Answer:
Assume that the cost of the milk is x.
We are given that a sandwich costs 0.75$ more than the cost of milk. This means that:
cost of sandwich = cost of milk + 0.75
cost of sandwich = x + 0.75
Now, the customer bought 4 sandwiches and 4 containers of milk at the cost of 7$.
We will transform this into an equation as follows:
total cost = cost of 4 sandwiches + cost of 4 containers of milk
7 = 4(x+0.75) + 4(x)
Solve the above equation to get x as follows:
7 = 4x + 3 + 4x
7-3 = 8x
8x = 4
x = 0.5
Therefore:
cost of milk = x = $0.5
cost of sandwich = x+0.75 = 0.5+0.75 = $1.25
Answer:
$1.25
Step-by-step explanation:
3m+5=8 help plz on math
Answer:
m = 1
Step-by-step explanation:
Given -> 3m + 5 = 8
Subtraction -> 3m = 3
Division -> m = 1
Answer:
m= 1
Step-by-step explanation:
3m +5 = 8 Substract 5 to both sides
3m = 3 Divide 3 in both sides
m = 1
Rachel is driving from New York to Dayton Florida a distance of 1034 miles. How Much Time Is Saved By Doing The Trip At An Average Speed Of 60mph as compared with 55 mph? Round to the nearest half hour
By increasing her speed from 55 mph to 60 mph, Rachel can save approximately 1.5 hours on her 1034-mile trip from New York to Dayton, Florida.
Explanation:The subject of this question is Mathematics, specifically dealing with the concept of speed, distance, and time. To answer your question, we need to calculate how long the trip would take at each speed and then find the difference.
First, we calculate the time taken when the average speed is 55 mph. The formula to calculate time is distance divided by speed. So, 1034 miles divided by 55 mph equals about 18.8 hours.
Next, we do the same for 60 mph. 1034 miles divided by 60 mph equals about 17.2 hours.
The difference between the two times will give the time saved by increasing the speed to 60 mph from 55 mph. So, 18.8 hours - 17.2 hours equals 1.6 hours, which is approximately 1.5 hours when rounded to the nearest half hour.
Therefore, Rachel can save about 1.5 hours driving at an average speed of 60 mph compared to 55 mph over the distance of 1034 miles.
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find three consecutive even integer with the sum of -84
Kristina, Liz, and Heather all made cookies. Kristina made 2.4 dozen less than 6 times as many dozen as Heather. Liz made 1.8 dozen more than 5 times as many dozen as Heather. If Kristina and Liz made the same number of cookies, how many dozen cookies did Heather make?
Answer:
Based on the number of cookies each girl made and if Kristina and Liz made the same number of cookies, then Heather made 4.2 dozen cookies.
Step-by-step explanation:
In order to find the number of cookies that Heather made, you need to set up two equations that represent the number of cookies that Kristina and Liz each made. Since Kristina made 2.4 dozen less than 6 times as many dozen as Heather, we can represent that with the equation 6c - 2.4. Since Liz made 1.8 dozen more than 5 times as many dozen as Heather, we can represent that with the equation 5c + 1.8. We can set both equations equal to each other since Liz and Kristina made the same number, so 6c - 2.4 = 5c + 1.8. Solving for 'c', which represents how many dozen cookies Heather made, we get 4.2
Let's assign a variable to represent the number of dozens of cookies Heather made. We'll call this variable \( H \).
According to the problem:
- Kristina made \( 6 \times H - 2.4 \) dozen cookies.
- Liz made \( 5 \times H + 1.8 \) dozen cookies.
We are also given that Kristina and Liz made the same number of cookies, so we can set these two expressions equal to each other to find the value of \( H \):
\[ 6H - 2.4 = 5H + 1.8 \]
Now, we'll solve this equation for \( H \).
Step 1: Isolate the variable \( H \) on one side.
To do this, we'll first subtract \( 5H \) from both sides of the equation:
\[ 6H - 5H - 2.4 = 5H - 5H + 1.8 \]
\[ H - 2.4 = 1.8 \]
Step 2: Now we need to get \( H \) alone, so we'll add \( 2.4 \) to both sides:
\[ H - 2.4 + 2.4 = 1.8 + 2.4 \]
\[ H = 4.2 \]
So, Heather made \( 4.2 \) dozen cookies.
To ensure this is the correct number of dozens Heather made, we can plug this value back into the original expressions for Kristina and Liz's cookies to verify that they made the same amount:
Kristina: \( 6 \times 4.2 - 2.4 = 25.2 - 2.4 = 22.8 \) dozen cookies
Liz: \( 5 \times 4.2 + 1.8 = 21 + 1.8 = 22.8 \) dozen cookies
Both Kristina and Liz made 22.8 dozen cookies, confirming our solution that Heather made 4.2 dozen cookies.
Arrange the angles in increasing order of their cosines.
3pie/4
pie
7pie/6
5pie/3
7pie/4
4pie/3
3pie/2
2pie
Answer:
[tex]\pi,\ \dfrac{7\pi}{6},\ \dfrac{3\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{7\pi}{4},\ 2\pi.[/tex]
Step-by-step explanation:
Convert each angle in degree measure:
[tex]\dfrac{3\pi}{4}=135^{\circ},\\ \\\pi=180^{\circ},\\ \\\dfrac{7\pi}{6}=210^{\circ},\\ \\\dfrac{5\pi}{3}=300^{\circ},\\ \\\dfrac{7\pi}{4}=315^{\circ},\\ \\\dfrac{4\pi}{3}=240^{\circ},\\ \\\dfrac{3\pi}{2}=270^{\circ},\\ \\2\pi=360^{\circ}.[/tex]
Then
[tex]\cos \dfrac{3\pi}{4}=\cos 135^{\circ}=-\dfrac{\sqrt{2}}{2},\\ \\\cos \pi=\cos 180^{\circ}=-1,\\ \\\cos \dfrac{7\pi}{6}=\cos 210^{\circ}=-\dfrac{\sqrt{3}}{2},\\ \\\cos \dfrac{5\pi}{3}=\cos 300^{\circ}=\dfrac{1}{2},\\ \\\cos \dfrac{7\pi}{4}=\cos 315^{\circ}=\dfrac{\sqrt{2}}{2},\\ \\\cos \dfrac{4\pi}{3}=\cos 240^{\circ}=-\dfrac{1}{2},\\ \\\cos \dfrac{3\pi}{2}=\cos 270^{\circ}=0,\\ \\\cos 2\pi=\cos 360^{\circ}=1.[/tex]
Therefore, the angles in increasing order of their cosines are
[tex]\pi,\ \dfrac{7\pi}{6},\ \dfrac{3\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{7\pi}{4},\ 2\pi.[/tex]
Answer:
Step-by-step explanation:
Adeline types 150 words in 2 minutes. Enter the number of words Adeline types in 6 minutes at this rate
Answer:
450
Step-by-step explanation:
please help ??????????????
Answer:
First box: 6x
Second box: 24
Step-by-step explanation:
9(16)=6x
144 = 6x | divide by 6
144/6 = 6x/6
24 = x
A line has a Y-intercept of 6 and a slope of 8. What is its equation in slope-intercept form?
Answer:
y = 8x + 6
Step-by-step explanation:
The slope intercept form is: y = mx + c
where m ⇒ slope
c ⇒ y-intercept
(x,y) is a point on the graph the satisfy the equation representing that graph. x is the x-coordinate of a point on the line and y is the y-coordinate of a point on the line.
m = 8
Y-intercept = 6
y = mx + c ⇒ y = 8x + 6
480 divided by 8 long division
Answer:
60
Step-by-step explanation:
The required result is 60 when 480 is divided by 8, with no remainder.
What is the long division?In mathematics, divides left-hand operands into right-hand operands in the division operation.
To divide 21,900 by 25, we can perform long division as follows:
8 ) 480 ( 60
- 480
________
0
When we divide the first digit of 480 (which is 4) by the divisor 8, which gives us 60 with a remainder of 0.
Therefore, 480 divided by 8 is 60, with no remainder.
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The complete question would be as:
What is the result when 480 is divided by 8 long division?
Walking on his own, the distance, D, in feet, that Roberto can cover in M, minutes is given by the function D(m)=264m. When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m m minutes is given by the function A(m)=440m. Let B be the distance, in feet, that Roberto would travel on the moving sidewalk in m m minutes if he were standing still. Write a formula for B(m) in terms of D(m) and A(m).
Answer:
B(m)=A(m)-D(m)
B(m)=176m
Step-by-step explanation:
we are given
Walking on his own, the distance, D, in feet, that Roberto can cover in M, minutes is given by the function
D(m)=264m
When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m m minutes is given by the function
A(m)=440m
B is the distance, in feet, that Roberto would travel on the moving sidewalk in m minutes if he were standing still
moving sidewalk distance = standstill distance + walking distance
A(m)=D(m)+B(m)
so, we get
B(m)=A(m)-D(m)
now, we can plug values
B(m)=440m-264m
B(m)=176m
Final answer:
To find the distance B(m) that Roberto would travel on a moving sidewalk in m minutes if he stood still, one must subtract the function for walking alone D(m) from the function for walking on a moving sidewalk A(m). Thus, B(m) is calculated as B(m) = A(m) - D(m), resulting in B(m) = 176m.
Explanation:
The student needs to find the formula for the distance B(m) that Roberto would travel on the moving sidewalk in m minutes if he stands still, in terms of the functions D(m) and A(m). The function D(m) = 264m represents the distance Roberto covers by walking on his own in m minutes, and A(m) = 440m represents the distance covered while walking on a moving sidewalk.
Since A(m) represents the combined effect of walking and the moving sidewalk, and D(m) represents just walking, the difference A(m) - D(m) will give us the contribution of the moving sidewalk alone, while Roberto stands still. Thus, the formula for B(m) is:
B(m) = A(m) - D(m)
B(m) = 440m - 264m
B(m) = 176m
The formula B(m) indicates the distance Roberto would cover on the moving sidewalk if he did not walk and just stood still.
If f(x)=x2-2x-8 and g(x)=1/4x-1 for which value of x is f(x)=g(x)
[tex]f(x)=x^2-2x-8;\ g(x)=\dfrac{1}{4}x-1\\\\f(x)=g(x)\iff x^2-2x-8=\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4x^2-8x-32=x-4\qquad\text{subtract x from both sides}\\\\4x^2-9x-32=-4\qquad\text{add 4 to both sides}\\\\4x^2-9x-28=0\\\\4x^2-16x+7x-28=0\\\\4x(x-4)+7(x-4)=0\\\\(x-4)(4x+7)=0\iff x-4=0\ \vee\ 4x+7=0\\\\x=4\ \vee\ 4x=-7\\\\\boxed{x=4\ \vee\ x=-\dfrac{7}{4}}[/tex]
A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays $61 for 8 turkey sandwiches. How much does each turkey sandwich add to the cost of the delivery? Explain how you know.
Answer:
$7. Based on the assumption that both offices paid the same amount for delivery, the difference in the total cost paid is due to the difference in the number of turkey sandwiches ordered, which is 4. The cost of each sandwich is a quarter of this difference in cost.
Step-by-step explanation:
In mathematical working, the explanation above can be written in the form of equations, where we work to solve the value of a variable. In this case, we are interested to find the value of t.
Define variables:
Let the cost of a turkey sandwich be $t while the delivery fee be $d.
Form 2 equations:
Assuming that the sandwich stores charges the same delivery fee for both offices,
4t + d= 33 -----(1)
8t + d= 61 -----(2)
Solve by elimination:
(2) - (1):
4t= 61 - 33
4t= 28
Divide both sides by 4:
t= 7
Thus, each turkey sandwich adds $7 to the cost of the delivery.
To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.
Explanation:To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.
For the first office, they paid $33 for 4 turkey sandwiches. Let's assume the cost of delivery is 'x'. So the equation to represent the total cost is: 4x + 33 = total cost.
Similarly, for the second office, they paid $61 for 8 turkey sandwiches. Let's assume the cost of delivery is 'y'. So the equation to represent the total cost is: 8y + 61 = total cost.
Now we can solve both equations to find the values of 'x' and 'y' which will represent the cost of delivery. Once we have those values, we can calculate how much each turkey sandwich adds to the cost of delivery by dividing the cost of delivery by the number of turkey sandwiches ordered.
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The local market is selling fresh fruit in baskets. The weights and amounts charged are shown below. For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00. For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50. For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00. For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50. For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00. Which graph represents the function described?
Answer:
The graph is shown below.
Step-by-step explanation:
Let x be the weight of fruit in pounds and P(x) be the price of fruit.
For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00.
P(x) = $2.00 for 0.01 ≤ x ≤ 0.5
For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50.
P(x) = $3.50 for 0.5 < x ≤ 1.0
For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00.
P(x) = $5.00 for 1.0 < x ≤ 1.5
For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50.
P(x) = $6.50 for 1.5 < x ≤ 2.0
For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00.
P(x) = $8.00 for 2.0 < x ≤ 2.5
It is a piecewise floor function. We have open circle on left side of each floor except first floor because the sign of inequality in all other is < .
We have closed circle on right side of each floor because the sign of inequality is ≤ .
The graph is shown below.
Anna charges $8.50 per hour to babysit. How much will she earn in 3,3 1/2,4 hours?
Anna earns $8.50 per hour babysitting. For 3, 3.5 and 4 hours of work, she will earn $25.50, $29.75, and $34.00 respectively.
Explanation:Anna earns $8.50 per hour for babysitting. To calculate her earnings, we simply need to multiply the number of hours she worked by her hourly rate.
For 3 hours, she will earn $8.50 * 3 = $25.50. For 3.5 hours, she will earn $8.50 * 3.5 = $29.75. For 4 hours, she will earn $8.50 * 4 = $34.00.Learn more about Hourly Wage Calculation here:
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Geometry, Angle Relationships Theorems question
I'm sure this looks a lot harder than it really is, but any help would be appreciated because I'm stumped. I'm supposed to fill in the green boxes but I can't figure out what to do. Thanks :)
Answer:
Step-by-step explanation:
1. <3 = <4 1 Given
2. <2 <3 are supplementary 2. non common sides in opposite rays
3. <2 + <3 = 180 3. Definition of supplementary angles
4. <2 + < 4 = 180 4 substitution
5. <1 = <4 5 Opposite angles are equal
6 <2 + <1 = 180 6 Substitution
7. <1, <2 are supplementary 7. Definition of supplementary angles
The only word I am not sure of is the last word in 2
PLEASE SHOW WORK
Solve using substitution
x=y+6
y=x+4
Answer:
no solution
Step-by-step explanation:
1. Substitute the value of into the equation. y = y + 6 + 4
2. Solve. the system has no solution because y = y.
Given: KLMN is a trapezoid, m∠N=m∠KML, FD=8, LM KN = 3 5 F∈ KL , D∈ MN , ME ⊥ KN KF=FL, MD=DN, ME=3 5 Find: KM
Answer:
The length of side KM is [tex]\sqrt{109}[/tex] units.
Step-by-step explanation:
Given information: KLMN is a trapezoid, ∠N= ∠KML, FD=8, LM:KN=3:5, F∈ KL, D∈ MN , ME ⊥ KN KF=FL, MD=DN, [tex]ME=3\sqrt{5}[/tex].
From the given information it is noticed that the point F and D are midpoints of KL and MN respectively. The height of the trapezoid is [tex]3\sqrt{5}[/tex].
Midsegment is a line segment which connects the midpoints of not parallel sides. The length of midsegment of average of parallel lines.
Since LM:KN=3:5, therefore LM is 3x and KN is 5x.
[tex]\frac{3x+5x}{2}=8[/tex]
[tex]\frac{8x}{2}=8[/tex]
[tex]x=2[/tex]
Therefore the length of LM is 6 and length of KN is 10.
Draw perpendicular on KN form L and M.
[tex]KN=KA+AE+EN[/tex]
[tex]10=6+2(EN)[/tex] (KA=EN, isosceles trapezoid)
[tex]EN=2[/tex]
[tex]KE=KN-EN=10-2=8[/tex]
Therefore the length of KE is 8.
Use pythagoras theorem is triangle EKM.
[tex]Hypotenuse^2=base^2+perpendicular^2[/tex]
[tex](KM)^2=(KE)^2+(ME)^2[/tex]
[tex](KM)^2=(8)^2+(3\sqrt{5})^2[/tex]
[tex]KM^2=64+9(5)[/tex]
[tex]KM=\sqrt{109}[/tex]
Therefore the length of side KM is [tex]\sqrt{109}[/tex] units.
The answer is [tex]\sqrt{70}[/tex]
The following graph depicts the total cost of purchasing blueberries at Blue Basket Farm at certain price per pound.
The graph is: A) linear. B) nonlinear.
The graph represents a: A) discrete function
B) continuous function
Answer:
A.) Linear
B.) Continuous function
Step-by-step explanation:
Its linear because it is not all over the place and continuous because it does not stop it will keep going because it is a ray
Answer: The graph is A) Linear
The graph represents a B) Continuous function.
Step-by-step explanation:
Since we have given a figure which depicts the total cost of purchasing blueberries at Blue Basket Farm at certain price per pound.
Since the graph is linear .
As we can write it as :
At x = 1, y = 4
At x = 2 , y = 8
At x = 3, y = 12
So, it will become
[tex]y=kx[/tex], where k = 4 units.
So, it is linear graph.
The graph is continuous function as it does not break any where and it is unbroken line.
hence, the graph is A) Linear
The graph represents a B) Continuous function.
The graph shows the function f(x).
What is the function's average rate of change from x = 9 to x = 15?
Enter your answer in the box.
Answer:
3/2
Step-by-step explanation:
To find the rate of change
f(x2) - f(x1)
------------------ = rate of change
x2-x1
Looking at the graph
f(15) = 12
f(9) = 3
Substituting this into the equation
12-3
---------
15-9
9
------
6
3/2
The rate of change is 3/2
The average rate of change of a function from x = 9 to x = 15 is calculated by the slope of the secant line, which is (f(15) - f(9)) / (15 - 9). Specific function values are needed to perform this calculation.
Explanation:To calculate the function's average rate of change from x = 9 to x = 15, you can use the formula for the slope of the secant line between these two points on the graph of the function. This is given by the difference in the function values at these points divided by the difference in x-values:
Average Rate of Change = (f(15) - f(9)) / (15 - 9).
You would need the specific function values f(15) and f(9) in order to calculate this. If the function is linear, like the one represented by f(x) = 7x, you would substitute these x-values into the function to get f(15) = 7*15 and f(9) = 7*9, and then perform the calculation. However, without the actual function values, we cannot complete this calculation.
Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side ZX measures 4x – 2. Find the value of x.
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
In similar triangles, corresponding sides' ratio are equal.
Side AB corresponds to Side XYSide BC corresponds to Side YZSide CA corresponds to Side ZXWe can set up a ratio of [tex]\frac{SideAB}{Side XY}=\frac{SideCA}{Side ZX}[/tex]
Hence, we can write (and solve):
[tex]\frac{Side AB}{Side XY}=\frac{Side CA}{SideZX}\\\frac{2}{4}=\frac{x+7}{4x-2}\\2(4x-2)=4(x+7)\\8x-4=4x+28\\8x-4x=28+4\\4x=32\\x=\frac{32}{4}=8[/tex]
So, x = 8
what is the x and y intercept
8y=-9x-12
Answer:
X-intercept:(-4/3,0)
Y-intercept:(0,-3/2)
Step-by-step explanation:
The x-intercept is (-4/3, 0) and the y-intercept is (0, -3/2).
Explanation:To find the x-intercept of the equation 8y= -9x-12, we substitute y with 0 and solve for x. This gives us:
8(0) = -9x-12
0 = -9x-12
-9x = 12
x = -12/9
x = -4/3
Therefore, the x-intercept is (-4/3, 0).
To find the y-intercept, we substitute x with 0 and solve for y. This gives us:
8y = -9(0)-12
8y = -12
y = -12/8
y = -3/2
Therefore, the y-intercept is (0, -3/2).
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What are the real and complex solutions of 0=x^4+3x^2-4
Answer:
(2i,0) (-2i,0)
(1,0) (-1,0).
Step-by-step explanation:
The graph below shows that there are only 2 real solutions at x = 1 and x = - 1
Expressed as points, these two are (1,0) and (-1,0). However that is not the complete answer. There are 2 complex points.
y = x^4 + 3x^2 - 4
y = (x^2 - 1)(x^2 + 4)
These two binomials can be equated to 0
x^2 - 1 = 0x^2 = 1sqrt(x^2) = sqrt(1)x = +/- 1Expressed as points (1,0)(-1,0)================
x^2 + 4 = 0x^2 = - 4sqrt(x^2) = sqrt(-4)x = +/- 2 iExpressed as "points" these two can be written as (2i,0) (-2i,0)Daniel worked for 2/13 hours and earned $18.20.
How much would he make if he worked for 5 1/4 hours?
624.75
first get the numeric values simplified
2/13h=0.153h
so 18.20÷0.153=119
meaning he earned 119 dollars every hour
now you can multipy this number with 5.25 to get the answer which is 624.75 dollars
ASAP what is the value of a number raised to the power of 1?
Final answer:
The value of any number raised to the power of 1 is the number itself, as it implies a single multiplication of the number by 1.
Explanation:
The value of a number raised to the power of 1 is always the number itself. This is because an exponent represents how many times to multiply the number by itself. When the exponent is 1, you are simply multiplying the number by 1, which does not change its value.
For example:
51 = 5101 = 10-31 = -3PLZ DO I NEED ASAP
What is the equation of the line –3x–2y=30 in slope-intercept form? y = mx + b is slope-intercept form Enter your answer in the box.
Answer:
y = -3/2 x -15
Step-by-step explanation:
–3x–2y=30
To get the equation is slope intercept form y=mx+b, we need to solve for y
Add 3x to each side
–3x+3x–2y=3x+30
-2y = 3x+30
Divide by -2
-2y/-2 = 3x/-2 + 30 /-2
y = -3/2 x -15
The slope is -3/2 and the y interceot us -15
what is the value of the sum? Drag and drop the answer into the box to match the sum with its value. -3/8 + 5/16. Answer Choices----------- -11/16, -1/16, 1/16, 1/4, 11/16.
Which sequence is geometric and has `1/4` as its fifth term and `1/2` as the common ratio?
Answer:
4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....
Step-by-step explanation:
Fifth term (a₅) = [tex]\frac{1}{4}[/tex]
Common ratio (r) = [tex]\frac{1}{2}[/tex]
n = 5
The formula to find the [tex]n^{th}[/tex] term of a geometric sequence is
a₅ = a₁r⁽ⁿ⁻¹⁾
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(5-1)}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})^{(4)}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})*(\frac{1}{2})[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁* [tex]\frac{1*1*1*1}{2*2*2*2}[/tex]
=> [tex]\frac{1}{4}[/tex] = a₁*[tex](\frac{1}{16})[/tex]
Flip the sides of the equation
a₁*[tex](\frac{1}{16})[/tex] = [tex]\frac{1}{4}[/tex]
Multiply both sides by 16
a₁*[tex](\frac{1}{16})[/tex]*16 = [tex]\frac{1}{4}[/tex]*16
Cancelling out the 16's from the top and bottom of the left side
a₁ = [tex]\frac{16}{4}[/tex]
=> a₁ = 4
So, first term of the geometric sequence is 4.
Common ratio = [tex]\frac{1}{2}[/tex]
Second term = First term * Common ratio
= 4* [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
Third term = Second Term * Common ratio
= 2 * [tex]\frac{1}{2}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Fourth term = Third Term * Common ratio
= 1 * [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{2}[/tex]
Fifth term (given) = [tex]\frac{1}{4}[/tex]
So, the geometric sequence would be
4, 2, 1, [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex], .....
turn improper fraction into mixed number please help its easy
Answer:
2 1/2
Step-by-step explanation:
You divide and there are 2 two’s that can go into 5 with a remainder of 1
Answer: 2 1/2
Step-by-step explanation:
divide 5/2
you get 1 as a remainder and two at the top
2 1/2
Can someone help me
Answer:
The scale factor used was 1/2
hope this helped
Step-by-step explanation:
Caroline wants to give 8 equal size packets of flower seed to her friends .She has ½ pound of flowers seeds. How much will each packet of seeds weigh?
Answer:
16
Step-by-step explanation:
We want to divide 1/2 pound in 8 equal parts
1/2 dividend by 8/1 is the same as
1/2 multiplied by 1/8 =1•1/2•8=1/16
Each package will weigh 1/16 of a pound
Or 1 ounce since 1 pound = 16 oz