Answer: 20 and 14
Step-by-step explanation:
Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.
[tex]20^2 = 400\\14^2=196[/tex]
[tex]20^2-14^2 = 204[/tex]
A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.
Hope this helped :)
Answer:
14 and 20
Step-by-step explanation:
Let x and y be two numbers where x < y.
We are given :
y - x = 6
y² - x² = 204
Then
y - x = 6
(y - x)(y + x) = 204
Then
y - x = 6
6 × (y + x) = 204
then
y - x = 6 (Equation 1)
y + x = 34 (Equation 2)
Then
(Equation 1) + (Equation 2) ⇒ 2y = 40 ⇒ y = 20
Now ,we substitute y by 20 in equation 1 :
y - x = 6
⇔ 20 - x = 6
⇔ 20 - 6 = x
⇔ x = 14
Question 10 of 25
Which pair of functions are inverses of each other?
[tex]f(x) = \sqrt[3]{11x} \\ y = \sqrt[3]{11x} \\ x = \sqrt[3]{11y} \\ x {}^{3} = 11y \\ y = \frac{x {}^{3} }{11} [/tex]
Option A eliminated[tex]f(x) = \frac{x}{7} + 10 \\ y = \frac{x}{7} + 10 \\ x = \frac{y}{7} + 10 \\ x - 10 = \frac{y}{7} \\ y = \frac{x - 10}{7} [/tex]
Option B eliminated[tex]f(x) = \frac{7}{x} - 2 \\ y = \frac{7}{x} - 2 \\ x = \frac{7}{y} + 2 \\ x - 2 = \frac{7}{y} \\ y = \frac{7}{x - 2} [/tex]
Option C eliminatedBy elimination it's DConfirmation:[tex]f(x) = 9x - 6 \\ y = 9x - 6 \\ x = 9y - 6 \\ x + 6 = 9y \\ y = \frac{x + 6}{9} = g(x)[/tex]
What’s an Inequality?
Answer:
mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Answer:
The quality of being unequal or uneven is known as the inequality.Solve the equation: (4x - 5)^4 = 81.
hope this helps
by
aman10we
The value of x after solving this equation is 2
What is a polynomial?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here, the equation as : (4x - 5)^4 = 81.
(4x - 5)^4 = 3⁴.
4x - 5 = 3
x = 2
Hence, the value of x is equal to 2
Learn more about polynomials here:
https://brainly.com/question/11536910
#SPJ2
need heeeelp please
Answer:
376.99112cm²
Step-by-step explanation:
A=2 pi rh + 2 pi r²
A=(2 x pi x 5 x 7) + (2 x pi 5²)
pi 22/7
what is 4,928 will rounded to the nearest hundred
Answer:
4,928 rounded to the nearest hundred = 4,900
Step-by-step explanation:
Greetings!
Determine the two consecutive multiples of 100 that bracket 4,928.4,928 is between 4,900 and 5,000.4,950 is the midpoint between 4,900 and 5,000.As illustrated on the number line, 4,928 is less than the midpoint (4,950).Therefore, 4,928 rounded to the nearest hundred = 4,900.Hope it helps!
Answer:
The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
PLATO Type the correct answer in each box. Use numerals instead of words. In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line A T at C, and R respectively such that the angle D C R is 77 degrees. Complete the given statement. The measure of ∠CRQ is °, and the measure of ∠CRS is °.
Answer:
c
Step-by-step explanation:
The measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line AT at C, and R respectively such that the angle ∠DCR is 77 degrees.
We know that the angle ∠DCR & ∠SRT and ∠DCR & ∠SRT are corresponding angles. Then they are equal to each other.
∠DCR = ∠SRT = 77°
∠CRQ = ∠CRS
We know that the angle ∠CRQ and ∠CRS are supplementary angles. Then we have
∠CRQ + ∠SRT = 180°
∠CRQ + 77° = 180°
∠CRQ = 103°
Then the measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.
The diagram is given below.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ2
The Tortoise and the Hare is a fable about a race with the
moral, “Slow and steady wins the race.” The Tortoise and the
Hare decide to “race” across the United States from
Washington D.C. to Los Angeles.
a. Charles Darwin studied the tortoises when he was on
the Galapagos in 1835. He thought they moved relatively quickly. “One large one, I found by pacing, walked at the rate of 60 yards in 10 minutes” he wrote in Zoology Notes.
i How many inches per minute does the Galapagos tortoise walk?
ii. How long would it take a Galapagos tortoise to walk across the U.S.? Use the most
appropriate unit for time.
b. The Hare can run up to 30mph.
i. How many inches per minute does the Hare run?
ii. How long would it take the Hare to complete the race across the U.S.? Use the
most appropriate unit for time.
c. In the fable, the Hare, confident that he is so far head, relaxes and takes a nap. How long would the Hare need to nap for the Tortoise to pass him and win the race?
a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).
a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).
b.i) The Hare runs 31,680 inches per minute (1,900,800/60).
b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).
c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).
What are the equivalent values for calculating distance?In this exercise, the following equivalent values are used for computing the distance and speed:
1 mile = 1,760 yards1 yard = 36 inches1 hour = 60 minutesDistance from Galapagos to the U.S. = 600 miles600 miles = 1,056,000 yards (600 x 1,760).Data and Calculations:Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)
Speed of Hare = 30mph
30 miles = 52,800 yards (30 x 1,760)
52,800 yards = 1,900,800 inches (52,800 x 36)
= 880 yards per minute (52,800/60)
Learn more about computing distance and speed at https://brainly.com/question/26046491
#SPJ1
Find the mean for the amounts: $17,484, $14,978, $13,521, $14,500, $18,540, $14,978
Answer:
$15666.83 (2dp)
Step-by-step explanation:
Mean = Total of all values / Number of Values
= [tex]\frac{17484+14978+13521+14500+18540+14978}{6}[/tex]
=[tex]\frac{94001}{6}[/tex]
= $15666.83 (2dp)
X=y
Y=x
Is this is inverse equation
The inverse equation of x = y is y = x
What are inverse equations?Inverse equations are the opposite of an original equation
How to determine the inverse equation?The equation is given as
x = y
Swap the positions of x and y in the above equation
y = x
This means that the inverse equation of x = y is y = x
Read more about inverse equations at:
https://brainly.com/question/14391067
#SPJ1
The width of a rectangle measures
(7h+3) centimeters, and its length measures
(8h−4) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter of the rectangle is 30h - 2
How to determine the perimeter expression?The dimensions of the rectangle are given as:
Length = 7h + 3
Width = 8h - 4
The perimeter of the rectangle is given as:
P = 2 * (Length + Width)
Substitute the known values in the above equation
P =2 * (7h + 3 + 8h - 4)
Evaluate the like terms
P = 2 * (15h - 1)
Evaluate the product
P = 30h - 2
Hence, the expression that represents the perimeter of the rectangle is 30h - 2
Read more about perimeter at:
https://brainly.com/question/24571594
#SPJ1
FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
IF P(A OR B) = 0.9, P(A) = 0.5, AND P(B) = 0.6, FIND P(A AND B)
The value of the probability P(A and B) is 0.20
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.9
P(A) = 0.5
P(B) = 0.6
To calculate the probability P(A and B), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
P(A and B) = 0.5 + 0.6 - 0.9
Evaluate the expression
P(A and B) = 0.2
Hence, the value of the probability P(A and B) is 0.20
Read more about probability at
https://brainly.com/question/25870256
#SPJ1
mary is making a batch of chocolate chip cookies the recipe calls for 9 cups of flour and 2 4/7 cups of sugar she isshort on flour cuts the recipe down to 7 cups if flour how much sugar should she add
Answer:
2
Step-by-step explanation:
2. What is the length of the hypotenuse k?
Answer:
k ≈ 50.77
Step-by-step explanation:
using the cosine ratio in the right triangle
cos19° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{48}{k}[/tex] ( multiply both sides by k )
k × cos19° = 48 ( divide both sides by cos19° )
k = [tex]\frac{48}{cos19}[/tex] ≈ 50.77 ( to 2 dec. places )
Hi :)
————————————————We'll use sohcahtoa to solve this problem
[tex]\Large\boxed{\begin{tabular}{c|1} \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~\div \text{hyp}\\\sf{Cah} & Adj \div \text{hyp}\\\sf{Toa} & Opp \div \text{adj} \end{tabular}}[/tex]
Looking at our triangle, we can clearly see that we have :
adj. side = 48 (adjacent to the angle)hyp. k (the one we need)Set up the ratio
[tex]\longrightarrow\darkblue\sf{cos(19)=\dfrac{48}{k}}[/tex]
solve for k
[tex]\longrightarrow\darkblue\sf{k\cos(19)=48}[/tex] > multiply both sides by k to clear the fraction
[tex]\longrightarrow\darkblue\sf{k=\dfrac{48}{\cos(19)}}[/tex] > divide both sides by cos (19)
[tex]\star\longrightarrow\darkblue\sf{k\approx50.77}\star[/tex]
[tex]\tt{Learn~More ; Work\ Harder}[/tex]
:)
(02.03)
Figure ABCD is transformed to A′B′C′D′, as shown:
A coordinate plane is shown. Figure ABCD has vertices A at 3 comma 1, B at 3 comma 4, C at 5 comma 5 and D at 5 comma 3. Figure A prime B prime C prime D prime has vertices A prime at negative 5 comma 1, B prime at negative 5 comma 4, C prime at negative 7 comma 5 and D prime at negative 7 comma 3.
Which of the following sequences of transformations is used to obtain figure A′B′C′D′ from ABCD? (4 points)
Group of answer choices
Reflection about the x-axis followed by a translation right by 2 units
Reflection about the y-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units
What is the type of Transformation used?
As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.
Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).
Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)
Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).
Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).
This is the coordinates for A'.
Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.
Read more about Transformation Types at; https://brainly.com/question/4289712
#SPJ1
What is the solution to 3/4 a>-16?
O a>-21/3
O a<-21
O a> 21-1/
O a <21/13
[tex] \frac{3a}{4} > - 16 \\ 3a > - 64 \\ a > \frac{ - 64}{3} \\ a > 21 \frac{1}{3} [/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > - \dfrac{16}{1}}[/tex]
[tex]\huge\textbf{Divide \boxed{\dfrac{4}{3}} to both sides:}[/tex]
[tex]\mathsf{\dfrac{4}{3}\times\dfrac{3}{4}a > -16\times\dfrac{4}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{a > \dfrac{4}{3}\times -16}[/tex]
[tex]\mathsf{a > - \dfrac{16}{1} \times\dfrac{4}{3}}[/tex]
[tex]\mathsf{a > \dfrac{-16\times4}{1\times3}}[/tex]
[tex]\mathsf{a > \dfrac{-64}{3}}[/tex]
[tex]\mathsf{a > -\dfrac{64}{3}}[/tex]
[tex]\mathsf{a > -21 \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{- \frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Which expressions are equivalent to 2(4f + 2g)?
Answer:
For example, 8f + 4g is one of the most used expression
Another example is 4 (2f + g), is correct too
One fifth increase over 400
Answer:
480
Step-by-step explanation:
1/5 of 400 = 1/5 * 400 = 80
increase 400 by 80 = 480
Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously.
intorntic compounded semiannually is approximately
a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.
b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
How is the future value determined?The future value can be determined using an online finance calculator.
Data and Calculations:
a) Compounded Semiannually:Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Semi-Annually
Time (t in years): 8 years
Result:
A = $11,949.50
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,244.94
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 8,704.56(1 + 0.04/2)(2)(8)
A = 8,704.56(1 + 0.02)(16)
A = $11,949.50
b) Compounded Continuously:Using the formula A = Pert
Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Continuously
Time (t in years): 8 years
Result:
A = $11,987.29
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,282.73
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A, using the mathematical constant, e = 2.71828
A = Pert
A = 8,704.56(2.71828)(0.04)(8)
A = $11,987.29
Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
Learn more about compounding interest at https://brainly.com/question/24274034
#SPJ1
Suppose f(x) = x2. What is the graph of g(x) = f(4x)?
[tex]g(x)=f(4x)=(4x)^2 = 16x^2[/tex]
The graph is shown in the attached image.
I need help please yall
use orders of operation and simplify
Answer: [tex]\large\boxed{12x^3-30x+3=0}[/tex]
Step-by-step explanation:
[tex]Solve:\\\ 6(2x^2-5)x=-3\\\\Use\ distributive\ property\ first\\\\(12x^2-30)x=-3\\\\Now\ multiply\ the\ terms\ in\ ()\ by\ 'x'\\\\12x^3-30x=-3\\\\\large\boxed{12x^3-30x+3=0}[/tex]
Complete the square -3x^2+12x-7
Answer:
[tex]-3(x-2)^2+5[/tex]
Step-by-step explanation:
First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].
Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].
In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].
What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]
Finally, plugging [tex]b = -2[/tex] that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get [tex](x^2 - 4x + 4) = (x-2)^2[/tex].
So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].
In summary, the procedure is
[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]
A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $29. For 5 pounds of trail mix and 2 pounds of jelly beans, the total cost is $20. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
the price of one pound of trail mix is $3
the price of one pound of jelly beans is $2.5
Step-by-step explanation :
let t be the price of one pound of trail mix.
and b be the price of one pound of jelly beans.
This statement:
“For 3 pounds of trail mix and 8 pounds of jelly beans,
the total cost is $29”
Can be translated mathematically like this :
3t + 8b = 29
This statement:
“For 5 pounds of trail mix and 2 pounds of jelly beans,
the total cost is $20”
Can be translated mathematically like this :
5t + 2b = 20
We obtain a system of two equations :
3t + 8b = 29
5t + 2b = 20
Solving the system:
3t + 8b = 29 (equation 1)
5t + 2b = 20. (equation 2)
3t + 8b = 29
20t + 8b = 80 [4×(equation 2)]
3t + 8b = 29
17t = 51 [4×(equation 2) - equation 1]
3t + 8b = 29
t = 51/17 = 3
9 + 8b = 29
t = 3
8b = 20
t = 3
b = 20/8 = 5/2
t = 3
b = 5/2
t = 3
Therefore ,the solution to our system is (3 , 2.5)
Help me with this equation, please. (Image Attached)
So, the equation is sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)
The question has to to with trigonometric identities?
What are trigonometric identities?Trigonometric identities are equations that show the relationship between the trigonometric ratios.
How to solve the equation?Given the equation sin(x + y)/sin(x - y)
Using the trigonometric identities.
sin(x + y) = sinxcosy + cosxsiny andsin(x - y) = sinxcosy - cosxsinySo, sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/(sinxcosy + cosxsiny)
Dividing the rnumerator and denominator of ight hand side by sinx, we have
sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/sinx/(sinxcosy + cosxsiny)/sinx
sin(x + y)/sin(x - y) = (sinxcosy/sinx + cosxsiny/sinx)/(sinxcosy/sinx + cosxsiny/sinx)
= (cosy + cotxsiny)/(cosy + cotxsiny) (since cosx/sinx = cotx)
Dividing the numerator and denominator of the right hand side by cosy, we have
= (cosy + cotxsiny)/cosy/(cosy + cotxsiny)/cosy
= (cosy/cosy + cotxsiny/cosy)/(cosy/cosy + cotxsiny/cosy)
= (1 + cotxstany)/(1 + cotxtany) [since siny/cosy = tany]
So, sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)
Learn more about trigonometric identities here:
https://brainly.com/question/28034981
#SPJ1
Consider the equation
x/x − 1 = 6x + 1/x − 1
What is the LCD?
Multiply both sides of the equation by the LCD and rewrite the resulting quadratic equation in general form. _____=0
Solve the equation and check the solutions in the original equation. (Enter your answers as a comma-separated list.) x=________
The solution to the original equation is 1, 1/6
Solving equationEquations are expressions separated by mathematical operations.
Given the equation below
x/x − 1 = 6x + 1/x − 1
From the given expression, the least common denominator is x -1
Multiply both sides by x-1 to have;
x = 6x(x-1) +1
Expand
x = 6x^2-6x + 1
Equate to zero
6x^2-6x-x + 1 = 0
6x^2-7x +1= 0
The resulting quadratic equation in general form is 6x^2-7x +1 = 0
Factorize
6x^2 -6x-x + 1 = 0
Group the result
6x(x-1)-1(x-1) = 0
(6x-1)(x-1) = 0
6x - 1 = 0 and x -1 = 0
x = 1 and 1/6
Hence the solution to the original equation is 1, 1/6
Learn more on equation here: https://brainly.com/question/13763238
#SPJ1
Find the slope of the line. On a coordinate plane, a line goes through (0, negative 6) and (2, 0). a. Negative one-third c. 3 b. One-third d. Negative 3 Please select the best answer from the choices provided A B C D
The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.
What is the Slope of a Line?The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.
How to Find the Slope of a Line?If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).
Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:
(0, -6) = (x1, y1)
(2, 0) = (x2, y2)
Plug in the values into the slope formula to find the slope:
Slope (m) = (0 - (-6)) / (2 - 0)
Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]
Slope (m) = (6) / (2)
Slope (m) = 3
Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.
Learn more about slope on:
https://brainly.com/question/3493733
#SPJ1
Solve for x
Please write your work
Answer:
Step-by-step explanation:
12 + 2x + 24 = 27 + x
2x + 36 = 27 + x
x + 36 = 27
x = -9
2(-9) + 24 = -18 + 24 = 6
12 + 6 = 18
27 + (-9) = 18
(pls help)
5. Write the rule for the linear function. Remember a function rule is written using using f(x).
The linear function whose points are given is f(x)=[tex]x/5 +1[/tex]
Given the points of the function f(-10)=-1,f(0)=1,f(10)=3.
We are required to find the function whose points are given.
Function is relationship between two or more variables that are expressed in equal to form. In function each value of x must have a corresponding y value.
x value is known as domain and y value if known as codomain of the function.
Take two points (-10,-1) and (0,1) and we can form one equation as under:
y+1=(1+1/0+10) * (x+10)
y+1=2/10 (x+10)
y+1=x/5 +10/5
y+1=x/5+2
y=x/5+2-1
y=x/5+1
Hence the linear function whose points are given is [tex]f(x) = x/5 +1[/tex]
Learn more about function at https://brainly.com/question/10439235
#SPJ1
points a,b, and c make the triangle ABC and are at the coordinates A(-2,9), B(-33,13) and c(-21,25) point D is the midpoint of BC and AD is a median of ABC, the equation of the median can be given by ax+by=c where A B and C
what is most simple way to answer this
Answer:
[tex]2x+5y=41[/tex]
Step-by-step explanation:
Median of a triangle: A line segment that connects a vertex of a triangle to the midpoint of the opposite side.
Vertex: The point where any two sides of a triangle meet.
Given vertices of a triangle:
A = (-2, 9)B = (-33, 13)C = (-21, 25)Step 1Find the midpoint of BC (Point D) by using the Midpoint formula.
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\text{Let }(x_1,y_1)=\sf B=(-33,13)[/tex][tex]\text{Let }(x_2,y_2)=\sf C=(-21,25)[/tex]Substitute the defined endpoints into the formula:
[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]
Therefore, D = (-27, 19).
Step 2Find the slope of the median (line AD) using the Slope formula.
Define the points:
[tex]\textsf{let}\:(x_1,y_1)=\sf A=(-2,9)[/tex][tex]\textsf{let}\:(x_2,y_2)=\sf D=(-27,19)[/tex]Substitute the defined points into the Slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]
Therefore, the slope of the median is -²/₅.
Step 3Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]
Simplify and rearrange the equation so it is in standard form Ax+By=C:
[tex]\implies 5(y-9)=-2(x+2)[/tex]
[tex]\implies 5y-45=-2x-4[/tex]
[tex]\implies 2x+5y-45=-4[/tex]
[tex]\implies 2x+5y=41[/tex]
ConclusionTherefore, the equation of the median is:
2x + 5y = 41
Identify the slope and y-intercept of the line y = ×/2 -7
Answer:
Slope: [tex]-\frac{1}{5}[/tex] Y-intercept: (0,0)
Step-by-step explanation:
By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].
Which equation represents a parabola with a vertex at (7,-3)
Answer:
See Below
Step-by-step explanation:
y = a (x-7)^2 -3 where 'a' is any number except 0