Answer:
[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex] is equivalent to [tex]\frac{1}{2}\left(\log \:_b\left(57\right)-\log \:_b\left(74\right)\right)[/tex].
Hence, option 'c' is true.
Step-by-step explanation:
Given the expression
[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex]
Rewrite as
[tex]=\log _b\left(\left(\frac{57}{74}\right)^{\frac{1}{2}}\right)[/tex]
[tex]\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0[/tex]
[tex]=\frac{1}{2}\log _b\left(\frac{57}{74}\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _c\left(\frac{a}{b}\right)=\log _c\left(a\right)-\log _c\left(b\right)[/tex]
[tex]=\frac{1}{2}\left(\log _b\left(57\right)-\log _b\left(74\right)\right)[/tex] ∵ [tex]\log _b\left(\frac{57}{74}\right)=\log _b\left(57\right)-\log _b\left(74\right)[/tex]
Therefore,
[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex] is equivalent to [tex]\frac{1}{2}\left(\log \:_b\left(57\right)-\log \:_b\left(74\right)\right)[/tex].
Hence, option 'c' is true.
Solve this equation.
23x−15x=x−1
Answer:
x = -1/7
Step-by-step explanation:
25x - 15x = x - 1
combine like terms
7x = -1
divide
x = -1/7
Answer:
x = -1/7 (the whole fraction is negative)
Step-by-step explanation:
23x−15x=x−1
8x = x - 1
8x - x = x - 1 - x
7x = -1
x = -1/7
Original price: $264.91
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The sale price is $
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes.
A dolphin was swimming 28 meters below the ocean's surface. It changed its depth to avoid a
predator and ended up 21 meters below the surface.
What was the change in the dolphin's depth?
A gardener measures the heights of 2 plants at the end of every week. The function y=3x+8.5 of plant A in centimeters at the end of x weeks. The function y=2.5x+14.5 gives the height of plant B in centimeters at the end of x weeks.
Answer: Plant A and plant B will be the same height at the end of week 12.
Step-by-step explanation: You don't care about this
What is the solution of the proportion 3/5=13/x ? Round to the nearest tenth if necessary.
Answer: x = 21 2/3
Step-by-step explanation:
3/5 = 13/x
cross multiply 5 × 13, then divide by 3.
65/3 = 21 2/3
It's like multiplying both sides by the reciprocal of the left side.
The members of a crew team can weigh no more than 165 pounds each. Write an INEQUALITY for the acceptable weights. Graph the solutions.
Answer:
shut up b
sorry gad will elp you
Step-by-step explanation:
A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60
kilometers from the runway. What is the angle of depression for the descent of the plane?
Round to the nearest degree.
Answer:
Angle of depression = 3.37°
Step-by-step explanation:
We are told that A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60
kilometers from the runway.
I've attached an image of a triangle depicting this question.
From the triangle, we can find the angle of depression θ from trigonometric ratio since it's a right angle triangle.
Thus;
3.5/60 = tan θ
tan θ = 0.0583
θ = tan^(-1) 0.0583
θ = 3.37°
could i please get some help?
Write the equation of the line, in point slope form that goes through the given point with the given slope. through: (-2,5), slope = -4* O y + 2 = 5(x + 4) O y - 2 = 5(x-4) O y + 5 = -4(x +2) O y- 5 = -4(x + 2)
Answer:
y-5 = -4(x + 2)
Step-by-step explanation:
The point slope form is;
y-y1 = m(x-x1)
where m represents the slope
(x1, y1) represents the given point
Thus;
y-5 = -4(x + 2)
Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sister who is two years younger than him. If the product of his sisters' ages is 70, how old is Richard?
Answer:
7 years
Step-by-step explanation:
Given that:
Let Richard's age = x
Elder sister's age = 2x
Youngwr sister's age = x - 2
Product of sisters ages = 70
2x * (x - 2) = 70
2x² - 4x = 70
2x² - 4x - 70 = 0
x² - 2x - 35 = 0
x² - 7x + 5x - 35 = 0
x(x - 7) +5(x - 7) = 0
(x - 7) or (x + 5) = 0
x = 7 or x = - 5
X can't be negative
Hence, x = 7
Richard is 7 years
entlying
A and B are forces acting on a falling object. Which
force, A or B, represents gravity in the diagram?
Force
is gravity because it attracts the ball
to the ground.
Answer:
B... Because indicates the direction of gravity because its direction is downward
Answer:b
Step-by-step explanation:
solve for p2. p1v1 = p2v2
Answer:
P₂ = [tex]\frac{P_{1} V_{1} }{V_{2} }[/tex]
Step-by-step explanation:
Given expression:
Boyle's law:
P₁ V₁ = P₂ V₂
Problem is to find P₂;
Solution:
P₁ V₁ = P₂ V₂
To solve this problem, multiply both sides by [tex]\frac{1}{V_{2} }[/tex];
P₁ V₁ x [tex]\frac{1}{V_{2} }[/tex]; = P₂ V₂ x [tex]\frac{1}{V_{2} }[/tex];
[tex]\frac{1}{V_{2} }[/tex] cancels out V₂ on the right hand side;
P₂ = [tex]\frac{P_{1} V_{1} }{V_{2} }[/tex]
Solve the equation y = ax − b for the variable x.
Answer:
x = y/a + b/a
? is that what you meant
Step-by-step explanation:
Answer:
the answer is d) x = y/a+ b/a
Step-by-step explanation:
brainliest pleasee
What is the solution set for |x/2|=8?
Answer:
D) x=16 and x=-16
Step-by-step explanation:
D) x=16 and x=-16
If you replace x with either one of them and then take the absolute value, you would have 8.
Plz help...kinda confused.....only answer if ya know....:)
-3=-v+7
v=
Answer:
-3 = -v + 7
-3 - 7 = -v
3+7 = -v
-10 = -v
10 = v
Step-by-step explanation:
this is the answer i got, using basic algebra...
i hope this helps....
have a great day ahead :)
Answer:
v = 10
Step-by-step explanation:
[tex]-3=-v+7\\\\-v+7=-3\\\\-v+7-7=-3-7\\\\-v=-10\\\\\frac{-v=-10}{-1}\\\\ \boxed{v=10}[/tex]
Hope this helps.
f/13 = 6.2 what is the value of f
Answer:
The value of f is 80.6.
Step-by-step explanation:
We are given the equation and asked to solve for f.
If we are given a fraction with a variable in the numerator, we can multiply both sides of the equation by the denominator to isolate it.
For example, if you look at this equation:
[tex]\displaystyle\frac{a}{26}=17.9[/tex]
We can multiply both sides by 26 to get the a by itself so the equation can be solved.
[tex]\displaystyle26\times\frac{a}{26}=17.9\times26\\\\a = 465.4[/tex]
Therefore, we can apply this same technique to the equation [tex]\frac{f}{13}=6.2.[/tex]
[tex]\displaystyle\frac{f}{13}=6.2\\\\13\times\frac{f}{13}=6.2\times13\\\\f = 80.6\ \text{or} \ \frac{403}{5}[/tex]
Therefore, the value of f is 80.6.
Answer:
f = 80.6
Step-by-step explanation:
Multiply both sides by 13.
f /13 =6.2
( f /13 )*(13)=(6.2)*(13)
f = 80.6
What is the answer to this math problem; 12 5/6x-14x+ 1/6x
Answer: wyd are you mad at me
Answer: Who are
Step-by-step explanation:
3 and 11
Find the midpoint
Answer:
7
Step-by-step explanation:
Delta owns a D.C. 10 airplane that has seats for 318 people. The company flies this airplane only if there are at least 96 people on the plane. Write a compound inequality to show the possible number of people on a Delta flight. Let n represent the amount of people.
Answer: n greater than or equal to 96 or n is greater than or less than 318
Step-by-step explanation:
Brainliest plz
PLZ HELP ASAP 30 POINTS!!! write the equation of the line in standard form and slope-interpret form.
standard form:
slope-interpret form:
PLEASE HELP!!Choose the slope and y-intercept that
correspond with the graph.
the answer is -1/3 y-incercept= -1
Answer:
The first one
Step-by-step explanation:
It’s y intercept is 1 and the slope is 1/3 because it goes up one and to the left 3 . I know it’s negative because it’s going down to the right.
What is the slope of a line that is perpendicular to a line that has a slope of -7
Please help ya girl out :))
y = (x - 4)(x-8)
Distribution
Answer:
[tex]y= x^{2} -12x+32[/tex]
Explanation:
[tex]y=x^{2} -8x-4x+32\\y= x^{2} -12x+32[/tex]
Use long division to find the quotient below.
(15x2 + 2x2 - 75) - (3x-5)
O A. 5x2 - 9x + 15
B. 5x2 + 9x + 15
C. 5x2 + 12x + 15
D. 5x2 - 12x + 15
What is the nth term rule of the quadratic sequence below?
-5, -3,3, 13, 27, 45, 67, ...
Answer:
the pattern is +2, +6, +10, +14, +18 etc
so its in increment of 4
the rest is trivial
Step-by-step explanation:
Answer:
[tex]u_{n} = 2n^{2} -4n-3[/tex]
Step-by-step explanation:
a +b + c = - 5 First term in sequence
3a + b = 2 Difference between first two terms
2a = 4 Difference between the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)
2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so b = -4; 2 - 4 + c = -5 → -2 + c = -5 so c = -3
Which table of ordered pairs represents a proportional relationship?
Answer:
Insert the table
Step-by-step explanation:
There is no table above
what the slope of (15,9) (-10,3)
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[tex]slope = \frac{3 - 9}{ - 10 - 15} \\ [/tex]
[tex]slope = \frac{ - 6}{ - 25} \\ [/tex]
[tex]slope = \frac{6}{25} \\ [/tex]
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Answer:
The slope is [tex]\frac{6}{25}[/tex] or [tex]0.24[/tex].
Step-by-step explanation:
This is the formula to calculate the slope from two given points: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] . Now, substitute (x1, y1) and (x2, y2) for (15,9) and (-10,3). [tex]slope=\frac{3-9}{-10-15}[/tex] . That equation becomes [tex]slope=\frac{-6}{-25}[/tex] . You have to change [tex]\frac{-6}{-25}[/tex] to [tex]\frac{6}{25}[/tex] . The slope is 6/25 or in decimal form, 0.24.
Which relation is a function?(click all that apply)
Answer:
Step-by-step explanation:
y=2x+1
y=x^2
The other one isn't a function because it won't pass the vertical line test. You can not use the same X in a function.
Which exponential function is represented by the graph?
O f(x) = 2( 1/2 )x
O f(x) = 1/2(2)x
O f(x) = 1/2(1/2)x
Of(x) = 2(2)x
PLEASE HELP MEE!
Answer:
f(x) = [tex]\frac{1}{2}[/tex] [tex](2)^{x}[/tex]
Step-by-step explanation:
Using the standard form of the exponential function
y = a [tex]b^{x}[/tex]
To find a and b , substitute ordered pairs from the graph
Using (0, 0.5 ), then
0.5 = a[tex]b^{0}[/tex] [
a = 0.5 , so
y = [tex]\frac{1}{2}[/tex] [tex]b^{x}[/tex]
Using (1, 1) , then
1 = [tex]\frac{1}{2}[/tex][tex]b^{1}[/tex] , thus
b = 2
f(x) = [tex]\frac{1}{2}[/tex][tex](2)^{x}[/tex] ← exponential function representing graph