The garment that had the greater amount cut off is the skirt
Explanation:
Amount cut off from skirt = 1/2
Amount cut off from pants = 1/6
To determine the grament witht he greater cut, we need to find the LCM of the fractions
[tex]\text{LCM of the denominator, 2 and 6 = 12}[/tex][tex]\begin{gathered} \frac{1}{2},\frac{1}{6}=\frac{6(1),2(1)}{12}=\frac{6,\text{ 2}}{12} \\ \text{the fraction with higher number of numerator had the greater amount cut off} \end{gathered}[/tex]The fractor with higher number in the numerator = 1/2 has it has 6 has the numerator
In other words, 1/2 > 1/6
The garment that had the greater amount cut off is the skirt
Write an exponential equation using y = a(b)^x“ thatrepresents the growth or decay of the situation.A house was purchased for $370,000. The house has anannual appreciation rate of 3%. Please write a let statementand an equation that represents the house's value over time.
Let:
PV = Initial value = 370000
r = appreciation rate = 3% = 0.03
x = time
the equation will be given by
[tex]\begin{gathered} y=PV(1+r)^x \\ so\colon \\ y=370000(1+0.03)^x \\ y=370000(1.03)^x \end{gathered}[/tex]Hi, can you help me to find (Ir possible) the complement andsupplement of the angle of exercise
The angle is given 24 degree.
To determine the complement angle ,
[tex]90^{\circ}-24^{\circ}=66^{\circ}[/tex]To determine the supplement angle ,
[tex]180^{\circ}-24^{\circ}=156^{\circ}[/tex]I need help with this, I need it step by step please.
In this problem we have a translation
the rule is
(x,y) ------> (x-6,y)
that means
the translation of the point is 6 units at left
so
we have
E(2,4) ------> E'(2-6,4)
E'(-4,4)
you must to subtract 6 units from the x coordinate
F(4,4) -----> F'(4-6,4)
F'(-2,4)
G(2,1) -----> G'(2-6,1)
G'(-4,1)
Solve the system by the method of your choice. Identify inconsistent systems and systems with dependent equations, using set notation to express solution sets
The given system of equations is
[tex]\begin{gathered} y=3x+5\rightarrow(1) \\ 5x-2y=-7\rightarrow(2) \end{gathered}[/tex]Substitute y in equation (2) by equation (1)
[tex]5x-2(3x+5)=-7[/tex]Simplify the left side
[tex]\begin{gathered} 5x-2(3x)-2(5)=-7 \\ 5x-6x-10=-7 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (5x-6x)-10=-7 \\ -x-10=-7 \end{gathered}[/tex]Add 10 to both sides
[tex]\begin{gathered} -x-10+10=-7+10 \\ -x=3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-x}{-1}=\frac{3}{-1} \\ x=-3 \end{gathered}[/tex]Substitute x in equation (1) by -3 to find y
[tex]\begin{gathered} y=3(-3)+5 \\ y=-9+5 \\ y=-4 \end{gathered}[/tex]The solution of the system of equations is {(-3, -4)}
Since the system has only one solution then it is an independent consistent system.
Find all possible rational roots of f(x)=4x^3-13x^2+9x+2
Polynomial
[tex]f(x)=4x^3+13x^2+9x+2[/tex]Find the area of the figure. (Sides meet at right angles.) Check 7 yd 5 yd 3 yd 3 yd 13 yd 3 yd 5 yd 7 yd yd²
Given:
The figure with sides measurements.
Required:
Find area of the figure.
Explanation:
First we will draw figure
In figure, we can see that all figure ABIJ, CDHI and EFGH are rectangles.
So, we need area of rectangle formula. That is
[tex]A=length\times width[/tex]So, area of given figure
[tex]\begin{gathered} A=\text{ Area of ABIJ +Are of CDHI + Area of EFGH} \\ ABIJ=EFGH \\ So, \\ A=2\times(ABIJ)+CDHI \\ A=2\times(7\times5)+(4\times3) \\ A=70+12 \\ A=82yd^2 \end{gathered}[/tex]Find x, where a=14 degrees and b=22 degrees. Find the measure of each angle of the polygon. Shown below.
To answer this question, we need to remember that the sum of the interior angles of a quadrilateral is equal to 360º (in fact, we can divide a quadrilateral into two triangles, and the sum of interior angles of a triangle is equal to 180º).
Then, we have that a = 14º and b = 22º, then we can state the next equation:
[tex](2x+14^{\circ})+(3x+22^{\circ})+2x+x=360^{\circ}[/tex]And now, we can solve the equation for x as follows:
1. Add the like terms as follows:
[tex](2x+3x+2x+x)+14^{\circ}+22^{\circ}=360^{\circ}[/tex][tex]8x+36^{\circ}=360^{\circ}[/tex]2. Subtract 36º from both sides of the equation:
[tex]8x+36^{\circ}-36^{\circ}=360^{\circ}-36^{\circ}\Rightarrow8x=324^{\circ}[/tex]3. Divide both sides by 8 as follows:
[tex]\frac{8x}{8}=\frac{324^{\circ}}{8}\Rightarrow x=40.5^{\circ}[/tex]Therefore, the value for x = 40.5º
Then, we can find the values for the measure of angle A as follows:
[tex]m\angle A=2(40.5^{\circ})+14^{\circ}=95^{\circ}[/tex]The measure of angle B is
[tex]m\angle B=3(40.5^{\circ}_{})+22^{\circ}=143.5^{\circ}[/tex]The measure of angle C is
[tex]m\angle C=x^{\circ}=40.5^{\circ}[/tex]The measure of angle D is
[tex]m\angle D=2(40.5^{\circ})=81^{\circ}[/tex]A) Find the simple interest amount earned for $5500 at 6.5% for 5 months. b)What is the total value of the investment?
The simple interest I on an amount P invested at an interest rate R %, for a period of time T per annum is evaluated as
[tex]I\text{ = }P\times R\times T[/tex]A) The interest earned at $5500 at 6.5% for 5 months is thus evaluated as
[tex]\begin{gathered} P\text{ = 5500} \\ R\text{ = 6.5\% = }\frac{6.5}{100} \\ T\text{ = 5 months = }\frac{5}{12}\text{ year} \\ thus, \\ I\text{ = }5500\times\frac{6.5}{100}\times\frac{5}{12} \\ \Rightarrow I\text{ = \$ 148.958} \end{gathered}[/tex]thus, the interest earned for $5500 at 6.5% for 5 months is $ 148.985.
B) Total value of the investment.
The total value of the investment is the sum of the interest earned and the initial amount invested.
Thus,
[tex]\begin{gathered} Total\text{ value of investment = interest earned + amount invested} \\ A\text{ = I + P} \\ A\text{ = 148.985 + 5500} \\ \Rightarrow A\text{ = \$ 5648.985} \end{gathered}[/tex]Hence, the total value of the investment is $ 5648.985.
A rectangular garden is 15 feet wide. If its area is 1050ft², what is the length of the garden?
The width is w=15 ft.
The area is A=1050 sq ft.
The length of the garden is,
[tex]\begin{gathered} L=\frac{A}{w} \\ =\frac{1050ft^2}{15ft} \\ =70ft \end{gathered}[/tex]Thus, the length of the garden is 70 ft.
For the polynomial below, -3 and 1 are zeros. Express f (x) as a product of linear factors.
Explanation
Since -3 and 1 are zeros of the functions, it implies that
[tex](x+3)\text{ }and\text{ }(x-1)[/tex]are factors of the equation.
Therefore we can find the remaining factors below
[tex](x+3)(x-1)=x^2+2x-3[/tex]By long division
[tex]remaining\text{ expression =}\frac{x^4+6x^3+7x^2-8x-6}{x^2+2x-3}=x^2+4x+2[/tex]By quadratic formula
[tex]\begin{gathered} x_{1,2}=\frac{-4\pm\sqrt{4^2-4\times1\times2}}{2\times1} \\ x_1=\frac{-4+2\sqrt{2}}{2},x_2=\frac{-4-2\sqrt{2}}{2} \\ x=-2+\sqrt{2},x=-2-\sqrt{2} \\ therefore \\ (x+2-\sqrt{2})(x+2+\sqrt{2}) \end{gathered}[/tex]The linear factor are
Answer:
[tex]f(x)=(x+3)(x-1)(x+2-\sqrt{2})(x+2+\sqrt{2})[/tex]
Emily reads 22 pages per hour. In all, how many hours of reading will Emily have to do this week in order to have read a total of 44 pages?
Answer:
The number of hours of reading it will take Emily to read a total of 44 pages is;
[tex]2\text{ hours}[/tex]Explanation:
Given that Emily reads 22 pages per hour.
Her rate of reading is;
[tex]r=22\text{ pages/hour}[/tex]The amount of time she needs to read 44 pages will be the number of pages divided by the rate;
[tex]\begin{gathered} t=\frac{\text{number of pages}}{\text{rate}}=\frac{44}{22}\text{hour} \\ t=2\text{ hours} \end{gathered}[/tex]Therefore, the number of hours of reading it will take Emily to read a total of 44 pages is;
[tex]2\text{ hours}[/tex]Find the area of a shaded region shown below, which was formed by cutting an isosceles trapezoid out of the top half of a rectangle. The width of the rectangle is 32 in, the height of the rectangle in 24 in. The leg of the isosceles trapezoid is 15 in.
Step 1: Redraw the diagram and label it.
From the figure, the hypotenuse of triangles A and B is 15 in and the height is 12 in. We can apply the Pythagoras theorem to find the base.
Let base of the triangle A and B be the adjacent.
Opposite = 12
Adjacent = ?
Hypotenuse = 15
[tex]\begin{gathered} Next,\text{ apply the Pythagoras theorem to find the adjacent.} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 12^2+Adj^2=15^2 \\ 144+Adj^2\text{ = 225} \\ \text{Collect like terms.} \\ \text{Adj}^2\text{ = 225 - 144} \\ \text{Adj}^2\text{ = 81} \\ F\text{ ind the square root of both sides.} \\ \sqrt[]{Adj^2\text{ }}=\text{ }\sqrt[]{81} \\ \text{Adj = 9 in} \end{gathered}[/tex]The area of the shaded region = Area of A + Area of B + Area of C
[tex]\begin{gathered} \text{Area of A = }\frac{Base\text{ x Heigth}}{2} \\ \text{Base = 9} \\ \text{Height = 1}2 \\ \text{Area of A = }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ =54in^2 \\ \text{Area of B = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ \text{= 54 in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of rectangle C = Length }\times\text{ Breadth} \\ Lenght\text{ = 32} \\ \text{Breadth = 12} \\ \text{Area of C = 32 x 12} \\ =384in^2 \end{gathered}[/tex]Therefore,
Area of the shaded region = 54 + 54 + 384 = 492 inches square
Final answer
Area of the shaded region = 492 inches square
Debra is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices: company A has no initial fee but charges 80 cents for every mile driven. Company B charges an initial fee of $75 and an additional 70 cents for every mile driven. For what mileages will company A charge at least as much as company B? Use m for the number of miles driven, and solve your inequality for m.
Given that m is the number of miles driven by the truck.
From the information given,
The charge by Company A would be:
[tex]0+80\times m=80m[/tex]The charge by Company B would be:
[tex]75+70\times m=75+70m[/tex]If company A charges at least as much as company B, then
[tex]A\ge B[/tex]Therefore,
[tex]\begin{gathered} 80m\ge75+70m \\ 80m-70m\ge75 \\ 10m\ge75 \\ m\ge\frac{75}{10}=7.5 \\ \text{The mileage is 7.5}\frac{miles}{cent} \end{gathered}[/tex]hello can you help me with this trigonometry question read carefully of how it has to be answered
Area of a circle = πr²
Replacing with radius = 8.4 in:
Area of a circle = π(8.4)²
Area of a circle = 221.6708 in²
This area corresponds to 2π radians. To find the area corresponding to 2.37 radians, we can use the next proportion:
[tex]\frac{2\pi\text{ rad}}{2.37\text{ rad}}=\frac{221.6708^{}}{x^{}}\text{ }[/tex]Solving for x:
[tex]\begin{gathered} 2\pi\cdot x=221.6708\cdot2.37 \\ x=\frac{525.359796}{2\pi} \\ x=83.6136\text{ sq. in} \end{gathered}[/tex]Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy:The ratio of CD:GH is 2:3. What is the length, in meters, of side EH on the photocopied image?
Solution
The length of EH is;
[tex]\begin{gathered} \frac{2}{3}=\frac{8}{EH} \\ \\ \Rightarrow EH=\frac{3}{2}\times8=12 \\ \\ \Rightarrow EH=12 \end{gathered}[/tex]*Express the end behavior of the followingFunction in limit notation.G(x)=-x(x^2 + 3) (x - 2)^3 (x + 5)^2
we have the function
[tex]g(x)=-x(x^2+3)(x-2)^3(x+5)^2[/tex]In this problem, we have that
the leading coefficient is negative (-1)
The degree of the function is 8 (even)
therefore
the end behavior of the function is
f(x)→−∞, as x→−∞
f(x)→−∞, as x→+∞
(8.5-2x)(11-2x)(x) what is the approximate value of x that would allow you to construct an
open-top box with the largest volume possible from one piece of paper
The largest volume possible from one piece of paper for open-top box is 64.296 cubic unit.
What is meant by the term maxima?The maxima point on the curve will be the highest point within the given range, and the minima point will be the lowest point just on curve. Extrema is the product of maxima and minima.For the given question dimensions of open-top box;
The volume is given by the equation;
V = (8.5-2x)(11-2x)(x)
Simplifying the equation;
V = x(4x² - 39x + 93.5)
Differentiate the equation with respect to x using the product rule.
dV/dx = x(8x -39) + (4x² - 39x + 93.5)
dV/dx = 8x² - 39x + 4x² - 39x + 93.5
dV/dx = 12x² - 72x + 93.5
Put the Derivative equals zero to get the critical point.
12x² - 72x + 93.5 = 0.
Solve using quadratic formula to get the values.
x = 4.1 and x = 1.9
Put each value of x in the volume to get the maximum volume;
V(4.1) = 4.1(4(4.1)² - 39(4.1) + 93.5)
V(4.1) = 3.44 cubic unit.
V(1.9) = 1.9(4(1.9)² - 39(1.9) + 93.5)
V(1.9) = 64.296 cubic unit. (largest volume)
Thus, the largest/maximum volume possible from one piece of paper for open-top box is 64.296 cubic unit.
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Determine the domain and range of the quadratic function. f(x)=−2(x+8)^2−4
Since the given is a polynomial with a degree of 2, there are no restrictions to its domain. The domain therefore is
[tex]\text{Domain: }(-\infty,\infty)[/tex]The given function is in the vertex form
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ \text{where} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]By inspection, we determine that the vertex of the function is at (-8,-4), and since a = -2, then the parabola opens up downwards. This implied that its output peaks at y = -4, and the graph continues towards negative infinity.
We can conclude therefore that the range is
[tex]\text{Range: }(-\infty,-4\rbrack[/tex]The rabbit population in a certain area is 200% of last year's population. There are 1100 rabbits this year. How many were there last year?
As per the given percentage, the population of rabbits in the area is 2200 in last year.
Percentage:
Percentage refers the ratio or the fraction that is multiplied and divided by 100. And it will be represented by the symbol "%".
Given,
The rabbit population in a certain area is 200% of last year's population. There are 1100 rabbits this year.
Now, we need to find the population of rabbit in last year.
Let us consider x be the total number of rabbit in last year.
We know that the rabbit in the current year is 110.
And we also know that, there are 200% of rabbits in last year.
So, we have to write it in the following expression,
200% of 1100 = x
so, the value of x is,
x = 200/100 x 1100
x = 2200
Therefore, there are 2200 rabbits in last year.
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Bryce is cutting tree trunks into circular pieces of wood 1 inch thick to make wall art for log cabins. Match the circumferences of each wood circle to its diameter or radius.
The circumference of a circle of radius r can be calculated as:
[tex]C=2\pi r[/tex]If the diameter d is given, then the formula is:
[tex]C=\pi d[/tex]Calculate the circumference of the following circles:
1 d = 8 inches.
[tex]\begin{gathered} C=\pi(8\text{ inches}) \\ C=3.14\cdot8\text{ inches} \\ C=25.12\text{ inches} \end{gathered}[/tex]1 matches with b
2 d = 7 inches
[tex]\begin{gathered} C=\pi(7\text{ inches}) \\ C=3.14\cdot7\text{ inches} \\ C=21.98\text{ inches} \end{gathered}[/tex]2 matches with d
3 r = 2 inches
[tex]\begin{gathered} C=2\pi(2\text{ inches\rparen=4}\cdot3.14\text{ inches} \\ C=12.56\text{ inches} \end{gathered}[/tex]3 matches with a
4 r = 3 inches
[tex]\begin{gathered} C=2\pi(3\text{ inches\rparen=6}\cdot3.14\text{ inches} \\ C=18.84\text{ inches} \end{gathered}[/tex]4 matches with c
So the question is A local theater sells admission tickets for $9.00 on Thursday nights, where n is the number of customers M(n) the amount of money the theater takes What is the domain of M( n ) in this context
We have the function M(n):
M( n ) = 9 · n
which describes the amount of money the theater takes.
Since the domain of a function refers to the values n can take and n is the number of costumers
In this particular case we do not have a restriction of the number of costumers. Then n can take the following values:
n = 0, 1 , 2, 3, ...
Domain: all non- negative integers
If the maximum capacity of the theater is 100 costumers then
n = 0, 1, 2, 3, ..., 100
Therefore its domain would correspond to
Domain: all non- negative integers less than or equal to 100
Donovan took a math test and got 20 correct questions and 5 incorrect answers. What was the percentage of correct answers?
ANSWER
80%
EXPLANATION
Donovan got 20 questions correct and 5 questions incorrect.
This means that the total number of questions he attempted in the test is the sum of correct and incorrect questions:
Total = 20 + 5
Total = 25
To find the percentage of correct answers, we have to divide the number of correct answers by the total number of questions attempted and multiply by 100 (per cent).
That is:
[tex]\begin{gathered} \frac{20}{25}\cdot\text{ 100 = }\frac{4}{5}\cdot\text{ 100} \\ =\text{ 80\%} \end{gathered}[/tex]That is the percentage of correct answers.
An adult elephant drinks about 225 liters of water each day. Is the number ofdays the water supply lasts proportional to the numberof liters of water the elephant drinks?Is it proportional
An elephant drinks 225 liters of water per day, then in 2 days it drinks 2*225 = 450 liters, in 3 days it drinks 3*225 = 675 liters.
time (days) | 1 | 2 | 3
water (L) | 225 | 450 | 675
If an elephant drinks more water per day, the number of days the water supply lasts decrease. Then these two variables are inversely proportional.
arina runs up 4 flights and runs down 4 flights of stairs does this situation repreasent additive inverses explain . A. Yes; The numbers combine to eight B. Yes; The numbers are combine to zero C. No;The numbers are both represented by the same integer. D. No; The numbers cannot be added together.
B. Yes; The numbers are combine to zero
is additive inverses because the sum is 0
[tex]\begin{gathered} 4+(-4) \\ =0 \end{gathered}[/tex]When asked to find f ( g ( x ) ), what should you do? plug f (x) into g (x)plug g (x) into f (x)multiply f (x) by g (x)none of the above
From the given question,
f(g(x)) means,
Plug g(x) into f(x)
Hence, the correct option is B
Consider the following expression and determine which statements are true. z? + 5y: -8 Choose 2 answers: There are 3 terms. The variables are z, y. and . The coefficient of zis 2 The term Syz is made up of 2 factors.
we have:
the expression has 3 terms and 3 variables, they are x, y and z. Therefore
answer:
A and B
Find (3/5x+3/4)−(1/3x−1/8)
The answer is [tex]\frac{32x+105}{120}[/tex].
The area of mathematics known as algebra is used to represent situations or problems using mathematical expressions. In algebra, we combine integers with variables like x, y, and z.
A fraction is a number that is a component of a whole. In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.
The given equation is an algebraic fraction having variables in the numerator. This equation is written as,
[tex]\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)[/tex]
First combine, x with the nearby fraction,
[tex]\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}+\frac{3}{4}\right)-\left(\frac{x}{3}-\frac{1}{8}\right)\\&=\frac{3x}{5}+\frac{3}{4}-\frac{x}{3}+\frac{1}{8}\end{aligned}[/tex]
Now, group the fraction with a common denominator,
[tex]\begin{aligned}\left(\frac{3}{5}x+\frac{3}{4}\right)-\left(\frac{1}{3}x-\frac{1}{8}\right)&=\left(\frac{3x}{5}-\frac{x}{3}\right)+\left(\frac{3}{4}+\frac{1}{8}\right)\\&=\left(\frac{3x\cdot3}{15}-\frac{x\cdot5}{15}\right)+\left(\frac{3\cdot2}{8}+\frac{1}{8}\right)\\&=\left(\frac{9x-5x}{15}\right)+\left(\frac{6+1}{8}\right)\\&=\frac{4x}{15}+\frac{7}{8}\\&=\frac{32x+105}{120}\end{aligned}[/tex]
Therefore, the final answer is [tex]\frac{32x+105}{120}[/tex].
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Find FG.FL x + 113x + 1EН.FG=
Answer:
FG = 16
Explanation:
The triangles EFG and EHG are congruent because they share the side EG and they have the same interior angles.
If they are congruent the lengths of the corresponding sides are equal, so we can write the following equation:
FG = GH
Then, subtitute FG = x + 11 and GH = 3x + 1 to get:
x + 11 = 3x + 1
So, solving for x, we get:
x + 11 = 3x + 1
x + 11 - 1 = 3x + 1 - 1
x + 10 = 3x
x + 10 - x = 3x - x
10 = 2x
10/2 = 2x/2
5 = x
Then, replacing x by 5, we get that FG is equal to:
FG = x + 11
FG = 5 + 11
FG = 16
So, the answer is FG = 16
In 10 seconds, Jake travels 550 feet on his bike. At this speed. How many fert can he travel in 1 minute.
We can find out how many feet can Jake travel using a rule of three:
[tex]\begin{gathered} 10s\rightarrow550ft \\ 60s\rightarrow xft \\ \Rightarrow x=\frac{60\cdot550}{10}=3300 \\ x=3300ft \end{gathered}[/tex]therefore, Jake can travel 3300ft in 1 minute
Meri invests 15000 into an account the interest is compounded monthly for 17 years. The account balance will be 87,219.93 at the end of 17 years. What is the annual interest rate?
Annual interest rate will be 11.95% or 12% approx.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods
formula for compound interest is [tex]P [(1 + i)^n - 1][/tex]
According to the question
P=15000
i = ?
compound interest = 87,219.93
n=17 years
Therefore
[tex]87219.93=15000 [(1 + i)^1^7 - 1][/tex]
[tex]\frac{87219.93}{15000} = [(1 + i)^1^7 - 1][/tex]
[tex]6.814662 = (1+i)^1^7[/tex]
[tex](6.814662)^\frac{1}{17} = (1+i)[/tex]
i =1.1195-1
i =0.1195
i.e. 11.95%
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