Answer:
[tex](9, 8), \\(0, -7), \\(6, 3), \\[/tex]
Step-by-step explanation:
There is! Algebraically, we can find the equation of the line. Any points that the line passes through should make the equation of the line true.
In slope-intercept form, the equation of a line is given by [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope of the line, [tex]b[/tex] is the y-intercept, and [tex](x,y)[/tex] represents any point the line passes through.
The slope of a line is given by the change in y-values over the change in x-values of two points the line passes through. We're given that the line passes through the points (-6, -4) and (-3, 1).
Let:
[tex](x_1, y_1)\implies (-6, -4)\\(x_2,y_2)\implies (-3, 1)[/tex] (doesn't matter which point you assign to which)
The slope of the line that passes through these points is [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-4)}{-3-(-6)}=\frac{5}{3}[/tex]
Now substitute [tex]m=\frac{5}{3}[/tex] and any point (x, y) that the line passes through to solve for [tex]b[/tex] in [tex]y=mx+b[/tex]:
Using (-3, 1):
[tex]1=\frac{5}{3}(-3)+b, \\\\\frac{3}{3}=-\frac{15}{3}+b,\\\\b=\frac{3}{3}+\frac{15}{3}=\frac{18}{3}=6[/tex]
Thus, the equation of the line is [tex]y=\frac{5}{3}x+6[/tex].
I just realized that it's asking for the points that the line parallel to this line and passing through point [tex]p[/tex] goes through, but I'll keep all the information above as it may be useful.
Parallel lines always have equal slopes, by definition. Therefore, the slope of the line that passes through point [tex]p[/tex] and is parallel to the line above also has a slope of [tex]5/3[/tex]. Point [tex]p[/tex] is located at (3, -2). Thus, to find [tex]b[/tex], plug in [tex]m=5/3[/tex] and [tex]x=3, y=-2[/tex] into [tex]y=mx+b[/tex]:
[tex]-2=\frac{5}{3}(3)+b, \\-2=5+b, \\b=-2-5=-7[/tex]
Therefore, the equation of this line must be [tex]y=\frac{5}{3}x-7[/tex].
You can algebraically determine if a certain point passes through this line by seeing if the point makes this equation true. From the answer choices, the following points are passed through by this line:
[tex](9, 8)\:\checkmark, \\(0, -7)\:\checkmark, \\(6, 3)\:\checkmark, \\[/tex]
Sarah's family traveled 5 8 of the distance to her grandmother's house on Saturday. They traveled 1 3 of the remaining distance on Sunday. What fraction of the total distance to her grandmother's house was traveled on Sunday?
Answer: The fraction of the total distance to her grandmother's house was traveled on Sunday = [tex]\dfrac18[/tex]
Step-by-step explanation:
Let x be the total distance to grandmother's house .
As per given,
Distance traveled on Saturday = [tex]\dfrac58x[/tex]
Remaining distance = [tex]x-\dfrac58 x[/tex]
[tex]=\dfrac38x[/tex]
Distance traveled of Sunday = [tex]\dfrac13[/tex] of Remaining distance
= [tex]\dfrac13\times\dfrac{3}{8}x[/tex]
= [tex]\dfrac18 x[/tex]
The fraction of the total distance to her grandmother's house was traveled on Sunday = [tex]\dfrac18[/tex]
What is the slope of the line that passes through the points (-10, -8) and
(-8, -16)? Write your answer in simplest form.
Answer:
Slope is - 4
Step-by-step explanation:
The slope of the line will be (-16-(-8))/(-8-(-10))=-8/2=-4
Answer:
-4
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -16 - -8)/(-8 - -10)
= (-16+8)/ (-8+10)
= -8/2
- 4
Ivan and Adeline are in a classroom with a chalkboard. They are standing on different halves of the board, and on each half, the number is written. When Ivan's teacher gives a signal, Ivan multiplies the number on his side of the board by and writes the answer on the board, erasing the number he started with. Adeline does the same on each signal, except that she multiplies by . The teacher gives 10 signals in total. How many times (including the initial number) do Ivan and Adeline have the same number written on the board
Answer:
6 times
Step-by-step explanation:
Given
[tex]Start=2[/tex]
[tex]Ivan=-2[/tex] ---- i.e. multiplies by -2
[tex]Adeline = 2[/tex] --- i.e. multiplies by 2
[tex]n=10[/tex] --- signals
Required
Number of times they have the same number
First, we list out all results of Ivan calculations.
To calculate Ivan's list, we simply multiply the current term by -2.
The 10 signals together with the first term, means there will be 11 terms in total
So, we have:
[tex]Ivan = \{2,-4,8,-16,32,-64,128,-256,512,-1024,2048\}[/tex]
Next, list Adeline's
[tex]Adeline = \{2,4,8,16,32,64,128,256,512,1024,2048\}[/tex]
Compare the elements of the two lists, we have:
[tex]Common= \{2,8,32,128,512,2048\}[/tex]
Hence, they have the same number 6 times.
2
Which expression is equivalent to
What is the value of x in the triangle?
Enter your answer in the box. Round your final answer to the nearest hundredth.
x = _cm
Answer:
180 degrees, because the sum of all the angles of a triangle always equals 180 degress.
I Needham help without this one I will give you brainlist
Answer:
hi, it can be 0 or also 1
please mark as brainiest:)
Answer:
tricky
Step-by-step explanation:
Heather earned $8.42 per hour during the first month of her new job. Then she got a raise and earned $9.08 per hour. What was the amount of her raise?
Answer:
.66 cents?
Step-by-step explanation:
i just subtracted but i feel like theres a catch
Answer:
.66 per hour raise
Step-by-step explanation:
9.08-8.42=.66 per hour raise
whats the value of x? -5(x + 7) = -14 + 2x
Answer: x=-3
Step-by-step explanation:
Ok let's start by using the distributive property
[tex](-5)(x)+(-5)(7)=-14+2x\\-5x-35=-14+2x[/tex]
Now subtract 2x from both sides
[tex]-5x-35-2x=2x-14-2x\\-7x-35=-14[/tex]
Next add 35 to both sides
[tex]-7x-35+35=-14+35\\-7x=21[/tex]
Finally divide both sides by -7
[tex]\frac{-7x}{-7} =\frac{21}{-7} \\x=-3[/tex]
Answer:
x = -3
Step-by-step explanation:
First, we compute -5(x + 7). -5(x + 7) = -5x - 35. Plugging this into the equation, we have -5x - 35 = -14 + 2x Next, we combine like terms by moving all terms with the variable x to the left side. We have -5x - 2x = -14 + 35. We simplify the equation into -7x = 21. Divide 21 by -7, and we get x = -3.
Se desean plantar 361 plantas de limón, en un terreno cuadrado, de manera que en cada fila queden a un metro de distancia.
Respuesta:
19
Explicación paso a paso:
Si se van a plantar 361 limoneros en un campo cuadrado;
Entonces, el número de plantas en cada fila debe ser el mismo por columna;
Sea el número de plantas por hilera = x
Número total de plantas = x²
361 = x²
Saca la raíz cuadrada de ambos lados
√361 = √x²
19 = x
Número de plantas por hilera = 19
PLEASE HELP ME ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
94
Step-by-step explanation:
the sample size of the first survey is 15+26+7 = 48
so, for 48 surveyed teachers we get 15 SUV drivers.
our expectations is to get the same ratio also for other sample sizes (like 300).
15/48 = x/300
x = 15×300 / 48 = 15×75 / 12 = 93.75 ≈ 94
A: 105
B : 1,050
C: 9,450
D: 21
Answer:
1050
Step-by-step explanation:
We can use a ratio to solve
First find how many jam
210 - 189 =21
We want to find how many jam for 10500 printed
21 jam x jam
----------- = ----------------
210 printed 10500 printed
Using cross products
21 * 10500 = 210x
Divide each side by 210
21*10500/210 =x
1050=x
PLS ANSWER ASAP DUE AT 9:15
Answer:
answer for this solution is D
Answer:
answer is D
hope this helps:)
ali's age is half of his fathers age but 15 years ago his age was just 1/3 of his fathers age find his present age
Answer:
30 for the son 60 for the dad
Step-by-step explanation:
Take away 15 from the son and dad you get 45 and 15 which is 1/3 before t that was 15 years ago which makes it 30 for the son and 60 for the dad
g(x) = 2x-5. Find g(3), g( 1/2), g(0), g(4), g(4). If g(a) - 99, find a.
f(x)= 3-4x. Find f(1), f(3), f(-2) ,f(1/2)
f(x)= x+3. find f(1), f(2), f(-3),f(0),f(1/2).
solve these please right now. no silly answer wolud not be allowed.
Please help this is due today!!
Answer:
Answer is C
Hope this helped!
Find the measure of each interior angle and each exterior angle of a regular nonagon (a nine-sided polygon).
Measure of each interior angle =
x
5
?
Measure of each exterior angle =
Answer:
Interior-140° Exterior-40°
Step-by-step explanation:
The sum of the interior angles of a polygon are given by 180(n-2) where n is the number of sides.
Therefore, the sum of all interior angles in a nonagon is 180(9-2) or 180×7. This equals to 1260°.
To get the individual interior angle, you use [tex]\frac{s}{n}[/tex], with n defined above and s being the sum of interior angles.
Therefore, each angle is [tex]\frac{1260}{9}[/tex]°, which can be solved to 140°.
The value of an individual exterior angle is given by 180-i, with i being the individual interior angle (this is because the 2 angles form a straight line).
In this case, 180-140=40°.
Each interior angle of a nonagon is 140°, and each exterior angle is 40°.
**This content involves angles of polygons, which you may want to revise. I'm always happy to help!
Mr. Pratt was building a house. A ladder that is 10 ft. long is leaning against the side of a
building. If the angle formed between the ladder and the ground is 65 degrees, how far is
the bottom of the ladder from the base of the building? (Round to two decimal places)
Step-by-step explanation:
the answer is in the above image
Which of the following number lines shows the sum of the number above and 2.2?
Answer:
W
Step-by-step explanation:
hope this helps
Find the area of the shaded figure. The area is square units (AREA OF COMPOSITE FIGURES)
Answer:
28 square units
Step-by-step explanation:
count the middle and edgr squares then u can just put the parts of the square together
Help question 7 pleaseeeee
Brainliest
Answer:
[tex]\frac{1}{20}[/tex]
Step-by-step explanation:
To solve this problem, we can use the definition of probability: the amount of desirable outcomes divided by the total amount of outcomes. In order to find the probability of dependent events, events that depend on each other, we multiply the probability of the first event by the probability of the second event happening after the outcome of the first. Our two events are choosing a blue marble and then choosing a yellow.
There are a total of 16 marbles as given by the problem, this is our total number of outcomes. There are 4 outcomes where we can pick a blue marble, so the probability of choosing a blue marble is [tex]\frac{4}{16}[/tex] or [tex]\frac{1}{4}[/tex].
Now, we need to find the probability of choosing a yellow marble after the blue marble. If we already chose a blue marble, in total, there will only be 15 marbles instead of 16, because it is with out replacement. This gives us the total amount of outcomes. Next, we picked a blue already, so it does not affect the amount of yellow marbles left, which is 3 yellow marbles. From this, we can say the probability of picking a yellow marble given a blue marble was already picked is [tex]\frac{3}{15}[/tex] or [tex]\frac{1}{5}[/tex].
All we have to do now is multiply the two probabilities to find what we are looking for: [tex]\frac{1}{4} *\frac{1}{5} =\frac{1}{20}[/tex]. So, the probability of drawing a blue marble followed by a yellow marble is [tex]\frac{1}{20}[/tex]
find the surface area of the prism
Answer:
SA=96
Step-by-step explanation:
formula for triangular prism=bh+l(s1+s2+s3)
3*4/2*2=12
4*7=28
3*7=21
5*7=35
12+28=40+21=61+35=96
The agricultural practice of irrigation leaves behind which pollutant in the
soil?
O A. Salt
B. Acidic compounds
C. Nitrogen compounds
D. Pesticides
The answer is Salt !!
10 points, will give brainliest . look at the picture!
Answer:
y/2
Step-by-step explanation:
Answer: y, because ΔABC ~ ΔEDC
Step-by-step explanation:
In the image we can see that angle D is equal to angle B because they are both marked as 65 degrees. Angle BCA is equal to DCE because they are vertical angles and vertical angles are congruent. Know that those are equal to each that must mean CED is equivalent to CAB because that's the last angle that corresponds with another. So, CED is y.
Please help, no links
Step-by-step explanation:
[tex]\text{Use:}\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\=============================[/tex]
[tex]A.\ \dfrac{5^3}{5^6}=5^{3-6}=5^{-3}=\left(\dfrac{1}{5}\right)^3\\\\B.\ (14^3)^6=14^{3\cdot6}=14^{18}\\\\C.\ 8^3\cdot8^6=8^{3+6}=8^9\\\\D.\ \dfrac{16^6}{16^3}=16^{6-3}=16^3\\\\E.\ (21^3)^{-6}=21^{3\cdot(-6)}=21^{-18}=\left(\dfrac{1}{21}\right)^{18}\\\\F.\ 100^0=1\\\\G.\ \dfrac{\left(\frac{2}{5}\right)^8}{\left(\frac{2}{5}\right)^6}=\left(\dfrac{2}{5}\right)^{8-6}=\left(\dfrac{2}{5}\right)^2\\\\H.\ (0.15)^{-2}\cdot(0.15)^4=(0.15)^{-2+4}=(0.15)^2\\\\I.\ 7^{-5}=\left(\dfrac{1}{7}\right)^5[/tex]
[tex]J.\ 4\cdot4^3=4^{1+3}=4^4[/tex]
If f(x) = (x + 9 and g(x) = --6, which describes the range of (f + g)(x)?
O (f+g)(x) 3 for all values of x
Given:
Consider the below figure attached with this question.
To find:
The value of [tex](f+g)(x)[/tex].
Solution:
The given functions are:
[tex]f(x)=|x|+9[/tex]
[tex]g(x)=-6[/tex]
Now,
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex](f+g)(x)=|x|+9+(-6)[/tex]
[tex](f+g)(x)=|x|+9-6[/tex]
[tex](f+g)(x)=|x|+3[/tex]
We know that,
[tex]|x|\geq 0[/tex]
Adding 3 on both sides, we get
[tex]|x|+3\geq 0+3[/tex]
[tex](f+g)(x)\geq 3[/tex]
So, [tex](f+g)(x)\geq 3[/tex] for all values of x.
Hence, the correct option is A.
Someone please help?? Solve for angle DCE
Answer:
58 degrees
Step-by-step explanation:
By looking at the diagram we can see that angle DCE is an outside angle
There is a special relationship between the outside angle and the arcs it intercepts
The theorem states that the outside angle is equal to half the difference of the intercepted arcs
In other words [tex]outside angle= \frac{arc AC - arc BD (the difference of the arcs)}{2}[/tex]
Knowing this formula we can solve for DCE
So it would be [tex]angle DCE= \frac{238-arcDE}{2}[/tex]
Well we do not know what arcDE is
Since we are given that the other arc is 238 we can take 238 and subtract is from 360
this will give us 122
so you have angle DCE= 238-122/2
238 minus 122 is 116
Angle DCE-=116/2
Angle DCE=58 degrees
There are other ways you can do this but this is just one of them
The eighth term in the series 2, 6, 18, 54, ___ is
4122
4374
5643
7434
Answer: I think it's 163
Step-by-step explanation:
it's multiplied by 3's
Using the formula for area of parallelograrn, find the area of the following parallelograr if
your base 5ft. and your height is 3ft
Answer:
15
Step-by-step explanation:
the formula for area of a parallelogram is base times height
Two of the three views of a solid are shown. A. What is the greatest number of unit cubes in the solid? Greatest number of unit cubes: cubes b. What is the least number of unit cubes in the solid? Least number of unit cubes: cubes Question 2
Answer: hello the views attached to your question is missing hence I will provide a more general answer based on the scope of your question
answer :
a) 8 unit cubes
b) 1 unit cube
Step-by-step explanation:
The number of views a solid figure can have are : Top view , Front view and side view and The greatest number of unit cubes in a solid depends on the side length of the unit cube
a) For a unit cube with side length half ( 1/2) the Unit length of the given solid the greatest number of unit cubes = 8 while
b) The least number of unit cube = 1
Please help me with my math asap
Answer:
90 - 63 = 27 degree
Step-by-step explanation: