y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.
Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.
In terms of symmetry, the graph of this function has no symmetry.
The function has no rotational symmetry because it is not repeated after any rotation around the origin.
Given: \overline{DC} DC bisects \angle ACB∠ACB and \overline{AC} \cong \overline{BC}. AC ≅ BC . Prove: \triangle ACD \cong \triangle BCD△ACD≅△BCD.
The congruent angles, ∠ACD and ∠BCD formed by the angle bisector [tex]\overline{DC}[/tex] the congruent segments [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex], and the segment [tex]\overline{DC}[/tex] (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS
What is the SAS congruency rule?The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.
The specified information are;
The bisector of ∠ACB = [tex]\overline{DC}[/tex]
Segment [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]
Required; to prove that ΔACD ≅ ΔBCD
The two-column method can be used to prove the congruency of the triangles as follows;
Step [tex]{}[/tex] Statement [tex]{}[/tex] Reasons
1. [tex]{}[/tex] [tex]\overline{DC}[/tex] bisects ∠ACB Given
[tex]{}[/tex] [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]
2. [tex]{}[/tex] ∠ACD ≅ ∠BCD Definition of bisected angles
3. [tex]{}[/tex] [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex] Reflexive property of congruency
4. [tex]{}[/tex] ΔACD ≅ ΔBCD SAS congruency rule
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suppose you play a game where you roll a set of 2 fair dice. if you roll a 4, 5, or 6, you will lose $6, but if you roll anything else, then you win $3. how much money will you gain or lose per each throwing?
Answer:
The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.
For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.
There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.
So your expected gain/loss per roll is:
(3/9) * $3 + (3/9) * (-$6) = -$1
Therefore, on average, you will lose $1 per each throwing.
Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function.
R(x)=8x/x+19
Answer:
Below in bold.
Step-by-step explanation:
R(x) = 8x/(x + 19)
When x = -19 the denominator = zero so there is a vertical asymptote which is
x = -19.
If we divide 8x by x + 19 we get 8 remainder -152.
So horizontal asymptote is R(x) = 8.
As the degree of the numerator and denominator are the same ( both 1) there is no oblique asymptote.
How many unique triangles can be drawn with side lengths 5 inches 15 inches and 30 inches
Answer:
Step-by-step explanation:
The idea is, for each triangle, sort all of its sides and then store it in a map, if all those three sides are already present in the map then increase the frequency by 1, else its frequency will be 1. The count of elements of the map which have frequency 1 in the end will be the answer.
decision point: determining the first step as the marketing consultant for bolt, you need to determine the first step in understanding the underlying motivations of bolt's consumers. what method of research do you think would best help bolt understand its consumers' purchase motivations? select an option from the choices below and click submit. talk in depth to a few consumers for an extended period of time. ask many consumers many questions in a representative statistical sample. ask many consumers a few brief questions
I would recommend asking many consumers a few brief questions in a survey. This method would help Bolt quickly and easily obtain a broad view of its consumers’ purchase original cost motivations, which could then be analyzed to develop more targeted strategies.
Surveys are a great way to quickly obtain a broad view of a target audience’s motivations for purchase. By asking many consumers a few brief questions, Bolt can gain insight into what motivates them to purchase their products, or why they may choose not to purchase them. This data can then be analyzed to develop more targeted strategies to increase sales. Surveys also provide an efficient way to sample a large number of people, allowing Bolt to get a representative statistical sample of its consumers’ motivations. This data can also be used to inform future marketing campaigns, allowing Bolt to better target their customers and maximize sales.
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which is the best measure of center for third period, and why? interquartile range, because there is 1 outlier that affects the center standard deviation, because there are no outliers that affect the center mean, because there are no outliers that affect the center median, because there is 1 outlier that affects the center
Mean, because there are no outliers that affect the center
third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
The mean = ΣX / n
n = sample size, n = 15
Mean = 34 / 15 = 2.666
The median = 1/2(n+1)th term.
1/2(16)th term = 8th term.
The 8th term = 2
The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.
Both interquartile range and standard deviation are measures of spread and not measures of centre.
complete question
A survey was taken of students in math classes to find out how many hours per day students spend
on social media. The survey results for the first., second-, and third-period classes are as follows:
First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0
Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3
Which is the best measure of center for second period and why? (5 points)
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Find the following functions. Simplify your answers.
Answer:
[tex]f(g(x)) = \boxed{\dfrac{x}{2}}[/tex]
[tex]g(f(x)) = \boxed{2x - 5}[/tex]
Step-by-step explanation:
We have the following two functions
[tex]f(x) = \dfrac{1}{x-5}\\\\g(x) = \dfrac{2}{x}+\:5[/tex]
To find [tex]f(g(x))[/tex] substitute the expression for [tex]g(x)[/tex] wherever you see an [tex]x[/tex] in [tex]f(x)[/tex]
[tex]\mathrm{For}\:f=\dfrac{1}{x-5}\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{2}{x}+5[/tex]
[tex]=\dfrac{1}{\dfrac{2}{x}+5-5}\\\\[/tex]
[tex]=\dfrac{1}{\dfrac{2}{x}}\\\\\\= \dfrac{x}{2}[/tex] ANSWER
To find [tex]g(f(x)[/tex], substitute the expression for [tex]f(x)[/tex] wherever you see an [tex]x[/tex] in [tex]g(x)[/tex]
[tex]\mathrm{For}\:g=\dfrac{2}{x}+5\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{1}{x-5}\\\\=\dfrac{2}{\dfrac{1}{x-5}}+5\\\\[/tex]
[tex]=2\left(x-5\right)+5\\\\= 2x - 10 + 5\\\\= 2x - 5\\\\[/tex]ANSWER
Note:
[tex]\dfrac{2}{\dfrac{1}{x-5}}=2\left(x-5\right)\\\\[/tex]
How do I solve this?
Answer:
y=200/9. x= 329/9
Step-by-step explanation:
3x=-43-3y; x=-43/3-y. 5(43/3-y)-8y=5; y=200/9. x= 329/9
If the floor of a cuboidal hall has a perimeter of 225m and height 25m then find (i). lateral surface area (ii). Total cost to paint its four walls if it costs Rs.9/- per sq.m
The lateral surface area is 1562.5 If the floor of a cuboidal hall has a perimeter of 225m and height 25m.
What is volume of Cuboid ?
volume of cuboid can be defined as the product of length , breadth and height.
Given,
If the floor of a cuboidal hall has a perimeter of 225m and height 25m
Lateral Surface area = 2h(l+b)
Given perimeter is 225m
so,
perimeter = 4 (l+b+h)
225 = 4 (l+b+25)
Given h = 25
225 = 4(l+b) + 100
4(l+b) = 225-100
4(l+b) = 125
l+b = 125/ 4
So,
Lateral surface area = 2h (l+b)
= 2 * 25 * ( l+b)
= 50*125/4
= 1562.5
Hence , The lateral surface area is 1562.5 If the floor of a cuboidal hall has a perimeter of 225m and height 25m.
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please help me find this answer!
Answer:
[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]
Step-by-step explanation:
djdkkwkwnsjididjfjrje
List and explain at least three popular sixteenth-century dance types, including the style, common instrumentation, and use in court, society, or both.
One of the most popular dance types of the sixteenth century was the pavane, another one are galliard and allemande.
What is instruments?Instruments in math are tools or processes used to perform mathematical operations and calculations. Examples of instruments in math include calculators, rulers, compasses, protractors, and computers. These instruments can be used to solve problems, analyze data, and understand mathematical concepts. Additionally, instruments in math can be used to teach students about problem-solving and allow them to gain a deeper understanding of mathematics.
This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The pavane was often used as a ceremonial dance in courts and was usually performed by couples.
Another popular dance type of the sixteenth century was the galliard. This was a lively, energetic dance, usually in triple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The galliard was often used as a dance for entertainment and was usually performed by couples.
The third popular dance type of the sixteenth century was the allemande. This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The allemande was often used as a ceremonial dance and was usually performed by couples. It was usually danced in a line or circle formation, with each dancer taking the lead in turn.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 7600(1.262)
This exponential function represents growth at a rate of 26.2% per unit increase in x.
This represents growth at a rate of 26.2% per unit increase in x.
This is an exponential function, so it will represent either growth or decay. To determine whether it is growth or decay and what rate it is, we need to look at the coefficient of the exponential term, which in this case is 1.262. Since this is larger than 1, the function is growing, and the rate of increase is equal to the coefficient minus 1, which is 26.2%.
This exponential function represents growth at a rate of 26.2% per unit increase in x.
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find the area of the parallelogram with vertices a(−3, 0), b(−1, 7), c(9, 6), and d(7, −1).
Th area of parallelogram with vertices (-3, 0), b(-1, 7), c(9, 6), and d(7, -1) is 46.5 square units.
The vertices of a parallelogram are a (-3, 0), b(-1, 7), c(9, 6), and d(7, -1).
Area of triangle abc= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\-1&7&1\\9&6&1\end{array}\right][/tex]
=1/2[-3(7-6)-1(-6-63)]
= 1/2[-3(1)-1(-66)]
=1/2[63]
=63/2 sq. units
Area of triangle acd= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\9&6&1\\7&-1&1\end{array}\right][/tex]
=1/2[-3(6+1)-1(-9-42)]
= 1/2[-3(7)-1(-51)]
=1/2[-21 + 51]
=1/2[30]
=15
Area of parallelogram abcd = Area of triangle abc + Area of triangle acd
= 63/2 + 15
= (63 + 30)/2
= 46.5 sq units.
Therefore, the area of the parallelogram is 46.5 sq. units.
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Answer:
correct answer is 72
Step-by-step explanation:
medians are drawn from point $a$ and point $b$ in this right triangle to divide segments $\overline{bc}$ and $\overline{ac}$ in half, respectively. the lengths of the medians are 6 and $2\sqrt{11}$ units, respectively. how many units are in the length of segment $\overline{ab}$?
The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
What is right triangle ?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.
We know that the medians are 6 and $2\sqrt{11}$ units, respectively.
Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$
so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$
so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.
Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.
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Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welcome to stay, but she charges $10 per person. She expects guests to check out by 10 a.m. and charges an extra $5 per hour for late checkouts. Select the linear equation that correctly represents how much Martina collects for one night of stay in her home.
The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z
The linear equation to represent how much Martina collects for one night of stay in her home is:
y = 25 + 10x - 5z
where:
y is the total amount collected in dollars
x is the number of additional guests (besides the first one)
z is the number of hours the guests check out late
This equation represents the flat fee of $25 per night for the first guest, the additional fee of $10 per person per night for additional guests, and the extra fee of $5 per hour for late checkouts.
Therefore, The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z
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What is a 3 regular graph?
A 3-regular graph is called a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has an equal number of neighbors in common, and every non-adjacent pair of vertices has an equal number of neighbors in common.
In the mathematical field of graph postulate, a cubic graph is a graph in which all vertices have a degree of three. In other terms, a cubic graph is a 3-regular graph. Cubic graphs are also known as trivalent graphs.
A bicubic graph is called a cubic bipartite graph.
In graph theory, a regular graph is a graph where each vertex has an equal number of neighbors; i.e. every vertex has an equal degree or valency.
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Look at picture for question.
Answer: $23,800
Step-by-step explanation:
It was worth $37,000 at first and now it's worth $1800.
So we have 37,000 - 1800 = $35,200 that left away.
And we know that 8 years passed away.
So we have 35,200/8 = $4400 each year.
We are looking for 3 years later.
So we have 440*8 = $13,200 that left after 3 years.
And lastly, it's worth 37,000 - 13200 = $23,800 3 years later.
The wood you are using for the floor costs 3.50 per square foot. how much will it cost to buy the material assuming you can buy a piece exactly the right size
On solving the provided question, we can say that by equation it cost to buy the material assuming you can buy a piece exactly the right size = $350.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the floor costs = 3.50 per square foot
assuming we can buy a piece exactly the right size = x
then cost =
x * 3.50
let x be 100
cost = $350
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Suppose the slope of a line is positive. Describe what happens to the graph of the line as you move from left to right.
As you move the graph of the line from left to right, the output value of the function increases.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the initial value of the linear function.The slope determines if the function is increasing or decreasing over it's domain, as follows:
Positive slope: increasing function.Negative slope: decreasing function.A positive slope means that the function increases when it moves from left to right, that is, when x increases.
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Daniel LaRusso borrows $1,200 from a bank with 8% simple interest per year. How much will he have to pay back TOTAL (principal AND interest combined) in 2 years?
$150
$192
$1,350
$1,392
Answer:
Step-by-step explanation:
To calculate the total amount Daniel LaRusso will have to pay back in 2 years, we first need to calculate the interest he will owe on the loan.Simple Interest (I) = P * r * t
where P is the principal (the amount borrowed), r is the annual interest rate (expressed as a decimal), and t is the time (in years) for which the loan is borrowed.In this case, the principal is $1,200, the annual interest rate is 8%, and the time is 2 years.I = $1,200 * 0.08 * 2 = $192So, he will have to pay back a total of $1,200 (principal) + $192 (interest) = $1,392So, Daniel LaRusso will have to pay back a total of $1,392 in 2 years.
Answer:
D) $1392---------------------------------
The amount of interest at 8% simple for 2 years is 16% of the loan:
$1200* 16% =$1200*16/100 = $192The total amount including both the principal and interest is:
$1200 + 192 = $1392Correct choice is D.
Can anyone help me please
Answer:
2
Step-by-step explanation:
-4+6=2
Pls answer soon !!!!!!!!!
The required solution of the given simultaneous equation is x = 5 and y = -9.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
here,
Given a system of equations,
6x + 5y = -15 - - - - -(1)
-4x - y = -11 - - - - (2)
Multiply equation 1 by 1 and multiply equaiton 2 by 5 then add both the equation,
6x + 5y -20x -5y = -15 -55
-14x = -70
x = 5
Now,
-4(5) - y = -11
-20 - y = -11
-y = -11 +20
y = -9
Thus, the required solution of the given simultaneous equation is x = 5 and y = -9.
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B. Reviewing Key Terms
Complete each sentence by writing the correct term in the blank.
15. When a bank borrows money from another bank, the interest rate it pays is called the
16. Ownership of more than one bank constitutes a
17. When a bank customer writes a check, the check will go through the process of
M
18. A bank's total assets minus its total liabilities make up its
19. Banks repay loans from the Federal Reserve at a rate of interest called the
The correct term for each term is -
Federal Fund Rate
Bank holding company
Check clearing
Net worth
Discount rate
What is an account?
A certain kind of financial asset or debt that is kept and owned in your name.
When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.
Ownership of more than one bank constitutes a bank holding company.
When a bank customer writes a check, the check will go through the process of check clearing.
A bank's total assets minus its total liabilities make up its net worth.
Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.
Therefore, these are the key terms used in banking.
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every time Musa distributes 100,105&110 oranges to a group of students he is left with 1, 3 ,5 oranges respectively.Find the maximum number of oranges he can distribute to the group
The maximum number of oranges he can distribute to the ground would be = group C with a total of 115 oranges.
What is a maximum number?A maximum number is defined as the number that is equal to or greater than other values in a data set.
The various number of oranges distributed by Musa include the following:
Group A Students = 100 oranges
Remaining oranges from group A = 1
Total = 101 oranges
Group B students = 105 oranges
Remaining oranges from group B = 3
Total = 108 oranges.
Group c students = 110 oranges
Remaining oranges from group C = 115 oranges.
Therefore the maximum oranges he distributed was for group C which was 115 in total number.
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Absolute value of |3x+6|=12
Answer:
x = 2, -6
Step-by-step explanation:
3x + 6 = ±12
=> If 3x + 6 = 12
3x = 6
x = 2
=> If 3x + 6 = -12
3x = - 18
x = -6
Answer: 2
Step-by-step explanation: To find the value of x, we need to use the order of inverse operations. Inverse operation(s) means to do the opposite of the operations used. So, instead of adding, we subtract, instead of multiplying, we'll divide. So, the opposite of 6 + 12 is 12 - 6. So, that's 6. Now, instead of multiplying 6 by 3, we need to divide 6 by 3. That's 2. Therefore x = 2. Now, to check our answer, we plug 2 in for 6. So, | 3(2) + 6 | is the positive value of 3(2) + 6, which is 6 + 6.
12 = 12
So, therefore the absolute value of |3x+6|=12 is 2. I hope this helped!
the amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. a student claims that the average travel time to school for his large district is 20 minutes. to further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. he would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. what are the appropriate hypotheses?
Answer: The appropriate hypotheses for this significance test are:
Null hypothesis (H0): The true mean travel time for all students who attend this school is equal to 20 minutes.
Alternative hypothesis (Ha): The true mean travel time for all students who attend this school is greater than 20 minutes.
The null hypothesis states that there is no difference between the claim (20 minutes) and the sample mean (22.4 minutes). The alternative hypothesis states that there is a difference and the sample mean is greater than the claim. The student will use the sample data and a chosen significance level (such as α = 0.05) to decide whether to reject or fail to reject the null hypothesis.
Step-by-step explanation:
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
A(−7, — 5), B(-2, 0); 1 to 4
The coordinates of P are
Therefore , the solution of the given problem of ratio comes out to be the coordinate P = (7, 0.4).
A ratio is defined.A ratio as well as fraction in mathematics shows how frequently one value is present in another. For instance, if there are eight grapefruit and six lemons in a fruit plate, the ratio from oranges to citrus is eight to six, or 8:6, which is comparable to the ratios 4:3 or the decimal 1.333.
Here,
Ratios are a useful tool for segmenting lines into smaller units.
P's coordinate is P = (7, -0.4)
The criteria are as follows:
A = (8,0)\sB = (3,-2) (3,-2)
m: n=1:4
Using P = mx2+nx1 my2+ny
m+n
m+n, line ratio is computed.
The result is:
P 1x3+4x8 /1x-2+4x0 = 1+4 / 7
=> P = 35, 2
=>P = (7, -0.4) (7, -0.4)
1+4
P therefore has the coordinate P = (7, 0.4).
Therefore , the solution of the given problem of ratio comes out to be the coordinate P = (7, 0.4).
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find the limit, if it exists. (if an answer does not exist, enter dne.) lim x → [infinity] arctan(ex)
The limit exists, where limx→+∞ ex=+∞ and limx→+∞ arctanx=π\2
This problem can be solved by dividing it into smaller parts.
Let f(x)=ex and g(x)=arctan(x)
The range of the function arctan(ex) is equal to the intersection of the ranges of f(x) and g(x).
Since the range of f(x) is [0,∞] and the range of g(x) is [−π/2,π/2], the intersection is [0,∞] ∩ [−π/2,π/2] or [0,π/2]
but the limit as x approaches infinity or limx→∞.
Since the highest number in the possible range is π/2, that is the limit as x approaches infinity.
if x is approaching negative infinity or limx→−∞, the answer would be the lowest value in the function's range. Therefore, it would be 0
So, as x→∞, ex→∞ so that, letting t=ex we have limx→∞ arctan(ex)=limt→∞ arctan(t)=π/2.
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Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point) The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime
The correct option when Triangle ABC is transformed to triangle A′ B′ C is A.The measure of angle BCA = The measure of angle C prime A prime B prime.
How to illustrate the triangle?Triangle ABC is changed into triangle A′B′C′ and on the x- and y-axes, a coordinate grid ranging from -4 to -4 to 4 is displayed. A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0 in the triangle ABC.
A triangle Primes A, B, and C have A prime is at ordered pair minus 1, minus 3, B prime is at ordered pair minus 0, and C prime is at ordered pair minus 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Therefore,
<BAC = <B'A'C'
<ABC = <A'B'C'
<ACB = <A'C'B'
In this case, the correct option is A.
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The long jump pit was recently rebuilt to make it level with the runway. volunteers provided pieces of wood to frame in the pit. each piece of wood provided measures 6 ft, which is approximately 1.8 to 8 7. determine the amount of wood, in meters, needed to rebuild the frame.
The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.
What is amount and example?
amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.
To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:
wood (m) = (wood (ft) x 0.3048) / 6
Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:
wood (m) = (6 ft x 0.3048) / 6
wood (m) = 1.8288 m
Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.
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