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Given the line shown in the figure passes through the points (-3, -4) and (1, 2)
We will write the equation of the line.
First, we will find the slope of the line using the following formula:
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute with the given points:
[tex]m=\frac{2-(-4)}{1-(-3)}=\frac{2+4}{1+3}=\frac{6}{4}=\frac{3}{2}=1.5[/tex]The equation of the line in point-slope form will be as follows:
[tex]\begin{gathered} y+4=1.5(x+3) \\ or \\ y-2=1.5(x-1) \end{gathered}[/tex]Convert tot he slope-intercept form, so, the equation will be:
[tex]\begin{gathered} y=1.5(x+3)-4 \\ y=1.5x+4.5-4 \\ \\ y=1.5x+0.5 \end{gathered}[/tex]Now, we will check the options to see the correct equations.
So, the answer will be, we will select the options:
A. y+4 = 1.5 (x+3)
B. y = 1.5x + 0.5
C. y - 2 = 1.5 (x - 1)
Related Questions
In which pair do both decimals represent rational numbers? O A. 9.0032812373025549382... and 0.12333.. OB. 0.115 and 0.12333... O C. 3.10382947305718274... and 0.123 O D. 9.0032812373025549382... and 0.115
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Rational numbers can be formed by dividing 2 integers. It can be represented in this format x/y where y is not 0. Rational numbers, in decimal form are not repetitive and unending.
Therefore,
geometry angels.PLS HELP I ONLY HAVE Until 10:00pm on 12/1 then I get a ZERO
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We know that the angle 2 and the anlge 4 are equal because of oposite angles so:
[tex]4x-28=3x-9[/tex]and we can solve for x so:
[tex]\begin{gathered} 4x-3x=-9+28 \\ x=19 \end{gathered}[/tex]So:
[tex]\angle2=\angle4=3(19)-9=48º[/tex]Now we also know that angle 1 and 3 are equal and the sum of the internal angles must be:
[tex]\begin{gathered} 360=2(48)+2(y) \\ \frac{360-96}{2}=y \\ y=132 \end{gathered}[/tex]So angle 1 is equal to 132º
help please to find the answer of the blanks
Answers
The associated matrix associated to the linear transformation is A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex].
How to find the associated matrix associated to a linear transformation
Linear transformations are applications between two vector spaces that preserves the properties of vector addition and the product of a vector and a scalar. In this problem, we find the following linear transformation between the two bases:
W → V
(w₁, w₂, w₃, w₄) → v₁
Then, there is the following relationship:
V = A · W
Where A is the associated matrix. The matrix V has four rows and one column and the matrix W has two rows and one column. Then, by property of multiplication of matrices, the associated matrix has four rows and two columns. Then, the associated matrix is:
A = [tex]\left[\begin{array}{cc}5&-6\\1&- 3\\8&- 2\\0 & - 4\end{array}\right][/tex]
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Vector A and B are at right angles and have the same initial point. Find the magnitude and direction from vector A of the resultant vector.
Answers
We need to find the magnitude and direction from vector A of the resultanr vector.
i would appreciate so much if you could answer this and atleast explain a little how you did it (optional)
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Answer:
a.
Fee of whole band = Fee of writer + guitarist + singer
Fraction of fee of whole band = 4/12 + 1/12 + 1/12
= 4+1+1/12
=6/12
=1/2
b.
Fee of writer= 4/12 of £3000
=3000 × 4/12
= £1000
Fee of singer= 1/12 of £3000
= 3000 × 1/12
= £250
Fee of guitarist= Fee of singer
= £250
Determine whether the function has a minimum or maximum value and then find that value.()=−^2+2−7
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Given function is
[tex]f(x)=-x^2+2x-7[/tex]Now,
[tex]\begin{gathered} f(x)=-(x^2-2x+7) \\ =-(x^2-2x+1+6) \\ =-\lbrack(x-1)^2+6\rbrack \\ =-(x-1)^2-6 \end{gathered}[/tex]Being a perfect square,
[tex](x-1)^2\ge0[/tex]Therefore,
[tex]-(x-1)^2\leq0[/tex]So,
[tex]f(x)\leq-6[/tex]Theerfore, the maximum value of the given function is -6.
lan and Matthew went shopping. lan spent $20 less than twice as much as Matthew spent. In total, they spent $130.
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Using linear algebra, we concluded, the Mathew spent $50 and lan spent $80
What is Linear Algebra?
Vectors, matrices, vector spaces, and linear transformations are all topics covered in the mathematical field of linear algebra. Linear algebra is much better understood than other areas of mathematics, which are regularly stimulated by novel concepts and unresolved issues.
According to the question,
Let Mathew spent $x
lan spent = 2x - 20
Total money spent = $130
⇒ 2x - 20 + x = 130
⇒ 3x - 20 = 130
⇒ 3x = 150
⇒ x = 50
2x - 20 = 2(50) - 20
= 80
So, Mathew spent $50 and lan spent $80
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I need help with 3x-2y=24 find the y and x intercept and the slope
Answers
3x-2y=24
3x - 2y + 2y = 24 +2y Adding 2y to both sides of the equation
3x - 24 = 2y + 24 - 24 Subtracting 24 from both sides of the equation
(3x - 24)/2= 2/2y Dividing by 2 on both sides of the equation
3/2x - 12 = y
From this form of the equation we deduce the slope (coefficient of x) is 3/2 and the y-intercept is equal to -12.
To find the x-intercept, we replace y= 0 in the equation and isolate x
3/2x - 12 = 0
3/2x - 12+12 = 0+12 Adding 12 to both sides of the equation
x= 12/(3/2) Isolating x
x= 8
The x-intercept is 8
The density of copper is 9.86 g/cm".
Work out the mass of the solid copper cuboid in kg
10 cm
3 cm
5 cm
Step by step
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10x3 thousands=?How many thousands are in the answer?
Answers
Given:
[tex]10\times3\text{ thousands}[/tex]Required:
We need to find the number of thousands.
Explanation:
Multiply 10 and 3.
[tex]10\times3\text{ =30}[/tex][tex]10\times3\text{ thousands=30 thousands}[/tex]The number of thousands is 30.
Final answer:
There are 30 thousands.
Let f(x) = 2x^2 – 3 and g(x) =x+1/2Find the value of (fof )(-1)A -1B-3C 0.5D 95
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use basic trigonometric identities to simplify the expression: sin^3 (x) + cos^2 (x) sin (x)
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Given the following trigonometric expression:
[tex]sin^3x+cos^2x*sinx=?[/tex]We will simplify the expression as follows:
First, taking sin (x) as a common
[tex]=sin\text{ }x*(sin^2x+cos^2x)[/tex]Second, we will use the following trigonometric identity:
[tex]sin^2x+cos^2x=1\rightarrow(1)[/tex]Finally, substitute the trigonometric identity number (1) into the given expression
[tex]=sin\text{ }x*1=sin\text{ }x[/tex]So, the answer will be sin (x)
How would I multiply these two exponents?
Answers
The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.
Identify the reasoning that would justify each step in solving for m
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Given
[tex]\frac{3}{4}(m-500)=8000+4000[/tex]Notice that the right side of the equation consists of like terms (they do not depend on m). Therefore, Step 1 goes with Combine like terms.
Then,
[tex]\frac{3}{4}(m-500)=\frac{3}{4}*m+\frac{3}{5}(-500)=\frac{3m}{4}-375\rightarrow\text{ distributive property}[/tex]Step 2 applies the distributive property.
As for the properties of the equality,
[tex]\begin{gathered} a=b\Rightarrow a+c=b+c\rightarrow\text{ addition property of equality} \\ a=b\Rightarrow ac=bc\rightarrow\text{ multiplication property of equality\rbrack} \\ a=b\Rightarrow\frac{a}{c}=\frac{b}{c}\rightarrow\text{ division property of inequality} \end{gathered}[/tex]Thus, steps 3 through 5 are:
Step 3 - Addition property
Step 4 - Division property
Step 5 - Multiplication property
Hello I need help on this math questionYou can zoom in the picture
Answers
In this problem, we have the transformation
A(-3,4) -------> A'(-15,20)
so
The rule is
(x,y) -----> (5x,5y)
the answer is option b
The box and whisker plot summarizes the data collected on the number of Broadway tickets sold and the actual number of attendees at the plays. Which statement is TRUE about the statistics?
A.) The majority of the data values fall in the upper quartile for both sets of data.
B.) There were fewer tickets purchased than people attending the plays.
C.) The medians of the populations are the same.
D.) There were fewer attendees than purchased tickets.
The plot:
Answers
The true statement based on the information is that D. There were fewer attendees than purchased tickets.
Whet is a box and whisker plot?A box and whisker plot is a graphical representation of variance in a set of data. A histogram analysis is sufficient in most circumstances, but a box and whisker plot can provide more detail while allowing different sets of data to be displayed in the same graph.
The box and whisker figure highlights data on the number of Broadway tickets sold and actual attendance at the performances. In this case, the graph shows that the number of tickets are more.
Therefore, the correct option is D.
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Name the point that lies on this line: y = 2 + 5(x + 7)
Answers
(1, 42)
1) Since we have an equation of the line y = 2 + 5(x + 7) let's find one point that ∈ to this line.
2) Let's plug into that for x, the value of x=1
y= 2+ 5(1+7)
y= 2 +5(8)
y= 2 +40
y= 42
3) So one of the points that lie on this line is (1, 42) i.e. belong to that line.
if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3
Answers
Answer:
18
Step-by-Step Explanation:
[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]
The balance of an account after t years can be found using the expression 4,500(1.75)^t where the initial balance was $4,500. By what percent does the account increase annually?
Answers
Solution
The Amount after t years is given by
[tex]A(t)=4500(1.75)^t[/tex]The Percentage annual increase is
[tex]\begin{gathered} \frac{A(1)-A(0)}{A(0)}\times100\% \\ \Rightarrow\frac{4500(1.75)-4500}{4500}\times100\% \\ \Rightarrow0.75\times100\%=75\% \end{gathered}[/tex]Hence, the account increase 75% annually
In August, a giant panda named Lucky was born at the Silver City Zoo. In September, Lucky
weighed 3.07 pounds. Today, Lucky is weighed again and he is heavier than before. Now
Lucky weighs 10.81 pounds.
Use an equation to find the amount of weight Lucky gained between September and today.
Answers
Using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.
What is a Linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.So, in September, Lucky weighed = 3.07 pounds
Today's Lucky weighed = 10.81 poundsThe equation form is:
Let x = weight to find Lucky3.07 + x = 10.81This is a linear equationSo, now solve this linear equation and find 'x' as follows:
3.07 + x = 10.81=> x = 10.81 - 3.07=> x = 7.74Therefore, using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.
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a real life situation for -2 × 4
Answers
How many miles of gas does my car travel if it used 2 gallons of gas with a speed of 4 mi/h?
What is 30 percent of 120?
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Explanation:
30/100 times 120 = 36
Answer:
30 percent of 120 is 36
i need help asp ;-;
Which of the following values is less than −|58|?
A. −48
B. 68
C. −68
D. 48
Answers
Answer:
C. -68
Step-by-step explanation:
Using absolute value symbols, it makes any negative number a positive. But, the negative sign is outside the absolute value signs, making the number -58. -68 is the only number less than -58.
Using FUNCTION NOTATION, assume you are given the function: y = 3x - 2. This can be rewritten as ________ = 3x - 2, since y can be replaced with _______.
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The complete statement is:
This can be rewritten as _f(x)_ = 3x - 2, since y can be replaced with _f(x)__.
How to use function notation?A general relation is written as:
y = something that depends of x.
This is a relation that relates the variable y with the variable x, where we define x as the input and y as the output.
If this is a function, we can use the notation:
y = f(x).
(or any letter of x, f(x) is the most common notation used)
in this case, we have:
y = 3x - 2
And in function notation, this will be writen as:
f(x) = 3x - 2
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two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90.write and solve a system of equations to determine the the price of one plain pizza(only an algebraic solution can receive full credit.)
Answers
Let:
x = Cost of one plain pizza
y = Cost of one soda
two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. so:
[tex]\begin{gathered} x+2y=15.95_{\text{ }} \\ \end{gathered}[/tex]later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90. so:
[tex]3x+5y=45.90[/tex]Let:
[tex]\begin{gathered} x+2y=15.95_{\text{ }}(1) \\ 3x+5y=45.90_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for x:
[tex]x=15.95-2y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 3(15.95-2y)+5y=45.90 \\ 47.85-6y+5y=45.90 \\ -y=-1.95 \\ y=1.95 \end{gathered}[/tex]Replace the value of y into (3):
[tex]\begin{gathered} x=15.95-2(1.95) \\ x=12.05 \end{gathered}[/tex]Therefore, the price of one plain pizza is $12.05
1. What is the reciprocal of 5? 6 Show your work below! (click "Show Work Type a response OD
Answers
Answer:
1/5
Step-by-step explanation:
a reciprocal is the multiplicative inverse
Answer:
The reciprocal of 5 is 1/5
Step-by-step explanation:
The reciprocal of a number is the fraction flipped upside down
6/1 = 1/6
⇒ 5/1 = 1/5
Help me rewrite this problem to satisfy the provided boxes please
Answers
EXPLANATION
Since we have the expression:
Removing the parentheses:
[tex]5x^2+6x+5+6x^2-6x-5[/tex]Rearranging terms:
[tex]5x^2+6x^2+6x-6x+5-5[/tex]Adding like terms:
[tex]11x^2+0x+0[/tex]The final expression is as follows:
[tex]undefined[/tex]wildlife shelter in North Carolina is home to native species of birds. mammals, and reptiles. If cat chow is sold in 20 lb bags, what is the least number of bags of cat chow needed for one year at this shelter
Answers
At least 26 bags of cat chow is required for a period of one year to fulfil the demand at the wildlife shelter in North Carolina
Quantity of cat chow sold in each bag = 20 lb
Consumption in lb of cat chow per week in the wildlife shelter = 10 lb
Number of weeks in a year = 52 weeks
The total quantity of cat chow required for 52 weeks = Weekly consumption of cat chow*Number of weeks
= 10*52
= 520 lb
Number of bags required = Toal quantity of cat chow required for 52 weeks/ Quantity of cat chow sold in each bag
= 520/20
= 26 bags
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The area of a window measures 336 Square inches. If the window is 16 inches wide. How long is the window?
Answers
The window has a length of 21 inches
How to determine the length of the window?From the question, we have the following parameters
Area of the window = 336 square inches
Width of the window = 16 inches
The area of the window is the product of its dimensions
So, we have
Area = Width of the window x Length of the window
Substitute the known values in the above equation
So, we have the following equation
336 = 16 * Length
Divide both sides by 16
Length = 21
Hence, the length is 21 inches
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Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP HELP I WILL GIVE BRAINLIEST AND 100 POINTS
!!
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The solution for the inequality is 11.746 ≤ x ≤ 24.44
Kali earns a 15.75 plus a flat fee of 50 from her job.
She wants to earn between 200 and 400.
Let 'x' denote her earning potential.
Then the inequality for her earning potential is given by,
200 ≤ 15.75x + 50 ≤ 400
We solve this inequality for x.
Subtract 50 from the inequality,
⇒ 200 -15 ≤ 15.75x ≤ 400 -15
⇒ 185 ≤ 15.75x ≤ 385
Divide by 15.75,
⇒ 11.746 ≤ x ≤ 24.44
is the solution for the inequality.
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