Answer:
Corresponding sides touch the same two angle pairs.
Step-by-step explanation:
Answer:
In a pair of similar triangles, the corresponding sides are proportional. Corresponding sides touch the same two angle pairs.
When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number.
2^3 + (-16) / 4^2 x 5 - (-3)
One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer
One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). the x-intercepts and the y-intercept of the graph of f(x) are
x = 2, x = 3, and x = 4.(0, -6), (2, 0), (3, 0), and (4, 0). RespectivelyWhat are the x-intercepts?Generally, To find the x-intercepts, we set y equal to 0 and solve for x. In this case, the equation we need to solve is:
f(x) = x^3 - 6x^2 + 11x - 6 = 0
To solve this equation, we can use the fact that (x - 3) is a factor of the function. This means that we can write the function as:
f(x) = (x - 3)(x^2 - 3x + 2)
If (x - 3) is a factor, then x - 3 must equal 0. This gives us one x-intercept at x = 3.
To find the other x-intercepts, we can set the quadratic factor (x^2 - 3x + 2) equal to 0 and solve for x. This gives us the following equation:
x^2 - 3x + 2 = 0
We can use the quadratic formula to solve this equation:
x = (3 +/- √(9 - 8)) / 2 = (3 +/- √(1)) / 2 = (3 +/- 1) / 2
This gives us two more x-intercepts at x = 2 and x = 4.
So the x-intercepts of the graph of f(x) are x = 2, x = 3, and x = 4.
To find the y-intercept, we set x equal to 0 and solve for y. In this case, the equation we need to solve is:
f(0) = 0^3 - 6(0)^2 + 11(0) - 6 = -6
This gives us a y-intercept at (0, -6).
So the y-intercept of the graph of f(x) is (0, -6).
All of the intercepts of the graph of f(x) are, therefore (0, -6), (2, 0), (3, 0), and (4, 0).
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1/4+1/6 in fractions
Please help me I’m giving you 25 pints things
Which of the following statements regarding the expansion of (x + y)^n are
correct?
A. The coefficients of x-1 and y- 1 both equal 1.
B. For any term xay in the expansion, a - b = n.
C. The coefficients of x and y both equal 1.
D. For any term xay in the expansion, a + b = n
The true statements are,
A. The coefficients of xⁿ and yⁿ both equal 1.
D. For any term x and y in the expansion, a + b = n
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (x + y)ⁿ
Now,
We know that;
A binomial expansion is,
⇒ [tex](x + y)^n = x^n + nx^n^-^1 y + ^{n} C_{2} x^n^-^2y^2 + ..... + nxy^n^-^1 + y^n[/tex]
Clearly, For Option A:
The coefficients of xⁿ and yⁿ both equal 1.
If we see first and last term of the expansion, This statement is true.
For Option D:
For any term xᵃyᵇ in the expansion, a + b = n.
Let we take 3rd term of expansion
Here, a = n-2 and b=2
So, a + b = n-2+2 = n
Thus, a + b = n is true statement.
For Option B:
For any term xᵃyᵇ in the expansion, a - b = n.
Let we take 3rd term of expansion
Here, a=n-2 and b=2
If we do a-b = n-2-2=n-4≠n
Thus, a-b=n is false statement.
Thus, The true statements are given below,
A. The coefficients of xⁿ and yⁿ both equal 1.
D. For any term x and y in the expansion, a + b = n
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On May 26, your balance is $897.96. On May 27, you write check #117 to your landlord, Mrs. Wall, for $366.00. On May 28, you use receive a rebate check for $62.52. On May 29, you write a check for $137.32 to Bank of America for your car payment. On May 30, you receive your monthly check from your employee of $658.50 On May 31, you write a check for $685 to your parents for supporting you the previous month. What is the ending balance for the month of May?
Bank reconciliation is an accounting process to bring the balance as per the bank statement to agree with the balance as per the checkbook.
What is bank reconciliation?The journal entry to adjust the checkbook balance is as follows:
May 1 Debit Bank Charges $20
Credit Checkbook $20
The preparation of the Bank Reconciliation Statement is as follows:
Balance as per bank statement $16,833.19
Add Uncleared Deposits $1,650.00
Less Outstanding Checks $2,040.84
Balance as per adjusted checkbook $16,442.35
Checkbook balance on May 31 = $16,462.35
Bank Statement balance on May 31 = $16,833.19
Uncleared Deposits:
May 29 $575
May 30 $1,075 $1,650
Outstanding Checks:
Check 189 - $127.50
Check 191 - $462.19
Check 192 - $569.42
Check 194 - $881.73 $2,040.84
Bank charges = $20.00
Checkbook Adjustment:
Balance as per checkbook $16,462.35
Less Bank charges 20.00
Adjusted checkbook balance $16,442.35
Transaction Analysis for Journal:
Bank Charges $20 Checkbook $20
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A student is to be selected randomly from a group of students. For each classification of freshman and sophomore, there is a math major, an art major, and a biology major. The probability of each individual being selected is given in the following table:
Find the probability that
(a) a freshman is selected.
(b) an art major is chosen.
(c) a freshman math major or a sophomore biology major is chosen.
A freshman has a 0.35 chance of being chosen. A freshman has a 0.38 chance of being chosen. The likelihood of a freshman being chosen is 0.23.
What is probability?A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%. It is predicated on the likelihood of something occurring. The rationale underlying probability is the foundation of theoretical probability. If a coin is tossed, the theoretical probability of receiving a head is 12.
Here,
.................. Math .. Art . Biology Total
Freshman . 0.10 . 0.08 . 0.17 .... 0.35
Sophomore 0.22 . 0.30 . 0.13 ... 0.65
Total ......... 0.32 . 0.38 . 0.30 ...... 1
(a) 0.35
(b) 0.38
(c) 0.10 + 0.13 = 0.23
The probability that a freshman is selected is 0.35. The probability that a freshman is selected is 0.38. The probability that a freshman is selected is 0.23.
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what are the coordinates of the point 3/5 of the way from A(3,-4) to B(13, 11)?
Which of the following is a true statement? A. All real numbers are rational numbers. B. All whole numbers are natural numbers. C. All integers are whole numbers. D. All natural numbers are integers.
Answer: It is D
Step-by-step explanation:
American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. A random sample of 40 children is selected. What is the probability the mean number of hours of television they watch per week is less than 22? Question 15 options: 1) 0.3520 2) 0.0089 3) 0.9911 4) 0.6480
If American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. the probability the mean number of hours of television they watch per week is less than 22 is: 2) 0.0089.
How to find the probability?First step is to find the standard deviation
σ = 8/√40
σ = 1.2649
Using this formula to find the Z-score
Z = x - μ/σ
Z =22-25/1.2649
Z = -3//1.2649
Z = -2.37
Hence,
P-value=P(Z < -2.37)
P-value =0.0089
Therefore the correct option is 2.
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A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments. Find her monthly payment and total interest paid if the interest rate is 5.5%.
If the interest rate is 5%, the monthly payment and total interest would be $2.439.
Define interest.Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.
Given,
A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments.
A $10,000 subsidized student loan
Ten-year term of repayment
5.5% interest rate
First, we must determine the loan's future value (FV) over the next six months using the formula below:
FV in 6 months
= Loan Amount× (1 + Interest Rate)⁶ ($10,000×(1 + 0.055) ×6
= $2.7680.
Second, the formula for determining future value is used to determine the monthly payment:
M = FV in 6 months / (((((r)n) - 1) / r).......... (1)
When you enter all the pertinent values into equation (1), you get:
M = $2.7680 / ((((1 + 0.00466666666666667)^144) – 1) / 0.00466666666666667)
M = $2.439
Therefore, if the interest rate is 5.5%, the total amount paid in interest plus monthly payments would be $2.439.
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pls help
A. G
B. H
C. The functions have the same y-intercept.
Answer:
A.) G
Step-by-step explanation:
I'd say A.) G because when you look at the graph the y-intercept is 4. When you look at the equation the y-intercept is 6. 6 is bigger than 4 so then the answer should be A.) G
What are the solutions to this system? Select all that apply. Y+2x^2 =14
y= 3x^2-6
The solution to the system of equation y + 2x² = 14 , y = 3x² - 6 is as follows:
x = 2y = 6How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let's solve the system of equation by substitution method.
Therefore,
y + 2x² = 14
y = 3x² - 6
Therefore, using substitution method,
3x² - 6 + 2x² = 14
5x² - 6 = 14
5x² = 14 + 6
5x² = 20
x² = 20 / 5
x² = 4
x = √4
x = 2
Therefore, let's find the value of y using y = 3x² - 6.
y = 3x² - 6
y = 3(2)² - 6
y = 12 - 6
y = 6
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A cake recipe asks for 1/4 cup of oil for each cake. How many cakes can be made from a bottle of oil that has 4 cups in it?
Answer: 16
Step-by-step explanation:
there are 4 1/4 in 1 cup. so it'll be 4 cakes for each cup of oil you have. multiply the number of cakes that can be made per cup (4) by the number of cups you have (4)
(4) x (4) = 16
The graph of linear function k passes through the points (-7, 0) and (1, 8).
Domain
2
Range
Slope
Y-intercept
X-intercept
The linear function is y = x + 7 and it has it domain and range at (-∞, ∞) respectively while it x and y - intercepts are (-7, 0) and (0, 7) respectively.
Linear FunctionA linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
The linear function always model the form of y = mx + c
m = slopec = y-interceptTaking the points, we can find the slope of the line
m = y₂ - y₁ / x₂ - x₁
m = 8 - 0 / 1 - (-7)
m = 8 / 8
m = 1
The slope of the line is 1
Using the slope to find the y - intercept;
y = mx + c
8 = 1(1) + c
8 = 1 + c
c = 8 - 1
c = 7
The linear function is y = x + 7
The range of this function is (-∞, ∞) and the domain of the function is
(-∞, ∞).
The x and y -intercept of the function are
x - intercept = (-7, 0)
y - intercept = (0, 7)
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Work out the surface area of this solid
prism.
10cm
8cm
27cm
6cm
17cm
30cm
The diagram is not drawn to scale.
Answer:
2064 cm²
Step-by-step explanation:
You want the surface area of a prism that is 30 cm between bases that are trapezoids with parallel sides 27 cm and 6 cm that are 8 cm apart, and slant sides that are 10 cm and 17 cm.
Base areaThe area of each trapezoidal base is ...
A = 1/2(b1 +b2)h
There are two identical bases, so their total area is ...
2A = (b1 +b2)h = (27 cm +6 cm)(8 cm) = 264 cm²
Lateral area
The lateral area of the prism is the area of the four rectangular faces. Each is 30 cm wide, and their total length is the perimeter of the base;
P = 27 cm +10 cm +6 cm +17 cm = 60 cm
lateral area = Ph = (60 cm)(30 cm) = 1800 cm²
Total surface area
The total surface area of the prism is the sum of the base area and the lateral area:
total area = base area + lateral area
total area = 264 cm² +1800 cm² = 2064 cm²
The surface area of the solid prism is 2064 cm².
Yes, by ASA and AAS
yes SAS
Yes by HL
yes by SSS
the two triangles are not congruent
Answer:
yes, by ASA
Step-by-step explanation:
sum of interior angles of a triangle = 180°
180 - (45+63) = 180 - 108 = 72°
the two triangles have two congruent angles and the side between them.
They are congruent for (ASA) angle side angle
-15x + 20y = 15
0=18x + 24y - 18
Answer:
Step-by-step explanation:
given:
-15x + 20y =15
0 = 18x + 24y -18
let's get the 2nd equation into a form like the top equation
-18x -24y = -18
multipy thur by -1
18x +24y = 18
we'll need to use substitution for this problem. elimination has a zero issue.
18x = -24y +18
x = -[tex]\frac{4}{3}[/tex] y + 1
now plug this into the 1st equation
-15( -[tex]\frac{4}{3}[/tex] y + 1 ) + 20 y = 15
20y -15 +20y = 15
40y = 30
y = 3/4
now that we've found y, plug that into our x = -[tex]\frac{4}{3}[/tex] y + 1 , to find x
x = -1 +1
x = 0
work out the area of a rectangle with base, b = 9.6mm and hight, h = 2mm
Answer: 19.2mm^2
Step-by-step explanation: the area of a rectangle is simply base x height
so do 9.6 x 2 to get 19.2mm^2
a small bookshelf is 8/12 yard long. How many books can fit on the shelf if the width of each book is 1/24 yard? Explain
Answer:
16 books
Step-by-step explanation:
8/12 is equivalent to 16/24. If each book is 1/24 width, 16/1 = 16
r²-6 r+9 can be factorized to give an expression of the form (r+a)²,
where a is an integer.
Work out the value of a.
The value of a in the expression is -3
How to determine the value of a?From the question, we have the following parameters that can be used in our computation:
r²-6 r+9 can be factorized to give an expression of the form (r+a)²
This means that
r² - 6r + 9 = (r+a)²
Factorize the expression r² - 6r + 9
So, we have
(r - 3)² = (r + a)²
By comparison, we have
a = -3
Hence, the solution of a is -3
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Dajon already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 15 years
in an account paying 2.05% interest, how much could the annuity provide each week? Round your answer to
the nearest dollar.
The annuity provide each week is $547.59 (approx.)
Define Annuity
A fixed sum of money paid to someone each year, typically for the rest of their life.
Given,
Dajon already knows that he will have $500,000 when he retires.
P = $500,000
Next, he sets up a payout annuity for 15 years in an account paying 2.05% interest.
r = 2.05 % or 0.0205
t = 15 years
Since, annuity provide each week then
n = 52 weeks (in a year)
The Annuity formula is,
P = d [ ( 1 + r/n)^nt - 1 ] / (r/n)
where, d = regular deposit
Now, plug in the values and find the value of d
P = d [ ( 1 + 0.0205/52)^52*15 - 1 ] / (0.0205/52)
Calculate the value it gives,
P = $547.5936993 or 547.59
Hence, the annuity provide each week is $547.59 (approx.)
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I need help with my math homework
Answer: Work shown below. Have a nice day! :)
For Christmas you want to get your parents a framed family picture. At the framing store, there are 4 different styles each available in 5 different colors. You decide to use a blue mat board and there are 3 different shades of blue to choose from. How many different frames can you create?
The number of different frames you can create, if There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from, is 12.
What is the combination?A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.
Given:
There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,
Calculate the total number of frames, we can create as shown below,
The number of frames = different styles available for blue color × shades of blue
The number of frames = 4 × 3
The number of frames = 12
Thus, the number of frames you can create is 12.
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Nine less than two times a number is five more than this number.
The statement as an expression is 2x - 9 = 5 + x
How to determine the statement as an expression?From the question, we have the following statement that can be used in our computation:
Nine less than two times a number is five more than this number.
Express the numbers properly
So, we have the following representation
9 less than 2 times a number is 5 more than this number.
Introduce the equality symbols
So, we have the following representation
9 less than 2 times a number = 5 greater than this number.
Next, we apply the mathematical operators
So, we have the following representation
2 times a number - 9 = 5 + number.
Express the number as x
So, we have
2x - 9 = 5 + x
Hence, the expression is 2x - 9 = 5 + x
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Caroline went to the grocery store and bought bottles of soda and bottles of juice.
Each bottle of soda has 30 grams of sugar and each bottle of juice has 15 grams of sugar. Caroline purchased a total of 6 bottles of juice and soda which collectively contain 150 grams of sugar. Graphically solve a system of equations in order to determine the number of bottles of soda purchased, ∞, and the number of bottles of juice purchased, y.
The solution of the system of equations is the point of intersection (4, 2), as shown in the graph below.
Caroline bought 4 soda bottles.
Caroline bought 2 juice bottles.
How to Solve a System of Equations?In order to determine the solution to this problem, use the information given to create two equations.
Number of soda bottle = x.
Number of juice bottle = y.
First Equation for the total number of bottle that Kelvin bought
x + y = 6 --> eqn. 1
Second Equation 2 for the total sugar in the soda bottles and total sugar in juice bottles that equals 150 grams of sugar.
30x + 15y = 150
Simplify by dividing by 5
6x + 3y = 30 --> eqn. 2
Rewrite eqn. 1:
y = 6 - x
Solve simultaneously for the variables of x and y, by substituting the value of y into equation 2:
6x + 3(6 - x) = 30
6x + 18 - 3x = 30
3x + 18 = 30
3x = 30 - 18
3x = 12
3x/3 = 12/3
x = 4
Caroline bought 4 soda bottles.
Substitute x = 4 into equation 1 to find the value of y:
x + y = 6
4 + y = 6
y = 6 - 4
y = 2
Caroline bought 2 juice bottles.
The graph below shows the point of intersection, (4, 2), which is the solution.
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What is the solution and how do I solve?
20 + 4x+2 = 6x+8 --- By exterior angle
4x+22=6x+8
4x-6x=8-22
-2x=-14
x=7
Hope it helps
In an adjacency ____ representation, corresponding to each vertex v is a linked list such that each node of the linked list contains the vertex u, and there is an edge from v to u.
In an adjacency list representation, corresponding to each vertex v is a linked list such that each node of the linked list contains the vertex u, and there is an edge from v to u.
This is a common way to represent a graph in computer memory, where each vertex is represented by an object that stores its adjacent vertices in a list. This representation is useful when the graph is sparse, meaning it has relatively few edges compared to the number of vertices it has. It is not as efficient for dense graphs, where the number of edges is close to the maximum possible number of edges.
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Can someone evaluate these for me
1×(– 6 × –18 –8) ÷4
4– – 20+ – 5 ×( –11 – –18)
13– – 10 × 16 ÷ (14 + –16)
1– – 9 × 12 ×(–19 +20)
The answer of the given expression using BODMAD rule is 25.
What is BODMAS rule?
The BODMAS rule states that the brackets must be solved first, then powers or roots (i.e., of), Division, Multiplication, Addition, and finally Subtraction. Only when the BODMAS rule or the PEDMAS rule is used to solve an expression is the solution deemed to be correct.
(a) 1 x (-6 x -18 - 8) ÷ 4
By using first to simplify the bracket.
1 x ((-6 x -18) - 8) ÷ 4
1 x (108 - 8) ÷ 4
(1 x 100) ÷ 4
100 ÷ 4
25
Hence, the answer of the given expression using BODMAD rule is 25.
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For the function f(x) x 9, find (f f 1)(5)
the value of [tex]f o f^{-1}[/tex](5) of the function f(x) = x + 9 is 5
What is the inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f^-1 or F^-1. One should not confuse (-1) with exponent or reciprocal here.
[tex]f^{-1}[/tex](x) =
if f(x) = x + 9
setting x + 9 = y and making x the subject we have
y = x + 9
x = y - 9
replacing x with [tex]f^{-1}[/tex](x) and y with x we have
[tex]f^{-1}[/tex](x) = x - 9
so the f o [tex]f^{-1}[/tex](x) can be gotten by substituting x in f(x) with x - 9 so that we have
f o [tex]f^{-1}[/tex](x) = (x - 9) + 9
f o [tex]f^{-1}[/tex](x) = x
so f o [tex]f^{-1}[/tex](5) will be x = 5
which becomes
f o [tex]f^{-1}[/tex](5) = 5
In conclusion f o [tex]f^{-1}[/tex](x) is 5
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Solve for m in the equation below. It may be helpful to convert the equation into exponential form. Write answer as an integer or reduced fraction. -2. log,(m) - 24 = - 20 m = > Next Question Find the largest value of 2 that satisfies: log, () – log (2 + 1) = 9 =
The largest possible value of 2 that satisfies the equation is approximately 1.1.
What is Exponential Form Equation?
Since y=bx, y = b x is a one-to-one inverse of the exponential function, x=by x = b y, it too is a function. We simply swap x and y and solve for y to discover the inverse function, as is the case with all inverse functions.
To solve for m in the equation -2 * log(m) - 24 = -20, we can start by converting the equation into exponential form. To do this, we can raise both sides of the equation to the power of e:
[tex]e^(-2 * log(m) - 24) = e^(-20)[/tex]
Then we can simplify:
[tex]m^(-2) = e^(-20)[/tex]
Then we can solve for m:
[tex]m = sqrt[e^20]\\\\= sqrt[20*e^9]\\\\= sqrt[20] * sqrt[e^9]\\\\= 2 * 3^(1/2)= 2 * 1.732\\\\= 3.464[/tex]
So m is approximately equal to 3.464
To find the largest value of 2 that satisfies the equation [tex]log(2^2) - log(2 + 1) = 9[/tex], we can start by expanding the left-hand side of the equation:
[tex]log(2^2) - log(2 + 1) \\\\=log(2^2 / (2 + 1))\\\\ = log(4/3) = 9[/tex]
Then we can rewrite the equation as:
log(4/3) = 9
Then we can solve for 2:
[tex]2 = (4/3)^(1/9)\\\\= (4^(1/9)) / 3^(1/9)\\\\= 1.5874010519681994 / 1.4422495703074083\\\\= 1.1[/tex]
So, The largest possible value of 2 that satisfies the equation is approximately 1.1.
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