Slope formula: y2-y1/x2-x1
Plug in: -15-0/-11-3 = -15/-14 = 15/14 = slope
For this case we have by definition, the slope of a line can be found by the following formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Two points are needed through which the line passes.
According to the data we have:
[tex](x_ {1}, y_ {1}) :( 3,0)\\(x_ {2}, y_ {2}): (- 11, -15)[/tex]
Substituting we have:
[tex]m = \frac {-15-0} {- 11-3} = \frac {-15} {- 14} = \frac {15} {14}[/tex]
ANswer:
The slope is [tex]\frac {15} {14}[/tex]
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
-15m = -4m
-7m - 8 = m - 4
-3m - 8 = 4 - m
m - 4 = -7m - 8
-8 - 7m = -4 + m
-8 - 3m = 4 - m
Answer:
B) -7m - 8 = m - 4
D) m - 4 = -7m - 8
E) -8 - 7m = -4 + m
Step-by-step explanation:
Solve all of the equations to see if they end up with the same result. Start with the original:
-2m - 5m - 8 = 3 + (-7) + m
-7m - 8 = -4 + m (now we know B and D and E are correct)
-7m - m - 8 = -4 + m - m
-8m - 8 = -4
-8m - 8 + 8= -4 + 8
-8m = 4
Answer:
-7m - 8 = m - 4
m - 4 = -7m - 8
-8 - 7m = -4 + m
Step-by-step explanation:
Given equation,
-2m - 5m - 8 = 3 + (-7) + m,
Combining like terms,
-7m - 8 =-4 + m
Subtract m from both sides,
-8m - 8 = -4
Add 8 on both sides,
-8m = 4
Divide both sides by -8,
m = [tex]-\frac{1}{2}[/tex]
(i) -15m = -4m ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0
(ii) -7m - 8 = m - 4 ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]
(iii) -3m - 8 = 4 - m ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6
(iv) m - 4 = -7m - 8 ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m = [tex]-\frac{1}{2}[/tex]
(v) -8 - 7m = -4 + m ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]
(vi) -8 - 3m = 4 - m ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6
1. Describe the domain and range of this equation.
y = 3(x + 1)^2 – 6
If f(x) = 2x2 + 3x and g(x) = x – 2, what is (f + g)(2)?
Answer:
14
Step-by-step explanation:
(f + g)(x) = f(x) + g(x) = 2x² + 3x + x - 2 = 2x² + 4x - 2
To evaluate (f + g)(2) substitute x = 2 into (f + g)(x)
(f + g)(2) = 2(2)² + 4(2) - 2 = 8 + 8 - 2 = 14
Answer:
14
Step-by-step explanation:
First find an algebraic formula for (f + g)(x). To do this, combine like terms from f and g: (f + g)(x) = 2x^2 + 4x -2
Next, substitute 2 for x: (f + g)(2) = 2(2)^2 + 4(2) - 2 = 8 + 8 - 2 = 14
Ryans final exam has true false questions with two points each multiple-choice questions worth five points each . let X be the number of true false questions he gets correct and let Y be the number of multiple choice questions he gets correct... he needs at least 90 points on the exam to get an a in the class . using the values of variables given write an inequality describing this
Answer: 2X+5Y≥ 90
Step-by-step explanation:
since you get two points per/ each (key word of multiplication) true & false question, this will be represented by 2X
since you get five points per/ each multiple choice question, this will be represented by 5Y
he needs at least 90 points in total to get an A in his class
What is the value of x?
Answer:
x = 8
Step-by-step explanat
Answer:
6
Step-by-step explanation:
Which of the following lists the angles from smallest to largest?
ORST
STR.
OTRS
Which of the following lists the angles from smallest to largest?
Answer:
T, R, S
In two or more complete sentences, prove how to find the third term of the expansion of (2x + y)4.
Answer:
The third term is [tex]24x^2y^2[/tex]
Step-by-step explanation:
The formula used to find the third term of the expansion (2x+y)^4 is called Binomial Theorem
The Binomial Theorem is:
[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]
In the given question x = 2x
a = y
n = 4
We have to find the third term, so value of k will be 2 as k starts from 0
Putting the values in the Binomial Theorem
[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex]
[tex]{n \choose k}==\frac{n!}{k!(n-k)!}[/tex]
Putting the values:
[tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]
So, the third term is [tex]24x^2y^2[/tex]
Choose the table that represents g(x) = 3⋅f(x) when f(x) = x − 1.
x g(x)
1 2
2 1
3 0
x g(x)
1 2
2 5
3 8
x g(x)
1 5
2 8
3 11
x g(x)
1 0
2 3
3 6
[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]
[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]
The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;
x g(x)
1 0
2 3
3 6
We are given;f(x) = x − 1
We want to find; g(x) = 3⋅f(x)
This means that; g(x) = 3(x - 1)
Looking at the options, the input values to be used are x = 1, 2 3.
Thus;When x = 1; g(x) = 3(1 - 1 )
g(x) = 0
When x = 2; g(x) = 3(2 - 1)
g(x) = 3
When x = 3; g(x) = 3(3 - 1)
g(x) = 6
Looking at the options, only the table in option D is correct.
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The solution to the system of equations shown is (2,0).
3x – 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two
equations is equivalent to 7x = 14
Which system of equations will also have a solution of (2,0)?
Answer:
D
Step-by-step explanation:
The system of equation will also have a solution of (2,0) are,
x + 4y = 2, 7x = 14.
Given that,
The solution to the system of equations shown is (2,0).
3x – 2y = 6 , x + 4y = 2
When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14.
We have to determine,
Which system of equations will also have a solution of (2,0).
According to the question,
To determine the system of the equation after applying all the given conditions in the steps, follow all the steps given below.
System of equations; 3x – 2y = 6 , x + 4y = 2.
Step1; Multiply the first equation by 2,[tex]2 \times (3x-2y) = 2 \times 6\\\\6x - 4y = 12[/tex]
Step2; Adding equation 1 after multiplying by 2 from equation 2.[tex]6x - 4y + x + 4y = 12+ 2\\\\7x = 14\\\\x = \dfrac{14}{7}\\\\x = 2[/tex]
Step3; When x = 2 the value of y is,
[tex]6(2) - 4y = 6\\\\12-4y = 6\\\\-4y = 6-12\\\\-4y == -6\\\\y = \dfrac{-6}{-4}\\\\y = \dfrac{3}{2}[/tex]
Hence, The required system of equation will also have a solution of (2,0) are, x + 4y = 2, 7x = 14.
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A direct variation function contains the points (-8,-6) and (12,9) which equation represents the function
Answer:
y = 0.75x
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k substitute either of the 2 points into the equation
Using (12, 9 ), then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{9}{12}[/tex] = 0.75, so
y = 0.75x ← equation of variation
can somebody help me
Explain why 1 cm3 = 1000 mm3.
Answer:
The answer in the procedure
Step-by-step explanation:
Remember that
[tex]1\ cm=10\ mm[/tex]
Elevated to the cube both sides
[tex](1\ cm)^{3}=(10\ mm)^{3}[/tex]
[tex](1)^{3}\ cm^{3}=(10)^{3}\ mm^{3}[/tex]
[tex]1\ cm^{3}=1,000\ mm^{3}[/tex]
A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it?
Answer:
[tex]\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]
Step-by-step explanation:
we know that
Te volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=(r/2)\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (r/2)^{2}h[/tex]
[tex]V=\frac{1}{12}\pi r^{2}h[/tex]
Te volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we know that
To find the volume of the space remaining in the cylinder after the cone is placed inside it, subtract the volume of the cone from the volume of cylinder
so
[tex]\pi r^{2}h-\frac{1}{12}\pi r^{2}h=\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]
Heather has $45.71 in her savings account. She bought six packs of markers to donate to her school. Write an expression for how much money she has in her bank account after the donation.
Answer: 45.71 - 6x = y
Step-by-step explanation:
45.71 - 6x = y
x= the amount 1 pack of markers cost
y= how much money Heather has after the donation
Answer: The required expression for amount left in her bank after the donation is given by [tex]Amount\ left=45.71-6x[/tex]
Step-by-step explanation:
Since we have given that
Amount of her saving = $45.71
Number of packs of markers to donate to her school = 6
Let the cost of each pack of markers be 'x'.
So, Amount left in her bank account after the donation is given by
[tex]Amount\ left=45.71-6x[/tex]
Hence, the required expression for amount left in her bank after the donation is given by
[tex]45.71-6x[/tex]
The net of a triangular prism is shown below.
The perimeter of the base of the prism is
units.??
The prism's base perimeter is 28 units, calculated by summing the lengths of its sides or using the rectangle perimeter formula.
Step 1: Identify the Prism and Its Base
Given a triangular prism, focus on the rectangular base formed by sides S1, S2, S3, and S4.
Step 2: Understand Perimeter Calculation
Recall that the perimeter of any shape is the sum of all its sides.
Step 3: Label the Sides of the Base
Define the sides of the rectangular base:
S1 = 4 + 5
S2 = 5
S3 = 4 + 5
S4 = 5
Step 4: Apply Perimeter Formula
Utilize the formula for the perimeter of a rectangle: P = 2 * (length + width).
For the rectangular base, length = S1 + S3 and width = S2.
Step 5: Calculate Perimeter
Substitute the values into the formula: P = 2 * (9 + 5) = 2 * 14 = 28 units.
Step 6: Verify Using Summation
Confirm the result by adding the individual sides: P = S1 + S2 + S3 + S4 = 9 + 5 + 9 + 5 = 28 units.
Writing Equations of Parallel Lines
What is the equation of the line parallel to the given line
with an x-intercept of 4?
y =
5
4 -3 -2 -1
Answer:
y= 4x + (-16)
Step-by-step explanation:
The slope of the given lime is m=4
x-intercept of the parallel line: (4,0)
plug that into the equation y= mx+b to find that b= -16
since the slope stays the same for parallel lines, and we just found b, we have the new line equation
The equation of parallel line with x intercept of 4 will be : y= 4x + (-16)
Given,
x intercept : 4
Slope = 4
Now,
x-intercept of the parallel line: (4,0)
As the equation of line to be obtained is parallel . Thus both lines will have same slope .
Slope of parallel line = 4
Substitute the value to find y intercept,
y = mx + b
0 = 4(4) + b
b = -16
So,
Equation of parallel line: y = 4x + (-16)
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Graph the linear equation. Find three points that solve the equation, then plot on the graph. -y=x+1
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
-y=x+1
Find the y-intercept
For x=0
-y=0+1
y=-1
The y-intercept is the point (0,-1)
Find the x-intercept
For y=0
-0=x+1
x=-1
The x-intercept is the point (-1,0)
Find a third point
For x=1
-y=1+1
-y=2
y=-2
The third point is (1,-2)
Plot the three points to graph the linear equation
see the attached figure
Note Remember that to graph the linear equation is sufficient with two points
Answer:
(2,1) (0,-1) (-6,7)
Step-by-step explanation:
Perform the indicated operation.
Answer : The correct answer is, [tex]29\frac{62}{7}[/tex]
Step-by-step explanation :
The given expression is:
[tex]10\frac{3}{7}+19\frac{5}{9}[/tex]
Step 1 : Convert mixed fraction into fraction.
[tex]\frac{73}{7}+\frac{176}{9}[/tex]
Step 2 : Taking L.C.M
[tex]\frac{(9\times 73)+(176\times 7)}{63}[/tex]
[tex]\frac{(657)+(1232)}{63}[/tex]
[tex]\frac{1889}{63}[/tex]
Step 3 : Convert fraction into mixed fraction.
[tex]=29\frac{62}{7}[/tex]
Thus, the correct answer is, [tex]29\frac{62}{7}[/tex]
when using rational root theorem, which of the following is a possible root of the polynomial function below F(x)=3x^3-x^2+4x+5
a.-7
b.6
c.-3/5
d.4/3
Answer:
C is your answer I did this test before.
Step-by-step explanation:
good luck.
C is your answer
We have given that,
when using the rational root theorem, which of the following is a possible root of the polynomial function below
F(x)=3x^3-x^2+4x+5
What is the rational root theorem of plynomial?
The rational root theorem says, a rational zeros of a polynomial is of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
p/q=±a0/a1
from the given polynomial a1=3 and a0=5
p/q=±3/5
+3/5 is not in the option so the correct option -3/2
So the root of the given polynomial is -3/5
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What is AB?
a. 6cm
b. 9cm
c. 4cm
d. 2.2cm
Answer:
AB = 4 cm
Step-by-step explanation:
The tangent and secant are drawn from an external point to the circle.
Then the square of the measure of the tangent is equal to the product of the external part of the secant and the entire secant.
let AB = x, then
x(x + 5) = 6²
x² + 5x = 36 ( subtract 36 from both sides )
x² + 5x - 36 = 0 ← in standard form
(x + 9)(x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 9 = 0 ⇒ x = - 9
x - 4 = 0 ⇒ x = 4
However x > 0 ⇒ x = 4 ⇒ b = 4 CM
Use the given information to determine the exact trigonometric value.
Answer: [tex]\bold{a.\quad -\dfrac{2\sqrt{6}}{5}}[/tex]
Step-by-step explanation:
[tex]sin\theta=\dfrac{y}{h}\implies y=-1, h=5\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2 + y^2 = h^2\\x^2 + (-1)^2=5^2\\x^2+1=25\\x^2=24\\x=\sqrt{24}\\x=2\sqrt{6}[/tex]
[tex]\text{Since }\theta\text{ is between }\pi\text{ and }\dfrac{3\pi}{2} \text{ (Quadrant III)},\text{ then x and y are negative.}\\\implies x=-2\sqrt{6}\\\\\\cos\theta = \dfrac{x}{h}\quad =\boxed{-\dfrac{2\sqrt{6}}{5}}[/tex]
Tim knows the volume and base area of a wooden chest that is in the shape of a rectangular prism. If the volume is 524 cubic unit and the base area is 15 square unit, what is the height of the chest? 124 unit 1124 units 112 unit 1112 units
Answer: 34.93 units
Step-by-step explanation:
The volume of a rectangular prism can be calculated with this formula:
[tex]V=Bh[/tex]
Where "V" is the volume, "B" is the base area and "h" is the height.
Since we need to find the height, we must solve for "h":
[tex]h=\frac{V}{B}[/tex]
We know that the volume of that wooden chest (which is in the shape of a rectangular prism) is 524 cubic units and the base area is 15 square units. Then:
[tex]V=524units^3\\B=15units^2[/tex]
Subsitituting these values into [tex]h=\frac{B}{V}[/tex], we get that the height of the chest is:
[tex]h=\frac{524units^3}{15units^2}=34.93units[/tex]
Solve using cross multiplication method, ax + by = a^2 ; bx + ay = b^2
Answer:
x=a²+ab+b²/a+b , y=-ab/a+b
Step-by-step explanation:
The system of the given equation may b written as:
ax+by-a²=0
bx+ay-b²=0
Here,
a1=a,b1=b,c1= -a²
a2=b,b2=a and c2= -b²
By cross multiplication we get
x/b*(-b²)-(-a²)*a = -y/a*(-b²)-(-a²)*b = 1/a*a-b*b
x/-b³+a³ = -y/-ab²+a²b = 1/a²-b²
Now
x/-b³+a³ = 1/a²-b²
x=a³-b³/a²-b²
x=(a-b)(a²+ab+b²)/(a-b)(a+b)
x=a²+ab+b²/a+b
And,
-y/-ab²+a²b = 1/a²-b²
-y=a²b -ab²/a²-b²
y=ab²-a²b/a²-b²
y=ab(b-a)/(a-b)(a+b)
y= -ab(a-b)/(a-b)(a+b)
y= -ab/a+b
Hence x=a²+ab+b²/a+b , y=-ab/a+b....
Simplify.
(5y + 9) + y
6y + 9
14 + y
14y
15y
The answer you are looking for is 6y + 9.
In the equations (5y + 9) + y, you'd combine like terms to find the answer. You aren't distributing anything into the parenthesis, and 5y and 9 are not like terms (since the 9 doesn't have a "y" after it). That being said, you simply add "y" and 5y together to get 6y, and add the 9 to the end. Thus getting 6y + 9 as an answer.
I hope this helps!
Answer:
A. 6y+9
Step-by-step explanation:
Distributive property:
↓
[tex]A(B+C)=AB+AC[/tex]
First, you remove parenthesis.
5y+9+y
Group like terms:
↓
5y+y+9
Then, you add by similar into elements.
5y+y=6y
6y+9 is the correct answer.
Columbia,South Carolina, is located at 34degrees north latitude. Use the equation to estimate the average annual snowfall for Columbia.
The question is missing the specific equation needed to estimate average annual snowfall for Columbia, South Carolina at 34 degrees north latitude. Factors like latitude and climate patterns influence snowfall levels, and based on Columbia's location, low snowfall would be expected.
Explanation:The student is asking about an equation to estimate average annual snowfall for a specific location based on its latitude, in this case, Columbia, South Carolina, which is at 34 degrees north latitude. Unfortunately, the explicit equation needed to estimate the snowfall is not provided in the question or the contextual information. Generally, to estimate snowfall or precipitation levels using latitude, additional climatic data such as elevation, proximity to oceans or large bodies of water, and prevailing wind patterns are also necessary.
However, referring to the geographical regions mentioned, it's noted that certain latitudes often correspond with specific climate patterns. The comparison with other regions suggests that areas farther away from the equator, especially those close to either the Arctic Circle or the Antarctic Circle, experience more extreme temperatures and snowfall. Given the subtropical zone where Columbia, South Carolina, is located, the expected average snowfall would likely be relatively low compared to higher latitudes.
what is the factorization of the polynomial below? x^2+6x+8
Answer:
(x+2) (x+4)
Step-by-step explanation:
x^2+6x+8
What 2 numbers multiply together to give us 8 and add together to give us 6
(2*4) =8
(2+4) = 6
(x+2) (x+4)
Answer:
(x + 4)(x+2)
Step-by-step explanation:
We must multiply 8 and 1, and find two numbers which add to 6:
8 * x(suppose x is 1) = 8
Two numbers which add to 6, but also multiply to 8:
4 and 2
4 * 2 = 8
4 + 2 = 6
Hence, the answer would be (x + 4)(x+2)
What statement about the scatter plot is true ?
Answer:
the first one
Step-by-step explanation:
the number of mistakes went from 19 the first week of class to 0 the 20th week
Multiply: 4x^3/4x^2(2^3
Answer:
The answer is B
Step-by-step explanation:
happy cheating
Answer:
The answer is B
Step-by-step explanation:
And it's not cheating just trying to make it through high school.
A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.
Explain how to find the arc length exactly, and then approximate it to one decimal place.
Answer:
Part 1) The exact value of the arc length is [tex]\frac{25}{6}\pi \ in[/tex]
Part 2) The approximate value of the arc length is [tex]13.1\ in[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=5\ in[/tex]
substitute
[tex]C=2\pi (5)[/tex]
[tex]C=10\pi\ in[/tex]
step 2
Find the exact value of the arc length by a central angle of 150 degrees
Remember that the circumference of a circle subtends a central angle of 360 degrees
by proportion
[tex]\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in[/tex]
step 3
Find the approximate value of the arc length
To find the approximate value, assume
[tex]\pi =3.14[/tex]
substitute
[tex]\frac{25}{6}(3.14)=13.1\ in[/tex]
Answer:
13.1 (rounded to tenths)
Step-by-step explanation:
150 ° into radian is 5/6.
150°/1 (π/180) =5π/6.
Then multiply the radian angle by the radius.
5π/6 (5) = 25π/6
25π/6 = 13.1 (rounded to tenths)
Find the value for b.
3x^2– X – 10 = 0
Entor the correct answer
[tex]b=-1[/tex]
.............................
Answer:
X=2, X= -5/3
Step-by-step explanation:
let's solve your equation step-by-step
3x^2-x-10=0
step 1: factor left side of equation.
(3x+5)(x-2)=0
step 2: set factors equal to 0.
3x+5=0 or x-2=0
x= -5/3 or x=2
To complete such a customer at your store needs to purchase vertical brackets to attach to the wall the customer wants to show them to be at least 48 inches in 60 in section 248 inspection cost 1295 to 16 section cost 6095 the brackish if you want switch from each end and no more than 24 inches apart what will the total cost of the brackets before tax
Answer:
67
Step-by-step explanation:
you have to divide
Answer
Step-by-step explanation:$149.50 is the answer