How do i graph the line y=2/3x+ 490 using the slope intercept method?
Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
What is slope?
"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."
Formula used
standard equation of line
y = mx + c
m = slope of the line
c = y- intercept
According to the question,
Given equation of line,
[tex]y = \frac{2}{3} x+490[/tex]
Compare it with standard equation of line y = mx + c we get,
Slope [tex]m = \frac{2}{3}[/tex]
y-intercept = 490
Calculate x-intercept by putting y=0
x-intercept = -735
Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]
Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
Learn more about slope here
https://brainly.com/question/3605446
#SPJ3
What is the area the shaded triangle?
Answer:
96
Step-by-step explanation:
The area of the shaded triangle will be 96 mm² so option (B) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given two inscribed triangles.
The bigger one is the right-angle triangle.
The area of the right-angle triangle will be as,
A = 1/2 x 8 x (6 + 24)
A = 4 x 30= 120 mm².
The area of the smaller right-angle triangle,
a = 1/2 x 8 x 6 = 24 mm²
The area of the shaded triangle = 120 - 24 = 96 mm².
Hence "The area of the shaded triangle will be 96 mm²".
For more about triangles,
https://brainly.com/question/2773823
#SPJ2
What is the value for B, after the equation A=3/7(B-25) is rearranged?
Answer:
[tex]B=\frac{7A}{3}+25[/tex]
Step-by-step explanation:
We have been given an equation [tex]A=\frac{3}{7}(B-25)[/tex]. We are asked to find the value of B for our given equation.
Upon multiplying both sides of our equation by [tex]\frac{7}{3}[/tex], we will get:
[tex]\frac{7}{3}*A=\frac{7}{3}*\frac{3}{7}(B-25)[/tex]
[tex]\frac{7}{3}*A=B-25[/tex]
[tex]\frac{7A}{3}+25=B-25+25[/tex]
[tex]\frac{7A}{3}+25=B[/tex]
[tex]B=\frac{7A}{3}+25[/tex]
Therefore, the value of B is [tex]\frac{7A}{3}+25[/tex].
Find the directrix of the parabola y = (1/8)(x – 5)2 - 3.
Answer:
y= -5
Step-by-step explanation:
rewrite as standard form [tex]4.2(y-(3-))=(x-2)^{2}[/tex]
(h.k) = (2, -3), P=2
y= -3 -P
y= -3 -2
y= -5
Evaluate the following expression using the values given: Find 3x − y − 3z if x = −2, y = 1, and z = −2. −13 −1 1 13
The correct answer is -1
If $10,000 is invested in an account at the rate of 6.25% compounded monthly, then the amount after 15 years is approximately
The amount after 15 years is approximately $26,971.67.
Explanation:To calculate the amount after 15 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amountP = the principal amount (initial investment)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = number of yearsIn this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:
A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).
Learn more about Compound Interest here:https://brainly.com/question/14295570
#SPJ3
A student reader is making $5.90 per hour and gets a $0.52 raise. what is the percent increase? (round to the nearest tenth of a percent.)
Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we need to find the largest perfect square that is less than or equal to $n + 23$. The largest such $n$ is $41$.
Explanation:To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we can start by considering the numerator. The expression $(n + 1)^2$ is a perfect square, so it will always be divisible by $n + 23$ if $n + 23$ is also a perfect square. Therefore, we need to find the largest perfect square that is less than or equal to $n + 23$.
Let's consider some examples. If $n + 23 = 25$, then $n = 2$. If $n + 23 = 36$, then $n = 13$. If $n + 23 = 49$, then $n = 26$. If $n + 23 = 64$, then $n = 41$. Therefore, the largest value of $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer is $41$.
There are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.
To find the largest positive integer $n$ such that $\frac{(n + 1)^2}{n + 23}$ is an integer, we need to consider the factors of the numerator and denominator.
Let's expand the numerator, $(n + 1)^2$, using the binomial expansion formula:
$(n + 1)^2 = n^2 + 2n + 1$
Now, we divide this expression by $n + 23$ and express the result as an integer:
$\frac{n^2 + 2n + 1}{n + 23}$
We can use polynomial long division to divide $n^2 + 2n + 1$ by $n + 23$:
- (n - 21)
__________
n + 23 | n^2 + 2n + 1
- (n^2 + 23n)
_____________
-21n + 1
- (-21n - 483)
_____________
484
We obtain a remainder of 484. In order for the fraction to be an integer, the remainder must be 0. However, in this case, the remainder is not 0, which means that $\frac{(n + 1)^2}{n + 23}$ is not an integer for any positive integer $n$.
Therefore, there are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.
Complete question :-
There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.
A bag contains 5 apples and 3 oranges. if you select 4 pieces of fruit without looking, how many ways can you get 4 apples?
Answer:
5 ways
Step-by-step explanation:
I got it correct on founders edtell
If f(x)=5x-7 and g(x)√x-2 which statement is true?
-5 is in the domain or
-5 is not in the domain
-5 is in the domain of the function f(x)=5x-7, but not in the domain of the function g(x)√x-2. The domain of a function is the set of all acceptable input values.
Explanation:The question is asking whether -5 is in the domain of the given functions, f(x)=5x−7 and g(x)√x−2. The domain of a function is the set of all permissible inputs or arguments, i.e. x-values that can be inserted into the function.
In the case of f(x)=5x-7, the domain is all real numbers, as we can substitute any real number into 'x' and obtain a valid result. Hence, -5, indeed, is in the domain of the function f(x). However, for the function g(x)√x-2, the domain is all non-negative real numbers since we can't take the square root of a negative number in the real number system, hence -5 is not in the domain of g(x).
Thus, the statement '-5 is not in the domain' would be true if we are referring to g(x). However, if we are referring to f(x), the statement would be false because -5 is in the domain.
Learn more about Domain of a function here:https://brainly.com/question/28599653
#SPJ12
Complete the solution of the equation. find the value of y when equals -7
-3x+6y=-21
The value of y when equals -7 would be equal to -7.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given the equation as-3x+6y=-21
if x = -7 then we get;
-3x+6y=-21
Substitute;
-3(-7) +6y = -21
21 + 6y = -21
6y = -42
y = -7
Learn more about solving equations here:
https://brainly.com/question/18015090
#SPJ2
Pythagoras is planting a rose garden in the center of his rectangular yard, which is 20 feet long and 8 feet wide. He wants to dig up an area in the shape of an equilateral triangle with sides 5 feet each. After he digs up the rose-bed section, approximately how much grass will be left? Round to the nearest foot.
Answer:
The approximate remaining grass area is 144 square feet.
Explanation:
To find the area of the rectangular yard, we use the formula:
Area of rectangle [tex]= \text{length} \times \text{width} \)[/tex]
Given that the length is 20 feet and the width is 8 feet, we have:
Area of Rectangle [tex]= 20 \times 8 = 160 \text{ square feet} \)[/tex]
Next, we find the area of the equilateral triangle. Since we know the length of each side (5 feet) and an equilateral triangle can be divided into two congruent 30-60-90 triangles, we can use the formula for the area of an equilateral triangle:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (\text{side length})^2 \)[/tex]
Plugging in the value of the side length (5 feet), we get:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (5)^2 \)[/tex]
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times 25 \)[/tex]
Area of equilateral triangle [tex]= \frac{25\sqrt{3}}{4} \text{ square feet} \)[/tex]
Now, to find the remaining grass area after Pythagoras digs up the rose-bed section, we subtract the area of the equilateral triangle from the total area of the rectangle:
Remaining grass area [tex]= \text{Area of rectangle} - \text{Area of equilateral triangle} \)[/tex]
Remaining grass area [tex]= \ 160 - \frac{25\sqrt{3}}{4} \)[/tex]
Using a calculator, we find:
Remaining grass area [tex]\approx 144.3 \text{ square feet} \)[/tex]
Rounded to the nearest foot, the approximate remaining grass area is 144 square feet.
what is the correct name for the angle shown
Answer: The correct name is (B) ∠S.
Step-by-step explanation: We are given to find the correct name for the angle shown in the figure.
We can see in the figure that the rays RS and ST are intersecting at the point S. Therefore, RS and ST are making an angle at the point 'S'.
So, the name of the angle will be ∠S or ∠RST or ∠TSR.
First option is ∠R. This is not correct.
Second option is ∠S. This is the correct option.
Third option is ∠RTS. This is also not correct.
Fourth option is ∠SRT. This is not correct.
Thus, the correct option is (B) ∠S.
Katie earned $54.30 in interest from two accounts. One account Paid 4.1% apr and the other paid 3.2% apr. if she had a total of $1500 in the two accounts, How much was in each account?
Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius round to the nearest hundredth
volume for cylinder = pi x r^2 x h
radius = half the diameter = 8/2 =4
height = 3 times the radius = 3*4 =12
using 3.14 for pi
volume = 3.14 x 4^2 x 12 = 602.88 cubic inches
How many ways are there to arrange the first five letters of the alphabet?
Answer:
120 ways
Explanation:
Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them. In other words, there are 5 slots to place the first letter in, then 4 slots for the second letter, 3 for the third, 2 for the fourth, and then the last letter goes in the 1 slot that is left.
I hope this is correct and if it is I hope it helps. I hope you have a great day and remember it doesn't matter what other people say or think about you, you are still and always will be strong, smart, and an amazing person. Have a wonderful day.
I am happy to help with anything.
At what angle do the angle bisectors of two same side interior angles intersect in construction with two parallel lines and a transversal?
Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
A) Find the average rate of change of each section. (4 points)
80 POINTS!
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (give the polynomial with the GCF of 2 AND give two more forms and explain how you got it.
What is the sum of the measures of the exterior angles of any convex polygon
Answer:
360 degrees is sum of the measures of the exterior angles of any convex polygon.
Step-by-step explanation:
Convex Polygon:
A convex polygon is a polygon with all its interior angle less than 180 degrees.Thus, all the vertices of the polygon will be away from the interior of the polygon.If all the angles are not less than 180 degrees then it becomes concave polygon.Example: Triangle is a convex polygon with three sides.Exterior angle sum Property:
If we extend the side of the polygon, then the angle formed by the extended side and polygon side is an exterior angle.The sum of all the exterior angles if a convex polygon is 360 degrees.If this convex polygon is a regular polygon, then the sum is 360 degrees and each exterior angle is equal to [tex]\frac{360}{n}[/tex], where n is the number of sides in regular polygon.The sum of the measures of the exterior angles of any convex
polygon is 360°.
What is a Convex polygon?This is the polygon that is the boundary of a convex set and has
all the interior angles to be less than 180°.
The interior angles is 180(n-2) degrees and each exterior angle
is supplementary to its interior angle thereby resulting in the
sum of the exterior angles to be 360°.
Read more about Convex polygon here https://brainly.com/question/520645
Classify the variable as discrete or continuous. weights of backpacks of first graders on a school bus
WILL GIVE A BRAINLIEST ANSWER IF UR 100% CORRECT!!
Which of the following expressions is not equal to p^2?
A.
p^-3 * p^5 * p^-2 * p^2
B.
p^-9 * p^0 * p^2 * p^5
C.
p^-3 * p^-1 * p * p^5
D.
p^-5 * p^9 * p^-2 * p^0
Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].
Here,
We have to find the expression is not equal to p^2.
What is Property of addition in power of number?
This property states that when multiplying two powers with the same base, we add the exponents.
Now,
Let an expression [tex]x^{a} x^{b}[/tex]
Then it can be written as, [tex]x^{a} x^{b} = x^{a+b}[/tex]
So, Option B is given as,
[tex]p^{-9} *p^{0} * p^{2} *p^{5} = p^{-9+0+2+5} = p^{-2}[/tex]
Which is not equal to [tex]p^{2}[/tex].
Similarly, we check all options.
We get only option B is not equal to [tex]p^{2}[/tex].
Hence,
Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].
Learn more about the Property of addition in power of number visit:
https://brainly.com/question/13429877
#SPJ2
If ABCDE is translated 3 units to the right and 4 units down, what will happen to the polygon?
When polygon ABCDE is translated 3 units to the right and 4 units down, its shape and size remain unchanged, but its position on the coordinate plane changes, maintaining the same orientation and angles.
Explanation:If a polygon ABCDE is translated 3 units to the right and 4 units down, the shape and size of the polygon will remain the same, but its position will change. Each vertex (point) of the polygon will move 3 units to the right on the x-axis and 4 units down on the y-axis. This type of transformation is known as a translation, which is a slide of the entire figure in a specific direction. As a result, the translated polygon will maintain the same orientation and angles; it will simply be in a different location on the coordinate plane.
Please help me I'm so confused and it's due at 7:30
Prove that for any x in the reals 5 divides x if and only if 5 divides x squared
find the slope of the line through points (1,8) and (2,7). write the answer in simplest form.
Evaluate the expression:
the difference of 26 and 22
Select one:
a. 48
b. 91
c. 4
d. 13/11
Rewrite in simplest radical form 1/x^3/6.
Can anyone solve this.
solve the equation 14.50-p=53 please help