Answer:
Suppose we have a system of two linear equations, this can be written as:
y = a*x + b
y = c*x + d
Now, we have 3 possible cases here.
The solutions of the system are the points where the graphs of the linear equations do intersect.
Then, if for example, we have two parallel lines (two parallel lines never intersect) we have no solutions.
And we know that two lines are parallel if they have the same slope and different y-intercept.
Then the system:
y = a*x + b
y = a*x + c
has no solutions.
If we have both equal lines, then the lines intersect in infinitely many points, meaning that we have infinite solutions, then the system:
y = a*x + b
y = a*x +b
has infinite solutions.
And if the lines intersect only one time we have one solution, and this happens when the slopes are different, so the system:
y = a*x + b
y = c*x + d
has only one solution.
Now, if we have more equations:
y = a*x + b
y = c*x + d
y = k*x + n
We have more equations than variables, then this system only has one solution of the 3 lines intersect at the same point, which is really rare.
One case where we have a solution here is if the 3 equations have the same y-intercept:
y = a*x + b
y = c*x + b
y = d*x + b
where the solution is the point (0, b)
Of course, there are other possible solutions, but these are not as formulaic as this ones.
ABCD is a parallelogram. If a CDA - 57 then BCD-_?
The diagram is not to scale.
133
57
114
123
Answer:
57
Step-by-step explanation:
It is given in the question that length CDA = 57.
Since the shape is a parallelogram, then we know that length AD=BC and AB=CD.
CDA = CD + AD
BCD = BC + CD
Since BC=AD and CD=CD
BCD = BC + CD is the same as CD + AD = CDA
Therefore BCD is the same length as CDA = 57
In other words, CDA is made up of a long side and a short side = 57
BCD is also made up of a long side and a short side, and since the longs sides are equal to each other and the short sides are also equal to each other in a parallelogram, BCD is the same length as CDA = 57.
Hope this helped!
Can anyone solve this question??? plss plsss its my request to all if any one can solve this question I will mark him/ her the brainliest
Answer:
a) ∠EAB = 180° - 90° - 30° = 60°
∠EBA = 180° - 90° - 60° = 30°
a) ∠EBA = 30°
b) ∠DCA = 180° - 90° - 30° = 60°
∠EBA ≅ ∠DAC, ∠EAB ≅ ∠DCA, ∠AEB ≅ ∠CDA
ΔEBA ≅ ΔDAC because of the AAA postulate
c) EB ≅ DA, EA ≅ DC, AB ≅ CA
d) AB = CA given
sin ∠EAB = EB/AB (sin 60°) EB = (0.8660)AB
cos ∠EAB = EA/AB (cos 60°) EA = (0.5)AB
cos ∠DAC = AD/CA (cos 30°) AD = (0.8660)CA
sin ∠DAC = CD/CA (sin 30°) CD = (0.5)CA
ED = EA + AD
ED = (0.5)AB + (0.8660)CA
since AB = CA, ED = 1.366CA
since EB = (0.8660)AB and AB = CA, then EB = 0.866CA
since CD = 0.5CA,
EB + CD = 0.866CA + 0.5CA = 1.366CA
EB + CD = 1.366CA
1.366CA = 1.366CA
Proof: ED = EB + CD
A number x divided by 6 is at least 16 .
Answer:
x = 96
Step-by-step explanation:
Answer:
x/6≥16
Step-by-step explanation:
If p(t)=5t4+17t3–8t2+13t–12, use synthetic division to find p( – 4).
Answer:
the value of this function p(t) at t = -4 is also 0
Step-by-step explanation:
Recall that synthetic division in a problem such as this one returns a remainder, which is sometimes zero and is sometimes not. If not, then the remainder is the value of the given polynomial when evaluated at a given argument. We are to determine the remainder here when t = -4:
Setting up synthetic division:
-4 / 5 17 -8 13 -12
-20 12 -16 12
------------------------------------
5 -3 4 -3 0
Since the remainder is 0, the value of this function p(t) at t = -4 is also 0.
There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and over (http://factfinder.census.gov). A sample of 1000 persons is selected at random.
a. Approximate the probability that more than 200 persons in the sample have a disability.
b. Approximate the probability that between 180 and 300 people in the sample have a disability.
Answer:
The answer is "0.274 and 0.841"
Step-by-step explanation:
Given:
In this question, let X the binomial random variable with the parameters:
[tex]n = 1000\\\\P = 0.193[/tex]
Calculating the random variable Z:
[tex]Z= \frac{X - np}{\sqrt{np(l - p)}}=\frac{x -193}{12.48}[/tex]
is an approximately regular, cumulative random variable with [tex]\Phi[/tex] specified in the back of the book in the tables.
Using the continuity and tables to calculate:
[tex]\to \mathbb{P} (X > 200) = \mathbb{P} (X\geq 200.5) \approx \mathbb{P}(Z\geq 0.6)=1- \Phi(0.6) \approx 0.274 \\\\\to \mathbb{P} (180 < X < 300) = \mathbb{P} (180.5 \leq X \leq 299.5) = \approx \mathbb{P} (-1 \leq Z\leq 8.53) = \approx 1- \Phi(-1) \approx 0.841[/tex]
(a) The probability that more than 200 persons throughout the sample have a disability will be "0.08691".
(b) The probability that between 180 - 300 people throughout the sample have a disability will be "0.85122".
ProbabilityAccording to the question,
Majority percentage, P = 19.3% or,
= 0.193
Sample person, n = 1000
Q = 1 - P
= 1 - 0.193
= 0.807
By using Normal approx. to Binomial,
→ Mean, E(X) = n × P
By substituting the values,
= 1000 × 0.193
= 193
Standard deviation, X = √n × p × Q
= √1000 × 0.193 × 807
= 12.4800
(a)
Z = [tex]\frac{X - \mu}{\sigma}[/tex]
= [tex]\frac{210-193}{12.48}[/tex]
= 1.36
The probability be:
→ P(X > 210) = 1 - P (Z < 1.36)
= 1 - 0.9131
= 0.08691
(b)
Z = [tex]\frac{X - \mu}{\sigma}[/tex]
= [tex]\frac{180-193}{12.48}[/tex] or, [tex]\frac{300-193}{12.48}[/tex]
= 8.57
hence,
The probability be:
→ P (180 < X < 300) = P(Z < 8.57) - P(Z < -1.04)
= 1 - 0.1488
= 0.85122
Thus the answers above are correct.
Find out more information about probability here:
https://brainly.com/question/24756209
What is the solution to the system of equations shown in the graph?
Answer/Step-by-step explanation:
Based on my knowledge, the solution of the system of equations on the graph would be the point where they all meet. Thus, the answer I would put down is:
(-5,2)
Hey! I appreciate any help on this question!
need help po thank you
Answer:
a) P
b) NP
c) P
d) p
e) p
1.30,35,40. add 5
2. 4,0,-4. take 4
3. -8,-10,-12. add -2
Find the value of x.
9
19
x = [?]
Answer:
14
Step-by-step explanation:
Answer:
looks like 18 not sure tho
Step-by-step explanation:
A plumber charges $75 for the service call and $25 per hour (h) for repairs. Write an algebraic expression to represent the total bill for all plumbing services.
A.
(75 + 25)h
B.
75 + 25h
C.
75h + 25
D.
75 + 25 + h
Answer:B i think if wrong im so sorry
Step-by-step explanation:
Answer:
B 75+25h
Step-by-step explanation:
$75 is the first charge for the service and is constant. $25(per hour) is not constant and changes as the time (hours) changes. That's why it has a h next to it, the h is the variable to hold the place for the hours that would be multiplied in the problem.
What is the solution of (x+8)/(5x+-1)>0?
Answer:
the solution set is (-infinity, -8) ∪ (-8, 1/5)
Step-by-step explanation:
x + 8 changes sign at x = -8.
I'll assume you meant 5x - 1 (as 5x+- is meaningless). 5x - 1 changes sign at x = 1/5.
Subdivide the x-axis using the two x-values found above:
(negative infinity, -8), (-8, 1/5), (1/5, infinity.
Choose a representative value from each interval. I'm choosing x = -10, x = 0 and x = 1.
Now test the given inequality at each of these x-values. Is the result true or false?
x + 8
---------- > 0
5x - 1
For x = -10:
-10 + 8
--------------- > 0 => -2/(-51) => 2/51 This is TRUE
5(-10) - 1
For x = 1:
1 + 8
---------- > 0 => 9/4 This is TRUE
5 - 1
For x = 0:
8
---------- > 0 This is FALSE
- 1
Therefore the solution set is (-infinity, -8) ∪ (-8, 1/5)
Rewrite in standard form. Find the center and radius of the circle. Show all of your work for full credit.
Where is the picture?
The monthly utility bills in a city are normally distributed with a mean of $100 and a standard deviation of $12. Find the probability that a randomly selected utility bill is more than $120
Plssss help and thank you
Answer:
1
Step-by-step explanation:
The y-intercept is when x=0, and by looking at this chart, we can see that when x=0, y=1, therefore it will be (0,1) and your y-intercept is 1.
f(x)= x^2 - 7x +12
The above equation is in standard form. Write the above equation in factored form
f(x) = (x-r1)(x-r2)
r1 represents first root, r2 represetnts second root
What are the roots?
Remember, x-r1 = 0 and x-r2=0
Answer:
f(x) = (x - 3)(x - 4)
Step-by-step explanation:
f(x)= x^2 - 7x +12 factors immediately into f(x) = (x - 3)(x - 4).
The roots are {3, 4}
a = 4, n = 8, y = 2, x = 10 Evaluate the algebraic expression x + 3y - n. 6 8 12 D 24
Answer:
B. 8
Step-by-step explanation:
By evaluate, they mean substitute in the values and solve.
x + 3y - n
= 10 + 3(2) - n
= 10 + 6 - 8
= 8
Please lmk if you have questions.
Answer:
It is 8!
Proof:
I took the activity.
can someone help my lil sister.
Answer:
78
Step-by-step explanation:
Given:
h + 9g
Required:
Evaluate when g = 8 and h = 6
Solution:
Plug in the values of the variables into the expression
Thus,
6 + 9(8)
= 6 + 72
= 78
NEED HELP ASAP
Which is a different way to express 5r?
5+r
2r+3r
r5
3r⋅2r
Answer:
2r+3r
Step-by-step explanation:
even though r5 looks correct, you always have to put the varible on the right side of a number. 2r+3r is correct because if you combine like terms, you get 5r
What do you do to both sides to
r? What is r? 3/8 r = 6 HELP ME
Answer:
r = 16
Step-by-step explanation:
[tex]\frac{3}{8}r = 6 \\\\[/tex]
Multiply both sides by 8
[tex]8*\frac{3}{8}r = 6*8\\\\3r = 48\\[/tex]
Divide both side by 3
[tex]\frac{3}{3}r=\frac{48}{3}\\\\r = 16[/tex]
OR
Multiply both side by (8/3)
[tex]\frac{8}{3}*\frac{3}{8}r=6*\frac{8}{3}\\\\r = 2*8\\\\r = 16[/tex]
write an equation to represent the information in this problem. Jerel runs five days each week. on each of 4 days, he runs 2.3 km. if jerel runs a total of 14km, how many kilometers does he run on the fifth day?
Let x be the distance run on the fifth day
Total distance run on all the four days = 2.3 * 4 = 9.2 km
Required equation : x + 9.2 = 14
x = 14 - 9.2
x = 4.8 km
What is the total number of digits required in numbering a book that has 1724 pages?
Answer:
5,789
Step-by-step explanation:
I got 5,789 because there are 9 one digit numbers. 1-9 -> 9x1=9. There are 90 two digit numbers. (10-99)-> 90x2=180. There are 900 three digit numbers. (100-999)-> 900x3=2700. There are 725 four digit numbers. (1000-1724)-> 724x4= 2900. Then, I added 9+180+2700+2900=5789.
In conclusion, the total number of digits required in numbering a book that has 1724 pages is 5789.
There are 5,789 digits in total required to number the pages of a book with 1,724 pages.
What is Numbering?A numbering is the assignment of natural numbers to a set of objects in some formal language, such as functions, rational numbers, graphs, or words, in computability theory.
Digits required in numbering a book that has 1724 pages?Given the total number of pages is 1,724
Let's break down the pages now to find the total digits.9
one-digit numbers (1-9) = 9 x 1 = 9 digits make up the number 1,724.90 numbers with two digits (10-99) = 90 x 2 = 180 digits900 three-digit numbers (from 100 to 999) = 900 times three = 2700 digits725 numbers with four digits (1000-1724) = 725 x 4 = 2900 digits
Let's add the digits now.9 + 180 + 2700 + 2900 = 5,789
As a result, the total number of digits required to number the pages of a 1,724-page book is 5,789.
Learn more about numbering here: https://brainly.com/question/251701
#SPJ2
Solve the right triangle. Round your answers to the nearest tenth.
Answer:
B = 44°
c = 27.8
b = 19.3
Step-by-step explanation:
m∡B = 180 - (90 + 46)
sin46° = 20/c
c = 20 / sin 46°
c = 27.8
b² + 20² = 27.8²
b² + 400 = 772.84
b² = 372.84
b = [tex]\sqrt{372.84}[/tex]
b = 19.3
If b = 5, what is 632
15
25
75
125
Answer:
Step-by-step explanation:
A
Find the surface area of the pyramid, round to the nearest tenth:
Answer:
YOU DONT KNOW THIS SMH
Step-by-step explanation:
LEAARN HOW TO WORK
If x=7 and y=−3, evaluate the following expression:3x−y2
Answer:
27
Step-by-step explanation:
3x−y2= ? if x= 7 & y= -3
Step 1 insert the numbers where they go:
3(7)-(-3)2=
Step 2 the two negatives become a positive:
3(7)+(3)2=
Step 3 multiply:
21+6=
Step 4 add:
27
how to solve -3x-6y=3 and 2x+7y=-17 using elimination method PLEASE SHOW WORK
Find the ratio of Cos (39).
A. 37/7
B.X/7
C.7/X
D.7
Answer:
x/7
Step-by-step explanation:
cos 39= adjacent/hypotenuse
=x/7
Complete the missing parts of the table for the following function. y = x
5
| -2 | -1 | 0 | 1 | 2 | 3 |
|________________
| 1/25 | 1/? | 1 | 5 | ? | ? |
Answer:
The function is:
y = [tex]5^x[/tex]Missing numbers:
x = -1 ⇒ y = 1/5x = 2 ⇒ y = 25x = 3 ⇒ y = 125two angles are supplementary. the bigger angle is three times as large as the smaller angle.find the measurement of the angles
Answer:
The bigger angle is 135, and the smaller angle is 45.
Step-by-step explanation:
First, you have to know that supplementary angles add up to 180°.
We have no equations for the angles, so I will use the variable x for the value of the smaller x.
The reason for this: the problem gave the value of the bigger angle, but relative to the smaller angle. Therefore, it would be safe to assume the use of a variable for the smaller angle.
Since the bigger angle is 3 times as large as the smaller, we can say that the bigger angle is 3x, or 3 times x.
Now, we can put this in an equation: 3x+x=180. Like I said before, both of the angles add up to 180 degrees.
To solve the equation:
1. Combine like terms
4x=180
2. Divide both sides by 4
x=45
Now that we have the value of x, we can plug that in to 3x and x to find the angles.
3*45=135, which is the bigger angle
45, which is the smaller angle.
Guided Practice
The answer is NOT letter A
Find the range of the function rule y=5x−2 for the domain.{−1/2, 1/4, 2/5}Find the range function rule
A.
{−1/2, 3 1/4, 4}
B.
{− 4 1/2, −3/4, 0}
C.
{3/10, 9/20, 12/25}
Answer:
B.
{− 4 1/2, −3/4, 0}
Step-by-step explanation:
find the range of the function rule y=5x-2 for the domain {-1/2, 1/4, 2/5}
domain
-1/2;1/4; 2/5
range
-5 1/2; (5/4-2);0
Graph.
y = 5 x − 2 { − 1 /2 , 1 /4 , 2 /5 }
{− 4 1/2, −3/4, 0}
Step-by-step explanation:
domain
-1/2;1/4; 2/5
range
-5 1/2; (5/4-2);0
{-1/2, 1/4, 2/5}
take the derivative of the equation 4 times. f 4 (x)=0.
Step-by-step explanation:
if you put in the values (-1/2, 1/4, 2/5) in the function
{–8, –2, 18}
Step-by-step explanation:
y = 5x − 2
x = −1.2 > y = 5(−1.2) − 2 = −6 − 2 = −8
x = 0 > y = 5(0) − 2 = 0 − 2 = −2
x = 4 > y = 5(4) − 2 = 20 − 2 = 18
{-1/2, 1/4, 2/5}
Step-by-step explanation:
All you have to do is go on a graphic calculator and input the equation by pressing y= then after putting it in to y= all you have to do is press 2nd (the only blue button) and graph and that will show you all the points to that equation (also known as range and domain)
Hope this helps. :)
Domain is inputs, input the domain for x
y=5(-1.2)-2
y=-6-2
y=-8
y=5(0)-2
y=0-2
y=-2
y=5(4)-2
y=20-2
y=18
range is {-8, -2, 18}
For x = 0,
we substitute zero into the equation to find its y value like so:
y = 5x-2
y = 5(0)-2
y = -2
There you go.
Take the derivative of the equation 4 times. f 4 (x)=0.
Y = 5x – 2
domain. {–5, –1, 0, 2, 10}
x = -5 then y = 5(-5) – 2 = -27
x = -1 then y = 5(-1) – 2 = -7
x = 0 then y = 5(0) – 2 = -2
x = 2 then y = 5(2) – 2 = 8
x = 10 then y = 5(10) – 2 = 48
answer
{–27, –7, –2, 8, 48}
A washer and a dryer cost $766 combined. The washer costs $66 more than the dryer. What is the cost of the dryer?
Answer:
416
Step-by-step explanation:
for 700 350 plus 350 then for dryer 66 extra so 350 plus 66