost 15 cents each minute. the amount of credit, c (in dollars), remaining on the card following x minutes of calls
It can be written as,
C(x) = 30.50 - 0.15x
C(x) = 30.50-(0.15 x 15)
after Lena uses it for 15 minutes,
C(x) = 30.50 – 2.25 = $28.25 in remaining credits.
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been stuck on this for ages
A bearing is a measurement of direction that uses North as a point of reference. Your bearing is 00° if you are moving north.
The angle from north to this bearing, measured counterclockwise, is the actual bearing. Utilize the knowledge that west is 270° from the north, south is 180°, and east is 90°.
The number of degrees in the angle measured counterclockwise from the north line to the line connecting the center of the compass is the bearing of a point.
How do you determine bearing angle?
The bearing is the angle subtracted in a clockwise direction from north to west. The bearing is 270° - 17° = 253° since the angle from north to west is 270°.
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-9 (-5 - 4c) simplify the expression and show your work. please this is due tomorrow
The simplified value of the expression given as -9 (-5 - 4c) is 45 + 36c
How to simplify the expression?From the question, the expression is given as
-9 (-5 - 4c)
To simplify the expression, we start by opening the bracket
So, we have the following equation
-9 (-5 - 4c) = -9 (-5 - 4c)
Remove the brackets
So, we have
-9 (-5 - 4c) = -9 x -5 -9 x - 4c
Evaluate the products
So, we have
-9 (-5 - 4c) = 45 + 36c
Hence, the value of the expressions is -9 (-5 - 4c) = 45 + 36c
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When Elizabeth left her phone in her house this morning
Solve for y:
4x-8y=32
Answer: y = -4 + x/2
Step-by-step explanation:
In this case, I need to find the value of x. Whatever x is I need to substitute it into the expressions representing sides. I am informed that this is an isosceles triangle.
Remember all angles of a triangle equal 180 degrees, and all the other geometry stuff.
Please help :)
Answer:
x = ?
Step-by-step explanation:
Since there are two congruent angles, their respective sides are also congruent (an angle's respective side is the side opposing it, the side that it does not touch). Meaning, the 3x-7 side is congruent to the 2x side.
So just set them equal to each other to find x.
3x - 7 = 2x
x = ? (You can do this. Solve for x algebraically.)
The 4x-10 doesn't really matter here since you just need to find x.
In a race, Kara ran eight- eighteenths of a kilometer and cycled sixteen-eighteenths of a kilometer. Estimate how many kilometers the race was in all.
a) 1/2 kilometer
b) 1 kilometer
c) 1 1/2 kilometers
d) 2 kilometers
Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.
What is addition of two fractions?To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.
Now, total distance in race
8/18 + 16/18
= (8+16)/18
= 24/18
= 4/3
= [tex]1\frac{1}{3}[/tex] kilometers
Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
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PLEASE FOLLOW THE DIRECTIONS IN THE PICTURES. PLEASE HURRY. Thank you very much
Answer:
E
Step-by-step explanation:
[tex]\sqrt{144} = 12\\ \frac{234}{3}= 78\\[/tex]
12, 68.12, 78
?????????? Image attached!
I will gladly take your help!
Answer:
-1/2; take both points which equals to -1/2
Step-by-step explanation:
A line passes through the points (–3, –4) and (6, 2).
A coordinate plane.
What is the x-intercept of this line?
Answer:
x intercept is -3
Step-by-step explanation:
We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1) = (2- -4)/(6- -3) = (2+4)/(6+3) =6/9 = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3
How do properties of interger exponents help you write equivalent expressions
Answer:
The product of powers property says that when we multiply powers with the same base, we just have to add the exponents. So, xaxb = x(a + b). As you can see, we keep the base the same and add the exponents together.
Step-by-step explanation:
In the figure below, AX'Y'Z' is a dilation of AXYZ. Find the scale factor of the dilation, andspirit as an enlargement or a reduction. What is the scale factor?What is the Classify?
The scale factor can be obtained by determining the ratio of the length of the sides of the old and new figures.
In other words, it can be obtained by stating that:
[tex]\text{scale factor=}\frac{lengthofsideoftriangleX^IY^IZ^I}{\text{length of side of triangle XYZ}}\text{ }[/tex]Specifically, we can say that:
[tex]\text{scale factor=}\frac{X^IY^1}{XY}=\frac{X^IZ^I}{XZ}=\frac{Y^IZ^I}{YZ}[/tex]Now, if each block (or cell) on the graph represents 1 units, we have that:
X'Y' = 10 units and XY = 5 units
Therefore:
[tex]undefined[/tex]2. LeRoy purchased 6 gallons of gasoline for
$19.56. Which describes the constant of
proportionality?
A.
B.
C.
D.
$2.26 per gal
$3.26 per gal
$3.29 per gal
$3.39 per gal
Find the value of $x$ that makes this equation true:
\[2x + 5 = 1.99x + 22.\]
Please help quick!
The value of x that makes the equation 2x+5 = 1.99x + 22 is 1700
The equation is
2x+5 = 1.99x+22
First we have to rearrange the given term and combine the like terms, then we have to find the value of x
Move 1.99x to left hand side of the equation and move 5 to the right hand side of the equation
2x+5 = 1.99x+22
2x-1.99x = 22-5
We have to do the subtraction in like terms
(2-1.99)x = 22-5
0.01x = 17
Move the number 0.01 to the right hand side of the equation
x = 17/0.01
Division
x = 1700
Hence, the value of x that makes the equation 2x+5 = 1.99x + 22 is 1700.
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Lydia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.10 plus $2.50 per mile. The total fare was $36.60, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride.
Answer:
4.10 + 2.50x = 36.60
x = 13 miles
Step-by-step explanation:
I hope this helped
have a good day ^^
Find the two square roots of 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 1/16 = 1/4
they probably
The telephone company offers two billing plans for local calls. Plan 1 charges $24 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
Answer:
plan b
Step-by-step explanation:
unless your making 120 calls or more plan B is better
24-18=6
6/0.05
=120
My friend sandy bought 3 pair of jeans and 7 shirts for $60. my friend dan bought 2 pair of jeans and 3 shirts for $30. what are the prices for jeans and shirts?
The prices for jeans and shirts are $6 and $6
Calculations and ParametersGiven that:
3 pairs of jeans and 7 shirts for $60.
And 2 pairs of jeans and 3 shirts for $30.
Let jeans be x
Let shirts be y
3x + 7y = 60.... eq 1
2x + 3y = 30...... eq 2
Let us make x the subject formula from equation 2
2x = 30-3y
x= (30-3y)/2..... eq 3
Put the value of x into equation 1
3 * (30-3y)/2 + 7y = 60
(90- 9y)/2 + 7y = 60
45 - 4.5y + 7y = 60
2.5y =15
y = 6
Then, put the value of y into eq 3
x= (30-3(6))/2
x= 15 - 9
x= 6
Hence, we can see that the values of x and y are 6 apiece.
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Answer:
yeah it's correct , very much well
An aquarium has dimensions 2x feet, (x â€" 1) feet, and (x 2) feet. The aquarium volume must be no more than 280 cubic feet. What are the possible values of x? (1, 5) (1, 5] [1, 5) [1, 5]
The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]
The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:
V = 2x (x - 1) (x + 2) ≤ 280
Divide both sides by 2:
x (x - 1) (x + 2) ≤ 140
x³ + x² - 2x - 140 ≤ 0
(x - 5) (x² + 6x + 28) ≤ 0
Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:
x - 5 ≤ 0
or x ≤ 5
Using the interval notation, x = (-∞, 5]
However, remember that the dimension is always a positive number.
Hence,
x - 1 ≥ 0
or x ≥ 1
Therefore, the solution is [1, 5]
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Which rational number also belongs to the set of whole numbers
A 0.3333
B. -9
C. 0
D. 5/6
Answer:
0
Step-by-step explanation:
Whole numbers are 0.1.2.3... Follows that pattern forever.
Select the correct answer from each drop-down menu. a cash card has a starting value of $25. if the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month. the relationship between the number of months after the first year and the amount remaining on the card is . the independent variable is the . the dependent variable is the .
The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)
a) the independent variable is the: Number of month after the first year
b) the dependent variable is the: Amount remaining on the card
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Starting value= $25Decrease= $2.50 per monthWriting the equation according to the information gave, we have:
y = 25 - (2.50x)
Where:
Amount remaining on the card = yNumber of month after the first year = xThe relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0
Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.
Write the given lines in standard form
Line a -5x + y = -3
Line b x + 5y = 2
Line c -2x - 10y = 0
a1 = -5, b1 = 1, c1 = -3
a2 = 1, b2 = 5, c2 = 2
a3 = -2, b3 = -10, c3 = 0
a1/a2 = -5/1
b1/b2 = 1/5
c1/c2 = -3/2
As we see that
a1/a2 ≠ b1/b2
Hence, lines a and b are intersecting.
a1/a3 = -5/-2
b1/b3 = 1/-10
As we see that
a1/a3 ≠ b1/b3
Hence, lines a and c are intersecting.
a2/a3 = 1/-2
b2/b3 = 5/-10 = 1/-2
c2/c3 = 2/0
As we see that
a2/a3 = b2/b3 ≠ c2/c3
Hence, lines b and c are parallel.
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