Answers
Vertically opposite angles are equal.
So,
(11y - 36)° = 63°
=> 11y - 36 = 63
Answer:
11y-36=63
Step-by-step explanation:
use the concept of vertically opposite angle
Related Questions
There are 200 blue balls and 10 red balls in an urn. Suppose that 10 balls are taken random;ly from the urn and let X denote the number of red balls selected.
a) The distribution of the random variable X is___.
i) Binomial.
ii) Hypergeometric.
iii) Poisson.
iv) Normal.
v) Exponential.
vi) Uniform
b) Find P(all 10 balls are red).
c) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X? With this approximation find P(X = 10).
Answers
Answer:
Hypergeometric
Kindly check explanation
Step-by-step explanation:
For a hypergeometric distribution, the following conditions must be met :
1.) The total number of samples must be fixed.
2.) Sample size will be a portion of the population
3.) The probability of success changes per trial. This is because sampling is done without replacement
The above scenario meets the condition described:
Total number of samples = 210
Sample size, n = 10
Blue balls = 200 ; red balls = 10
P(10 red balls)
Using the hypergeometric distribution function and the calculator :
X ~ H(n, N, M)
X ~ (10, 200, 210) = 0.6072
if 8km=5miles.how many miles are in 56m?
Answers
Answer:
89.6 miles
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]
5x = 448
x=89.6
Step-by-step explanation:
if 8km=5
x =56km
5x=8×56
5x=448
x=89.6 miles
The following integral requires a preliminary step such as long division or a change of variables before using the method of partial fractions. Evaluate the following integral. x^4 + 7/x^3 + 2x dx Find the partial fraction decomposition of the integrand. x^4 + 7/x^3 + 2x dx
Answers
Division yields
[tex]\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}[/tex]
Now for partial fractions: you're looking for constants a, b, and c such that
[tex]\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}[/tex]
[tex]\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a[/tex]
which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then
[tex]\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}[/tex]
Now, in the integral we get
[tex]\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx[/tex]
The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get
[tex]\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}[/tex]
A Professor at a Nigerian University sent his phone number in a disorderly manner to his students. The disordered phone number was 82002273285.To know his real phone number, he gave the student the following conditions:(1) Eight (8) must come between two zeros (0's). (2)The first number after the first condition is met must not be an odd number and it must be greater than 5. (3)The seventh number must be 1. (4) The fifth and sixth numbers must be two numbers whose difference is 1 and the bigger number must come first.(5)The fifth and sixth numbers are greater than 2.(6)The ninth and tenth numbers are the same.(7)The eighth number is greater than the last number (8) The phone number must be 11 digits. What is the Professor's real phone number?
Answers
Answer:
I think you have a type.. "the seventh number must be a 1"
there are no 1's in the original set of numbers
Step-by-step explanation:
It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon. A recent survey was conducted from 1000 of these individuals. For the sampling distribution of the sample proportion to be reasonably Normal, the sample must have been obtained in the right way (ideally, a simple random sample) and the sample size must be large (so that at least 10 or more successes and failures). Are these conditions met
Answers
Answer:
Random sample, [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], so yes, both conditions were satisfied.
Step-by-step explanation:
60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.
This means that [tex]p = 0.6[/tex]
A recent survey was conducted from 1000 of these individuals.
This means that [tex]n = 1000[/tex]
Also, a random sample, so the first condition was satisfied.
The sample size must be large (so that at least 10 or more successes and failures).
[tex]np = 1000*0.6 = 600 \geq 10[/tex]
[tex]n(1-p) = 1000*0.4 = 400 \geq 10[/tex]
So yes, both conditions were met.
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answers
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
AY
5
The slope of the graphed line is 2. Which formulas HELP PLEASEEEE
3
represent the line that is graphed? Check all that apply.
4
1(4,4)
3
(1/2)
Oy-1 = {(x-2)
Oy-2 = {(x - 1)
Oy-4 = (x - 4)
x
2 3 4 5
2
o flux) = { x + 1
3
47
4
f(x) = 2 x + 4
5
Answers
Answer:
y - 2 = 2/3 (x-1)
ORy - 4 = 2/3(x-4)
NOTE ;ALL WILL GIVE THE SAME RESULTStep-by-step explanation:
With this graph,the equation can be found on a straight line as the graph is .
So the formula is
[tex]y - y1 = m(x - x1)[/tex]
where your m is your gradient or slope as already said,the equation can be used by this formula (note;after finding your normal slope (not on a straight line ) firstly)
When you are done take any of the points connecting to the x axis and y axis directly as in (4,-4) or (2,1)
Let your first number be x1 and second y1 and place it in the formula .
NOTE: Y and x is constant and your general solution should be in the form;y = mx +cwhere m is still your normal slope.
HELP PLEASE- ASAP
What is the probability that a point selected randomly in will be one of the points inside segment RS? Enter your answer as a decimal numbers
Answers
Answer:
0.2
Step-by-step explanation:
The total number of points in PS is a sum of the number of points in :
PQ + QR + RS ;
PQ = 7 ; QR = 13 ; RS = 5
PS = (7 + 13 + 5) = 25
Probability that point selected at random is in RS ;
Required outcome = point in RS
Total possible outcomes = points in PS
Probability = RS / PS = 5 / 25 = 0.2
14. In this picture, three straight lines intersect at a point. Form an equation in x and solve for x.
Answers
Answer:
6x = 180
x = 30
Step-by-step explanation:
Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1
Answers
Answer:
[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method:
[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] x is the radius[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is the volumeStep-by-step explanation:
Step 1: Define
Identify
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
Step 2: Sort
We are revolving around a horizontal line.
[Function] Rewrite in terms of y: x = √y[Graph] Identify bounds of integration: [0, 4]Step 3: Find Volume Pt. 1
[Shell Method] Find distance of radius x: [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]: [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply: [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
Jack and Diane are jogging back and forth along a one-mile path. They started out at 9:00 A.M. from opposite ends of the path. They passed each other in 10 minutes when Diane has gone 1/3 mile. What time will they first meet at one end of the path? You have to assume they keep jogging at the same speeds.
Explain :
Answers
Answer:
30 minutes
Step-by-step explanation:
that problem description is imprecise.
I think what is meant here : they each keep jogging at their own same speed.
Diane's speed is 1/3 miles / 10 min.
Jack's speed is 2/3 miles / 10 min.
now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.
60/10 = 6.
so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.
Diane : (1/3 × 6) / hour = 2 miles / hour
Jack : (2/3 × 6) / hour = 4 miles / hour
since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).
Diane running 1 mile going 2 miles/hour takes her 30 minutes.
Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.
so, they will meet at his starting point after 30 minutes.
A ice cream shop sells 8 different flavors of ice cream with A choice of three different styles of calls how many different ice cream cones are possible if you select one ice cream flavor with one type of ice cream cone
Answers
Explanation:
There are 8 different flavors and 3 types of cones. This means there are 8*3 = 24 different combos possible.
Imagine a table with 8 rows and 3 columns. Each row is a different flavor and each column is a different cone type. The table formed has 24 inner cells to represent a different combination of flavor + cone type. So that's why we multiplied those values earlier.
Note: This only works if you're only able to select one type of flavor.
Find three consecutive odd integers whose sum is -213.
Answers
Answer:
-73, -71, -69
Step-by-step explanation:
Suppose the middle of the 3 integers is x.
(x-2)+(x)+(x+2)=-213
x-2+x+x+2=-213
3x=-213
x=-71
The integers are -69, -71, and -73
Answer:
-73,-71,-69
Step-by-step explanation:
Let x represent an odd interger
Odd intergers are serpated by the value of 2 so let the three consective intergers be represented by
[tex](x )+ (x + 2) +( x + 4)[/tex]
Set that equation equal to 213.
[tex]x + x + 2 + x + 4 = - 213[/tex]
[tex]3x + 6 = - 213[/tex]
[tex]3x = - 219[/tex]
[tex]x = - 73[/tex]
Plug -73 in the consective intergers expression.
[tex] - 73 + ( - 73 + 2) + ( - 73 + 4)[/tex]
So our three intergers are
[tex] - 73[/tex]
[tex] - 71[/tex]
[tex] - 69[/tex]
Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20
Answers
Answer:
(4, 2 )
Step-by-step explanation:
Given the 2 equations
3x + y = 14 → (1)
7x - 4y = 20 → (2)
Rearrange (1) making y the subject by subtracting 3x from both sides
y = 14 - 3x → (3)
Substitute y = 14 - 3x into (2)
7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side
7x - 56 + 12x = 20
19x - 56 = 20 ( add 56 to both sides )
19x = 76 ( divide both sides by 19 )
x = 4
Substitute x = 4 into (3) for corresponding value of y
y = 14 - 3(4) = 14 - 12 = 2
solution is (4, 2 )
Answer:
[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]
Simplify i need help
Answers
Answer:
c
Step-by-step explanation:
when we take the 5 inside the root the 5 vil be 5^2 times 2 which is equal to 50
answer plz pix inside plz find both answers
Answers
Answer:
pixxer
Step-by-step explanation:
please pick inside please
Answer:
I dont now
Step-by-step explanation:
plz conprendation
The slope of diagonal OA IS__,
and its equation is__
Answers
Answer:
[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA
[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation
Step-by-step explanation:
Given
The attached graph
Solving (a): Slope of OA
First, we identify two points on OA
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
So, the slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4-0}{3-0}[/tex]
[tex]m = \frac{4}{3}[/tex]
Solving (b): The equation
This is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Recall that:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]m = \frac{4}{3}[/tex]
So, we have:
[tex]y = \frac{4}{3}(x - 0) + 0[/tex]
[tex]y = \frac{4}{3}(x)[/tex]
[tex]y = \frac{4}{3}x[/tex]
What is an amount between $2 and $10?
Answers
Answer:
6
Step-by-step explanation:
Angela’s average for six math tests is 87. on her first four tests she had scores of 93, 87, 82, and 86. on her last tests she scored 4 points lower than she did on her fifth test what scores did Angela receive on her firth and sixth tests?
Answers
Answer:
the scores on her last test is x (x > 0)
because on her last tests she scored 4 points lower than she did on her fifth test
=> the scores in the 5th test is x + 4
because Angela’s average for six math tests is 87, we have:
[tex] \frac{93 + 87 + 82 + 86 + x + x + 4}{6} = 87 \\ \\ < = > \frac{352 + 2x}{6} = 87 \\ \\ < = > 352 + 2x = 522 \\ \\ < = > 2x = 170 \\ \\ < = > x = 85[/tex]
=> on her last test, she had 85
=> on her 5th test, she had 85 + 4 = 89
Indicate the method you would use to prove the triangles congruent. If no
method applies, enter "none."
O SSS
k O SAS
O ASA
© None
Answers
Step-by-step explanation:
I suspect we don't see the full information for the problem here.
all listed 3 methods are typically used to prove that triangles are congruent (= when turned to have the same orientation, they would simply cover each other completely - no overhanging parts from either triangle).
I guess there is a diagram with 2 triangles and what is known about them.
and since we cannot see them, we cannot tell you which method would apply here.
just remember
SSS means all 3 sides of one triangle are exactly the same as the 3 sides of the other triangle. if you know the lengths of all 3 sides, there is only one triangle you can create. you can only orient it differently.
SAS means two sides and the enclosed angle are the same. again, only one triangle can be created with that information.
ASA means one side and the 2 angles at the end points of that side are known. again, only one triangle can be created with that information.
Write an expression that is equal to 8 using only four 3s and any number of math symbols
Answers
Answer:
(3 × 3) - (3 ÷ 3) = 8
Step-by-step explanation:
We want to find an expression that when solved will be equal to 8.
But we are restricted to using only the number "3" four times with any Maths operation.
Thus let's try;
(3 × 3) - (3 ÷ 3) = 9 - 1 = 8
A shopkeeper supplies 42 kg of vegetables to a school canteen in the morning and 58 kg of vegetables in the evening if cost of 1kg vegetable is 16 rupees how much money is due to the canteen per day?
Answers
Add both instances of supplying vegetables in 1 day together.
42 kilograms + 58 kilograms = 100 kilograms
Since each kilogram of vegetables equals 16 rupees, 100 kilograms of vegetables is just this number multiplied by 100.
16 rupees * 100 = 1600 rupees
PLEASE HELP!!! I tried using different formulas, adding, subtracting, dividing, multiplying you name it and I have yet to find the correct answer. How would I should this problem?
Answers
Answer:
19.14
Step-by-step explanation:
You have a half circle and a square, look at them separate then add for the area.
Circle
Your radius is half the diameter, so 4/2
Radius = 2
[tex]A = 3.14 * radius\\A = 3.14 * 2\\A = 6.28[/tex]
This is for the entire circle, half of that would be 3.14
Square
[tex]A = 4^{2} \\A = 16[/tex]
Add them both together for a total area of 19.14 square miles
find the equation of the line
Answers
Answer:
y = x + 6
Step-by-step explanation:
rise = 1
run = 1
slope = rise/run = 1
y-intercept = 6
y = mx + b
y = x + 6
Thirty-six percent of customers who purchased products from an e-commerce site had orders exceeding 110. If 17% of customers have orders exceeding 110 and also pay with the e-commerce site's sponsored credit card, determine the probability that a customer whose order exceeds 110 will pay with the sponsored credit card.
Answers
Answer:
The right solution is "0.5".
Step-by-step explanation:
According to the question,
P(pay with the sponsored credit card | order exceeds $110)
= [tex]\frac{P(Pay \ with \ the \ sponsored \ credit\ card\ and\ order\ exceeds\ 110)}{P(order \ exceeds \ 110)}[/tex]
= [tex]\frac{P(A \ and \ B)}{P(A)}[/tex]
By putting the values, we get
= [tex]\frac{0.17}{0.34}[/tex]
= [tex]0.5[/tex]
Thus, the above is the right solution.
4
920
26°
?
74°
find the missing angle.
Answers
9514 1404 393
Answer:
44°
Step-by-step explanation:
The sum of the marked angles on the right is equal to the sum of the marked angles on the left:
? + 74 = 92 + 26
? = 92 +26 -74 = 44
The missing angle is 44°.
_____
Additional comment
The vertical angles in the center of the figure are v = 62°, the measure required to bring the total to 180° in each triangle. We have shortcut the equation(s) ...
? + 74 + v = 180 = 92 + 26 + v
by subtracting v from both sides, giving ...
? +74 = 92 +26
Help and explain explain !!!!!!!!!!
Answers
Answer:
[tex]x=-1\text{ or }x=11[/tex]
Step-by-step explanation:
For [tex]a=|b|[/tex], we have two cases:
[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]
Therefore, for [tex]18=|15-3x|[/tex], we have the following cases:
[tex]\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}[/tex]
Solving, we have:
[tex]\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}[/tex].
Therefore,
[tex]\implies \boxed{x=-1\text{ or }x=11}[/tex]
If the domain of a function that is reflected over the x-axis is (1, 5), (2, 1), (-1, -7), what is the range?
A. (1, -5), (2, -1), (-1, 7)
B. (5, 1), (1, 2), (-7, -1)
C. (-5, -1), (-1, -2), (7, 1)
D. (-1, 5), (-2, 1), (1, -7)
Answers
Answer:
A. (1, -5), (2, -1), (-1, 7)
Step-by-step explanation:
Reflecting a function over the x-axis:
When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:
[tex](x,y) \rightarrow (x,-y)[/tex]
To find the range:
We apply the transformation to the points in the domain. Thus:
[tex](1,5) \rightarrow (1,-5)[/tex]
[tex](2,1) \rightarrow (2,-1)[/tex]
[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]
Thus the correct answer is given by option a.
Answer:
It is letter A and please give me brainliest
Step-by-step explanation:
URGENT!!! Picture included
Answers
Paul writes newspaper articles. He earns a base rate of $500 per month and an additional $100 per article he writes. Last month he earned $2000.
Write an equation to determine the number of articles (a) he sold last month.
Answers
Answer:
Total earning last month with x articles is:
x*100 + 500This is same amount as 2000
The equation is:
100x + 500 = 2000