What value of x would make the expression below equal to 8? Photo provided! 20points!
Answers
For this case, we must find the value of "x" so that the given expression is equal to 8.
That is to say:
[tex](\sqrt [5] {8 ^ 3}) ^ x = 8[/tex]
We apply "ln" to both sides of the equation to remove the exponent variable:
[tex]ln ((\sqrt [5] {8 ^ 3}) ^ x) = ln (8)\\xln (\sqrt [5] {8 ^ 3}) = ln (8)\\xln (\sqrt [5] {512}) = ln (8)[/tex]
We rewrite 512 as:
[tex]512 = 32 * 16 = 2 ^ 5 * 16\\xln (\sqrt [5] {2 ^ 5 * 16}) = ln (8)[/tex]
By definition of power properties we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]xln (2 \sqrt [5] {16}) = ln (8)[/tex]
We clear x:
[tex]x = \frac {ln (8)} {ln (2 \sqrt [5] {16})}[/tex]
In decimal form, [tex]x = 1.6[/tex] periodic number
ANswer:
[tex]x = \frac {ln (8)} {ln (2 \sqrt [5] {16})}\\x = 1.6\ periodic\ number[/tex]
Related Questions
Which of the following is equal to 4.6?
A. 1.6+(3×4)−2÷2
B. 1.6+3×4−2÷2
C. [1.6+(3×4)]−(2÷2)
D. (1.6+3)×(4−2)÷2
Answers
Answer: D
Step-by-step explanation:
PEMDAS.
1.6+3=4.6
4.6x2 = 9.2
9.2/2 = 4.6
Answer:D
Step-by-step explanation:
Given that (x,y)=(5,10), find r
Answers
ANSWER
[tex]r = 5 \sqrt{5 } [/tex]
EXPLANATION
Given that (x,y)=(5,10), we want to find r.
We use the relation:
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
We substitute x=5 and y=10 into the formula to get,
[tex]r = \sqrt{ {5}^{2} + {10}^{2} } [/tex]
This implies that,
[tex]r = \sqrt{ 25+ 100 } [/tex]
[tex]r = \sqrt{125} [/tex]
[tex]r = 5 \sqrt{5 } [/tex]
Given: EFGH inscribed in k(O) m∠FHE = 45°, m∠EGH = 49° Find: m∠FEH
Answers
Answer:
[tex]m<FEH=86\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
step 1
Find the measure of arc EF
[tex]m<FHE=\frac{1}{2}(arc\ EF)[/tex]
we have
[tex]m<FHE=45\°[/tex]
substitute
[tex]45\°=\frac{1}{2}(arc\ EF)[/tex]
[tex]arc\ EF=90\°[/tex]
step 2
Find the measure of arc EH
[tex]m<EGH=\frac{1}{2}(arc\ EH)[/tex]
we have
[tex]m<EGH=49\°[/tex]
substitute
[tex]49\°=\frac{1}{2}(arc\ EH)[/tex]
[tex]arc\ EH=98\°[/tex]
step 3
Find the measure of arc FGH
[tex]arc\ FGH=360\°-(arc\ EH+arc\ EF)[/tex]
substitute the values
[tex]arc\ FGH=360\°-(98\°+90\°)[/tex]
[tex]arc\ FGH=172\°[/tex]
step 4
Find the measure of angle FEH
[tex]m<FEH=\frac{1}{2}(arc\ FGH)[/tex]
we have
[tex]arc\ FGH=172\°[/tex]
substitute
[tex]m<FEH=\frac{1}{2}(172\°)=86\°[/tex]
what is the inverse of y=cos(x-pi/2)
Answers
Answer:
[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]y=\cos(x-\frac{\pi}{2})[/tex]
To find the inverse of this function, we interchange x and y.
[tex]x=\cos(y-\frac{\pi}{2})[/tex]
Take the inverse cosine of both sides to obtain;
[tex]\cos^{-1} x=y-\frac{\pi}{2}[/tex]
[tex]\cos^{-1} x+\frac{\pi}{2}=y[/tex]
Therefore the inverse of the given cosine function is;
[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex] where [tex]-1\le x\le 1[/tex]
Answer:
the answer is B
y=tanx- pie/2
The width of a rectangle is 12 cm less than the length. The area is 64cm^2 find the length and width. Use quadratic equations by factoring.
Answers
Answer:
length=16, width=4
Step-by-step explanation:
Use l as length and make an equation:
64 = x*(x-12)
Solve using quadratics, x=16.
Subtract 12 and get 4.
I need help with this USA TEST PREP question
Answers
Answer:
The Answer is C
Step-by-step explanation:
The volume of the cylinder increases by a factor of 25 when the radius is increased by a factor of 5.
The volume of a cylinder is given by the formula:
Volume = π * (radius^2) * height
If the radius is increased by a factor of 5, the new radius is 5 times the original radius. Let's call the original radius "r" and the new radius "5r." The height remains the same.
Now, let's calculate the new volume with the increased radius:
New Volume = π * (5r)^2 * height
New Volume = π * 25r^2 * height
To find the effect on the volume, we can compare the new volume to the original volume:
Effect on Volume = (New Volume) / (Original Volume)
Effect on Volume = (π * 25r^2 * height) / (π * r^2 * height)
The π, height, and r^2 terms cancel out:
Effect on Volume = (25r^2) / (r^2)
Effect on Volume = 25
So, the volume of the cylinder increases by a factor of 25 when the radius is increased by a factor of 5.
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9. Which of the following is the representation of a decimal number? A. 1/2 B. 23 C. 33/10 D. .25
Answers
Answer:
B because there is a dot in front of the 25 which is also known as a decimal point.
For this case we have that by definition, a decimal number is a number that is composed of a whole part, which can be zero, and by another lower than the unit, separated from the whole part by a point.
Examples:
0.05
1.76
According to the options given, we have:
A. [tex]\frac {1} {2},[/tex] it is a fraction
B. 23, is a whole number
C.[tex]\frac {33} {10}[/tex], it is a fraction
D. 0.25, is a decimal number.
Answer:
Option D
A parabola opening upward shifted 7 units rights and 4 units down
Answers
Answer:
y + 4 = a(x - 7)^2
Step-by-step explanation:
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
and if we start with the simplest case, y = a(x)^2 and translate its graph 7 units to the right and 4 units down, we get y - {-4] = a(x - 7)^2, or
y + 4 = a(x - 7)^2
The answer is y + 4 = a(x - 7)^2.
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
And if we start with the simplest case,
y = a(x)^2 and
translate it Into 7 units to the right and 4 units down,
we get
y - {-4] = a(x - 7)^2
then we get the equation is y + 4 = a(x - 7)^2.
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Which type of sequence is represented by the given table?
x
1
2
3
4
y
4
-9.6
23.04
-55.296
A.
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
B.
The table represents an arithmetic sequence because the successive y-values have a common difference of -17.
C.
The table represents a geometric sequence because the successive y-values have a common ratio of 0.4.
D.
The table represents an arithmetic sequence because the successive y-values have a common difference of 4.2.
Answers
Answer:
A.
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
Step-by-step explanation:
A geometric sequence, with a first term a and common ratio r, is generally represented as;
[tex]a,ar,ar^{2},ar^{3},ar^{4},............ar^{n}[/tex]
The first term refers to the first number that appears in the sequence. The common ratio is the constant that multiplies a preceding value to obtain the successive one. That is, to obtain [tex]ar^{2}[/tex] from [tex]ar[/tex] we multiply [tex]ar[/tex] by the common ratio r.
In the table given the y-values are as follows;
4, -9.6, 23.04, -55.296
To obtain the common ratio we simply divide each value by the preceding one;
(-9.6)/4 = -2.4
23.04/(-9.6) = -2.4
(-55.296)/23.04 = -2.4
Since the sequence of numbers has a common ratio then it qualifies to be a geometric sequence. Thus, the table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
Answer:
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4
What is 265,200 rounded to the nearest hundred thousand
Answers
265,000
Hope this helps!
Because the number in the ten thousands place is over 4, it’s going to turn the 2 in the hundred thousands place into a 3, making the answer 300,000
What is the domain of the function?
y= sqrt 5x-10
Answers
I don't know if this will help but I found this on YAHOO!
Answer: Domain of definition of a function is the set of numbers which the variable attains and for which the function is defined.
Step-by-step explanation:
f(x) = sqrt (5x-10)
Here x can have value equal to any real number >=2 because if x attains value less that 2, 5x-10 becomes negative and sqrt(5x-10) has no real value.
therefore the domain of the function f(x) is (2, infinity) inclusive of 2.
The domain of the above function is (2, ∞) .
What is a Domain ?Let y = f(x) be a function with an independent variable x and a dependent variable y.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.
For the given function [tex]y = \sqrt{5x-10[/tex]
The domain will be the value that satisfies the function and produces a value of y
For any value less than 2 , the value of v will be an imaginary number .
As the square root of a negative number will be an imaginary number.
Therefore (2, ∞) is the domain of the above function.
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Give some examples of perpendicular lines inside or outside your classroom.
Answers
Answer: Well for example two roads that are meeting with each other and they form a right angle,
Step-by-step explanation:
Answer:
1. A Christian cross.
2. Roads that meet at intersections
3. Hospital crosses.
Step-by-step explanation:
Perpendicular lines are lines that touch each other, or are slanted in a way that they will eventually touch each other. The examples I used are all crosses, which are two line that cross.
Compare the three functions below. Which has a greater period? A) y = 3cos(2x+1), B) y=5cos(4x +8), and C) y=cos(2x+4) (4.3)
Answers
Comparing the periods of the given cosine functions indicates that functions A) and C) both have the greatest period of π, which is longer than the period of function B), π/2.
Explanation:To compare the periods of the given functions, let's first understand what the general form of a cosine function tells us about its period.
The general form is y = A cos(Bx + C), where A is the amplitude, B affects the period, and C is the phase shift.
The period of such a function is given by 2π / |B|.
For function A) y = 3cos(2x+1), B = 2, thus its period is π.
For function B) y=5cos(4x +8), B = 4, yielding a period of π/2.
Lastly, for function C) y=cos(2x+4) (4.3), assuming the (4.3) is an unrelated notation and focusing on the given cos component with B = 2, its period is also π.
The function with the greatest period among A, B, and C is thus A) and C), both having the same period of π, which is greater than the period of B).
Two polygons are similar. The perimeter of the smaller polygon is 48 centimeters and the ratio of the corresponding side lengths is 2/3 . Find the perimeter of the other polygon.
Answers
Answer:
= 72 cm
Step-by-step explanation:
The ratio of lengths of two similar figures is called the linear scale factor.
In this case, the linear scale factor is 2/3
The linear scale factor is also equivalent to the ratio of the perimeter of two similar figures.
Therefore, 2/3 = 48/x
x = 48 × 3/2
= 72 cm
The perimeter of the other polygon is 72 cm
Answer:
72 cm
Step-by-step explanation:
Given in the question, there are two similar polygons and the ratio of the corresponding side lengths is 2/3.
Perimeter of the smaller polygon = 48 cm
let perimeter of the larger polygon = x cm
We know that if two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
So,
Perimeter of smaller polygon / Perimeter of larger polygon = 2 / 3
48 / x = 2 / 3
48(3) = 2(x)
144 = 2x
x = 72 cm
Find the area of each circle, both in terms of pi and to the nearest tenth. use 3.14 for pi
Circle with radius 9 in.
Answers
Answer: 254.47
Step-by-step explanation: A=3.14*r to the power of two=3.14*9 squared=254.47
3.14*9^2=254.34 this would be the answer
Kara rotates a square around its horizontal axis of symmetry to make a solid figure. Which of following could be the shape of a horizontal cross section of the solid figure
Answers
Answer:
I am pretty sure the answer is square
Tim mails two boxes of cookies to friends. One box weighs 1 3/4 pounds, and the other weighs 2 2/3 pounds. What is the total weight of the two boxes?
Answers
the answer would be 4 5/12 pounds
The total weight of the two boxes will be 4 and 5/12 pounds.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Tim mails two boxes of cookies to friends. One box weighs 1 and 3/4 pounds, and the other weighs 2 and 2/3 pounds.
Then the total weight of the two boxes will be
Total weight = 1 + 3/4 + 2 + 2/3
Total weight = 3 + 17/12
Total weight = 3 + 1 + 5/12
Total weight = 4 + 5/12
The total weight of the two boxes will be 4 and 5/12 pounds.
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A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.
Answers
Answer:
The radius is [tex]r=5\ cm[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<C =(1/2)[arc\ AB][/tex]
[tex]m<C =90\°[/tex]
substitute
[tex]90\°=(1/2)[arc\ AB][/tex]
[tex]arc\ AB=180\°[/tex]
That means----> The length side AB of the inscribed triangle is a diameter of the circle
Applying Pythagoras Theorem
Calculate the length side AB
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]
[tex]AB^{2}=8^{2}+6^{2}[/tex]
[tex]AB^{2}=100[/tex]
[tex]AB=10\ cm[/tex] -----> is the diameter
Find the radius
[tex]r=10/2=5\ cm[/tex] -----> the radius is half the diameter
A standard six-sided number cube is rolled. What is tge probability a 3 or a 5 will land face up?
Answers
Answer:
It's 1/3
Step-by-step explanation:
6 possible outcomes, 2 desired.
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
There are 6 different possible numbers the cube can land on. Because it is a standard cube, all of the sides will have equal probability of getting landed on. 3 and 5 make up 2 out of 6 possibilities hence a probability of
[tex]\frac{2}{6}[/tex]
or
[tex]\frac{1}{3}[/tex]
Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 3
B) 3.5
C) 4
D) 4.5
Answers
Answer:
B) 3.5 ^_^
Step-by-step explanation:
1. To calculate the height of a tree,
Marie measures the angle of elevation
from a point A to be 34º. She then
walks 10 feet directly toward the tree,
and finds the angle of elevation from
the new point B to be 41°. What is the
height of the tree?
Answers
Answer:
h ≈ 30.10 ft
Step-by-step explanation:
Marie measures the angle of elevation from a point A to a tree as 34° . She works 10 ft directly towards the tree and discovered the new angle of elevation is 41°. The height of the tree can be computed below.
let
a = distance from point B to the tree
h = height of the tree
The right angle triangle formed from point B, we can use tan to find the height of the tree.
tan 41° = opposite /adjacent
tan 41° = h/a
cross multiply
h = a tan 41°
The right angle formed from point A
tan 34° = opposite/adjacent
tan 34° = h/(a + 10)
(a + 10)tan 34° = h
Therefore,
a tan 41° = (a + 10)tan 34°
0.8692867378
a = 0.6745085168(a + 10)
0.8692867378a = 0.6745085168a + 6.7450851684
collect like terms
0.8692867378a - 0.6745085168a = 6.7450851684
0.194778221a = 6.7450851684
a = 6.7450851684/0.194778221
a = 34. 629565532 ft
height of the tree can be find with
h = a tan 41°
h = 34. 629565532 × 0.8692867378
h = 30.103022053 ft
h = 30.10 ft
The basketball team sold t-shirts and hats as a fundraiser they sold a total of 23 items and made a profit of $246 they made a profit of $10 for every t shirt they sold and $12 for every hat they sold dertermine the number of t shirts and the number of hats the basketball team sold
Answers
The basketball team sold a total of 23 items (t-shirts and hats) and made $246. By setting up and solving a system of equations, it was determined that they sold 15 t-shirts and 8 hats.
To determine the number of t-shirts and hats sold by a basketball team for a fundraiser, given that they sold a total of 23 items and made a profit of $246, with a profit of $10 per t-shirt and $12 per hat sold. To solve this problem, we can set up a system of linear equations and solve for the two variables representing the number of t-shirts (T) and the number of hats (H).
Let T represent the number of t-shirts and H represent the number of hats.
We know that T + H = 23 (since 23 items were sold in total).
We also know that the profit from t-shirts is $10 per t-shirt, and the profit from hats is $12 per hat. Therefore, 10T + 12H = $246 (total profit).
We can now set up the equations:
T + H = 23
10T + 12H = $246
From the first equation, we can express H in terms of T: H = 23 - T.
Substitute H = 23 - T into the second equation:
10T + 12(23 - T) = $246
Simplify and solve for T:
10T + 276 - 12T = $246
-2T + 276 = $246
-2T = $246 - 276
-2T = -$30
T = 15 (number of t-shirts sold)
Now, we can find the number of hats by substituting T back into H = 23 - T. Since T is 15, H = 23 - 15 = 8 (number of hats sold).
Therefore, the basketball team sold 15 t-shirts and 8 hats.
which of the following statements is true about the question ?
Answers
Answer:
second one :p
Second one I think ;-;
what is the solution to 8(y + 7) > 8y + 3
Answers
Answer:
y can be any real number
Step-by-step explanation:
8(y + 7) > 8y + 3
Distribute
8y+56 > 8y+3
Subtract 8y from each side
8y-8y +56 > 8y-8y +3
56 > 3
This is always true so the inequality is always true
y can be any real number
PLS HELP!!!!What are the sine, cosine and tangent ratios of
angle W in the triangle below
Answers
Step-by-step explanation:
Remember SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
The side adjacent to W is 4. The side opposite of W is 3. The hypotenuse is 5.
Therefore:
Sine = 3 / 5
Cosine = 4 / 5
Tangent = 3 / 4
Which situation allows you to have the most saved?
A) Having a set amount set aside for savings each time you are paid
B) Having a set minimum or percentage for savings whichever is greater
C) Having a percentage set aside for savings
D) Having a percentage set aside for savings when your pay is higher and hours are more
Answers
Answer:
having a set minimum or percentage for savings; whichever is greater
Step-by-step explanation:
Most saved situation is,
A) Having a set amount set aside for savings each time you are paid.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
To find Most saved situation.
Now,, We know that;
When, having a set amount set aside for savings each time you are paid- this can be the most possible answer.
And, Technically a person should save 20% to 25% of his income and this amount increases with income.
So, each time when you are paid, set aside the savings amount.
Thus, Most saved situation is,
A) Having a set amount set aside for savings each time you are paid.
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Ignore the top just answer both of the questions at the bottom plz
Answers
Answer:
y = 5x+2 , y=x-6
Step-by-step explanation:
just by looking at the table you can see for the first one 5x + 2 satisfies the table, and x-6 satisfies the right table.
for the first table the equation is:
[tex]x(5) + 2 = y[/tex]
and for the second it's:
[tex]x - 6 = y[/tex]
The circle below is centered at the point (5,3) and has a radius of length 4. What is it’s equation
Answers
[tex] {x}^{2} + {y}^{2} - 10x - 6y + 18 = 0[/tex]
Answer:
[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle
Step-by-step explanation:
The circle below is centered at the point (5,3) and has a radius of length 4
To find the center form of equation, we use formula
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
where (h,k) is the center and 'r' is the radius of the circle
given center is (5,3)
h=5 and k =3
radius r= 4, plug in all the values in the equation
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
[tex](x-5)^2 + (y-3)^2= 4^2[/tex]
[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle
Find the surface area of the composite solid. Round the answer to the nearest hundredth
Answers
Answer:
135.39
Step-by-step explanation:
The solid consist of 4 triangles and a 5 rectangles.
Formula to calculate area of triangle is
1/2 (height) (base)
Formula to calculate area of rectangle is
length x width
so
Total surface area of the composite solid is
2( 4(4) + 6(4) + 1/2(√13)(4) + 1/2(2√2)(6) ) + 6(4)
111.39 + 24
135.39
Answer:
Total area = 135 .39 square yard
Step-by-step explanation:
Given : composite figure.
To find : Find the surface area of the composite solid. Round the answer to the nearest hundredth.
Solution : We have given a composite figure with rectangle base and four triangles .
Base of two triangle = 4 yd .
Height of two triangle = √13 yd .
Base of other two triangle = 6 yd .
Height of other two triangle = 2√2 yd .
Area of rectangle = length * width .
Area of rectangle = 6 *4
Area of rectangle = 24 square yard .
Area of all rectangle = 3 *24 = 72 square yard
Area of two square = 2( 4*4) = 32 square yard.
Area of triangle = [tex]\frac{1}{2} base * height[/tex].
Area of triangle= [tex]\frac{1}{2} 4 *√13 [/tex].
Area of triangle = 2√13 .
Area of two triangle = 2 * 2√13 .
Area of two triangle = 4√13 square yard.
Area of other triangle = [tex]\frac{1}{2} 6 * 2√2 [/tex].
Area of other triangle = 3* 2√2
Area of other triangle = 6√2.
Area of other two triangle = 2 *6√2.
Area of other two triangle = 12√2 square yard.
Total area = Area of 3 rectangle + Area of two triangle + Area of other two triangle + area of square
Total area = 72 + 4√13 + 12√2 + 32
Total area = 135 .39 square yard.
Therefore, Total area = 135 .39 square yard.
Jefferson High School is looking to expand its student parking lot by expanding the existing lot as
shown below.
(Picture Attached)
The size of the new parking lot will be twice the size of the old parking lot. How many feet, x, was the
old parking lot expanded by?
Answers
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This was already answered.
Answer:
The value of x is 60 ft.
Step-by-step explanation:
The area of a rectangle is
[tex]A=length \times width[/tex]
The area of school is
[tex]A=165\times 300=49500[/tex]
The area of old lot with school is
[tex]A=(165+75)(300+75)=90000[/tex]
The area of old lot without school is
[tex]A_1=90000-49500=40500[/tex]
The area of new lot with school is
[tex]A=(165+75+x)(300+75+x)=x^2 + 615 x + 90000[/tex]
The area of old lot without school is
[tex]A_2=x^2 + 615 x + 90000-49500=x^2 + 615 x + 40500[/tex]
It is given that the area of new parking lot will be twice the size of the old parking lot.
[tex]2A_1=A_2[/tex]
[tex]2(40500)=x^2 + 615 x + 40500[/tex]
[tex]0=x^2 + 615 x -40500[/tex]
[tex]0 = (x - 60) (x + 675)[/tex]
[tex]x=60,-675[/tex]
The value of x can not be negative. Therefore the value of x is 60 ft.