a. The scale factor is: 3/2
b. The pairs of corresponding angles are, <J and <P; <K and <Q; <L and <R.
c. The ratios are: JK/PQ = KL/QR = JL/PR.
How to Find the Scale Factor?The scale factor, also known as the ratio of similitude, is used to describe the relationship between the size of two similar figures. It is the ratio of the corresponding measurement of the new figure to the original figure.
a. scale factor from triangle JKL to triangle PQR = PQ/JK
= 9/6
= 3/2
b. The pairs of corresponding angles are:
<J and <P
<K and <Q
<L and <R
c. The ratios of the corresponding side lengths in a statement of proportionality will be: JK/PQ = KL/QR = JL/PR.
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five quare cake of ide 30cm i arranged to from a rectangle, Find the perimeter of the cake
The perimeter of five square and perimeter of rectangular cake is equal,
So, the perimeter of cakes is 600 cm.
The perimeter of a two-dimensional figure is the distance covered around it. It defines the length of shape, whether it is a triangle, square, rectangle or a circle. Area and perimeter are the two major properties of a 2D shape, which describes them.
We have five square cakes of side 30cm.
the perimeter of one cake is =4a
=4×30
=120 cm
So, the perimeter of five cake = 5(120)
=600 cm
The perimeter of five square and perimeter of rectangular cake is equal,
So, the perimeter of cakes is 600 cm.
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through a combination of fertility rate and decreased poverty levels, a population’s energy use is growing exponentially 1% per year. how many years until the energy use doubles?
For the energy use to double it will take approximately 69.66 years.
To find out how many years it will take for the energy use to double, we can use the formula for exponential growth:
P = P₀ * (1 + r)^t
where P is the final amount of energy use, P₀ is the initial amount of energy use, r is the growth rate (1% per year in this case), and t is the number of years.
Setting P = 2 * P₀ and solving for t, we get:
2 * P₀ = P₀ * (1 + r)^t
Dividing both sides by P₀:
2 = (1 + r)^t
Taking the natural logarithm of both sides:
ln(2) = t * ln(1 + r)
Dividing both sides by ln(1 + r):
t = ln(2) / ln(1 + r)
Plugging in the values for r = 0.01 and using the natural logarithm function, we get:
t = ln(2) / ln(1 + 0.01) = 69.66 years
So it will take approximately 69.66 years for the energy use to double.
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(2, -3) is a solution of the equation 3x - y = 3.
I just need to know the value of s
Answer:
S = 25
Step-by-step explanation:
Since it's stated as a square, that means all sides equal each other
In other words;
s+50 = 3s
To get S alone, we will first subtract 50 on both sides
s = 3s-50
Let's now subtract 3s from both sides
s-3s = -50, aka -2s = -50
Changing those to positive, 2s = 50
Last step is to divide both sides by 2
s = 25
Write a function rule for “the output is the square of the input”
Answer:
y=x^2
Step-by-step explanation:
The equation of the line which passes through the point (0,-4) and has a gradient of 0. 5 is
The equation of the line which passes through the point (0,-4) and has a gradient of 0. 5 is (x-8)/2.
A straight line can be represented by the "Point-Slope" form of the line.
In point-slope form, we can deduce an equation of any line on the Cartesian coordinate system with the help of its slope/gradient "m" and a point through which it passes (x1,y1).
the equation of Point Slope form is,
(y-y1)=m(x-x1),
where, x and y are any general point on the line.
in the given question the value of the slope/gradient (m) is given as 0.5
and it passes across the point (0,-4)
so according to the equation of the point-slope form,
the equation of line must be,
(y-(-4))=0.5(x-(0))
= y+4=0.5x
= 2y+8=x
= 2y = x-8
= y = (x-8)/2
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100 Points + Brainliest. Please take your time and answer correctly.
The y intercept has been moved down, and the g(x) graph is less steep than the f(x) graph.
What is meant by linear parent function?the fundamental duty of a family. Y = x or f(x) = x is the parent function for linear functions. Transformation: Modification of a figure's size or position. Child Function: The parent function is f(x) = x for all linear functions. y = x.
The simplest function in a family of functions that yet preserves the definition (or shape) of the entire family is known as a parent function in mathematics.
When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear.
Therefore, the correct answer is option C. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted down.
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A line passes through the points (-1,-9) and (1,7) write it’s equation in slope intercept form 
The equation of the line in slope intercept form is y = 8x -1.
What is slope intercept form?
The graph of the equation y = mx + b is a line with slope m and y-intercepts b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.
The slope, m, of a line indicates how steep it is. The gradient of a line is another name for the slope of a line. The y-intercept of a line is the y-coordinate of the location where the line's graph crosses the y-axis.
We are given two points which are (-1,-9) and (1,7).
First, we need to find the slope(m)
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]m=\frac{7 +9 }{1+1 }[/tex]
m = 16/2
m = 8
We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)
So,
⇒b = (-9) + 1(7 + 9)/(1+1)
⇒b = -9 + 8
⇒b = -1
The equation comes out to be
⇒y = mx + b
⇒y = 8x -1
Hence, the equation of the line in slope intercept form is y = 8x -1.
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Determine the solution to the inequality. one half times the absolute value of the quantity x plus 1 end quantity is greater than or equal to 6 x ≤ −13 or x ≥ 13 x ≤ −13 or x ≥ 11 x ≤ −4 or x ≥ 11 x ≥ 2 or x ≤ −4
The solution to the inequality:
(1/2)*|x + 1| ≤ 6
is:
x ≤ 11 or x ≥ -13
How to solve the absolute value inequality?Here we want to solve the inequality below:
(1/2)*|x + 1| ≤ 6
To solve it we need to isolate x, so let's start by multiplying both sides by 2:
2*(1/2)*|x + 1| ≤ 2*6
|x + 1| ≤ 12
Now we can break the absolute value part into two inequalities:
(x + 1) ≤ 12
(x + 1) ≥ -12
Solving these two we will get:
x ≤ 12 - 1 = 11
x ≥ -12 -1 = -13
That is the solution.
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What operation does the expression x + 5 involve?
Answer:
addition
Step-by-step explanation:
there's only one sign + so it means addition
Answer: addition
Step-by-step explanation:
15 first-year algebra students are learning how to solve two-step equations. the teacher notices that the students are not using precise mathematical language. which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? choose 2 answers
Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.
However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.
So the list goes as
1. Exponents
2. Roots
3. Multiplication
4. Division
5. additional
6. Subtraction
However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.
Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.
Furthermore, the preferred behavior norm for division and multiplication is different.
Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.
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Simplify: 2 3/20 + 1/10
Answer: 2 1/4
Step-by-step explanation: Exact Form:
9/4
Decimal Form:
2.25
Mixed Number Form: 2 1/4
HELP ME ASAPPPPP please make it right because i’m in so much trouble rn.
The top four winners in a golf tournament share the prize money in the ratio 9:5:2:1. If the top prize winner receives $45,00, then how much prize money is awarded in total?
(explanation would be appreciated I have to write it down)
$85000 is the prize money is awarded in total.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that top four winners in a golf tournament share the prize money in the ratio 9:5:2:1.
The top prize winner receives $45,000
We need to find the prize money is awarded in total.
9+5+2+1=17
9/17 x = 45000
Divide both sides by 9/17
x=$85000
Hence, $85000 is the prize money is awarded in total.
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Number 14
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Answer: 14
Step-by-step explanation: your correct
What is in mathematics 24divided4x2-2=
Answer:
10
Step-by-step explanation:
PEMDAS
hi help pls n thanks
The function represents the domain of a function is x ≥ -2.
What is a graph of a quadratic function?
A graph of a quadratic function is a type of parabola, which is a symmetric, U-shaped curve that opens either upward or downward. The equation of a quadratic function is y = ax² + bx + c, where x and y are variables, and a, b, and c are constants.
The graph of a quadratic function is determined by the value of the coefficient a. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The vertex of the parabola is the highest or lowest point on the graph and it is the point of symmetry of the parabola. The x-coordinate of the vertex is given by -b/(2a) and the y-coordinate of the vertex is given by the value of the function at that point.
In the given figure, we can see that it is a parabola, and if we look towards the options, then the third option is a domain of the given function
x ≥ -2
So we can say this is the perfect match for the given figure.
Hence, the function represents the domain of a function is x ≥ -2.
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A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees Rita?
|x – 42.80| = 12
|x + 42.80| = 12
|x – 12| = 42.80
|x + 12| = 42.80
The solution is Option A.
The value of the modulus function is | x - 42.80 | = 12
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the modulus function be represented as A
Now , the equation will be
The amount James borrowed from Rita or Rita borrowed from James = $ 12
And , Let x be the amount of money James will have after he sees Rita
The amount of money with James in his wallet = $ 48
So ,
when James pays Rita , the equation will be
x = 42.80 - 12
On subtracting 42.80 on both sides of the equation , we get
x - 42.80 = -12 be equation (1)
And , when James receives the amount from Rita , the equation is
x = 42.80 + 12
On subtracting 42.80 on both sides of the equation , we get
x - 42.80 = 12 be equation (2)
Now , the modulus function will be
| x - 42.80 | = 12
Hence , the function is | x - 42.80 | = 12
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Round 849 to the nearest ten
Answer:
850
Step-by-step explanation:
Everything above 5 goes to the next tenth. Example:
17 = 20
Everything below 5 goes to the next below tenth. Example:
13 = 10
You get it or more expantion?
*
The equation p(n) = 12/5n²-17 represents the overall profit
from production for a company where p is the total profit
in dollars and n is the number of hours per day that
the production line operates. Determine the profit when
n = 101/2 hours.
The profit when n = 101/2 hours is $1,842.50.
Determine the profit when n = 101/2 hours.When the production line operates for 101/2 hours, the total profit can be determined using the equation p(n) = 12/5n²-17.When n = 101/2, the equation becomes p(101/2) = 12/5(101/2)²-17.By simplifying this equation, we can find that the total profit for 101/2 hours of production time is p(101/2) = $723.Therefore, when the production line operates for 101/2 hours, the total profit for the company will be $723.The equation p(101/2) = 12/5(101/2)^2 - 17 can be used to determine the total profit when the production line operates for 101/2 hours. To solve this equation, the expression 12/5(101/2)^2 can be simplified to 12(101)^2/25 which evaluates to 12,405. Subtracting 17 from this result yields a total profit of 12,388 dollars when the production line operates for 101/2 hours. The profit when n = 101/2 hours can be calculated by substituting the value of n into the equation p(n) = 12/5n²-17. This yields a total profit of $323.36 when the production line operates for 101/2 hours.To learn more about the overall profit from production refer to:
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to raise money, a physics club sells tickets to a physics demo extravaganza. the tickets cost $6 for adults over 18 and $4 for younglings. after the show, they have raked in a total of $438 from the 82 people who came. how many adults and how many younglings attended?
There are 55 adults and 27 younglings attended the club.
let the number of adults attended the club be x
let the number of younglings attended the club be y
total people attended the club = 82
so,
x + y = 82.....[1]
cost for the adult = $6
cost for the younglings = $4
so total amount collected = $438
so, equation formed is ,
6x + 4y = 438.......[2]
from equation [1]
x + y = 82
x = 82 - y
put this in equation [2]
6(82 - y) + 4y = 438
492 - 6y + 4y = 438
492 - 2y = 438
492 - 438 = 2y
2y = 54
y = 27
put this value in equation [1]
x + y = 82
x + 27 = 82
x = 82 - 27
x = 55
so, there are 55 adults and 27 younglings attended the club.
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Could someone help please!! i really need these done
The specified equations in the question are in logarithmic form. The exponential form of the equations are as follows;
x³ = y10² = 1003³ = 2710⁰ = 1a¹ = a[tex]10^y[/tex] = x[tex]5^q[/tex] = py²⁰ = x2⁴ = 165² = 25What is the logarithmic form of an exponential equation?The logarithmic form of an exponential equation is the form logₐ(c) = b
The exponential form from which the logarithmic form is obtained, is the form aᵇ = c
The form of the equations in the question are in the logarithmic form, the exponential form of the equation are found as follows;
(1) 3 = logₓy
Therefore, x³ = y
(2) log₁₀100 = 2
Therefore, 10² = 100
(3) log₃27 = 3
Therefore, 3³ = 27
(4) log₁₀1 = 0
Therefore, 10⁰ = 1
(5) logₐa = 1
Therefore, a¹ = a
(6) log₁₀x = y
Therefore, [tex]10^y[/tex] = x
(7) log₅p = q
Therefore, [tex]5^q[/tex] = p
(8) [tex]log_yx=20[/tex]
Therefore, y²⁰ = x
(9) log₂16 = 4
Therefore, 2⁴ = 16
(10) log₅25 = 2
Therefore, 5² = 25
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Which value is equivalent to the expression 2power of 3 plus 3power of 4
Answer:
The value equivalent to the expression 2^3 + 3^4 is 19
GIVING 35 POINTS!!
The solids are similar. Find the volume V of the smaller solid.
Volume =
Answer:
Step-by-step explanation:
Answer:
Volume =936.3 ft³
Step-by-step explanation:
Solution Given:
The mathematics tells us that the cube of the ratio of the lengths is equal to the ratio of the volumes.
[tex]{(\frac{Side\: of\: bigger \: solid}{Side \: of \: smaller \: solid} )}^3 = \frac{volume\: of \: bigger \: solid}{volume \: of \: smaller \: solid} [/tex]
let volume of smaller solid be x.
by equation
[tex] {(\frac{12}{8} )}^3 = \frac{3160}{x} [/tex]
doing criss cross multiplication
12³*x=3160*8³
we get
[tex]x = \frac{3160 \times 8^3}{12^3} [/tex]
x= 936.296296296 ft³
The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.
a. If the car has gone 140 miles, how much gas was used? Show your thinking.
b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles
The amount of gas used for 140 miles is 3.5 gallons and the inverse equation is g = m/40
How to determine the amount of gas usedFrom the question, we have the following parameters that can be used in our computation:
m = 40g
The number of miles is given as
m = 140
substitute the known values in the above equation, so, we have the following representation
40g = 140
Divide by 40
g = 3.5
Hence, the amount of gas is 3.5 gallons
How to determine the inverse functionRecall that, we have
m = 40g
Divide by 40
g = m/40
Hence, the inverse is g = m/40
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gradient of 1 and passing through (0,4)
The equation of line with a gradient of 1 which runs through the point (0,4) is y = x + 4.
What is the equation of line with a slope of 1 and passing through (0,4)?The slope-intercept form is expresses as;
y = mx + b
Where m is slope and b is y-intercept.
The point-slope form is expressed as;
y - y₁ = m( x - x₁ )
Given that, the slope of the line m = 1 and it passes through (0,4)
Plug the slope m = 1 and point ( 0,4 ) into the point-slope form above and simplify.
y - y₁ = m( x - x₁ )
y - 4 = 1( x - 0 )
y - 4 = x - 0
y - 4 = x
Add 4 to both sides
y = x + 4
Therefore, the equation of the line is y = x + 4.
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what is the vertex of this quadratic function?
y=(x+4)^2-9
( , )
Step-by-step explanation:
the vertex form of a quadratic function is
y = (x - h)² + k
with (h, k) being the vertex.
luckily for us the function is already defined in that form.
so, when we compare
y = (x + 4)² - 9
with the general form about (h, k) above we see
h = -4
k = -9
so, the vertex is (-4, -9).
Harold brought two loaves of raisin bread to share with his friends. If there are 12 people total, including Harold, how much of the bread does each person receive?
A. 0.06
B. The decimal is 0.16 with 6 repeating.
C. 0.25
D. The term states the decimal 0.3 repeating.
Several classes in your school are going on a field trip. To transport the students, the teachers rent buses and vans. A total of 120 students are going on this field trip. Each bus can seat 24 students, and each van can seat 8 students. (a) Write a linear equation that describes the relationship of the number of buses and the number of vans needed, assuming exactly 120 students need transportation. (b) If the teachers rent 4 buses, how many vans will they need to transport all the students? (c) If the teachers rent 6 vans, how many buses will they need to transport all the students? (d) Suppose the teachers rented only vans. How many vans would they need? Show your work, and explain your answer. (e) Suppose the teachers rented only buses. How many buses would they need? Show your work, and explain your answer.
a) A linear equation that describes the relationship between the number of buses and the number of vans needed for 120 students is 24x + 8y = 120.
b) If the teachers rent 4 buses, the number of vans they will need to transport all the students is 3.
c) If the teachers rent 6 vans, the number of buses they will need to transport all the students is 3.
d) If the teachers rent only vans, the number of vans needed will be 15.
e) Suppose the teachers rented only buses, the number of buses needed will be 5.
What is a linear equation?A linear equation is an algebraic equation of the form y = mx+b.
A linear equation involves a constant and a first-order (linear) term, with m as the slope and b as the y-intercept.
The total number of students on the field trip = 120
The number of students a bus can seat = 24
The number of students a van can seat = 8
Linear equation:Let the number of buses = x and the number of vans = y
24x + 8y = 120
b) Renting 4 buses, the number of vans needed:
24(4) + 8y = 120
96 + 8y = 120
8y = 24
y = 3
c) Renting 6 vans, the number of buses will be:
24x + 8(6) = 120
24x = 48 = 120
24x = 72
x = 3
d) Renting only vans, the number needed will be:
24(0) + 8y = 120
8y = 120
y = 15
e) Renting only buses, the number needed will be:
24x + 8(0) = 120
24x = 120
x = 5
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Zeke is buying a rare car for 120,000. The dealership told Zeke that this car will gain interest at an annual rate of 1. 4% per year and he plans to sell the car after 10 years. How much will the car be worth after 10 years?
Part A: Write an Exponential Function to model the situation.
A(t)=
(
) ^ t
Part B: Round your answer to the nearest dollar.
After 10 years the car will be worth $
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &120000\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=\textit{elapsed time}\dotfill &10\\ \end{cases} \\\\\\ A = 120000(1 + 0.014)^{10} \implies A \approx 137898.90 ~\hfill \boxed{A=120000(1.014)^t}[/tex]