write the equation of the line that passes through the points (7,-4) and (-1,3), first in point slope form
Answers
The given line that passes through the points (7,-4) and (-1,3).
The slope is
[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]
The point-slope form is obtained using:
[tex]y-y_1= m (x-x_1) [/tex]
When (7,-4) is used the point-slope form is
[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]
We expand now to get;
[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]
This implies that,
[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]
Related Questions
A line has a rise of 6 and a slope of 1/20. What is the run?
Answers
Answer:
120
Step-by-step explanation:
Slope = rise / run
1/20 = 6 / run
run = 120
Write the expression in complete factored
form.
5n_(c - 3) - n(C - 3) =
Answers
Answer:
(c-3) (4n)
Step-by-step explanation:
5n(c - 3) - n(C - 3) =
Factor out (c-3) from each term
(c-3) (5n-n)
Simplify the 2nd term
(c-3) (4n)
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
O 12A cubic inches
O 367 cubic inches
0 647 cubic inches
O 817 cubic inches
Answers
Answer:
The volume is 113.04 cubic inches
Step-by-step explanation:
We are given:
Radius = r = 3 inches
As we know the formula for finding the volume of sphere is:
[tex]V=\frac{4}{3} \pi r^{3} \\Putting\ values\ of\ \pi \ and\ r\\V = \frac{4}{3} * 3.14 * (3)^3\\= \frac{12.56}{3} * 27\\= \frac{339.12}{3}\\ =113.04\ cubic\ inches[/tex]
The volume is 113.04 cubic inches ..
What type of triangle has side lengths 2, √12, and √19?
Answers
Answer:
Is an scalene obtuse triangle
Step-by-step explanation:
step 1
Find the type of triangle by the measure of the interior angles
we know that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] ----> we have a right triangle
[tex]c^{2} > a^{2}+b^{2}[/tex] ----> we have an obtuse triangle
[tex]c^{2}< a^{2}+b^{2}[/tex] ----> we have an acute triangle
where
c is the greater side
we have
[tex]c=\sqrt{19}\ units[/tex]
[tex]a=2\ units[/tex]
[tex]b=\sqrt{12}\ units[/tex]
substitute
[tex]c^{2}=(\sqrt{19})^{2}=19[/tex]
[tex]a^{2}+b^{2}=(2)^{2}+(\sqrt{12})^{2}=16[/tex]
so
[tex]19 > 16[/tex] -----> [tex]c^{2} > a^{2}+b^{2}[/tex]
we have an obtuse triangle
step 2
Find the type of triangle by the measure of the sides
we have that
The measure of its three sides is different
therefore
Is an scalene triangle
Write an equation of the line given the two points below (Write your equation in slope-intercept form, y=mx+b): (-4, 4) and (6, -4)
Answers
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-4}{6-(-4)}\implies \cfrac{-8}{6+4}\implies \cfrac{-8}{10}\implies -\cfrac{4}{5}[/tex]
[tex]\bf \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-4=-\cfrac{4}{5}[x-(-4)]\implies y-4=-\cfrac{4}{5}(x+4) \\\\\\ y-4=-\cfrac{4}{5}x-\cfrac{16}{5}\implies y=-\cfrac{4}{5}x-\cfrac{16}{5}+4\implies y=-\cfrac{4}{5}x+\cfrac{4}{5}[/tex]
Slallau
Solve for x.
16x – 6 = 26
Answers
Answer:
Step-by-step explanation:
X=2
u cross out the 6 and add it to 26 and then u get 16x=32 and divide both by 16 to get x alone and u get 2
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12
Y=7 when x=3
Answers
3/7 = 12/21
Which number times 3 is equal 12
3(4) = 12
So 7(4) = 28
X= 12 , y= 28
drako found an emarald in a cave at a depth between negative 1\2 and negative 1 2\3 meters. Which number could represent the depth at which the emerald is located ?
Answers
Answer:
[tex](-\frac{7}{6} )[/tex]
Step-by-step explanation:
From the question the emerald was located at a depth which is between -1/2 and -1 2/3 meters
This statement can be written as
[tex](-1\frac{2}{3}) -(-\frac{1}{2} )[/tex]
To get the depth, you find the depth of the emerald location, you find difference between the two mentioned depths
[tex]-(1\frac{2}{3} )-(-\frac{1}{2} )\\\\[/tex]
Change first term to improper fraction
[tex]=-(\frac{5}{3} )-(-\frac{1}{2} )\\\\[/tex]
Find the LCM to solve the operation the involves the fractions.The Least common multiple here is 6 i.e 3*2
[tex]=(-\frac{5}{3} )-(-\frac{1}{2})\\[/tex]
[tex]=\frac{-5}{3} +\frac{1}{2} =\frac{-10+3}{6} =\frac{-7}{6}[/tex]
The number that could represent the depth at which the emerald was located is
[tex]=\frac{-7}{6}[/tex]
Which is not an equation of the line going through (3,6) and (1, -2)?
O A. y+ 2 = 4(x - 1)
O B. y- 2 = 4(x+1)
O c. y= 4x- 6
O d. y-6 = 4(x – 3)
Answers
Step-by-step explanation:
Answer is B but what kind of question is this? You don't even have to find the equation just find which one is different from the others.
A) y+2 = 4x-4
y = 4x-6
B)y-2 = 4x+4
y= 4x+6
C)y = 4x-6 (same with A )
D)y-6 = 4x-12
y= 4x-6 (Same with A and C)
So b is the different one.
(a) Find the differential dy.
y = cos(x)
dy =?
(b) Evaluate dy for the given values of x and dx. (Round your answer to three decimal places.)
x = π/3, dx = 0.1.
dy=?
Answers
a. Practically speaking, you compute the differential in much the same way you compute a derivative via implicit differentiation, but you omit the variable with respect to which you are differentiating.
[tex]y=\cos x\implies\boxed{\mathrm dy=-\sin x\,\mathrm dx}[/tex]
Aside: Compare this to what happens when you differentiate both sides with respect to some other independent parameter, say [tex]t[/tex]:
[tex]\dfrac{\mathrm dy}{\mathrm dt}=-\sin x\dfrac{\mathrm dx}{\mathrm dt}[/tex]
b. This is just a matter of plugging in [tex]x=\dfrac\pi3[/tex] and [tex]\mathrm dx=0.1[/tex].
[tex]\boxed{\mathrm dy\approx-0.087}[/tex]
The differential dy for y = cos(x) is evaluated by finding the derivative of y which is -sin(x), then multiplying by dx. For x = π/3 and dx = 0.1, the calculated differential dy is approximately -0.0866 when rounded to three decimal places.
Explanation:The differential dy of a function y with respect to x is given by the derivative of y with respect to x, multiplied by dx. For the function, y = cos(x), the derivative of y is -sin(x), hence dy = -sin(x)dx.
To evaluate dy for x = π/3 and dx = 0.1, we substitute x into -sin(x) and multiply by dx. This results in dy = -sin(π/3) × 0.1, which simplifies to dy = -0.1 √3/2. Rounding to three decimal places, dy ≈ -0.0866.
Find (fog)(x).
1 =
x
+
2
g(x) = x² + 6
Answers
Answer:
fog(x)=[tex]x^2+8[/tex]
Step-by-step explanation:
Here we are given two functions
f(x) = x+2
g(x)=[tex]x^2+6[/tex]
We are required to find fog(x)
fog(x) is a composite function.
fog(x) = f(g(x))
g(x) = [tex]x^2+6[/tex]
f(g(x)) = f( [tex]x^2+6[/tex] )
f(x)= x+2
Hence we replace x in f(x) with [tex]x^2+6[/tex]
f(g(x))=([tex]x^2+6[/tex])+2
f(g(x))=[tex]x^2+8[/tex]
Hence
fog(x) = [tex]x^2+8[/tex])
In triangle DEF, FE=3 and M^F =37 find DE to the nearest tenth
Answers
U ARE GOING TO MULTIPLY THEM ALL TOGETHER
Shawn solved the system of equations below and found that x = 3. Which
ordered pair is the solution to the system?
2x+4y = 34
6x +2y = 32
A. (3,7)
B. (3,9)
C. (3,6)
D. (3,8)
Answers
Answer:
A
Step-by-step explanation:
it would equal 34 nd on the bottom would be 32 so AAAA
(3,7) ordered pair is the solution to the system.
What is a system of equations?A finite collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.
Given
2x+4y = 34
6x +2y = 32
x = 3
[tex]2*3[/tex] + 4y = 34
[tex]6*3[/tex] + 2y = 32
18 + 2y = 32
y = 7
(3,7) ordered pair is the solution to the system.
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What is the approximate circumference of the circle shown below?
Answers
Answer: D. 61.2 cm
Step-by-step explanation:
The formula to calculate the circumference of a circle is given by :-
[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.
In the given picture., we have the diameter of circle = 19.5 cm
Then , the circumference of the circle is given by :-
[tex]C=(3.14) (19.5)=61.23\approx61.2\ cm[/tex]
Hence, the circumference of the circle = 61.2 cm
Answer:
61.2
Step-by-step explanation:
write the equation of the graph shown below in factored form
Answers
Answer:
[tex]f(x)=(x-3)^{2}(x-2)(x-1)[/tex]
Step-by-step explanation:
we know that
The roots (or x-intercepts) of the equation are
x=1 -----> with multiplicity 1
x=2 -----> with multiplicity 1
x=3 -----> with multiplicity 2 (because is a turning point)
so
The factors are
[tex](x-1), (x-2), (x-3),(x-3)[/tex]
The equation is equal to
[tex]f(x)=(x-3)(x-3)(x-2)(x-1)\\ \\f(x)=(x-3)^{2}(x-2)(x-1)[/tex]
To write a quadratic equation in factored form, find two binomials that when multiplied together yield the original quadratic. Factoring is essential in understanding the roots and the shape of a parabolic graph. For more complex quadratics, techniques like completing the square might be required.
Explanation:When we are looking to write the equation of a graph in factored form, we are typically dealing with a polynomial function, and specifically when the graph is of a parabola, we are working with a quadratic equation. Factoring a quadratic equation involves finding two binomials that when multiplied together give us the original quadratic. For example, if we have a graph of a quadratic with its roots at x = p and x = q, the factored form would be y = a(x - p)(x - q), where a represents the leading coefficient.
If given an equation like 6x² + xy - y² - 17x - y + 12 = 0, it can be factored into two linear terms, which represents the intersection of two lines. In cases where completing the square is needed, such as x² - ( ) x = -() y, we add to each side (half the coefficient of x)² to form a perfect square on the left-hand side, leading us to an equation of the form (x − A)² = -4a(y − B).
Learning about graphing polynomials provides insights into how the constants in an equation affect the shape of the curve. By adjusting coefficients and analyzing the individual terms, we can understand how these terms combine to produce the overall graph of the polynomial.
If LP = 15 and PR = 9, find LR. Explain.
Answers
Answer:
LR is 12
Step-by-step explanation:
LP is hypotenuse and PR is base so LR is perpendicular
formula to calculate perpendicular is
p^2=H^2 -b^2
p^2=15^2-9^2
p^2=225-81
p^2=144
p=12(root of 144 is 12)
Answer:
it would be 24 cuz 15 + 9 = 24
Consider the function y = -2-3cos (x+pi). What effect does the -2 have on the basic graph
Answers
ANSWER
-2 shift the graph of the basic function down by 2 units.
EXPLANATION
The given cosine function is:
[tex]y = - 2 - 3 \cos(x + \pi) [/tex]
This equation can be rewritten as:
[tex]y = - 3 \cos(x + \pi) + - 2[/tex]
We compare this to
[tex]y = a \cos(bx + c) + d[/tex]
The effect d has on the graph is that, it shifts the graph up by d units.
If d is negative the graph shifts down by d units.
Since d=-2, the graph will shift down by 2 units.
Answer:
Vertical Shift Down 2 Units
Step-by-step explanation:
How do you solve this? 2/10 • 9/12
Answers
Answer:
3/20
Step-by-step explanation:
First simplify the fractions
2/10 Divide top and bottom by 2
= 1/5
9/12 Divide top and bottom by 3
= 3/4
2/10 * 9/12
1/5*3/4
Multiply the top
1*3 = 3
Multiply the bottom
5*4=20
3/20
16 is 64% of what number
Answers
Answer:
25
Step-by-step explanation:
Is means equals and of means multiply
16 = 64% * W
Change to decimal form
16 = .64 * W
Divide each side by .64
16/.64 = .64W/.64
25 = W
Answer:
25
Step-by-step explanation:
We can model this question with:
16 = 0.64x
x represents "what number."
0.64x = 16
Divide 0.64 from both sides
0.64x ÷ 0.64 = 16 ÷ 0.64
16 ÷ 0.64 = 25.
Therefore, 16 is 64% of 25.
Marlena has 3 straws. Two straws have the lengths
shown. She does not know the length of the shortest
straw, but when she forms a triangle with all three, the
triangle is obtuse. Which are possible lengths of the
shortest straw? Check all that apply.
5 inches
6 inches
7 inches
8 inches
9 inches
Answers
Answer:
5 6 7 is the correct answer
Step-by-step explanation:
The possible lengths of the shortest straw are 5 inches, 6 inches, 7 inches and 8 inches
How to determine the possible lengths of the strawThe lengths of the two straws are given as: 9 inches and 12 inches
Represent the length of the shortest straw with x.
So, we have the following inequality
[tex]x + 9 > 12[/tex]
Subtract 9 from both sides
[tex]x > 3[/tex]
This means the length of the shortest straw is greater than 3 inches
Hence, the possible lengths are 5 inches, 6 inches, 7 inches and 8 inches
Read more about triangles at:
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Each side length of a triangle is 4cm what type of triangle is it
Answers
Answer:
equilateral
Step-by-step explanation:
If all 3 sides of a triangle are the same length, then it is an equilateral triangle.
scalene: no sides the same length
isosceles: 2 sides the same length
equilateral: 3 sides the same length
20 points: Use long division to find the quotient below.
(16x3 + 40x2 + 72)/ (2x + 6)
Answers
Answer:
8x2-4x+72. good luck.
What is the midpoint of the segment below?
(2, 3)
(-3.-2)
Answers
The formula for finding the midpoint of a line segment is[tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]. Plug in and solve:
[tex](\frac{2-3}{2} , \frac{3-2}{2})[/tex]
(-1/2, 1/2)
(-0.5, 0.5)
Hope this helps!!
The midpoint of the segment is (-0.5, 0.5)
What is midpoint of the segment?The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
Given points: (2, 3) and (-3.-2).
The formula for midpoint is
(x1+x2/2, y1+y2/2)
= (2-3/2, 3-2/2)
=(-1/2, 1/2)
= (-0.5, 0.5)
Hence, the midpoints of the segment is (-0.5, 0.5).
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What is the measure of 3?
Answers
Answer:
∠3 = 60°
Step-by-step explanation:
Since g and h are parallel lines then
∠1 and ∠2 are same side interior angles and are supplementary, hence
4x + 36 +3x - 3 = 180
7x + 33 = 180 ( subtract 33 from both sides )
7x = 147 ( divide both sides by 7 )
x = 21
Thus ∠2 = (3 × 21) - 3 = 63 - 3 = 60°
∠ 2 and ∠3 are alternate angles and congruent, hence
∠3 = 60°
The measure of angle 3 is 60 degrees, the correct option is B.
Given
In the diagram, g is parallel to h.
The measurement of angle 1 is (4x +36).
The measurement of angle 2 is (3x-3).
Interior angles;
The angles that lie in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles.
∠1 and ∠2 are the same side interior angles and are supplementary then the sum of both angles is equal to 180 degrees.
[tex]\rm 4x+36+3x-3=180\\\\7x+33=180\\\\7x=180-33\\\\7x=147\\\\x=\dfrac{147}{7}\\\\x=21[/tex]
The measure of the angle 2 is = 3(21)- 3= 63 - 6 = 60 degrees.
Hence, Angle 2 and ∠3 are alternate angles and congruent then the measure of angle 3 is 60 degrees.
To know more about Parallel lines click the link given below.
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Thank you for this a lot
Answers
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case:
m = -5
b = -8
so...
y = -5x - 8
Hope this helped!
Answer:
B
Step-by-step explanation:
Slope-intercept form of a line:
y = mx + b
m = slope
b = y-intercept
The question asks for a line w/ a slope of -5 and y-int of -8.
B would be the correct choice as in y = -5x - 8,
m (slope) = -5 and
b (y-int) = -8.
Which is a solution to (x - 2)(x + 10) = 13?
O x = 3
Ox=8
x = 10
x = 11
Answers
For the equation
(X-2)(x+10)=13
The required solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.
What is simplification?Simplification involves using rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
We can solve the equation (x - 2)(x + 10) = 13 using the following steps:
Expand the left-hand side of the equation: x² + 10x - 2x - 20 = 13Simplify the left-hand side by combining like terms: x^2² + 8x - 20 = 13Move the constant term to the right-hand side: x² + 8x - 33 = 0Factor the quadratic expression: (x + 11)(x - 3) = 0Apply the zero product property and solve for x: x + 11 = 0 or x - 3 = 0x = -11 or x = 3Therefore, the solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.
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The circle below is centered at the point (3,1) and has a radius length of 2.What is its equation
Answers
Answer:
C. [tex](x-3)^2+(y-1)^2=2^2[/tex]
Step-by-step explanation:
The standard equation of a circle, given the radius r units and center (h,k) is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From the question, we have the center of the circle to be (3,1) and the radius is 2 units.
We substitute the center and radius of the circle into the equation to get:
[tex](x-3)^2+(y-1)^2=2^2[/tex]
The correct answer is C
Which graph represents a function?
Select one:
Answers
Answer:
C
Step-by-step explanation:
Because none of the X coordinates are the same.
Complete this statement:
36x3a + 45xa? = 9xal
Enter the correct answer.
Answers
Answer:
[tex]\large\boxed{36x^3a+45xa=9xa(4x^2+5)}[/tex]
Step-by-step explanation:
[tex]36x^3a=(9xa)(4x^2)\\\\45xa=(9xa)(5)\\\\36x^3a+45xa=(9xa)(4x^2)+(9xa)(5)=9xa(4x^2+5)[/tex]
Which statement is true about f(x)=-6x+5-2
Answers
Not enough information (attach the statements).