Answer:
log 56 = a + b
Step-by-step explanation:
log8 = a and log7 = b (Given)log 56 = log (8*7)-> log 56 = log 8 + log 7-> log 56 = a + bW is the midpoint of SU, TU ⊥ SU and SU ⊥ SV. Complete the proof that Δ SVW ≅ Δ UTW.
Statement Reason
1. W is the midpoint of SU Given
2. TU ⊥ SU Given
3. SU ⊥ SV Given
4. ∠S ≅ ∠U All right angles are congruent
5. ∠ SVW ≅ ∠ UTW Definition of midpoint
6. Δ SVW ≅ Δ UTW.
The proof that Δ SVW ≅ Δ UTW is given by ASA congruence criterion.
What do you mean congruence of triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.
The symbol of congruence is’ ≅’.
Given:W is the midpoint of SU
⇒ SW = WUTU ⊥ SU and SU ⊥ SV
To prove:Δ SVW ≅ Δ UTW
Proof:In Δ SVW and Δ UTWSW = UW (given)
∠S ≅ ∠U (given)
∠ SVW ≅ ∠ UTW (vertically opposite angle)
Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)
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A lamina occupies the region inside circle x2 +y2 = 2y but outside circle x2 +y2 = 1. Find the center of mass if the density atany point is inversely proportional to its distance from theorigin.
the answer is {0, [3√3/2(3√3-π)]}
Ф {0, [3√3/2(3√3-π)]}
The poster above has good diagrams ; so , I will just go through the calculations .
The region of integration is with in the circle x ^2+y^2=2y but outside the circle x^2+y^2=1.
I would convert to polar . With polar , we have x^2+y^2=r^2 ,x=rcosФ and y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r, and you get r=2sinФ(1).
This is the upper circle in the previous posters diagrams .
The other equation of a circle becomes :
x^2 + y^2 = 1 ⇒ r^2 = 1 ⇒ r = 1 (2)
These two curves intersect at :
r= 2sinФ =1 ⇒ sinФ=1/2 ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X coordinate of the center of mass is zero
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2 ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ They say the area mass density is inversely proportional to the distance from the origin .
This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=
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Write a function in any form that would match the graph shown below.
if the pic is blurry just zoom in!!
please need ASAPP!!!
-3/2 passes through (-4, 3)
what is the y intercept and equation
(in slope intercept form)
03 Multiple Choice
Select all of the expressions that are equivalent to 2/3 (9x + 6) -1/2(8x - 4)
M. 2(x + 1)
P. 2x+6
R. 2x + 2
S. 2(x + 3)
T. 8x
Answer:
The answer is 2x + 6 or 2(x + 3)
Step-by-step explanation:
2/3 (9x + 6) -1/2(8x - 4)
(18x + 12)/3 - (8x + 4)/2
6x + 4 - 4x + 2
Rearrange it
6x - 4x + 4 + 2
Combine like terms
2x + 6
Take 2 as common
2(x + 3)
Thus, The answer is 2x + 6 or 2(x + 3)
need the answer pls help ots
Answer:
Your answer is x = 47.
Step-by-step explanation:
First, you need to move the constant to the right-hand side and change its sign.
4x = 180 + 8
Now, you need to add the numbers.
4x = 188
Last but not least, you need to divide both sides of the equation by 4, which gets you to:
x = 47
Your chances of being killed or injured in such a crash are ____ times greater when you are thrown from your car than when you are buckled up.Answer: 5
Your chances of being killed or injured in such a crash are 5 times greater when you are thrown from your car than when you are buckled up
The safest decision that drivers and passengers can make is to use their seatbelts.
The national seat belt use rate was 90.4% in 2021, indicating that many Americans are aware of the life-saving benefits of seat belts.
In 2017, it is projected that 14,955 lives were saved by seat belt use in passenger automobiles.
Recognize the potentially devastating repercussions of not using a seat belt and discover how to always buckle up properly for you and your family.
Buckling up keeps you safe and secure within your car, whereas not doing so increases your chance of being completely ejected from the vehicle in an accident, which is virtually always fatal.
You need more protection than air bags.
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Four friends paid a total of $32 for bowling. What is the ratio $32 for 4 people written as a unit rate?
Answer:
$8 per person
Step-by-step explanation:
32 divided by 4 is 8
32 : 4 = 8 : 1
A system of equations and its graph are shown.
y = 3/4x+3
y = -1/4x + 1
What is a solution to the system
Answer:
(-2, 1.5)
Step-by-step explanation:
When graphed their solution is (the point where both the line intercept/touch) (-2,1.5)
I graphed this equations online**
alice is interested in making deductible charitable contributions, but she does not want to incur the expense of drafting a private trust agreement. which of the following planning techniques will meet her needs?
As per the expenses, the planning technique that is suitable for Alice is strategic planning
The term expenses in math refers the cost that businesses incur in running their operations.
Here we have given that allice is interested in making deductible charitable contributions, but she does not want to incur the expense of drafting a private trust agreement.
And we need to find planning techniques will meet her needs
While we looking into the given question, we have identified that she does not want to incur the expense of drafting a private trust agreement.
Based on these one, she would prefer strategic planning includes a high-level overview of the entire business and it is the foundational basis of the organization and will dictate long-term decisions.
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which of the following commands is most likely to display the tls handshake between a client and the server at
A widely used security technology called Transport Layer Protection, or TLS, enables privacy and data security for communications over the Internet. Encrypting communication between online applications and servers, such as when web browsers load a webpage, is one of the main applications of TLS.
When a user accesses a website through HTTPS and the browser initially starts to enquire about the website's origin server, a TLS handshake occurs
Together, the client and server will perform the following during a TLS handshake:
Indicate the TLS version (TLS 1.0, 1.2, 1.3, etc.) they'll be using.
Select the cipher suites they'll employ (see list below).
Using the server's public key and the SSL certificate authority's digital signature, confirm the server's identity.
After the handshake, generate session keys to enable symmetric encryption.
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You win an online auction for a toy. Your winning bid of $30 is 60% of your maximum bid. How much more were you willing to pay for the toy than you actually paid?
Answer:
I was willing to pay $20 more for the toy than I actually paid.
Step-by-step explanation:
Let us take the maximum bid be y
So,
(y × 60) ÷ 100 = 30
60y/100 = 30
60y/100 × 100 = 30 × 100
60y = 3000
60y/60 = 3000/60
y = 50
60% of $50 is $30
So,
50 - 30 = 20
Thus, I was willing to pay $20 more for the toy than I actually paid.
Choose the best way to complete each statement. Use the graph to help you.
Options
A: A little less than, A little greater than, Exactly
B: 1, 2.3, 12
C: 1, 2.3, 12
Anything helps.
The value will be 13.
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
According to the given graph of
⇒ f(x) = 3ˣ
The point for f(x) = 12
We can see that such x is situated between 2.2 and 2.3
Thus the solution for this be;
⇒ (2.2 + 2.3)/2
⇒ 2.25
As above the solution of 3ˣ = 12
Is x = 2.25 which is about 2
Now, put x = 2.3
Therefore;
3²°³ = 12.51 ≈ 13
Thus it is about 13.
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Which statement correctly demonstrates using limits to determine a vertical asymptote of g (x) = StartFraction 2 (x + 4) squared Over x squared minus 16 EndFraction
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = negative infinity and limit of g (x) as x approaches 4 plus = infinity
The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
g(x) = 2(x + 4)²/(x² - 16)
Simplifying the denominator gives;
(x² - 16) = (x + 4)(x - 4)
Thus, our function is;
g(x) = 2(x + 4)²/[(x + 4)(x - 4)]
(x + 4 ) will cancel out to give;
g(x) = 2(x + 4)/(x - 4)
Vertical asymptote:
Point in which the denominator is 0, so:
(x - 4) = 0
x = 4
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Calculate the margin of error of a confidence interval for the difference between two population means using the given information. Round your answer to six decimal places.σ1=5.94σ1=5.94, n1=98n1=98, σ2=2.87σ2=2.87, n2=79n2=79, α=0.05
The margin of error of a confidence interval 0.5432
In statistics, the term margin of error is calculated by multiplying a critical factor with the population standard deviation and then the result is divided by the square root of the number of observations in the sample.
Margin of Error = Z * ơ / √n.
Here we have to calculate the margin of error of a confidence interval for the difference between two population means using the given information.
While we looking into the given question we have given the values,
σ1=5.94
n1=98
σ2=2.87
n2=79
α=0.05
Here we have to calculate the margin of error for the value 1, n1, and α
First, find the critical value: zα2=1.9599
Next, find the standard error of the mean which is
SE = 297√2/√700
Finally, the margin of error is 1.1760
Similarly, the value for the nest set of values is,
First, find the critical value: zα2=1.9599
Next, find the standard error of the mean: SE = 287√79/√7900
Finally, the margin of error is ME = 0.6328
Then the difference between these population is
=> 1.1760 - 0.6328
=> 0.5432
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A die is rolled. Find the probability of the given event. Write your answers as whole numbers or reduced fractions. (a) The number showing is a 6 P(6)= (b) The number showing is an even number P(even) = (c) The number showing is greater than 5 P(greater than 5) =
Answer:lol
Step-by-step explanation:lol
Find the value of k given that both points lie on a line passing through the origin. (−12,−2) and (k, 8)
Using the slope, the required value of k is 48.
What is the slope?In mathematics, the steeper direction of a line is overall processed by the slope or gradient of the line.
A line's slope can be used to determine how steep it is.
Theoretically, the gradient is calculated as "rise over run" (change in y divided by change in x).
Given is a line that crosses through the origin:
y = mx
Let,s take x = -12 and y = -2.
y = mx
-2 = -12m
m = -2/12
m = -1/6
m is the slope.
The equation now:
y = mx
y = -1/6x
Now, insert:
x = k and y = 8
y = mx
8 = -1/6x
x = 6*8
x = 48
Therefore, using the slope, the required value of k is 48.
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Write a function that matches the graph.
A function that will match the given graph is; f(x) = 2(x - 5)²(x + 2)
How to interpret Polynomial Graphs?In polynomial graphs, we know that the roots are the points where the graph crosses or touches the x-axis.
In this given graph, we see that the graph touches the x-axis at x = 5 and then crosses the x-axis at x = -2. Thus;
The roots of the equation are -2 and 5.
However, when the graph changes sign at a point on the x-axis, it means that point represents double roots. Thus, we will now have three roots which are -2, 5 and 5. The factors of the polynomial are;
(x + 2), (x - 5)²
Now, we see that when x = 0, y = 100 from the graph. Thus;
a(0 + 2)(0 - 5)² = 100
a(50) = 100
a = 100/50
a = 2
Thus, the equation would now be;
f(x) = 2(x - 5)²(x + 2)
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NO LINKS!! Please help me with this problem Part 2hh
Joe buys a sound system for $650 with his credit card.
If Joe pays the minimum monthly payment of $21.45:
a. How long will it take him to pay for the sound system in full?
b. What's the total amount he will pay for the sound system?
c. What's the total cost of using his credit card for the purchase?
THIS IS NOT MULTIPLE CHOICE!!!
Answer:
a. 31 months
b. $818.32
c. $168.32 interest
Step-by-step explanation:
Given that Joe makes a minimum payment of $21.45 on his credit card purchase of $650 with an APR of 19.85%, you want to know ...
how long until the purchase is paid offthe total amount paidthe cost of using the credit carda. Payoff timeIf the balance is reduced by $21.45 per month, it will take ...
$650/($21.45/mo) ≈ 30.3 months
to pay off the balance.
Joe will be making payments for 31 months.
b. Payoff amountThe total amount Joe pays for his sound system is the sum of its initial cost and the total of interest payments. That sum is ...
cost + interest = total paid
$650 +168.32 = $818.32
Joe will pay a total of $818.32.
c. Credit chargesThe total amount of interest Joe pays is $168.32.
__
Additional comment
If the total payment each month is $21.45, then it will take 43 months to pay off the system, for a total cost of $909.61, of which $259.61 is the cost of the credit. (The finance charge is paid first from this payment amount, so the amount that goes to reduce the balance is less.)
.
Your final grade in a class is based on your score on two tests and the final exam. You scored a 74% and 82% on the tests and an 80% on the final exam
The average grade received on two tests and the final exam is 78.67%
What is average?
The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.
The average formula has numerous practical uses. If we were asked to determine the average male height in India or the average age of the men and women in a group, we would add up all the data and divide it by the total number of data points.
Given, the grades in tests are 74% and 82%. Also, the grade on final exam is 80%.
Now, considering that we have to find the average grade in tests and final exams combined, we put the average formula.
Average grade = Sum of percentages of each exam/Total exams
Thus, average is
= (74+82+80)%/3
= 236%/3
= 78.67%
The average grade received on two tests and the final exam is 78.67%.
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Part A
Stand on-2. Which values on your number line are less than-2?
The values on a number line that are less than -2 include -3, -4 etc
What is a number line?A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that each real number and each point on a number line correspond to one another.
The horizontal straight lines known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.
It should be noted that -3, and above are less than -2.
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Evaluate. Write your answer as a fraction in simplest form.
(2/5)³
The fraction in simplest form is [tex]\frac{8}{125}[/tex].
What is a fraction?
The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
Given, [tex](\frac{2}{5})^{3}[/tex]
= [tex]\frac{2}{5} *\frac{2}{5} *\frac{2}{5}[/tex]
= [tex]\frac{8}{125}[/tex]
Hence, the fraction in simplest form is [tex]\frac{8}{125}[/tex].
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Which properties determine whether a quadrilateral is a parallelogram?
A. both pairs of opposite sides of a quadrilateral are both congruent and parallel
B. one pair of opposite sides of a quadrilateral is both congruent and parallel
C. it has 4 right angles
D. one pair of opposite sides of a quadrilateral is parallel
c is the answer. jdjsisiao
Write an equation and solve.
When two times the difference of a number x and three is increased by five, the result is nine. What is the number?
With all this information, and reading our question carefully, we can decipher the following:
9(n-3) = 3 + (9n + 3n)
9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)
9n - 27 = 3 + 12n (Step 2. Combine like terms; 9n + 3n = 12n)
-9n -9n (Step 3. Subtract 9n from both sides to isolate the variable)
______________
-27 = 3 + 3n
-3 -3 (Step 4. Subtract 3 from both sides)
________________
-30 = 3n
----- ----
3 3 (Step 5. Divide 3 from both sides)
________________
-10 = n
Therefore, n = -10
What is Distributive property?Distributive property explains that the operation performed on numbers, available in brackets that can be distributed for each number outside the bracket. It is one of the most frequently used properties in Maths. The other two major properties are commutative and associative property.The distributive property is easy to remember. There are a number of properties in Maths which will help us to simplify not only arithmetical calculations but also the algebraic expressions. In this article, you will learn what is distributive property, formula, and solved examples.to learn more about distributive property refer to:
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Use the vertex and intercepts to sketch the graph of each quadratic function give the equation of the parabola axis of symmetry use the graph to determine the function domain and range f(x)=(x-1)^2+2
The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.
Given that,
Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.
We have to determine the function domain and range using the graph is f(x) = (x-1)²+2
We know that,
Its vertex A quadratic function's form is provided by
f(x) = a(x-h)²+k
So, (h,k) is the vertex of the parabola
Take
f(x) = (x-1)²+2
(1,2) is the vertex of the parabola.
Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.
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Enrique made $277.50 last week. He also made 10% commission on the $300 of sales he
made last week. How much did he make in total last week?
Answer:
307.50
Step-by-step explanation:
277.50 + .1(300)
277.50 + 30
307.50
If line BG and CF are parallel,then the supplement of BIE = the supplement of GMD. Is this statement correct? Explain your answers
The supplement of BIE equals the supplement of GMD is a false assertion if lines BG and CF are parallel.
Describe the supplement angle.Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the total of angle 130° and angle 50° is 180°, hence they are supplementary angles.
Lines BG and CF are parallel, as shown in the figure.
If BIE = X, then its supplement of BIE will be 180 - X;
similarly, if GMD = Y, then its supplement of GMD will be 180 - Y.
Since BG and CF are parallel, the supplements of BIE and GMD are interior angles on the same side ( as shown in figure)
and for parallel line the interior angle on the same side is 180
so 180 - X and 180 -Y there sum should be 180
They cannot be equal
line BG and CF are parallel, then the supplement of BIE = the supplement of GMD are not equal.
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PLEASE ANSWER!!! (20 POINTS) Find the volume of the composite solid.
The volume of the composite solid is 47.2 cubic cm
How to determine the volume of the composite solid?From the question, we have the following parameters that can be used in our computation:
The composite solid
From the composite solid, we have the following shapes
Cube: Side length = 4 cm
Cone = Radius = 2 cm, Height = 4 cm
The volume of a cube is
Cube = Side length³
Substitute the known values in the above equation, so, we have the following representation
Cube Volume = 4³
Cube Volume = 64
The volume of a cone is
Cone = 1/3 * πr²h
Substitute the known values in the above equation, so, we have the following representation
Cone Volume = 1/3 * 22/7 * 2² * 4
Cone Volume = 16.8
The volume of the composite solid is
Volume = Cube Volume - Cone Volume
So, we have
Volume = 64 - 16.8
Volume = 47.2
Hence, the volume is 47.2 cubic cm
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Which set of factors corresponds to a third-degree polynomial with rational coefficients that has zeros x=2 and x=3i
(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.
What is polynomial?
In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Main body:
as the polynomial with rational coefficients that has zeros x=2 and x=3i
(x-2) and (x-3i) are factors of third-degree polynomial.
so ,
⇒(x-2)(x-3i)
solving (x-3i)
x = 3i
squaring both sides,
x² = -9
so , (x²+9) is a factor.
hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.
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Find the value of the variables in the given parallelogram.
Answer:
x = 58, y = 61
Step-by-step explanation:
We can use two properties of a parallelogram to solve this
1. The opposite angles of a parallelogram are equal
2. The sum of the 4 interior angles of a parallelogram equal 360
Using property 1,
the angle opposite angle y is also y(bottom left)2x + 3 = y + xUsing property 2
(2x - 3) + y + (y + x) + y = 360
3x + 3y + 3 = 360
3x + 3y = 360 - 3 = 357
Divide both sides by 3 to get
x + y = 357/3
x + y = 119 [2]
Add [1] and [2] together to eliminate y and get
x - y + x + y = -3 + 119
2x = 116
x = 116/2 = 58
Use equation [2]
x + y = 119
58 + y = 119
y = 119 - 58
y = 61
