given logx 2=p and logx 7=q , express log7 4x³ in terms of p and q.
Answer: (2*p + 3)/q
Step-by-step explanation:
First, let's remember the relationships:
Logₙ(a) = Ln(a)/Ln(n)
Ln(A*B) = Ln(A) + Ln(B)
Ln(a^n) = n*Ln(a)
Now, we know that:
Logₓ(2) = p
Logₓ(7) = q
We want to express:
Log₇(4*x^3) in terms of p and q.
First, we can rewrite the first two relations as:
Ln(2)/Ln(x) = p
Ln(7)/ln(x) = q
then we have:
Ln(2) = p*Ln(x)
Ln(7) = q*Ln(x)
Ok:
Now let's play with our equation:
Log₇(4*x^3)
First, this is equal to:
Ln(4*x^3)/Ln(7)
We now can rewrite this as:
(Ln(4) + Ln(x^3))/Ln(7)
= (Ln(2^2) + Ln(x^3))/Ln(7)
= (2*Ln(2) + 3*Ln(x))/Ln(7)
Now we can replace Ln(2) by p*Ln(x) and Ln(7) by q*Ln(x)
(2*p*Ln(x) + 3*Ln(x))/(q*Ln(x)) = (2*p + 3)/q
This is the expression we wanted.
simplify this ratio
question a
Answer:
1:5:6
Step-by-step explanation:
The greatest common factor is 2, so divide by 2 for all of them.
The table shows the number of teams that make the playoffs
in four professional sports: hockey (NHL), basketball (NBA),
football (NFL), and baseball (MLB).
About what percentage of hockey teams make the playoffs?
Answer:
I believe it's 53% cause 16 divided by 30 sums up to 53
What is the slope of the following line: 2y-4x=-16
Answer:
The slope is 2
Step-by-step explanation:
So convert the equation into point slope form
y=mx+b
Isolate the 2y by adding 4x to both sides using inverse operations
2y=-16+4x
now divide 2 on both sides to make y isolated
y=-8+2x
Now convert
y=2x-8
the slope is 2
PLS HELPPPP! PLEASE DONT ANSWER IF U DONT KNOW!
Answer:
-3x³ + 8x² + 7x - 12
Step-by-step explanation:
hope this helps. Could you pls give me brainliest f correct,I am only 3 away from leveling up!!
1. A hotel has 300 rooms which are all occupied. Each room can have either 1 or 2 guests and there are 420 guests staying in total. How many rooms are occupied by 2 guests?
Answer:
60
Step-by-step explanation:
420 - 300 = 120
120/2 = 60
Here are two similar rectangles.
1 cm
2 cm
4 cm
Work out the area of the larger rectangle.
Answer:
8cm^2
Step-by-step explanation:
4*2=8
The area of the larger rectangle will be 8 cm.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that the sides of the small rectangle are 1cm and 2cm. One side of the larger rectangle is 4cm so the other side will be 2cm.
The area of the rectangle is calculated by using the formula below:-
Area = 4 x 2
Area = 8 cm
Therefore, the area of the larger rectangle will be 8 cm.
To know more about the area follow
https://brainly.com/question/25292087
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The perimeter of a rectangle is 24 inches. If the length of
the rectangle is less than the width of the
rectangle, which of the following best illustrates the
domain for the length of this rectangle?
Answer:
Option B
Step-by-step explanation:
Let the length of the rectangle = l inches
And width of the rectangle = w inches
Perimeter = 2(l + w) = 24 inches
(l + w) = 12
w = 12 - l --------(1)
Length of the rectangle is less than the width,
l < w
By substituting the value of w from equation (1),
l < 12 - l
2l < 12
l < 6
Since, length of the rectangle will be greater than zero,
l > 0
Inequality that best illustrate the domain of the length will be,
0 < l < 6
Option (B) will be the answer.
Instructions: Find the measurement of the diagonal indicated in the following parallelogram. Please help :)
Answer:
ZD = 10
Step-by-step explanation:
In a parallelogram
Every two opposite sides are parallelEvery two opposite sides are equalEvery two opposite angles are equalEvery two adjacent angles are supplementaryThe two diagonals bisect each other (meet each other at their midpoint)Let us solve the question
∵ ABCD is a parallelogram
∵ AC and DB are its diagonals
→ By using the 5th property above
∴ AC and BD bisect each other
∵ AC ∩ BD at point Z
→ That means Z is the midpoint of them
∴ Z is the midpoint of BD
→ That means Z divides BD into 2 equal parts BZ and ZD
∴ BZ = ZD
∵ BZ = 10
∴ ZD = 10
A 55m and 35m broad park is surrounded by a 2.5m wide path.
(i). Find the area of the path.
(ii).Calculate the cost of paving the path with stones at Rs 120 per sq. metre.
Step-by-step explanation:
☄ [tex] \underline {\underline{ \text{Given}}} : [/tex]
Length of a park ( l ) = 55 mBreadth of a park ( b ) = 35 mWidth running outside the park ( d ) = 2.5 mRate of paving the path with stones = Rs 120 per sq.metre☄ [tex] \underline{ \underline{ \text{To \: find}}}: [/tex]
Area of the parkCosy of paving the path with stones at Rs 130 per sq.metre☄ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]
Part 1 : [tex] \boxed{\text{Area \:of \:a \:path \: running \:outside = 2d(l + b + 2d)}}[/tex]
plug the known values and simplify :
⟹ [tex] \sf{2 \times 2.5(55 + 35 + 2 \times 2.5)}[/tex]
⟹ [tex] \sf{5 \times 95}[/tex]
⟹ [tex] \sf{475 \: {m}^{2} }[/tex]
Part 2 : [tex] \boxed{ \sf{Total \: cost = Area \: of \: paths \: \times Rate}}[/tex]
⟹ [tex] \sf{475 \times 120}[/tex]
⟹[tex] \sf{Rs \: 57000}[/tex]
[tex] \purple{ \boxed{ \boxed{ \sf{ \tt{⟿ \: Our \: final \: answer : (i) = 475 \: {m}^{2} \: and \: (ii ) = Rs \: 57000}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day /night ツ
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.......Please someone help......
Answer:
2c. is y-3 = 3/4 ( x - 5 ) y - y^1 =m ( x- x^1)
the slope of the line is 3/4
(5,3) must be included on the graph of the line
2a. is (y^2-y^1)/ (x^2-x^1)
that the slope formula
2b. They are similar because they both use x^1 and y^1
also both use and need the slope
Find the missing side. Round your
answer to the nearest tenth.
Work Shown:
sin(angle) = opposite/hypotenuse
sin(68) = 28/x
x*sin(68) = 28
x = 28/sin(68)
x = 30.1989727949723
x = 30.2
Make sure your calculator is in degree mode.
If you solve the equationx - 3 = 7, what information will you have?
Answer:
x=4
Step-by-step explanation:
both sides, add 7
Hey there!
“x – 3 = 7”
• FIRST: ADD by 3 on BOTH sides
• x – 3 + 3 = 7 + 3
• CANCEL out: –3 + 3 because that gives you 0
• KEEP: 7 + 3 because that helps us solve for your x-value
• NEW EQUATION: x = 7 + 3
• FLIP THE EQUATION: 7 + 3 = x
“Solve above and you have your answer!”
• ANSWER: x = 10 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
find the values of y for which the distance between the point p2,-3 and q 10, y is 10 units
Answer:
y = - 9, y = 3
Step-by-step explanation:
Calculate distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (10, y)
d = [tex]\sqrt{(10-2)^2+(y+3)^2}[/tex]
= [tex]\sqrt{8^2+(y+3)^2}[/tex]
Given distance between points is 10, then
[tex]\sqrt{64 +(y+3)^2}[/tex] = 10 ( square both sides )
64 + (y + 3)² = 100 ( subtract 64 from both sides )
(y + 3)² = 36 ( take the square root of both sides )
y + 3 = ± [tex]\sqrt{36}[/tex] = ± 6 ( subtract 3 from both sides )
y = - 3 ± 6 , thus
y = - 3 - 6 = - 9
y = - 3 + 6 = 3
1. The volume of a rectangular shape 5 feet
high, 6 feet thick, and 13 feet long is
a. 24 cu ft
b. 43 ft
c. 95 ft
d. 390 cu ft
is this for the test on schoolobjects?
Answer:
The answer is d 390cubic feet
Step-by-step explanation:
multiply 5x13x6=390
HELP QUICK!Determine the approximate value of side a.
Answer:
35 degrees PLEASE MARK ME BRAINLIEST
Step-by-step explanation:
ZB
Round your answer to the nearest hundredth.
B
?
9
С
А
6
Answer:
B = 41.81
Step-by-step explanation:
sin B = opposite/ hyp
sin B = 2/3
Take the inverse sin of each side
sin ^-1 sin (B) =sin ^-1 (2/3)
B =41.8103149
To the nearest hundredth
B = 41.81
NEED HELP ASAP pls help right now!!! Pleeeease
Help me quickly just give the answer
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
48 divided by 8 = 6 or 8 x 6 = 48
7th grade math help me please :)
Answer:
105 pounds
Step-by-step explanation:
What is the following sale price
for a phone charger with an
original price of $12.99 after
applying a discount of 45%?
Answer:
$5.85
Step-by-step explanation:
To find the percentage of things you can use the percentage formula
p%*x=y
45%*12.99=y
.45*12.99=y
y=5.8455
I rounded up but the question may call for something different. Hope this Helps!
Please help
Write the word sentence as an inequality. Then solve the inequality. Six times a number x is at least −24. An inequality is________ . The solution of this inequality is _________.
Answer:
6x ≥ -24
An inequality is "a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions."
The solution to this inequality is:
x ≥ -4
Step-by-step explanation:
There's no explanation needed.
I just converted the words into an equation, then solved it by dividing both sides by 6. I looked up the definition of an inequality and pasted it here.
Help please!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
Slope is something that goes left to right or up to down in a graph going that 120 steps doesn't makes sense.
So now the choice is either A or B
The choice is B because the slope 2 represents the price per square foot painted
The variable d models drone's distance from the safe zone (in meters) t seconds after the drone started flying. D=-5t+4. What is the speed of the drone?
Answer:
v = 5 m/s
Step-by-step explanation:
The variable d models drone's distance from the safe zone (in meters) t seconds after the drone started flying is :
d = -5t+4
We need to find the speed of the drone. Speed is the rate of change of position.
[tex]v=\dfrac{dd}{dt}\\\\=\dfrac{d}{dt}(-5t+4)\\\\v=-5\ m/s[/tex]
Hence, the speed of the drone is 5 m/s.
Fatima has a total of $8 to spend to make fruit smoothies. She plans on spending all of the money and will use two types of fruit. Mango cost $0.50 per cup and strawberries cost $1.00 per cup. Write an equation for this situation.
Answer:
0.5x+y= 8---------------1
Step-by-step explanation:
Given data
let the mango be x
and strawberries be y
So the equation for the cost is
[tex]0.5x+y= 8---------------1[/tex]
1. The wrestler Blue Cyclone weighs 120
pounds is gaining ten pounds a month.
The Red Tornado weighs 150 pounds and
is gaining four pounds each month. How
many months will it take for them to be the
same weight?
Answer:
5 months
Step-by-step explanation:
cause 120+ 10× 5= 170 and
150+4×5= 170
If you were filling the cylinder up with water using a cone that has the same height and diameter, how many cones will it take to fill up the cylinder?
Answer:
It required 3 cones to fill up the cylinder with the same height and diameter.
Step-by-step explanation:
Let the radius of the cone and cylinder be r.
Let the height of the cone and cylinder be h.
As we know that [tex]\text{Volume of cylinder}=\pi r^2h[/tex] ....(1)
[tex]\text{Volume of cone}=\frac{1}{3}\pi r^2h[/tex]
It can be observed that the volume of a cone is [tex]\frac{1}{3}[/tex]rd the volume of the cylinder. so, multiply the volume of the cone by 3.
[tex]3 \times \text{Volume of cone}=3 \times \frac{1}{3}\pi r^2h[/tex]
[tex]3 \times \text{Volume of cone}= \pi r^2h[/tex]
[tex]3 \times \text{Volume of cone}= \text{Volume of cylinder}[/tex] (From equation 1 )
Hence, It required 3 cones to fill up the cylinder with the same height and diameter.
SIMPLE INTEREST
Interest = $40
Principal = $400
Interest rate = ?
Time = 2 years
Answer:
the interest rate is .4% or .0041666 etc. It's not a very realistic
Step-by-step explanation:
Tom simplified an expression in three steps, as shown: x to the power of negative 2 multiplied by y to the power of 4, over y multiplied by x to the power of 4 multiplied by x to the power of 4 multiplied by y to the power of negative 2, the whole to the power of 4 equal to x to the power of 2 multiplied by y to the power of 8, over y to the power of 4 multiplied by x to the power of 8 multiplied by x to the power of 8 multiplied by y to the power of 2 equal to x to the power of 2 multiplied by y to the power of 8, over y to the power of 6 multiplied by x to the power of 16. Which is the first incorrect step and why? (5 points) Step 1, all the exponents are increased by 4 Step 2, the exponents of the same base are added during multiplication Step 3, the exponents of the same base are subtracted during division Step 3, all the exponents are added during division
Answer:
Step 1, all the exponents are increased by 4Step-by-step explanation:
The three steps are
(x⁻² × y⁴ /y × x⁴ × x⁴ × y⁻²)⁴ = x²×y⁸/y⁴×x⁸×x⁸×y² =x²×y⁸/y⁶×x¹⁶Correct solution should be:
(x⁻² × y⁴ /y × x⁴ × x⁴ × y⁻²)⁴ = all powers inside the parenthesis should be multiplied by 4 as per power of the power (xᵃ)ᵇ = xᵃᵇThis would give next steps:
x⁻⁸×y¹⁶/y⁴×x⁸×x⁸×y⁻⁸ =x⁻⁸×y¹⁶/x¹⁶×y⁻⁴ =y²⁰/x²⁴Answer options:
Step 1, all the exponents are increased by 4
There should be multiplication of powers. (It is close option but is not fully correct as not all the exponents increased by 4, for example y became y⁴)Step 2, the exponents of the same base are added during multiplication
It was done correctlyStep 3 wasn't performed yet, there was step 1 and 2.
So answers about step 3 are irrelevantAnswer:
It would be number 3.
Step-by-step explanation:
the table shows for a quadratic function.
what is the average rate of change for this function for the interval from from x=3 to x=5
Answer:
the average rate of change is 12
Step-by-step explanation:
The computation of the average rate of change is shown below:
As from the attached table
f(b) = f(5) = 32
f(a) = f(3) = 8
Now the average rate of change is
= (32 - 8) ÷ ( 5 - 3)
= (24 ÷ 2)
= 12
Therefore the average rate of change is 12
So the same is relevant and considered too