Answer:
y = 17x-67
Step-by-step explanation:
The one point form of line also called slope point form is given by
[tex](y-y_1)=m(x-x_1)[/tex]
where (x1, y1) is the point and m is slope
Given: (x1, y1) = (4,1) and m= 17
Substituting these values in above equation to find equation in point-slope form
(y-1)=17(x-4)
y-1 = 17x-68
y = 17x-67
the point -slope form of equation y = 17x-67
What are examples of perfect square Trinomials?
Example of perfect square trinomial is: x² + 6x + 9 it is expressed as
(x + 3)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Example:
x² + 6x + 9
= x² + 3x + 3x + 9
= (x +3) (x + 3)
= (x + 3)²
so, this is a perfect square trinomial.
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The auditorium seated 375, but this was enough for only 30% of those who wanted a seat. How many wanted a seat but couldn't get one?
Answer: 875 people
Step-by-step explanation:
The 375 people seated represent 30% of the total number of people who wanted seats but these ones got them.
This means that the number of people who wanted seats is 70% of the number of people who wanted seats.
Assume the number of people who wanted seats is x:
30% * x = 375
x = 375 / 30%
x = 1,250 people wanted seats.
Those who wanted seats but couldn't get:
= 1,250 * 70%
= 875 people
The population of a town is 20,000. It decreases at a rate of 9% per year. In about how many years will the population be fewer than 13 2007
In 5 years the population will be fewer than 13000.
What is percentage ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified percentage.
20000( 1 - 9% )^5
≈ 12481
12481 < 13000
ie 5 years
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dentify the relationship between angles x and y
the x & y angles are alternate angles.
What is alternate angles?The alternate exterior angle theorem states that if two lines are parallel and are intersected by a transversal, then the alternate exterior angles are considered as congruent angles or angles of equal measure.
Here, we have,
from the given figure , we get,
the x & y angles are alternate angles.
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Triangle DEF was dilated according to the rule DO,One-third(x,y)(one-third x, one-third y) to create similar triangle D'E'F'.
On a coordinate plane, (0, 0) is the center of dilation. Triangle F D E is dilated to create smaller triangle F prime D prime E prime. Triangle F D E has points (negative 9, 3), (negative 9, 9), (negative 6, 6). Triangle F prime D prime E prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).
Which statements are true? Select three options.
∠F corresponds to ∠F'.
Segment EE' is parallel to segment FF'.
The distance from point D' to the origin is One-third the distance of point D to the origin.
The measure of ∠E' is One-third the measure of ∠E.
△DEF △D'E'F'
A. ∠F corresponds to ∠F' is True.
B. Segment EE' is parallel to segment FF' is False.
C. The distance from point D' to the origin is One-third the distance of point D to the origin is True.
D. The measure of ∠E' is One-third the measure of ∠E is False.
E. △DEF ~ △D'E'F' is True.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given:
As triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'.
and, The center of dilation = (0, 0)
Also, Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).
Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)
A) ∠F corresponds to ∠F'. ( True)
B) Segment EE' is parallel to segment FF'. (False)
As they intersect each other at the origin.
C) The distance from point D' to the origin is One-third the distance of point D to the origin. ( True)
Now, the length of DE
D = √(-9-0)² + (-9-0)²
D = 9√2
and, length of D'E'
D = √(-3-0)² + (-3-0)²
D = 3√2
Thus, DE / D'E' = 3√2/ 9√2 = 1/3
D) The measure of ∠E' is One-third the measure of ∠E. ( False)
E) △DEF ~ △D'E'F'. ( True)
As they are similar triangles.
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Answer:
A. ∠F corresponds to ∠F'.
C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.
E. △DEF ~△D'E'F'
Step-by-step explanation:
got it right on edge 23
A cross-shaped pattern is made by arranging four identical rectangles
around the sides of a square, as shown in the diagram.
The area of the square is 36 cm2.
The area of each rectangle is one and a third times the
area of the square.
Find the perimeter of the cross-shaped pattern.
Show your working and state the units of your answer.
Answer:
88 cm^2
Step-by-step explanation:
one rectangle = perimeter of 28 and times 4 equals 112 but you have to subtract 24 the perimeter of the square and get your answer
—PLEASE HELP QUESTION IS IN THE PIC—
Answer:
I'm pretty sure the answer is B.
Step-by-step explanation:
so you multiply 3x4 and get 12. Then you multiply 5x11 and get 55. last but not least multiply 12 and 55 and get 660 so yeah hope it helps
A map is drawn using a scale of 2 cm : 75 miles. Two cities are 325 miles
apart. How far apart are the two cities on the map?
Answer:
The answer is 8.67
Step-by-step explanation:
Divide the distance by 75 since it's the actual distance of the scale factor
325/75=4.33
Multiply the answer by the scale factor
4.33×2=8.67
Use a calculator to simplify: N (-8 - 92.5) / -32
Answer:
3.14
Step-by-step explanation:
-8 - 92.5 = -100.5, and then -100.5/(-32) = 3.14
Alternatively, type in (-8 -92.5)/(-32)
HELP HELP HELP HELP
Emily purchased a television that is priced at $155.75. If the sales tax rate is 4% what will be the amount of sales tax on Emily's purchase?
Answer:
$6.23
Hope this helps! :)
What value of n makes the equation true? Show your work.
Answer:
n=13
Step-by-step explanation:
When multiplying two numbers with the same base, add the exponents
[tex]8^{9} *8^{4} =8^{13}[/tex]
When dividing two numbers with the same base, subtract the exponents[tex]\frac{(8^{n})^{3}}{8^{2} } =(8^{n})^{3-2}=(8^{n})^{1}=8^{n}[/tex]
So
[tex]8^{13} =8^{n}[/tex]
The bases are the same, so you can cancel them
13=n
n=13
How do you find the ordered pair?
On a Cartesian (or "coordinate") plane in which each point is represented by an ordered pair (x , y) belongs to x coordinate , y coordinate .
An ordered pair is a set of numbers in which it gives the location of a point on a coordinate plane.
The ordered pair is always expressed exactly the same way (x , y).
The first number in an ordered pair represents the x coordinate on the plane while the second number in an ordered pair represents the y coordinate.
The x-coordinate shoes that how far away the point is horizontally from the x-axis.
The y-coordinate shows that how far away the point is vertically from the x-axis.
Quadrant I: the upper-right quadrant of the plane in which all points in this quadrant have the positive x coordinates and positive y coordinates as { (+,+)} , {(+,+)}
Quadrant II: the upper-left quadrant of the plane in which all points in this quadrant have negative x coordinates and positive y coordinates
{ (+,-)}{ (+,-)}
Quadrant III: the lower-left quadrant of the plane in which all points in this quadrant have negative x coordinates and negative y coordinates
{ (-,-)}{(-,-)}
Quadrant IV: the lower-right quadrant of the plane in which all points in this quadrant have positive x coordinates and negative y coordinates
{(+,-)}{ (+,-)}
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Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Step-by-step explanation:
[tex] {x}^{2} + 3x - 5 = 0[/tex]
a =1. b = 3. c = -5
Quadratic equation
[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 \: + \sqrt{ {3}^{2} \: - 4(1)( - 5) } }{2} \\ = \frac{ - 3 \: + \: \sqrt{29} }{2} [/tex]
Note: the plus sign in the quadratic equation should read "+-"
Therefore, the roots of the quadratic equation are
[tex]\frac{ - 3 \: + \: \sqrt{29} }{2} \: \: and \: \: \frac{ - 3 \: - \: \sqrt{29} }{2} [/tex]
What is the perimeter?
Help plz...And No links!!I repeat No links!!
Answer:
36 units
Step-by-step explanation:
First calculate the length of side a. Using the Pythagorean Theorem, we find that 15^2 = 12^2 + x^2, or 225 - 144 = x^2. Thus, x^2 = 81 and the length of side a is √81, or 9, units.
Then the perimeter is the sum of all three side lengths:
15 + 9 + 12 = 36 units
A construction company plans to lean a 15ft ladder against a building from 7ft away. How far up the building will if reach?
Answer:
8 Feet
Step-by-step explanation:
15 feet subtract 7 feet is 8 feet
A worker earned a 2% increase in her annual salary for each of 4 years. She plans to continue working in her position for an additional n years. If she continues to earn a 2% increase in her annual salary, which statement describes the expression that can be used to calculate the total percent increase in her annual salary from the first year to the last year? A The expression 1.02(4n) can be used because (1.0244)" = 1.02(An). The expression 1.02(4n) can be used because 1.024 x 1.02” = 1.02(4n). The expression 1.02(4+n) can be used because 1.024 x 1.02n = 1.02(4+n). The expression 1.02(4+n) can be used because 1.024 +1.02” = 1.02(4+n). B D
ummm help ig please................
Answer:
Cost of 500 g of standard pack = € 7.50
Cost of 1 g of standard pack = 7.50/500
Cost of 100 g of standard pack = 7.50/500 ×100
= 7.50/5
= € 1.50
Hope it helps uh dear
what is the volume of this rectangular prism? (answer the picture)
Answer:
20.7 yd(rounded)
21 yd (exact)
Step-by-step explanation:
Since it goes 7 wide, do 7 x1/3 = 2.3 The 1/3rd comes from measurement given.
The length is 3 x 1/3 = 1 yd., so each level is 2.3 (repeating).
Since the height is 9, 9x2.3 = 20.7 yds (rounded)
If you want to be exact, 2.3333333333 x 9 = 21 (exact)
john is 7 years younger than jane. the sum of their age is 10 years ago was 55 years. how old are they now
Answer: John is 29 years old and Jane is 36 years old.
Step-by-step explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[tex](y-7)+y=65[/tex] [combine like terms]
[tex]2y-7=65[/tex] [add both sides by 7]
[tex]2y=72[/tex] [divide both sides by 2]
[tex]y=36[/tex]
Now we know that y=36, we can plug that into either equations to find x.
[tex]x+36=65[/tex] [subtract both sides by 36]
[tex]x=29[/tex]
This concludes that John is 29 years old and Jane is 36 years old.
1) The sum of two numbers is 6. If one number is subtracted from the other, their difference is 4. Find the
numbers.
Answer:
One number is 5 and the other is 1.
Step-by-step explanation:
Let the numbers be x and y. Then x + y = 6 and x - y = 4. We must solve this system of equations:
x + y = 6
x - y = 4
Combining these equations temporarily eliminates y:
x + y = 6
x - y = 4
--------------
2x = 10
Then x = 5. Since x - y = 4,
5 - y = 4
and so y must be 1.
The solution is (5, 1). One number is 5 and the other is 1.
What is the modulus of 2 - 3i?
Oi
O √√√5
O
1-√√5
O√13
The modulus of 2 - 3i is √13. So, the correct option is d.
What is modulus?Modulus is a mathematical operation used to find the remainder when dividing two numbers. This is called a percent sign (%) and is represented by a single number such as 12. Used to determine if two numbers are divisible (no remainder). You can also use the modulus to compare two numbers to see which is greater or lesser. Additionally, this module can be used to calculate the distance between two points on the coordinate plane.
It is computed by taking the square root of the sum of the squares of the real and imaginary components, so √(2^2 + (-3)^2) = √13. The modulus of a complex number, also called absolute value, is a measure of distance from the origin.
Let z = -2 - 3i
z = (-2) + (-3)i
Modulus of z = √((-2)² + (-3)²)
√(4 + 9) = √13
Modulus of z = √13
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What percent of Greg’s gym attendance falls above a 90?
Answer:
100
Step-by-step explanation:
hope this helps
Please awnswer the question below
Answer:
- ANTIFRAGILE -
Anti-ti-ti-ti fragile, fragile
Anti-ti-ti-ti fragile
Anti-ti-ti-ti fragile, fragile
(Anti-fragile)
(Anti-fragile)
가시밭길 위로 riding, you made me boost up (ah-ah-ah-ah)
거짓으로 가득 찬 party 가렵지도 않아
내 뒤에 말들이 많아, 나도 첨 듣는 내 rival
모두 기도해 내 falling 그 손 위로 I'ma jump in
Yes, gimme that
걸어봐 위엄 like a lion
눈빛엔 거대한 desire (nan-na-na-eh)
더 부어 gasoline on fire
불길 속에 다시 날아 rising (nan-na-na-eh)
잊지 마, 내가 두고 온 toe shoes
무슨 말이 더 필요해?
무시 마, 내가 걸어온 커리어
I go to ride 'til I die, die
더 높이 가줄게
내가 바랐던 세계 젤 위에 (ah-ah)
떨어져도 돼
I'm anti-fragile, anti-fragile (ah-ah)
난 지금 on my way
갖다버려 줘 너의 fairy tale (ah-ah)
Now you know my name
I'm anti-fragile, anti-fragile
Anti-ti-ti-ti fragile, fragile
Anti-ti-ti-ti fragile
Anti-ti-ti-ti fragile, fragile
(Anti-fragile)
(Anti-fragile)
Lovey, lovey, lovey
Dovey, dovey, dovey
멋대로 정하네 나란 애에 대해
I don't know what to say, I can't feel it
뜨거운 관심은 환영, 귀여운 질투는 go ahead
줄 달린 인형은 no thanks 내 미랠 쓸 나의 노래
Yeah, gimme that
걸어봐 위엄 like a lion
눈빛엔 거대한 desire (nan-na-na-eh)
더 부어 gasoline on fire
불길 속에 다시 날아 rising (nan-na-na-eh)
잊지 마, 내가 두고 온 toe shoes
무슨 말이 더 필요해?
무시 마, 내가 걸어온 커리어
I go to ride 'til I die, die
더 높이 가줄게
내가 바랐던 세계 젤 위에 (ah-ah)
떨어져도 돼
I'm anti-fragile, anti-fragile (ah-ah)
난 지금 on my way
갖다버려 줘 너의 fairy tale (ah-ah)
Now you know my name
I'm anti-fragile, anti-fragile
Anti-ti-ti-ti fragile, fragile
Anti-ti-ti-ti fragile
Anti-ti-ti-ti fragile, fragile
(Anti-fragile)
(Anti-fragile)
We can break it baby
Rock it, twist it, lock it baby
All I know is you can't chain me
'Cause I'm gonna break out
Gonna, gonna break out, out
We can break it baby
Rock it, twist it, lock it baby
All I know is you can't chain me
'Cause I'm gonna break out
Gonna, gonna break out, out (whoa-uh-oh-oh!)
더 높이 가줄게
내가 바랐던 세계 젤 위에 (ah-ah)
떨어져도 돼
I'm anti-fragile, anti-fragile (ah-ah)
난 지금 on my way
갖다버려 줘 너의 fairy tale (ah-ah)
Now you know my name
I'm anti-fragile, anti-fragile
Anti-ti-ti-ti fragile, fragile
Anti-ti-ti-ti fragile
Anti-ti-ti-ti fragile, fragile
(Anti-fragile)
(Anti-fragile)
- song by Le Sserafim
- song title : anti fragile
- stan Le Ssefarim for a better life <3
xoxo
Step-by-step explanation:
Pete borrowed $400 for one year. He paid back a total of $440. What was the interest rate per year?
How do I do this function stuff I’m been kinda confused
Explanation:
When solving a function, you plug in the given [tex]x[/tex]-value (what's inside the parentheses next to the [tex]g[/tex] or [tex]f[/tex]) into the corresponding equation (what [tex]f(x)[/tex] and [tex]g(x)[/tex] are set equal to).
Before starting the worksheet, take a simpler example:
Given the function [tex]h(x) = x + 2[/tex],
the following work solves for [tex]h(3)[/tex].
[tex]h(3) = 3 + 2[/tex]
[tex]h(3) = 5[/tex]
Essentially, to solve for the value of a function for a given [tex]x[/tex]-value, simply plug in that value in for [tex]x[/tex] and simplify the resulting expression.
Onto problem 14 from the given worksheet:
We are given [tex]f(x) = 3x + 2[/tex] and are asked to solve for [tex]f(4)[/tex].
Hence, all we have to do is plug [tex]4[/tex] in for [tex]x[/tex]:
[tex]f(4) = 3(4) + 2[/tex]
[tex]f(4) = 12 + 2[/tex]
[tex]f(4) = 14[/tex]
You can apply this concept to the rest of the problems.
9.
Choose the linear inequality that describes the graph. The gray area represents the shaded region.
A. 4x – y ≥ 4
B. 4x + y < 4
C. 4x + y > 4
D. 4x + y ≥ 4
Answer:
D. 4x + y ≥ 4
Step-by-step explanation:
Please help with this question
Answer:
92°
Step-by-step explanation:
We can say that the angle that is of x degrees is an inscribed angle because its vertex is on the circle and its sides are made up of rays. When you have an inscribes angle, it measures exactly half the angle it intercepts. In this case that angle is 184°. So, because of this we can say:
x = 184° / 2
x = 92°
Using the clues below, what is the value of the bigger number?
Clue 1: The sum of two numbers is ten.
Clue 2: The difference of the numbers is two.
Answer:
6
Step-by-step explanation:
Call the bigger number a, smaller b
a + b = 10
b + 2 = a
a + b + 2 = a + a = 2a = 12
a = 12 : 2
a = 6
Perform the indicated operation. Be sure the answer is reduced.
Answer:
It's the middle option
Step-by-step explanation:
What is the quotient of 1. 782 x 109 and 8. 1 x 106 expressed in scientific
notation?
The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.
What are the rules for exponents?Several rules for exponents are
Product rule → aⁿ × aˣ = aⁿ⁺ˣQuotient rule → aⁿ / aˣ = aⁿ⁻ˣPower of a product rule → (ab)ⁿ = aⁿ × bⁿPower of a quotient rule → (a/b)ⁿ = aⁿ / bⁿPower of a power rule → (aⁿ)ˣ = aⁿˣZero rule → a⁰ = 1Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!
Dividing the first number by the second using the quotient rule, it would be
= (1.782 × 10⁹) / (8.1 × 10⁶)
= (1.782/8.1) × (10⁹/10⁶)
= 0.22 × 10⁹⁻⁶
= 0.22 × 10³
In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
So,
0.22 × 10³ = 2.2 × 10²
Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².
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