The system of equations:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]This comes from the fact that if we multiply the first equation by 3 then we have:
[tex]3x-18y=12[/tex]But this clearly contradicts the second one. Then the system has no solutions.
a.
To find a system with one solution we only have to change one of the coefficients of the equation. If we change the first x coefficient from 1 to 2. then we have the system:
[tex]\begin{gathered} 2x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]which has one solution.
b.
To find a system with an infinite number of solutions we can change the constant of the second equation to 12, then:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=12 \end{gathered}[/tex]then if we multiply the first by 3 then we have the second one, therefore the equations are the same and the system will have and infinite number os solutions.
Solve: x^3= -65 This is for homework
Step 1
Solve the equation by graphing
You can rewrite the equation as
[tex]x^3+65=0[/tex]step 2
Using a graphin calculator as Desmos
x=-4.021
The solution is x=-4.021
-
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12y-2x = 108
Answer: y= x/6+9
Step-by-step explanation:
z divided by 13=28 i need the answers this is hard for me
Answer:
364
Step-by-step explanation:
z/13 = 28
z = 13 x 28
z = 364
need to show 1,242 ÷ 23 = and 732 x 268 = show answers on graph
1,242 ÷ 23 = 54
and
732 x 268 = 196, 176
Preform the indicated Operation g(n)=2n^2-4nh(n)=n-1find g(h(1-b))
GIven:
The expressions are given as,
[tex]\begin{gathered} g(n)=-2n^2-4n \\ h(n)=n-1 \end{gathered}[/tex]The objective is to find g(h(-1-b)).
Explanation:
To find h(-1-b):
The value of h(-1-b) can be calculated by replacing the n with (-1-b) in the expression of h(n).
[tex]\begin{gathered} h(n)=n-1 \\ h(-1-b)=-1-b-1 \\ h(-1-b)=-2-b\text{ . . . . . . (1)} \end{gathered}[/tex]To find g(h(-1-b)):
The value of g(h(-1-b)) can be calculated by replacing the n with h(-1-b) in the expression g(n).
[tex]\begin{gathered} g(n)=-2n^2-4n \\ g(h(-1-b))=-2(-2-b)^2-4(-2-b)\text{ . . . . (2)} \end{gathered}[/tex]On further solving the equation (2),
[tex]undefined[/tex]The graph shows a relationship between two quantities.ДУ200018001600140012001000800600400200ХOd-8 -6 4-2 0 2 4Which equation best represents the relationship between the variables?
First let't find the slope
Pick any two point and locate its coordinate
(0, 1500) and (2, 1800)
x₁ = 0 y₁=1500 x₂=2 y₂=1800
substitute the values into the formula below to find the slope
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{1800-1500}{2-0}[/tex][tex]=\frac{300}{2}=150[/tex]The y-intercept(b) of the graph is b=1500
Substitute the values of the slope and intercept into y=mx +b
This gives the equation of the graph.
That is:
[tex]y=150x\text{ + 1500}[/tex]A linear function contains the following points.
X
y
What are the slope and y-intercept of this function?
A. The slope is 4.
The y-intercept is (0, -1).
5
B. The slope is.
The y-intercept is (0, -1).
C. The slope is.
The y-intercept is (-1,0).
D. The slope is.
0
-1
The y-intercept is (0, -1).
5
3
The slope will be 4/5.
And, The y - intercept will be (0, - 1)
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The points are,
(0, - 1) and (5, 3)
Now,
Since, The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is;
m = (y₂ - y₁) / (x₂ - x₁)
So, The slope of the line passing through the points (0, - 1) and (5, 3) is;
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-1)) / (5 - 0)
m = (3 + 1) / 5
m = 4/5
And, The y - intercept is at x = 0
Thus, The slope will be 4/5.
And, The y - intercept will be (0, - 1)
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What is the yintercept of O A. (0,0) O B. (0,1) O C. (1,0) OD (9)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y-intercept = ?
f(x) = (1/2) ^ x
Step 02:
y-intercept :
x = 0
[tex]\begin{gathered} y\text{ = (}\frac{1}{2})^0=1 \\ \end{gathered}[/tex]The answer is:
y-intercept
(0 , 1)
Graph the linear function g(x) = -4+7xGraph the linear function G (x equals negative 4 + 7x
Given a function,
[tex]g(x)=-4+7x[/tex]At x = 0,
[tex]g(0)\text{ = -4}[/tex]At g(x) = 0,
[tex]\begin{gathered} -4+7x=0 \\ x=\frac{4}{7} \end{gathered}[/tex]At x= 1,
[tex]g(1)\text{ = 3}[/tex]Therefore, the required graph is,
hXL for School: Practice & Problem Solving 5.2.PS-19 Question Help Equivalent ratios can be found by extending pairs of rows or columns in a multiplication table. Write 3 3 ratios equivalent to using the multiplication table. 5 Click the icon to view the multiplication table. 3 Find three ratios that are equivalent to 5 12 6 4 IA. B. OC. 20 10 6 15 15 9 OD OE. F. 9 30 15 Click to select your answer(s) and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 7 of 12 Back Next >
To find equivalent ratios to 3/5, we just have to multiply each part by 4, 2, and 3.
[tex]\begin{gathered} \frac{3\cdot4}{5\cdot4}=\frac{12}{20} \\ \frac{3\cdot2}{5\cdot2}=\frac{6}{10} \\ \frac{3\cdot3}{5\cdot3}=\frac{9}{15} \end{gathered}[/tex]Hence, the right answers are A, B, and F.Graph each line given the slope and y-intercept.Label each one
A)
Equation:
[tex]y=\frac{1}{3}x-3[/tex]B)
Equation:
[tex]y=0.5x+1.5[/tex]C)
Equation:
[tex]y=-2x-5[/tex]D)
Equation:
[tex]y=\frac{3}{2}x+2[/tex]Write down the expansion of (2x+y)^4
Use the following formula:
[tex](a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex]Let:
[tex]\begin{gathered} a=2x \\ b=y \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} (2x+y)^4=(2x)^4+4(2x)^3y+6(2x)^2y^2+4(2x)y^3+y^4 \\ (2x+y)^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4 \end{gathered}[/tex]1) The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent? ) The variable p represents the ticket price The number 5 represents the number of tickets Today there is a discount of $10 off a purchase of 5 or more movie tickets. Which expression can you use to find the total price of 5 movie tickets after the discount? 10p + 5 5p - 10 10p - 5 5p + 10
Solution
The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent?
The variable p represents the ticket price The number 5 represents the number of tickets
For this case the correct answer would be:
5p -10
The coefficient 5 represents the price of 1 ticket
for the next part the answer would be:
7 +3x
And the last part
2/3 y -6
How do you figure out what the order pairs are in this equation? 2x-2=y
Equations express relationships between variables and constants. The solutions to two-variable equations consist of two values, known as ordered pairs, and written as (a, b) where "a" and "b" are real-number constants. An equation can have an infinite number of ordered pairs that make the original equation true.
Here, the given equation is,
[tex]2x-2=y[/tex]Rewriting this equation in terms of x, we have,
[tex]\begin{gathered} 2x-2=y \\ 2x=y+2 \\ x=\frac{y+2}{2} \end{gathered}[/tex]So, now creating a table, with the values, we get the ordered pair. For example, let us take x as 1, then ,
[tex]\begin{gathered} 1=\frac{y+2}{2} \\ 2=y+2 \\ y=0 \end{gathered}[/tex]So, (1,0) is an ordered pair in this equation.
If x =0,
[tex]y=0-2=-2[/tex]So the pair is, (0,-2).
7 m The side lengths of the base of a triangular prism are 7 meters, 5 meters, and 8 meters. The height of the prism is 12.5 meters. 12.5 m 6 m What is the lateral surface area of the prism in square meters? 5 m
Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]Therefore, the lateral surface area in square meters is 225
Suppose a spherical snowball is melting and the volume is decreasing at a constant rate, changing from 12 in^3/min to 10in^3/min in 30min. How fast is the radius changing when the volume is 8in^3/min? (Answer in terms of pi)
The radius changing when the volume is 8in^3/min by: -512π /30 in³ /min.
How to find the radius?First step is to find the radius changing over time at a constant rate
dr/dt = 10-12 /30
= -2/30 in/min
Now let find the how fast is the radius changing using this formula
dV/dt = 4πr²(dr/dt)
Where,
r =8
Hence,
dV/dt = 4π (8in)² × -2/30 in/min
dV/dt = 4π (64in) × -2/30 in/min
dV/dt = -512π /30 in³ /min
Therefore the change in radius is -512π /30 in³ /min.
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what does 1,580÷25=I know the answer, I need to show how I got it.
In the image below ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯∥⎯⎯⎯⎯⎯⎯⎯⎯⎯LM¯∥OP¯. Given the lines are parallel, ∠≅∠∠LMN≅∠PON because and that ∠≅∠∠LNM≅∠ONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = .
Given:
Required:
We need to answer the questions
Explanation:
Angle LMN and angle PON are the congruent because both are alternate angles
Now angle LNM and angle ONP are also congruent because those two triamgles are similar and both are internal angles
Now to find the value of x
[tex]\begin{gathered} \frac{NP}{MN}=\frac{NO}{LN} \\ \\ \frac{20}{x+6}=\frac{15}{2x-3} \\ \\ 40x-60=15x+90 \\ 25x=150 \\ x=6 \end{gathered}[/tex]Final answer:
x=6
Find the reference angle for a rotation of 129º.
In order to find a reference angle, we need to find the smallest possible angle formed between the x-axis and the terminal line of the given angle, going either clockwise or counterclockwise.
Since the given angle is 129°, and 90<129<180, it will look something like this:
As we can see, the reference angle will be
[tex]180-129=51[/tex]so it will be 51°.
determine the type and key parts of the graph of the second equation
ANSWER
[tex]\begin{gathered} \left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6 \\ major\text{ axis;vertical} \\ minoraxis;horizontal \end{gathered}[/tex]EXPLANATION
The second equation;
[tex]\frac{x^2}{9}+\frac{y^2}{36}=1[/tex]It is an Elipse.
Ellipse standard equation;
[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]Rewrite the given equation in the form of the standard equation;
Hence, we have;
[tex]\frac{\left(x-0\right)^2}{3^2}+\frac{\left(y-0\right)^2}{6^2}=1[/tex]Therefore the ellipse properties are;
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6[/tex]Major axis is;
[tex]\begin{gathered} 2a \\ =2\times6=12 \end{gathered}[/tex]Minor axis is;
[tex]\begin{gathered} 2b \\ =2\times3=6 \end{gathered}[/tex]How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10?
First, we have to find the height using the following equation:
[tex]h\text{ = }b\sin (B)[/tex][tex]h\text{ = 10}\times\sin (\frac{\pi}{6})=5[/tex]We have found the height. If h < b < a, we can have only one triangle. That is the case. So the answer will be 1 triangle.
Determine the smallest integer value of x in the solution of the following inequality.3x + 4> -18
We have the following inequality:
3x + 4 > -18
Subtracting 4 from both sides we got:
3x > -22
Dividing both sides by 3 we got:
x > -22/3
Since -22/3 is between -7 and -8 and x must be equal or greater than -22/3, the smallest integer value in the solution of the inequality is -7 (note that -8 isn't part of the solution)
It is equally probable that the pointer on the spinner Shown will land on any one of the eight regions number one through eight if the pointer lands on the borderline spin again. find the probability that the pointer will stop on an even number or number greater than three
SOLUTION
The even numbers here are 2, 4, 6 and 8. That is 4 numbers.
The numbers greater than 3 are 4, 5, 6, 7, and 8, that is 5 numbers.
And we have a total of 8 numbers.
Let P(A) be the probability of the pointer landing on an even number
Let P(B) be the probability of the pointer landing on a number greater than 3
Let P(A or B) be the probability that the pointer stops on an even number or number greater than three
From the probability formula,
[tex]P(\text{A or B) = P(A) + P(B) - P(A}\cap B)[/tex][tex]\text{ P(A}\cap B)\text{ means probability of A and B}[/tex]Hence
[tex]\begin{gathered} P(A)=\frac{4}{8} \\ P(B)=\frac{5}{8} \end{gathered}[/tex][tex]\begin{gathered} \text{ For P(A}\cap B)\text{ we can s}ee\text{ that betwe}en\text{ } \\ \text{the even numbers 2, 4, 6, 8 and } \\ n\text{umbers greater than 3, which are 4, 5, 6, 7, 8} \\ \text{what is common is 4, }6,\text{ 8} \\ So,\text{ } \\ \text{P(A}\cap B)=\frac{3}{8} \end{gathered}[/tex]Therefore, P(A or B) becomes
[tex]\begin{gathered} \frac{4}{8}+\frac{5}{8}-\frac{3}{8} \\ \frac{4+5-3}{8} \\ \frac{6}{8} \\ =\frac{3}{4} \end{gathered}[/tex]How to find the inverse of the matrix Question number 19
Okay, here we have this:
We need to find the inverse of the matrix, let's do it:
[tex]\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {1} & {-1} \\ {1} & {4} & {0}\end{bmatrix}[/tex]For that we are going to make the augmented form with the identity matrix and convert the original matrix into the identity:
[tex]\begin{gathered} \begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ -1 & 1 & -1 & | & 0 & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix} \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix}\text{ }R_2\leftarrow R_2+\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 2 & -\frac{1}{2} & | & -\frac{1}{2} & 0 & 1\end{pmatrix}\text{ }R_3\leftarrow R_3-\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -\frac{1}{6} & | & -\frac{5}{6} & -\frac{2}{3} & 1\end{pmatrix}R_3\leftarrow R_3-2/3R_2 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_3\leftarrow-6R_3 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow R_2+\frac{1}{2}R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow\frac{1}{3}R_2 \\ =\begin{pmatrix}2 & 0 & 0 & | & -8 & -8 & 10 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-4R_2 \\ =\begin{pmatrix}1 & 0 & 0 & | & -4 & -4 & 5 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow\frac{1}{2}R_1 \end{gathered}[/tex]Finally the inverse is on the right side of the augmented matrix:
[tex]=\begin{pmatrix}-4 & -4 & 5 \\ 1 & 1 & -1 \\ 5 & 4 & -6\end{pmatrix}[/tex]between 1993 and 1996 there where 6545 injured horses find the ratio of injuries per year
First, we have to know the total number of years between 1993 and 1996. If we subtract, we find the there are 3 years in between.
Now, we divide the total number of injured horses by the total numbers of years.
[tex]r=\frac{6545}{3}=2,181.7[/tex]However, we can't round to 2,182 because horses are not incomplete.
Therefore, the total number of injured horses per year is 2,181.Every rational number is also an integer.TrueorFalse
Every rational number is also an integer.
we have that
The rational numbers include all the integers
so
the answer is trueWhich quadrant includes every points with a negative x-coordinate and a negative y-coordinateA) Quadrant IVB) Quadrant IC) Quadrant IID) Quadrant III
Hello!
Let's analyze the points from each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
So, the answer is:
Alternative D) Quadrant III.
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a blue sock? Round your answer to the nearest tenth.15.4%25%22%15.38%
The formula for determining probability is expressed as
Probability = number of favorable outcomes/number of total outcomes
number of favorable outcomes = number of blue socks = 2
number of total outcomes = number of all socks = 3 + 4 + 2 + 4 = 13
Thus, the probability of picking a blue sock is
2/13 = 0.1538
Converting to percentage, we would multiply by 100. We have
0.1538 x 100
= 15.38%
How do I simplify -88/4
What is the answer
(3t/t^5)^-5
The resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
What exactly are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.To evaluate an algebraic expression, you must substitute a number for each variable and perform the arithmetic operations.The previous example's variable x is equivalent to 6 because 6 plus 6 = 12.If we know the values of our variables, we can replace the original variables with those values before evaluating the expression.So, solve the expression as follows: (3t/t^5)^-5
Apply exponent rule:
(3t/t^5)^-51/((3t/t^5)^5)Simplify as shown:
(3t/t^5)^5: 243/t²⁰1/243/t²⁰Apply function rule:
t²⁰/243Therefore, the resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
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