Answer:
64.9 inches
Step-by-step explanation:
3 * 7.8 = 23.4
5 * 9.2 = 46
23.4 + 46 = 64.9 inches
69.4 inches of string does susie have altogether.
What is Addition?
Addition (usually denoted by a plus sign +) is one of the four basic arithmetic operations, the other three being subtraction, multiplication, and division. Adding two integers gives the sum or sum of their values. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (ie "3 plus 2 equals 5").
In addition to counting items, addition can also be defined and performed without reference to specific objects, using instead abstractions called numbers, such as integers, real numbers, and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another branch of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces, and subgroups.
Addition has several important properties. It is commutative, which means that the order of the operands does not matter, and it is associative, which means that if you add more than two numbers, the order of addition does not matter (see Addition). Repeated addition of 1 is the same as counting (see successor function). Adding 0 does not change the number. Addition also follows predictable rules for related operations like subtraction and multiplication.
Here given,Susie has 8 pieces of string and 3 pieces are 7.8 inches long ,and 5 pieces are 9.2 inches long.
So,total length of 3 pieces of string [tex] = (3 \times 7.8) = 23.4 \: inches[/tex]
and total length of 5 pieces of string [tex] = (5 \times 9.2) = 46 \: inches[/tex]
So,Susie have altogether (23.4+46) = 69.4 inches string.
Addition related one more question:
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Factor
x + x²y + x³y²
and
10ℎ³????³ – 2h????² + 14hn
Write the augmented matrix for each system of equations.
9x-4y-5z=9
7x+4y-4z=-1
6x-6y+z=5
Answer:
a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
Step-by-step explanation:
The given system of equation is
[tex]9x-4y-5z=9[/tex]
[tex]7x+4y-4z=-1[/tex]
[tex]6x-6y+z=-5[/tex]
The coefficient matrix is :
[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]
The constant matrix is
[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]
The augmented matrix is obtained by combining the coefficient matrix and the constant matrix.
[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
The correct choice is A
A parking space is 20 feet long. A pickup truck is 6 yards long. How many inches longer is the parking space than the truck
1 yard = 3 feet.
Multiply the length of the truck by 3 to get total feet:
6 x 3 = 18 feet.
Subtract the length of the truck from the length of the parking space:
20 - 18 = 2 feet
1 foot = 12 inches.
Multiply 2 feet by 12:
2 x 12 = 24 inches longer.
Example 5 suppose that f(0) = −8 and f '(x) ≤ 9 for all values of x. how large can f(3) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 3] . there exists a number c such that f(3) − f(0) = f '(c) − 0 so f(3) = f(0) + f '(c) = −8 + f '(c). we are given that f '(x) ≤ 9 for all x, so in particular we know that f '(c) ≤ . multiplying both sides of this inequality by 3, we have 3f '(c) ≤ , so f(3) = −8 + f '(c) ≤ −8 + = . the largest possible value for f(3) is .
[tex]f'(x)[/tex] exists and is bounded for all [tex]x[/tex]. We're told that [tex]f(0)=-8[/tex]. Consider the interval [0, 3]. The mean value theorem says that there is some [tex]c\in(0,3)[/tex] such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]
Since [tex]f'(x)\le9[/tex], we have
[tex]\dfrac{f(3)+8}3\le9\implies f(3)\le19[/tex]
so 19 is the largest possible value.
Given a differentiable function with f(0) = -8 and f'(x) ≤ 9 for all x, we use the Mean Value Theorem to find that f(3), at its largest, can be 1.
Explanation:In this mathematics problem, we are given that f is a differentiable function with f(0) = -8 and its derivative f'(x) ≤ 9 for all x. We aim to calculate the possible maximum value of f(3). To do this, we apply the Mean Value Theorem for the interval [0, 3]. By this theorem, there exists a number 'c' in this interval such that the derivative at that point is equal to the slope of the secant line through the points (0, f(0)) and (3, f(3)). Thus, we get the equation: f(3) - f(0) = f'(c). Rearranging this, we get f(3) = f(0) + f'(c). Substituting the given values, f(3) = -8 + f'(c).
Since we know f'(x) ≤ 9 for all x, this means f'(c) ≤ 9 as well. Replacing this in the equation we get f(3) ≤ -8 + 9 = 1. Hence, the largest possible value for f(3) is 1.
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One angle of a triangle measures 60°. The other two angles are in a ratio of 7:17. What are the measures of those two angles?
Answer:
35° and 85°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Since one angle = 60° then the sum of the other 2 angles = 120°
Sum the parts of the ratio 7 + 17 = 24 parts, hence
[tex]\frac{120}{24}[/tex] = 5° ← value of 1 pat of the ratio, hence
7 parts = 7 × 5° = 35°
17 parts = 17 × 5° = 85°
note that 60° + 35° + 85° = 180°
Use the trigonometric subtraction formula for sine to verify this identity: sin((π / 2) – x) = cos x
Answer:
Step-by-step explanation:
[tex]sin (\frac{\pi}{2} - x) = cos x \\\\ sin (a - b) = sin a.cos b - sin b.cos a \\\\ sin (\frac{\pi}{2} - x) = sin \frac{\pi}{2}.cos x - sin x.cos \frac{\pi}{2} \\\\ sin \frac{\pi}{2} = 1; cos \frac{\pi}{2} = 0 \\\\ sin (\frac{\pi}{2} - x) = 1.cos x - sin x.0 \\\\ sin (\frac{\pi}{2} - x) = cos x[/tex]
I hope I helped you.
By substituting a = π/2 and b = x into the trigonometric subtraction formula and considering that sin(π / 2) equals 1 and cos(π / 2) equals 0, we can verify the identity sin((π / 2) – x) = cos x
Explanation:The question asks us to use the trigonometric subtraction formula for sine to verify the identity: sin((π / 2) – x) = cos x. From the trigonometric subtraction formulas, we know that sin(a - b) = sin a cos b - cos a sin b.
In this case, a = π/2 and b = x. Substituting these values into the formula, we ge: sin((π / 2) - x) = sin(π / 2) cos x - cos(π / 2) sin x.
Since sin(π / 2) equals 1 and cos(π / 2) equals 0 (from the Unit Circle in trigonometry), our equation simplifies to: sin((π / 2) - x) = 1 * cos x - 0 * sin x, which further simplifies to sin((π / 2) - x) = cos x.
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The ratio of petunias to geraniums in the greenhouse was 15 to 2. Combined there was 1020. How many geraniums were in the greenhouse.
in short, we simply split the total amount by the given ratio, so we'll split or divide 1020 by (15 + 2) and then distribute accordingly.
[tex]\bf \cfrac{petunias}{geraniums}\qquad 15:2\qquad \cfrac{15}{2}~\hspace{7em}\cfrac{15\cdot \frac{1020}{15+2}}{2\cdot \frac{1020}{15+2}}\implies \cfrac{15\cdot \frac{1020}{17}}{2\cdot \frac{1020}{17}} \\\\\\ \cfrac{15\cdot 60}{2\cdot 60}\implies \cfrac{900}{120}\implies \stackrel{petunias}{900}~~:~~\stackrel{geraniums}{120}[/tex]
The total number of geraniums in the greenhouse is 120. This was determined by calculating the value of each 'part' in the provided petunia to geranium ratio and then multiplying the number of geranium 'parts' by this value.
Explanation:The question provides a ratio of petunias to geraniums in the greenhouse, which is 15:2. This is the same as saying for every 15 petunias, there are 2 geraniums. If you combine the parts of the ratio, you get a total of 17 parts (15 petunias + 2 geraniums). We know that the total number of flowers in the greenhouse is 1020.
Now, we'll figure out what each 'part' is equal to in the real world. To do that, we divide the total number of flowers by the total number of parts, so 1020 ÷ 17 = 60. This tells us each 'part' in our ratio is equal to 60 flowers.
From there, since we need to find the number of geraniums, we multiply the number of geranium 'parts' by the value of each 'part'. So, the number of geraniums in the greenhouse is 2 (The geranium 'parts') x 60 = 120 geraniums.
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Find three consecutive even integers that sum up to -72.
Answer:
-26, -24 and -22Step-by-step explanation:
[tex]n,\ n+2,\ n+4-\text{three consecutive even integers}\\\\\text{The equation:}\\\\n+(n+2)+(n+4)=-72\\\\n+n+2+n+4=-72\qquad\text{combine like terms}\\\\3n+6=-72\qquad\text{subtract 6 from both sides}\\\\3n+6-6=-72-6\\\\3n=-78\qquad\text{divide both sides by 3}\\\\\dfrac{3n}{3}=-\dfrac{78}{3}\\\\n=-26\\\\n+2=-26+2=-24\\\\n+4=-26+4=-22[/tex]
Help pleaseee!!! (Photo attached)
Answer:
length of base is 10
Step-by-step explanation:
The area of the entire firgure is 1600 cm^2. There are 4 equal sized pennants, so each pennant is 1600/4 = 400
the bottom pennant has area 400 and is triangular shaped. the area of a triangle is 1/2 b h.
A = 1/2 b h given height is 80 and area is 400. plug these values in
400 = 1/2 b (80)
400 = 40 b divide both sides by 40
b = 10
Elmer body skateboard ramp for his son he wants to surprise him with it so he wants to wrap the ramp with special paper what is the minimum amount of wrapping paper he will need to wrap the ramp.
Answer:
480 feet
Step-by-step explanation:
Dana walks 3/4 miles in 1/4 hours. What is dana's walking rate in miles per hour?
Dana’s waking rate in miles per hour is 3 mph.
I did 3/4 x 4 = 3 because she walked 1/4 a mile and I needed to figure out the miles per one whole hour.
I hope this made sense and helped you.
help
Which expression is equivalent to 8(a-6)
a. 8a-48
b. 2a
c. 8a-6
d. 48a
The correct answer would be A.
A.
You can distribute the 8
Distribute 8 to a and multiply them = 8a
Distribute 8 to -6 and multiply them = -48
= 8a-48
You randomly choose one of the tiles. Without replacing the first tile. What is the event of the compound event? Write your answer as a fraction or percent rounded to the nearest tenth. 20 is the number of
Answer:
87777777777777777777777777
Step-by-step explanation:
10+(2x3)2/4x1/2 3 zzzzzzzzzzzzzzzzz
Answer: 233/23
Step-by-step explanation:
A cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddie can travel if he has $15 to spend.
Answer:
I think it's 53 miles
Step-by-step explanation:
After flat fee of $1.75 leaves him $13.25. Then use the remainder to calculate miles. Each dollar allows 4 miles × 13 = 52+1=53
The inequality is:
[tex]1.75+0.25x\leq 15[/tex]
The solution of the inequality is:
[tex]x\leq 53[/tex]
Step-by-step explanation:Let Eddie could travel x miles.
It is given that:
A cab charges $1.75 for the flat fee and $0.25 for each mile.
This means that the fee charged by Eddie if he travels x miles excluding the flat fee is:
$ 0.25x
Total amount the cab will charge Eddie is:
1.75+0.25x
Also, it is given that:
He has only $ 15 to spend this means that he can spend no more than 15 on riding in a cab.
Hence, the inequality is given by:
[tex]1.75+0.25x\leq 15[/tex]
Now on solving the inequality i.e. finding the possible values of x from the inequality.
We subtract both side of the inequality by 1.75 to obtain:
[tex]0.25x\leq 13.25[/tex]
Now on dividing both side of the inequality by 0.25 we get:
[tex]x\leq 53[/tex]
Hence, Eddie could travel less than or equal to 53 miles .
Ava started a savings account with $500 after 6 months her savings account balance was $731 find the rate of change
Answer:
$38.50/mo
Step-by-step explanation:
Rate of change = change in balance/time.
Change in balance = $731 - $500 = $231
Rate of change = $231/6 mo = $38.50/mo
Answer:
31.60%
Step-by-step explanation:
(731−500)÷731=0.3160
0.3160×100=31.60%
Hope it helps!
If 5 bags of apples weigh 12 1/7 pounds, how many pounds would you expect 1 bag of apples to weigh?
Answer:
2 and 3/7 pounds
Step-by-step explanation:
Convert the mixed number to an improper fraction
12 1/7 becomes 85/7
This represents 5 bags, so divide it by 5 to see what one bag should weigh...
(85/7)/5 becomes (85/7)/(5/1)
which becomes
(85/7)*(1/5) (division is the same as multiplying by the reciprocal)
85/35
17/7 (reduce the fraction by factoring out a 5 from top and bottom)
2 and 3/7 pounds
Please help! I'll mark brainiest!
Match the x-coordinates with their corresponding pairs of y-coordinates on the unit circle.
Answer:
Step-by-step explanation:
2 on top goes to last on the bottom or b goes to d
1st one one top goes to the 2nd one on bottom or a goes to b
last one on top goes to the third one on bottom or d goes to c
The last two witch are 3rd on top and first one together
Hope this helped it took me a long time :)
The x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.
[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex][tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex][tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex][tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]What is the equation of the circle with radius r units, centered at (x,y) ?If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
A unit circle refers to a circle with unit radius (r = 1 unit) and positioned at center ( coordinates of origin = (h,k) = (0,0))
Thus, the equation of unit circle would be:
[tex]x^2 + y^2 =1[/tex]
Getting expression for y in terms of x,
[tex]x^2 + y^2 =1\\\\y = \pm \sqrt{1 - x^2}[/tex]
Using this equation to evaluate x for all given y:
Case 1: y = ±√5/3[tex]\pm \dfrac{\sqrt{5}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{5}{9} = 1 - x^2\\\\x^2 = \dfrac{4}{9}\\\\x = \pm \dfrac{2}{3}[/tex]
From the options available, the fourth block seems valid.
Thus, we get:
[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex]
Case 2: y = ±√7/3[tex]\pm \dfrac{\sqrt{7}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{7}{9} = 1 - x^2\\\\x^2 = \dfrac{2}{9}\\\\x = \pm \dfrac{\sqrt{2}}{3}[/tex]
From the options available, the fourth block seems valid.
Thus, we get: [tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex]
Case 3: y = ±3/5[tex]\pm \dfrac{3}{5} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{9}{25} = 1 - x^2\\\\x^2 = \dfrac{16}{25}\\\\x = \pm \dfrac{4}{5}[/tex]
From the options available, the fourth block seems valid.
Thus, we get: [tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex]
Case 4: y = ±2√2/3[tex]\pm \dfrac{2\sqrt{2}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{8}{9} = 1 - x^2\\\\x^2 = \dfrac{1}{9}\\\\x = \pm \dfrac{1}{3}[/tex]
From the options available, the fourth block seems valid.
Thus, we get: [tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]
Thus, the x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.
[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex][tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex][tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex][tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]Learn more about equation of a circle here:
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Find the exact value of sine, cosine, and tangent of A and T for each triangle.
Answer:
See below
Step-by-step explanation:
14)
14² = 8² + TV²
196 = 64 + TV²
TV² = 132
TV =√132 = √(4 × 33) = 2√33
sinA = TV/AT = (2√33)/14 = √33/7
cosA = AV /AT = 8/14 = 2/7
tanA = TV/AV = (2√33)/8 = √33)/4
sinT = AV/AT = 8/14 = 4/7
cosT = TV/AT = (2√33)/14 = √33/7
tanT = AV/TV = 8/(2√33) = (4√33)/33
16)
6² = 3² + GT²
36 = 9 + GT ²
GT² = 27
GT = √27 = √(9 × 3) = 3√3
sinA = GT/AT = (3√3)/6 = √3/2
cosA = AG/AT = 3/6 = ½
tanA = GT/AG = (3√3)/3 = √3
sinT = AG/AT = 3/6 = ½
cosT = GT/AT = (3√3)/6 = √3/2
tanT = AG/GT = 6/(3√3) = (2√3)/3
18)
13² = 8² + TX²
169 = 64 + TX²
TX² = 105
TX = √105
sinA = TX/AT = (√105)/13
cosA = AX/AT = 8/13
tanA = TX/AX = (√105)/8
sinT = AX/AT = 8/13
cosT = TX/AT = (√105)/13
tanT = AX/TX = 8/(√105) = (8√105)/105
The trail is 2982 miles long.It begins in city A and ends in city B.Manfred has hiked 2/7 of the trail before.How many miles has he hikes?
Answer:
852
Step-by-step explanation:
what is the best approximation of the area of a circle with a diameter of 17 meters? Use 3.14 to approximate pi.
a. 53.4 m2
b. 106.8 m2
c. 226.9 m2
d. 907.5 m2
[tex]\bold{Hey\ there!}[/tex]
[tex]\bold{What\ is\ the\ best\ approximation\ of\ the\ area\ of\ a\ circle\ with\ a\ diameter\ of\ 17\ meters.}[/tex] [tex]\bf{Use\ 3.14\ to \ approximate\ pi\}[/tex][tex]\bold{Firstly,\ highlight\ your\ key\ terms:} \\ \bold{\bullet \ \underline{Approximation\ of\ the\ area\ of\ a \ circle\ with\ a\ diameter\ of\ 17.}}}\\ \\ \bold{\bullet\ \underline{Use\ 3.14\ to\ approximate\ pi}}[/tex][tex]\bold{17\times3.14=53.38}[/tex][tex]\bold{If\ we're\ rounding\ upward\ then\ your\ answer\ would\ be\ A.53.4m^2}[/tex][tex]\boxed{\boxed{\bold{Answer:A).53.4m^2}}}}\checkmark[/tex][tex]\bold{Good\ luck\ on\ your\ assignment\ \& enjoy\ your\ day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Answer:
The answer is c 226.9 m2
Step-by-step explanation:
Hope this helps
What value of k causes the terms 7, 6k, 22 to form an arithmetic sequence?
29/12
5/4
11/6
5/2
Answer: first option
Step-by-step explanation:
To form an arithmetic sequence, you have that for the sequence [tex]7,6k,22[/tex]:
[tex]6k-7=22-6k[/tex]
Therefore, to calculate the value of k to form an arithmetic sequence, you must solve for k, as following:
- Add like terms:
[tex]6k+6k=22+7\\12k=29[/tex]
- Divide both sides by 12. Then you obtain;
[tex]k=\frac{29}{12}[/tex]
Answer:
[tex]k=\frac{29}{12}[/tex]
Step-by-step explanation:
The given sequence is 7, 6k, 22.
For this to be an arithmetic sequence, there must be a common difference.
[tex]6k-7=22-6k[/tex]
Group similar terms;
[tex]6k+6k=22+7[/tex]
Simplify;
[tex]12k=29[/tex]
Divide by 12
[tex]k=\frac{29}{12}[/tex]
The height of a wooden pole, h, is equal to 20 feet. A taut wire is stretched from a point on the ground to the top of the pole. The distance from the base of the pole to this point on the ground, b, is equal to 15 feet.
What is the length of the wire, l?
A. 625 feet
B. 20 feet
C. 13 feet
D. 25 feet
ANSWER
D. 25 feet
EXPLANATION
The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.
According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.
Let the hypotenuse ( the length of the ) taught wire be,l.
Then
[tex] {l}^{2} = {h}^{2} + {b}^{2} [/tex]
[tex]{l}^{2} = {20}^{2} + {15}^{2} [/tex]
[tex]{l}^{2} = 400 + 225[/tex]
[tex]{l}^{2} = 625[/tex]
[tex]l= \sqrt{625} = 25ft[/tex]
Answer:
25
Step-by-step explanation:
Which is the definition of a line segment?
a.a figure formed by two rays that share a common endpoint
b.the set of all points in a plane that are a given distance away from a given point
c.a part of a line that has one endpoint and extends indefinitely in one direction
d.a part of a line that has two endpoints
Answer:
The answer is d
Step-by-step explanation:
A line segment is a portion of an infinite line separated by two end points
9 minutes left to finish this!! I need help!
Joey is 17 years older than his sister Pat. In 6 years, Joey will be 7 more than twice Pat’s age then. How old are Joey and Pat today?
Answer:
p = 4
j = 21
Step-by-step explanation:
Joey = j
Pat = p
j = p + 17
(j+6) = 2*(p + 6) + 7 Simplify this. Remove the brackets.
j + 6 = 2p + 12 + 7 combine like terms
j + 6 = 2p + 19 Subtract 6 from both sides
j +6-6 = 2p +19-6
j = 2p + 13
================
Equation j = 2p + 13 and j = p + 17
2p + 13 = p + 17 Subtract p from both sides
2p-p+13 =p-p + 17
p + 13 = 17 Subtract 13 from both sides
p = 17-13
p = 4
============
j = p + 17
j = 4 + 17
j = 21
Answer:
Joey is 21; Pat is 4
Step-by-step explanation:
The problem statement supports two equations in Joey's age (j) and Pat's age (p):
j - p = 17
(j +6) -2(p +6) = 7
Subtracting the second equation from the first, we have ...
(j -p) -((j +6) -2(p +6)) = (17) -(7)
p +6 = 10 . . . . . simplify
p = 4 . . . . . . . . . subtract 6
J = 17 +4 = 21
Joey is 21; Pat is 4.
Evaluate each log without a calculator
[tex]log_{243^{27} }[/tex]
[tex]log_{25} \frac{1}{5}[/tex]
QUESTION 1
The given logarithm is
[tex]\log_{243}(27)[/tex]
Let [tex]\log_{243}(27)=x[/tex].
We rewrite in exponential form to get;
[tex]27=243^x[/tex]
We rewrite both sides of the equation as an index number to base 3.
[tex]3^3=3^{5x}[/tex]
Since the bases are the same, we equate the exponents.
[tex]3=5x[/tex]
Divide both sides by 5.
[tex]x=\frac{3}{5}[/tex]
[tex]\therefore \log_{243}(27)=\frac{3}{5}[/tex]
QUESTION 2
The given logarithm is
[tex]\log_{25}(\frac{1}{5} )[/tex]
We rewrite both the base and the number as power to base 5.
[tex]\log_{5^2}(5^{-1})[/tex]
Recall that: [tex]\log_{a^q}(a^p)=\frac{p}{q} \log_a(a)=\frac{p}{q}[/tex]
We apply this property to obtain;
[tex]\log_{5^2}(5^{-1})=\frac{-1}{2}\log_5(5)=-\frac{1}{2}[/tex]
A right triangle has side lengths that are consecutive integers and has a perimeter of 12 ft. What are the angles of the triangle
Answer:
The 3 angles are 36.87, 53.13 and 90 degrees.
Step-by-step explanation:
This right triangle ABC has sides 3, 4 and 5 units.
To find the angles:
sin A - 3/5 gives m < A = 36.87 degrees
sin B = 4/5 gives m < B = 53.13 degrees.
Algebra !! Please help, I have been stuck on this for a long time.
Answer:
x+3
Step-by-step explanation:
Factor x² + 6x + 9 = (x+3)(x+3)
Factor x² + 5x + 6 = (x+3)(x+2)
We can see that (x+3) is the LCM since it goes into x² + 6x + 9 and
x² + 5x + 6
write an explicit formula formula for the sequence 2, 8, 14, 20, 26,...
a. a_n= 2n-2
b. a_n= 2n+2
c. a_n=4n+2
d. a_n = 6n-4
Answer:
d. a_n = 6n - 4.
Step-by-step explanation:
The common difference (d) is 8-2 = 14-8 = 20-14 = 26-20 = 6.
This is an Arithmetic Sequence with the first term (a1) is 2.
The general form of the explicit formula is a_n = a1 + d(n - 1) so this sequence has the formula:
a_n = 2 + 6(n - 1)
a_n = 2 + 6n - 6
a_n = 6n - 4.
The sequence is an illustration of an arithmetic sequence.
The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
We have:
[tex]a_1 = 2[/tex] -- the first term
Next, we calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
So, we have:
[tex]d = 8 -2[/tex]
[tex]d = 6[/tex]
The explicit formula is calculated using:
[tex]a_n = a_1 + (n - 1)d[/tex]
So, we have:
[tex]a_n =2 + (n - 1) \times 6[/tex]
Open bracket
[tex]a_n = 2 + 6n - 6[/tex]
Collect like terms
[tex]a_n = 6n - 6 + 2[/tex]
[tex]a_n = 6n - 4[/tex]
Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
Read more about arithmetic sequence at:
https://brainly.com/question/18109692
An airplane's altitude changes -378 feet over 7 minutes. What was the mean change of altitude in feet per minute?
The mean altitude will be -54 per minute
Step-by-step explanation:We are given with altitude change as -378 feet over 7 minutes
Now
We need feet per minute
So -378 / 7 will give us the altitude change per minute
-378 / 7 = -54
Therefore the mean change of altitude in feet per minute is -54 per minute