Step-by-step explanation:
[tex] \frac{1}{4} \: log_4 16 \\ \\ = \frac{1}{4} \: log_4 {4}^{2} \\ \\ = \frac{1}{4} \times 2\: log_4 {4} \\ \\ = \frac{1}{4} \times 2\: \times 1 \\ \\ = \frac{1}{2} \\ \\ \huge \blue{ \boxed{\therefore \: \frac{1}{4} \: log_4 16= \frac{1}{2} }}\\ [/tex]
identify the terms, coefficients, and constants in the expression.
1. 3 + c + e
2. 5m + 9
3. 3p2 + 7
Answer:
1. 3 is a constant term of the expression.
2. 9 is constant term of the expression.
3.7 is a constant term of the expression.
Step-by-step explanation:
1. 3+c+e
Here 3 is a constant term of the expression.
c and e are the variables.
The coefficient of c is 1.
The coefficient of e is 1.
It is a trinomial expression.
2.
5m +9
9 is constant term of the expression.
m is a variable of the expression.
The coefficient of m is 5.
It is a binomial expression.
3.
3p²+7
7 is a constant term of the expression.
p is the variable.
The coefficient of p² is 3.
It is a binomial expression.
spinner at the right is spun 12 times. It lands on blue 1 time.
What is the experimental probability of the spinner landing on blue?
Answer:
1/12
Step-by-step explanation:
Bonds are a(n) _______________ instrument.
Answer:
indebtedness
Step-by-step explanation:
in rectangle PQRS, shown below, the diagonal PR is 15 meters. if the sine of angle SPR is 7/10, what is the value of RS?
Answer:sin =perpendicular/hypotenuse
Step-by-step explanation:
Sin angle is given use tan theta or cos theta to find the RS
- The lengths (in feet) of the sides of a pentagon can be represented by these
expressions: 6a, a, 4, 8, and 2a. Write a simplified expression for the perimeter
of the pentagon in feet.
Answer:
9a+12
Step-by-step explanation:
The perimeter is the sum of the side lengths, so is ...
6a + a + 4 + 8 + 2a
= a(6 +1 +2) + (4 +8)
= 9a +12
how much do u need to subtract from 41/6 to make 6
RS and ST are 2 sides of a regular 12-sided polygon.
RT is a diagonal of the polygon.
Work out the size of angle STR.
You must show your working.
Answer:
15°
Step-by-step explanation:
The exterior angle at vertex S is 360°/12 = 30°. That angle has a measure that is equal to the sum of the congruent angles at R and T of ΔRST. In other words, ...
∠T = 30°/2 = 15°
The size of angle STR is 15°.
The sides of a regular polygon are congruent.
The size of STR is 15 degrees
The polygon is 12-sided.
This means that:
[tex]\mathbf{n =12}[/tex]
The sum of angles in a regular hexagon is 360.
So, the angle at vertex S is:
[tex]\mathbf{\theta = \frac{360}{n}}[/tex]
This gives
[tex]\mathbf{\theta = \frac{360}{12}}[/tex]
[tex]\mathbf{\theta = 30^o}[/tex]
The external angle of a triangle equals the sum of the opposite internal angles.
This means that:
[tex]\mathbf{\theta = \angle STR + \angle SRT}[/tex]
Where:
[tex]\mathbf{ \angle STR = \angle SRT}[/tex]
So, we have:
[tex]\mathbf{\theta = \angle STR + \angle STR}[/tex]
[tex]\mathbf{\theta = 2\angle STR}[/tex]
Substitute [tex]\mathbf{\theta = 30^o}[/tex]
[tex]\mathbf{30^o = 2\angle STR}[/tex]
Divide both sides by 2
[tex]\mathbf{15^o = \angle STR}[/tex]
Rewrite as:
[tex]\mathbf{\angle STR = 15^o }[/tex]
Hence, the size of STR is 15 degrees
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True or false 4.62 < 4.67
True, 4.62 is less than 4.67
what is 3.40425532 reduced
Given the equation y=-1/3x-7, what are the slope and the y-intercept?
Answer: slope is -1/3 and the y intercept is -7
Step-by-step explanation:
Find the distance between the points (2,8) and (-1,9)
Use the distance formula: D=sqrt((x2-x1)^2+(y2-y1)^2)
Plug in:
D=sqrt((9-8)^2+(-1-2)^2)
D=sqrt(1^2+(-3)^2)
D=sqrt(1+9)
D=sqrt(10)
So the distance is about 3.16 units
Hope this helped!
Luna mixes 2 cup of orange juice with 2 cup of cranberry juice. She gives
cup of the juice to Mags. How much is left in Luna's glass?
If the function f(x) = (2x - 3)^3is transformed to g(x) = (-2x - 3)^3, which type of transformation occurred?
A. vertical shift
B. horizontal reflection
C. horizontal shift
D.vertical reflection
PLS HELP! WILL MAKR BRAINLIEST AND GIVE 20 POINTS!!!!
Answer:
See attached table for the answers.
Step-by-step explanation:
Because 1/4 inches is 2 feet, 1 inch is 8 feet, making the conversion factor x8.
Answer:
The scale factor is 1/4 inch to 2 feet but can be simplified to 8 feet per inch.
1. Lobby drawing length is 2 inches.
2. Principal's Office actual length is 10 feet.
3. The library's drawing length is 2.5 inches.
4. The science lab's actual length is 12 feet.
5. The cafeteria's drawing length is 6 inches.
6. The music room's actual length is 32 feet.
8. The gym's actual length is 104 feet.
9. The auditorium's drawing length is 7 inches.
10. The teachers' lounge's actual length is 14 feet.
I hope this helped you. If you would mark brainliest that would be appreciated.
You start driving north for 7 miles, turn right, and drive east for another 24 miles. At the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]AC = 25\ miles[/tex]
Step-by-step explanation:
Given:
Distance for north side = 7 miles.
Distance for east side = 24 miles.
We need to find the displacement.
Solution:
Figure shows Point A is starting point and AB = 7 miles is North side distance and BC = 24 miles is east side distance and AC is shown as displacement.
Using Pythagoras theorem to find displacement (AC).
[tex](AC)^{2}=(AB)^{2}+(BC)^{2}[/tex]
Substitute AB = 7 and BC = 24 in above equation.
[tex](AC)^{2}=(7)^{2}+(24)^{2}[/tex]
[tex](AC)^{2}=49+576[/tex]
[tex](AC)^{2}=625[/tex]
[tex]AC = \sqrt{625}[/tex]
[tex]AC = 25\ miles[/tex]
Therefore, displacement of the car [tex]AC = 25\ miles[/tex]
Find the sine...... Pls
Answer:
72/97
Step-by-step explanation:
Sinus is calculated by dividing opposite by hypotenuse so the answer is 72/97
Answer:
72/97
Step-by-step explanation:
Sin(X) = opposite/hypotenuse
Sin(X) = 72/97
The - - - - - - - - - - - - - - - -,f(x)=x, is formed by the composition of a function and its inverse (2 words)
Answer:
Identity function
What is the answer
Answer:
A
Step-by-step explanation:
Move the entire triangle left 6 units.
Answer: A
Step-by-step explanation:
1 > 5 (b - 14) + 16 help me please
Answer:
b < 11
Step-by-step explanation:
Given
1 > 5(b - 14) + 16 ← distribute and simplify right side
1 > 5b - 70 + 16
1 > 5b - 54 ( add 54 to both sides )
55 > 5b ( divide both sides by 5 )
11 > b, thus
b < 11
What two numbers multiply to -27 and add to 1
Answer:
3 x 9, 1 x 27, 9 x 3
Step-by-step explanation:
you have to multiple 3 x 9 to get to 27. you have to multiple 1 x 27 to get 27. you have to multiple 9 x 3 to get 27.The two numbers that multiply to -27 and add to 1 are 9 and -3.
To find two numbers that multiply to -27 and add to 1, we can use the method of factoring and algebraic manipulation.
Let the two numbers be x and y.
Step 1: Set up the equations based on the given conditions:
xy = -27 (the two numbers multiply to -27)
x + y = 1 (the two numbers add to 1)
Step 2: Solve one of the equations for one variable in terms of the other.
From the second equation, we can express y in terms of x:
y = 1 - x
Step 3: Substitute the value of y into the first equation:
x(1 - x) = -27
Step 4: Expand and rearrange the equation:
x - x^2 = -27
Step 5: Rewrite the equation in standard quadratic form:
x^2 - x - 27 = 0
Step 6: Factor the quadratic equation:
(x - 9)(x + 3) = 0
Step 7: Set each factor equal to zero and solve for x:
x - 9 = 0 --> x = 9
x + 3 = 0 --> x = -3
So, the two numbers are 9 and -3, as 9 * -3 = -27, and 9 + (-3) = 1.
In conclusion, the two numbers that multiply to -27 and add to 1 are 9 and -3. By setting up and solving the system of equations and factoring the quadratic equation, we obtained these two values that satisfy the given conditions.
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Sarai is mixing a solution. She pours all the liquid from a full small beaker into a larger beaker. The liquid fills the large beaker to 15% of its capacity. If the small beaker holds 300 mL, how much does the large beaker hold?
Answer:
2000 ml
Step-by-step explanation:
Given: Sarai pours all the liquid from a full small beaker into a larger beaker.
The liquid fills the large beaker to 15% of its capacity.
The small beaker holds 300 ml.
Lets assume capacity of large beaker to hold be "x".
As given, Sarai pours all the liquid from a full small beaker into a larger beaker
∴ [tex]15\% \times x= 300\ ml[/tex]
⇒ [tex]0.15x= 300[/tex]
Dividing both side by 0.15
⇒[tex]x= \frac{300}{0.15}[/tex]
∴ [tex]x= 2000\ ml[/tex]
Hence, the large beaker can hold 2000 ml of liquid.
Which expression represents the phrase the sum of twice a number and 7
Answer:
2n+7
Step-by-step explanation:
A snowboard is on sale for $476. If the
original price was $560, what is the
percent discount?
Answer:
15%
Step-by-step explanation:
we call the original price 100% and to find the discount amount :
Multiply 100 by $476 then divide by $560
100 × $476 ÷ $560 = 85
$476 is 85% of the original price therefore the amount of discount as in percentage is 100 - 85 = 15%
A regular pentagon is dilated by a scale factor of 73 to create a new pentagon. How does the perimeter of the new pentagon compare with the original perimeter?
Question:
A regular pentagon is dilated by a scale factor of 7/3 to create a new pentagon. How does the perimeter of the new pentagon compare with the original perimeter?
Answer:
The perimeter of the new pentagon is equal to [tex]\frac{7}{3}[/tex] times the perimeter of the original pentagon
Solution:
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let ,
z is the scale factor
x is the perimeter of the new pentagon
y is the perimeter of the original pentagon
Then,
Scale factor = ratio of perimeters
[tex]z=\frac{x}{y}[/tex]
In this problem we have
[tex]z=\frac{7}{3}[/tex]
Substituting we get,
[tex]\frac{7}{3} = \frac{x}{y}\\\\x = \frac{7}{3}y[/tex]
Which means,
[tex]perimeter\ of\ the\ new\ pentagon = \frac{7}{3} \times \text{ perimeter of the original pentagon}[/tex]
Therefore , the perimeter of the new pentagon is equal to [tex]\frac{7}{3}[/tex] times the perimeter of the original pentagon
Which statement is best supported by the dot plot? Choose ONE and explain your
answer.
I. The range of the number of miles Amanda skated in August is less than the range
of the number of miles she skated in July.
II. The distribution of data is approximately symmetrical in both sets of data.
III.The mode of the number of miles Amanda skated in July is equal to the mode of
the number of miles skated in August.
Answer:
The statement that is best supported by the dot-plot is iii)
The mode of the number of miles Amanda skated in July is equal to the
mode of the number of miles skated in August.
This is a true statement.
The mode of the number of miles Amanda skated in July is equal to 1.
The mode of the number of miles Amanda skated in August is equal.
Step-by-step explanation:
i) The range of the number of miles Amanda skated in August is less than the
range of the number of miles she skated in July.
This is a true statement.
the range of the number of miles Amanda skated in August is 1 to 3
the range of the number of miles Amanda skated in July is 1 to 4
ii) The distribution of data is approximately symmetrical in both sets of data.
This is NOT a true statement.
the distribution of data of the number of miles Amanda skated in August
is not symmetrical.
the distribution of data of the number of miles Amanda skated in August
is approximately symmetrical.
iii) The mode of the number of miles Amanda skated in July is equal to the
mode of the number of miles skated in August.
This is a true statement.
The mode of the number of miles Amanda skated in July is equal to 1.
The mode of the number of miles Amanda skated in August is equal.
PLEASE HELP ! Trying to make honor roll !
Which point represents the solution to the system of equations below?
Answer:
B
Step-by-step explanation:
Because it is higher than the others and also includes the number 2, as it says in the fraction and is located in 1/2
Answer:
Point A
Step-by-step explanation:
You already know y is -2. Just substitute that to the top equation and solve for x. X would be -4.
(-4, -2)
Find the point on the graph and you'll see it falls on point A.
With a simple interest rate of 12%, how much will an investment of $20,000 be worth in 10 years
Answer:
$24,000
Step-by-step explanation:
If each year you get 12% of interest 20,000 dollars x 0.12 = 1 year worth of interest or $2400 then if its over a 10 year span it would be $2,400 x 10 (amount of years) = $24,000
Answer: $44,000
Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 Find f(g(4)). f(g(4)) =
Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
f(x) = x-7
g(x) = x^2
f(4) = 4-7 = -3
g(f(4)) = (-3)^2
(-3)^2 = 9
g(f(4)) is 9
Find f(g(4)).
f(g(4)) = f(g(4)) = 9
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
Composition of the functions is sometimes commutative.
hope this helps!! have an amazing day <3
2021 edg
How many times smaller is 2 × 10-3 than 4 × 10-2? PLEASE HELP
A.
20
B.
200
C.
2,000
D.
0.2
Step-by-step explanation:
Let x be the smaller than 4 ×[tex]10^{-2}[/tex].
To find, the number of times smaller is 2 × [tex]10^{-3}[/tex] than 4 × [tex]10^{-2}[/tex] = ?
∴ x = [tex]\dfrac{4\times 10^{-2}}{2\times 10^{-3}}[/tex]
= 2 × [tex]10^{-2}[/tex] × [tex]10^{3}[/tex]
Using the identity,
[tex]a^{m}=\dfrac{1}{a^{-m}}[/tex]
= 2 × [tex]10^{-2+3}[/tex]
Using the identity,
[tex]a^{m} \timesa^{n}=a^{m+n}[/tex]
= 2 × [tex]10^{1}[/tex]
= 2 × 10
= 20
Thus, the required "option A) 20" is correct.
Add the following numbers and use the checking method (add down and then add up) to make sure your answer is correct. (Copy carefully on scratch paper to work the problem.)
471
+
582
To add 471 and 582, line up the numbers by place value and add each column, carrying over as needed. The sum is 1053. You check by reversing the order of the numbers and adding again; the sum should remain the same.
Explanation:To add the following numbers and use the checking method (add down and then add up), perform the following steps:
Write down the numbers vertically aligned by their place values: 471 + 582 Add the ones place values (1+2) to get 3. Add the tens place values (7+8) to get 15, write down 5 and carry over 1. Add the hundreds place values (4+5) along with the carried over 1 to get 10, write down 0 and carry over 1. Write the carried over 1 in the next left column to get the final sum: 1053 To check, add the sum upwards: 582 + 471 You should arrive at the same sum: 1053.
If you obtain the same result by both adding down and adding up, your answer is verified as correct.
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