The area of a 2D form is the amount of space within its perimeter. The length of the rectangle is 29 inches and the width of the rectangle is 12 inches.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the sheet be represented by x and the length be represented by y.
Area = x × y
348 = xy
x = 348/y
Perimeter = 2(x+y)
82 = 2(x+y)
41 = x + y
41 = (348/y) + y
0 = y² - 41y + 348
y = 29, 12
Therefore, the length of the rectangle is 29 inches and the width of the rectangle is 12 inches.
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50 POINTS! Should I buy an Eric Emanuel hoodie or a Cdg Hoodie
Answer:
Step-by-step explanation:
A 20-foot ladder is leaning against a building. The ladder forms an angle of 55" with the ground.
Part A: How far away from the building is the bottom of the ladder? Round the answer to the nearest tenth.
Part B: How far up the building does the ladder go? Round the answer to the nearest tenth.
Part C: If the ladder is repositioned, and the base is now 9 feet from the building, what is the new angle that the ladder makes with the ground? Round the answer to the nearest tenths place.
NO LINKS!!! Part 1:
What is the Transformation of f(x)= x^3:
THIS IS NOT MULTIPLE CHOICE!!!!
1. f(x)= 1/5x^3
2. f(x)= (x-5)^3
3. f(x)= x^3 + 5
Answer:
1. Vertical shrink by a factor of ¹/₅
2. Right 5
3. Up 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 1
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3[/tex]
Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.
Therefore, the transformation is:
[tex]y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}[/tex]
As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say: Vertical shrink by a factor of ¹/₅
Question 2
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x-5)^3[/tex]
Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.
Therefore, the transformation is:
[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]
Question 3
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=x^3+5[/tex]
Comparing the parent function with the given function, we can see that 5 has been added to the parent function.
Therefore, the transformation is:
[tex]f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}[/tex]
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Answer:
1) Vertical shrink by a factor of 1/5
2) Right 5
3) Up 5
Explanation:
Given main function: f(x) = x³
1.) f(x) = 1/5 (x³)
Comparing with a(f(x)) which gives vertical stretch or compression.
Here the function f(x) has been shrinked vertically by a factor of 1/5
2.) f(x) = (x - 5)³
Comparing with f(x - c) which gives horizontal translation c units right.
Here the function f(x) has been shifted 5 units to the right.
3.) f(x)= x³ + 5
Comparing it with f(x) + d which gives vertical translation d units up.
Here the function f(x) has been moved 5 units up.
given that the circumferential of a circle is 22cm calculate its diameter
Answer:
diameter =7 cm
Step-by-step explanation:
circum=2pi×r
[tex]2\pi \times r[/tex]
2×pi×r=22
2×22÷7×r=22
r=22×7÷44
r=7÷2
r=3.5
d=2×r=2×3.5=7
The sum of three consecutive even integers is –78. What are the integers? Describe how you would use the strategy of writing an equation to solve the given problem. Which of the following did you include in your description? Check all of the boxes that apply. Let x = the smallest even integer, x + 2 = the next even integer, and x + 4 = the largest even integer. Write the equation x + x + 2 + x + 4 = –78. Simplify the equation as 3x + 6 = –78. Solve the equation by subtracting 6 and dividing by 3 on both sides of the equation. Check that the sum of the integers –28, –26, and –24 is –78.
Answer:
456_487= 57,548 that it try it and lete know
Rhoda is asked to graph this system of equations:
5x-6y=4
3y+2x=7
How many times will the lines intersect?
A. The lines will not intersect
B. The lines will intersect once.
C. There is no way to tell without graphing the lines first.
D. The lines will intersect infinitely many times, because they are identical.
Answer back fast!
I will award Brainliest too!
Answer: B. The lines will intersect once.
Step-by-step explanation:
Multiplying the bottom equation by 2, we get 6y+4x=14.
Adding this to the first equation, this gives 9x=18, and thus x=2.
Therefore, since this means there will be 1 solution, the lines will intersect once.
Estimate the average rate of change from x=4 to x=5 .
Answer:
Average rate of change = 4/3
Step-by-step explanation:
We have to calculate the average rate of change of the graph at x = 2 to x = 5.
From the graph attached,
At x = 2,
f(2) = 3
At x = 5,
f(5) = 7
Since, average rate of change of the function between x = a and x = b is defined by,
Average rate of change = f (b)-f (a) / b - a
Therefore, average rate of change of the function represented by the graph will be =7-3/5-2
= 4/3
I need help with the question that says the area of the triangle is…. What is one way to write the equation?
Answer:
A = b(h/2)
Step-by-step explanation:
Any rewrite of the equation can make use of the commutative and associative properties of multiplication.
What are the properties of multiplication?The commutative property of multiplication lets you change the order of the operands. The given equation can have any of 6 different orders of operands:
A = (1/2)bh = (1/2)hb = b(1/2)h = bh(1/2) = h(1/2)b = hb(1/2)
The associative property of multiplication lets you change the grouping of the operands:
A = ((1/2)b)h = (1/2)(bh)
These ways of grouping operands can apply to any of the 6 different orders of operands, so there are 12 ways to write the equation.
One way to write the equation is ...
A = b(h/2)
__
Additional comment
Please note that the way we have written the equation helps you see that the area of a triangle is equivalent to the area of a rectangle that has half the height. This can sometimes be useful when computing the areas of composite figures.
A = bh . . . . . . . rectangle areaA = b(h/2) . . . . triangle area with the same heightAnswer:
[tex] A = \dfrac{bh}{2} [/tex]
Step-by-step explanation:
[tex]A = \dfrac{1}{2}b \cdot h[/tex]
[tex] A = \dfrac{bh}{2} [/tex]
Write this ratio as a fraction in simplest form without any units. 28 quarts to 9 gallons You can use the table below to help convert the units. Length Weight Capacity (Volume) 1 foot 12 inches 1 yard = 3 feet 1 pound = 16 ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts
Answer:
7/9
Step-by-step explanation:
In order to write the fraction without any units (as a pure number), we must have units in the numerator and denominator that are the same. Then the units cancel.
Convert to gallonsWe are given the conversion ...
4 quarts = 1 gallon
Multiplying by 7, we see ...
28 quarts = 7 gallons
RatioThis lets us write the desired fraction as ...
(28 quarts)/(9 gallons) = (7 gallons)/(9 gallons) = 7/9
The ratio in simplest form is 7/9.
help please. been stuck on this for the past hour!!
Answer:
A) 100 terms, B) 63 terms, C) 101 terms==========================
Given sequences:A) 1, 4, 4², ..., 4⁹⁹B) 11, 15, 19, 23, ..., 259C) 44, 45, 46, ..., 144To findThe number of terms.SolutionA) We know any number with power of zero equals 1, therefore the sequence can be expressed as powers of 4:
4⁰, 4¹, 4², 4³, ... , 4⁹⁹The number of terms from zero to 99 is:
99 + 1 = 100B) This is a AP with the first term of 11 and common difference of 4.
The nth term equation is:
aₙ = a₁ + (n - 1)dSubstitute the values and solve for n:
259 = 11 + (n - 1)*44(n - 1) = 259 - 114(n - 1) = 248n - 1 = 248/4n - 1 = 62n = 63C) Same as above, the sequence is AP, with the first term 44 and common difference 1.
Applying the nth term formula:
144 = 44 + (n - 1)*1n - 1 = 144 - 44n - 1 = 100n = 101What is the range of the function f(x)=1/2√x?
A. all real numbers
B. all real numbers greater than but not equal to 0
C. all real numbers less than or equal to 0
D. all real numbers greater than or equal to 0
Answer:
D. all real numbers greater than or equal to 0
Step-by-step explanation:
The range is the set of y-values.
What's the least common denominator of 34, 45, and 237
O A. 20
OB. 12
O C. 15
O D. 60
Answer:
120870
Step-by-step explanation:
Your answer choices are not correct. The least common denominator of 34, 45, and 237 would be 120870.
LCD(1/34, 1/45, 1/237) = LCM(34, 45, 237) = 2×32×5×17×79 = 120870
1/34= 3555/120870
1/45= 2686/120870
1/237= 510/120870
HOPE THIS HELPS!!
Question An old vinyl record is played on a turntable that turns at a rate of 45 rotations per minute. Find the angular speed in radians per second. Give your answer as a fraction and do not include units. Keep your answer in terms of if necessary.
The angular speed of the turntable is = 4.7 rad/sec.
Calculation of angular speedAngular speed can be defined as the rate at which angular displacement changes with respect to time.
Speed can be defined as the distance traveled by an object at a particular time interval.
The rate of rotation of the turntable = 45 rotations per minute.
That is, the time taken to complete one rotation in seconds = 1/45 ×60sec = 1.34secs
This is taken to be the period of rotation (T)
Therefore, the angular speed is calculated using the formula, 2π/T
= 2×3.14/1.34 = 4.7 rad/sec.
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calculate a four day moving average for a price of the stock for the end of day 7.day1=32,day2=56,day3=50,day4= 60, day5=59 ,day6 =55,day7=59,day8=63
The moving average of the stock for the end of day 7 is 53
How to determine the averageNote that
Average = Day 1 + Day 2 + Day3 + Day 4 = Day 5 + Day 6 + Day 7/ 7
We have
Average = 32 + 56 + 50 + 60 + 59 + 55 + 59 /7
Average = 371/ 7
Average = 53
Therefore, the moving average of the stock for the end of day 7 is 53
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Mia counts on in steps of 100 she starts at 946. Write the next number she says
Answer:
100+946=1046
Ao the next no. Is 1046
Pls help! Geometry
What is the perimeter of the shape above?
What is the area of the shape above?
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
Geometry Perimeter and area
A)
B)
C)
(b) Solve the trigonometric equation and verify that its solutions are the x-coordinates of the maximum and minimum points of f. (Calculus is required to find the trigonometric equation. For each solution, give an exact answer and then round to four decimal places. Enter your answers from smallest to largest.)
The given trig equation is obtained by solving for the critical points of [tex]f[/tex], which is done by differentiating [tex]f[/tex] and setting the derivative equal to zero.
We have
[tex]18 \sin(x) \cos(x) - 9 \sin(x) = 0[/tex]
[tex]9 \sin(x) (2 \cos(x) - 1) = 0[/tex]
[tex]9 \sin(x) = 0 \text{ or } 2 \cos(x) - 1 = 0[/tex]
[tex]\sin(x) = 0 \text{ or } \cos(x) = \dfrac12[/tex]
In the interval [tex]0\le x< 2\pi[/tex], we have
[tex]\sin(x) = 0 \implies x = 0 \text{ or } x = \pi[/tex]
and
[tex]\cos(x) = \dfrac12 \implies x = \dfrac\pi3 \text{ or } x = \dfrac{5\pi}3[/tex]
In order from smallest to largest, that's
[tex]x = 0 \text{ or } x = \dfrac\pi3 \text{ or } x = \pi \text{ or } x = \dfrac{5\pi}3[/tex]
The solution to the Trigonometric equation is given as below.
What is a Trigonometric equation?A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is represented in terms of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles.
The solution to the above problem is?The provided trigonometric equation is produced by determining the critical points of f by differentiating and setting the derivative to zero.
Thus,
18 sin (x) cos (x) - 9 sin (x) = 0
8 sin(x) = 0 or 2 cos (x) - 1 = 0
Sin (x) = 0 or Cos (x) = 1/2
Given the interval of 0 ≤ x ≤ 2π
→ Sin (x) = 0 → x = 0 or x = π
and
Cos (x) = 1/2
→ x = π/3 or x = 5π/3
Arranging the values from the smallest to the largest, we have:
x = 0 or x = π/3
x = π or x = 5π/3
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la longitud del jardínde Carme es 15 m 24 cm. la longitud del jardín de su amigo es 2 m 98 cm más que el de Carmen . ¿cuál es la longitud del jardín de su amigo?
la longitud del jardín del amigo de Carmen es 18 m 22 cm.
¿Qué es una ecuación?Una ecuación es un enunciado matemático que se forma cuando una expresión algebraica se iguala mediante un signo igual a otra expresión algebraica o una constante.
Se da que la longitud de Carme
Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.
y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.
Sea La longitud del jardín de Carmen es x m
Entonces la ecuación se convierte en
La longitud del jardín de su amigo = x + 2m 98 cm
ahora ,
x = 15m 24cm
Sustituyendo los valores en la ecuación
La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm
1m = 100cm
La longitud del jardín de su amigo = 17 m 122 cm
as 100 cm = 1m
122 cm = 1 m 22 cm
so ,
La longitud del jardín de su amigo = 18 m 22 cm.
Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.
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Golf Clubs R Us had a set of 10 golf clubs that were marked on sale for $720. This was a discount of 15% off the original selling price.
The original selling price is $847.10
How to determine the original selling price?The given parameters are:
Discount price = $720
Discount = 15%
The original selling price is calculated as:
Discount price = Original selling price * (1 - Discount)
This gives
720 = Original selling price * (1 - 15%)
Evaluate the difference
720 = Original selling price * 0.85
Divide by 0.85
Original selling price = 847.10
Hence, the original selling price is $847.10
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Simplify the slope of AC.
B (b,c)
C (a+b, c)
Al(0, 0)
D (a,0)
Enter the value that
belongs in the green box.
Slone Formula: Y2-1
[?]
+b
Answer:
[tex] \boxed{\bf \cfrac{\boxed{c}}{\boxed{a }+ b}} [/tex]
Step-by-step explanation:
Given:
[tex] \tt (x_1,y_1) : A (0,0)[/tex]
[tex]\tt (x_2,y_2) : C (a+b, c) [/tex]
[tex]\boxed{\tt Slope= \cfrac{y_2,y_1}{x_2,x_1}} [/tex]
[tex]\tt \cfrac{c - 0}{a + b - 0} [/tex]
Add zero (Anything plus zero gives itself).
[tex] \tt \cfrac{c}{a + b + 0} [/tex]
[tex]\tt \cfrac{c}{a + b} [/tex]
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
Find the exact values of the trigonometric functions of theta if theta terminated in quadrant 4. Tangent of theta = -3/4
Answer:
sin=-3/5
cos=4/5
tan-3/4
csc=5/-3
sec=5/4
cot=4/-3
Step-by-step explanation:
you draw a right triangle in the fourth quadrant and then use pythagoreas theorem to find the length of the hypotenuse(2 sides are -3 and 4, hypotenuse is 5), and then just use the sides to find all 6 trigonometric functions.
Factoring Inequalities,
Please help as I do not know how to progress after this.
The factored inequality is [tex]x^2-3x+6\geq 0[/tex]
Factoring InequalitiesThe given inequality is:
[tex]-x^2+3x-6\leq 0[/tex]
This can be further simplified as:
[tex]-(x^2-3x+6)\leq 0[/tex]
The inequality can be re-written as:
[tex]x^2-3x+6\geq 0[/tex]
Since the question does not state that we should solve the inequality, the simplest we can get after factoring is [tex]x^2-3x+6\geq 0[/tex]
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so much summer school :(
The quotient of the division operation is [tex]\frac{5}{9}[/tex]
Division operationFrom the question, we are to find the quotient of the division operation
The given division operation is
[tex]\frac{2}{3} \div \frac{6}{5}[/tex]
1. The divided is [tex]\frac{2}{3}[/tex]
2. The divisor is [tex]\frac{6}{5}[/tex]
3. The reciprocal of the divisor is [tex]\frac{5}{6}[/tex]
4. The equivalent multiplication of the division problem is
[tex]\frac{2}{3} \times \frac{5}{6}[/tex]
5. The multiplication gives
[tex]\frac{2}{3} \times \frac{5}{6}=\frac{10}{18}[/tex]
6. Simplifying the quotient, we get
[tex]\frac{10}{18}=\frac{5}{9}[/tex]
Hence, the quotient of the division operation is [tex]\frac{5}{9}[/tex]
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Is the function one-to-one? {(-19,9),(-2,9),(-7,-16)}
Answer:
no
Step-by-step explanation:
the y coordinate 9 repeats twice
Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts.
He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture.
On day 1, he mixes 4 cans of blue and 6 cans of yellow.
On day 2, he mixes 6 cans of blue and 9 cans of yellow.
Fill in the blanks to find the highest number of cans of each color Marc can mix to make the same shade of green on day 3.
Answer:
mark on day three can use up to 4 cans of blue paint and 5 cans of yellow paint
Step-by-step explanation:
given--started with 14 cans of blue paint
given--started with 20 cans of yellow paint
given--used 10 cans of blue paint and 15 cans of yellow paint in total
by subtracting the blue paint he used with the amount he started with you get an answer of 4 blue paint cans--- vice verse--20 yellow paint cans minus 15 yellow paint cans equal 5 yellow paint cans.
Graph the solution to this system of inequalities in the coordinate plane.
By using Geogebra online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.
What is an inequality?An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Given the following system of inequalities:
3y > 2x + 12 ⇒ 3y - 2x > 12
2x + y ≤ -5
By using Geogebra online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.
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Leroy wants to tile the floor in his kitchen. The floor is 10 feet by 12 feet. Each tile is 6 by 8 inches. How many tiles will he need to finish the job?
a. 124 tiles
b. 360 tiles
c. 412 tiles
d. 514 tiles
Answer:
B
Step-by-step explanation:
Convert everything to inches first
The floor is 120 inches by 144 inches
The floor can be covered with (120/6) * (144/8) tiles
(120/6) * (144/8) = 20*18=360 tiles, hence b.
In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests,
Paul has scored 91, 88, and 93 on the first three. What range of scores on the fourth test will give Paul a C for the
semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.
Express your answer in interval notation.
Answer:
[8, 44]
Step-by-step explanation:
The average of equally-weighted values is their sum divided by their number.
SetupFor some fourth test score x, Paul wants an average between 70 and 79. This gives rise to the inequality ...
70 ≤ (91 +88 +93 +x)/4 ≤ 79
SolutionMultiplying by 4, we have ...
280 ≤ 272 +x ≤ 316
8 ≤ x ≤ 44 . . . . . . . . . . subtract 272
Paul will get a C if his fourth test score is in the interval [8, 44].
Which linear inequality is represented by the graph?
Answer: 3
Step-by-step explanation: