Answer:
The first term will be 38.375
Step-by-step explanation:
aₙ = a₁ + (n - 1) * d
a₂₀ = -40
a₂₈ = -73
-40 = a₁ + 19d
-73 = a₁ + 27d
When we have two similar equations with two unknowns, we can subtract them to get an answer.
-40 = a₁ + 19d --> -40 = a₁ + 19d
-(-73 = a₁ + 27d) --> 73 = -a₁ - 27d
-------------------------------------------------
33 = -8d
Solve for d by dividing by -8
d = -4.125
Now plug d into one of the original equations to solve for a₁
-40 = a₁ + 19(-4.125)
-40 = a₁ - 78.375
a₁ = 38.375
How do solve this in geometry?
Answer:
x=0.4
Step-by-step explanation:
Put both equations equal to each other:
16x+2=7x+6
Now, Solve:
16x+2=7x+6 Set the equation
16x-7x=6-2 Move like terms together
9x=4 Subtract like terms
x=4/9 Simplify
x=0.4 Answer
The length of the rectangle is 5 more than twice the width. If the perimeter is 10 times that of the width, what is the width, length, and perimeter of the rectangle?
Width of the rectangle is 2.5, Length is 10 and perimeter is 25
Given
Length of rectangle is 5 greater than double of width
let us say width = w
According to the question length L = 5 + 2w
Perimeter is 10 times the width
P= 10w
we know that perimeter of a rectangle is 2(L+W)
Substituting the values in the formula we get
10w = 2(5+2w + w)
10w = 10 + 6w
w= 2.5
From this length L = 5+2(2.5)
L = 10
Perimeter P = 10W
P= 10(2.5)
P= 25
Hence the length is 10, width is 2.5 and perimeter is 25
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1. Henry wants to go on a vacation. He knows it will cost $300 per
day that he's on vacation plus $650 for miscellaneous activities. He
has $2750 dollars in his savings account. How many days can he go
on vacation?
The number of days Henry can go on vacation is 7 days.
Given that, Henry knows it will cost $300 per day that he's on vacation plus $650 for miscellaneous activities.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of days be x.
Henry has $2750 dollars in his savings account.
So equation is 300x+650=2750
The obtained equation can be solved as follow
300x=2750-650
⇒ 300x = 2100
⇒ x = 2100/300
⇒ x = 7
Therefore, the number of days Henry can go on vacation is 7 days.
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The measure of a base angle of an isosceles triangle is 20 degrees. What is the measure of the vertex?
Answer:
140 degrees
Step-by-step explanation:
isosceles triangle so two angles are equal 20 and 20
ALL of the angles sum to 180 degrees
20+ 20 + vertex = 180
vertex = 140°
ASAP!!
3x + 9x = 6x + 42
Solve the equation for X and include all steps for Branliest.
Answer:
x = 7
Step-by-step explanation:
3x + 9x = 6x +42
12x = 6x +42
12x - 6x = 6x -6x +42
6x = 42
[tex]\frac{6x}{6} = \frac{42}{6}[/tex]
x = 7
Simplify
8(x + 3)2/2(x + 3)
Answer:
4x + 12Step-by-step explanation:
[tex] \sf \cfrac{8(x + 3)^{2} }{2(x + 3)} [/tex]
Cancel out 2(x+3) in both numerator and denominator:
[tex]\sf 4(x + 3)[/tex]
Use the distributive property to multiply 4 by x+3:
[tex]\sf 4x + 12[/tex]
》》》》》》》》》》》》》》
Hope this helps!!
Have a nice day
Pls help ASAP
The question is in the picture
Answer:
1. x = 0 , x = 3
2. x = -2 , x = 2
3. (x - 1)²
will give 30 points if its right need asap please
Answer:
2y + 1 maybe??????
Step-by-step explanation:
hope its correct if not please tell me
GEOMETRY PLEASE HELP ASAP
The function which will represent the given Translation will be T(x, y) = (x + 3, y - 2).
Translation may be defined as the shifting of the curve on a graph or shifting of the plotted points on a graph. The translation can be horizontal or vertical. In horizontal direction it can be shifted either left or right and in vertical direction it can be shifted either up or down. Horizontal translation always occurs on the x axis and vertical translation always occurs on the y axis. A function may be defined as an expression in which for input variable x there is output variable y. We need to translate a function T(x, y) 3 units right so the new coordinate will be T(x + 3, y). Now, translation occurs 2 units down. so, new coordinates will be T(x + 3, y -2) which is the required function.
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Given the function:
g(x)=8-2.5x
Find the following values.
a) g(6)
b) g(0)
c) g(-6)
A) g(6)
g(6) = 8 -2.5*6
g(6) = 8 - 15
g(6) = -7
B) g(0)
g(0) = 8 -2.5*0
g(0) = 8 - 0
g(0) = 8
C) g(-6)
g(-6) = 8 -2.5*-6
g(-6) = 8 + 15
g(-6) = 23
Ivan has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Using combinations, there are a total of 20 distinct voting combinations.
We now have five bands. We'll refer to them as A, B, C, D, and E.
John will choose two bands from the available five if he is required to vote for his favorite and second-favorite.
We must pair bands and discover every possible combination in order to determine the TOTAL number of different possibilities.
The results/totals are as follows:
AB, AC, AD, AE
BA, BC, BD, BE
CA, CB, CD, CE
DA, DB, DC, DE
EA, EB, EC, ED
Thus, there are a total of 20 distinct voting combinations.
Since you already know that each of the five initial bands (A, B, C, D, and E) will result in a multiple of four, you may accomplish it more simply without listing by taking the five bands.
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Use the equation below to find P, if a = 5, b= 10, and c = 12
P = a + b + c
Answer: The answer is 27
Step-by-step explanation:
if a=5 and b=10 and c=12 then just put the numbers in place of the letters so that's going to be :
P=5+10+12
P=15+12
P=27
An 8-foot roll of butcher paper costs $6.72. What is the price per inch?
Answer:
$0.84
Step-by-step explanation:
To solve this problem, divide 6.72 by 8.
6.72/8=0.84
It costs $0.84 per inch.
Hope this helps! :D
Rahul solved the equation 2(x – ) – 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction x = 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction . In which step did he use the addition property of equality?
A table titled Rahul's Solution with 2 columns and 5 rows. The first column, Steps, has the entries 1, 2, 3, 4. The second column, Resulting equations, has the entries, 2 x minus StartFraction 1 Over 4 EndFraction minus StartFraction 3 Over 5 EndFraction x equals StartFraction 55 Over 4 EndFraction, StartFraction 7 Over 5 EndFraction x minus StartFraction 1 Over 4 EndFraction equals StartFraction 55 Over 4 EndFraction, StartFraction 7 Over 5 EndFraction x equals StartFraction 56 Over 4 EndFraction, x equals 10.
Step 1
Step 2
Step 3
Step 4
Mark this and return
In step 2 addition property is used.
2x + (1 ÷ 4) - (3 ÷ 5)x = 55 ÷ 4
Simplifying x,
2x - (3 ÷ 5)x - (1 ÷ 4) = 55 ÷ 4
(10x - 3) ÷ 5 - (1 ÷ 4) = 55 ÷ 4
(7x ÷ 5) - (1 ÷ 4) = 55 ÷ 4
Add (1 ÷ 4) on both sides,
(7x ÷ 5) - (1 ÷ 4) + (1 ÷ 4) = 55 ÷ 4 + (1 ÷ 4)
(7x ÷ 5) = (55 + 1) ÷ 4
(7x ÷ 5) = 56 ÷ 4
Multiplying (5 ÷ 7) on both sides,
(7x ÷ 5) × (5 ÷ 7) = (56 ÷ 4) × (5 ÷ 7)
x = 10
In step 2 - Add (1 ÷ 4) on both sides, the addition property is being used.
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Answer:
its c step three
Step-by-step explanation:
standard form. (-3,0) and (0,8)
Answer:
8x−3y=−24
Step-by-step explanation:
Julia owns a food truck that sells tacos and burritos. She only has enough supplies to make 67 tacos or burritos. She sells each taco for $3.75 and each burrito for $6. Julia must sell no less than $330 worth of tacos and burritos each day. If 42 burritos were sold, determine all possible values for the number of tacos that Julia must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
The point would be the solution (25,40).
Let
The number of tacos sold is represented by x.
x denotes the quantity of burritos sold.
We are aware of this,
⇒ x + y 62
⇒ 3.75x + 6y = 330
The triangle shaded region is the answer
(25,40)
The point is one possible solution (25,40).
Remember that if an ordered pair is a solution to a system of inequalities, then the ordered pair must reside on the solution's region.
That indicates there were 30 tacos sold and 30 burritos sold.
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A piggy bank contains $2.65 in nickles and dimes. if the number of nickles is 7 less than three times the number of dimes. how many of each are there
In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes. Then There are 29 nickels and 12 dimes in the piggy bank.
We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.
Let x be the number of nickels and y be the number of dimes.
We know that, 1 dollar = 20 nickels
and 1 dollar = 10 dimes
So, we get an equation
0.05x + 0.1y = 2.65 ...........(1)
Also the number of nickels is 7 less than three times the number of dimes.
x = 3y - 7 .................(2)
Substitute above value of x in equation (1)
0.05(3y - 7) + (0.1)y = 2.65
0.15y - 0.35 + 0.1y = 2.65
0.25y = 2.65 + 0.35
0.25 y = 3
y = 12
Substitute above value of y in equation (2)
x = 3(12) - 7
x = 29
Therefore, there are 29 nickels and 12 dimes in the piggy bank.
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What is the complete factorization of 2 - 2ab + b2?
F. (a - b)(a + b)
G. (a + b)(a + b)
H. (a + b)(-a-b)
J. (a - b)(a - b)
Answer:
J
Step-by-step explanation:
assuming the 2 is a squared s a*a is a2 2*a*-b is -2ab
and -b* -b is b2
a) Find the value of 8*1/3
b) Find the value of 8*2/3
c) Find the value of 164*3/4
1. 8/3
2. 16/3
3. 123
*some words for 20 symbols*
HELP PLS Write the equation of the line in fully simplified slope-intercept form.
The equation of the line that passes through the x-intercept ( -2,0 ) and y-intercept ( 0,1 ) is y = (1/2)x + 1.
What is the equation of line of the graph?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
From the graph, the x and y-intercept are; ( -2,0) and (0,1 )
Point 1 ( -2,0 )
x₁ = -2y₁ = 0Point 2( 0,1 )
x₂ = 0y₂ = 1First, we determine the slope of the line.
Slope m = y₂ - y₁ / x₂ - x₁
Slope m = 1 - 0 / 0 - (-2)
Slope m = 1 / 0 +2
Slope m = 1/2
Next, determine the y-intercept b by substituting the slope and a point into the equation of line formula.
y = mx + b
0 = (1/2)(-2) + b
0 = -2/2 + b
0 = -1 + b
b = 1
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/2)x + 1
Therefore, the equation of the line is y = (1/2)x + 1.
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how do i simplify (x+9)(x-9)
everything u need is in the picture
One teacher wants to give each student 4/9 of a slice of pizza. if the teacher has 4 slices of pizza, then how many students will she be able to hand out pizza to?
ou have three jars of gumballs. the first jar has 100 white gumballs and 25 green, the second jar has 50 white and 150 blue, and the third jar contains 500 white and 10 red. if you randomly draw one gumball from each jar, what is the probability for at least one white gumball?
The probability for at least one white gumball is 0.196
Consider the following:
First jar:100 whites, 25 green
Total=100+25
=125 gumball
P(White)=100/125=0.8
Second jar:50 whites, 150 blue
Total=50+150
=200 gumballs
P(White)=50/200=0.25
Third jar:500 whites, 10 red
Total=500+10
=510
P(White)=500/500=0.98
Now, probability for at least one white is
=P(white in jar 1)*P(white in jar 2)*P(white in jar 3)
=0.8*0.25*0.98
=0.196
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HELP ASAP!!
Solve the inequality divided by negative 3. 2 is greater than or equal to 7. 6 for r.
A. ) r ≥ −24. 32
B. )r ≤ −24. 32
C. )r ≥ 2. 375
D. ) r ≤ −2. 375
Answer:
B. )r ≤ −24. 32
Step-by-step explanation:
5. The table shows how far a car is from its destination after x hours.
Hours
Miles
1
150
2
100
50
لیا
3
The function f(x) = 210-60x represents a second trip, where f(x) is the number of miles
the car is from its destination after x hours. Which trip takes less time? Explain.
Answer:
the trip represented by f(x) takes less time
Step-by-step explanation:
Given a table of time and distance to go, and a function f(x) = 210-60x representing the same for a different trip, you want to know which trip takes less time.
TableThe table has values ...
(time in hours, remaining distance in miles) = (1, 150), (2, 100), (3, 50)
This shows you the remaining distance decreases by 50 miles for every hour added to the travel time. That means the remaining 50 miles will be reduced to zero after 4 hours.
The trip represented by the table takes 4 hours.
EquationThe function f(x) = 210-60x will have a value of zero when ...
0 = 210 -60x
0 = 3.5 -x . . . . . . divide by 60
x = 3.5 . . . . . . . . add x
The trip represented by the function f(x) takes 3.5 hours.
The second trip takes less time.
Write an equation that represents the line.
Use exact numbers.
y=1.5x+3
Observing the graph
Let,
A(0,3) -----> this point is the y-intercept of the line
B(2,6)
We know that
The equation of the line into slope intercept form is equal to
y = mx + c
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem
b=3
Find the slope of the line m
The formula to calculate the slope between two points is equal to
m = y2-y1 / x2-x1
substitute the values
m = 6-3 / 2-0
m = 3/2
m = 1.5
The equation of the line is
y= 1.5x+3
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Use I = PTR to solve
(time is in years)
I=$252
R=7% find T.
P=$900
The time period in years T = 4 years
The simple interest amount = $252
The rate of interest per year as percentage = 7%
The principal amount = $900
The simple interest I = PTR
Where I is the interest amount
P is the principal Amount
T is the time period involved in years
R is the rate of interest per year as a percent
Substitute the values in the equation
252 = 900 × T × (7 / 100)
252 = 900 × T × 0.07
252 = 63 × T
Move the 63 to other side
T = 252 / 63
T = 4 years
Hence, the time period in years T = 4 years
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Sanjay bought T-shirts for his friends on the debate team.
The cost of the T-shirts (in dollars) is given by the equation c = 9.5t, where c is the total cost of the T-shirts and t is the number of T-shirts. If Sanjay bought 14 T-shirts, he paid $
.
The cost of t shirt is $ 133.
What does cost price mean?Cost price is the complete sum of money that a manufacturer must spend to create a specific good or render a specific service.
For instance, Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)
Given: c = 9.5 t
Sanjay bought 14 t shirts
And t in the above equation stands for the number of t shirts
thus c = 9.5 × 14 = $ 133
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Which postulate could we use to prove that the angles
Answer:
you can use the angle addition postulate I think that's what it's called
plssssss helpppppppppppppppppp