Answer:
The translation rule is (x , y) → (x - 12 , y - 4)
Step-by-step explanation:
Let us revise the translation of a point
If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y) ⇒ T (x , y) → (x + h , y)If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y) ⇒ T (x , y) → (x - h , y)If the point (x , y) translated vertically up by k units then its image is (x , y + k)→ (x + h , y) ⇒ T (x , y) → (x , y + k)If the point (x , y) translated vertically down by k units then its image is (x , y - k) ⇒ T (x , y) → (x , y - k)An object is translated from A (-6, -4) to A' (-18, -8)
∵ A is (-6 , -4)
∵ A' is (-18 , -8)
∴ x-coordinate = -6
∴ x'-coordinate = -18
- By using the translation rule above
∵ x' = x + h
∴ -18 = -6 + h
- Add 6 to both sides
∴ -12 = h
∴ h = -12
∵ h is a negative value
- That means A translated to the left 12 units
∴ The rule is (x , y) → (x - 12 , y)
∵ y-coordinate = -4
∴ y'-coordinate = -8
∵ y' = y + k
∴ -8 = -4 + k
- Add 4 to both sides
∴ -4 = k
∴ k = -4
∵ k is a negative value
- That means A down 4 units
∴ The rule is (x , y) → (x , y - 4)
The translation rule is (x , y) → (x - 12 , y - 4)
Give the approximate: square root 48
Final answer:
The approximate square root of 48 is found by locating it between the perfect squares of 36 (6²) and 49 (7²), leading to a closer estimation of about 6.9 when considering 48 as 16 * 3 and simplifying.
Explanation:
The question asks to find the approximate square root of 48. To do this, we first recognize that the exact square root of 48 is not a whole number, and therefore, we need to find two perfect squares between which 48 lies. The perfect squares closest to 48 are 49 (7²) and 36 (6²). Since 48 is closer to 49, we can estimate that the square root of 48 is slightly less than 7. A more refined method involves thinking of 48 as 16 * 3, which then gives us √16 * √3 = 4√3. Knowing that √3 is approximately 1.732, we can multiply this by 4 to get an approximation of 6.928. Therefore, a good approximation for the square root of 48 is approximately 6.9.
A hypothetical square grows so that the length of its diagonals are increasing at a rate of 8m/min. How fast is the area of the square increasing when the sides are 8m each.
Answer: The area of the square is increasing at a rate of 90.4 m2/min (square meters/minute)
Step-by-step explanation: Please see the attachments below
Answer:
The area of the square is increasing at 90.51m^2/min
Step by step explanation:
Given;
Change in diagonal length ∆d = 8m/min
Length l = 8m
When l = 8m
d^2 = 2l^2 = 2×8^2 = 128
d = √128
Area of a square = l^2 = (d^2)/2
d = diagonal
Change in area = ∆A = dA/dd
∆A = 2 × d/2 × ∆d = d×∆d
∆A = √128 × 8 = 90.51m^2/min
A rectangle or piece of paper has a width is 3 inches less than its link it is cut in half along a diagonal to create two congruent right triangles with areas of 44 in.²
The length and width of the rectangle is 11 in and 8 in respectively.
Step-by-step explanation:
Given,
The width of a rectangle is 3 in less than the length.
The area of each congruent right angle triangle = 44 in²
To find the length and width of the rectangle.
Formula
The area of a triangle with b base and h as height = [tex]\frac{1}{2}[/tex]bh
Now,
Let, the width = x and the length = x+3.
Here, for the triangle, width will be its base and length will be its height.
According to the problem,
[tex]\frac{1}{2}[/tex]×(x+3)×x = 44
or, [tex]x^{2} +3x = 88[/tex]
or,[tex]x^{2} +3x-88 = 0[/tex]
or, [tex]x^{2}[/tex]+(11-8)x-88 = 0
or, [tex]x^{2}[/tex]+11x-8x-88 =0
or, x(x+11)-8(x+11) = 0
or, (x+11)(x-8) = 0
So, x = 8 ( x≠-11, the length or width could no be negative)
Hence,
Width = 8 in and length = 8+3 = 11 in
A pilot flew his single-engine airplane 6060 miles with the wind from City A to above City B. He then turned around and flew back to City A against the wind. If the wind was a constant 3030 miles per hour, and the total time going and returning was 1.31.3 hours, find the speed of the plane in still air.
Answer: the speed of the plane in still air is 101.2 mph
Step-by-step explanation:
Let x represent the speed of the plane in still air.
The pilot flew his single-engine airplane 60 miles with the wind from City A to above City B. If the wind was a constant 30 miles per hour, it means that the total speed at which he flew the plane while going is (x + 30) mph.
Time = distance/speed
Time spent while going is
60/(x + 30)
He then turned around and flew back to City A against the wind. it means that the total speed at which he flew the plane while returning is (x - 30) mph.
Time spent while returning is
60/(x - 30)
If the total time going and returning was 1.31.3 hours, it means that
60/(x + 30) + 60/(x - 30) = 1.3
Cross multiplying, it becomes
60(x - 30) + 60(x + 30) = 1.3(x - 30)(x + 30)
60x - 1800 + 60x + 1800 = 1.3(x² + 30x - 30x - 900)
120x = 1.3x² - 1170
1.3x² - 120x - 1170 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1.3
b = - 120
c = - 1170
Therefore,
x = [- - 120 ± √(- 120² - 4 × 1.3 × - 1170)]/2 × 1.3
x = [120 ± √(14400 + 6080)]/2.6
x = [120 ± √20480]/2.6
x = (120 + 143.1)/2.6 or x = (120 - 143.1)/2.6
x = 101.2 or x = - 8.9
Since the speed cannot be negative, then x = 101.2 mph
what is the midpoint of the segment shown below -1 5 -6 -2
The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is calculated using the midpoint formula and is (-3.5, 1.5).
The question seems to be asking for the midpoint of a segment with given endpoints. However, the numbers provided (-1, 5, -6, -2) do not clearly define a specific segment in a conventional two-dimensional coordinate system. Typically, a line segment in two-dimensional space is represented by the coordinates of its endpoints, such as (x₁, y₁) and (x₂, y₂).
If we assume the numbers are pairs of coordinates, we could interpret them as the endpoints (-1, 5) and (-6, -2). To find the midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂), you use the midpoint formula: Midpoint M = [tex](\frac{x_1 + x_2}{ 2}, \frac{y_1 + y_2}{2})[/tex]
Applying this to the given points: M = [tex](\frac{-1 + (-6)}{ 2}, \frac{5 + (-2)}{ 2} = (\frac{-7}{ 2}, \frac{3 }{ 2})[/tex] = (-3.5, 1.5).
The midpoint of the segment with endpoints (-1, 5) and (-6, -2) is (-3.5, 1.5).
Is 0.424242424242 a rational or irrational number?
Answer:
Rational, 0.424242... = 42/99
Step-by-step explanation:
let x = 0.4242424242....
We can convert this to a fraction
100x = 42.424242....
100x - x = 42
99x = 42
x = 42/99 a rational number
Answer: 0.424242424242 is a rational number
Step-by-step explanation:
At a concession stand, five hot dogs and two hamburgers cost $9.25; two hot dogs and five hamburgers cost $10.00. Find the cost of one hot dog and the cost of one hamburger.
Answer:
hot dogs- $1.25
hamburgers- $1.50
Step-by-step explanation:
let hot dogs be x and hamburgers be y∀
five hot dogs and two hamburgers cost $9.25
5x + 2y = $9.25 (eq. 1)
5x=9.25-2y
divide both sides by 5x
x= 1.85-0.4 (insert this in eq. 2)
two hotdogs and five hamburgers cost $10.00
2x + 5y = $10.00 (eq. 2)
2×(1.85-0.4) +5y=10.00
3.7 - 0.8 + 5y = 10.00
-0.8+5y=10.00-3.7
4.2y=6.3
divide both sides by 4.2 to evaluate the variable
6.3 divided by 4.2
y=1.50
now find x
x=1.85-0.4×1.5
x=1.85-0.6
x= 1.25
twiddle dee dee types 22 words in 20 seconds what is her rate per hour
Answer: Twiddle dee dee can type 3960 words per hour.
Step-by-step explanation:
There are 3600 seconds in an hour.
3600 ÷ 20 = 180
Therefore, she/he can type 22 words 180 times during the hour.
22 · 180 = 3960
So, twiddle dee dee can type 3960 words per hour. (or 66 words per minute). This is my first answer, but I do hope this helps!
Her typing rate per hour is 3,960 words.
To determine Twiddle Dee Dee's typing rate per hour, we first need to convert the rate from words per second to words per hour. Twiddle Dee Dee types 22 words in 20 seconds. To find out how many words she types in one minute, we divide the number of seconds in a minute by the time it took her to type those 22 words:
60 seconds / 20 seconds = 3
Now we multiply this factor by the number of words:
22 words × 3 = 66 words per minute
Now to find the rate per hour, we multiply the words per minute by the number of minutes in an hour:
66 words/minute × 60 minutes/hour = 3,960 words/hour
Therefore, Twiddle Dee Dee's typing rate per hour is 3,960 words.
The perimeter of a rectangle is 64cm it’s width is 9cm what is its length
Answer:
The width is 23cm
Step-by-step explanation:
9*2 = 18
64-18 = 46
46/2 = 23
Does anyone know this?!
Answer:
i think b
Step-by-step explanation:
tell me if im wrong
13. You are at the top of a lighthouse that is 400 ft. Tall. You look down towards the ocean and see a whale located 700 ft. From the shore. What is the angle of depression from your position?
Answer:
29.7°
Step-by-step explanation:
In a right triangle representing the geometry of the problem, the side opposite the angle is the height of your observation (400 ft). The side adjacent to the angle is the distance from shore (700 ft).
You know the tangent ratio is ...
Tan = Opposite/Adjacent
so your angle of depression satisfies ...
tan(angle of depression) = (400 ft)/(700 ft)
Using the inverse function, we find ...
angle of depression = arctan(4/7) ≈ 29.745°
The angle of depression is about 29.7°.
Karissa has registered to win a new necklace from a raffle drawing. She purchased 9 out of the 150 tickets sold. What percent chance does Karissa have of winning the necklace
Answer:
6%
Step-by-step explanation:
we know that
To find out the percentage chance that Karissa has of winning the necklace, divide the number of tickets purchased by the total number of tickets
so
[tex]\frac{9}{150}=0.06[/tex]
Convert to percentage (multiply by 100)
[tex]0.06(100)=6\%[/tex]
How many centimeters are in x meters??
Answer:
Multiply by 100
Step-by-step explanation:
There are 100 centimeters in a meter, so multiply your value for meters by 100
100 i learned this before so if you have 2 meters there are 200 centimeters
A fish population in a lake decreases by 2% each year. What is the common ratio? (Write your answer as a decimal)
Answer:
the common ratio is 0.98.
Step-by-step explanation:
A fish population in a lake decreases by 2% each year. We are asked to find the common ratio.
The decrease of population of fish 2% annually means the population becomes next year 100% - 2% = 98%
Therefore, the common ratio would be 98%. Upon converting 98 percent to a decimal we will get,
98% = [tex]\frac{98}{100}=0.98[/tex]
Therefore, the common ratio or decay factor is 0.98.
Answer:
D. .98
Step-by-step explanation:
Just got it right on the test
2. What is 75% of 300?
Answer:6.25
Step-by-step explanation:divide 75 of 300
Answer:
210
Step-by-step explanation:
70% of 300
70%= 0.7
0.7*300
=210
Eli has saved $8 more than 1/3 of Angela's savings.If they each save $10 more Eli will have saved &4 more than Angela's savings.How much has Eli saved?
Answer:
Eli has saved $10
Step-by-step explanation:
Let us use the first letters of their names to represent them.
A for Angela and E for ELi
So, from the first statement, we can write out an equation: E = [tex]\frac{1}{3}[/tex]A + 8, that is, one-third of Angela's savings + $8 will give us Eli's savings
From the second statement, we can write out: E + 10 = (A + 10) + 4 which means that if $10 is added to both their savings, Eli will still have $4 more than Angela.
So, we can solve both equations;
Equation 1: E = [tex]\frac{1}{3}[/tex]A + 8
Equation 2: E + 10 = (A + 10) + 4; which can be rewritten as E + 10 = A + 14
and then E = A + 4
The two equations (in bold), can then be solved simultaneously.
Let us carry out this operation to eliminate the E: Subtract equation 1 from equation 2, so that;
A + 4 - ( [tex]\frac{1}{3}[/tex]A + 8) = E - E
[tex]\frac{2}{3}[/tex]A - 4 = 0
[tex]\frac{2}{3}[/tex]A = 4
A = 4 × [tex]\frac{3}{2}[/tex] = 6
So, if A is 6, and E = A + 4 (from equation 2, that means that E = 6 + 4 = 10
So, Eli has saved $10, while Angela has saved $6.
If we check what was said in the question about their savings, which is what we have represented using the equations, the answers can be confirmed.
Answer:
Eli has saved $10
Step-by-step explanation:
Let us denote Angela's saving by "x".
If Eli's saving is $8 more than one-third of Angela's saving, then Eli's saving is:
[(1/3 × x) + 8 = x/3 + 8]
We will make x/3 + 8 to have a common denominator:
x/3 + 8 = (x+24)/3
If Eli and Angela each saved $10 more, then their respective savings would have been:
(x+24)/3 + 10 for Eli
x+10 for Angela.
At this savings, Eli would have been $4 richer than Angela.
i.e [((x + 24)/3) + 10] - (x+10) = $4
We will make [(x+24)/3] + 10 to have common denominator.
(x + 24 + 30)/3
= (x + 54)/3
Then:
[(x+54)/3] - [(x+10)/1] = 4
[x+54-(3x+30)]/3 = 4/1
(-2x + 24)/3 = 4
cross multiply
-2x + 24 = 12
-2x = -12
x = -12/-2
x = 6
Since Eli's saving = x/3 + 8
Then his actual saving
= 6/3 + 8
= 2 + 8
= $10
If the original function () = 22 − 1 is shifted to the left 3 units to make the
function (), which expression would represent ()?
A horizontal translation is expressed by transforming
[tex]f(x)\mapsto f(x+k)[/tex]
If [tex]k[/tex] is positive, the function is translated to the left. If [tex]k[/tex] is negative, the function is translated to the right.
So, a 3-units left shift is given by [tex]k=3[/tex]. So you have
[tex]f(x)=2x^2-1 \implies f(x+3)=2(x+3)^2-1[/tex]
What is the area of the parallelogram?
Answer:
a=bh
Step-by-step explanation:
the answer is 70
im sorry if thats not right
Answer:
The answer to your question is Area = 70 cm²
Step-by-step explanation:
Data
height = 5 cm
base = 14 cm
side = 13 cm
To solve this problem just look for the formula and substitute the values. It is not necessary the length of the short side.
Formula
Area = base x height
-Substitution
Area = 14 x 5
-Result
Area = 70 cm²
Which ratio completes the probability distribution table?
Answer:
16/48
Step-by-step explanation:
When you look for a pattern from frequency to probability, it is clear that the frequency will become the numerator for the probability and the denominator will remain 48. This appears to be the rule of the probability distribution table, so using this established rule, we can use 16 as the numerator for the probability, and then remember that 48 is always the numerator, which gives you 16/48 in result.
Help me answer this please
Answer:
x=115 y=65
Step-by-step explanation:
You get 115 for X because angle x is vertical to 115 degrees.
You get 65 because y is supplementary to x, and 180-65=115.
Answer:
x = 115 degree and y = 65 degree
Step-by-step explanation:
Here we can see
x = 115 ( being vertically opposite angles )
So Now
x + y = 180 ( being linear pair )
115 + y = 180
y = 180 - 115
Therefore y = 65
Hope this helps
ayla is buying fence for two triangular sections of her garden. How much fence would she need for ΔDFG?
a. 80 ft
b. 82 ft
c. 85 ft
d. 83 ft
Answer:
80 ft
Step-by-step explanation:
Answer:
A. 80 ft.
Step-by-step explanation:
Triangle ABC is similar to Triangle DFG so they are proportional. 20/4=5; 25/5=5; so 7*5=35.
20+25+35=80
Amelie is making a recipe that uses 134 cups flour. She is making 212 times the original recipe. Amelie draws this model to represent the number of cups of flour she needs. How many cups of flour does Amelie need? Enter your answer as a mixed number in simplest form by filling in the boxes.
Amelie needs [tex]\( 28\frac{1}{4} \)[/tex] cups of flour for her recipe.
Amelie's recipe uses [tex]\( \frac{1}{4} \)[/tex] cups of flour and she's making [tex]\( 2\frac{1}{2} \)[/tex]times the original recipe. To find the total amount of flour needed, we multiply the two quantities:
1. Original Quantity of Flour: [tex]\( \frac{1}{4} \)[/tex] cups
2.Multiply by the Recipe Multiplier: [tex]\( 2\frac{1}{2} \times \frac{1}{4} \)[/tex]
3.Convert Mixed Number to Improper Fraction: [tex]\( 2\frac{1}{2} = \frac{5}{2} \)[/tex]
4. Perform the Multiplication:
[tex]\[ \frac{5}{2} \times \frac{1}{4} = \frac{5}{8} \][/tex]
Since Amelie is using [tex]\( \frac{5}{8} \)[/tex] of the grid and each square represents 1 cup, we can calculate the total cups by multiplying the number of squares in the grid by [tex]\( \frac{5}{8} \)[/tex]:
5.Total Squares in the Grid: [tex]\( 8 \times 4 = 32 \)[/tex]
6.Total Flour Needed:
[tex]\[ 32 \times \frac{5}{8} = 4 \times 5 = 20 \text{ cups} \][/tex]
However, since the grid seems to represent a multiplication model for the entire recipe amount, and we've been given that she's using[tex]\( 1\frac{3}{4} \)[/tex] cups and multiplying it by [tex]\( 2\frac{1}{2} \)[/tex], we should calculate as follows:
1. Convert [tex]\( 1\frac{3}{4} \)[/tex] cups to an improper fraction: [tex]\( \frac{7}{4} \)[/tex] cups.
2. Multiply[tex]\( \frac{7}{4} \) by \( 2\frac{1}{2} \)[/tex] (which is [tex]\( \frac{5}{2} \)[/tex] as an improper fraction):
[tex]\[ \frac{7}{4} \times \frac{5}{2} = \frac{35}{8} \][/tex]
3. Convert \( \frac{35}{8} \) to a mixed number:
[tex]\[ \frac{35}{8} = 4\frac{3}{8} \text{ cups} \][/tex]
Looking at the model provided, the total grid represents[tex]\( 2\frac{1}{2} \)[/tex]times the original recipe, which is [tex]\( 1\frac{3}{4} \)[/tex] cups of flour. The full grid has [tex]\( 8 \times 4 = 32 \)[/tex]squares, where each square represents [tex]\( \frac{1}{4} \)[/tex] cup of flour, giving us a total of 8 cups represented by the full grid. Since we want [tex]\( 2\frac{1}{2} \) or \( \frac{5}{2} \)[/tex] of this grid, we multiply:
[tex]\[ \text{Total flour} = 8 \times \frac{5}{2} = 4 \times 5 = 20 \text{ cups} \][/tex]
However, the discrepancy arises because the image shows a grid that is partially shaded, suggesting that we're looking at a portion of the full recipe's flour amount. Without clear visibility or description of the image, the precise interpretation of the grid is ambiguous.
Given this, the correct interpretation based on the model provided would be to calculate as follows:
[tex]\[ \frac{32}{4} \times \frac{5}{2} = 8 \times \frac{5}{2} = 20 \text{ cups} \][/tex]
If the grid is fully shaded, which means the entire grid is being used to represent the amount of flour, then Amelie needs 20 cups of flour for her recipe. If the grid is partially shaded and we are to use the fraction[tex]\( \frac{35}{8} \) (or \( 4\frac{3}{8} \) cups)[/tex] from the shaded portion, then the amount of flour needed would be [tex]\( 4\frac{3}{8} \)[/tex] cups. The mixed number in simplest form for the latter calculation would be [tex]\( 4\frac{3}{8} \)[/tex] cups.
complete question given below:
Amelie is making a recipe that uses 1 3/4 cups flour. She is making 2 1/2 times the original recipe.Amelie draws this model to represent the number of cups of flour she needs.How many cups of flour does Amelie need?Enter your answer as a mixed number in simplest form by filling in the boxes.
A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?
10 ft.
16 ft.
21 ft.
Answer:
The correct option is;
21 ft
Step-by-step explanation:
The equation of the parabolic arc is as follows;
y = a(x - h)² + k
Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)
We therefore have;
y = a(x - 20)² + 25
Whereby the parabola starts from the origin (0, 0), we have;
0 = a(0 - 20)² + 25
0 = 20²a + 25 → 0 = 400·a + 25
∴a = -25/400 = -1/16
The equation of the parabola is therefore;
[tex]y = (-\frac{1}{16})(x-20)^2 + 25[/tex]
To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28
Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;
[tex]y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft[/tex].
Final answer:
By creating and solving the equation of a parabola which matches the description of the arch, it is found that the height of the arch 8 feet from the center is 21 feet.
Explanation:
To determine how high the parabolic arch is 8 feet from each side of the center, we can use the properties of a parabola to set up an equation. The vertex of the parabola (the highest point) is in the center of the arch, so we know that the parabola is symmetrical about the vertex.
The general form of a parabolic equation is y = ax^2 + bx + c. In this scenario:
The vertex is at the origin (0,25).
The arch has a span (width) of 40 feet, so its x-intercepts, or roots, are at (-20,0) and (20,0).
To find the parabolic constant, a, we use the x-intercepts to establish the equation 0 = a(20)^2, which simplifies to a = -25/400 = -1/16 because we know that the height at the x-intercepts is 0.
The parabolic equation for the arch is then y = -1/16x^2 + 25. To find the height 8 feet from the center, we substitute x with 8:
y = -1/16(8)^2 + 25 = -1/16(64) + 25 = -4 + 25 = 21
Therefore, the arch is 21 feet high 8 feet from each side of the center.
The measure of angle 1 is 130°. 2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 4, 3, 2. Which other angle must also measure 130°? angle
The angle that must also measure 130° is angle 4.
Angle 4 must also measure 130°. When two lines intersect, the vertically opposite angles are congruent, meaning angle 1 and angle 4 are equal. Therefore, if angle 1 measures 130°, angle 4 must also measure 130°.
If angle 1 measures 130°, angle 3 must also measure 130°.
When two lines intersect, they form pairs of angles known as vertical angles or vertically opposite angles. These angles are congruent, meaning they have the same measure. The key property of vertical angles is that they are formed by opposite rays.
In the given scenario:
Angle 1 and angle 3 are vertically opposite angles because they are formed by the intersecting lines and share the same vertex.
Since angle 1 measures 130°, according to the properties of vertical angles, angle 3 must have the same measure.
This is a fundamental property of vertical angles: they are always congruent. Therefore, if angle 1 measures 130°, angle 3 must also measure 130°.
For complete question refer to image:
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what is the perimeter of triangle SOW
Answer:
2322
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
What is the 72nd term of arithmetic sequence-27,-11,5
Answer:
1109
Step-by-step explanation:
you can subtract the terms to see the difference between them
-11-(-27)=16
The sequence is increasing by 16
you can plug that 16 in the formula for d
a_n=a_1+(n-1)d
a_n=a_1+(n-1)16
n represents the term you want to find in this case the 72nd
a sub 1 is the first term of the sequence in this case -27
a_72=-27+(72-1)16
a_72=-27+(71)16
a_72=-27+1136
a_72=1109
The 72nd term of the given arithmetic sequence is 1109.
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
The given arithmetic sequence is -27, -11, 5...
The common difference of the arithmetic sequence is:
d = -11 - (-27)
d = 16
The nth term of an arithmetic sequence is:
aₙ = a₁ + (n-1)d
= -27 + (n-1)16
= -27 +16n -16
= 16n - 43
To find the 72nd term, substitute n = 72 into the above equation:
a₇₂ = 16(72) -43
a₇₂ = 1109
Hence, the 72nd term of the given arithmetic sequence is 1109.
Learn more arithmetic sequences here:
https://brainly.com/question/15412619
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Dan was thinking of a number. Dan halves the number and gets an answer of 18.8. Form an
equation with 2 from the information.
Answer: the equation is x/2=18.8
Step-by-step explanation: you start with x because that’s the number and you divide it by 2 because that’s the same as halving then you write =18.8.
Final answer:
To form the equation based on the information provided, use the fact that Dan halves the number and gets 18.8. Solve by applying basic algebra to find the original number Dan was thinking of.
Explanation:
Equation: Let the original number that Dan was thinking of be represented by x. Given that Dan halves the number and gets 18.8, we can form the equation:
x / 2 = 18.8
Solving for x: Multiply both sides by 2 to find that the original number Dan was thinking of is x = 18.8 x 2 = 37.6.
You have 4 reindeer, Bloopin, Balthazar, Gloopin, and Prancer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line
Answer:
P43=4!(4–3)!=241=24 24 possible choices
Step-by-step explanation:
There are four choices you can make for the lead reindeer. For each possible choice, there are then three remaining you can choose to fly second, making 4×3=12 choices for the lead pair. For each possible choice there are two remaining reindeer to take up the back position, making 12×2=24 choices for the team of three.
This type of problem is called a permutation problem, and we write Pnr for the number of ways of choosing r items from n possibilities when the order of the items matters. In this case we are choosing 3 reindeer from 4 possibilities, and the order they appear in the flying line does matter, so the answer we want is P43. The general formula is Pnr=n!(n−r)!. For the answer we are looking for we therefore have:
P43=4!(4–3)!=241=24
Brainliest?
what is 10/15 in simplest form?
Answer:
2/3
Step-by-step explanation:
Answer: 2/3
Step-by-Step:
divide 10 by 5 = 2, then divide 15 by 5 =3, so 2/3
What is the equation of the axis of symmetry?
Answer:
For a quadratic function in standard form, y=ax2+bx+c
the axis of symmetry is a vertical line x=−b2a .
Step-by-step explanation:
Hope this helps !