If ABCD is the rectangle, then AB and BC are perpendicular.
Let m₁ and m₂ - slopes of perpendicular lines. Therefore
m₁m₂ = -1 → m₂ = -1/m₁.
We have m₁ = 2/3 then m₂ = -1/(2/3) = -3/2.
Answer: The slope of BC is -3/2.The slope of BC is -3/2.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
We are given ABCD is the rectangle, then AB and BC are perpendicular.
Let m₁ and m₂ are slopes of perpendicular lines. Therefore.
m₁m₂ = -1
m₂ = -1/m₁.
We have m₁ = 2/3 then;
m₂ = -1/(2/3) = -3/2.
Hence, The slope of BC is -3/2.
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All I want is to learn how to solve this, not just a quick answer, a step by step explanation. Please help me out.
What is the solution to this system of equations?
3x - y = -5
x + 4y = 7
I am really just looking to see how to solve more questions like these so please don't be vague.
Answer:
Well, since they are lined up correctly already, you can combine the like terms and get 4x + 3y = 2.
Is that all you wanted?
Answer:
A) 3x - y = -5
B) x + 4y = 7
Whenever you have to solve for 2 unknowns, you need 2 equations. (These are called solving simultaneous equations.)
Perhaps the easiest way to solve these is by the elimination of variables.
Looking at Equation A) we see that if we multiply it by 4, and add it to equation B), the "y" variable will be eliminated.
Multiplying equation A) by 4 we get
A) 12x - 4y = -20 then adding this to B)
B) x + 4y = 7 we get
EDITD TO CORRECT**************************************************
13x = -13
x = -13 / 13= -1
Then we can get x = -1 and insert it into either equation. (Let's choose B)
B) -1 + 4y = 7
B) 4y = 8
y = 2
*******************************************************************************************
For a double-check we can insert x = -1 and y = 2 into either equation. (Let's choose equation B)
B) -1 + 4 * 2 = 7
B) -1 + 8 = 7
And since -1 + 8 DOES equal 7, we know that we have solved for "x" and "y" correctly!
Source:
https://en.wikipedia.org/wiki/System_of_linear_equations
Elimination of variables
Step-by-step explanation:
Help plzzzzz ASAP I NEED HELP
Answer:
a
Step-by-step explanation:
all that happned was community property if numbers are switced around in an addition sentence then the answer will always be the same
Brainliest + Points!
Which statement describes data that is negatively skewed?
A.
The majority of the data is to the left of the mean.
B.
The majority of the data is to the right of the mean.
C.
The majority of the data is in the center with the mean.
D.
The majority of the data is split to the right and left of the mean.
Answer:
The majority of the data is to the left of the mean or The majority of the data is split to the right and left of the mean.
hope this helps
Step-by-step explanation:
A. The majority of the data is to the left of the mean
In 1992, Jason bought a gallon of gas for $1.23. Yesterday, he bought a gallon of gas for $2.09. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent. A. 30.1% B. 41.1% C. 58.9% D. 69.9%
Answer:
47.8% increase, or B since it's the closest.
Step-by-step explanation:
Answer:The answer to this problem is actually 69.9%
Step-by-step explanation:
Trapezoid ABCD is similar to trapezoid EFGH. Side AD is proportional to side ___
Answer:
Side EH
Step-by-step explanation:
Side AD is proportional to side EH. If you look at ABCD, and compare it to EFGH, the ends of the name, AD, correspond with the ends of the other, EH.
Side AD of trapezoid ABCD is proportional to side EH of trapezoid EFGH due to the properties of similar geometric figures, where corresponding sides of similar shapes are in proportion.
The question asks which side of trapezoid EFGH is proportional to side AD of trapezoid ABCD, given that the two trapezoids are similar. In similar figures, corresponding sides are proportional. Therefore, if side AD of trapezoid ABCD corresponds to side EH of trapezoid EFGH, then these sides are proportional to each other.
Since we are discussing proportions and similarity of shapes, particularly trapezoids, we can reference several mathematical concepts. By the AAA theorem, which stands for angle-angle-angle, we know that if two or more corresponding angles in two figures are equal, then the figures are similar and the sides opposite these angles are proportional. Also, the proportions of corresponding sides can be determined using theorems regarding triangles and trapezoids.
We conclude that side AD is proportional to side EH because of the properties of similar geometric figures.
In the figure to the right point O is the midpoint of segment
AB
. Through point O is drawn a line
OX
.perpendicular to
AB
. Prove that any point on line
OX
is equidistant from A and B.
Answer:
See proof below
Step-by-step explanation:
Point O is the midpoint of segment AB. Through point O is drawn a line OX perpendicular to AB. Consider two triangles AOX and BOX. These triangles are right triangles, because OX is perpendicular to AB. In these triangles:
OX=OX (reflexive property of congruence);AO=OB (by the definition of the midpoint O).Thus, [tex]\triangle AOX\cong \triangle BOX[/tex] by LL theorem.
Congruent triangles have congruent corresponding sides, then AX=BX. This means that point X is equidistant from points A and B.
how many terms are in the following expression 6+2x-4y+5z
1
2
3
4
Answer:
4
Step-by-step explanation:
A term no matter how long it is, is ended by some sort of sign. so 6 is a term 2x is a term -4y is a term and 5z is a term. The term could be 5xyz^6a^2bc^7 + 2, and there are only 2 terms.
Answer:
4
Step-by-step explanation:
There are 4 terms in the expression. Terms are separated by the addition or subtraction sign.
Please help please!!!!!!!!!!!!
Answer:
1
Step-by-step explanation:
Answer:
The correct answer would be, B, one
Step-by-step explanation:
PLZ HURRY
Which graph represents the function f(x) = 2|x|?
Answer:
the third one............ not the second
Step-by-step explanation:
The graph of the absolute function f(x) = |2x| is option B
What is graph of an absolute function?The graph of an absolute function, also known as an absolute value function, is a V-shaped graph that is symmetric with respect to the y-axis. The absolute value function is defined as:
f(x) = |x|,
where |x| represents the absolute value of x.
The graph of the absolute value function consists of two parts:
For x ≥ 0, the function f(x) = x. This portion of the graph appears as a straight line with a positive slope, starting from the origin (0,0) and extending upwards to the right.For x < 0, the function f(x) = -x. This portion of the graph is also a straight line with a positive slope, starting from the origin (0,0) and extending upwards to the left.Using a graphing calculator;
f(x) = 2|x|
The graph of the function is attached below;
From the graph attached below the answer is option B.
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does 2/3 and 10/16 form a proportion? explain
20 POINTS WILL GIVE BRAINLIEST HELP QUICKLY!!
Two functions are represented in different formats function one:
X. Y
0. 5
2. 11
5. 20
8. 29
Function 2
(A graph intersecting through point -1 on y axis and 2 on x axis)
Which statements are true?
Select each correct answer
1.function 1 has a greater rate of change than function 2
2. Function 2 has a greater rate of change than function 1
3. Function 1 has a greater y-intercept thank function 2
4. Function 2 has a greater y-intercept than function 1
Answer:
Statement 3 as well as statement 1 are true
Step-by-step explanation:
Answer:
1.function 1 has a greater rate of change than function 2
3. Function 1 has a greater y-intercept than function 2
Step-by-step explanation:
Using the table we can find the slope using
m = (y2-y1)/ (x2-x1)
m = (29-5)/ (8-0)
= 24/8
= 3
The rate of change for the table is 3
The y intercept is (0,5)
Using the graph (0,-1) and (2,0)
m = (y2-y1)/ (x2-x1)
m = (0--1)/ (2-0)
= (0+1)/2
= 1/2
The y intercept is (0,-1)
Since 3>1/2 , function 1 has a greater rate of change than function 2
Since 5>-1, function 1 has a greater y-intercept than function 2
On Tuesday at 2 p.m., the ocean’s surface at the beach was at an elevation of 2.2 feet. Winston’s house is at an elevation of 12.1 feet. The elevation of his friend Tammy’s house is 3 1/2 times the elevation of Winston’s house.
How many times greater is the elevation of Tammy’s house than the elevation of the ocean’s surface at 2 p.m.?
Answer:
the answer is 9.9
Step-by-step explanation:
12.1-2.2=9.9
The elevation of Tammy’s house is greater than the elevation of the ocean’s surface at 2 p.m. will be 9.9.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, on Tuesday at 2 p.m., the ocean’s surface at the beach was at an elevation of 2.2 feet. Winston’s house is at an elevation of 12.1 feet. The elevation of his friend Tammy’s house is 3 1/2 times the elevation of Winston’s house.
We have to find the elevation of Tammy’s house greater than the elevation of the ocean’s surface at 2 p.m.
Suppose the greater is the elevation of Tammy’s house than the elevation of the ocean’s surface at 2 p.m be x,
x=12.1-2.2
x=9.9
Thus, the elevation of Tammy’s house is greater than the elevation of the ocean’s surface at 2 p.m. will be 9.9.
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I need a explanation.
Answer:
For #5, there are no solutions because when you solve 3(-2x+y)=12, you get y=2x +4. It has the same slope with the first equation but a different y-intercept meaning that they are parallel lines and won’t intersect
Step-by-step explanation:
Need help on this
Z+4>2z
Answer: z < 4
z+4 > 2z
z+4-z > 2z-z ..... Subtract z from both sides
4 > z
z < 4
So the solution set for z is any number that is less than 4, which could be something like z = 2 or z = 3.
what value of c makes x2-24x+c a perfect square trinomial?
Answer:
144
Step-by-step explanation:
Perfect square formula: a^2 - 2ab + b^2 (because that equals (a-b)^2)
x^2-2*12x+c
a = 1
b = 12
12^2 = 144
Answer:
The value of [tex]c =144[/tex] makes [tex]x^{2}-24x+c[/tex] perfect square.
Step-by-step explanation:
We have to make [tex]x^{2}-24x+c[/tex]
Since, Perfect square formula: [tex]a^{2} - 2ab + b^{2}=(a-b)^{2}[/tex]
Re-write [tex]x^{2}-24x+c[/tex] as,
[tex]x^{2}-2\times 12x+c[/tex]
Compare above with [tex]a^{2} - 2ab + b^{2}[/tex]
Where a = x and b= 12
so, [tex]b=12[/tex]
⇒ [tex]c =12^{2}=144[/tex]
Hence, [tex](a-b)^{2}=(x-12)^{2}[/tex]
Therefore, the value of [tex]c =144[/tex] makes [tex]x^{2}-24x+c[/tex] perfect square.
Drag each tile to the correct box. Arrange the complex numbers in order according to the quadrant in which they appear, starting with the first quadrant. (3 − 4i) (-1 − 3i) (4 + i) (-2 + 2i)
Answer:
see explanation
Step-by-step explanation:
(4 + i) → first quadrant
(- 2 + 2i) → second quadrant
(- 1 - 3i) → third quadrant
(3 - 4i) → fourth quadrant
Eli's office recycled a total of 12 kilograms of paper over 6 weeks. After 9 weeks, how many kilograms of paper will Eli's office have recycled
[tex]\begin{array}{ccc}6\ weeks&-&12\ kg\\9\ weeks&-&x\ kg\end{array}\qquad\text{cross multiply}\\\\(6)(x)=(9)(12)\\\\6x=108\qquad\text{divide both sides by 6}\\\\\boxed{x=18}\\\\Answer:\ \text{Eli's office recycled 18\ kg\ of\ paper.}[/tex]
Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0.04 liters. Then, he wants to fill the tank with water until it's completely full. If he uses 50 marbles, he will have to add 33 liters of water. What is the volume of the tank?
Answer: 35 liters
Step-by-step explanation:
Volume of 1 marble = 0.04 Liters
volume of 50 marbles = 50 x 0.04 liters = 2 liters
volume of water added = 33 liters ( Given)
Volume of tank = Volume of water + Volume of 50 marbles
= 33 liters + 2 liters
= 35 liters
What is 11/16 as a percent
⭕ 11\16= %
⭕ 11÷16= 68.75%
⭕ 68.75%
To convert a fraction to a percentage, we would multiply the fraction by 100%, and the result would be the percentage.
In this case:
11/16 x 100%
=0.6875 x 100%
=68.75%
Therefore the answer is 68.75%
Hope it helps!
Please help need this answer
Answer:
There are no solutions
Step-by-step explanation:
4x-1 = 2(2x-1)
The first step is to distribute the 2
4x-1 = 2*2x-2*1
4x-1 = 4x-2
Subtract 4x from each side
4x-4x-1 = 4x-4x-2
-1=-2
Since this is not true, there are no solutions
Convert 4 1/2 inches to a decimal
Answer:
Convert 4 1/2 inches to a decimal = 11.43 cm
Step-by-step explanation:
Answer:
I would say 4.5 in.
I hope this helps!
Cheers, July.
Step-by-step explanation:
The weights (in pounds) of 18 preschool children are
32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29
Answer:
22.8 and 37.5
Step-by-step explanation:
Given the
The weights (in pounds) of 18 preschool children are
32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29
To find its 20th percentile and 75th percentile.
In ascending order we get like this
Position X (Asc. Order)
1 20
2 21
3 22
4 23
5 24
6 25
7 27
8 29
9 30
10 31
11 32
12 33
13 34
14 37
15 39
16 41
17 44
18 45
Percentile position = (no of entries +1)20/100 = 19/5 = 3.8
Since posiiton is not integer we use interpolation method.
The value of 3.8 - 3 = 0.8 corresponds to the proportion of the distance between 22 and 23 where the percentile we are looking for is located at.
Hence 20th percentile = [tex]22+0.8(23-22)=22.8[/tex]
So answer is 22.8
----------------------
75th percentile
Percentile posiiton = 19(75)/100 = 14.25
75th percentile= [tex]37+0.25(39-37)=37.5[/tex]
Answer:
22.8 and 37.5
1. Intervention may be called A.addicts, mentally ill people,
or abused spouses
2. People in need of intervention may include
B. interference in someone’s
life
C.violent or suicidal
3. People in need of intervention may be
Answer: 1. mentally ill people
2. c
3.answer choices ?
Step-by-step explanation:
The ages of three brothers are consecutive even integers. Five times the age of the youngest brother exceeds the oldest brother's age by 60 years. The equation 5x − (x + 4) = 60 models the age, x, of the youngest brother. What is the age of the oldest brother?
A) 16
B) 20
C) 24
D) 28
Answer:
The oldest brother is 20 years old. PLEASE GIVE BRAINLIEST!!!
Step-by-step explanation:
Youngest = 5x - (x+4) = 60 Oldest = 5x - 60
5x - 1(x+4) = 60 5(16) - 60 =
5x - x - 4 = 60 80 - 60 = 20
4x - 4 = 60
4x = 60 + 4
4x = 64
x = 64 ÷ 4 x = 16
Youngest = 16
Middle = 18
Oldest = 20
Answer:
the older brothers age is 20 years old have a fantastic day or evening :)
Step-by-step explanation:
A line is represented by the equation x + 2y=4. What is the slope of the line with that equation?
Answer:
the slope is 1
Step-by-step explanation:
Answer:
The slope is -1/2
Step-by-step explanation:
x + 2y=4
Lets get the equation in the form y= mx+b
where m is the slope and b is the y intercept.
x + 2y=4
Subtract x from each side
x-x+2y = -x+4
2y = -x+4
Divide each side by 2
2y/2 = -1/2 x +4/2
y = -1/2x +2
The slope is -1/2
A 3 foot stick is broken into two pieces. The ratio of the two pieces is 5:7. How big are the two pieces
The 3 foot stick broken in a 5:7 ratio results in two pieces measuring 1.25 feet and 1.75 feet, respectively.
Explanation:The question involves a 3 foot stick that is broken into two pieces with a ratio of 5:7.
To find the lengths of the two pieces, we first add the parts of the ratio together, which gives us 12 parts in total.
Since the whole stick is 3 feet long, each part of the ratio represents \(\frac{3 feet}{12 parts}\) or \(\frac{1}{4} foot\) per part.
Thus, the length of the smaller piece is 5 parts (\(5 \times \frac{1}{4} = \frac{5}{4} feet\) or 1.25 feet) and the length of the larger piece is 7 parts (\(7 \times \frac{1}{4} = \frac{7}{4} feet\) or 1.75 feet).
a school cafetiria has 40 tables. 35%of the tables have 8 chairs at each table. The remaining 65% of the tables have 6 chairs at each table. Complete the model Then complete the statement to find the total number of chairs in the cafeteria.
Answer:
Can i have a picture of the model
Step-by-step explanation:
Answer:
328 chairs
Step-by-step explanation:
40×35%=14 tables ×8=112
36remaining tables×6=216
216+112= 328
Total=328
What is the volume of the following rectangular prism?
Volume =_____units^3
To find the volume of a rectangular prism, multiply the length, width, and height. The formula is V = l * w * h.
Explanation:To find the volume of a rectangular prism, you need to multiply the length, width, and height of the prism.
The formula for the volume of a rectangular prism is: V = l * w * h.
So, to find the volume of a rectangular prism, you need to know the measurements of its length (l), width (w), and height (h) in the same unit of measurement.
Multiply these values together to find the volume in cubic units (such as cubic centimeters or cubic meters).
For example, if a rectangular prism has a length of 5 centimeters, a width of 3 centimeters, and a height of 2 centimeters, you would calculate the volume as follows: V = 5 cm * 3 cm * 2 cm = 30 cm³.
The volume of the rectangular prism, obtained from the product of the known face area and the width is 11 2/3 cube units
Volume = 11 2/3 units³
The details of the steps used to find the volume of the prism can be presented as follows;
The dimensions of the rectangular prism includes a face area and the width of the prism
Area of a face of the rectangle = 3 1/3 square units
Width of the rectangular prism = 1 2/5 units
Area of a rectangular prism = Length × Width × Height
The length and the height of the rectangular prism form the face with the known area of 3 1/3 square units
Therefore; Area of a rectangular prism = Width × Area of the vertical face perpendicular to the width of the rectangular prism
Area of a rectangular prism = 1 2/5 units × 3 1/3 square units
1 2/5 units × 3 1/3 square units = (7/2) × (10/3)
(7/2) × (10/3) = 70/6
70/6 = 11 2/3
Area of the rectangular prism is 11 2/3 units³
Brainliest + Points!
Does anyone know how to do this?
For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean, and compare the result to the expected percentage of a normal distribution.
{55, 54, 66, 38, 53, 56, 57, 66, 45, 65}
A.
50%; This percentage is lower than expected in a normal distribution.
B.
60%; This percentage is lower than expected in a normal distribution.
C.
70%; This percentage is close to the expected percentage in a normal distribution.
D.
80%; This percentage is higher than expected in a normal distribution.
Answer:
A. 50%; This percentage is lower than expected in a normal distribution
Answer:
A) 50%; This percentage is lower than expected in a normal distribution.
Step-by-step explanation:
Data points given:
55, 54, 66, 38, 53, 56, 57, 66, 45, 65
n = 10
The mean for the data points:
[tex] \frac{55+54+66+38+53+56+57+66+45+65}{10} [/tex]
Mean = 55.5
Standard deviation of data points:
[tex] = \sqrt{\frac{55-55.5)^2+(54-55.5)^2+(66+55.5)^2+(38-55.5)^2+(53-55.5)^2+(56-55.5)^2+(57-55.5)^2+(66-55.5)^2+(45-55)^2+(65-55)^2}{10}} [/tex]
= 8.59
Now let's find the data points that lie between 64.09 i.e (55.5 + 8.59) and 46.91 i.e (55.5-8.59)
We can see that 5 data points lie between 64.09 and 46.91 which are { 55,54,53,56,57}
The correct option is A, which states that 50% percentage is lowee than expected.
the formula for blood flow rate can be described by the formula f=N-O/R are where F represents the blood flow rate, N represents the pressure in the inlet, O represents the pressure in the outlet, and R representative vascular resistance
True or false: The following equation is correctly solved for the vascular resistance.
R=F+O-N
Answer:
FALSE
Step-by-step explanation:
F = (N - O)/R Multiply both sides by R
RF = N – O Divide both sides by F
R = (N – O)/F
FALSE. The given solution is incorrect.
Final answer:
The statement provided is false. The correct formula for vascular resistance R in terms of blood flow F, inlet pressure N, and outlet pressure O should be R = (N - O) / F.
Explanation:
The statement is false. The correctly solved equation for vascular resistance R, based on the formula F = (N - O) / R where F is blood flow rate, N is the pressure at the inlet, O is the pressure at the outlet, would be R = (N - O) / F. If we isolate R in the equation by multiplying both sides by R and dividing by F, we would get R = (N - O) / F, not R = F + O - N as incorrectly stated in the question.
To further understand the relationships among the factors affecting blood flow, the Poiseuille's equation plays a significant role. This equation includes critical variables like the radius (r) to the fourth power, vessel length (λ), and viscosity (n) of the fluid. Changes in these variables can significantly affect blood flow and resistance within the vascular system.