The value of y is 2.33924.
What is equation?
An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.
Given:
(1/8)²-3y = [tex]2^{y}[/tex]-2
1/64 - 3y = [tex]2^{y}[/tex]-2
1/64+ 2 = [tex]2^{y}[/tex]+3y
129/2 = [tex]2^{y}[/tex]+3y
Taking log on both side
log 129 - log 2 = y log 2 + 3 log y
2.11 - 0.301 = 0.301 y + 3 log y
1.809 = 0.301 y + 3 log y
1.809/3= 0.1 y + log y
0.603 = 0.1 y + log y
y = [tex]10^{\frac{603-100y}{1000}}[/tex]
y= 2.33924
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Let f(r) = 42 - 5, find f(3).
if 13 sin θ=12 cos θ, find the value
From the given information, we have
[tex]13\sin(\theta) = 12\cos(\theta) \implies \dfrac{\sin(\theta)}{\cos(\theta)} = \dfrac{12}{13}[/tex]
In the expression of interest, divide through everything by [tex]\cos^2(\theta)[/tex] to get
[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\frac{\sin(\theta)}{\cos(\theta)}}{1 - \frac{\sin^2(\theta)}{\cos^2(\theta)}}[/tex]
Then plugging in the given info, we get
[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\times \frac{12}{13}}{1 - \left(\frac{12}{13}\right)^2} = \boxed{\dfrac{312}{25}}[/tex]
Which of the following is a like radical to 3√6x^2
x(3√6x)
6 (3√x²)
4 (3√6x²)
x(3√6)
Answer:
x(3√6)
Step-by-step explanation:
Radicals:
Take out a variable or number for every pair of the variable or number inside the radicals
[tex]\sf 3\sqrt{6x^2}=3*\sqrt{6*x*x}\\\\[/tex]
[tex]\sf = 3x \sqrt{6}[/tex]
A=(1+1/2).(1+1/3). ... .(1+1/2020)
[tex]A=\left(1+\dfrac{1}{2}\right)\cdot \left(1+\dfrac{1}{3}\right)\cdot\ldots\cdot \left(1+\dfrac{1}{2020}\right)=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\ldots\cdot \dfrac{2021}{2020}=\dfrac{\dfrac{2021!}{2}}{2020!}=\\\\=\dfrac{2021}{2}=1010.5[/tex]
4x²-12x+9 = 5
☐ A. x= -√√5 +
312
B. x= √√4-3
C. X = -√√4-3
O D. x = √5 + 2/
□ E. x= -√5 +3
2
OF. x = √5 +3
2
Answer:
x = 3/2 ± [tex]\sqrt{5}[/tex] /2
Step-by-step explanation:
4x²-12x+9 = 5
Rearrange:
4x²-12x+4 = 0
Solve using the quadratic equation:
x = 3/2 ± [tex]\sqrt{5}[/tex] /2
After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds
Answer:
3 seconds
proofi took the test
The object reaches its maximum height after 3 seconds.
The correct option is 3 seconds.
To find the time at which the object reaches its maximum height, we need to determine the vertex of the parabolic function[tex]h(t) = -16t^2 + 96t + 6[/tex] . The vertex form of a parabola is given by [tex]h(t) = a(t - h)^2 + k[/tex], where (h, k) represents the vertex.
In this case, a = -16, so the vertex is given by t = -b/2a. Plugging in the values, we get t = -96/(2 x (-16)) = 96/32 = 3 seconds.
Therefore, the object reaches its maximum height after 3 seconds.
Option B, 3 seconds, is the correct answer.
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The complete Question:
The function [tex]h(t) = -16t^2 + 96t + 6[/tex] represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
After how many seconds does the object reach its maximum height?
A. 2 seconds
B. 3 seconds
C. 6 seconds
D. 9 seconds
11. rewrite the function in the form y=a (1+r)*
or y=a (1-r) ² then state the growth or decay
rate. y = a (6) t/a
Please help!!
Problem 10
The two functions are inverses of each other. Why? Because we can think of f(x) = (x-7)/(-2) as y = (x-7)/(-2).
Swap x and y to get x = (y-7)/(-2). Solving for y leads to y = -2x+7 showing that g(x) = -2x+7 is the inverse of f(x) = (x-7)/(-2). This process can be done in reverse to get the same result.
===================================================
Problem 11
y = a(6)^(t/2)
y = a( 6^(1/2) )^t
y = a(2.4494897)^t
y = a( b )^t
where b = 6^(1/2) = 2.4494897 approximately
Set b equal to 1+r and solve for r
1+r = 2.4494897
r = 2.4494897-1
r = 1.4494897
This rounds to about r = 1.45
The r value is the decimal form of the percentage, which means we move the decimal point over two spots to the right to get 145% approximately
Answers:
The equation is roughly y = a(1 + 1.4494897)^t
The growth rate is approximately 145%
===================================================
Problem 12
You have the correct answer. Nice work.
===================================================
Problem 13
You are very close to the correct answer. However, you're missing the base of the log.
The answer should be [tex]\log_{49}(343) = \frac{3}{2}[/tex]. So you'll need to write in a small "49" under the log.
The general rule is that exponential equations in the form [tex]b^x = y[/tex] are equivalent to the log version of [tex]\log_{b}(y) = x[/tex]. For each equation, b is the base. The idea of logs is to isolate the exponent.
The coordinates of triangle LMN are shown. L(-1,4) M(-1, -3) V N (4, -1) What is the length of LM? Enter the answer in the box. unit(s) The coordinates of triangle LMN are shown . L ( -1,4 ) M ( -1 , -3 ) V N ( 4 , -1 ) What is the length of LM ? Enter the answer in the box . unit ( s )
Answer:
7
Explanation:
Use the distance formula to find the answer
Answer:
7 units
Step-by-step explanation:
since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.
LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7
or
LM = | - 3 - 4 | = | - 7 | = 7
What is the least common
denominator?
3
-7
5
4xy'z ' 8xºy ' 12yz2
[ ? ]x[ y[ ]z Q
Z
Which function has an x-intercept of - 4 and a y-intercept of 3 when graphed?
The function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3
Intercepts of a lineThe x-intercept of a line is the point where the line crosses the x-axis while the y-intercept of a line is the point where the line crosses the y-axis.
For the x-intercept, y = 0
For the function f(x) = 3/4x + 3
0 = 3/4x + 3
0 = 3x + 12
-3x = 12
x = -4
This shows that the function has an x-intercept of -4
For the y-intercept, x = 0
For the function f(x) = 3/4x + 3
y = 3/4(0) + 3
y = 3
This shows that the function has an y-intercept of 3
Hence the function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3
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URGENT!!! PLEASE HELP!!! Find x and y.
Answer:
x is 48 and y is 100
Step-by-step explanation:
Angle y = 100 degree
Angle x = 48 degree
Write an equation for the n
term of each geometric
nth
sequence.
1, 4, 16, ...
which statements could be an interpretation of the graph x intercept or y intercept
Answer:
If you attach the answers i can help you better
Step-by-step explanation:
Each car on the lot at a car dealership has 4 tires and 2 headlights. Which pair correctly describes tires and headlights?
Answer: 4 : 2
Step-by-step explanation:
I am going to assume you want a ratio between number of tires to headlights which is
4 : 2
Select the correct answer.
The radius of the ball bearings produced at a factory must be 1.25 centimeters, with a tolerance of 0.1 centimeter. Which equation can be used
to find the minimum and maximum radil accepted? (Assume rrepresents the actual radius of any given ball bearing.)
OA /r-1.25/= 0.1
OB. 11.25r-1.25/= 0.1
OC. /r-0.1/= 1.25
OD. /r-0.1r/= 1.25
The absolute value equation that can be used to find the minimum and maximum radius accepted is:
A. |r - 1.25| = 0.1.
What is the absolute value?The absolute value function is defined as follows:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
It measures the distance of a point x to the origin.
In this problem, the absolute value of the difference between the radius and 1.25 cm must be of 0.1 to find the thresholds, hence the equation is:
A. |r - 1.25| = 0.1.
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Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
Jaime is incorrect, the angle does not depend on the radius of the circles.
Is Jaime correct?Remember that an angle that defines an arc on a circle, does not depend on the radius of the circle.
So, if we have an angle with a measure of π/3 radians in a circle with a radius of 3 inches and an angle with a measure of π/3 radians in a circle with a radius of 6 inches, these two angles are exactly the same thing.
The radius of the circle only has an impact on the length of the arc defined by the angle.
So Jaime is clearly incorrect.
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If a(x) = 3x + 1 and b (x) = square root of x-4, what is the domain of (b o a)(x)
( 1, ∞) is the domain of (b o a)(x)
What is Function?
A function is defined as a relation between a set of inputs having one output each.
According to the question,
[tex]a(x) = 3x + 1 \\\\b (x) =\sqrt{x+4}[/tex]
To find the domain of the composite function,
[tex](b o x) (x) = b(a(x))\\\\(b o x) (x) = b(a(3x-1))\\\\(b o x) (x) = \sqrt{3x+ 1 -4} \\\\(b o x) (x) = \sqrt{3x -3}\\\\[/tex]
Therefore,
[tex]3x - 3 \geq 0\\3x \geq 3\\x \geq 1\\\\[/tex]
Hence , [ 1, ∞ ] is is the domain of (b o a)(x).
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Please help with this question
Answer:
4
Step-by-step explanation:
the second column and the second row so, the answer is 4
Which statements are true about the linear inequality y > three-fourthsx – 2? select three options.
The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
What is linear inequality?Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.
Using the general formula for linear inequality,
y >mx+ b
y > 3/4x - 2
Where m = slope of the graph
b = interception at y axis
Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).
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The simple interest on $2000 at 2% per annum for 3 months is
Step-by-step explanation:
s.i= P×T×R/100
=2000×0.25×2/100
= 1000/100
= 10
Answer:
$10
Step-by-step explanation:
[tex]2000 \times .02 \times \frac{1}{4} = 10[/tex]
find the value of cosec^2 30 degree - sin^45 - sec^60
For this question, I will be writing 'csc' instead of 'cosec'
[tex]\sin 30^{\circ}=\frac{1}{2} \implies \csc 30^{\circ}=2\\\\\sin 45^{\circ}=\frac{1}{\sqrt{2}}\\\\\cos 60^{\circ}=\frac{1}{2} \implies \sec 60^{\circ}=2\\\\\\\therefore \csc^{2} 30^{\circ}-\sin^{2} 45^{\circ}-\sec^{2} 60^{\circ}=2^{2}-\left(\frac{1}{\sqrt{2}} \right)^{2}-2^{2}=\boxed{-\frac{1}{2}}[/tex]
Which is equivalent to 4√9 1/2x?
Answer:
second branch..................
(x^2 + x - 17) + (x − 4) divide using polynomial long division
Answer: x+5 with a remainder of 3 (can also be said as 3/x-4)
Step-by-step explanation: See attachment
2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
The value of x is 77 cm which will make the triangles similar by SSS similarity theorem
Given length of the three sides of one triangle are 35 , 20 and 20
and length of the three sides of another triangle are x, 44,44
We need to find the values of x by using SSS Similarity theorem
We know that triangles are are similar by side - side - side similarity creation and hence the sides are in the same ratio
As both the triangles are isosceles triangles
Therefore ,
x/35 = 44/20=44/20 (Using ratio)
Solving the equation we get
x=44*35/20
x= 77
Hence the value of x is 77cm
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Which formula can be used to describe the sequence? negative two-thirds, −4, −24, −144,...
Answer:
Step-by-step explanation:
The height of each story in a hotel is feet. The height is measured from the ceiling to the floor. The hotel has 2 underground levels that are used as banquet halls. Stephen is a waiter who works two levels below ground. At what elevation are Stephen’s feet? Assume the ground level of the hotel is at 0 feet.
A.
feet
B.
feet
C.
D.
feet
Please help me with my math
Answer:
x = 72
y = 15
Step-by-step explanation:
m and n are parallel lines so we can write the following equation:
108 + x = 180 because these angles are supplementary
if we subtract 108 from both sides
x = 72 we can also write the following equation:
5y - 3 = x because these are alternate angles
5y - 3 = 72 add 3 to both sides
5y = 75 divide both sides by 5
y = 15
what is the measure of an angle if it is 260 less than three times its own supplement
Answer:
130 degrees
Step-by-step explanation:
Let's assume that the angle is X. If angle is x, then:
x+260 = 3x
subtract x from both sides:
260 = 2x
130 = x because 260/2 is 130
so the answer is 130 degreees
Answer:
I feel like the answer is 70 degrees
Step-by-step explanation:
3(180-x)-260=x
540-3x-260=x
-3x+280=x
280=4x
x=70
Choose the variable expression that matches this phrase.
the sum of the number of crew members on the tour boat and the 5
passengers.
A. 5-c
B. 5c
C. 5+ c
D. 5÷c
The sum of the number of crew members (c) on the tour boat and the 5 passengers is 5 + c. Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The sum of the number of crew members (c) on the tour boat and the 5 passengers.
This can be written as in the form of the mathematical form.
⇒ 5 + c
Then the correct option is C.
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A/n ____ is a part of a circle that represents an angle.
Answer:
An Arc is a part of a circle that represents an angle.
3/5x + 3 = 6 whats is x?
Answer:
X = 3/53/5x + 3 = 6
3/5x = 6 - 5
3/5x = 1
Multiplying both the sides with 5x3/5x (5x) = 1* 5x
3 = 5x
3/5 = X