Answer:
Infinite.
Step-by-step explanation:
[tex]-17+2(1+3x)=x-5(3-x)[/tex]
Expand:
[tex]-17+2+6x=x-15+5x[/tex]
[tex]6x+15=6x+15[/tex]
[tex]6x=6x[/tex]
[tex]0=0[/tex]
Since 0=0 is true, then there are infinite solutions as no matter what value you put in for x, it will never affect the outcome of 0=0 which is true.
Solve −3x2 + 30x − 90 = 0
Step-by-step explanation:
so, it is a quadratic equation :
-3x² + 30x - 90 = 0
the first thing we can do is divide by 3
-x² + 10x - 30 = 0
remember, the formula to solve and find the 2 solutions is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case here
a = -1
b = 10
c = -30
x = (-10 ± sqrt(100 - 4×-1×-30))/-2 =
= (-10 ± sqrt(100 - 120))/-2 = (-10 ± sqrt(-20))/-2 =
= (-10 ± sqrt(4×5)i)/-2 = (-10 ± 2×sqrt(5)i)/-2 =
= 5 ± -sqrt(5)i
x1 = 5 - sqrt(5)i
x2 = 5 + sqrt(5)i
remember, i = sqrt(-1), a complex number.
Write an equation for the nth term of the arithmetic sequence –1, –3, –5, –7,
Answer:
[tex]a_n=-1+(n-1)(-2)[/tex]
Step-by-step explanation:
The arithmetic sequence formula looks like this:
[tex]a_n=a_1+(n-1)d[/tex]
where aₙ is the nth term, a₁ is the first term, n is the index, and d is the common difference.
Each consecutive term is decreased by 2 over the last, so d = 2. The first term is -1 of course, so you can write this equation:
[tex]a_n=-1+(n-1)(-2)[/tex]
Just to confirm:
[tex]a_n=-1+(n-1)(-2)\\a_3=-1+(2)(-2)\\a_3=-1-4\\a_3=-5[/tex]
And it works, -5 is the 3rd term in the sequence.
Answer:
[tex]a_{n}[/tex] = 1 - 2n
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 1 and d = a₂ - a₁ = - 3 - (- 1) = - 3 + 1 = - 2 , then
[tex]a_{n}[/tex] = - 1 - 2(n - 1) = - 1 - 2n + 2 = - 2n + 1 = 1 - 2n
A calculator is selling for $80 with an 8.5% tax. How much will you pay in tax for the calculator?
Answer:
$86.80
Step-by-step explanation:
What is the value of x if a slope is 2, and a line passing through (x, 3) and (1,5).
Answer:
x = 0
Step-by-step explanation:
Slope = change in y/change in x
Slope = 5-3/1-x
2 = 2/1-x
2(1 - x) = 2
2 - 2x = 2
2 = 2 - 2x
0 = -2x
x = 0
-Chetan K
expand and simplify
(y – 2) (+1) (y+3)
Answer:
y² + y - 6
Step-by-step explanation:
(y - 2)(+ 1)(y + 3) simplifies to
(y - 2)(y + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
y(y + 3) - 2(y + 3) ← distribute parenthesis
= y² + 3y - 2y - 6 ← collect like terms
= y² + y - 6
Given f(x) = 2x - 5 , find the average rate of change of f(x) from x = 2 to x = 5?
[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=2x - 5 \quad \begin{cases} x_1=2\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(2)}{5-2}\implies \cfrac{[2(5)-5]~~ - ~~[2(2)-5]}{3} \\\\\\ \cfrac{5-(-1)}{3}\implies \cfrac{5+1}{3}\implies 2[/tex]
Solve the triangles for X: include the steps if you can
Answer:
10) x=9
11) x=25
Step-by-step explanation:
a triangle is 180º total
10) 2x+8x+90=180
10x=90
x=9
11) 3x+1+2x+2+2x+2=180
7x+5=180
7x=175
x=25
50 points! Help (Vectors)
The magnitude of a vector a is the length of the vector.
We write it ||a||
We can draw a right triangle and apply the pythagoras theorem. The magnitude of a will be the hypotenuse :
||a||² = 3² + 3²
||a||² = 9 + 9
||a||² = 18
||a|| = √18 = √(9*2) = 3√2 ≈ 4.24
So the answeer is 4.24
Good Luck
100 POINTS!
A local theater has a maximum capacity of 1000 people. For their latest production, adult tickets cost $25 and youth tickets cost $12.5. The theater needs to make at least 15,000 for the show to continue.
Write and graph a system of linear equations, and write two possible solutions.
Answer:
a+y≤1000 and 25a+12.50y>15000
Step-by-step explanation:
Please check the mcq in the following picture and thank you
Answer 2nd one
Step-by-step explanation:
525, 650, 539, 643, 764, 539, 687
What is the interquartile range of these numbers
Answer:
148
Step-by-step explanation:
sorry, im not sure how to solve it, but its 148
hope this kinda helped :)
mark me brainliest :D
Line l is a reflection in the x-axis of line k. Write an equation that represents line k.
Answer:
(-4,3)
Step-by-step explanation:
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Answer: y = (5/3)x + -1
Step-by-step explanation:
The slope is -5/3, so since its a reflection in the x - axis, the new slope would be the opposite, 5/3. Now for the +1, you just have to find the y intercept by plotting the dots at the opposite version of the y number that is already there. For example because the point (0,1) has 1 as its y number, you make it into -1, and for example if you have the point (3,-4) since -4 is the y number you change it to 4.
I need help on this ASAP… Line A passes through the points (-4,5) and (0,2). Line B…
Answer:
Parallel lines: Line B and C
Perpendicular lines: Line A and B; Line A and C
Step-by-step explanation:
To answer this question, we only need to find the slope of each equation. The formula for slope is attached in a picture.
LINE A
Substituting the first line into the formula, we will get...
(2 - 5)/(0 -(-4))
-3/4
LINE B
Substituting the second line's points into the formula we will get...
(2 - 6)/(3 - 6)
-4/-3
4/3
LINE C
Substituting the third line's points into the formula we will get...
(3 -(-1)/(0 -(-3))
4/3
So, parallel lines have the same slope, right? Since line b and line c have the same slope, they are parallel.
And, perpendicular lines have negative reciprocal slopes, right? (reciprocal means x/y -> y/x) Since -3/4 and 4/3 are negative reciprocals of each other, they are perpendicular.
Therefore...
Parallel lines: Line B and C
Perpendicular lines: Line A and B; Line A and C
sets if 98% of households have at least one television set and 4 households are selected, find the probability that at least one household has a television set.
Using the binomial distribution, it is found that there is a 0.99999984 = 99.999984% probability that at least one household has a television set.
For each household, there are only two possible outcomes, either it has at least one television set, or it does not. The probability of a household having at least one television set is independent of any other household, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
4 households are selected, hence [tex]n = 4[/tex].98% have at least one television set, hence [tex]p = 0.98[/tex]The probability that at least one household has a television set is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.98)^{0}.(0.02)^{4} = 0.00000016[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.00000016 = 0.99999984 [/tex]
0.99999984 = 99.999984% probability that at least one household has a television set.
A similar problem is given at https://brainly.com/question/24863377
Simplify the expression. w+w+5w
Answer:
w+w+5w = 7w
Step-by-step explanation:
Answer:
7w
Step-by-step explanation:
2. Find the simple interest paid to borrow $4800 for 6 years at 7%.
Answer:
$2016
Step-by-step explanation:
Simple Interest equation: I = Prt
So,
P = $4800
r = [tex]\frac{7}{100}[/tex] = 0.07
t = 6
I = (4800) · (0.07) · (6)
Thus,
The simple interest is $2016.
Owen paid $15 to download some of his favorite songs. He paid $2.50 per song. How many songs did he download?
The first step is to by a power of ten, so the divisor is a whole number.
The next step is to by figuring out how many times 250 goes into 1500.
What is the slope-intercept equation of the line that includes (0, 12) and
(4,36)?
Answer:
The slope is 6, but the equation is below.
Step-by-step explanation:
Y2 - Y1/X2 - X1
36-12/4-0
Or
12-36/0-4
=6
You'll get the same answer either way.
7.
Identify the vertex of the parabola.
A. (1, 2)
B. (−2, −1)
C. (−1, −2)
D. (−3, 2)
Answer: I can't find the answer :(
B. (−2, −1)
Step-by-step explanation: I don't know :(
From when I am looking at the graph it looks like the answer would be
P= (-2, -1)
Q= (1, -2)
.........................
Answer:
[tex]2[/tex]
Step-by-step explanation:
Let [tex][n][/tex] denote the area of some polygon [tex]n[/tex].
The sum of the area of quadrilaterals BCDE and MNDE is equal to [tex][ABC]-([MBE]+[NDC]+AMN])[/tex] (big triangle subtracting the three smaller triangles that aren't part of BCDE or MNDE).
Let the area of triangle ABC be [tex]\alpha[/tex].
Triangle AMN is similar to triangle ABC. Because their side lengths are in ratio 1:2 respectively, the ratio of the area of triangle AMN to triangle ABC is [tex]1:2^2=1:4[/tex].
Therefore, [tex]\displaystyle [AMN]=\frac{1}{4}[ABC]=\frac{1}{4}\alpha[/tex].
Now for triangle NDC, NDC is similar to triangle AMC. Since M is the midpoint of AB, AMC is half the area of ABC. The ratio of the side lengths between triangle NDC and triangle AMC is [tex]1:2[/tex] because the D is the midpoint of MC, so it follows the ratio of their areas must be [tex]1:4[/tex], respectively.
Therefore, [tex]\displaystyle[NDC]=\frac{1}{4}[AMC]=\frac{1}{8}[ABC]=\frac{1}{8}\alpha[/tex].
We can use the same concept for triangle MEB. Triangle MEB is similar to triangle ANB, and the ratio of their sides is also [tex]1:2[/tex], since E is the midpoint of BN. Their areas are in the ratio [tex]1:2^2=1:4[/tex] and we have [tex]\displaystyle [MBE]=\frac{1}{4}[ANB]=\frac{1}{8}\alpha[/tex].
Thus,
[tex]\displaystyle \frac{[ABC]}{[BCDE]+[MNDE]}=\frac{\alpha}{\alpha-\frac{1}{4}\alpha-\frac{1}{8}\alpha-\frac{1}{8}\alpha}=\frac{\alpha}{0.5\alpha}=\frac{1}{\frac{1}{2}}=\boxed{2}[/tex]
If ΔPQR ≅ ΔTSR, what are the congruent corresponding parts?
Answer:
If ΔPQR ≅ ΔTSR
Angles:
P and T
Q and S
R and R
Lines:
PQ and TS
QR and SR
PR and TR
Please I did help with this
Answer:
13.1
Step-by-step explanation:
A store sells previously viewed movies. The table shows the cost of buying 1, 2, 3, or 4 movies.
a. Which mapping diagram represents the data in the table
Question 2
b. Is the relation a function? Explain.
Each input has exactly one output. Therefore, the relation is a function.
Question 3
c. Describe the pattern. How does the cost per movie change as you buy more movies?
The pattern is that for each input
increase
of
1
, the output
increases
by $1,2,3,4,6,12
less than the previous increase. For each additional movie you buy, your cost per movie
decreases
by $1,2,3,4,6,12
how much did the output increase in dollars and how much did the movie decrease
A relation may or may not represent a function.
The relation of the movie and its costs is a function.The pattern is that, as unit cost of each movie decreases as the number of movies increases.The costs are given as:
1 movie costs $102 movies cost $183 movies cost $244 movies cost $28(a) The mapping diagram
To do this, we simply point the number of movies, to the corresponding costs, using arrows
See attachment for the mapping diagram.
(b) Is the relation a function
From the attached mapping, we can see that:
The costs of each movie are different.
This means that: the relation is a function.
(c) Describe the pattern
Notice that as the number of movies increases, the cost also increases;
However, the unit cost decreases.
Hence, the unit cost of each movie decreases as the number of movies increases.
Read more about mappings, functions and relations at:
https://brainly.com/question/8892191
A circle has a radius of 20 cm . Use 3.14 for pie and round your final answers to the nearest tenth . If applicable, include a thousands comma
Answer
If you are trying to find the area the answer would be 1,256cm
Step-by-step explanation:
1. A≈π r^2
2. A≈(3.14) (20)^2
3. A≈(3.14) (400)
4. A≈ 1,256^2
Find the equation of the line L.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (8, 0) ← 2 points on the line
m = [tex]\frac{0-4}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex]
The line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line L
plzz help asap plzzzzz
Answer:
5.45 then 6.454 then 5425 then 12825
Step-by-step explanation:
During the 2005 football season,team tackle beat team sack by 10 points. If their combinded scores totaled 36 find the individual team scores
Answer:
Step-by-step explanation:
t = tackle score
s = sack score
t = s + 10
t + s = 36
s + 10 + s = 36
2s = 26
s = 13 points
t = 13 + 10 = 23 points
What is the area of the following circle?
Either enter the exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answer:
25π or 78.5
Step-by-step explanation:
Area of circle = π[tex]r^{2}[/tex]
r = 5
A = π * 5^2
= 25π
= 78.5
(1.2•10^9) divided by (3•10^5)
Answer:
4000
Step-by-step explanation: First multiply the first two equations and will give you 1200000000 divided by 300000. Now logically 12/3is 4 so u do the same in the equation and it gives you 4000. Pls give brainly if i was right
Answer:
4000Step-by-step explanation:
(1.2•10^9) divided by (3•10^5)
(1.2 * 10^9) : (3 * 10^5) =
(1.2 * 1000000000) : (3 * 100000) =
1200000000 : 300000 =
4000
On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. Assuming a binomial distribution, what is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent
Answer:
Answer:
60
Step-by-step explanation:
Given : On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism.
To find : What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?