Answer:
$2,750
Step-by-step explanation:
Total spending = Rent + Cost
= $750 + $2000
= $2750
4. Solve the following system of equations for x.
2x + 3y = -14
y = 6x + 22
A. X = -2
B. X = 2
C. X = -4
D. X = 4
We are given the system of equations -:
[tex] \large{ \begin{cases} 2x + 3y = - 14 \\ y = 6x + 22 \end{cases}}[/tex]
Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.
[tex] \large{2x + 3(6x + 22) = - 14}[/tex]
Expand 3 in the expression so we can combine like terms and isolate x-variable.
[tex] \large{2x + 18x + 66 = - 14}[/tex]
Then combine like terms.
[tex] \large{20x + 66 = - 14}[/tex]
Get rid of 66 from the left side by subtracting both sides by itself.
[tex] \large{20x + 66 - 66 = - 14 - 66} \\ \large{20x = - 80}[/tex]
To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.
[tex] \large{ \frac{20x}{20} = \frac{ - 80}{20} }[/tex]
Simplify to the simplest form.
[tex] \large{x = - 4}[/tex]
Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.
Answer
x = -4I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!
Answer:
A. x = -2
C. x = -4
Step-by-step explanation:
y = 6x + 22
2x + 3•(6x+22) = -14
20x = - 80
x = -4
y = 6x+22
y = 6(-4)+22 = -2
can someone answer pleaseeee
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
I need to match them but I don't know how
Given:
The system of equations is:
[tex]x+3y=5[/tex]
[tex]x-3y=-1[/tex]
The given matrices are [tex]\left[\begin{array}{cc}5&3\\-1&-3\end{array}\right] [/tex], [tex]\left[\begin{array}{cc}1&5\\1&-1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}1&3\\1&-3\end{array}\right][/tex].
To find:
The correct names for the given matrices.
Solution:
We have,
[tex]x+3y=5[/tex]
[tex]x-3y=-1[/tex]
Here, coefficients of x are 1 and 1 respectively, the coefficients of y are 3 and -3 respectively and constant terms are 5 and -1 respectively.
In the x-determinant, the coefficients of x are in the first column and the constant terms are in the second column. So, the x-determinant is:
[tex]\left[\begin{array}{cc}1&5\\1&-1\end{array}\right][/tex]
In the y-determinant, the constant terms are in the first column and the coefficients of y are in the second column. So, the y-determinant is:
[tex]\left[\begin{array}{cc}5&3\\-1&-3\end{array}\right] [/tex]
In the system determinant, the coefficients of x are in the first column and the coefficients of y are in the second column. So, the system determinant is:
[tex]\left[\begin{array}{cc}1&3\\1&-3\end{array}\right][/tex]
Therefore, the first matrix is y-determinant, second matrix is x-determinant and the third matrix is the system determinant.
Consider rolling two fair dice and observing the number of spots on the resulting upward face of each one. Letting A be the event that at least one of the dice results in 6 spots on its upward face, and E be the event that exactly one of the dice results in 6 spots on its upward face, give the value of P(E|A). (Note: This value can be easily obtained by looking at p. 2.3 of the class notes and using a reduced sample space. In fact, such an approach makes the solution so trivial, that for this problem, you don’t have to give any justification for your answer.)
Answer:
[tex]P(E|A)= \frac{10}{11}[/tex]
Step-by-step explanation:
Given
Two rolls of die
[tex]E \to[/tex] one of the outcomes is 6
[tex]A \to[/tex] atleast one is 6
Required
P(E|A)
First, list out the outcome of each
[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]
So:
[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]
Where:
[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]n(E\ n\ A) = 10[/tex]
[tex]n(A) = 11[/tex]
So:
[tex]P(E|A)= \frac{10}{11}[/tex]
What is the graph of 4x + 2 < 10
Express the terms of the following sequence by giving an explicit formula. 5 , 2 , -1 , -4, -7 , .
Answer:
Step-by-step explanation:
a1=5
d=2-5=-3
[tex]a_{n}=5+(n-1)(3)\\a_{n}=5+3n-3\\a_{n}=3n+2[/tex]
Find the value for the side marked below.
Round your answer to the nearest tenth.
13
23°
у
у
[?]
Enter
Answer:
y = 30.96
Step-by-step explanation:
take 23 degree as reference angle
using tan rule
tan 23 = opposite / adjacent
0.42 = 13/y
y = 13/0.42
y = 30.96
Graph the Image of square KLMN after a translation 3 units left .
Answer:
N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)
Step-by-step explanation:
To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.
The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the square be represented as KLMN
Now , the coordinates of the square KLMN is
K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )
Now , let the translated square be represented as K'L'M'N'
When translating the square to three units to the left , the x coordinate of the square gets reduced by 3
So , the new coordinate of the square will be ( x - 3 , y )
Substituting the values in the equation , we get
K' = K ( -5 - 3 , 3 )
L' = L ( 1 - 3 , 3 )
M' = M ( 1 - 3 , 9 )
N' = N ( -5 - 3 , 9 )
So , on simplifying the equation , we get
The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )
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Suppose you and a friend are playing this game. You draw a card from a bag. Each card has one letter on it.
There is one card for every letter in the words WHO WILL WIN.
If you draw a W, you win,
If your friend draws an L, she wins.
Is this a fair game? Explain.
Answer:
No it is not fair how can two people win
PLS HELP ME!!!! use the properties of exponents to simplify the expression
Answer:
According to Indices
(a⁴)²... The exponents will multiply each other to give (a⁶)
Using this here
The two Index would Multiply to give
½ x ⅔ = ⅓
= (27)⅓
Any Number to the Index of ½ simply means its Square root
so also...
Any Number to the index of ⅓ means its cube root...
Cube root of 27 = 3.
So
Option B is your answer.
It is A (45). Hope this helps!
Which of the following is most likely the next step in the series?
B
Answer:
C
Step-by-step explanation:
The pattern seems to go as follows:
1. Top left portion is in blue
2. Top left portion is in blue as well as the rest of the upper half filled with red.
3. Another portion of blue is added directly underneath the red.
This leads me to believe that the colors are alternating from blue to red to blue to finally, red. This makes your answer C. Please let me know if you still need help!
What are the 2 \ 3 parts of a right angle in a whole wheel?
Answer:
[tex]\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} \ of \ a \ right \ angle \ = \frac{2}{3} \times 90^{\circ} = 60^{ \circ}\\\\A \ whole \ wheel \ is \ = 360^ {\circ}\\\\[/tex]
Now to find what part of 360 is 60 :
[tex]Let \ it \ be \ x\\\\x \times 360 = 60 \\\\x = \frac{60}{360} = \frac{1}{6}[/tex]
Therefore ,
[tex]\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.[/tex]
A group of people were asked if they had run a red light in the last year. 315 responded "yes", and 190 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
0.624
Step-by-step explanation:
Number who have run a red light = 315
Number who haven't run a red light = 190
From the data :
The total number of people sampled = total possible outcome = (315 + 190) = 505
Selecting a person at random, probability that the selected person has run a red light :
P = required outcome / Total possible outcomes
Required outcome = Number who have run a red light = 315
P(having run a red light) = 315 / 505 = 0.624
Standard form equation
Answer:
5x+4y=24
Step-by-step explanation:
So Ax+By=C is the standard form equation of a line.
y=mx+b (in which m is the slope and b is the y-intercept) is the equation that most people start off with.
Since the line intersects the y-axis at (0,6), the y-intercept is 6.
So, we can substitute 6 with b, which is y=mx+6.
Now, we can find the slope (m) by either inserting a known point (x,y) or using rise/run. Either way, you get the slope as -5/4 because we go five units DOWN and four units RIGHT from (0,6), one known point, to (4,1), another known point.
The y=mx+b equation becomes: y=(-5/4)x+6.
Now, we subtract (-5/4)x on both sides to get (5/4)x+y=6
Multiply 4 on both sides because standard form requires no fractions or decimals.
The final answer is 5x+4y=24.
That's your answer, fully simplified!
the cost price of an articles was 4000 find the marked price of the article so that there will be profit of 20%after allowing a discount of 20%
Answer:
The marked price of the article was $ 6000.
Step-by-step explanation:
Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:
4000 x X x 0.8 = 4000 x 1.2
4000 x X x 0.8 = 4800
4000 x X = 4800 / 0.8
4000 x X = 6000
X = 6000/4000
X = 1.5
4000 x 1.5 = 6000
Therefore, the marked price of the article was $ 6000.
Which of the following is an example of data organization?
A. administering questionnaires
B. calculating a standard deviation
c. representing data with a histogram
D. declaring a statistically significant difference between groups
c) representing data with a histogram is an example of data organization
find the 11th term of the series
8,14,20,26.......
Answer:
a11 = 8+(11-1)6
a11 = 8+54
a11=68
hopefully this is correct
Step-by-step explanation:
7a - 2b = 5a + b
a = 2b
a = 3b
a = a equals StartFraction 3 Over 2 EndFraction b.b
a = a equals StartFraction 2 Over 3 EndFraction b.b
Answer:
iii) a=3b/2
Step-by-step explanation:
7a-2b= 5a+b
7a-5a=2b+b
2a=3b
a=3b/2
I hope this helps!
How many different license plates are possible if digits and letter can be repeated if the configuration is 3 letters, 2 digits, 2 letters?
Answer:
1,188,137,600 possible combinations
Step-by-step explanation:
The first three and last two digits can be any letter while the middle two digits can be any number.
26*26*26*10*10*26*26=1,188,137,600
is the function given by G(x) - 1/x-6 continuous over the interval (1, ∞)? Why or why not?
a. No, the function is not continuous at x=
b. Yes, the function is continuous over (1,∞) because lim x>a G(x)= G(a) for all a in (1,∞).
Answer:
No, the function is not continuous at x=
Need help ASAP!! Giving brainliest!
Pls ASAP Select the correct answer.
What is the sum of this geometric series?
9514 1404 393
Answer:
D. 21/2
Step-by-step explanation:
It is probably easiest to add up the three terms.
For n=1, the first term is ...
8(1/4)^(0) = 8
The second term is ...
8(1/4)^1 = 2
The third term is ...
8(1/4)^2 = 8/16 = 1/2
The sum of the series is ...
8 + 2 + 1/2 = (16 +4 +1)/2 = 21/2
The perimeter of a rectangle is 12cm the area is 5cm square what is the length of the sides
Answer:
???
Step-by-step explanation:
Find the following list of data calculate a demean be the maid and see mode or mothers for the following numbers listed in the picture above above
Answer:
Mean = 4.8875
Median = 4.6
Mode = 4.5 and 7.7
Step-by-step explanation:
Mean is the sum of total of data divided by the sample size
Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5
Sum total = 39.1
Sample size = 8
Mean = 39.1/8
Mean = 4.8875
To get the median we need to first rearrange
1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7
Median = 4.5 + 4.7/2
Median = 4.6
Hence the median is 4.6
Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7
2) find an equation of the line theough the given
points. Give the final answer in slope-intercept form.
(2,-2) (-1,4)
Answer:
y = -2x + 2
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (2, -1)
Points on the y-axis (y1, y2) = (-2, 4)
To find the equation of line in slope intercept form;
First of all, we would determine the slope of the line.
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]
[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]
[tex] Slope, m = \frac {6}{-3} [/tex]
Slope, m = -2
Next, we would use the following formula to find the equation of the line;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - (-2) = -2(x - 2)
y + 2 = -2x + 4
y = -2x + 4 - 2
y = -2x + 2 = mx + c
Which function is a translation of the parent absolute value function?
f(x) = 2x1
f(x) = |x+6| f(x)=|x| f(x)=-4|x|
15 + 36 not-equals 41, so those lengths will not form a triangle.
15 squared + 36 squared = 1,521
41 squared = 1,681
Since a squared + b squared not-equals c squared, it will not be a right triangle.
15 squared + 36 squared = 297
41 squared = 82
Step-by-step explanation; did it on the website euphoria
The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the transformation of the function be a translation , where
The parent function is f ( x ) = | x |
And , the translated function is f ( x ) = | x + 6 |
So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
And , the function is translated 6 units to the left
Hence , the translated function is f ( x ) = | x + 6 |
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Tìm căn bậc hai của số phức z=1+i√3
Write z in polar form:
z = 1 + √3 i = 2 exp(i π/3)
Taking the square root gives two possible complex numbers,
√z = √2 exp(i (π/3 + 2kπ)/2)
with k = 0 and k = 1, so that
√z = √2 exp(i π/6) = √(3/2) + √(1/2) i
and
√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i
A table is made using the following two patterns.
Pattern 3: Starting number: 5, Rule: add 1
Pattern y: Starting number: 10, Rule: add 2
Complete the table for the given patterns.
Answer:
x = 6, y = 12
x = 7 y = 14
Step-by-step explanation:
im pretty sure that right, hope this helps!
The prices of a term of notebooks are between $2 and $5. If
you plan to spend $10 on notebooks, calculate the least
number of notebooks you can buy in this situation.
notebooks
Answer: Number “2”
Step-by-step explanation: I took the ck-12 Applications with Inequalities
