In the given geometric sequence
a) The expression of the common ratio r = -6 and (m+8)/2
b) The possible value of m = -28
c) The possible value of r = -6
The geometric sequence is
-1 , 6, m+8
The the common ratio = second term / first term
= 6 / -1
= -6
The common ratio = third term / second term
= (m+8)/6
The two expressions of common ratio is -6 and (m+8)/6
Part b
The third term = second term × common ratio
= 6 × -6
= -36
Then,
m +8 = -36
m = -36 + 8
m = -28
The possible value of m = -28
Part c
The possible value of r = -6
Hence, in the given geometric sequence
a) The expression of the common ratio r = -6 and (m+8)/2
b) The possible value of m = -28
c) The possible value of r = -6
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8. Consider a $2 principal investment with a 10% annual simple interest rate.
a. Write and graph the simple interest equation that represents the situation.
b. What does the y-intercept represent?
c. What does the slope of the graph represent?
d. What does the point (5, 3) represent on the graph?
9. AMORTIZATION Car loans are often spread into multiple regular payments over
in collod amortization. Each payment reduces the remaining
Answer:
Step-by-step explanation: 0.2
Graph equations that represent the growth rates of hamburgers sold
and wraps sold in the same coordinate plane. Compare the steepness
of the graphs. What does this mean in the context of the problem?
(a) Hamburgers sells faster than Wraps ,
(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .
In the question ,
it is given that
the rate at which the hamburgers are selling = 160 hamburgers per hour ,
we need to find the rate at which the wraps are selling
From the table ,
we can see that the wraps are sold in an Arithmetic Progression ,
So , at 60 minutes the wraps sold = 2.5 + (n-1)d
= 2.5 + 59×2.5
= 2.5 + 147.5
= 150
So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .
Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .
So, the hamburgers sells faster than wraps .
the slope(steepness) of the hamburgers = (number of hamburgers sold)/60
= 160/60
= 2.667
the slope(steepness) of the wraps = (number of wraps sold)/60
= 150/60
= 2.5
from the above data , we can see that the steepness of hamburgers is more ,
which means that the hamburgers sells faster than wraps .
the equation that denotes the number of hamburgers sold is y = 2.667x
the equation that denotes the number of wraps sold is y = 2.5x
where x is time in minutes .
The graph that represents the growth rate of hamburger and wraps is shown below .
Therefore , (a) Hamburgers sells faster than Wraps ,
(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .
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s: Practice
Question 3 of 5
Type the correct answer in each box. Use numerals Instead of words. If necessary, use / for the fraction bar(s).
A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6.
The equation below represents the situation, where x is the cost of each friend's meal.
6 + az = 41
The cost of each friend's meal in terms of a is
The cost of each friend's meal when the number of friends is 5 is $
Submit
Reset
Answer:
$7
Step-by-step explanation:
You want to know the cost of each friend's meal if 5 friends spend $41 on their food, which includes a $6 delivery charge.
CostFor 'a' friends spending 'x' on each meal, the total cost is ...
6 + ax = 41
Solving for x, we have ...
ax = 41 -6 = 35
x = 35/a
5 FriendsWhen the number of friends is a = 5, the cost of a meal is ...
x = 35/5 = 7
The cost of each friend's mean when the number of friends is 5 is $7.
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you send e-mails to tell your four friends about the school fair.Then those people send e-mails to four more people. Which formula can be used in this situation
The formula used in the situation of sending the emails is distributive property of multiplication and simple addition formula
How to determine the formula to be usedinformation gotten from the question
you send e-mails to tell your four friends about the school fair
Then those people send e-mails to four more people
From the first statement the number of emails sent is 4
The second statement says that the 4 persons sent to 4 more people hence each person sent one email
The total number of email sent is solved by
= 4 emails sent by you + 1 email sent by each friend * 4 (distributive property)
= 4 emails sent by you + 4 emails sent by friends
= 8 emails
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1). If Y Varies inversely as the square of X . If Y= 10 when X=4, Find Y when X=3
2). If Y Varies inversely as X and summing that Y=8 when X=6 find the relationship between X and Y. Also, find Y when X=3
The value of Y = 17.77 when X = 3, and the value of Y = 16 when X = 3
The equation which represents "Y varies inversely as the square of X" can be written as:
Y = k/X² where "k" is a constant.
Substitute the values of X=4 and Y= 10 in the variation equation and solve for k:
⇒ 10 = k/(4)²
⇒ 10 = k/16
⇒ k = 160
The variation equation :
⇒ Y = 160/X²
Substitute the values of X = 3 in the above equation and solve for Y:
⇒ Y = 160/(3)²
⇒ Y = 160/9
⇒ Y = 17.77
Thus, the value of Y = 17.77 when X = 3
The equation which represents "Y Varies inversely as X" can be written as:
Y = k/X where "k" is a constant.
Substitute the values of Y=8 and X=6 in the variation equation and solve for k:
⇒ 8 = k/(6)
⇒ k = 48
The variation equation :
⇒ Y = 48/X
Substitute the values of X = 3 in the above equation and solve for Y:
⇒ Y = 48/(3)
⇒ Y = 16
Thus, the value of Y = 16 when X = 3
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PLEASE HELP 50 POINTS!! NO LINKS
The solution for the intersection point of a triangle is given below.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of angle of a triangle is always 180°
Perpendicular bisectors of the sides is circum center.
The bisector of angles of a triangle is in center.
Intersection point of medians is centroid
The intersection point of altitudes is ortho center.
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two of the squares of a $7 \times 7$ checkerboard are painted yellow, and the rest are painted green. two color schemes are equivalent if one can be obtained from the other by rotating the board. how many different (non-equivalent) color schemes are possible?
300 different (non-equivalent) color schemes are possible.
For starters, there are 49 boxes in total and there are 49[tex]c_{2}[/tex] ways of picking the two yellow boxes which are 1176 ways
clearly, there are far fewer than 1176 "magical" setups
At first, I attempted to brute force this problem but realized that it was too hard to do that
according to a source, there are (1176−24)/4+24/2 =300. This is the same numerical answer as your formula, after simplification.
the system of making something much less complicated and consequently less complicated to do or recognize, or the issue that results from this technique: The corporation advises on the simplification of change strategies. this is a gross simplification of what truly took place. one of the earliest proponents of person simplification was Lufei Kui, who proposed in 1909 that simplified characters need to be used in education.
Bracket (Brackets are solved in order of (), {} and [] respectively. Of Þ multiplication, however, it's miles to be completed earlier than division. So for simplifying expressions, we ought to observe the above collection. in the previously given instance, we first divide 8 through four and upload it to 12 as division (D) is before more than one (M) in BODMAS. Simplification of terms inside the brackets may be achieved immediately. which means we are able to carry out the operations in the bracket inside the order of division, multiplication, addition, and subtraction.
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If f(x) =4x^6+ x^4+4,then what is the remainder when f(x) is divided by x-1
The remainder for the given polynomial is 9
A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division (No division operation by a variable). It is a function that only uses non-negative integer powers or positive integer exponents of a variable
Given f(x) = 4x^6+ x^4+4
Now f(x-1) = 0
X= 1
Substitute the x value in the function
f(x) = 4x^6+ x^4+4
f(x) = 4(1)^6+ (1)^4+4
f(x) = 4+ 1+ 4
f(x) = 9
Therefore the remainder for the given polynomial is 9
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3x - 5y = -22 (find x and y)
Answer:
x = −22/3 + 5y/3
y = 22/5 + 3x/5
Step-by-step explanation:
Solve each equation. Write each answer as a whole number or simplified fraction using the form a/b. a. 25=x15; x= b. 43=x7; x= c. 75=28x; x= d. 114=5x; x=
The solution for the equation are a. x = 5/3 or 2
b. x= 43/7 or 6
c. x =114/5 or 23
d. x =114/5 or 23
What is simplified fraction?
Simplified fraction are fraction in there lowest value or reduced form.
a. 25=x15
Divide both sides by 15
25/ 15 = 15x/15
X = 25/ 15 = 5/3
Therefore, the value of x is 5/3 or 2.
b. 43=x7
Divide both sides by 7
43/7 = 7x/7
x= 43/7 = 6.14
Therefore, the value of x is x= 43/7 or 6
c. 75=28x
Divide both sides by 28
75/28 =28x/28
x = 75/28 =2.67
Therefore, the value of x is x= 75/28 or 3
d. 114=5x
Divide both sides by 5
114/5 = 5x/5
x =114/5 =22.8
Therefore, the value of x is x =114/5 or 23
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What is the y-intercept of g(x) = -|x +6|+ 4
Answer: -2
Step-by-step explanation:
since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2
A number is increased by 13, then doubled to get 72
who doesnt just use this for the awnsers
A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what values of t is the particle moving to the right? responses the particle is moving to the right only if 0
The particle will move to the right for t > a .
In the question ,
it is given that ,
a particle moves along the x axis , such that at any time t ≥ 0 ,
its position is given by the equation
x(t) = 12(a−t)² ,
where a is = positive constant
to find value of the particle moves right ,
we differentiate x(t) , with respect to "x" .
x'(t) = 12×2(a - t)×(-1)
v(t) = -24(a-t) ..... because x'(t) = v(t)
for particle to move right , v(t) > 0 .
-24(a-t) > 0
dividing both sides by "-24" , we get
a - t < 0
a < t
t > a .
Therefore , The particle will move to the right for t > a .
The given question is incomplete , the complete question is
A particle moves along the x-axis so that at any time t ≥ 0 its position is given by x(t)=12(a−t)² , where a is a positive constant. For what values of t is the particle moving to the right ?
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Give an example of how u worked it out, please.
a. The value of 9.9² × 1.79 is 175.44.
b. The value of ✓97.5 + 1.96 is 11.83
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 9.9² × 1.79 will be:
= 9.9² × 1.79
= 98.01 × 1.79
= 175.44
The value of ✓97.5 + 1.96 will be:
= ✓97.5 + 1.96
= 9.87 + 1.96
= 11.83
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8 points
Megan and Desmond each added the same amount of water to their aquariums. Megan mixed
5 mL of a chemical solution with every gallon of water for her aquarium. Desmond mixed
8 mL of the chemical solution with every 2 gallons of water for his aquarium.
Which of these statements is true?
A Megan used more solution per gallon of water than Desmond, because 5:1 is greater
than 8: 2.
B Megan used more solution per gallon of water than Desmond, because 5 mL is greater
than 2 mL.
C Desmond used more solution per gallon of water than Megan, because 8 mL is greater
than 5 mL.
D Desmond used more solution per gallon of water than Megan, because 8:2 is greater
than 5: 1.
Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.
Both the length and width of the rectangle are approximately 31.62 m each.
The Area of a rectangle is calculated by multiplying the length by the width.
A = L x W
We have given that area of rectangle is 1,000 m²
1000 = W× L => W = 1000/L ---(1)
The circumference of rectangle is twice the sum of the dimensions. That is,
P = 2L + 2(1000/L)
Now, it is provided that perimeter is minimum so, we differentiate perimeter with respect to L then put first order derivative equal to zero.
dP/dL = 2 + 2000(-1/L²) = 0
=> 2-2000/L²=0
=>2000/L²=2
=> L²=2000/2
=> L²= 1000
=> L= 31.622
putting value of L in (1) we get , W= 31.622m
Therefore the length and width of the rectangle are both approximately 31.622m .
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Find all real numbers $x$ such that $x^2 < 4$. Give your answer in interval notation.
All the real numbers x which satisfy the given inequality x²<4 , in interval form is (-2, 2).
As given in the question,
Given inequality is given by :
x²< 4
Simplify the given inequality x² < 4 to get all the real numbers x we have,
x² < 4
⇒ x² - 4 < 0
⇒ x² - 2² < 0
Apply a² - b² = ( a - b ) ( a + b ) we get,
⇒ ( x - 2 ) ( x + 2 ) < 0
⇒ x ∈ ( -2 , 2 ) as less than symbol represent open interval.
Therefore, all the real numbers x which satisfy the given inequality x²<4 , in interval form is (-2, 2).
The complete question is :
Find all real numbers x such that x^2 < 4. Give your answer in interval notation.
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A student estimated the sum 7. 95 + 8. 11 + 78. 5 + 8. 05 + 79. 4 + 0. 815 as: all the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0. 8 = 184. 8 explain why this reasoning is not accurate.
Reasoning is not accurate because we cannot take 79.4 and 0.815 has cluster estimates of 8.
Given:
A student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: All the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0.8 = 184.8
7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815
8 + 8 + 80 + 8 + 80+ 0.8 = 184.8
Cluster estimation is used to estimate sums and products when the numbers being added or multiplied cluster near/ close in value to a single number.
Here 79.4 does not cluster around 8
And 0.815 does not cluster around 8
Therefore reasoning is not accurate because we cannot take 79.4 and 0.815 has cluster estimates of 8.
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At Target, shirts were on sale for $16 each. This price was 80% of their original price. What was the original price of the shirt?
Answer: 20 dollar because every 20% is 4$ therefore 100% is 20$
Houa works at an electronics store as a salesperson. Houa earns a 4% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Houa had $600 more in computer sales than in phone sales and earned a total of $129 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
The system of equations for determining the dollar amount of phone and computer sales are Sc = Sp + 600 and 0.05Sc + 0.04Sp = 1200
How to write a system of equations to determine the dollar amount of phone and computer sales?
A commission is defined as the compensation paid to a person or entity based on the sale of a product. It is calculated on a percentage basis
Given:
Phone sales commission = 4%
Computer sales commission = 5%
Total commission = $129
Let Sc and Sp represent the dollar amount of phone sales and computer sales respectively
If Houa had $600 more in computer sales than in phone sales, the equation can be written as:
Sc = Sp + 600
Since Houa earns a 4% commission on phone sales and a 5% commission on computer sales, and a total commission of $129. Thus, the equation for the commission can be written as:
0.05Sc + 0.04Sp = 1200
Note: 5% = 5/100 = 0.05 and 4% = 4/100 = 0.04
Therefore, the system of equations for determining phone and computer sales are Sc = Sp + 600 and 0.05Sc + 0.04Sp = 1200
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lx²-10 + 3x = 0
a
b
C=
La ecuación es completa o incompleta? (Quisiera que me explicaran si la ecuación tiene “x” al cuadrado osea “x2” pero con el dos chiquito y no tiene ningún numero como en esta ecuación seria completa)
Three sisters have ages that are consecutive even integers. Find their ages If the sum of twice the youngest and three times the oldest is Pourteen more than four times the middle sister's age
Answer:
12 ; 13 ; 14
Step-by-step explanation:
x = sister one
x+ 1 = sister two
x+2 = sister three
2x + 3(x+2) = 4(x+1) + 14
2x + 3x + 6 = 4x + 4 + 14
5x + 6 = 4x + 18
5x - 4x = 18 - 6
x = 12 (sister one)
12 + 1 = 13 (sister two)
12 + 2 = 14 (sister three)
What are the coordinates of the point on the directed line segment from (-6, 8)(−6,8) to (-2, -8)(−2,−8) that partitions the segment into a ratio of 5 to 3?
Please help im having issue with this
The coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3 are [-3.5, -2].
How to determine the coordinates of P?In this exercise, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.
Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point (x, y)= (-6, 8)Point (x, y) = (-2, -8)m:n = 5:3Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(5(-2) + 3(-6))/(5 + 3)], [(5(-8) + 3(8))/(5 + 3)]
P(x, y) = [(-10 + (-18))/(5 + 3)], [(-40 + 3(8))/(5 + 3)]
P(x, y) = [(-10 - 18)/(8)], [(-40 + 24)/(8)]
P(x, y) = [(-28)/(8)], [(-16)/(8)]
P(x, y) = [-3.5, -2]
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Rosario paid $2.50 for 3 pounds of apples. Select all of the rates that are equivalent to the rate Rosario paid. 6.RP.3, 6.RP.3b $0.80 for 1 pound 14.50 for 5 pounds $7.50 for 9 pounds $9.60 for 11 pounds $10.00 for 12 pounds
The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds.
What are the rates?
A rate is a unique ratio where the two words are expressed in several units.
Rate formula
r = d/t
Here, we calculate different rates
a. Per pound price of apples = Total cost / total weights of apples
= 0.80 / 1 = $0.80
Cost of 3 pounds of apples = 3 × 0.80 = $2.4
b. Per pound cost of apples = Total cost / total weights of apples
= 14.50 / 5 = $2.9
Cost of 3 pounds of apples = 3 × 2.9 = $8.7
c. Per pound cost of apples = Total cost / total weights of apples
= 7.50 / 9 = $0.833
Cost of 3 pounds of apples = 3 × 0.833 = $2.49
d. Per pound cost of apples = Total cost / total weights of apples
= 9.60 / 11 = $0.872
Cost of 3 pounds of apples = 3 × 0.872 = $2.61
e. Per pound cost of apples = Total cost / total weights of apples
= 10 / 12 = $0.833
Cost of 3 pounds of apples = 3 × 0.833 = $2.49
Hence, The rates that are equivalent to the rate Rosario paid are $0.80 for 1 pound, $7.50 for 9 pounds, and $10.00 for 12 pounds.
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Complete by solving the square!(need help asap!)
Explain step by step!
3x^2+x-2=0
Answer: x = -2/3 , 1
Step-by-step explanation:
step 1 (hardest step!) factor by grouping:
(3x + 2)(x-1) = 0
the rest is easy:
3x + 2 = 0 or (x-1) = 0
Solve each for x:
3x + 2 = 0
x = -2/3
x-1 = 0
x = 1
So your 2 solutions for x are -2/3 and 1
-0.6a^2b*(-10ab^2) PLEASE HELP!!!!!!!!
Answer: 6a^3b^3
Step-by-step explanation:
Answer:
6a³b³
Step-by-step explanation:
-0.6a^2b*(-10ab^2) =
= -0.6 × (-10) × a² × a × b × b²
= 6a³b³
can you substitute y=2x+4 and 6x-3y=-12
Answer: x=0 y=4
Step-by-step explanation:
6x - 3(2x + 4) = 12
6x - 6x - 12 = 12
0 = 0
therefore, x = 0
substitute x=0 into y = 2x + 4
y = 2(0) + 4 = 4
Label each point on the number line with the correct value.
Click each dot on the image to select an answer. Choices:
Answer:B= 7/9 C=10/9 A=0.62
Step-by-step explanation:
i know this because i multiplyed by 1/3 by 3 to get 3/9 6/9 9/9 for the number line
Calvin paints pictures and sells them at art shows. He charges $156 for a large painting.
He charges $95 for a small painting. Last month he sold six large paintings and three
small paintings. How much did he make in all?
Answer:
1221
Step-by-step explanation:
if you do 156 times 6 and add that to 95 times 3, you get 1221
Answer:
$1,221
Step-by-step explanation:
156 x 6 = 936
95 x 3 = 285
936 + 285 = $1,221