Answer:
x=-7, y=2
Step-by-step explanation:
You are given the matrix equation
[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right][/tex]
Find the inverse matrix for the matrix
[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right][/tex]
1. The determinant is
[tex]\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4[/tex]
2.
[tex]a_{11}=2 \Rightarrow A_{11}=3\\ \\a_{12}=-2 \Rightarrow A_{12}=-(-1)=1\\ \\a_{21}=-1 \Rightarrow A_{21}=-(-2)=2\\ \\a_{22}=3 \Rightarrow A_{22}=2[/tex]
3. Inverse matrix is
[tex]\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right][/tex]
So, the solution of the equation is
[tex]\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right][/tex]
Please help me I have to turn in by 8:00
Answer:
A 2
Step-by-step explanation:
When we divide x by 9 there is some whole number we will call y plus a remainder of 4
x/9 = y remainder 4
Writing this in fraction form
x/9 = y + 4/9
Multiplying each side by 9
9*x/9 = 9* y + 4/9 *9
x = 9y +4
Multiply each side by 2
2x = 2*(9y+4)
2x = 18y +8
Add 3 to each side
2x+3 = 18y +8+3
2x+3 = 18y +11
Divide each side by 9
(2x+3)/9 = 18y/9 +11/9
= 2y + 9/9 +2/9
=(2y+1 + 2/9)
We know y is a whole number and 1 is a whole number so we can ignore 2y +1 when looking for a remainder)
2/9 is a fraction
Taking this back from fraction form to remainder from
(2y+1) remainder 2
what is the eqaution of a vertical line passing through (-5,-2)?
Answer:
x=-5
Step-by-step explanation:
Vertical lines have the same x value all the time. They are of the form x=
Since it passes through the point (-5,-2) the x value must be -5
x=-5
The graph of f(x) = |x| is transformed to g(x) = [X + 11-7. On which interval is the function decreasing?
Answer:
The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
Step-by-step explanation:
* Lets explain how to solve it
- Decreasing function means a function with a graph that moves
downward as it is followed from left to right.
- For example, any line with a negative slope is decreasing function
- Lets look to the attached graph to understand the meaning of the
decreasing function
∵ f(x) = IxI ⇒ green graph
∵ g(x) = Ix + 1I - 7 ⇒ purple graph
- From the graph f(x) translated 1 unit to the left and 7 units down to
form g(x)
- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}
- The range of f(x) is {y : y ≥ 0}
- The range of g(x) is {y : y ≥ -7}
# For f(x)
- The slope of the green line from (-∞ , 0) is negative
- The slope of the green line from (0 , ∞) is positive
# For g(x)
- The slope of the purple line from (-∞ , -1) is negative
- The slope of the purple line from (-1 , ∞) is positive
∵ The line with negative slope represent decreasing function
∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)
∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)
The function g(x) = |x+11|-7 is a transformed absolute value function, which is decreasing on the interval (-infinity, -11) due to the horizontal shift to the left by 11 units.
The question is asking about the transformation of the absolute function f(x) = |x| into a new function g(x). The function provided, g(x) = |x+11|-7, is a transformed version of f(x) where the graph has been shifted horizontally and vertically. To determine on which interval g(x) is decreasing, we need to consider the properties of the absolute value function and its transformations.
The graph of the standard absolute value function, f(x) = |x|, is shaped like a 'V', increasing for x > 0 and decreasing for x < 0. When we introduce a horizontal shift to the function (such as adding 11 to x), this shifts the vertex of the 'V' horizontally. For g(x), the graph is shifted to the left by 11 units due to the '+11' inside the absolute value. Therefore, the function will be decreasing on the interval (-infinity, -11) since the function will decrease to the left of the vertex (which is now located at x = -11). The vertical shift (subtracting 7) simply moves the graph down but does not affect the intervals of increasing or decreasing behavior.
Francesca drew point (-2,-10) on the terminal ray of angle x which is in standard position she found values for the six trigonometric functions using the steps below
Answer:
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
Step-by-step explanation:
Francesca made her first error in step 3 because her sine, cosine, and tangent trigonometric ratio values are incorrect.
How to work with trigonometric ratios?The correct steps to use in this regards are as follows;
Step 1;
A unit circle is shown. A ray intersects point (-2, -10) in quadrant 3. θ is the angle formed by the ray and the x-axis in quadrant 1.
Step 2;
r = √[(-2)² + (-10)²] = √104 = 2√26
Step 3;
cos θ = -2/(2√26) = -1/√26 = -(√26)/26
sin θ = -10/(2√26) =-5/√26 = -5(√26)/26
tan θ = -10/-2 = 5
sec θ = 1/sin θ = 1/-(√26)/26 = -26/√26
cosec θ = 1/cos θ = 1/-5(√26)/26 = -(√26)/5
cot θ = 1/tan θ = 1/5
Thus, Francesca made her first error in step 3 because the correct sine, cosine, and tangent ratios above differ from hers which was incorrect which lead to incorrect values of cosecant, secant, and tangent functions.
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Subtract
(6x^2 + 5) - (4x-3)
[tex](6x^2+5)-(4x-3)=6x^2+5-4x+3=6x^2-4x+8[/tex]
ANSWER B
I took the test and that was the correct answer
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 + 2x = 17
need the awnswer now!!
Answer:
x = -5.24 or x = 3.24Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(8)\\\\x^2+2x=17\\\\x^2+(2)(x)(1)=17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(1)+1^2}_{(*)}=17+1^2\\\\(x+1)^2=18\iff x+1=\pm\sqrt{18}\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt{18}\\\\x\approx-1-4.24=-5.24\ \vee\ x\approx-1+4.24=3.24[/tex]
You need to catch two different buses to get to the shops Bus 1 is due to leave at 2 o'clock and arrive at 2.30. You have a half hour wail between getting off the first bus and getting on the second bus.
Bus 2 is due to arrive at the shops at 3.15.
(a) What time is bus 2 scheduled to leave? Bus 2 leaves 15 minutes early
(b) What time does it leave? () What time does it anive?
Bus 1 is 15 minutes late.
(c) What time does it arrive?
Answer:
rxch.ace_
Step-by-step explanation:
Final answer:
Bus 2 is scheduled to leave at 3:00 pm, but if it leaves 15 minutes early, it departs at 2:45 pm and arrives at the shops at 3:00 pm. If Bus 1 is 15 minutes late, it arrives at 2:45 pm, the same time Bus 2 leaves, preventing the transfer.
Explanation:
To solve the question regarding bus schedules and arrival times, let's break down each part of the problem step by step.
Part (a): Scheduled Departure Time of Bus 2
Bus 1 arrives at the first stop at 2:30 pm. There is a half-hour wait, so the earliest you can board Bus 2 is at 3:00 pm. Since Bus 2 arrives at the shops at 3:15 pm, and it leaves 15 minutes before its scheduled arrival time, Bus 2 is scheduled to leave at 3:00 pm.
Part (b): Bus 2 Leaves Early
Bus 2 is supposed to leave 15 minutes early. If its scheduled departure was 3:00 pm, it actually leaves at 2:45 pm. Since it leaves 15 minutes early and the travel time remains unchanged, Bus 2 would still arrive at 3:00 pm at the shops.
Part (c): Bus 1 is Late
Bus 1 is 15 minutes late. Instead of leaving at 2:00 pm, it leaves at 2:15 pm and arrives at the first stop at 2:45 pm. Since Bus 2 leaves at 2:45 pm, you would not be able to transfer from Bus 1 to Bus 2 since their arrival and departure times coincide.
Angles 4 and 5 form what type of angles?
complementary angles
supplementary angles
vertical angles
obtuse angles
Answer:
the answer will be verticle angles
Step-by-step explanation:
∠4 and ∠5 form vertical angles.
What is vertical angles?When two lines intersect each other, then non-adjacent opposite angles are called vertical angles.
Vertical angles are always equal in measurement.
If line AB and CD intersect each other at point O, ∠AOC and ∠BOD are vertical angles, similarly, ∠AOD and ∠BOC are also vertical angles.
Here lines 1 and 2 intersect each other.
So ∠4 and ∠5 are formed which are non-adjacent and opposite also.
Therefore ∠4 and ∠5 form vertical angles.
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Which ordered pair is a solution of this equation x-7y=-3
Answer:
-3,0
Step-by-step explanation:
this is the answer hope u like it
How would you find f(-3)?
Answer:
f(-3) = 12
Step-by-step explanation:
-3 < 2; 9 + 3 = 12 [(-3)² - -3 (double negative)]; DO NOT change -3 to 3.
I hope this helps, and as always, I am joyous to assist anyone at any time.
The digits I through 4 are randomly arranged to create
a four-digit number. What is the probability that the number formed is not divisible by 4?
The probability that the four-digit number formed is not divisible by 4 is approximately 0.875 or 87.5%.
To calculate the probability that the four-digit number formed is not divisible by 4, we need to determine the total number of possible arrangements of the digits I through 4 and then find the number of arrangements that are not divisible by 4.
Total number of arrangements:
Since there are four digits (I, 2, 3, 4), there are 4! (4 factorial) ways to arrange them without repetition.
4! = 4 × 3 × 2 × 1 = 24
Now, let's find the arrangements that are not divisible by 4:
For a number to be divisible by 4, the last two digits must form a number divisible by 4. The possible combinations of the last two digits that are divisible by 4 are: 12, 24, and 32.
So, we have three combinations (12, 24, and 32) where the number formed is divisible by 4.
Now, to find the arrangements that are not divisible by 4, subtract these three combinations from the total:
Arrangements not divisible by 4 = Total arrangements - Divisible by 4 arrangements
Arrangements not divisible by 4 = 24 - 3 = 21
Now, we can calculate the probability:
Probability = (Number of arrangements not divisible by 4) / (Total number of arrangements)
Probability = 21 / 24
Probability ≈ 0.875
So, the probability that the four-digit number formed is not divisible by 4 is approximately 0.875 or 87.5%.
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Approximately how many milligrams of sodium
remain after 8.4 years?
no your wrong its 85.2
What is the perimeter of AYXZ?
3.5 in.
5.3 in.
6.4 in.
7.8 in.
Answer: The perimeter of ΔYXZ6.4
Answer:6.4
Step-by-step explanation:
In ∆ABC, m<A = 72 and m<B = 83. What is the measure of <C?
Answer:
25 degrees.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees therefore:
m < C = 180 - 72 - 83
= 180 - 155
= 25 degrees.
Answer:
25
Step-by-step explanation:
Theorem:
The sum of the measures of the interior angles of a triangle is 180 degrees.
The theorem is can be written as the equation below.
m<A + m<B + m<C = 180
We know the measures of angles A and B, so we substitute the values for those measures, and we solve for the measure of angle C.
72 + 83 + m<C = 180
Add like terms on the left side.
155 + m<C = 180
Subtract 155 from both sides.
m<C = 25
Answer: m<C = 25
Are the triangles similar? if so, what postulate or theorem proves their similarity?
A. yes, by SSS Similarity Theorem
B. yes, by SAS Similarity Theorem
C. yes, by AA Similarity Theorem
D. no the triangles are not similar
Answer: A. yes, by SSS Similarity Theorem
Step-by-step explanation:
From the given picture, it can be seen that we have all the sides of bothe the triangles.
SSS Similarity Theorem says that if the ratio of lengths of the corresponding sides of two triangles are then the triangles must be similar.
From the given picture , the ratio of the sides is given by :-
[tex]\dfrac{10}{35}=\dfrac{2}{7}\\\\\dfrac{12}{42}=\dfrac{2}{7}\\\\\dfrac{11}{36.5}=\dfrac{2}{7}[/tex]
Thus, the ratio of lengths of the corresponding sides of two triangles are equal.
Hence, the triangles must be similar by SSS similarity theorem.
I’ve been stuck on this for a while now can someone please help me out please
Step-by-step explanation:
i think its 4.2m^2+1.5n
Answer:
4.2m^2+1.5n
Step-by-step explanation:
1.7m^2 + 6.5n - 4n + 2.5m^2 - n
First, rearrange the numbers so that they can be added or subtracted with their like terms.
It would look like this:
(1.7m^2 + 2.5m^2) + (6.5n - 4n - n)
All you have to do is solve from here
this would simplify into:
4.2m^2+1.5n
Hope this helped!
The length of a rectangle is three times its width. The perimeter is 160 cm. What is the number of square centimeters in the area of the rectangle?
Answer:
1200 cm²
Step-by-step explanation:
width = x cm
length = 3x cm
perimeter = 160 cm
2(x + 3x) = 160
4x = 160/2
4x = 80
x = 80/4
x = 20 cm - width
length = 3x = 3 · 20 = 60 cm
Area = length · width = 60 · 20 = 1200 cm²
The rectangle's width is 20 cm and its length is 60 cm. Thus, the area of the rectangle is 1200 square centimeters.
Explanation:We are given that the length of a rectangle is three times its width. Let's denote the width as 'w'. Consequently, the length would be '3w'.
The perimeter of a rectangle is given by the formula: 2*(length + width). Given that the perimeter is 160 cm, we can substitute our variables into the formula: 2*(w + 3w) = 160. This simplifies to 8w = 160. Therefore, the width (w) equals 20 cm, and the length is 60 cm (3w).
The area of a rectangle is calculated by multiplying its length and width. Hence, the area of our rectangle is: 60 cm * 20 cm = 1200 square centimeters.
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Help with number 3 it might be hard to read but it is possible
Answer:
This is B because as we can see the X axis increases in value to y decreases making it negetive
Answer:
the answer is B because the X axis increases in value as y decreases making it negative
Step-by-step explanation:
The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln (9t + 4), where y is the number of mowers sold. How many mowers will be sold 4.5 years after a model is introduced?
Answer:
20875
Step-by-step explanation:
Given:
y = 5500 ln (9t + 4
y is number of mowers sold
t is years after a particular model is introduced
f(t)= 9t+4
How many mowers will be sold 4.5 years after a model is introduced?
t=4.5
putting t=4.5 in given function we get,
y= 5500ln(9(4.5) +4)
= 20875.19
20875 mowers will be sold 4.5 years after a model is introduced!
A triangle has two sides of lengths 5 and 12. What value could the length of the third side be?
Answer:
Third side must be greater than 7 and less than 17
Step-by-step explanation:
If a triangle has two sides of lengths 5 and 12, the value for the length of the third side be greater than 7 and less than 17.
.
In which quadrants do solutions for the inequal
the inequality
[tex]y \leqslant \frac{2}{3}x - 4[/tex]
exist.
A.I, III, and IV
B.I, II, and III
C.I and IV
D.All four quadrants
Answer:
A.I, III, and IVStep-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
If m > 0, then the function is increased
If m < 0, then the function is decreased
We have
[tex]m=\dfrac{2}{3}>0[/tex] - the function is increased
[tex]b=-4[/tex] - the y-intercept is -4 → (0, -4)
Therefore the line passes through III, IV and I quadrant.
========================================
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
========================================
We have [tex]y\leq\dfrac{2}{3}x-4[/tex] → ≤ - shaded region below the line.
Therefore the inequal the inequality exist in I, III and IV quadrant.
Look at the picture.
The inequality exists in quadrants A.I, III, and IV.
The answer is option A
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the line
slope(m)=tan∅=y axis/x axis.
If m > 0, then the function is increased
If m < 0, then the function is decreased
=function is increased
=y-intercept is -4 = (0, -4)
Therefor the line passes through III, IV and I quadrant.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
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Please answer this correctly
Answer:
3/10
Step-by-step explanation:
because the pattern is -0.15;
9/10= 0.9
3/4= 0.75
3/5= 0.6
9/20= 0.45
3/10= 0.3
QUESTION 3
In the set of ordered pairs {(4, 7), (4, -3), (-5, -9)}, the range is:
{(4, 7), (4, -3), (-5, -9)}
{(7, 4), (-3, 4), (-9, -5)}
{-5, 4}
{-9, -3, 7
The function consists of three points, as shown in the graph below. Determine the range of the function.
graph of three points, (negative 4, negative 2), (2, 1), and (4, 1)
{-4, 2, 4}
{-2, 1}
{-2, 0, 1}
none of these
QUESTION 5
Select the table that represents the following graph.
line through the points (negative 4, 4), (negative 2, 2), (1, negative 1), (3, negative 3), and extends beyond in both directions
x y
-3 2
-1 1
0 -1
2 -3
x y
-4 3
-2 2
1 -2
3 -4
x y
-2 3
0 1
2 -3
4 -5
x y
-4 4
-2 2
1 -1
3 -3
QUESTION 6
Select the table that represents the function. f (x) = x^2 -4x
x y
-1 5
1 -3
2 -4
5 5
x y
-3 -3
-1 0
1 1
2 3
x y
-4 1
-3 2
0 3
2 4
x y
0 -5
1 -3
3 1
4 3
QUESTION 7
Which graph is represented by the following table?
x f(x)
-2 0
0 -4
1 -3
3 5
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (5, 1) and (negative 5, 1)
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (4, 4) and (negative 4, 4)
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (2, 0) and (negative 2, 0)
coordinate graph of a parabola that opens up with minimum at (0, negative 4) and goes through the points (2, 4) and (negative 2, 4)
QUESTION 8
Collette’s Superstore is having a sale on desk lamps. The following graph shows the number of desk lamps left in the store t minutes after opening. How many minutes after opening will the store only have 40 desk lamps remaining?
Graph with t in minutes on the x axis and number of desk lamps remaining on the y axis. Graph shows line hitting points (0, 120), (5, 110), (10, 100), (15, 90), (20, 80), (25, 70), and (30, 60)
30 minutes
35 minutes
40 minutes
45 minutes
3 points
Answer:
see explanation
Step-by-step explanation:
The range is the set of y- values of the ordered pairs without repeats.
3
given
(4, 7), (4, - 3), (- 5, - 9)
Then the values of y are 7, - 3, - 9
hence range is { - 9, - 3, 7 }
For
(- 4, - 2), (2, 1), (4, 1)
Then the values of y are - 2, 1, 1
Hence range is { - 2, 1 }
Could you guys please help me with number 1
Answer:
Option B 6 30 am
Step-by-step explanation:
step 1
Sum all the times
(45+5+10+30+15)=115 minutes
Convert minutes to hours
we know that
60 minutes = 1 hour
so
115 minutes=60+55= 1 hour 55 minutes
Subtract 1 hour 55 minutes from 8 25 am
(8 25 am)-(1 hour 55 minutes)=(8 25 am-1 hour)-(55 minutes)
=7 25 am-55 minutes
=7 25 am-(25+30) minutes
=(725 am-25 minutes)-(30 minutes)
7 00 am-30 minutes
=6 30 am
A car wash had to make their soap last 8 days .If they only have one-seventh of a gallon of soap ，how many should they use each day so it lasts 8 days ？
Answer:
1/56 gallon
Step-by-step explanation:
The car wash has 1/7 gallons of soap and they can use 1/8th of it each day. So, you would set up [tex]\frac{1}{7}[/tex] x [tex]\frac{1}{8}[/tex] = [tex]\frac{1}{56}[/tex].
In the diagram of circle o, what is the measure of ZABC?
O 30°
O 40°
O 50°
O 60
Answer:
30°
Step-by-step explanation:
Line AB and BC are tangents to the given circle.
[tex] \angle \: ABC = \frac{1}{2} ( 210 - 150)[/tex]
[tex] \angle \: ABC = \frac{1}{2} (60) = 30 \degree[/tex]
Alternatively, <ABC and <AOC are supplementary because AB and BC are tangents.
[tex] \angle \: ABC + 150 \degree = 180 \degree[/tex]
[tex] \angle \: ABC = 180 \degree - 150 \degree = 30 \degree[/tex]
The correct choice is A.
Answer:30
Step-by-step explanation:
Simplify 4(x - 3) - 2x + 9.
Answer:
2x-3
Step-by-step explanation:
4(x - 3) - 2x + 9
Distribute the 4
4x -12 -2x+9
Combine like terms
4x-2x -12+9
2x -3
Find the area of the image.
See the attached picture:
Which expression is equivalent to (7+4i) +(8+I)?
Answer: B) 15 + 5i
Step-by-step explanation:
(7 + 4i) + (8 + i)
Add like terms: (7 + 8) + (4i + i)
Simplify: 15 + 5i.
which set represents the domain of function shown? {(-3,6),(0,2),(4,7),(11,15)}
Answer:
{-3,0,4,11}
Step-by-step explanation:
{(-3,6),(0,2),(4,7),(11,15)}
The domain is the input values, or x coordinates
{-3,0,4,11}