Answer:
111.11111111111111111
Step-by-step explanation:
d) The diagonal of a rectangular garden measures 11½ m while its width measures 7m. Express the perimeter of the garden as a percentage of its area (3marks).
We need to know about area and perimeter of a rectangle to solve the problem. The perimeter of the garden as a percentage of its area is 50.5%
The perimeter of a rectangle is the total of all it's sides. The perimeter can be calculated by adding up the sides of the rectangle. The area of a rectangle can be calculated by multiplying the length with the breadth of the rectangle. The diagonal and width of a rectangle are given, we need to find the length using Pythagoras' theorem.
diagonal =11.5m
width=7 m
length=[tex]\sqrt{11.5^{2} -7^{2} }[/tex]=[tex]\sqrt{132.25-49} =\sqrt{83.25}[/tex]=9.12 m
perimeter=2x(l+b)=32.24 m
area= lxb= 9.12x7=63.84 [tex]m^{2}[/tex]
perimeter as percentage of area=32.24/63.84 x100=50.5%
Therefore the perimeter of the rectangle as a percentage of area is 50.5%.
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Please explain cos-cot equations. Then I would like to figure out the rest.If sin θ=3/5 and θ is in quadrant II, thencos(θ)=________ ;tan(θ)=________ ;cot(θ)=_________;sec(θ)=_________;csc(θ)=_________;Give exact values.
Remember that the sine of an angle in a right triangle is equal to the quotient between the side opposite to the angle and the hypotenuse of the triangle.
Since the sine of the given angle θ is equal to 3/5, we can represent θ as part of a right triangle whose hypotenuse has a measure of 5 and the side opposite to θ has a measure of 3:
The length of the side adjacent to θ must be equal to 4 in order to satisfy the Pythagorean Theorem:
[tex]3^2+4^2=5^2[/tex]On the other hand, the cosine of an angle is defined as the quotient between the side adjacent to the angle and the hypotenuse of the triangle. Then, the cosine of θ must be equal to 4/5:
[tex]\cos \theta=\frac{4}{5}[/tex]The rest of the trigonometric relations are defined in terms of the sine and the cosine as follows:
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \csc \theta=\frac{1}{\sin \theta} \end{gathered}[/tex]Since sinθ=3/5 and cosθ=4/5, then:
[tex]\begin{gathered} \tan \theta=\frac{3}{4} \\ \cot \theta=\frac{4}{3} \\ \sec \theta=\frac{5}{4} \\ \csc \theta=\frac{5}{3} \end{gathered}[/tex]Could you please check my answer? Use the equations to solve the system of equations:Y=0X=7My answer: (7,0)
ANSWER:
[tex](7,0)[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations
[tex]\begin{gathered} x=7 \\ y=0 \end{gathered}[/tex]In the case x = 7, it is parallel to the y axis, through the point 7 in x, and in the case y = 0, it is the same x axis, therefore the intercept is the point (7 , 0)
The solution is:
[tex](7,0)[/tex]Given m(x): { (9 0), (8, -8), (-4, 8), (0, -4) , (-8, 3) }. Find m(-8)
8
0
4
3
Answer:
B.C.
Step-by-step explanation:
how many pieces are there in 215 dozen elementary school
Answer:2580
Step-by-step explanation:215*12=2580
A rectangle with dimensions of 4 units by 5 units is enlarged by a scale factor of 1.2. By what percent does its area increase?
The area of any shape after dilation is equal to the area of the original shape multiplied by the square of the scale factor:
[tex]A_{\text{new}}=k^2\cdot A_{\text{original}}[/tex]Where
A_new indicates the area of the shape after the dilation
A_original is the area of the original shape
k is the scale factor
The first step is to determine the area of the original shape and the new shape, using the formula:
[tex]A=w\cdot l[/tex]The original shape has dimensions 4 and 5, so its area is:
[tex]\begin{gathered} A_{\text{original}}=4\cdot5 \\ A_{\text{original}}=20 \end{gathered}[/tex]Next is to determine the area of the shape after the dilation (A_new)
The scale factor is k=1.2
[tex]\begin{gathered} A_{\text{new}}=k^2\cdot A_{\text{original}} \\ A_{\text{new}}=(1.2)^2\cdot20 \\ A_{\text{new}}=1.44\cdot20 \\ A_{\text{new}}=28.8 \end{gathered}[/tex]Now that we calculated both areas, we can determine the increase percentage.
- First, calculate the increase (I), which is the difference between the area of the new shape and the area of the original shape:
[tex]\begin{gathered} I=A_{\text{new}}-A_{\text{original}} \\ I=28.8-20 \\ I=8.8 \end{gathered}[/tex]-Second, divide the increase by the original area and multiply the result by 100
[tex]\begin{gathered} \frac{I}{A_{\text{original}}}\cdot100 \\ \frac{8.8}{20}\cdot100 \\ 0.44\cdot100=44 \end{gathered}[/tex]This means that the area increased 44% after the dilation
I actually have the answer it just says it’s wrong when I try to submit it. It says that I need to enter the correct number and units. Can anyone help with this?
Input
[tex]36.2\text{ yards}[/tex]Not
[tex]b=36.2[/tex]on/8cc2ae7c-5cc0-4693-ab64-cce744de5774/b9c41130-96e8-4a04-a4cc-dbc9dab72adfNorfleet CasenReview -BookmarkThe art club has a goal to raise at least $500 by selling paintings to the student body for $15 each. They have already spent $70 buyingpaint. Which inequality could be used to find the number of paintings the art club needs to sell to reach their goal?
The art club has a goal to raise at least $500 by selling paintings to the student body for $15 each. They have already spent $70 buying
paint. Which inequality could be used to find the number of paintings the art club needs to sell to reach their goal?
we have that
Let
x -----> the number of paintings
so
the inequality that represent this situation is given by
[tex]15x-70\ge500[/tex]solve for x
[tex]undefined[/tex]Directions: Simplify by combining like terms in each of the following expressions.
1. 10s2 + 10s2 - 13st =
2. 13st + - 2st - t2 =
3. x2+ x2 + x3 =
4. 6 x - 6 x + 2 =
5. 24x - 3s - 4t =
6. 86 + 86x - 1 =
7. 4x + 3x - 2 =
8. 7s - 4s + 3s =
9. 12 +11x - 10 x =
10. 12x + 24 x - 3 x - 4 =
11. 16t + 8t - 12t =
12. 17g + 19g - 2g +g =
13. 16 + 16 -16 + 16x =
14. 4s - 3s + 3s =
15. 12t - 11t + t =
(math is my weakest subject pls help 22 points)
A method that is frequently used to make algebraic expressions simpler.
How to simplify expressions?A method that is frequently used to make algebraic expressions simpler.
1. 10s2 + 10s2 - 13st =s*(20s-13t)
2. 13st + - 2st - t2 = 11st-t2
3. x2+ x2 + x3 = 2x2+x3
4. 6 x - 6 x + 2 =2
5. 24x - 3s - 4t =24x - 3s - 4t
6. 86 + 86x - 1 =86x+85
7. 4x + 3x - 2 = 7x-2
8. 7s - 4s + 3s = 6s
9. 12 +11x - 10 x =x+12
10. 12x + 24 x - 3 x - 4 =33x-4
11. 16t + 8t - 12t =12t
12. 17g + 19g - 2g +g =35g
13. 16 + 16 -16 + 16x = 16+16x
14. 4s - 3s + 3s =4s
15. 12t - 11t + t =2t.
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Using the paths shown, how long is the shortest route from Hampton to Lexington?
In this case, we have to add mixed numbers to find the shortest path from the shown alternatives. We need to work with mixed numbers, fractions, and even decimals.
To answer this question, we know that:
1. The path from Hampton to Middletown is 8 + 1/4 mi.
2. Now, we have two alternatives to go from Middletown to Campbell:
First, we have a path that is equivalent to 6 + 1/8 mi (direct). On the other path, we need to go from Middletown to Danville, and then to Campbell. The measure of the latter path is then:
[tex]3\frac{3}{8}+3\frac{3}{8}=(3+\frac{3}{8})+(3+\frac{3}{8})=(\frac{8\cdot3+3\cdot1}{8})+(\frac{8\cdot3+3\cdot1}{8})[/tex]Thus, we have:
[tex]\frac{(24+3)}{8}+\frac{(24+3)}{8}=\frac{27+27}{8}=\frac{2\cdot(27)}{8}=\frac{2}{8}\cdot27=\frac{1}{4}\cdot27=\frac{27}{4}[/tex]Which is equivalent to:
[tex]\frac{27}{4}=\frac{24}{4}+\frac{3}{4}=6+\frac{3}{4}=6\frac{3}{4}=6.75mi[/tex]If we compare the measures of the two paths, we have that:
a. The path from Middletown to Campbell (directly) is equal to:
[tex]6\frac{1}{8}=6+\frac{1}{8}=6.125mi[/tex]b. The path from Middletown to Danville, and then from Danville to Campbell is equal to 6.75 miles (it is longer).
Therefore, the shortest path, in this part of the "journey", is equal to 6.125 miles or 6 + 1/8 miles.
Now, the complete measure of the path from Hamptom to Lexington is the sum of:
1. The measure of the path from Hamptom to Middletown (8 + 1/4 miles) plus
2. The measure of the path from Middletown to Campbell (6 + 1/8 miles) (directly) plus
3. The measure of the path from Campbell to Lexington (5 + 3/4 miles).
And this is, numerically, as follows:
[tex](8+\frac{1}{4})+(6+\frac{1}{8})+(5+\frac{3}{4})=8+6+5+\frac{1}{4}+\frac{3}{4}+\frac{1}{8}[/tex][tex]19+\frac{4}{4}+\frac{1}{8}=19+1+\frac{1}{8}=20+\frac{1}{8}=20\frac{1}{8}mi[/tex]We can express the latter result as a fraction as follows:
[tex]20+\frac{1}{8}=\frac{20\cdot8+1\cdot1}{8}=\frac{160+1}{8}=\frac{161}{8}mi[/tex]Therefore, the shortest route from Hamptom to Lexington is:
1. As a fraction:
[tex]\frac{161}{8}mi[/tex]2. Or as a mixed number:
[tex]20\frac{1}{8}mi[/tex][Notice that we sum two fractions with the same denominator above:
[tex]\frac{1}{4}+\frac{3}{4}=\frac{3+1}{4}=\frac{4}{4}=1[/tex].]
PLS HELP ASAP(100 POINTS)
A linear function is shown on the graph.
A linear function beginning with open circle at negative 3 comma negative 5 and ending with an open circle at 3 comma 7.
What is the domain of the function?
{y | −5 ≤ y ≤ 7}
{y | −5 < y < 7}
{x | −3 ≤ x ≤ 3}
{x | −3 < x < 3}
Answer:
{x | −3 ≤ x ≤ 3
Answer:
{x | −3 ≤ x ≤ 3}
Step-by-step explanation:
pretty sure its right
F(x)=2x and g(x)= sqrt(x+1)Find (fg)(x)
First, let us define what (fg)(x) is:
[tex](fg)(x)=f(x)\times g(x)[/tex]Given:
[tex]f(x)=2x[/tex][tex]g(x)=\sqrt[]{x+1}[/tex]So the solution to (fg)(x) will be:
[tex]\begin{gathered} =2x\times\sqrt[]{x+1} \\ =2x\text{ }\sqrt[]{x+1} \end{gathered}[/tex]ABCD is a rhombus. Find xA) x = 3B) x = 10 D) x = 5C) x = 2
ANSWER
5
EXPLANATION
The given shape is a rhombus
The sum of interior angles of a rhombus add up to 360 degrees
The opposite angles of a rhombus are equal to each other.
hence, adding up all the interior angles, we have;
[tex]\begin{gathered} 9x+9x+135+135=360 \\ 18x+270=360 \end{gathered}[/tex]collecting like terms, we have;
[tex]\begin{gathered} 18x=360-270 \\ 18x=90 \\ x=\frac{90}{18} \\ x=5 \end{gathered}[/tex]Therefore the value of x is 5
what is the slope of the line
I really want to go to bed I've been staying up all night pls help
Answer:
The slope is -2
Step-by-step explanation:
Use the rise÷run formula to find the slope of any linear equation
In this case, -2÷1 = -2
Therefore, the slope is -2
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
An apartment building is planning on replacing refrigerators in 42 of its units. If the refrigerators cost $501 each, estimate the total cost by rounding both numbers to the nearest 10
Total Cost = No of Units x Unit cost of refrigerators
Total Cost = 42 x $ 501 = $ 21, 042
Rounding off to the nearest tens,
We have to round down 42 (in $ 21, 042) to 40
Therefore, the total cost will be $ 21, 040
Answer: $21,040
4. A rectangular garage has a volume of 480 m, a length of 12 m and a width of 8 m. What isthe height of the garage?
Answer:
5 m
Explanation:
The volume of the rectangular garage can be calculated as:
[tex]\text{Volume }=\text{Length }\times\text{ Width }\times\text{ Height}[/tex]If we replace Volume by 480, Lenght by 12, and Width by 8, we get:
[tex]480=12\times8\times\text{ Height}[/tex]Now, we can solve the equation for the Height as:
[tex]\begin{gathered} 480=96\times\text{ Height } \\ \frac{480}{96}=\frac{96\text{ }\times Height}{96} \\ 5=\text{Height} \end{gathered}[/tex]Therefore, the height of the garage is 5 m
Describe how to transform the graph of g(x) - Inx into the graph of f(x)- In(x-4)+3
To transform the graph of g(x) = lnx into the graph of of f(x) = ln(x-4) + 3 we have to translate 4 units to the right and 3 units up.
What is graph transformation?
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
As given in the question,
Parent function g(x)=ln x
resultant function f(x)=ln(x-4)+3
By the translation rules :
If f(x) needs to be translated in f(x-h), it mean function shifted right by h unit
and if f(x) needs to be translated in f(x)+k it mean function shifted up by k unit.
As per these rules, graph of g(x) = lnx function shifted right by 4 unit and function shifted up by 3 unit.
Therefore, Translate 4 units to the right and 3 units up.
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is something is greater than 6 , do i include 6
No, 6 will not be included
Explanation:Let the number greater than 6 be represented by x
The statement "x greater than 6" can be written as:
x > 6
Therefore, 6 will not be included in the list
1.2 where was the Declaration of Independence signed
August 2, 1776, in the Pennsylvania State House.
Step-by-step explanation:After much debate, the Second Continental Congress ultimately agreed to the Declaration of Independence, and then signed it
1. MOVIES By the end of its first week, a
movie had grossed $2.3 million. By the
end of its sixth week, it had grossed
$6.8 million. Graph the data with the
week on the horizontal axis and the
revenue on the vertical axis, and draw a
line through the points. Then find and
interpret the slope of the line.
10
Revenue (millions of dollars)
OU
0 2 4 6 8 10
Week
Find the length of the segment JK in the parallelogram below.
Answer:
58
Step-by-step explanation:
3x-14=58
+14 +14
3x=72
x=24
solved that now we'll input the factor
3(24)-14
72-14
"58" is your answer
What are the rational numbers between 2 & 3
Answer:
The rational numbers between 2 & 3 include:
1. 4120
2. 4220
3. 4320
4. 4420
5. 4520
6. 4620
7. 4720
8. 4820
9. 4920
10. 5020
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 1 more to become an ACE!! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Franco is evenly dividing 3 and 1/3 pounds of flour into five containers and would like to know how many pounds of flour will be in each container. Franco sets up the following division problem to find his answer 3 and 1/3 divided by 5Convert Franco’s division problem into a product involving two fractions and find out how many pounds of flour each container will hold
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
3 and 1/3 pounds = flour
5 = containers
Step 02:
We must apply the algebraic rules to find the solution.
[tex]\begin{gathered} \text{flour:} \\ 3\text{ + }\frac{1}{3}\text{ = }\frac{9\text{ + 1}}{3}\text{ = }\frac{10}{3} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{10}{3}\cdot\text{ }\frac{1}{5}\text{ = }\frac{10}{15}\text{ = }\frac{2}{3\text{ }}\text{ (division =}==>\text{ product)} \\ \\ \end{gathered}[/tex]The answer is:
2/3 pounds of flour
What is the solution to the following system of equations? (1
point)
4x + 2y = 12
x - y = 3
(3,0)
(0, 3)
(0, -3)
(2,3)
What is the area of the polygon?
A=
? square units
Answer:
30 square units.
Step-by-step explanation:
Divide the full polygon into two halves. The left half is 5 wide by 5 tall, making the area of the left 25 square units. The right half is 4 wide by 5 tall, and is perfectly cut in half. We can calculate the area normally, and then cut it in half: (5×4)/2 = 10 square units. Add the two polygons together, totalling 30 square units.
Nate and his family plan to take a 2,438 mile cross-country trip this summer.if they drive 85 miles each day ,how many days will they be driving? explain your answer
28.68235294117647 days (29 days ) will be taken by nate and his family to take a cross country trip of 2438 miles .
What is division ?Divide is the polar opposite of multiply. You get four in each group when you divide twelve into three equal groups then multiply three groups of four to create twelve. Determining how many equal groups are formed or how many individuals are in each group following a fair distribution is the fundamental goal of splitting.
Calculationspeed = 85miles / day
distance = 2438
time = 2438 / 85 = 28.68235294117647 days
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Find the highest common factor (HCF) of 32, 48 and 72
What is the equation of the line below
The given graph is of the equation y = x - 2
How to represent an equation in a graph?Select x-values and enter them into the equation to graph a function. You will obtain a y-value once those values have been entered into the equation. The coordinates of a single point are made up of the x and y values.
Step 1 is to determine the variables.
Step 2: Establish the range of the variable
Determine the graph's scale in step three.
Step 4 is to give each axis a number, a label, and a title.
5. Select the data points and plot them on the graph.
6. Create the graph.
After understanding the "how" of drawing a graph you will surely understand how to decide which equation's graph it is.
The given graph is of the equation
y = x - 2
because as in the graph
the slope cuts the points x = 4 and y = 2
and when we substitute this value in the above mentioned equation we get
2 = 4 - 2
which satisfies the condition .
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help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The point of maxima and minima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as the rate change of its value at around a point. It can be written in mathematical form as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric meaning is that it is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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