Answers
(a)
Let:
w1 = Original width
l1 = Original length
w2 = New width
l2 = New length
A1 = Original area
A2 = New Area
so:
[tex]\begin{gathered} w2=3w1=3\cdot10=30ft \\ l2=2l1=2\cdot50=100ft \\ A2=w2\cdot l2=3000ft^2 \end{gathered}[/tex]Answer:
New length: 100ft
New width: 30 ft
New Area: 3000ft²
-------------------------------------------
(b)
[tex]\frac{A2}{A1}=\frac{3000}{500}=6[/tex]Answer:
The area of the new walkway will be 6 times the area of the current walkway
---------------------------------------
(c)
[tex]\begin{gathered} 8\cdot500=x\cdot50\cdot4\cdot10 \\ 4000=2000x \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{2000} \\ x=2 \end{gathered}[/tex]Answer:
Make the new length 2 times the current length.
Related Questions
-8x+3y= 313x-3y= -18x=y=
Answers
Given the pair of simultaneous equation;
[tex]\begin{gathered} -8x+3y=3 \\ 13x-3y=-18 \end{gathered}[/tex]We are going to use the method of elimination to solve this.
We will be eliminating the variable y first, since it has the same co-efficient in the two(2) equations.
Thus, we have:
[tex]\begin{gathered} -8x+13x=3-18 \\ 5x=-15 \\ x=-\frac{15}{5} \\ x=-3 \end{gathered}[/tex]To solve for y, we are going to substitute for x = -3 into any of the two(2) equations.
Thus, we have:
[tex]\begin{gathered} \text{from equation i}i) \\ 13x-3y=-18 \\ 13(-3)-3y=-18 \\ -39-3y=-18 \\ -3y=-18+39 \\ -3y=21 \\ y=-\frac{21}{3} \\ y=-7 \end{gathered}[/tex]How many different 5 card hands can be dealt from a deck of 52 cards if the hand consists of exactly 2 aces?
Answers
Solution
We need to remember that in a standard deck we have 4 aces and 48 other types of cards
For this case we can solve the problem with the follwoing operation:
[tex](4C2)\cdot(48C3)=\frac{4!}{2!2!}\cdot\frac{48!}{45!3!}=6\cdot17296=103776[/tex]So then we have 103776 ways to create the combination required
Of the following real functions of real variable it calculates: a) the domain, b) the intersections with the axes c) the limits at the ends of the domain. d) Draw the graph e) calculates the first derivative and identifies the minimum or maximum points of the function
Answers
Given:
[tex]g(x)=\frac{x+\sqrt{x}}{x+1}[/tex]Find-: Domain, intersection with axis, limit at end the domain, draw the graph, first derivative the minimum and maximum of the point is:
Sol:
Domain:
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
[tex]\begin{gathered} g(x)=\frac{x+\sqrt{x}}{x+1} \\ \\ Domain:x>0 \end{gathered}[/tex]The domain is greater than the zero "0" because the negative value of "x" is create undefine form inside the square root.
Intersection with axis:
For x-intersection value of "y" is zero so,
[tex]\begin{gathered} g(x)=\frac{x+\sqrt{x}}{x+1} \\ \\ 0=\frac{x+\sqrt{x}}{x+1} \\ \\ 0=x+\sqrt{x} \\ \\ \sqrt{x}(\sqrt{x}+1)=0 \\ \\ x=0,\sqrt{x}=-1 \\ \\ \sqrt{x}=-1\text{ Not possible } \\ x=0 \end{gathered}[/tex]For y intersection value of "x" is zero then,
[tex]\begin{gathered} y=\frac{x+\sqrt{x}}{x+1} \\ \\ y=\frac{0+\sqrt{0}}{0+1} \\ \\ y=0 \end{gathered}[/tex]Graph of function is:
The first derivative is:
[tex]\begin{gathered} g(x)=\frac{x+\sqrt{x}}{x+1} \\ \\ g^{\prime}(x)=\frac{(x+1)(1+\frac{1}{2\sqrt{x}})-(x+\sqrt{x)}}{(x+1)^2} \\ \\ g^{\prime}(x)=\frac{x+\frac{\sqrt{x}}{2}+1+\frac{1}{2\sqrt{x}}-x-\sqrt{x}}{(x+1)^2} \\ \\ g^{\prime}(x)=\frac{1+\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}}{(x+1)^2} \\ \\ \end{gathered}[/tex]For maximum is:
[tex]\begin{gathered} g^{\prime}(x)=0 \\ \\ 1+\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}=0 \\ \\ \frac{2\sqrt{x}+1-x}{2\sqrt{x}}=0 \\ \\ x-1=2\sqrt{x} \end{gathered}[/tex]Square both side then:
[tex]\begin{gathered} (x-1)^2=2\sqrt{x} \\ \\ x^2+1-2x=4x \\ \\ x^2-6x+1=0 \\ \\ x=\frac{6\pm\sqrt{36-4}}{2} \\ \\ x=\frac{6\pm\sqrt{32}}{2} \\ \\ x=5.83,x=0.17 \end{gathered}[/tex]For the maximum or minimum point are
(5.83) and 0.17
hi how do you find the area of this figuer
Answers
we can divide the figure in two parts, a triangule and a square. So the area is sum of the area fo each figure
[tex]A=3\cdot3+\frac{2\cdot3}{2}=9+3=12[/tex]therefore the area is 12m^2
[tex] \frac{1}{2} {x}^{2} + 1 = 2 \times - 1[/tex]Solve the equation
Answers
Solve the system of equations:
4x-2y=10 (1)
y=2x-5 (2)
We can substitute 2 in 1:
4x-2(2x-5)=10
4x-4x+10=10
0=0
Since the solution of the system of equation is 0=0 we can say that it has infinite solutions.
A department store is having a clothing sale. If a $35.00 pair of pants has a discount tag of 25% off, what is the sale price?
Answers
Given Data:
The prise of the pair of the pant is: p= 35
the percentage of discount is: 25%
The expression to calculate the discount sale price is,
[tex]d=p\times\frac{25}{100}[/tex]Substitute values in the above expression.
[tex]\begin{gathered} d=35\times\frac{25}{100} \\ =35\times0.25 \\ =8.75\text{ } \end{gathered}[/tex]Thus, the discount price of the pant is $8.75.
What are the roots for the trinomial below? *x2 – 2x – 15O x=-5,x=-3Ox=5,x=-3Ox=3,x=5O x=-5,x=3
Answers
ANSWER:
[tex]x=5,=-3[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]x^2-2x-15[/tex]We solve by factoring. We look for two numbers that product -15 and the sum is equal to -2:
[tex]\begin{gathered} 3\cdot-5=-15 \\ 3+(-5)=-2 \\ \text{Therefore:} \\ (x+3)\cdot(x-5)=0 \\ x+3=0\rightarrow x=-3 \\ x-5=0\rightarrow x=5 \end{gathered}[/tex]Find the volume of this right rectangularprism.3 ft15 ft10 ft[? ]ft3
Answers
Given the following question:
[tex]\begin{gathered} volume=l\times b\times h \\ l=15 \\ b=10 \\ h=3 \end{gathered}[/tex][tex]\begin{gathered} volume=l\times b\times h \\ volume=15\times10\times3 \\ 15\times10=150 \\ 150\times3=450 \\ v=450ft^3 \end{gathered}[/tex]Volume is equal to 450 feet^3.
I need help with 3 , 7 ,4 and 8
Answers
Solution:
Question 3:
The image below gives a vivid explanation of the question
Concept:
The sum of angles in a triangle is
[tex]=180^0[/tex][tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ \angle A=61^0 \\ \angle B=90^0 \\ \angle C=4f+1 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ 61^0+90^0+4f+1=180^0 \\ \text{collect similar terms, we will have} \\ 61+90+1+4f=180^0 \\ 152^0+4f=180^0 \\ 4f=180-152^0 \\ 4f=28^0 \\ \text{Divide both sides by 4} \\ \frac{4f}{4}=\frac{28}{4} \\ f=7^0 \end{gathered}[/tex]Hence,
The final answer is f = 7°
Similar PcIn this session, you will apply your knowledge of similar polygons to real-lifesituations.An artist plans to paint a picture. He wants to use a canvas that is similar to aphotograph with a height of 8 in, and a width of 10 in. If the longer horizontalsides of the canvas are 30 in. wide, how high should the canvas be?
Answers
24 in
Explanation / Steps:
Since the aim of the artists is to duplicate the photograph on a different scale canvas:
8 * 30 / 10 = 24 in
More details:
Since for a side of 8 in is requires a side of 10 in => a side of 1 in requires 8/10 ~ 0.8 in
then a side of 30 in requires 30 *0.8 = 24 in
17 people fit comfortably in a 7 feet by 7 feet area. Use this value to estimate the size of a crowd that is 21 feet deep on both sides of the street along a 3-mile section of a parade route. (Hint: 1mile= 5,280ft) Draw a diagram
Answers
In order to estimate the size of the crowd, let's find the area of the parade route.
The length is 3 miles, that is, 3 * 5280 = 15840 ft.
The width is 2 times 21, so 42 ft.
Therefore the area is:
[tex]A=15840\cdot42=665280[/tex]Now, to estimate the size of the crowd, let's use a rule of three, knowing that the area for 17 people is 7 * 7 = 49 ft²:
[tex]\begin{gathered} 17\text{ people}\to49\text{ ft}^2 \\ x\text{ people}\to665280\text{ ft}^2 \\ \\ \frac{17}{x}=\frac{49}{665280} \\ x=\frac{665280\cdot17}{49} \\ x=230811.43 \end{gathered}[/tex]Rounding to the nearest integer, we have 230,881 people.
Figure 2 is the image of Figure 1. What is the scale factor?
Answers
Answer
Scale factor = (2/5)
Explanation
The scale factor shows the extent to which the original image has been dilated (enlarged or reduced). It is given mathematically as
[tex]\text{Scale factor = }\frac{Length\text{ of a side of the image}}{Length\text{ of the corresponding side of the original figure}}[/tex]From the image attached we can see that
Length of a side of the image = 4 dots
Length of the corresponding side of the original image = 10 dots
Scale factor = (4/10) = (2/5)
Hope this Helps!!!
If we start with 5 people that have the coronavirus, and the number of cases increases by 26% each week. How many cases of coronavirus will there be
in 36 weeks?
Answers
Answer:
6600 new cases
Step-by-step explanation:
Marshall has a rectangular garden that he wants to enclose with a fence. To calculate the perimeter, he used the expression below; where w represents the width and I represents the length of the garden. 2w + 2L Which other expression could Marshall use to calculate the perimeter?A. wLB.2wLC.2(w+2L)D.2(w+L)
Answers
by factoring the expression, you can also write
[tex]\begin{gathered} 2w+2l \\ 2(w+l) \end{gathered}[/tex]00:00Drag a tile to each number to classify it as rational or irrational.rationalirrational9.682.010010001...✓ 64-57
Answers
the numbers are
[tex]undefined[/tex]A line that includes the point (10,5)and has a slope of 1.What is its equation in slope intercept form?
Answers
The line equation is y = x - 5
EXPLANATION
Given:
Point (10, 5)
x=10 and y=5
slope (m)=1
We need to first find the intercept(b).
Substitute x=10 , y=5 and m=1 into y=mx + b and solve for intercept(b).
That is;
5 = 1(10) + b
5 = 10 + b
5 - 10 = b
-5 = b
Form the equation by substituting m=1 and b=-5.
Hence, the line equation is y = x - 5
Joaquin has been working on homework for 3 1/2 hours. If each assignment takes him of 1/4 an hour, how many assignments has he completed? Select one OA. 13 O B. 14 OC. 15 OD. 16
Answers
The total amount of time he has spent doing homework:
[tex]3\frac{1}{2}[/tex]And the time it takes to complete each assignment:
[tex]\frac{1}{4}[/tex]To find the number of assignments he has completed in that time, we divide the total time 3 1/2 by the time for each assignment 1/4:
[tex]3\frac{1}{2}\div\frac{1}{4}[/tex]To make this division we need to convert 3 1/2 to a fraction as follows:
[tex]3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]We multiply the whole number by the denominator 3x2 and we add to that the numerator 1, and divide that by the original denominator 2.
Now instead of 3 1/2 we use 7/2 for our division:
[tex]\frac{7}{2}\div\frac{1}{4}[/tex]And we use the formula to divide two fractions, which is:
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}[/tex]Applying this to our division:
[tex]\frac{7}{2}\div\frac{1}{4}=\frac{7\times4}{2\times1}[/tex]Solving the operations:
[tex]\frac{7}{2}\div\frac{1}{4}=\frac{28}{2}=14[/tex]Answer: 14 assignments
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friendr walks 220 yards due west from your position and takes a bearing on the cabin of N 21.2°E. How far are you from the cabin?A. 638 yardsB. 608 yardsC. 567 yardsD. 589 yards
Answers
In the given right triangle
we have that
[tex]\begin{gathered} tan(21.2^o)=\frac{220}{x}\text{ -----> by TOA} \\ \\ solve\text{ for x} \\ \\ x=\frac{220}{tan(21.2^o)} \\ \\ x=567\text{ yrads} \end{gathered}[/tex]The answer is option Cthe problem was sent in a picture
Answers
The vertex of the given parabola is (h, k)=(0,0).
(x, y)=(2, -4) is a point on the parabola.
The vertex form of a parbola is,
[tex]y=a(x-h)^2+k\text{ ------(1)}[/tex]Here, (h, k) is the vertex of parabola.
Put h=0, k=0, x=2 and y=-4 in the above equation.
[tex]\begin{gathered} -4=a(2-0)+0 \\ \frac{-4}{2}=a \\ -2=a \end{gathered}[/tex]Put a=-2, h=0, k=0 in equation (1) to find the function.
[tex]y=-2x^2[/tex]Put y=0 to obtain a quadratic function and solve for x.
[tex]\begin{gathered} 0=-2x^2 \\ x=0 \end{gathered}[/tex]So, there is only one solution to the graph.
Short cut:
Since the parabola touches the x axis when the x intercept is zero, the solution of the quadratic function of the parabola is x=0. So, there is only one solution to the graph.
c(t)=2(t-4)(t+1)(t-6)
Answers
Question: find the x- or t intercepts of the polynomial function:
c(t)=2(t-4)(t+1)(t-6).
Solution:
the t-intercept (zeros of the function) of the given polynomial function occurs when c (t) = 0, that is when:
[tex]c(t)\text{ = 0 = }2\mleft(t-4\mright)\mleft(t+1\mright)\mleft(t-6\mright)[/tex]this can only happen when any of the factors of the polynomial are zero:
t-4 = 0, that is when t = 4
t + 1 = 0 , that is when t = -1
and
t-6 = 0, that is when t = 6.
then, we can conclude that the t-intercept (zeros of the function) of the given polynomial are
t = 4, t = -1 and t = 6.
would the answer be written as 47 ¹¹⁰/¹⁷³? my daughter has to write the answer as the remainder as a fraction. 8241 ÷ 173
Answers
8241 ÷ 173
173 will go into 8241 47 times an we will have a remainder of 110
So, it will be written as;
8241 ÷ 173
[tex]=47\text{ }\frac{110}{173}[/tex]Barry Bonds holds the major league home run record with 73 in one season. If Pete Alonso wants to break his record, how many homeruns would he have to hit on average over 162 games to break Bonds' record?
Answers
73 homeruns in one season
162 games Pete Alonso must do at least 74 homeruns
He must do 74 homeruns and 88 will not be homeruns.
On average he must do 74/162 = 0.45 homeruns per game
the post office and city hall are marked on a coordinate plane. write the equation of the line in slope intercept form that passes through these two points.
Answers
The given points are (1,6) and (-5,-3).
First, we have to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing given points, we have
[tex]m=\frac{-3-6}{-5-1}=\frac{-9}{-6}=\frac{3}{2}[/tex]Now, we use the point-slope formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{3}{2}(x-1) \\ y=\frac{3}{2}x-\frac{3}{2}+6 \\ y=\frac{3}{2}x+\frac{-3+12}{2} \\ y=\frac{3}{2}x+\frac{9}{2} \end{gathered}[/tex]Therefore, the equation would be y = 3/2x + 9/2Find the measure of angle A associated with the following ratios and round to the nearest degree.
Answers
For, CosA = 0.2785 value of angle m∠A = 73.8293° ≈ 74°
Inverse Cosine function:
The inverse cosine function is written as cos^-1(x) or arccos(x).
CosA = 0.2785
A = [tex]Cos^{-1}[/tex](0.2785)
A = 73.8293°
thus by calculation we can say,
m∠A = 73.8293°
≈ 74°
Thus,
For, CosA = 0.2785 value of angle m∠A = 73.8293°
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Convert the following Quadratic Equations from Vertex Form to Standard Form.
Answers
4)
Given:
The vertex form is given as,
[tex]y=-\frac{1}{3}(x+6)^2-1[/tex]The objective is to convert the vertex form to standard form.
The standard form can be obtained as,
[tex]\begin{gathered} y=-\frac{1}{3}(x+6)^2-1 \\ =-\frac{1}{3}(x^2+6^2+2(x)(6))-1 \\ =-\frac{1}{3}(x^2+36+12x)-1 \\ =-\frac{x^2}{3}-\frac{36}{3}+\frac{12x}{3}-1 \\ =-\frac{x^2}{3}-12+4x-1 \\ =-\frac{x^2}{3}+4x-13 \end{gathered}[/tex]Here,
[tex]\begin{gathered} a=-\frac{1}{3} \\ b=4 \\ c=-13 \end{gathered}[/tex]Hence, the required standard form of the equation is obtained.
6.[–/1 Points]DETAILSALEXGEOM7 8.3.006.MY NOTESASK YOUR TEACHERIn a regular polygon, each interior angle measures 120°. If each side of the regular polygon measures 4.6 cm, find the perimeter of the polygon in centimeters. cm
Answers
Given:
Measure of each interior angle = 120 degrees
Length of each side = 4.6 cm
Let's find the perimeter of the polygon.
Since the measure of each interior angle is 120 degrees, let's find the number of sides of the polygon using the formula below:
[tex]120=\frac{(n-2)*180}{n}[/tex]Let's solve for n.
We have:
[tex]\begin{gathered} 120n=(n-2)*180 \\ \\ 120n=180n-180(2) \\ \\ 120n=180n-360 \\ \\ 180n-120n=360 \\ \\ 60n=360 \end{gathered}[/tex]Divide both sides by 60:
[tex]\begin{gathered} \frac{60n}{60}=\frac{360}{60} \\ \\ n=6 \end{gathered}[/tex]Therefore, the polygon has 6 sides.
To find the perimeter, apply the formula:
Perimeter = number of sides x length of each side
Perimeter = 6 x 4.6
Perimeter = 27.6 cm
Therefore, the perimeter of the polygon is 27.6 cm
ANSWER:
27.6 cm
Question: Jack has an old scooter. He wants to sell it for 60% off the current price. The market price is $130.
What should his asking price be? Explain your reasoning.
Answers
The asking price for the scooter is $78.
How to calculate the price?From the information, Jack has an old scooter. He wants to sell it for 60% off the current price and the market price is $130.
In this case, the asking price will be:
= Percentage × Market price
= 60% × $130
= 0.6 × $130
= $78
The price is $78.
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Joe’s parents are making sandwiches for the class picnic they have 7230 size is 48 two slices and 96 tomato sauce is Y
Answers
We have to calculate the maximum common divisor of these 3 numbers in order to know what is the maximum ammount of sandwiches they can make.
We can list the factors of each number:
72: 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 72.
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 96.
To calculate this factors, we start by dividing by 2 and 3, and so on, and checking if the result is a whole number. If it is, the denominator is a factor.
The maximum common divisor is 24, so they can make 24 sandwichs, each one with 72/24=3 slices of turkey, 48/24=2 slices of cheese and 96/24=4 slices of tomatoes.
George's boxes
He has bought boxes at different prices.
3 boxes at $3.50 and 4 boxes at $3.00.
The cost of the first group of boxes is 3 boxes x 3.50 $/boxes = $10.50.
The cost of the second group is 4 boxes x 3.00 $/boxes = $12.
Then, if we add the cost, it is 10.50 + 12 = $22.50.
If we write it in the blanks we have:
3 boxes * 3.50 = 3 * 3.50
4 boxes * 3.00 = 4 * 3.00
(3 * 3.50) + (4 * 3.00) = 22.50
(underlined is what goes in the blanks)
(G.12, 1 point) Which point lies on the circle represented by the equation (x-4)2 + (y - 2)2 = 72? O A. (-1,4) B. (8,3) O C. (9,0) O D. (-2, 2)
Answers
To know if a point lies on a circle you use the (x,y) of each point in the equation and prove it that correspond to a mathematical congruence.
A. (- 1 , 4)
[tex]\begin{gathered} (-1-4)^2+(4-2)^2=7^2 \\ -5^2+2^2=49 \\ 25+4=49 \\ 29=49 \end{gathered}[/tex]As 29 is not equal to 49, this point doesn't lie in the circle
B. ( 8 , 3)
[tex]\begin{gathered} (8-4)^2+(3-2)^2=7^2 \\ 4^2+1^2=49 \\ 16+1=49 \\ 17=49 \end{gathered}[/tex]As 17 is not equal to 49, this point doesn't lie in the circle
C. (9 , 0)
[tex]\begin{gathered} (9-4)^2+(0-2)^2=7^2 \\ 5^2+(-2)^2=49 \\ 25+4=49 \\ 29=49 \end{gathered}[/tex]As 29 is not equal to 49, this point doesn't lie in the circle
D. (-2 , 2)
[tex]\begin{gathered} (-2-4)^2+(2-2)^2=7^2 \\ -6^2+0^2=49 \\ 36=49 \end{gathered}[/tex]As 36 is not equal to 49, this point doesn't lie in the circle
None of the points lies on the circle.The next graph represents the circle and the 4 given points:
Round to the nearest tenthRound to the nearest hundredthRound to the nearest whole number
Answers
Round to the nearest tenth
15. 7.953 is equal to 8.0 rounded to the nearest tenth.
16. 4.438 is equal to 4.4 rounded to the nearest tenth.
17. 5.299 is equal to 5.3 rounded to the nearest tenth.
18. 8.171 is equal to 8.2 rounded to the nearest tenth.
Round to the nearest hundredth
19. 5.849 is equal to 5.85 rounded to the nearest hundredth.
20. 4.484 is equal to 4.48 rounded to the nearest hundredth.
21. 0.987 is equal to 0.99 rounded to the nearest hundredth.
22. 0.155 is equal to 0.16 rounded to the nearest hundredth.
Round to the nearest whole number
23. 98.55 is equal to 99 rounded to the nearest whole number.
24. 269.57 is equal to 270 rounded to the nearest whole number.
25. 14.369 is equal to 14 rounded to the nearest whole number.
26. 23.09 is equal to 23 rounded to the nearest whole number.