Answer:
[tex]\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex] OR [tex]\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Choose the more appropriate answer
Step-by-step explanation:
I read your problem as [tex]3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y[/tex]:
[tex]\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]
Write this number in standard notation.
Answer:
12345678910
Step-by-step explanation:
TANQR
The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]
The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]
What is scientific notation?It is the way of writing a large number between 1 to 10 with a power of 10.
We have,
7,250,000
To write this number in standard notation, we can use powers of 10.
We start by counting the number of digits to the left of the decimal point.
In this case, there are 7 digits to the left of the decimal point.
We can then express this number in scientific notation as:
[tex]7.25 \times 10^6[/tex]
This means that we have 7.25 times 10 raised to the power of 6.
Now,
0.000045
To write this number in standard notation, we can again use powers of 10. We start by counting the number of digits to the right of the decimal point. In this case, there are 5 digits to the right of the decimal point.
We can then express this number in scientific notation as:
[tex]4.5 \times 10^{-5}[/tex]
This means that we have 4.5 times 10 raised to the power of -5.
Thus,
The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]
The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]
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The complete question.
Write this number in standard notation.
7,250,000
0.000045
Express 17 as a ratio of 68
Answer:
is it 1:4 or am I missing something
Step-by-step explanation:
At 3:40 P.M, the hour hand and the minute hand of a clock form an angle of:
Answer:
130 degrees
Step-by-step explanation:
3:40, it has traveled 6 * 40 = 240 degrees which is 110 degrees from vertical The difference is 240 - 110 = 130 degrees, which is the final answer.
Hope This Helped
HELP PLEASE! THIS IS DUE SOON! HELP ME! QUESTION BELOW!
Answer:
A) x = 113°
Explanation:
Given three sides: 6.4 cm, 5.8 cm, 10.2 cm
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert/put variables:
[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]
[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]
[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]
[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]
[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex] = 113.36° ≈ 113° (rounded to nearest degree)
identify the equivalent value of 2.4494897…
Squares are the results of multiplying a value by itself. The value of 2.4494897… is equivalent to √6.
What is square root?Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.
The value of 2.4494897… is equivalent to √6.
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find the modulus if the complex number 6-8i
[tex]|a+bi|=\sqrt{a^2+b^2}[/tex]
[tex]|6-8i|=\sqrt{6^2+(-8)^2}=\sqrt{36+64}=\sqrt{100}=10[/tex]
If f(x) = 2x² +2 and g(x)=x²-1, find (f- g)(x).
Your history book cost $43 dollars in 1999. The earlier edition sold for $37 in 1992. Comparing the converted costs, which book is more expensive? (Assume the 1999 CPI is 166.3 and the 1992 CPI is 140.3)
When the converted costs are compared, the earlier edition of the history book is more expensive.
Which book is more expensive?The consumer price index measures the changes in price of a basket of good. It is used to measure inflation.
Converted price of the earlier edition = (CPI in 1992 / CPI in 1999) x later edition of the book
(140.3 / 166.3) x $43 = $36.28
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Which of the following matches a quadrilateral with the listed characteristics
below?
1. Figure has 4 right angles
2. Figure has 4 congruent sides
3. Both pairs of opposite sides parallel
A. Rectangle
B. Parallelogram
C. Trapezoid
D. Square
The quadrilateral that matches the characteristics is a square.
What is a quadrilateral?A quadrilateral is a 2 dimensional figure with 4 sides. Example of quadrilaterals are rectangle, rhombuses, square, parallelograms and many more.
Therefore, the quadrilateral that matches the characteristics is a square.
Properties of a square
It has 4 right angles.It has 4 congruent sides.Both pairs of opposite sides are parallel.learn more on quadrilateral here: https://brainly.com/question/13805601
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Graph f(x)=2^x what is the answer?
Graph is in attached image.
Simplyfy 56 64 I want to simplify
Answer:
56/64 simplified is 0.875 or 7/8 as a fraction
Draw the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D'
What are the two points?
The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.
From the graph:
The two points are (-4, -2) and (4, 5)
The line equation passing through two points:
[y - 5] = (5+2)/(4+4)[x - 4]
y - 5 = 7/8[x - 4]
8y - 40 = 7x - 28
8y = 7x + 12
Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.
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Write the solution to -9×+4<40??
Answer:
Simplifying
-9 + 4 = 40
Combine like terms: -9 + 4 = -5
-5 = 40
Solving
-5 = 40
Couldn't find a variable to solve for.
This equation is a the left and right sides are not equal, therefore there is no solution.
Hope This Helped
Help!!!!! Meeee!! Asappppp
Reason:
Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.
You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.
Write a story that could represent this math problem. 2/6 times 3/4
AD are tangent to OC. Find the value of x.
NEED HELP WITH THIS QUESTION QUICK!!!
Answer:
x=5
Step-by-step explanation:
The two lines are the same length
2x+7 = 5x-8
15 = 3x
x = 5
A blimp, suspended in the air at a height of 600 feet, lies directly over a line from a sports stadium to a planetarium. If an angle of depression from the blimp to the stadium is 37 degrees and from the blimp to the planetarium is 29 degrees, find the distance between the sports stadium and the planetarium.
Step-by-step explanation:
so, this sounds like the blimp is located between the stadium and the planetarium.
we have a triangle :
the ground distance between the stadium and the planetarium is the baseline.
and the 2 lines of sight from the blimp on one side to the stadium and on the other side to the planetarium are the 2 legs.
we know the height of this triangle is 600 ft.
the angle of depression down to the stadium is 37°. which makes the inner triangle angle at the ground point at the stadium also 37°.
and the angle of depression down to the planetarium is 29°. which makes the inner triangle angle at the ground point at the planetarium also 29°.
and because the sum of all angles in a triangle is always 180°, we know the angle at the blimp is
180 - 37 - 29 = 114°
in order to solve this triangle, we need to split it into 2 right-angled triangles by using the height of the main triangle as delimiter.
we get a stadium side and a planetarium side triangle.
the baselines (Hypotenuses) of the 2 triangles are the corresponding lines of sight from the blimp.
the height of the large triangle is also a height and a leg in each small triangle.
and the stadium side part of the large baseline (between ground point and intersection with the height) is the second leg for the stadium side triangle.
and correspondingly, the planetarium side part of the large baseline (between ground point and intersection with the height) is the second leg for the planetarium side triangle.
the inner blimp angle of the stadium side triangle is
180 - 37 - 90 = 53°
and the inner blimp angle of the planetarium side triangle is
180 - 29 - 90 = 61°
now we can use the law of sine to get the lengths of the 2 parts of the baseline of the large triangle.
and when we add these 2 numbers we get the distance between stadium and planetarium.
law of sine is
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being opposite of the associated angles.
for the stadium side triangle we get
part1/sin(53) = 600/sin(37)
part1 = 600×sin(53)/sin(37) = 796.226893... ft
for the planetarium side triangle we get
part2/sin(61) = 600/sin(29)
part2 = 600×sin(61)/sin(29) = 1,082.428653... ft
the distance between the stadium and the planetarium is
part1 + part2 = 1,878.655546... ft
Solve |2x + 1| = 10?
[tex]|2x+1|=10\\2x+1=10 \vee 2x+1=-10\\2x=9 \vee 2x=-11\\x=4.5 \vee x=-5.5[/tex]
Answer:
[tex]x= \dfrac 92~~\textbf{or}~~x = -\dfrac{11}2\\\\[/tex]
Step-by-step explanation:
[tex]\underline {\textbf{Absolute value rule: }}\\\\\textbf{If}~ |a| = b~ \textbf{then} ~a =b~ \textbf{or}~ a =-b \\\\\underline{\textbf{Solution;}}\\\\\textbf{Given that,}\\\\~~~~~~~|2x+1| = 10\\\\\implies 2x +1 = 10~~~~~~\textbf{or} ~~~~~~~~~~~2x+1 = -10\\\\\implies 2x = 10-1~~~~~~\textbf{or}~~~~~~~~~~~2x = -10-1\\\\\implies 2x = 9~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~2x = -11\\\\\implies x= \dfrac 92~~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~x = -\dfrac{11}2\\\\[/tex]
A baseball "diamond" is actually a square with side lengths of 90 feet. In a game, a runner tries to steal second base. How far must the catcher throw from home plate to second base in order to get the runner out?
Answer:
about 127.28 feet
Step-by-step explanation:
The length of the hypotenuse of a right triangle with a base and a height of 90 feet each.
root (90)^2 + (90)^2
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
[?]%
Round to the nearest tenth of a percent.
Enter
Answer:
[tex]31.8\%[/tex]
Step-by-step explanation:
The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]
The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]
Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]
Nora buys milk and onions at the store. She pays a total of $35.67. She pays a total of $5.91 for the milk. She buys 6 bags of onions that each cost the same amount. How much does each bag of onions cost?
3/y-3=12/y+3, what is y?
Answer:
i am not sure about your question but if it is 3 divided by y-3 =12 divide by y+3 you can use this
Step-by-step explanation:
3÷y-3=12÷y+3
cross multiply
12(y-3)=3(y+3)............brackets off
12y-36=3y+9..............group the same
12y-3y=9+36
9y=45.......duved by 9 both sides
y=5
Write an expression to represent the given statement. Use n for the variable.
One number is 3 more than 2 times another. The sum of the numbers is 15 . Find the two numbers.
Answer:
4 and 11
Step-by-step explanation:
See attached image
Please Help I'm not really good at math
The true statements about the triangles RST and DEF are: (a), (d) and (e)
How to determine the true statements?The statement ΔRST ≅ ΔDEF means that the triangles RST and DEF are congruent.
This above implies that:
The triangles can be mapped onto each other by rigid transformations such as reflection, translation and rotationThe transformation does not include dilationCorresponding sides are congruentThe above means that the possible true statements are: (a), (d) and (e)
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A con is tossed 400 times what is the standard deviation
Answer:
deviation is 10
this will help you
What is the volume, in cubic meters, if the prism below?
=================================================================
Explanation:
Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.
The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.
Multiply this floor area with the height of the room (22 m) to get the volume of the room.
volume = (floor area)*(height) = 84*22 = 1848 cubic meters
Solve:
(√x + 2)(√x - 2) = 0
x = ?
Answer: x = 4
Step-by-step explanation:
(√x + 2)(√x - 2) = 0
√x*√x - 2√x + 2√x -4 = 0
x - 0 - 4 = 0
x = 4
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
(√x + 2)(√x - 2) = 0
√x × √x - √x · 2 + 2 · √x - 2 · 2 = 0
√xx - 2 × √x + 2 · √x - 4 = 0
√x^1+1 - 2 · √x + 2 × √x - 4= 0
√x² - 2 · √x + 2· √x - 4 = 0
x^2/2 - 2 × √x + 2 · √x - 4 = 0
x - 2· √x + 2 · √x - 4 = 0
x - 4 = 0
(x - 4) + 4 = 0
x - 4 + 4 = 0
x = 4
help please!! i need to turn this in
Answer:
a. [tex]x^{-2}[/tex]
b. [tex]x^{-6}[/tex]
c. 1
d. 1
e. [tex]x^{-6}[/tex]
f. [tex]x^{15}[/tex]
Step-by-step explanation:
find the quantity if v=5i-7j and w=3i+2j ||v||-||w||
[tex]\begin{cases} v=5i-7j\\\\ w=3i+2j \end{cases}\qquad \begin{cases} < \stackrel{a}{5}~~,~~\stackrel{b}{-7} > \\\\ < \stackrel{a}{3}~~,~~\stackrel{b}{2} > \end{cases}\qquad \qquad \stackrel{magnitude}{\sqrt{a^2 + b^2}} \\\\[-0.35em] ~\dotfill\\\\ ||v||~~ - ~~||w||\implies \sqrt{5^2+(-7)^2}~~ - ~~\sqrt{3^2 + 2^2}\implies \sqrt{74}-\sqrt{13} ~~ \approx ~~ 5[/tex]