Answer:
The answer is below
Step-by-step explanation:
a) The equation of a line passing through the point (0,0) and (16,4) is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-0=\frac{4-0}{16-4}(x-0)\\\\y=\frac{1}{4}x[/tex]
We have to find the equation of the line perpendicular to y = (1/4)x and passing through the point (4,6).
The line perpendicular to y = (1/4)x has a slope of -4 (product of their slope = -1).
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-6=-4(x-4)\\\\y-6=-4x+16\\\\y=-4x+22[/tex]
The slope of a line passing through the point (16,4) and (4,6) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{6-4}{4-16}=-\frac{1}{6}[/tex]
We have to find the equation of the line perpendicular to the line with slope of -1/6 and passing through the point (0,0).
The line perpendicular to a line with slope -1/6 has a slope of 6
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-0=6(x-0)\\\\y=6x[/tex]
Solving y = 6x and y = -4x + 22, gives:
x = 2.2, y = 13.2
Hence the orthocenter is at (2.2, 13.2)
b)
The slope of a line passing through the point (3,4) and (11,12) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{12-4}{11-3}=1[/tex]
We have to find the equation of the line perpendicular to the line with slope of 1 and passing through the point (8,15).
The line perpendicular to a line with slope 1 has a slope of -1
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-15=-1(x-8)\\\\y=-x+8+15\\\\y=-x+23[/tex]
The slope of a line passing through the point (11,12) and (8,15) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{15-12}{8-11}=-1[/tex]
We have to find the equation of the line perpendicular to the line with slope of -1 and passing through the point (3,4).
The line perpendicular to a line with slope -1 has a slope of 1
Hence:
[tex]y- y_1=m(x-x_1)\\\\y-4=1(x-3)\\\\y=x-3+4\\\\y=x+1[/tex]
Solving y = -x + 23 and y = x + 1, gives:
x = 11, y = 12
Hence the orthocenter is at (11, 12)
Pls help ;-;
Which number line shows all the values of x that make the inequality
-3x + 1 < 7 true?
Answer:
C
Step-by-step explanation:
A closed circle means inclusive, and -2 is included in values that would make the equation true. Then you just have to test another number greater than and less than -2 to see which way the arrow should point.
-3(-3) + 1 < 7
9 + 1 < 7
10 < 7 FALSE
-3(0) + 1 < 7
1 < 7 TRUE
All values (including -2) will make this equation true
Question:
Which number line shows all the values of x that make the inequality
-2x - 7 ≥ 13 true?
What would be the output (y-value) for the rule y = 4x - 5 if
you used an input of x = -2? Just write the number for your
answer.
I need help pls and thank, will give brainliest to who is willing to help me! :3
Answer:
2. Solve the system of equations.
1
ży 22
—1
x + 3y = 2 = 10
11/x + 2
+ z = -4
9514 1404 393
Answer:
(x, y, z) = (2, 1, -5)
Step-by-step explanation:
There are numerous equation solvers available on the web. The attached result is from one of them.
__
You may find it easier to solve these by hand if you eliminate fractions.
2x -y +z = -2x +3y -z = 10x +0y +2z = -8The first step is to look to see what you have, then formulate a strategy for getting a solution. Because the equations containing y have opposite coefficients, one of which is -1, we choose to use those to eliminate y. Immediately, we will have two equations in x and z.
If you multiply the first equation by 3 and add that to the second, then you will eliminate y. The third equation already has y eliminated, so you will then have two equations in x and z.
3(2x -y +z) +(x +3y -z) = 3(-2) +(10)
6x -3y +3z +x +3y -z = -6 +10
7x +2z = 4 . . . . [eq4]
Subtracting the third equation from this eliminates z, so you have ...
(7x +2z) -(x +2z) = (4) -(-8)
6x = 12
x = 2
Substituting into the third equation gives ...
2 +2z = -8
2z = -10
z = -5
Then using the first equation, you have ...
y = 2x +z +2 = 2(2) +(-5) +2 = 1
(x, y, z) = (2, 1, -5)
purchased a DVD player on sale. The original selling price was $. The sale price was $.
what are the prices?
5 divided by 9/10 as a fraction
Answer:
5/1. 9/10 ÷ 5 = 9/50
Step-by-step explanation:
a whole number 5 can be written as 5/1. 9/10 ÷ 5 = 9/50 in fraction form.
hope this helped. Let me know if i was right. Im sorry if I was wrong Im not so good at math.
THIS IS EASY!! PLS HELP ME! ASAP PLS
Eliza claims that the two squares are congruent. Which statement could be used to prove Eliza's claim?
A) Any two squares are congruent since all squares have angles of 90 degrees
B) The two squares are congruent since a translation carries one square onto the other.
C) Any two squares are congruent since all four sides of any square are congruent.
D) The two squares are congruent since a rotation about the origin carries one square onto the other.
Answer:
A
Step-by-step explanation:
I Hope this helps you out!
Eliza claims that the two squares are congruent. The statement that could be used to prove Eliza's claim can be found in Option A.
Any two squares are congruent since all squares have angles of 90 degrees.
A figure is said to be congruent if they have similar angles and the position of each shape corresponds to each other.
From the given figure attached to the question, we can see that the two shapes in the figure are squares, and they are located at 2 units each from the origin. The angles of each shape are 90° to the horizontal line and they are perpendicular to each other.
The two squares may not be congruent since not only translation carries one square onto the other, from the figure in the question, it may be a reflection and not only translation.
Also, only the sides of a shape cannot be used as a determining factor to determine if a shape is congruent or not.
Therefore, we can conclude that any two squares are congruent since all squares have angles of 90 degrees.
Learn more about congruent angles here:
https://brainly.com/question/16448127?referrer=searchResults
Need these proofs solved ASAP 45 pts I will give brainliest
Answer:
Step-by-step explanation:
im not sure buddy
What is 4and2/14 as an improper fraction in lowest terms
Answer: 58 14ths
Step-by-step explanation:
multiply 14 by 4 to get 56 14ths, then add the 2
Answer:
58/14
Step-by-step explanation:
4 and 2/14= 4*4*4*4 = 56 + 2 = 58/14
please help and don’t answer if you don’t know
Answer:
2 6
4 20
10 110
-3 6
5 30
7 56
1 2
[tex]rule \: \: y = {x}^{2} + x[/tex]
Step-by-step explanation:
First thing to do is look for a pattern with the current data. What I found was the pattern, ahich is the rule. See below.
[tex]y = {x}^{2} + x[/tex]
Now insert the given values for x and y into the rule.
[tex]y = - {3}^{2} - 3 \\ y = 6 \\ \\ 30 = {x}^{2} + x \\ x = 5 \\ \\ y = {1}^{2} + 1 \\ y = 2[/tex]
Which of the following is a solution to the system? Show your work.
3x+2y=-3
3x-y=6
Group of answer choices
(-1, 0)
(1, -3)
(2, 0)
LaTeX: (0,-\frac{3}{2})
Answer:
(1, -3) is a solution to the system of equations ⇒ B
Step-by-step explanation:
Let us solve the system of equations
∵ 3x + 2y = -3 ⇒ (1)
∵ 3x - y = 6 ⇒ (2)
→ Subtract equation (2) from equation (1)
∵ (3x - 3x) + (2y - -y) = (-3 - 6)
∴ (0) + (2y + y) = (-9)
∴ 3y = -9
→ Divide both sides by 3 to find y
∴ y = -3
→ Substitute the value of y in equation (2) to find x
∵ 3x - (-3) = 6
∴ 3x + 3 = 6
→ Subtract 3 from both sides
∵ 3x + 3 - 3 = 6 - 3
∴ 3x = 3
→ Divide both sides by 3 to find x
∴ x = 1
To check the answer substitute the values of x any in each equation if the two sides of the equation are equal, then the solution is right
∵ 3x + 2y = -3
∵ 3(1) + 2(-3) = -3
∴ 3 - 6 = -3
∴ -3 = -3
→ The two sides of the equation are equal
∵ 3x - y = 6
∵ 3(1) - (-3) = 6
∴ 3 + 3 = 6
∴ 6 = 6
→ The two sides of the equation are equal
∴ The solution satisfies the two equations
∴ (1, -3) is a solution to the system
Consider the table for f(x) and the graph for g(x). Which statement is true when comparing the y-intercepts of the functions?
A) The y-intercept for f(x) is greater than the y-intercept for g(x).
B) The y-intercept for both functions is (0,0).
C) The y-intercept for g(x) is greater than the y-intercept for f(x)
D) The y-intercept for both functions is (0, 2).
Answer:
Should be C
Step-by-step explanation:
The y-intercept for f(x) is greater than the y-intercept for g(x). Therefore, option A is the correct answer.
What is a y-intercept?In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
From the table, we have the coordinates (-2, 0) and (-1, 1).
Here, slope (m)=(1-0)/(-1+2)
m=1
Substitute m=1 and (x, y)=(-2, 0) in y=mx+c, we get
0=1(-2)+c
c=2
From the graph y-intercept is c=1
Therefore, option A is the correct answer.
To learn more about the y-intercept visit:
brainly.com/question/14180189.
#SPJ2
Solve the system by substitution.
-3x-4y=11
y=2x
Answer:
x = -1, y = -2
Step-by-step explanation:
-3x-4y=11
y=2x
Plug in 2x for y:
-3x-4(2x)=11
-3x-8x = 11
-11x = 11
x =-1
Plug in x in y = 2x
y = 2(-1)
y = -2
Answer:(-1,-2)
Step-by-step explanation:
)
Evaluate: 4+8= 2 (6 - 3)
16
33
25
18
Done
HURRY
The volume of 100 drops of a liquid is 0.1 fluid ounces what is the volume of 10,000 drops
Answer:
0.001 fluid oz.
Step-by-step explanation:
100 : 0.1 = 10,000 = 0.001
Please help. Line l is parallel to line m. Find the value of x.
Answer:
x = 32
Step-by-step explanation:
2x and 64° are corresponding angles and are congruent, thus
2x = 64 ( divide both sides by 2 )
x = 32
Simplify 4(-8x + 5) – (-33x – 26)
Answer:
the answer is most likely to be (x+46)
Determine if each sequence is an arithmetic sequence. If yes, find the common difference.
1. 10,12,15,19,…
2. If there is, what is the common difference?
Answer: Yes, add one more each time you add
Step-by-step explanation:
Complete the explicit formula for the sequence.
42, 47, 52, 57, 62, ...
Answer:
Step-by-step explanation:
67,72..
PLEASEEE HELP ILL GIVE BRAINLIEST btw there are 2 attachments so u could see all the answer choices
Answer:
1) C
Step-by-step explanation:
Step 1)
First we have to plot ↓
2x ≥ y + 2
And that looks like Image 1
Step 2)
Second we have to plot ↓
2x - 5y ≤ 10
and that looks like Image 2
2x - 2y = 6 3x + 2y = 9 Solve the system of equations. A) x = 0, y = 3 B) x = 3, y = 0 C) x = 1, y = -2 D) x = -2, y = 1 E) x = 6, y = 3
There are 2 ways to solve this system: by elimination or by graphing. I will solve it by elimination. First will solve for x.
[tex]2x - 2y = 6\\3x + 2y = 9\\\\5x = 15\\\\x = 3\\[/tex]
Now we will solve for y using what we got for x.
[tex]2(3) - 2y = 6\\\\6 - 2y = 6\\\\-2y = 0\\\\y = 0[/tex]
Solution:
A: [tex](0, 3)[/tex]
Meg is a veterinarian. She found that 10,or 33%,of the dogs she saw this week were boxers. Steve is also a veterinarian. He found that 4 of the 20 he saw this week were boxers. Does each person need to find the part, the whole, or the percent?
geo quiz!! don’t understand at all
There are 13 guests at Morgan's party. If each guest will be served exactly \tfrac{4}{5} 5 4 pint of ice cream, how many pints of ice cream will she need? Express your answer in simplest form.
Multiply number pf people by amount they are having:
13 people x 4/5 pint = (13 x 4)/5 = 52/5 = 10 2/5 pints.
They need 10 2/5 pints total. ( Simplest form)
Since you can't buy a fraction of a pint, they would actually need to buy 11 pints
The kindergarten section of Lost Valley School has 12 classrooms. If each classroom
has 15 students how many total kindergarten students are at Lost Valley School?
Answer:
180
Step-by-step explanation:
12x15=180 simple
What is the point slope form of the line with slope that passes through the point (-4, - 7)?
y+4= (x + 7)
y-4= }(x-7)
y-7= (x - 4)
y+7= (x+4)
Please help (15 points)
Answer:
a=5 b=8 c=4
Step-by-step explanation:i hope this is right
Please help me on this
Answer:
a: -1,-1
b: 2,3
c:6,7
d: 5, 7
Step-by-step explanation:
Answer:
A -1,-1
B 2,3
C 6,7
D 5,-3
Step-by-step explanation:
You have to plug in each plotted point into the formula that was given to you.
Ex - A is plotted point is (-4,-3) so you plug in (-4+3,-3+2) which will give you (-1,-1)
Jordan has traveled 255 miles out of 340 miles on a trip. What percent of the total distance has he traveled?
A. 73%
B. 82%
C.75%
D. 70%
Answer:
75%
Step-by-step explanation:
Just do long division and get c.75%
Pls mark brainliest
Answer:
75%
Step-by-step explanation:
I swear it is right.
In Beijing in 2008, the Women's 3,000 meter Steeplechase became an Olympic event. What is this distance in kilometers
Answer:
The distance would be 3 kilometers
Step-by-step explanation:
Each kilometer is 1,000 meters. Divide 3,000/1,000= 3