To find the slope and y-intercept of the equation -y = -0.9x + 4, multiply both sides by -1 to get y = 0.9x - 4, revealing a slope of 0.9 and a y-intercept of -4.
Explanation:To find the slope and y-intercept of the graph -y = -0.9x + 4, we first need to rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By multiplying both sides of the equation by -1, we get y = 0.9x - 4. Here, it's clear that the slope (m) is 0.9 and the y-intercept (b) is -4.
This means that for every increase of 1 on the horizontal axis (x), there is a rise of 0.9 on the vertical axis (y). Additionally, the point where the line intersects the y-axis is at y = -4.
What is the range of the given function?
O {x|x = -5, 1, 4, 6}
O {yl y=-7,-1, 0, 9}
O {x|x = -7, -5, -1,0, 1, 4, 6, 9}
O yly=-7, -5, -1, 0, 1, 4, 6, 9}
|__x__|__y__|
|_-5__|__9__|
|_1___|__0__|
|_4___|__-7_|
|_6___|__-1_|
(table above^)
Answer:
Step-by-step explanation:
we know that
The Domain of the function are all the values of x that can take the function
in this problem the domain is
The Range of the function are all the values of y that can take the function
in this problem the range is
therefore
{y | y = –7, –1, 0, 9} baaaam
know my brain hurts i hope this helped because i really tried haha sorry if it doesnt
LOOK AT PICTURE ↓↓↓↓↓↓↓↓↓↓↓
Answer:
2/5x - 2y≥ 2
Step-by-step explanation:
see attachment
Four ounces of oregano and 2 ounces of garlic powder are mixed to create a poultry seasoning. Oregano costs $4 per ounce, and garlic powder costs $3 per ounce. The table shows the costs of the ingredients.
What is the value of y in the table?
THE ANSWER IS 6
Answer:
y = $6
Step-by-step explanation:
In the image below, the table of your question is attached
Based on the information presented in the table.
1 ounce of oregano costs $4
Because there are 4 ounces, this means that
x = 4*($4) = $16
1 ounce of garlic powder $3
Because there are 2 ounces, this means that
y = 2*($3) = $6
Total cost of the ingredients = x+y = 22 $
Emma gets paid $5,000 per month.
1,250 a month for rent. What percent of her monthly pay goes to rent?
Answer:
25 percent.
Step-by-step explanation:
1,000 would be 20% of 5,000
250 is 5% of 5,000
20+5=25
25% of Emma's monthly income goes towards rent.
To calculate the percentage of Emma's monthly pay that goes towards rent, we need to divide the amount spent on rent by the total monthly income, and then multiply that result by 100 to convert it to a percentage.
Emma spends $1,250 a month on rent and earns $5,000 per month. The calculation is as follows:
Divide the monthly rent by the monthly income: $1,250 / $5,000 = 0.25.
Convert the decimal to a percentage: 0.25 * 100 = 25%.
Therefore, 25% of Emma's monthly income goes towards rent.
15 POINTSPLEASE HELP WITH MY MATH PROBLEM
Answer:
Another point is (3,1) and the vertex is (0,0)
Step-by-step explanation:
The vertex is still (0,0) since the parabola has only been stretched some way and not shifted from the parent function f(x)=x^2.
Enter in any x you like like 3 (I chose 3 because I see I'm going to multiply by 1/3). Anyways
g(3)=(1/3*3)^2=(1)^2=1 so another point on the parabola is (3,1)... Now just use the fact that all parabolas are symmetrical to graph it.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph with the function it represents
Graph Function
A f(x) = x
B f(x) = x^2
C f(x) = x^3
D f(x) = √(x - 1)
E f(x) = 1/x
To match each graph with the function it represents, we need to consider the shape of the graph and the equation of the function.
Graph A: This graph is a straight line that passes through the origin and has a slope of 1.
This indicates that the function is linear and has the following equation:
f(x) = x
Graph B: This graph is a parabola that opens upwards and has its vertex at the origin.
This indicates that the function is quadratic and has the following equation:
f(x) = x^2
Graph C: This graph is a cubic function that opens upwards and has a point of inflection at the origin.
This indicates that the function has the following equation:
f(x) = x^3
Graph D: This graph is a square root function. It has a vertical asymptote at x = 1 and a horizontal asymptote at y = 1.
This indicates that the function has the following equation:
f(x) = √(x - 1)
Graph E: This graph is a reciprocal function. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
This indicates that the function has the following equation:
f(x) = 1/x
When x = 5, the value of the expression 20/-25+ –2(x – 10) is a.–21 b. –9 c. 9 d. 19
Answer:
I get 9.2 but if the answer is rounded then 9 should be correct
Step-by-step explanation:
Plug in the 5 and solve.
Hope this helps a bit,
Flips
Witch of these has a slope of -3/4 and a y intercept of 3/2
Answer:
See explanation. (Also you can write an equation several different ways so without the choices I cannot tell you which)
Step-by-step explanation:
Slope-intercept form is y=mx+b
So one way to write the equation is y=-3/4 x +3/2
There are more ways to write it.
Every line about to write is a way to write it.
Multiply both sides by 4: 4y=-3x+6
Add 3x on both sides: 3x+4y=6
Subtract 6 on both sides: 3x+4y-6=0
There are a lot of ways to write an equation like this.
To better assist you I would need to see options.
Write y + 1 = –2x – 3 in standard form.
Question 8 options:
a)
x + 12y = −2
b)
2x + y = -4
c)
-2x-y = 4
d)
y = -2x-4
Answer:
b) 2x + y = -4
Step-by-step explanation:
To go from the Point-Slope Formula [y - y₁ = m(x - x)₁] to the Slope-Intercept Formula [y = mx + b], move -1 to the RIGHT side of the equivalence symbol to get this: y = -2x - 4. Although this is a correct answer choice, this is NOT what the question is looking for because you have to go an extra step further, Standard Formula. To go from the Slope-Intercept Formula to the Standard Formula [Ax + By = C], move 2x to the LEFT side of the equivalence symbol, and you will end up with this: 2x + y = -4. So, your answer is b).
Answer:
b) [tex]2x+y=-4[/tex]
Step-by-step explanation:
We have been given an equation [tex]y+1=-2x-3[/tex]. We are asked to write our given equation in standard form.
We know that standard form of an equation is [tex]Ax+By=C[/tex].
Let us convert our given equation in standard form as:
[tex]y+1-1=-2x-3-1[/tex]
[tex]y=-2x-4[/tex]
[tex]y+2x=-2x+2x-4[/tex]
[tex]2x+y=-4[/tex]
Therefore, the standard form of our given equation would be [tex]2x+y=-4[/tex].
Write the equation of the line that passes through the given points (2,3) (2,5)
Answer:
x = 2
Step-by-step explanation:
Note that the coordinates (2, 3) and (2, 5) both have the same x- coordinate.
This indicates that the points lie on a vertical line parallel to the y- axis.
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through.
In this case the x- coordinate is 2, hence the equation of the line is
x = 2
What is the equation of the line perpendicular to y=2/3x+1 that passes through the point (12, –6)?
A. 3x + 2y = 24
B. 3x + 2y = 6
C. 2x – 3y = 42
D. 2x – 3y = –48
Answer:
Step-by-step explanation:
Start with y=(2/3)x+1 . The slope of any line perpendicular to this is the negative reciprocal of 2/3: -3/2.
Then we have y = mx + b, which, using the given data (12, -6), becomes
-6 = (-3/2)(12) + b, or
-6 = -18 + b, so b = 12 and y = (3/2)x + 12.
We must put this into standard form. Mult. all three terms by 2:
2y = 3x + 24
At which root does the graph of f (x) = (x - 5)3 (x + 2)2 touch the xaxis
ANSWER
x=-2
EXPLANATION
The given polynomial function is:
[tex]f(x) = {(x - 5)}^{3} {(x + 2)}^{2} [/tex]
The polynomial has two factors, one with an odd multiplicity which is
[tex] {(x - 5)}^{3} [/tex]
and the other with an even multiplicity which is
[tex] {(x + 2)}^{2} [/tex]
The graph does not cross the x-axis at where the multiplicity is even.
Therefore the graph touches the x-axis at
[tex]x = - 2[/tex]
We got this by solving
[tex]{(x + 2)}^{2} = 0[/tex]
Quadrilateral PERK has vertices at P(4,4), E(12,4), R(10,−2), and K(2,−2). Find the vertices of the quadrilateral after a dilation with scale factor 32.
These are the options. 1,2,3, and 4.
1. P'(8/3, 8/3), E'(8, 8/3), R'(20/3, −4/3), and K'(4/3, −4/3)
2. P'(−6, −6), E'(−18, −6), R'(−15, 3), and K'(−3, 3)
3. P'(6, 6), E'(18, 6), R'(15, −3), and K'(3, −3)
4. P'(−8/3, −8/3), E'(−8, −8/3), R'(−20/3, 4/3), and K'(−4/3, 4/3)
Answer:
option 3
Step-by-step explanation:
Dilation by a scale factor of 3/2 multiplies each of the coordinate values by 3/2. For example, P' = (3/2)P = (3/2)(4, 4) = (6, 6).
The only choice with coordinates matching these is option 3.
What is the least common multiple of 16 and 3?
Answer:
48
Step-by-step explanation:
Multiply 16 and 3 together! This isn't usually the case but for this question it is. Hope this helps and have a nice day!
Answer:
48
explanation:
prime factorisation of 16 and 3.
[tex]16 = 2 \times 2 \times 2 \times 2 = {2}^{4} [/tex]
[tex]3 = 1 \times 3[/tex]
taking the greatest power from both the equation for multiplication
[tex]2 \times 2 \times 2 \times 2 \times 3 = 48[/tex]
hence the L.C.M of 16 and 3 is "48"
What’s the volume??
Answer:
5/96.
Step by Step explanation:
The volume = width * length * height
= 1/3 * 5/8 * 1/4
= 1*5*1 / 3*8*4
= 5 / 96.
=
On a number line 2.49 would be located where?
Answer:
In the middle of 2 and 3.
Step-by-step explanation:
2 < 2.49 < 3.
Therefore, 2.49 would be located in the middle of 2 and 3, assuming that the scale is 1.
Hope this helps!
It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.
What is the number line?
In math, a number line can be described as a straight line with numbers positioned at equivalent intervals or parts along its length. A number line can be expanded infinitely in any direction and exists usually expressed horizontally.
It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.
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Which equations represent the line that is perpendicular to the line 5x – 2y = -6 and passes through the point (5,-4)?
Check all that apply.
y=-x-2
L2x + 5y = -10
U 2x - 5y = -10
y+4 = (x - 5)
y-4 = (x + 5)
Answer:
None of these apply
Step-by-step explanation:
Step 1: Bring the equation into the form of y=mx+c
5x-2y = -6
-2y = -6-5x
y = 6+5x
2
y = 5/2x + 3
Step 2: Identify the slope (m)
Slope is the number with x (5/2)
Step 3: Find slope of the perpendicular line.
Slope of line 2 (perpendicular line) = -1/slope of line 1
m2 = -1/m1
m2 = -1/5/2
m2 = -2/5
Step 4: Find the y-intercept of the perpendicular line,
slope = -2/5
x and y coordinates = (5, -4)
y = mx + c
-4 = -2/5 (5) +c
-4 + 2 = c
c = 2
Step 5: Form equation of perpendicular line
y = mx + c
y = -2/5x + 2
Step 6: Check all equations and match with y = -2/5x + 2
a) y = x - 2 (It does not apply because this equation does not have a slope and y-intercept is not the same).
b) 2x + 5y = -10
5y = -10 -2x
y = -2/5x - 2 (This does not apply because the y-intercept does not match-it should be +2))
c) 2x - 5y = -10
-5y = -10 - 2x
y = 2/5x + 2 (This does not apply because the slope does not match-it should be -2/5)
d) y + 4 = (x - 5)
y = x-5-4
y = x-9 (This does not apply as the slope and y - intercept do not match)
e) y - 4 = (x + 5)
y = x + 9 (This does not apply as the slope and y - intercept do not match)
!!
Evaluate ƒ(x) when x = 10
Answer:
f(x) = 10² + 3 = 100 + 3 = 103
Final answer:
Without a specific definition of ƒ(x), we can't provide a precise evaluation at x = 10. However, if ƒ(x) is a constant function such as ƒ(x) = 20 for the range of 0 to 20, then ƒ(10) would be 20.
Explanation:
To evaluate the function ƒ(x) when x = 10, we need to know the specific form of the function. However, based on the information provided, which seems fragmented and from different contexts, I can assume that ƒ(x) is defined for certain ranges. There’s reference to a horizontal line graph representation of a function, which suggests that ƒ(x) could potentially be a constant function within a certain range. If the function ƒ(x) is indeed a constant function, such as ƒ(x) = 20 for 0 ≤ x ≤ 20, then evaluating it at x = 10 would simply give the constant value, which is 20.
From the other contexts provided, it's implied that there could be scenarios where ƒ(x) represents different mathematical or physics concepts, such as force, probability distribution, or equations of motion. Without a direct specification of ƒ(x) for the x value in question, the remaining information cannot be used to definitively evaluate ƒ(x) at x = 10.
30 points.Please answer with explanation
Answer:
m∠1 = 142
Step-by-step explanation:
38 + m∠1 = 180
m∠1 = 142
The tables represent two linear functions in a system,
What is the solution to this system?
(1,0)
(1,6)
(8, 26)
(8, -22)
Answer:
(8, -22)Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
First table:
(-4, 26), (0, 10) → b = 10
[tex]m=\dfrac{10-26}{0-(-4)}=\dfrac{-16}{4}=-4[/tex]
[tex]\boxed{y=-4x+10}[/tex]
Second table:
(-4, 14), (0, 2) → b = 2
[tex]m=\dfrac{2-14}{0-(-4)}=\dfrac{-12}{4}=-3[/tex]
[tex]\boxed{y=-3x+2}[/tex]
We have the system of equations:
[tex]\left\{\begin{array}{ccc}y=-4x+10&(1)\\y=-3x+2&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\-4x+10=-3x+2\qquad\text{subtract 10 from both sides}\\-4x=-3x-8\qquad\text{add 3x to both sides}\\-x=-8\qquad\text{change the signs}\\x=8\\\\\text{Put the value of x to (2):}\\\\y=-3(8)+2\\y=-24+2\\y=-22[/tex]
The solution to the given system of equations is (8, -22). Therefore, option C is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
From the table 1.
Slope (m) = (18-26)/(-2-(-4))
= -8/2
m=-4
Substitute m=-4 and (x, y)=(-2, 18) in y=mx+c, we get
18=-4(-2)+c
18=8+c
c=10
So, the equation is y=-4x+10 -----(i)
From table 2:
Slope (m)=(8-14)(-2-(-4))
m=-3
Substitute m=-3 and (x, y)=(-2, 8) in y=mx+c, we get
8=-3(-2)+c
c=2
So, the equation is y=-3x+2 --------(ii)
From equation (i) and (ii), we get
-4x+10 =-3x+2
x=8
Substitute x=8 in equation (i), we get
y=-4(8)+10
y=-22
So, the solution is (8, -22)
Therefore, option C is the correct answer.
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Find the slope of a line perpendicular to 3x + y =15.
5
-3
1/3
-1/3
[tex]\bf 3x+y=15\implies y=-3x+15\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{3}}}[/tex]
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
In the given equation 3x + y =15, the slope of the line will be,
3x + y = 15
y = 15 - 3x
y = -3x + 15
Thus, the slope of the equation is -3.
Now, the product of the slope of two perpendicular lines is always equal to -1. Therefore, the product can be written as,
-3 × m = -1
m = -1/-3
m = 1/3
Hence, the slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.
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What is the equation of a line that is parallel to the line 2x+5y=10 and passes through the point (-5,1)? Check all that apply.
Answer:
y=-2/5 x -1 (It says check all that apply... I hope this equation hasn't been written in a different form in your choices-let me know)
Step-by-step explanation:
Rearrange 2x+5y=10 into slope-intercept form.
First step: Subtract 2x on both sides: 5y=-2x+10
Second step: Divide both sides by 5 giving: y=-2/5 x+2
The slope is -2/5.
Parallel lines have the same slope.
So we know the equation of our new line is in the form y=-2/5 x+b.
We need to find the y-intercept of our line... let's just use the point they have our line going through to find it. Plug in and solve for b.
1=-2/5 (-5)+b
1=2+b
-1=b
So the equation is y=-2/5 x -1
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 2x + 5y = 10 into this form
Subtract 2x from both sides
5y = - 2x + 10 ( divide all terms by 5 )
y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex]
• Parallel lines have equal slopes, so
y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (- 5, 1) into the partial equation
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = - [tex]\frac{2}{5}[/tex] x - 1 ← in slope- intercept form
Multiply through by 5
5y = - 2x - 5 ( add 2x to both sides )
2x + 5y = - 5 ← in standard form
Find how many two digit numbers are divisible by 3
I'll use arithmetic series to find it.
First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.
So,
[tex]a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30[/tex]
There are 30 such numbers.
what is one root of this equation 2x^2-4x+9=0?
A. -2+sqrt14/2i
B. -1+sqtr14/2i
C. 1+sqrt14/3i
D. 1+sqrt14/2i
E. 2+sqrt14/2i
For this case we have the following quadratic equation:
[tex]2x ^ 2-4x + 9 = 0[/tex]
The solutions are given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 2\\b = -4\\c = 9[/tex]
Substituting:
[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (9)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-72}} {4}\\x = \frac {4 \pm \sqrt {-56}} {4}\\x = \frac {4 \pm \sqrt {-1 * 56}} {4}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 14}} {4}\\x = \frac {4 \pm2i \sqrt {14}} {4}\\x = \frac {2 \pm i\sqrt {14}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {2 + i \sqrt {14}} {2}\\x_ {2} = \frac {2-i \sqrt {14}} {2}[/tex]
Answer:
OPTION E: [tex]\frac{2+\sqrt{14}i}{2}[/tex]
Step-by-step explanation:
Given the Quadratic equation [tex]2x^2-4x+9=0[/tex], you can find the roots by applying the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
In this case you can identify that:
[tex]a=2\\b=-4\\c=9[/tex]
Then you can substitute values into the Quadratic formula:
[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(2)(9)} }{2(2)}[/tex]
[tex]x=\frac{4\±\sqrt{(56} }{4}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex], then:
[tex]x=\frac{4\±2\sqrt{14}i}{4}[/tex]
Simplifying, you get:
[tex]x=\frac{2(2\±i\sqrt{14}i)}{4}\\\\x=\frac{2\±\sqrt{14}i}{2}\\\\\\x_1=\frac{2+\sqrt{14}i}{2}\\\\x_2=\frac{2-\sqrt{14}i}{2}[/tex]
Melinda Randolph bought 1,500 shares of Huge Corporation stock for $155,250. She sold the stock for $101 per share and paid a sales commission of $39. What is the profit or loss from the sale? (Enter the dollar amount followed by a space and the word loss or profit.)
Can someone help me?
Answer:
3789.00 loss
Step-by-step explanation: Well She sold the stock but for every stock she sold she had to pay commission which was 39 Dollars for every stock sold. She only Made 2.5% of the Stocks sold, Which is an L, So the answer would be 3789.00, Loss.
The value of x is ___ ?
Answer:
159
Step-by-step explanation:
Please see attachment
Select the factors of x2 − 10x + 25.
Answer:
(x-5)2
Step-by-step explanation:
you must solve the expression (x-5)2 as the form (a-b)2 = a2 -2ab + b2
So it becomes x2-10x+25
Answer: (x-5)(x-5) or (x-5)²
Step-by-step explanation:
(a-b)(a-b)= a² - 2ab + b²
→ x² - 10x - 25
→ √25 = 5
so a= x, b= 5
this gives us (x-5)(x-5)
29, 20, 36, 44, 30, 32, and 40.
Answer:
can't understand the question.
What do you need? The mean? Mode? Median?
An airplane takes off at an angle of 75° from its starting point. When the plane has traveled a total distance of 600 feet, its vertical height above the runway to the nearest foot is 580 feet.
true or false
Which system of equations can be used to find the roots of the equation 4x5 - 12x4 + 6x = 5x? - 2x?
ANSWER
Last option
EXPLANATION
The given equation is
[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]
We can form a system of equations by equating each side of the equation to y.
Equating the left hand side to y, we get
[tex]y = 4 {x}^{5} - 12 {x}^{4} + 6x...(1)[/tex]
Equating the right hand side to y gives
[tex]y= 5 {x}^{3} - 2x...(2)[/tex]To find the solution to
[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]
We graph the two equations and locate the x-values of their points of intersection.
The last option is the correct answer
Answer:
D
Step-by-step explanation: