Answer:
1/4
Step-by-step explanation:
The change of base formula for logarithms is ...
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]
__
Using this with the given values, we have ...
[tex]\log_x(y)=\dfrac{\log_p(y)}{\log_p(x)}=\dfrac{5}{20}\\\\\boxed{\log_x(y)=\dfrac{1}{4}}[/tex]
The set of rational numbers include all the following numbers except...
O √120
6²
O 12.9
O1/3
Answer:
[tex] \sqrt{120} [/tex]
Step-by-step explanation:
√120 is irrational.
find the missing value. 2 + blank = -13
Answer:
-15
Step-by-step explanation:
-13-2= -15
(to check:2+ -15= -13)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2 + [blank] = -13}[/tex]
[tex]\large\textbf{CONVERT TO: }[/tex]
[tex]\mathsf{2 + b = -13}[/tex]
[tex]\mathsf{b + 2 = -13}[/tex]
[tex]\large\textbf{SUBTRACT 2 to BOTH SIDES: }[/tex]
[tex]\mathsf{b + 2 - 2 = -13 - 2}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{b = -13 - 2}[/tex]
[tex]\mathsf{b = -15}[/tex]
[tex]\huge\text{Therefore, the mystery number is: \boxed{\mathsf{-15}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
If x + y = 2 and x - y = 6, solve for x and y.
Answer:
Step-by-step explanation:
Givens
x + y = 2
x - y = 6
Solution
Just add the two equations together. The y's will drop out.
x + y = 2
x - y = 6 Add
2x = 8 Divide by 2
2x/2 = 8/2 Combine
x = 4 Substitute x = 4 into the top equation
x + y = 2
4 + y = 2 Subtract 4 from both sides
4-4+y=2-4 Combine
y = - 2
Answer
x = 4
y = -2
Find the equation of the line passing through the points -2x+1 (8,2)
The line that passes through (-2, 1) and (8, 2) is:
y = (1/10)*x + 12/10
How to find the equation of the line?I assume you want to find the equation of the line that passes through (-2, 1) and (8, 2).
A general linear equation is written as:
y = a*x + b
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that it passes through (-2, 1) and (8, 2), then:
[tex]a = \frac{2 - 1}{8 - (-2)} = 1/10[/tex]
Then the line is:
y = (1/10)*x + b
To find the value of b, we use one of the given points, for example if we use (8, 2), it means that when x = 8, we must have y = 2.
2 = (1/10)*8 + b
2 - 8/10 = b
20/10 - 8/10 = b
12/10 = b
Then the linear equation is:
y = (1/10)*x + 12/10
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how to graph y = 2|x + 3| - 4
The x-intercepts and the y-intercepts of the function is that determines the graph is:
x-intercepts = (-5,0) and (-1,0)y-intercepts = (0,2)How do we graph the function y = f(x) of an absolute equation?The function of an absolute equation can be graphed by determining the values of x-intercepts and the y-intercepts of the function.
From the given equation:
y = 2|x+3| - 4
To determine the y-intercepts, we need to set the values of x to zero, and vice versa for x-intercepts.
By doing so, the x-intercepts and the y-intercepts of the function is:
x-intercepts = (-5,0) and (-1,0)y-intercepts = (0,2)Therefore, since we know the x and y-intercepts, the graph of the absolute value can be seen as plotted below.
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which choice is equivalent to the expression below? square root of -64
Step-by-step explanation:
[tex] \sqrt{ - 64 } = - 8[/tex]
so the answer you got pls mark branlist
Solve the equation.
8-2x = -8x + 14
O x=-1
3
0x = - 1²/20
5
0x = ²/3
O x = 1
Answer:
D. x=1
Step-by-step explanation:
8-2x = -8x + 14
First, add 8x to both sides.
8+6x=14
Next, subtract 8 from both sides.
6x=6
Lasty, divide 6 from both sides.
x=1
Hope this helps!
If not, I am sorry.
PLEASE HELP FAST!!! A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.
The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
Angle of elevation and depressionThese method is used to determine the side and angles of a triangle
From the question given, we have the following parameters
Base of the building = 7feet (Adjacent side)
Height of the building = 18 feet (Opposite side)
Required
angle of elevation of the building
Using the SineOppositeHypotenuse CosineAdjacentHypotenuse TangentOppositeAdjacent identity
tanФ = opp/adj
tanФ = 18/7
Ф = 68.73 degrees
Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
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If f(x) is a linear function, which statement must be true?
O f(x) has no constant term.
O f(x) has no x²-term.
Of(x) has no terms with a coefficient other than 1.
Of(x) has no x-term.
Answer:
has no x^2 term
Step-by-step explanation:
Has no x^2 term <====== that would make it an exponential function, not linear
Calculate -0.4 as a percentage of 1.8
Answer:
-22.2222222222%
Step-by-step explanation:
-0.4/1.8×100
Seven times the twice of a number and 6 equals 4
Answer:
7(2a+6) = 4
and the answer is:
19/7
Step-by-step explanation:
7(2a+6) = 4
7*2a + 7*6 = 4
14a + 42 = 4
14a = 4 - 42
14a = -38
a = -38/14
a = -19/7
difference between compounded annually, monthly and daily.
Answer:
With monthly compounding, the bank will calculate interest on your account just once per month. It will not update your balance on a daily basis when it calculates how much interest it owes you. Assuming that the APR is the same, accounts with monthly compounding offer a lower APY than accounts with daily compounding.
Vanessa has 16 songs on a Classic Rock CD. Six of the songs are by the Beatles, 4 are by the Rolling Stones, 4 are by the Who, and 2 are by the Doors. Vanessa plays the CD. She selects a setting that randomly chooses songs to play.
Find the probability of each event:
a) The first 3 songs played are by the Beatles.
b) The first 2 songs played are by the Rolling Stones and the next 2 songs are by the Beatles.
c) The first 2 songs played are by the Doors, and the next song played is either by the Beatles or the Rolling Stones.
Using it's concept, it is found that the probabilities are given as follows:
a) 0.0527 = 5.27%.
b) 0.0088 = 0.88%.
c) 0.0098 = 0.98%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
6 out of 16 songs are of the Beatles, hence the probability of a single music being from the Beatles is:
[tex]pB = \frac{6}{16} = \frac{3}{8}[/tex]
Of three musics, the probability is:
[tex]p = \left(\frac{3}{8}\right)^3 = 0.0527[/tex]
Item b:
For the Rolling stones, the probability is:
[tex]pR = \frac{4}{16} = \frac{1}{4}[/tex]
For the four musics, the probability is:
[tex]p = \left(\frac{1}{4}\right)^2 \times \left(\frac{3}{8}\right)^2 = 0.0088[/tex]
Item c:
For the doors, the probability is:
[tex]pD = \frac{2}{16} = \frac{1}{8}[/tex].
For Beatles or Rolling stones, the probability is:
[tex]pBR = \frac{10}{16} = \frac{5}{8}[/tex]
For the three musics, the probability is:
[tex]p = \left(\frac{1}{8}\right)^2 \times \frac{5}{8} = 0.0098[/tex]
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Which shows all the exact solutions of 2sec^2 (x)-tan^4 (x)=-1? Give your answer in radians.
a) pi/3 + kpi and 2pi/3 + kpi
b) pi/3 +2kpi and 5pi/3 +2kpi
c) pi/4 +2kpi, 3pi/4 + 2kpi, 5pi/4 +2kpi, and 7pi/4 +2kpi
d) pi/3 + kpi, 2pi/3 +kpi, 4pi/3 +kpi, and 5pi/3 +kpi
Answer:
a. 1/3pi+kpi and 2/3pi+kpi
Step-by-step explanation:
2Sec²x
=2+2tan²x-(tan²x)²=-1
Let tan²x=u
-u²+2u+2=-1
-u²+2u+3=0
u²-2u-3=0
(u+1)(u-3)=0
u=-1,u=3
(tan x)²=-1(No solution)
(tan x)²=3
>>tan x=±sqrt(3)
I) tan x=sqrt(3)
>>tan(pi/3)=sqrt 3
Tan(pi+A) =tanA
Tan(pi+pi/3)=tan(pi/3)
>>tan(4/3pi)=sqrt(3)
>>x=4/3pi and 1/3pi
General solution: 1/3pi+kpi
ii) tan x=-sqrt(3)
x=2/3pi(At 2nd quadrant)
x=5/3pi(at 4th quadrant)
General solution: 2/3pi+kpi
1. (08.01 MC)
The graph shows two lines. A and B
Answer:
Part A:
A pair of linear equations can only have one solution or infinitely many solutions. In this case, there would only be one solution as they intersection at only one point.
Part B:
The solution would be (3, 4) because it is the point of intersection between the two linear lines.
Find the measure of angle DCF=
help me please :)) ty
Answer:
∠ DCF = 39°
Step-by-step explanation:
the secant- secant angle DCF is half the difference of the measures of the intercepted arcs, that is
∠ DCF = [tex]\frac{1}{2}[/tex] (EG - DF) = [tex]\frac{1}{2}[/tex] (127 - 49)° = [tex]\frac{1}{2}[/tex] × 78° = 39°
What are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
The value of (x,y) is (1.2 , -4.7) , Option D is the right answer.
The complete question is
On a coordinate plane, a line is drawn from point a to point b. point a is at (7, negative 2) and point b is at (negative 8, negative 9). what are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
What are Coordinates ?Coordinates are the location of a point in an (x,y) plot.
The given data is
Coordinates of
A = (7,-2)
B = (-8,-9)
m:n = 5:8
The coordinates of partition has to be determined
The formula used is
[tex]\rm (x,y) = \dfrac{1}{m+n} *(nx_1 + mx_2 , ny_1+ny_2)\\\\\\\rm (x,y) = \dfrac{1}{5+8} *(5*-8 + 8*7 , 5*-9+8*-2)[/tex]
(x,y ) = (1.2 , -4.7)
Therefore Option D is the correct answer.
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For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
The temperature that accurately describes the time that would have spent cooling is 300.
How to solve for the cooling time.We have the function as f(t) = 349.2(0.98)t
We have to solve for all of the values in the option
When t = 0
This would give us an infinite value for t hence it is not the answer.
When t = 100
we have 61.6
When t = 300
we have f(t) = 7.5
WHen t = 400
f(t) = -6.7
From the solved values the accurate one that has to talk about the time spent cooling is 300 at 7.5
Complete questionThe function f(t) = 349.2(0.98)t models the relationship between t, the time an oven spends cooling and the temperature of the oven. For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400
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Please help! I'm not quite understanding this.
Answer:
d.) 21
Explanation:
Rules:
-|a| = -a|-a| = ax = |a| then x = ±aSolve:
[tex]\rightarrow \sf \dfrac{4|a|}{2} + |a-3|[/tex]
[insert a = -6]
[tex]\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|[/tex]
[simplify the following]
[tex]\sf\rightarrow \dfrac{4(6)}{2} + 9[/tex]
[tex]\sf\rightarrow 12 + 9[/tex]
[tex]\sf\rightarrow 21[/tex]
PLEASE HELP TIMED!!!
Which of the following describes the growth rate of the exponential function in the graph below?
a) For each x increase of 1, the y increases by a common difference of 3.
b) For each x increase of 1, the y increases by a common factor of 3.
c) For each x increase of 1, the y increases by 4 more than the previous increase.
d) For each c increase of 2, the y increases by doubling and then adding one.
Answer:
B
Step-by-step explanation:
let me know if you want an explanation :))
Please help!!!! ASAP!!!!!!!!!!
Answer:
[tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
Step-by-step explanation:
Transform - y-25^2=-100
divide
simplify
x plus-minus [tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
ab (2a²b² - 4b) = what is the answer
Answer:
2ab(a2b−2)
Step-by-step explanation:
multiple answer problem
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: E.\:\: \overline{DC}[/tex]
or
[tex]\qquad \tt \rightarrow \: F.\:\:\overline{CD}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
A line with two dots at ends (two ends) represents a line segment.
And it can be represented as :
[tex]\qquad \tt \rightarrow \: \overline{DC}[/tex]
or
[tex]\qquad \tt \rightarrow \: \overline{CD}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
I'm pretty sure it is d... .......
Write a quadratic equation, in factored form solution are 0,and 6
Answer: [tex]x(x-6)=0[/tex]
19.
(05.06 MC)
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Which of the following is an appropriate line of best fit? (1 point)
Considering the given scatter-plot, the line of best-fit is given by:
y = 0.77857t + 3.7.
How to find the equation of the line of best-fit using a calculator?To find the equation, we need to insert the points (t,y) in the calculator.
In this problem, considering the scatter-plot, we have that:
The values of t are: 1, 2, 3, 4, 5, 6, 7.The values of y are: 3.8, 5.8, 6.2, 7.5, 7, 8.2, 9.2.Hence, using the calculator, the equation is:
y = 0.77857t + 3.7.
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please help me guys its math
A boat travels 333 km in 7 hours with a constant speed how far can it travel in 6 hours with the same speed
Answer:
258 km
Step-by-step explanation:
We can calculate the speed of the boat with (333km/7 hours) = 47.57 km/hr.
Assuming the same speed, the boat would travel (47.57 km/hr)*(6 hr) = 258 km
When the sum of a list of integers is divided by the mean of the integers, the result is x. What does x represent?
Answer:
it is the number of intigers in the list
Based on the concept of integer and the options available, x does represent the number of 2 integers in the list.
What is Integers?An integer is a mathematical term that is known as the number zero, a positive natural number, or a negative integer with a minus sign.
Generally, Integers the negative numbers are the additive inverses of the corresponding positive numbers.
In this case, it has been mathematically proven that when the sum of a list of integers is divided by the mean of the integers the result x represents the total number of integers in the list.
Hence, in this case, it is concluded that the correct answer is option H. The numbers if integers in the list.
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A cake decorator is rolling a square of fondant into a rectangle. the area of the rectangle can be represented by the expression 1.5s(2s). simplify the expression representing the area. 3.5s 3s2 3.5s2 3s
Answer:3.5s2
Step-by-step explanation:
because I said so
Answer:
3.5s2
Step-by-step explanation:
because that guy said so and it was right
