Answer:
Step-by-step explanation:
It's given in the question,
[tex]2^x=3^y=12^z[/tex]
[tex]2^x=12^z[/tex]
[tex]\text{log}2^x}=\text{log}12^z}[/tex]
[tex]x\text{log2}=z\text{log12}[/tex]
[tex]x=\frac{z\text{log}12}{\text{log2}}[/tex]
[tex]3^y=12^z[/tex]
[tex]\text{log}3^y}=\text{log}12^z}[/tex]
[tex]y\text{log}3}=z\text{log}12}[/tex]
[tex]y=\frac{z\text{log12}}{\text{log}3}[/tex]
Now substitute the values in the equation,
[tex]\frac{1}{y}+\frac{2}{y} =\frac{1}{\frac{z\text{log12}}{\text{log}3}}+\frac{2}{\frac{z\text{log}12}{\text{log2}}}[/tex]
[tex]=\frac{\text{log}3}{z\text{log}12}+\frac{2\text{log}2}{z\text{log}12}[/tex]
[tex]=\frac{\text{log}3+\text{log}2^2}{z\text{log}12}[/tex]
[tex]=\frac{\text{log}(3\times 2^2)}{z\text{log}12}[/tex]
[tex]=\frac{\text{log}(12)}{z\text{log}12}[/tex]
[tex]=\frac{1}{z}[/tex]
Hence proved.
Can anyone explain this step-by-step?
4(10x - 20) = 2,000
Answer: x = 52
Step-by-step explanation:
You'd first deal with the 4 outside the parentheses, multiplying 10x-20 by 4. This would result in 40x - 80 = 200.
You'd then further isolate x, adding 80 on both sides, resulting in 40x = 2080. Divide by 40 on both sides and You'd get your answer of x = 52.
Rhonda walked diagonally across a rectangular playground with dimensions 60 m by 45 m. She started at point C. Determine the angle, to the
nearest degree, between her path and the longest side of the playground.
B
45m
D
60 m
Answer:
37degrees
Step-by-step explanation:
In order to get the required angle, we will use the SOH, CAH, TOA identity.
Let;
Adjacent = 60m
Opposite = 45m
According to TOA:
tan theta = opp/adj
tan theta = 45/60
tan theta = 0.75
theta = arctan 0.75
theta = 36.86
Hence the angle, to the nearest degree, between her path and the longest side of the playground is 37degrees
Who can help me ????.
instruction find the missing length.
Answer:
19 is the answer i think.
find the missing length indicated
Answer:
192
Step-by-step explanation:
According to Euclidian theorem
x^2 = 144*(400-144)
x^2 = 144*256
x^2 = 36864 find the root of both
x = 192
Chen I’d bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cat fruit. The food cost is molded by the equation 5v + 7f = 28.70, where V represents the cost of 1 pint of cut veggies and F represents the cost of one pint of grapefruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (round to the nearest cent, as needed)
Answer:
answer to that is A 1.75 per pint
Please hurry I will mark you brainliest
A sunflower plant is growing at a constant rate. It was 4cm tall after 1 month and 32 cm tall after
9 months.
a) Express the growth of the plant as a rate of change.
b) Write an equation to show this relationship
Answer:
a) 3.5 cm / month
b y = 3.5(x-1) + 4, x >= 1
Step-by-step explanation:
the plant grew 32-4 = 28 cm in 9-1 = 8 months.
so, the growth rate is 28 cm / 8 months = 7 cm / 2 months, or (to norm it to a typical 1 unit denominator) 3.5 cm per month.
x = months of growth
y = height of plant
so, considering the "start" of 4 cm after one month, the equation is
y = 3.5(x-1) + 4, x >= 1
since we don't know anything about anything that happened before the first month was over, we cannot validate this equation for anything x<1.
solve the equation: q²+2q-8=0
Answer:
q = -4 q=2
Step-by-step explanation:
q²+2q-8=0
Factor
What 2 numbers multiply to -8 and add to 2
4*-2 = -8
4-2 = 2
(q+4)(q-2) =0
Using the zero product property
q+4 = 0 q-2 =0
q = -4 q=2
SIN TRIG PLEASE HELP 50 POINTS
If sin y° = s/8 and tan y° = s/t what is the value of sec y°
a. sec y° = 8s
b. sec y° = 8t
c. sec y° = 8/t
d. sec y° = t/8
Answer:
C
Step-by-step explanation:
We are given that:
[tex]\displaystyle \sin y^\circ = \frac{s}{8}\text{ and } \tan y^\circ = \frac{s}{t}[/tex]
And we want to find the value of:
[tex]\displaystyle \sec y^\circ[/tex]
Recall that tan(θ) = sin(θ) / cos(θ). Since sec(θ) = 1 / cos(θ), tan(θ) = sin(θ)sec(θ). Substitute:
[tex]\displaystyle \sin y^\circ \sec y^\circ = \frac{s}{t}[/tex]
Substitute:
[tex]\displaystyle \frac{s}{8}\sec y^\circ =\frac{s}{t}[/tex]
Solve for secant:
[tex]\displaystyle \sec y^\circ = \frac{8}{t}[/tex]
Hence, our answer is C.
Answer:
c. sec y° = 8/t
Step-by-step explanation:
I took the test
Determine the LCM of the following monomials listed below.
[tex]\boxed{\sf 60x^6y^4}[/tex]
Option d is correct8 ÷ -2 · 42 + 9 i need help please
If f(x) = x/2 -2 and g(x) = 2x+ +x= 3, find (f + g)(x).
Answer:
.
.
.❥︎ᴀᴀɴᴋʜ ᴜᴛʜɪ ᴍᴏʜᴀʙʙᴀᴛ ɴᴇ ᴀɴɢᴅᴀɪ ʟɪ ,
.ᴅɪʟ ᴋᴀ sᴀᴜᴅᴀ ʜᴜᴀ ᴄʜᴀɴᴅɴɪ ʀᴀᴀᴛ ᴍᴇ ❣︎
.
.
Instructions: Find the missing side of the triangle.
25
20
х
X =
Answer:
x = 15
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 20² = 25²
x² + 400 = 625 ( subtract 400 from both sides )
x² = 225 ( take the square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
Marking Brainliest. Can someone please how to do this with a fairly simple explanation? I'm not sure what to do.
Explanation:
In the LS column, you'll have these steps
3x - 1
3*4 - 1
12 - 1
11
Effectively, we replaced x with 4 and then simplified using PEMDAS.
And in the RS column, you'll have these steps
x + 7
4 + 7
11
We get the same thing at the bottom of each column. This shows that we end up with 11 = 11 after simplifying both sides. Therefore, we've confirmed that x = 4 is the solution to 3x - 1 = x + 7
Solve for x 3x -y =12
Answer:
[tex]\displaystyle x= \frac{y + 12}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 3x - y = 12[/tex]
Step 2: Solve for x
[Addition Property of Equality] Add y on both sides: [tex]\displaystyle 3x = 12 + y[/tex][Division Property of Equality] Divide 3 on both sides: [tex]\displaystyle x = \frac{12 + y}{3}[/tex]Answer:
x = y + 12 / 3
Step-by-step explanation:
3x - y =12
3x = y + 12
x = y + 12 / 3
Which is the right answer?
Answer:
b the answer
Step-by-step explanation:
Which polynomial is a binomial?
Can someone please help me with my maths question
Answer:
[tex]a. \ \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]b. \ \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Step-by-step explanation:
The question relates with rules of indices
(a) The give expression is presented as follows;
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}[/tex]
By expanding the expression, we get;
[tex]\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}[/tex]
Collecting like terms gives;
[tex]\dfrac{m^{(3 + 4 - 6)} \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
(b) The given expression is presented as follows;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4[/tex]
Therefore, we get;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n}[/tex]
Collecting like terms gives;
[tex]x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )[/tex]
[tex]x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right ) = \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n} =\dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Solve the following for the value of the pro-numeral:
(c - 7) / 2 = -5
Answer:
[tex] \frac{(c - 7)}{2} = - 5 \\ c - 7 = - 5 \times 2 \\ c - 7 = - 10 \\ c = - 10 + 7 \\ c = - 3[/tex]
I hope I helped you^_^
Which of the following should be the y-coordinate of left parenthesis (5,__) so that the ordered pair is a solution of 4x - y= -10
Answer:
y = 30
Step-by-step explanation:
Substitute x = 5 into the equation and solve for y
4(5) - y = - 10
20 - y = - 10 ( subtract 20 from both sides )
- y = - 30 ( multiply both sides by - 1 )
y = 30
Then (5, 30 ) is a solution of the equation
Help asap struggling
Answer:
..D).... x = 8..
Step-by-step explanation:
..x = 8..
HELP ME WITH THIS PLS IM FAILING REALLY BAD ITS PYTHAGOREAN THEOREM
Answer:
50 km
Step-by-step explanation:
c = √a^2+b^2
=√30^2+40^2
= √900 + 1600
=√2500
= 50 km
Answer:
50km
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(4, 2) \text{ and } (7, 6)
(4,2) and (7,6)
Answer:
( 5.5 , 4 )
Step-by-step explanation:
Use mid point formula shown in image
first x= (X+X)/2
x=(4+7)/2
x=11/2
x=5.5
y=(Y+Y)/2
y=(2+6)/2
y=8/2
y=4
(5.5,4)
Write an equation of the line that is parallel to the given line and passes through the given point.
1. y=2x+1; (0,4)
2. y= -x-3; (0,7)
3. y=-8x +9; (0,-2)
43. Para determinar la altura de un árbol nos apoyamos en los siguientes triángulos semejantes que se forman entre el árbol y
una lámpara
00
D
*ACB= 30°
3m
E
20 m
5 m
¿Cuál es la altura del árbol?
ООО
A. BA = 12 m
B. BA = 15 m
C. BA = 33.33 m
D. BA = 60 m
O
Respuesta:
A.) BA = 12 m
Explicación paso a paso:
Usando triángulos similares:
BA / AC = DE / EC
BA = x; AC = 20; DE = 3; EC = 5
POR ESO ; TENEMOS :
x / 20 = 3/5
Multiplicar en cruz:
5 * x = 20 * 3
5 veces = 60
5x / 5 = 60/5
x = 12
A fruits seller bought some lemon for Re 1 for 15 lemon. if he sold all lemons at 25% profit, how many lemons were sold for Rs 1.
Answer:
12 lemons
Step-by-step explanation:
CP of 15 lemon = ₹ 1
Profit = 25 %
SP of 15 lemons = [tex]\frac{100+profit}{100}*CP[/tex]
[tex]= \frac{125}{100}*1\\\\= \frac{5}{4}[/tex]
SP of 15 lemons = ₹ [tex]\frac{5}{4}[/tex]
Number of lemon for ₹ [tex]\frac{5}{4}[/tex] = 15
Number of lemons for ₹ 1 = 15 ÷ [tex]\frac{5}{4}[/tex]
[tex]= 15 *\frac{4}{5}\\\\= 3*4\\\\= 12[/tex]
find the area of the circle pi equals 3.14 and there's a radius of 16.
[tex]a = nr^{2} [/tex]
Radius is 16. DO NOT ROUND
Answer:
A = 803.84
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Circle Formula: A = πr²
r is radiusStep-by-step explanation:
Step 1: Define
Identify
r = 16
Step 2: Find Area
Substitute in variables [Area of a Circle Formula]: A = (3.14)(16)²Evaluate: A = 803.84a store is offering a 20% discount on all sales over $50. If you purchase a shirt and a pair of leans for $62.50, what is the amount of the discount you would receive?
Answer:
you would receive 12.5% of the discount
Step-by-step explanation:
20% off of 62.50 is 50; so you would pay $50
What is the total surface area of the square pyramid below?
14 cm
10 cm
10 cm
O 100 cm
O 200 cm
O 280 cm?
O 380 cm?
a
Rewrite in simplest terms (-9x-2y)+(4x-5y)
Answer:
-5x - 7y
Step-by-step explanation:
Solid #1
SA= 539 cm?
V = 2058 cm
Solid #2
SA = 704 cm?
V?
Answer:
2688 cm³
Step-by-step explanation:
2058×704/539 = 2688 cm³