Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
Answer:
8.6
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.[/tex]
Define the points:
[tex]\textsf{Let}\:(x_1,y_1)=(0,0)[/tex][tex]\textsf{Let}\:(x_2,y_2)=(7,5)[/tex]Substitute the defined points into the formula:
[tex]\implies d=\sqrt{(7-0)^2+(5-0)^2}[/tex]
[tex]\implies d=\sqrt{7^2+5^2}[/tex]
[tex]\implies d=\sqrt{49+25}[/tex]
[tex]\implies d=\sqrt{74}[/tex]
[tex]\implies d=8.6\;\;\sf (nearest\: tenth)[/tex]
Therefore, the length of one of the diagonals of the rectangle is 8.6.
A line on a graph passes through the points (15, 10) and (60, 20).
Answer:
Not complete, please recheck the question
89% means 89 out of?
Answer:
100
Step-by-step explanation:
What is the maximum number of solutions an
equation of the form ||ax − b| + c| = d can have?
Justify your reasoning with an example
Answer:
4 for c < 02 for c > 0Step-by-step explanation:
You want the maximum possible number of solutions to the equation
||ax -b| +c| = d
AnalysisThe values of 'a' and 'b' represent a vertical scale factor and a horizontal shift, so don't really contribute to the number of possible solutions. That means we can consider only the equation ...
||x| +c| = d
Positive c
We know |x| is always positive, and may have the same value for two different values of x. For positive 'c', the outside absolute value function does nothing, so the equation is effectively ...
|x| = d-c
For d < c, there can be no solutions. For d = c, there will be one solution, and for d > c, there will be two solutions.
Negative c
When 'c' is negative, then sum |x| +c may have either sign. This gives rise to another pair of possible solutions, for a total of four solutions.
GraphThe attached graph shows the two cases. The red graph shows the left side expression with c > 0; the purple graph shows the left side expression with c < 0. The orange horizontal line represents a value of 'd'. The number of intersection points with that horizontal line is the number of possible solutions to the given equation.
For c > 0, there are two possible solutions.
For c < 0, there are four possible solutions.
find xz
a 31.7
b 35.5
c 37.2
d 28.5
Answer:
I don't know I think it's b
X
What is the missing number 7 + = 15 - 4
Answer:4
Step-by-step explanation:
7+4=11
15-4=11
Un parque de diversiones quiere construir balsas con 3 troncos de palmera, los cuales miden 15, 9 y 6 metros, ¿cuánto
deben medir los pedazos de tronco si tienen que ser del mismo tamaño?, ¿cuántos pedazos de troncos saldrán?
Encontrando un factor comun entre los 3 números dados, concluimos que cada pedazo de tronco debe medir 3 metros, y se obtendran 10 pedazos en total.
¿cuánto deben medir los pedazos de tronco si tienen que ser del mismo tamaño?Sabemos que los troncos miden 15, 9, y 6 metros, si los queremos cortar en pedazos de igual longitud, de tal forma que nada se desperdicie, entonces debemos encontrar un factor comun entre esos 3 numeros.
Los podemos reescribir como:
15 = 3*5
9 = 3*3
6 = 2*3
Entonces el unico factor comun entre las 3 longitudes es 3.
El tronco de 15 metros dará:
15/3 = 5 pedazos de tronco.
El tronco de 9 metros dará:
9/3 = 3 pedazos de tronco.
El tronco de 6 metros dará:
6/3 = 2 pedazos de tronco.
Sumando eso obtenemos 5 + 3 + 2 = 10 pedazos en total.
Sí quieres leer más sobre factores comunes:
https://brainly.com/question/219464
#SPJ1
Rewrite each fraction as a percent and each percent as a fraction.
A florist prepares an order of daisies and roses. For every 5 daisies, she orders 2 roses. What two equations show the relationship between the number of daisies and the number of roses.
According to the solving the relationship between d and r are:
d = 2.5*r
r = d/2.5
What is relations in Mathematics?The relation in mathematics refers to the relationship between two or more types of values. Assume that x1 and x2 are two ordered pair sets. If set x is related to set y, the values of set x are referred to as domain, whereas the numbers of set y are referred to as range.
What exactly is a fundamental relationship?A base relation is simply a physical table that is maintained in a database. In contrast, a view is formed from base relations but it doesn't physically exist in the database; it only exists as either a structural definition that pulls data from a number of different base relations.
According to the given data:Given : 5 daises to 2 roses
d ∝ r
where d=daises and r=roses
d = kr
k = d/r
k = 5/2
k = 5.2
So,
d = 2.5 x r...............equation(1).
making r subject in eq (1)
r = d/2.5 ........................equation(2)
According to the solving the relationship between d and r are:
d = 2.5*r
r = d/2.5.
To know more about relations in Mathematics visit:
https://brainly.com/question/1995353
#SPJ9
Naveen Borah is a maintenance worker, He earns $12.80 per
hour for 40 hours and time and a half for overtime. He worked
48 hours last week. What is his pay for the week?
Answer: $563.2
Step-by-step explanation:
h=hours. T=total money earned in a week. o=overtime pay
o=12.8/2
o=6.4
T=12.8(40)+6.4(h-40)
T=512+6.4h-256
T=512-256+6.4h
T=6.4h+256
T=6.4(48)+256
T=307.2+256
T=$563.2
An employment agency specializing in temporary construction help pays heavy equipment operators $136 per day and general laborers $80 per day. If thirty-two people were hired and the payroll was $3960, how many heavy equipment operators were employed? How many laborers?
The number of heavy equipment operators employed is 26 while number of laborers employed is 6
How to solve Algebraic word problems?
Let x be the number of heavy equipment operators employed
Thus, If thirty-two people were hired, then we can say that;
32 - x represents the number of laborers employed
Thus, the equation to solve for x would be;
136x + 80(32 - x) = 3960
136x + 2560 - 80x = 3960
216x + 2560 = 3960
216x = 3960 - 2560
216x = 1400
x = 1400/216
x ≅ 6
Thus;
32 - x = 32 - 6 = 26
Thus, we conclude that number of heavy equipment operators employed is 26 while number of laborers employed = 6
Read more about Algebraic Word Problems at; https://brainly.com/question/13818690
#SPJ1
13 Aura 30% increase the new price of a book is $91.00. What was the original price of the book?
The old/Original value of the book before 30% increase in price is $70
Let us assume the old price of book before30% increase be x
Then the new price of the book after 30% increase would be x+ 30% of x
Which can be simplified as x+ 0.30x
Which further can be simplified 1.30x
As we are provided with the new price of book, we have to equate the above linear equation with the new price of the book
1.30x = $91
To solve the equation we need to move 1.30 from left hand side to right hand side which would change from to
X= 91/1.30
X=$70
Hence the old value of the book before 30% increase in price is $70
Correct question is if 30% increase in price of a book and the new price of a book is $91.00. What was the original price of the book?
to know more about linear equation - https://brainly.com/question/11897796
#SPJ9
Help me please with this! Thank you :)
Answer:
I'm pretty sure it's 5:4 or 5/4. I think this because there are 5 peaches and four oranges.
what is the range of h
Answer:
B
Step-by-step explanation:
h(x) is a discrete function, so its domain and range only contain individual points.
h(x) contains the points (-5, -2), (-4, 2), (0, 6), (2, -4), and (4, 4)
Look at the y-coordinates: -2, 2, 6, -4, 4
Arrange them in order: -4, -2, 2, 4, 6 ==> B
-
In AHIJ, m/H = (8x − 6)˚, m≤I = (2x − 4)°, and mZJ = (x − 8)˚. Find
m/H.
Answer: jus subtract untill u find x
Step-by-step explanation:
whether u do to one side do to the other
Select the part of speech for the underlined words below. Sometimes I am as ORNERY and STUBBORN as an old donkey. adverb conjunction preposition adjective
Answer:
Adjective
Those are describing words
I need help on this question
Answer: 225 yd³
Step-by-step explanation:
6*4*3=72
3*17*3=153
153+72=225 yd³
What is the vertex and minimum and maximum of
y= -2/3|x-1|
The vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum
How to determine the vertex and minimum and maximum of the function?The function is given as:
y = -2/3|x - 1|
The above function is an absolute value function
An absolute value function is represented as:
y = a|x - h| + k
Where the vertex is
Vertex = (h, k)
By comparing y = a|x - h| + k and y = -2/3|x - 1|, we have
(h, k) = (1, 0) --- vertex
a = -2/3
Because a = -2/3 is negative, then the vertex is a maximum
Hence, the vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum
Read more about absolute value function at
https://brainly.com/question/3381225
#SPJ1
-2(y + 1) + 5y = 3(y + 1) - 2
solve for y
Answer:
0 = 3 or No Solution
Step-by-step explanation:
a) Simplify both sides of the equation
−2(y + 1) + 5y = 3(y + 1) − 2
(−2)(y) + (−2)(1) + 5y = (3)(y) + (3)(1) + −2
−2y + −2 + 5y = 3y + 3 + −2
(−2y + 5y) + (−2) = (3y) + (3 + −2)
3y + −2 = 3y + 1
3y −2 = 3y + 1
b) Subtract 3y from both sides
3y − 2 − 3y = 3y + 1 − 3y
−2 = 1
c) Add 2 to both sides
−2 + 2 = 1 + 2
0 = 3 or No Solution
Solve for |y| = -18.
Answer:
18
Step-by-step explanation:
bc it is asking for the absolute value
what is the difference of twice a number and 3 is 11
Answer:
2x - 3 = 11
x = -21
Step-by-step explanation:
1. Round each decimal to the nearest whole number.
b. 34.972
a. 0.948
Answer:
34.972 ≈ 35
0.948 ≈ 1
Hope this helps :)
Step-by-step explanation:
To round to the nearest whole number look at the tenths place (the place right after the decimal). If the number is 1,2,3,4 then round down or keep the number the same. If the number is 5,6,7,8,9 then round up.
What is the image of the point (0,4)(0,4) after a rotation of 180^{\circ}180
∘
counterclockwise about the origin?
Answer:
(0,-4)
Step-by-step explanation:
I'm pretty sure it would be (0,-4) though it may be counted wrong. A whole 180° is like if you start from the highest point, you'd be at the lowest point right after the turn. It doesn't really matter the direction with 180° in this case cause it's going to be the same outcome anyways. (Or so I'd think).
Lisa is riding on a bike course that is 40 miles long .So far she has ridden 22 miles of the course.what percentage of the course has Lisa ridden so far
Answer:
55%
Step-by-step explanation:
She has ridden 22 out of 40 miles
22/40 is 0.55
0.55 = 55%
She has eight more miles or 45% left to go.
1. Name three acute angles.
a. NOK, JOK, KOL
b. NOM, JOK, KOL
c. NOM, JOK, KON
14. Which expressions are equal to 10^-5? Select all that apply.
10^5
10,000
10,000^-5
1/10^5
1/10,000
Answer:
It is C.
Step-by-step explanation:
Since 10 is to the power of negative five the number would be smaller than it was originally.
State (f/g)(x) and determine its domain
So um yeah this is a word problem for Honors Algebra and I can’t figure it out so maybe you can. It’s equations and inequalities but word form. So yeah good luck!! It’s number 4.
Answer:
5 trumpet players
Step-by-step explanation:
Given there are 10 fewer trumpet players than saxophone players, and the number of saxophone players is 3 times the number of trumpet players, you want to know the number of trumpet players.
SetupLet t represent the number of trumpet players. Then 3t is the number of saxophone players, and the difference in numbers is ...
3t -t = 10
SolutionCollect terms and divide by the coefficient of t:
2t = 10
t = 5
There are 5 trumpet players.
__
Additional comment
Check: There are 3 times as many sax players, so 15 of those. That's 10 more than the number of trumpet players.
You could have written the equation as ...
t +10 = 3t . . . . . . 10 more than the number of trumpets
Sometimes, when ratios are given:
t : s = 1 : 3
you can think in terms of "ratio units." Here, the difference is 3-1 = 2 ratio units, corresponding to a difference of 10 players. Then the multiplier of the ratio is 10/2 = 5:
t : s = 1 : 3 = 5 : 15 . . . . . . 5 trumpets and 15 saxophones.
PLEASE HELP (I HAVE PHOT)
IM LITTERALLY BEGGING YOU!!! Extra points and BRAINLIEST
Just please do 6,7,8,9,and10!!!
The responses to the questions involving the solution and equations of a straight line are;
6. The slope is -0.5
7. The equation is; y = x + 4
8. y = 7 - 0.25•x
9. The balance after m months is modeled by the equation;
B = 1,800 - 150•m
10. The slope is the monthly payment on the loan
How can a straight line equation be analyzed?6. The points on the graph in question 6 are; (0, 4), and (4, 2)
The slope is given by the ratio of the rise to the run of the graph as follows;
[tex]Slope = \frac{2 - 4}{0 - 4} = - 0.5[/tex]
The slope of the graph is -0.57. The equation in slope and intercept form is found as follows;
The given points are;
(-1, 3), and (-3, 1)
The slope and intercept form is presented as follows;
y = m•x + c
The point and slope form is presented as follows;
y - y1 = m•(x - x1)
Where m is the slope of the graph
m = (1 - 3)/(-3 - (-1)) = -2/-2 = 1
Which gives;
y - 3 = 1 × (x - (-1)) = x + 1
y = x + 1 + 3 = x + 4
y = x + 4The equation of the graph in slope and intercept form is; y = x + 4
8. The points are; (-4, 8), (4, 6)
Which gives;
m = (6 - 8)/(4 - (-4)) = -2/8 = -0.25
Therefore;
y - 8 = -0.25•(x - (-4)) = -0.25•x - 1
y = -0.25•x - 1 + 8 = -0.25•x + 7
y = 7 - 0.25•x9. The amount Zachary purchased the computer on loan = $1,800
The balance after 3 months = $1,350
The balance after 5 months = $1,050
Therefore;
The points on the graph of the equation that models the balance are therefore;
(0, 1,800), (3, 1,350), (5, 1,050)
Which gives;
B - 1800 = ((1,350-1,800)/(3-0))•(m - 0)
B - 1800 = -150•m
B = 1,800 - 150•mThe equation that models the balance, B, after m months is therefore;
B = 1,800 - 150•m10. The slope, ((1,350-1,800)/(3-0)) = -150, signifies the amount by which the balance reduces each month, which is the same as the amount Zachary pays each month, (the monthly payment).
Learn more about the equation of a straight line here:
https://brainly.com/question/25969846
#SPJ1
First, translate triangle FDE down 5 units. Second, reflect it over the y axis. Label the image F'D'E'.? what do I do
Answer:
Step-by-step explanation:
Answer:
first translate triangle FDE down 5 units
second reflect it over the y axis
The image
Step-by-step explanation: