Answer:
The Pythagorean theorem states that, for all 90-degree triangles, the relationship between the lengths of the sides is given by the formula a^2 + b^2 = c^2.
DISTANCE FORMULA
The study of geometry in a graphical environment is called co-ordinate geometry.
In co-ordinate geometry, the standard formula for calculating the distance between 2 points is called the distance formula.
Step-by-step explanation:
Answer:
Short answer: They are essentially the same thing.
The distance formula is derived from the Pythagorean Theorem
We have distance formula:
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Pythagorean Theorem:
[tex]a^2+b^2=c^2 \Rightarrow c=\sqrt{a^2+b^2}[/tex]
The shortest distance between two points if a line. If you draw a line in the cartesian plane both points will have an x-coordinate and y-coordinate. Note that it forms a right triangle! Therefore, the distance between those points is the hypotenuse.
We can have a point [tex]a=(x_{1}, y_{1})[/tex] and point [tex]b=(x_{2}, y_{2})[/tex]
But once [tex]a[/tex] and [tex]b[/tex] can be positive or negative:
[tex]c = \sqrt{a^2+b^2}= D = \sqrt{(\pm a)^2+(\pm b)^2}[/tex]
HEY PLEASE I NEED HELP IM OFFERING 30 POINTS
which point is a solution to the given system of inequalities
x+4y>12
3y>x+6
A.(-4,6)
B.(5,2)
C.(0,3)
D.(-2,3)
Answer:
the first option, (-4, 6)
Step-by-step explanation:
for this question, we can use the substitution method. this is where we substitute the coordinates in the answer choices into the given system of inequalities or equations to determine which one is true.
1. (-4,6)
x + 4y > 12
-4 + 4(6) > 12
20 > 12 is true
now we can substitute the second inequality.
3(6) > -4 + 6
18 > 2 is true, therefore making this set of points true.
it may be helpful to substitute the rest of the values of x and y into the inequalities to verify your answers :
5 + 4(2) > 12
5 + 8 > 12
13> 12 is true
3(2) > 5 + 6
6 > 11 is not true
the rest of the answer choices are also not true.
I hope this helped you!
Answer:
(-4, 6)
Step-by-step explanation:
WILL MARK AS BRAINLIST
Does the equation represent a direct variation? If so, find the constant of variation.
4x -5y = 0
a. yes; k = -5 b. no c. yes; k = 4/5 d. yes; k = - 4
Answer:
C
Step-by-step explanation:
4x-5y=0
5y=4x
y=4x/5, or rather y = (4/5)*x
k thus equals 4/5, and that is your constant of variation.
Answers: Yes, direct variation, k=4/5
1) Function B: x -> /5 -> +1 = y
find the inverse function of Function B
2) find an expression for m in terms of p.
Answer:
5x-35
Step-by-step explanation:
f(x)=5x+7
y=5x+7
x=5y+7
x-7=5y
5x-35=y
Simplify the following expression.
4 - (x - 3)
Answer:
4 - (x - 3) = - x + 7
Step-by-step explanation:
The students in Mrs. Willow's reading class are all reading the same novel independently. Four students create a graph of their reading rates, in words per minute, as shown below.
Which student reads the fastest?
Answer:
Sarah.
Step-by-step explanation:
Do not be fooled by how sharp the incline is, all of these graphs are labeled at different increments on both the x and y axes.
We will now solve this problem by figuring out each student's words per minute by dividing their words read (y-axis) by their time (x-axis).
Since the graphs are all linear, meaning they are constant and will never change. No matter what point we use on either graph we will come to the same words per minute for that student. For the sake of this explanation I will use the last point on each graph.
Charlie: Charlie read 1,750 words in 10 minutes, meaning he read at 175 words per minute. 1,750 / 10 = 175
Riley: Riley read 10,000 words in 50 minutes, meaning she read at 200 words per minute. 10,000 / 50 = 200
Sarah: Sarah read 1,300 words in 6 minutes, meaning she read at 216.67 words per minute. 1,300 / 6 = 216.67
Mason: Mason read 1,000 words in 5 minutes, meaning he read at 200 words per minute. 1,000 / 5 = 200
In conclusion, Sarah reads the fastest at 216.67 words per minute!
(02.07 LC)
Which relationship is always correct for the angles x, y, and z of triangle ABC?
A
x
C
Ox+ z = y
Oy + z = x
O x + y + z = 180 degrees
Ox + y + z = 90 degrees
Answer:
Ox+y+z=180
Step-by-step explanation:
The relationship which is always rue for the three angles x, y and z of triangle ABC is x + y + z = 180°.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
We know that a triangle has three angles.
Let x, y and z be the three angles of the given triangle.
We know that, the interior angles of a triangle sum up to 180°.
The given three angles are x, y and z.
So, x + y + z = 180°
Hence the correct relationship that describes all the three angles of the triangle is that x + y + z = 180°.
To learn more about Triangles, click on the link given :
https://brainly.com/question/19976619
#SPJ7
The rectangular field at Wilson Middle School is 300 feet long and 175 feet wide. In gym
class, students warm up by jogging along the edges of the field. What is the total number
of feet they jog?
475 feet
950 feet
52.500 feet
105.000 feet
the total number of feet they jog is 950 feet.
Mr. Smith saved $15 by buying a tool at a 10% discount. What was the original price for this tool?
Answer:16.5
Step-by-step explanation:
15 times 10 percent=1.5, Add 1.5 to 15 =16.5
Answer: $150
Step-by-step explanation:
PRICE x 10% = $15
PRICE x .1 =$15
PRICE = $15 /.1
PRICE = $150
Can someone help me on this math question?
Answer: 155º I think
which equation represents the function on the graph?
Answer:
the answer would be c the
third option
A rectangular pyramid was sliced perpendicular to its base and through its vertex. What is the shape of the cross section shown in the figure?
A rectangular pyramid. The cross section is a triangle.
a triangle that has the same dimensions as one of the sides of the pyramid
a triangle that does not have the same dimensions as one of the sides of the pyramid
a parallelogram that is not a rectangle
a rectangle
Answer:
d
Step-by-step explanation:
a rectangle
The cross-section of the shape will be that of a triangle, hence the correction option is A.
What is a cross-section?Cross-sections are basically flat shapes that are formed when we slice through a solid shape.
A good idea of a cross-section is when you slice through a piece of potato.
Learn more about cross-sections here:
https://brainly.com/question/21400791
#SPJ2
What is the solution to the equation? 5=2/5a
What is the volume of the solid figure? A rectangular prism on top of another longer rectangular prism. The top prism measures 5 inches by 5 inches by 5 inches. The bottom prism measures 20 inches by 5 inches by 5 inches. 625 in3 750 in3 800 in3 1,250 in3
Answer:
A
Step-by-step explanation:
V=5^(3)+20*5*5
V=125+500
V=625 in^3
Answer:
it is c
Step-by-step explanation:
Can someone please help with this math problem I'd really appreciate it.
Answer:
[tex]\mathrm{F}[/tex]
Step-by-step explanation:
[tex]y+8=4(x-5)[/tex]
[tex]x=5\\y=-8[/tex]
[tex](-8)+8=4((5)-5)[/tex]
[tex](-8)+8=4(0)[/tex]
[tex]0=0[/tex]
A researcher wanted to show that math test scores increased for students who attended extra study sessions for a particular school. The study sampled 5 honors students who attended the study session. Explain why this report is not reliable.
Answer:
This report is not reliable because:
A real increase could be proved with the sample of all the students who attended the study session, due to mustn't be many students (I believe the students regularly doesn't like the extra study sessions), where wouldn't just have honors students, but the regular students too, who probably would actually need increasing their math scores.
Step-by-step explanation:
To identify if a students population actually increased their math tests scores by a particular reason, the researcher should take a sample from the regular or bad students that attended to the extra session, or at least an equal sample with the same amount of good students and regular students ( or bad students), in this form he would compare the results in each individual and identify if it actually depended on the extra study sessions or from other reasons how study time in the house, learning disorders or others.
which statements correctly describe the association between the variables A and B ? select each correct answer.
Write the standard form of the equation for
the line that passes through the points
(-4. – 7) and (5. 1).
Answer:
8x-9y=31
Step-by-step explanation:
Which table represents a function?
The one on the far left
Please help me ASAP I will give brainliest
Answers The answer A
Step-by-step explanation:
Penny wrote the mixed number 4 2/7 as 8/7. Describe Penny's error, and EXPLAIN how she should of have written the improper fraction
Answer:
She must have multiplied 4 times 2/7 which is 8/7. She should have written it as 30/7.
Step-by-step explanation:
The midpoint of the coordinates (7,9) and (12,11) is ______.
A. (9.5, 10)
B. (13, 12)
C. (19, 20)
D. none of the above
Answer:
The answer is option a.
Step-by-step explanation:
=(7+12/2 , 9+11/2)
=(19/2, 20/2)
= ( 9.5 , 10)
Hope this helps.
What is 42.8 on its standard form???
Answer:
[tex]4.28 \times 10^{1}[/tex]
Step-by-step explanation:
[tex]42.8 \times 10^0=42.8[/tex]
[tex]4.28 \times 10^{1}=42.8[/tex]
Answer:
42.8 x 10^0
Step-by-step explanation:
A. Standard Form
Ax + By = C.
A, B, C are integers (positive or negative whole numbers)
No fractions nor decimals in standard form.
Traditionally the "Ax" term is positive.
Felicia drew a triangle with side lengths that measured 15 cm, 18 cm and 27 cm. To determine if Felicia drew a right triangle, she can use the equation:
Answer:
The equation should be h²=P²+b²
27²=15²+18²
729=225+324
729=549
thus, it is not right angle triangle
Which of the following terms correctly describe the figure given below?
Check all that apply.
A. Polygon
B. Prism
C. Cube
D. Pyramid
O E. Solid
O F. Polyhedron
PREVIOUS
The given solid is triangular prism. Therefore, option B is the correct answer.
What is a prism?A prism is a solid form that is enclosed by plane faces on all of its sides. A prism has two different kinds of faces. Bases refer to the identical top and bottom faces. The name "prism" refers to the form of these bases. For instance, a prism is referred to be a triangular prism if its base is triangular.
A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.
Therefore, option B is the correct answer.
Learn more about the prism here:
https://brainly.com/question/29722724.
#SPJ7
Find f(2) if f(x)=(x+1)^2
a. 9
b. 6
c. 5
Answer:
a. 9
Step-by-step explanation:
If f is at 2, then you subsitute anywhere that an x is with a 2. So in this particular equation we get
f(2) = (2+1)^2
f(2) = (3)^2
f(2) = 9
Use the distributive property to write the following sum as a product.
17a+17b
Answer:
17(a+b)
Step-by-step explanation:
17 is distributed in the initial equation to both the a and the b
Answer:
17(a+b)
Step-by-step explanation:
Factor out the common term
17a+17b
17(a+b)
some teachers traveled to school by car the table shows the number of teachers in the cars a) what was the modal number of teachers in a car b) what was the median number of teachers in a car c) what was the mean number of teachers in a car
Answer:
Step-by-step explanation:
since it is asking for the modal that means the most so it would be 3 teachers, and when asking the median we have to change the order so it would be 2,3,4,6 and we find the middle so it would be 3.5, and the mean is the total of the numbers divided by how many numbers there are so it would 2+6+4+3=
15/10 = 1.5
A mean is an arithmetic average of a set of observations. The model number, median, and mean of the number of teachers in a car are 3, 3, and 2.46667, respectively.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The given table can be written in the data form as 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4.
A.) The modal number is the mode of a given data set. Therefore, the mode of the given data set is 3.
B.) The median is the middle number of a given data set. Therefore, the median is 3.
C.) The mean is the average number of teachers in a car. Therefore, the mean is,
Mean = (1+1+1+2+2+2+2+3+3+3+3+3+3+4+4)/15 = 37/15 = 2.46667
Hence, the model number, median and the mean of the number of teachers in a car is 3, 3, and 2.46667, respectively.
Learn more about Mean:
https://brainly.com/question/16967035
#SPJ2
Which set a rational numbers are ordered from least to greatest?
Wrong answers will be reported!!!!
Answer:
The answer to this is A
Step-by-step explanation:
hope it helped
Answer:
A
Step-by-step explanation:
tell me if im right
Determine which sequence is an arithmetic sequence.
Question 18 options:
a)
–7, –3, 1, 5, ...
b)
15, 17,19, 111, ...
c)
−10, 5, −52, 54, ...
d)
3, 6, 12, 24, ...
Answer: A
Step-by-step explanation: An arithmetic sequence is a pattern in which the same number is repeatedly added or subtracted.
Notice that in the the first sequence shown, we add 4 to reach the next term in the sequence which means this is arithmetic.
The others are not arithmetic because the difference
between the terms does not remain constant.
What are the coordinates of the vertex of the graph of the absolute value function h(x) = 3|x + 5| + 2? A) (5,-2) B) (-5,2) C) (5,2) D) (2,-5)
Answer:
B) Vertex = (-5, 2)
Step-by-step explanation:
Vertex can be defined as defined as the point where two lines meet and form a particular angle with each other. It can also be described as the point where a line changes its direction
We can find vertex by two methods:
1) GRAPHWe can see in the graph attached below that the line changes its direction at point (-5, 2). So the vertex is (-5,2)
2) FORMULAGeneral form of equation of mod function is given by
y = a |x - h| + k
where Vertex = (h, k)
The given equation is
h(x) = 3 |x + 5| + 2
h(x) = 3 |x - (-5)| + 2
where h = -5 and k = 2
So the vertex is:
Vertex = (-5, 2)
Answer:
(–5, 2)
Step-by-step explanation:
