Answer:
[tex]3y - 2x = 13[/tex]
Step-by-step explanation:
Given
Points (-14,-5) and (4,7)
Required
Find its linear equation in a standard form
To find the linear form, we start by calculating the slope of the line
This is calculated as thus:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where [tex](x_1,y_1) = (-14,-5)\ and\ (x_2,y_2) = (4,7)[/tex]
So, [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{7 - (-5)}{4 - (-14)}[/tex]
[tex]m = \frac{7 + 5}{4 + 14}[/tex]
[tex]m = \frac{12}{18}[/tex]
Simplify fraction to lowest term
[tex]m = \frac{6*2}{6*3}[/tex]
[tex]m = \frac{2}{3}[/tex]
The equation of the line can then be calculated using any of the given points;
Using
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
[tex]Where\ (x_1,y_1) = (-14,-5)\ and\ m = \frac{2}{3}[/tex]
We have
[tex]\frac{2}{3} = \frac{y-(-5)}{x-(-14)}[/tex]
[tex]\frac{2}{3} = \frac{y+5}{x+14}[/tex]
Multiply both sides by 3
[tex]3 * \frac{2}{3} = \frac{y+5}{x+14} * 3[/tex]
[tex]2 = \frac{y+5}{x+14} * 3[/tex]
[tex]2 = \frac{3(y+5)}{x+14}[/tex]
Multiply both sides by x + 14
[tex]2 * (x + 14) = \frac{3(y+5)}{x+14} * (x + 14)[/tex]
[tex]2 * (x + 14) = 3(y+5)[/tex]
Open brackets
[tex]2 * x + 2 * 14 = 3* y+ 3 * 5[/tex]
[tex]2x + 28 = 3y+ 15[/tex]
Subtract 2x from both sides
[tex]2x - 2x + 28 = 3y+ 15 - 2x[/tex]
[tex]28 = 3y+ 15 - 2x[/tex]
Subtract 15 from both sides
[tex]28 - 15 = 3y+ 15 - 2x - 15[/tex]
[tex]28 - 15 = 3y - 2x + 15- 15[/tex]
[tex]13 = 3y - 2x[/tex]
Reorder
[tex]3y - 2x = 13[/tex]
Hence, the equation of the line in standard form is [tex]3y - 2x = 13[/tex]
Find the slope of the line through the points (13, 14) and (0, −1)
Answer:
[tex] \frac{15}{13} [/tex]
Step-by-step explanation:
gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
Thus, slope of line
[tex] = \frac{14 - ( - 1)}{13 - 0} \\ = \frac{14 + 1}{13} \\ = \frac{15}{13} [/tex]
PLEASE HELP! ILL GIVE WHOEVER ANSWERS BRANLIEST!
Question 1). Mrs. Cruz randomly surveyed 25 of her 125 students about their pets. Her survey indicated that 14 students have a dog, 7 students have a cat, 2 students have another kind of pet, and 8 students have no pet. (Note that some students have more than one pet). What is Mrs. Cruz’s best estimate of the total number of her students who have a dog? Justify your answer.
Answer: 70 I’m almost certain
Step-by-step explanation: 14 out of the 25 kids have a dog now if you were to have 125 kids which if 5 times the first 25 kids it would be 14x5 which is 70
What is the vertex of the parabola given by y = x2 − 10x + 17? A. (5, -8) B. (-5, 8) C. (5, 8) D. (-5, -8)
Answer:
A
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 ), then
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² - 10x + 17 ← is in standard form
with a = 1 and b = - 10, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5
Substitute x = 5 into the equation for corresponding value of y
y = 5² - 10(5) + 17 = 25 - 50 + 17 = - 8
vertex = (5, - 8 ) → A
Simply
(3x^2 y^3/x^3)^3
The answer is 27y^9/x^3
if multiple choice the answer is 27x^6 y^9/x^9
Pictures so you can see
Answer:
[tex]=\frac{27y^9}{x^3}[/tex]
Step-by-step explanation:
[tex]\left(\frac{3x^2y^3}{x^3}\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\\\left(\frac{3x^2y^3}{x^3}\right)^3=\frac{\left(3x^2y^3\right)^3}{\left(x^3\right)^3}\\=\frac{\left(3x^2y^3\right)^3}{\left(x^3\right)^3}\\\mathrm{Simplify}\:\left(3x^2y^3\right)^3:\quad 27x^6y^9\\=\frac{27x^6y^9}{\left(x^3\right)^3}\\\mathrm{Simplify}\:\left(x^3\right)^3:\quad x^9\\=\frac{27x^6y^9}{x^9}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]
[tex]\frac{x^6}{x^9}=\frac{1}{x^{9-6}}\\\frac{x^6}{x^9}=\frac{1}{x^{9-6}}\\=\frac{27y^9}{x^{9-6}}\\\mathrm{Subtract\:the\:numbers:}\:9-6=3\\=\frac{27y^9}{x^3}[/tex]
Two similar cylinder have radii 3 cm and 4 cm. If the first cylinder has a volume of 270cm³ , find the volume of the second cylinder.
Please help me , i need help.
Answer: 480 cu. cm
Step-by-step explanation:
Height of first cylinder: h = V/pi r^
= 9.55 cm
Volume of second cylinder = pi r^2 h
= 480
Answer:
360
Step-by-step explanation:
Find the relativeness: If 3 is to 270 then 4 is to ?
270/3 = 90
90 times 4 = 360
Therefore if
3 is to 270
then
4 is to 360
PLZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEE
A quadrilateral has two pairs of parallel sides. The opposite angles in the quadrilateral are congruent but do not measure 90 degrees. Which of the following best describes the quadrilateral? A. square B. parallelogram C. trapezoid D. rectangle
parallogram has opposite sides parallel
only with this point we can say that the given quadrilateral is a parallogram
Answer: i think its parallelogram.
Step-by-step explanation:
parallelogram has 2 sets of parallel sides, Opposite sides are congruent, opposite angles are congruent, all angles are NOT congruent, and all sides are NOT congruent.
hope its CORRECT :)
In a circle with radius 22, an angle measuring 2\pi2π radians intercepts an arc. Find the length of the arc in simplest form.
Answer:
15
Step-by-step explanation:
The length of the arc in its simplest form will be 138.16 units.
What is the arc length of the sector?Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
In a circle with a radius of 22, an angle measuring 2π radians intercepts an arc.
Then the length of the arc in the simplest form will be given as,
Arc = (2π/2π) 2π (22)
Arc = 44 x 3.14
Arc = 138.16 units
The length of the arc in its simplest form will be 138.16 units.
More about the arc length of the sector link is given below.
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Please help ASAP. Will mark as Brainliest.
∠A and ∠B are supplementary. If m∠A = 83° , what is the measure of ∠B?
7°
83°
97°
17°
suplementary means adds to 180
a+b=180
a=83
83+b=180
minus 83 both sidse
b=97
answer is 97 degrees
Answer:
97°
Step-by-step explanation:
Supplementary angles are a pair of angles whose sum is 180°.
If one angle of a pair of supplementary angles is given, it is easy to find the other angle.
It can be found out by subtracting the given angle from 180.
So here in this case, ∠A + ∠B = 180° where ∠A = 83°
83 + ∠B = 180
∠B = 180 - 83
∠B = 97°
So the m∠B = 97°
Hope this answer helps you.
PLS MARK ME AS BRAINLIESt.
6. Given the function f(x) = –5x + 2, find the range of f(x) for x = –1, 0, 1.
options:
A. –7, –2, 3
B. 7, 2, 3
C. –7, –2, –3
D. 7, 2, –3
Answer:
it is D = 7, 2, -3
Step-by-step explanation:
step 1
-5 x -1 + 2 = 7
step 2
-5 x 0 + 2 = 2
step 3
-5 x 1 + 2 = -3
hope this help's
Answer: D = 7, 2, -3
Step-by-step explanation:
What is the slope of the line shown below?
10
(6,2)
10 (-2,-3)
10
10-
O
A.
olm
O
B.
LOCO
O c.
D.
O
100
Helpppppp
PLS HELP IF U HAVE THE WORK PLS ADD I RLLY NEED HELP THANK YOU ITS OK IF U DONT KNOW ALL OF THEM BUT MORE THAN 5 WILL HELP A LOT
A line goes through points (-2, 18) and (4, 3). What is the slope of the line?
A. 12
B. -1.25
C. -2.5
D. -5
Answer:
-2.5
Step-by-step explanation:
The slope can be found by
m = (y2-y1)/(x2-x1)
= (3-18)/(4- -2)
= -15/(4+2)
=-15/6
= -5/2
-2.5
Answer:
C. -2.5
Step-by-step explanation:
Slope is: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-2,18) and (4,3).
[tex]m=\frac{3-18}{4-(-2)}= \frac{-15}{6} =-\frac{15}{6}= -\frac{5}{2}[/tex]
The options are given in decimals.
[tex]-5/2=-2.5[/tex]
Option C is the correct answer.
I need help with this too....Thanks In advance and will.give you five star and brainlist....
Answer:
1/8
Step-by-step explanation:
I think you mean under 5 minutes
1/4*1/2
1/8 probability that the next call will be a customer complaint and will be dealt with under five minutes
(I am not sure if I'm correct with the proportions)
(06.07 MC)
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (V), in mm, to
which it grows:
y = 4 + 2x
What does the slope of this function represent? (1 point)
Select one:
a The original height of the plant was 4 mm.
b. The original height of the plant was 2 mm.
C. The height of the plant increases by 2 mm for every hour of sunlight it receives.
d. The height of the plant increases by 4 mm for every hour of sunlight it receives.
What is the slope of a line that is perpendicular to 6x + 3y = -9?
A 2
B. 1
w
C. -2
D.
Ninh
1
Please select the best answer from the choices provided
Answer: 1/2
Step-by-step explanation:
The equation given is simplified into y= -2x-3. The slope being -2. When a line is perpendicular you find the opposite inverse. That being -1/2. You flip the top and bottem and top numbers of the fraction. Then make it (positive or negative) opposite of the original slope value. Making it now positive 1/2
EMERGENCY REALLY NEED HELP only answer this one queastion and i will give brainly and 30 points PLEASE HELP ME JESUS
Answer:
boundary lines are parallel
Step-by-step explanation:
When there are no solutions to a system of equations which consists of two lines, it means the lines are parallel, but have different y intercepts. This happens when the boundary lines are parallel
Answer:
The boundary lines are parallel
Amar tried to evaluate an expression step by step. -2 + 5 - (-3)
= -2 + 5 - 3 1
= -2 + 2 2
= 0 3
Find Amar’s mistake.
Choose 1 answer:
Ⓐ 1
Ⓑ 2
Ⓒ 3
Ⓓ Amar did not make a mistake.
Answer:
1.
Step-by-step explanation: - (-3) should be a positive 3 when simplified. Whenever there is two negative sign in front of a number it is going to be positive.
The solution to the expression is A = 6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the expression , we get
A = -2 + 5 - ( -3 )
On simplifying , we get
Step 1 :
A = -2 + 5 + 3
The - ( -3 ) becomes positive value and Amar made a mistake in Step 1
So , the value of A is
Step 2 :
A = -2 + 8
On simplifying the equation , we get
Step 3 :
A = 6
Therefore , the value of A is 6
Hence , the expression is A = 6
To learn more about equations click :
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Find the slope of a linear function passes through the points (3,2) and (-4,1)
Answer:
1/7
Step-by-step explanation:
We can use the slope formula(k=y₁-y₂/x₁-x₂) to solve this problem
k = 2-1/3-(-4) = 1/7
The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid.
Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger
pyramid?
9/16
3/4
4/3
16/9
Answer:9/16
Step-by-step explanation:
Since we know it's 3/4 use
r=(3/4)² .... [tex](\frac{3}{4} x\frac{3}{4} )[/tex] =[tex]\frac{9}{16}[/tex]
what is the inverse of the function f(x)= 19/x³
what is the value for Y
Answer: y = 27 degrees
Step-by-step explanation:
x = 90 degrees (right angle)
90 + 63 = 153
180 - 153 = 27
solve for y please !
Answer:3
Step-by-step explanation:
Please help! For the function f(x) = 2x^6 + 3x^4 - 4x^3 + (1/x) - sin(2x) find the first four derivatives.
Answer:
See the explanation
Step-by-step explanation:
We know that
f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x
Lets calculate the derivatives:
f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)
f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x
Similarly:
f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x
f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x
Rearrange:
f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24
f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x
Rearrange:
f''''(x) = 720x² + (24/x⁵) - 16sin2x +72
Help please I don’t understand it
Answer:
C
Step-by-step explanation:
The original price p is reduced by 3000 to obtain the new price
Solve for : 3 2 + −10 = 0. PLEASE HELP
Answer:
Step-by-step explanation:
32+(-10)
32-10
22 is not equal to 0
so its false
Answer: no solution
Step-by-step explanation:
Remove parentheses.
32+-10=0
Simplify 32+-10 to 32-10
32-10=0
Simplify 32-10 to 22
22=0
Since 22=0 is false, there is no solution.
solve for 3x2 + 15x = 12
Step-by-step explanation:
3x2 pls is this multiplication sign or it is (x)
15. The set of ordered pairs represents a function.
{(1,3), (2, 9), (k, 12), (5,9), (8,0)}
Which of these could be the value of k?
A. 0
B. 1
C. 5
D. 8
Answer:
A. 0
Step-by-step explanation:
In a function, all x-coordinates must be different.
The given function already shows 1, 2, 5, and 8 as x-coordinates, so you must choose a number other than those.
Answer: 0
The correct option will be Option A : the value of k will be 0.
What is a function?The function is a relation between two sets where one set is called the domain and another set is the codomain which is one one or many one relations.
If the x or input values are different then the relation will become a function.
So we can say if the x values are repeated and their corresponding y or output values are the same, then also the relation becomes a function.
If the x values are repeated and their corresponding y or output values are different, then the relation will not become a function.
Given the ordered pairs are {(1,3), (2, 9), (k, 12), (5,9), (8,0)
As we know the x value is repeated and the y value is different then the relation will not be a function.
So here in the given ordered pair, there is no any second 12. So k value should not be equal to 1,2,5,8 otherwise it will not be a function.
By checking all the options
0 is not present in x value of the given ordered pair.
Therefore the correct option will be Option A : the value of k will be 0.
Learn more about function
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Which of the following terms correctly describe the figure given below?
Check all that apply.
A. Polygon
B. Prism
C. Cube
D. Pyramid
O E. Solid
O F. Polyhedron
PREVIOUS
The given solid is triangular prism. Therefore, option B is the correct answer.
What is a prism?A prism is a solid form that is enclosed by plane faces on all of its sides. A prism has two different kinds of faces. Bases refer to the identical top and bottom faces. The name "prism" refers to the form of these bases. For instance, a prism is referred to be a triangular prism if its base is triangular.
A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.
Therefore, option B is the correct answer.
Learn more about the prism here:
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“Which expressions are equivalent to x + x + x + 2?”
Answer:
3x+2
Step-by-step explanation:
x+x+x=3x
Because there are three lots of x
You can’t add 2 to the x so 2 is going to be separate
Answer is
3x+2
Write the following as an algebraic expression. Subtract 6X +4 from 4X -14.
___________________________________
Hey!!!
Here's your answer:
4x-14-(6x+4)
=4x-14-6x-4
=4x-6x-14-4
=-2x-18
Hope it helps..
Good luck on your assignment_
________________________________
Answer:
[tex]= - 2x - 18 \\ = - 2(x + 9) \\ [/tex]
Step-by-step explanation:
[tex]4x - 14 - (6x + 4) \\ 4x - 14 - 6x - 4 \\ 4x - 6x - 14 - 4 \\ = - 2x - 18 \\ = - 2(x + 9)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
#stay safe#