The logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]
How to rewrite the expression?The expression is given as:
4^(1/2) = 2
Take the logarithm of both sides
log(4^(1/2)) = log(2)
Apply the change of base rule
1/2log(4) = log(2)
Divide both sides by log(4)
1/2 = log(2)/log(4)
Change the base
[tex]\frac 12 =\log_4(2)[/tex]
Rewrite as:
[tex]\log_4(2) = \frac 12[/tex]
Hence, the logarithmic expression of 4^(1/2) = 2 is [tex]\log_4(2) = \frac 12[/tex]
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A triangle is translated by using the rule (x,y) →(x-4.y+1). Which describes how the figure is moved?
O four units left and one unit down
O four units left and one unit up
O one unit right and four units down
O one unit right and four units up
Answer:
Four units left and one unit up.
Step-by-step explanation
Adding -4 to each x-coordinate shifts the figure to the left 4 units.
Adding +1 to each y-coordinate shifts the figure up 1 unit.
The figure is moved ...
four units left and one unit up
Answer:
2nd option
Step-by-step explanation:
x-4 = 4 left
y+1 = 1 up
2nd option
Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
BRAINLIEST, URGENT!!
Victoria dropped a basketball off the top of a building. Each time the basketball hit the ground, it bounced upward one-half the height that it fell. Victoria initially dropped the basketball from a distance of 60.0 feet above the ground. What was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?
Answer:
7.5 ft
Step-by-step explanation:
1st drop = 60 ft
2nd drop = 60/2 = 30 ft
3rd drop = 30/2 = 15 ft
4th drop = 15/2 = 7.5 ft
Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point (-4, 6.75)(4, 8)(4, 9.25)(4, 16), and its radius is 1.252.53.756.25 units. The equation of this circle in standard form is (x - 4)^2 + (y - 8)^2 = 2.5(x + 4)^2 + (y + 8)^2 = 2.5(x - 4)^2 + (y - 8)^2 = 6.25(x + 4)^2 + (y + 8)^2 = 6.25.
The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:
The center is (4,8).The radius is of 2.5 units.[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center is the midpoint of the chords, hence:
[tex]x_0 = \frac{4 + 4}{2} = 4[/tex].[tex]y_0 = \frac{5.5 + 10.5}{2} = 8[/tex].The radius is half the distance between the chords, hence:
[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].
Hence the equation is:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]
[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]
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What is the system of inequalities associated with the following graph?
A) {y>−2
{x+y≥1
B){y<−2
{x+y≥1
C){y<−2
{x+y<1
D){y< -2
{x+y> 1
Answer: C
Step-by-step explanation:
[tex]y=-2[/tex] is dotted and shaded below, so it represents [tex]y < -2[/tex].
Also, [tex]x+y=1[/tex] is shaded above, so it represents [tex]x+y < 1[/tex].
In an interview of 45 students, 12 liked Mathematics and Science, 5 liked Mathematics and English, 25 liked Mathematics; 23 liked Science; 4 liked all three subjects; 15 liked English; 10 liked Science and English. How many students did not like any of the subjects?
Answer:
Step-by-step explanation:
plus 18 and subtract 4
What is the measure of the corresponding central angle for XY in radians?
Answer:
4 radians
Step-by-step explanation:
Arc Length (Radians) = rθ
Given Arc Length XY = 40cm and radius, r = 10cm,
we will substitute these 2 values into the formula to find θ.
(10)θ = 40
θ = 40 / 10
= 4 radians
Answer:
A
Step-by-step explanation:
the length of arc XY is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{0}{2\pi }[/tex] ( r is radius and Θ is central angle )
here arc = 40 and r = 10 , then
2π × 10 ×[tex]\frac{0}{2\pi }[/tex] = 40
20π × [tex]\frac{0}{2\pi }[/tex] = 40 ( cancel 20π and 2π by 2π )
10Θ = 40 ( divide both sides by 10 )
Θ = 4 radians
Does dy/dx in a graph mean the value of f'(x), or the slope of f'(x) at the point?
Find the area of the figure to the nearest square unit 3 cm and 8 cm
The area of the given composite figure is 74.24cm^2
Area of composite figureThe figure is made up of semi circle and rectangle
Area = area of semicircle + Area of rectangle
Area = 3.14(4)^2 + 3(8)
Area = 50.24 + 24
Area. = 74.24cm^2
Hence the area of the given composite figure is 74.24cm^2
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Identical prizes are to be given to two winners from a group of 12 contestants. What counting formula would you use to determine how many ways the prizes could be given out
We will use a combination formula to determine how many ways the prizes could be given out.
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
The formulas nCk is popularly known as counting formula.
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A triangle has vertices as D(4,5), E(1,8) and F (1,2). Show that the height from D is also the median from D.
The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)
How can the height and median be calculated?The height from D is perpendicular to EF
The slope of EF = (8 - 2)/(1 - 1) = ∞
Therefore, the side EF is parallel to the y-axis.
Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)
The median is the midpoint of the side EF
The coordinates of the midpoint is found as follows;
[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]
Therefore;
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NEED HELP ASAP!!
This graph shows the total number of patients seen by a doctor over the course of a 5-day workweek.
What are the domain and range of this relationship??
Using the domain and range concepts, we have that:
The domain is: {0, 1, 2, 3, 4, 5}.The range is: {0, 12, 24, 36, 48, 60}.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x.The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y.Hence, considering the given graph:
The domain is: {0, 1, 2, 3, 4, 5}.The range is: {0, 12, 24, 36, 48, 60}.More can be learned about the domain and the range of a data-set at https://brainly.com/question/10891721
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Briefly explain how multiple regression enhances the two primary purposes of regression analysis.
The statistical goal of multiple regression analysis is to build a linear equation model that identifies the optimal weighted linear combination of independent variables in the study in order to optimally predict the reference variable.
Regression analysis is usually performed for one of two purposes. Predicting the value of the dependent variable of a person whose information about the explanatory variable is available, or estimating the effect of the explanatory variable on the dependent variable.
In multiple regression analysis, researchers can determine the strength of the relationship between the outcome (dependent variable) and multiple predictors, and the importance of each predictor in the relationship, often the effect of other predictors. It can be evaluated by statistically eliminating it.
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there are 12 students including 4 boys in a classroom. Find the number of girls in 8 such classrooms
Answer:
64 girls
Step-by-step explanation:
Number of boys in a classroom: 4
Total no. of students in the classroom: 12
Number of girls in 1 classroom: 12-4 = 8
Number of girls in 8 such classrooms: 8 × 8 = 64
Li invests money in a savings account. She wants to know the amount of simple interest that she will earn in 6 years at 3.75 percent. What additional information does she need to find this amount?
Answer:
She needs the starting amount of money to create an equation.
Step-by-step explanation:
The formula that she can use when she has the starting amount or the y-intercept is this one: f(t)=P(1+b)^t.
t=time
b=percent
P=starting value
The formula with the information given is: f(6)=P(1+3.75)^6
Hope this helps!
If not, I am sorry.
Answer:
Principal
Step-by-step explanation:
Since, the amount in the simple interest is,
Where, P is the principal amount,
r is the annual rate,
t is the time ( in years ),
Here, r = 3.75 %, t = 6 years,
Thus, By the above explanation,
It is clear that, we need the value of P, that is, principal to find the amount.
For which value of b can the expression x2 + bx + 18 be factored?
An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).
Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.
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Question 6 of 10
What is the solution to this equation?
2x+6=20
A. x = 13
B. x = 7
C. x = 52
OD. x=28
Answer:
x =7
Step-by-step explanation:
2x+6 = 20
To solve this equation, you first need to subtract 6 from each side
2x+6-6 = 20-6
2x = 14
Then divide each side by 2
2x/2 = 14/2
x = 7
How do I do this? :/
Answer:
13
Step-by-step explanation:
Since triangles CBA and DBA are equal, their lengths would also be equal, thus, DB = 13 as CA = 13
Answer:
CAB = DAB
CA is equivalent to BD
PLEASE HELP!!
Triangle not drawn to scale
Given: m & B = 18°, b = 9, and c = 20. Find
m & Co to nearest whole number.
Answer:
43°
Step-by-step explanation:
Calculating for the measure of angle C using
sine rule[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]
is 2x 2 times or 2x mean 2 x or 1x+1x or 0x+2?
Answer:
Generally x means times so the best and not dummest option is 2 times
2x and 2 x is the same the 2 x is spaced out a little
Step-by-step explanation:
I'm extremely bad at doing these
The first few terms of a geometric sequence with first term [tex]a[/tex] and common ratio [tex]r[/tex] look like
[tex]a, ar , ar^2, ar^3, \ldots[/tex]
and so on. Notice that the [tex]n[/tex]-th term (where [tex]n[/tex] is a natural number) is [tex]ar^{n-1}[/tex].
For this particular sequence, the first term is
[tex]a=3[/tex]
and the fourth term is
[tex]ar^{4-1} = ar^3 = 1029[/tex]
Substitute [tex]a=3[/tex] into the second equation and solve for [tex]r[/tex].
[tex]3r^3 = 1029 \implies r^3 = 343 \implies r = \sqrt[3]{343} = \sqrt[3]{7^3} = 7[/tex]
Then the two terms between the 1st and 4th - i.e. the 2nd and 3rd terms - are
[tex]ar = 3\times7 = \boxed{21}[/tex]
and
[tex]ar^2 = 3\times7^2 = \boxed{147}[/tex]
Answer:
Term 2 is 21, and term 3 is 147.
Step-by-step explanation:
The geometric sequence is 3, 3r, 3r^2, 1029.
[tex]r = \sqrt[3]{ \frac{1029}{3} } [/tex]
[tex]r = \sqrt[3]{343} = 7[/tex]
So we have 3, 21, 147, 1029.
In this assignment, you will explore how the volume is changed when you adjust the height or radius of a cylinder. You will drag points of reference on an interactive tool to represent various changes. The interactive will display the changed volume visually and in the calculations and dimensions. You will then use what you see happening to answer questions.
The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.
How to illustrate the volume?Let's assume that the height and radius are 14cm and 7cm. The volume will be:
= πr²h
= 3.14 × 7² × 14
= 2154.04cm³
When the radius and height are reduced to 5cm and 9cm, the volume will be:
= πr²h
= 3.14 × 5² × 9
= 706.5cm³
This illustrates that the volume reduces when the height and radius reduces.
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PLEASE HELP, kinda forgot how to do it
Answer:
20
Step-by-step explanation:
Rise over run
Answer:
m = 20
Step-by-step explanation:
(a) sin x° = 0.8
Given that x is an obtuse angle, find x.
(b) cos 127° = -cos yo
Given that y is an acute angle, find y.
The value of x is 126.87° and the value of y is 53°.
What is an obtuse and an acute angle?An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.
From the given information:
sin x° = 0.8
x = sin⁻¹ (0.8)
x = 53.13°
x + 53.1° = 180°
x = 180° -53.13°
x = 126.87°
If cos 127° = -cos y°,
-cos y = -0.6018
cos y = 0.6018
y = cos⁻¹ (0.6018)
y = 53°
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Substituting the equation y = 4x + 1 into the equation 2y = -x – 1 will produce the equation ________.
a.)
7x = -3
b.)
7x = 1
c.)
9x = -3
d.)
9x = 1
Answer:
C.
Step-by-step explanation:
This is substitution method in solving simulteanous equations.
given y = 4x + 1
we will substitute y into 2y = -x-1
[tex]2(4x + 1) = - x - 1 \\ 8x + 2 = - x - 1 \\ 8x + x + 2 = - 1 \\ 9x + 2 = - 1 \\ 9x = - 1 - 2 \\ 9x = - 3[/tex]
Therefore the answer is C.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Substituting the equation given into another equation will produce another equation. But which one?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{2y=-x-1}[/tex] | substitute the required equation
[tex]\bf{2(4x+1)=-x-1}[/tex] | solve in terms of x
[tex]\bf{8x+2=-x-1}[/tex] | carry on solving
[tex]\bf{9x+2=-1}[/tex] | carry on solving
[tex]\bf{9x=-3[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;third\;option}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta 1}}[/tex]
Solve the following linear system by elimination. Check your solution:
1. x + 5y =4
2. 4x + 12y = 8
Answer:
(- 1, 1 )
Step-by-step explanation:
x + 5y = 4 → (1)
4x + 12y = 8 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x
- 4x - 20y = - 16 → (3)
add (2) and (3) term by term to eliminate x
0 - 8y = - 8
- 8y = - 8 ( divide both sides by - 8 )
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (1)
x + 5(1) = 4
x + 5 = 4 ( subtract 5 from both sides )
x = - 1
As a check
substitute these values into the left side of both equations and if equal to the right side then they are the solution.
- 1 + 5(1) = - 1 + 5 = 4 = right side
4(- 1) + 12(1) = - 4 + 12 = 8 = right side
(- 1, 1 ) is the solution to the system of equations
Problem Set
Show instructions
Question 4 (1 point)
Given a triangle with sides of length 5 and 8, find the range of possible values for the third side. (Note: left
hand side of inequality in Blank 1 and right hand side in Blank 2)
Blank 1:
Blank 2:
____
Answer:
3 < x < 13
Step-by-step explanation:
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let x be the length of the unknown side.
Therefore, x will either be the longest side or one of the shorter sides.
Therefore:
x < 5 + 8
⇒ x < 13
And:
8 < 5 + x
⇒ 3 < x
So the range of possible values of the third side is greater than 3 and less than 13: 3 < x < 13
Write at least 1 full sentence explaining the steps you would take to evaluate an expression.
The step you would take to evaluate an expression is to follow the order of operation
What are expressions?Expressions are mathematical statements that involve variables, terms, coefficients and mathematical operators
How to determine the steps?Different expressions require different ways of solving
However, the general guide is that the order of operation must be followed
The order of operation is represented by the acronym BEDMAS
Which means
Bracket
Exponent
Division
Multiplication
Addition
Subtraction
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Solve for z square root of z^2-8- square root of 6z-17=0
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{z^{2}-8 }-\sqrt{6z-17}=0 \end{gathered}$}[/tex]
Simplify the left side. Yes n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-\sqrt{6z-17}=0 } \end{gathered}$}[/tex]
If n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-(6z-17)^{\frac{1}{2}} =0 } \end{gathered}$}[/tex]
Draw each side of the equation. The solution is the x value of the point of intersection.
[tex]\red{\underbrace{\overbrace{\boxed{\boldsymbol{\sf{\green{z=3}}}}} \ \ \to \ \ \ Answer}}[/tex]
{ Pisces04 }Answer:
Step-by-step explanation:
[tex]\sqrt{z^2-8} -\sqrt{6z-17} =0\\\sqrt{z^2-8} =\sqrt{6z-17} \\6z > 17\\z > \frac{17}{6} \\z^2-8=0\\z^2 > 8\\so \\z < -\sqrt{8} \\or\\z > \sqrt{8} \\combining\\z > \frac{17}{6} \\again\\z^2-8=6z-17\\z^2-6z-8+17=0\\z^2-6z+9=0\\z^2-3z-3z+9=0\\z(z-3)-3(z-3)=0\\(z-3)(z-3)=0\\z=3[/tex]
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 21 1 1.5 7.5 6 4.5 6.5 6.6
New York 20 1 3.5 7.5 4 5 6.5 5.2
Which of the choices below best describes how to measure the center of these data?
Both centers are best described by the mean.
Both centers are best described by the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
Choices for the measure of center that is best are: C. Rome data center is best described by the mean while that of New York data is best described by the median.
What are the Measures of Center?The measures of center include the mean and the median. Mean is best for a symmetrical data distribution while median is good for a skewed data distribution with an outlier.
The data for New work has an outlier, while that of Rome does not. Therefore, the best choices for the measure of center is: C. Rome data center is best described by the mean while that of New York data is best described by the median.
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