Answer:
[tex]\log\left(\dfrac{\sqrt{x}\:z^2}{4y^2}\right)[/tex]
Step-by-step explanation:
[tex]\dfrac12\log(x)-2\log(2y)+2\log(z)[/tex]
[tex]\textsf{Apply log power rule}: \quad n \log(x)=log(x)^n[/tex]
[tex]\implies \log(x)^{\frac12}-\log(2y)^2+\log(z)^2[/tex]
[tex]\textsf{Apply exponent rule}: \quad(ab)^c=a^cb^c[/tex]
[tex]\implies \log(\sqrt{x})-\log(4y^2)+\log(z^2)[/tex]
[tex]\textsf{Apply log quotient rule}: \quad \log(x)-\log(y)=log(\frac{x}{y})[/tex]
[tex]\implies \log\left(\dfrac{\sqrt{x}}{4y^2}\right)+\log(z^2)[/tex]
[tex]\textsf{Apply log product rule}: \quad \log(x)+\log(y)=log(xy)[/tex]
[tex]\implies \log\left(\dfrac{\sqrt{x}\:z^2}{4y^2}\right)[/tex]
3. Nine more than the quotient of a number and 4 is 12.
Answer: x = 12
Step-by-step explanation:
9 + (x/4) = 12
x/4 = 3
x = 12
How do graphs help you understand the data?
Answer:
Sometimes, data can be better understood when presented by a graph than by a table because the graph can reveal a trend or comparison.
Please help me. I will mark brainliest
Answer:
Step-by-step explanation:
After she finished making the cookies, Ashley had 0.945 kg of flour lett. How much flour did she use?
Answer:
[tex]she \: used \: 1.695 \: kg \: of \: flour.[/tex]
Step-by-step explanation:
[tex]2.64 - 0.945 = 1.695[/tex]
8th grade mathe help8th grademath heelp
Answer:So for number 35 you will put the qwestion in a calculator... now you have your answer so put that ansor to the side, and solve all of the ones in the answer choices and see which one has a common answer from the one in the problem
Step-by-step explanation:
HELPP PLEASE!!!! I have a screenshot of the question because I cant copy and paste it!
2³+3²-3×4-5²÷5+(7×4)
= 8+9-3×4-25÷5+7×4
=8+9-12-5+28
=28
What number has 6 tens and 1
more one than tens?
Answer:
17
Step-by-step explanation:
please help me if you can tysm! :))))
Answer:
9.9
Is the answer to the question
Consider parallelogram VWXY below.
Use the information given in the figure to find m∠YXV, m∠Y, and x.
Answer:
56°, 84°, 3 unitsStep-by-step explanation:
Properties of a parallelogram
Two adjacent angles are supplementaryOpposite angles are congruentOpposite sides are parallel and congruentUse the properties to find the required parameters
1) Find m∠YXV
m∠YXV + m∠VXW + m∠VWX = 180°m∠YXV + 40° + 84° = 180°m∠YXV = 180° - 124°m∠YXV = 56°2) Find m∠Y
m∠Y = m∠W = 84°3) Find x
2x = 6x = 6/2x = 3Answer:
m∠YXV = 56°
m∠Y = 84°
x = 3
Step-by-step explanation:
Sum of interior angles of a triangle = 180°
⇒ m∠W + m∠WVX + m∠VXW = 180°
⇒ 84° + m∠WVX + 40° = 180°
⇒ m∠WVX = 56°
As VW ║ YX and YV ║ XW then m∠WVX = m∠YXV
So m∠YXV = 56°
In a parallelogram, opposite angles are congruent
⇒ m∠Y = m∠W
⇒ m∠Y = 84°
In a parallelogram, opposite sides lengths are congruent
⇒ VW = YX
⇒ 2x = 6
⇒ x = 6 ÷ 2
⇒ x = 3
SOMEONE PLEASE HELP ME WITH THIS!!
IMAGE DOWN BELOW!!
ILL GIVE YOU BRAINLIST ANSWER!!
u²= s²+t²
= 4.3²+4.9²
= 42.5
u= V42.5
= V170 /2
≈6.52
Answer:
6.519 cm
Step-by-step explanation:
Mmkay, so, you have to use the Pythagorean Theorem to find the actual length, which is a^2 + b^2 = c^2
a = 4.9 cm
b = 4.3 cm
4.9^2 is 24.01
4.3^2 is 18.49
Now add the two together:
24.01 + 18.49 = 42.5
Finally, we need to find the square root of 42.5
sqrt(42.5) = 6.519 cm
(rounding to nearest thousandth cuz it said so right by the answer box lol)
Hope this helped :D
Zachary is an engineer and studies trains. He found this interesting problem involving a passenger train and a freight train:
A passenger train left New York and traveled North while a freight left from the same place, at the same time and traveled South. After traveling for 6 hours the trains were 720 miles apart. If the passenger train was traveling at 80 mph, how fast was the freight train traveling
Answer:
40 m/hr
Step-by-step explanation:
6 hours * 80 m/hr + 6 hours * x m/hr = 720 miles
6 * 80 + 6 * x = 720
x = 40 m/hr
In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato.
You can also make up your own pizza with extra toppings. You can choose from four
different extra toppings: olives, ham, mushrooms and salami.
Ross wants to order a pizza with two different extra toppings.
How many different combinations can Ross choose from?
The number of different topping combination illustrates combination
Ross have 6 different topping combination to select from
The number of different combinationThe given parameters are:
Extra toppings, n = 4
Toppings to select, r = 2
The number of extra topping that Ross can select is then calculated using the following combination formula
Toppings = nCr
This gives
Toppings = 4C2
Evaluate the combination expression
Toppings = 6
Hence, Ross have 6 different topping combination to select from
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3. The principal wants to know if students at Meadows Senior High School are in favor of a new dress code at their
school. The principal is not able to ask the opinion of every student at the school, so she needs to select an
appropriate sample of the students to represent the high school. Select which sample of students the principal
should choose.
A. Students randomly selected from a list of all students at the school.
B. Students sitting at randomly selected tables in the library.
C. Students she selects from the hall way between classes.
D. Students selected by the teachers.
Answer:
(A)
Step-by-step explanation:
(D) is already out since the teachers may have favorites or unfavorites.
(C) is already out since you can't be in all the halls at once.
There is only (A) and (B).
I think it's (A) and not (B) because it might not be a classes/grades library day.
23, 92, 368, ..
Find the 6th term.
Answer:
6th term = 23,552
Step-by-step explanation:
Mutilyby 4 from left to right
368/92 =4--------------- 92x4= 368
92/23=4--------------- 23x4 =92
1) 23
2) 23x4= 92
3) 92x4=386
4) 386x4=1,472
------and so on
Calculate the perimeter of the figure shown below.
5 ft
5 ft
10 ft
18 ft
Answer:
48
Step-by-step explanation:
10+5+18+15
pls mark brainliest
The length of a rectangular frame is represented by the expression 2x 4, and the width of the rectangular frame is represented by the expression 2x 10. write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches. 2x2 20x − 80 = 0 4x2 28x 40 = 0 4x2 28x − 80 = 0 x2 8x 20 = 0
The equation that can be ued to solve for the width of the rectangular frame is 2x² + 14x - 40 = 0.
What is the equation that can be used to solve for the width?A rectangle is a 2-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
(2x + 4) x (2x + 10) = 120
Expand the brackets
4x² + 20x + 8x + 40 = 120
Add similar terms
4x² +28x + 40 = 120
4x² +28x - 80 = 0
Divide through by 2
2x² + 14x - 40 = 0
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
Factor −4x^2 +6x. Is this a special product?
triangle BCD is similar to triangle ACE if these triangles are isosceles what is the length of AB?
Answer:
40
Step-by-step explanation:
As it is stated, the triangles are similar to find the length of AB we can use the proportion of sides'
Let x represent the missing length
BD/AE = CD/CE
(2.76)/22 = 5/x cross multiply expressions:
x(2.75) = 110 divide both sides by 2.75
x = 40
x^2-6x+1=0 solve by completing square
Answer:
x = 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
x² - 6x + 1 = 0 ( subtract 1 from both sides )
x² - 6x = - 1
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = - 1 + 9
(x - 3)² = 8 ( take square root of both sides )
x - 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( add 3 to both sides )
x = 3 ± 2[tex]\sqrt{2}[/tex]
How many members did not vote there is 75% and 60 people?
Answer:
15
Step-by-step explanation:
if 75% voted that is 45 people meaning 15 did not vote.
What is the approximate surface area of the figure? Use 3.14 for pi. 65.72 cm² 113.04 cm² 37.68 cm² 75.36 cm²
113.04 cm²
==========
The figure given is a sphere with a radius of 3 cm
formula for surface area of sphere : 4πr²
Solve:
⇒ 4πr²
⇒ 4(3.14)(3)²
⇒ 113.04 cm²
113.04 cm²
Solving it:
The SA given is 4πr²
To get your answer
First, you multiply these
4πr²
Add/ Plug-in the radius:
4(3.14)(3)²
And this is your answer:
113.04 cm²
I have attached an image showing this is the correct answer!
What is the equation of the line that is perpendicular two and has the same y-intercept as the line with (0,1) and (5,0)
Answer:
its all about reletives so if u take the number then multiply by five u get 56.3
Step-by-step explanation:
u know
who ever can answer this qustion will be marked as brainlest and will get 30points
Calculate the side lengths of the given scale.
Answer:
x: 4metres
y: 8metres
Step-by-step explanation:
using scale 1:4
x:16 ÷ 4
y: 2×4
Remove the largest possible common factor. Check your answer by multiplication. 9x^(4)+15x^(3)-12x
Factor out the greatest common factor.
Answer:
[tex]\bold{3x\left(3x^3+5x^2-4\right)}[/tex]Factor the following
[tex]\hookrightarrow \sf 9x^4+15x^3-12x[/tex]
rewrite the following
[tex]\hookrightarrow \sf 3\cdot \:3x^3x+3\cdot \:5x^2x-3\cdot \:4x[/tex]
factor out the common term 3(x)
[tex]\hookrightarrow \sf 3x\left(3x^3+5x^2-4\right)[/tex]
check for answer through multiplication
[tex]\dashrightarrow \sf 3x\left(3x^3+5x^2-4\right)[/tex]
[tex]\dashrightarrow \sf 3x\left(3x^3)+3x(5x^2)+3x(-4)[/tex]
[tex]\sf \dashrightarrow 9x^4+15x^3-12x[/tex]
Determine whether each set of data represents a linear, an exponential, or a quadratic function.
Answer:
See below ↓↓↓↓
Step-by-step explanation:
Set 1
[tex]\left[\begin{array}{ccc}x&y\\1&13\\2&6\\3&1\\4&-2\\5&-3\end{array}\right][/tex]
⇒ Quadratic [As it reduces at an unusual rate : -7, -5, -3, etc.]
Set 2
[tex]\left[\begin{array}{ccc}x&y\\-5&-34\\-4&-29\\-3&-24\\-2&-19\\-1&-14\end{array}\right][/tex]
⇒ y = 5x - 9
⇒ Linear
Set 3
[tex]\left[\begin{array}{ccc}x&y\\-2&0.0625\\-1&0.25\\0&1\\1&4\\2&16\end{array}\right][/tex]
⇒ Exponential [As seen by the perfect squares 0.0625, 0.25, 1, 4, 9..]
Set 4
[tex]\left[\begin{array}{ccc}x&y\\-6&28\\-3&19\\-1&13\\0&10\\3&1\end{array}\right][/tex]
⇒ Quadratic [As it reduces at an unusual rate : -9, -6, -3, etc.]
Write an expression that shows 104.
Answer:
k + 104
Step-by-step explanation:
k + 104
What is the square root of -2i?
Answer:
1-i and -1+i
Step-by-step explanation:
We are to find the square roots of [tex]z=0-2i[/tex]. First, convert from Cartesian to polar form:
[tex]r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2[/tex]
[tex]\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}[/tex]
[tex]z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})[/tex]
Next, use the formula [tex]\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr][/tex] where [tex]\displaystyle k=0,1,2,...\:,n-1[/tex] to find the square roots:
When k=1
[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr][/tex]
[tex]\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr][/tex]
[tex]\sqrt{2}\biggr(cis\frac{7\pi}{4}\biggr)[/tex]
[tex]\sqrt{2}(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4})\\ \\\sqrt{2}(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)\\ \\1-i[/tex]
When k=0
[tex]\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr][/tex]
[tex]\sqrt{2}\biggr(cis\frac{3\pi}{4}\biggr)[/tex]
[tex]\sqrt{2}(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})\\ \\\sqrt{2}(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\-1+i[/tex]
Thus, the square roots of -2i are 1-i and -1+i
Expand and simplify (4x−3y)(6x−5y).
Answer:
24x^2+15y^2-38xy
Step-by-step explanation:
(4x-3y)(6x-5y)
= 24x^2-20xy-18xy+15y^2
=24x^2+15y^2-38xy
Its easy pls help{6x+4y=14}{9x+6y=c}which value of c represents a system with infinitely many solutions?
The system of equations 6x+4y=14 and 9x+6y=c are linear equations
The value of c that makes the system have infinitely many solutions is 21
How to determine the value of c?The system of equations are given as:
6x+4y=14
9x+6y=c
Divide through the second equation by 3
3x + 2y = c/3
Multiply through by 2
6x + 4y = 2c/3
Subtract the first equation from the above equation
6x - 6x + 4y - 4y = 2c/3 - 14
Evaluate the differences
2c/3 - 14 = 0
Add 14 to both sides
2c/3 = 14
Multiply by 3/2
c = 21
Hence, the value of c that makes the system have infinitely many solutions is 21
Read more about system of equations at:
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