The perimeter of rectangle A is 10 cm and its area is 6 cm2. The perimeter of rectangle B is 20 cm. What is the area of rectangle B assuming these two rectangles are similar?
Answers
The perimeter of rectangle A is 10 cm
Perimeter of A = 2x+2y=10 cm, then:
Perimeter of A = 2(x+y)=10
Perimeter of A = x+y=5
We also know that the area of A= xy= 6 cm²
Then, we can admit x=3 and y=2.
Both rectangles are similar.
[tex]\frac{x_a}{y_a_{}}=\frac{x_b}{y_b}[/tex][tex]\begin{gathered} \frac{3}{2}=\frac{x_b}{y_b} \\ x_b=\frac{3y_b}{2_{}} \end{gathered}[/tex]Perimeter of B
[tex]\begin{gathered} 2x_b+2y_b=20 \\ x_b+y_b=10 \\ \frac{3y_b}{2}+y_b=10 \\ 3y_b+2y_b=20 \\ 5y_b=20 \\ y_b=4 \end{gathered}[/tex][tex]\begin{gathered} x_b=\frac{3y_b}{2} \\ x_b=\frac{3\cdot4}{2} \\ x_b=\frac{12}{2} \\ x_b=6 \end{gathered}[/tex]Therefore
Area of B = 4 x 6 cm² = 24 cm²
Related Questions
the function g(x) was obtained by transforming f(x)=1/x Use the description of the transformation to write the equation representing g(x).f(x) Is vertically stretched by a factor of 2, reflected about the X axis, then shifted 5 units.
Answers
Since f(x) is vertically strectched by a factor 2, we get
[tex]f(x)\longrightarrow\frac{2}{x}[/tex]next, it is reflectec about the x-axis, then we have
[tex]\frac{2}{x}\longrightarrow-\frac{2}{x}[/tex]Finally, its shifted 5 units on x axis, then we have
[tex]-\frac{2}{x}\text{ --> }-\frac{2}{x+5}[/tex]which corresponds to option 2
supposed your friend was born, your friends parents deposited $2000 in an account paying 3.5% interest compound monthly. what will the account balance be after 15 years?
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If we have a deposit of $2000, invested at an an annual interest rate of 3.5% compounded monthly, we can calculate the final value of that deposit in 15 years as:
[tex]FV=PV(1+\frac{r}{m})^{m\cdot n}[/tex]where:
FV: final value of the deposit.
PV: initial deposit (PV = 2000)
r: annual interest rate (r = 0.035)
m: subperiod (as the compound is monthly, and there are 12 months in a year, we have m = 12).
n: period (n=15)
Then, the expression gives us a value of:
[tex]\begin{gathered} FV=PV(1+\frac{r}{m})^{m\cdot n} \\ FV=2000(1+\frac{0.035}{12})^{12\cdot15} \\ FV\approx2000(1.002917)^{180} \\ FV\approx2000\cdot1.689 \\ FV\approx3378 \end{gathered}[/tex]Answer: the account balance after 15 years will be $3378.
$75.00 is shared among 3 people in the ratio 2:4:9 how much is the largest share?
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The ratio is 2:4:9, so we can consider the total parts we are dividing the total as 2+4+9 = 15.
Then, the first person receives 2/15, the second receives 4/15 and the third receives 9/15.
As the total is 75, we can calculate each part as:
[tex]\begin{gathered} p_1=75*\frac{2}{15}=10 \\ \\ p_2=75*\frac{4}{15}=20 \\ \\ p_3=75*\frac{9}{15}=45 \end{gathered}[/tex]Then, the largest share correspond to the third person and is $45.00.
Answer: $45.00
HURRRYYY Given that AD is congruent to DC , find the length of XC.
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The length of XC is 20
What does congruence of triangle mean?Triangles are said to be congruent if the three angles and three sides of a triangle are equal to the corresponding angles and sides of another triangle.
To be congruent, two triangles must have the same size and shape. The two triangles under consideration must overlap. If you rotate, flip, and/or move the triangle, its position and appearance will look different. In this case, we need to identify the six parts of one triangle and the corresponding parts of the other triangle.
For the triangles ΔAXD and ΔCXD
AD = DC ( congruent sides)
∠XDA = ∠XDC = 90° ( XD is perpendicular to AC)
XD is the common side.
This proves that triangles ΔAXD and ΔCXD are congruent
So it concludes, that XD = XC
2m + 10 = 4m
10 = 4m - 2m
10 = 2m
m = [tex]\frac{10}{2}[/tex]
m = 5
XC = 4m
XC = 4 × 5 = 20
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&Maps CClever | Portal e Learner Home e Learning Path - Eng... Mail- Makayla D. Submit Test R Pretest: The Real Number System rag the tiles to the boxes to form correct pairS. atch the pairs of equivalent expressions. (-1440)-1+ 46+ (54-26)+(28+) 8-15 -3-(8+6) -11 -10+8)+(76-5) -15 Dor Moxt
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hello
to solve this question, we need to write out the expressio
A teenager in a highrise building looks out his window at another building across the street and realizes a crime is being committed. If the buildings are 60 feet apart, and the teenager is looking down into the other building with an angle of depression of 20°, how many feet lower is the floor where the crime is being committed? If each floor is 10 feet, about how many floors down is it?
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Hello!
The first step to solving this exercise is to draw the situation, look:
Now we can solve this exercise. Notice that we want to know the height that I called "X".
To find it, we must use the tangent of 20º, look:
[tex]\tan (20\degree)=\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} \frac{0.364}{1}=\frac{60}{x} \\ \\ 0.364x=60 \\ x=\frac{60}{0.364} \\ \\ x\cong164.83 \end{gathered}[/tex]If each floor is 10 feet:
[tex]\frac{164.83}{10}=16.483\text{ floors}[/tex]If you have to approximate, you can say that it is 16.5 floors down.
Please help me help help me please help help me
Answers
When we are given a polynomial of the form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+..+d^{}[/tex]Then the number that is multiplied by no variable or contains no variables is called the constant of the polynomial. In the above example, it would be "d".
Therefore, in the given polynomial we have:
[tex]3x^9+4x+129[/tex]Therefore, the constant of the polynomial is 129.
Please help!
1.) You are the crew chief of the Algebra 2 formula racing team. Your current task is to
determine fuel consumption of both cars. Car A travel x² + 3x miles and Car B travels 2x + 8 miles. Based upon tire wear (x), the cars will use x² + 4x gallons of fuel.
a.) What is the mileage
(miles/gallons) for each car?
Car A:
Car B:
b.) What is the total mileage for both cars in simplified form? (3 points)
Total:
2.)Solve for x: (5 points)
3r+3=−x+6
Answers
The mileage of Car A, Car B, and the average of is (x+3)/(x+4), 2/x and [tex]\frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
It is given that the distance traveled by the car A = x² + 3x
And the distance traveled by car B = 2x + 8
The mileage is given by mile/gallon.
So, the mileage of Car A = distance traveled by car A/gallons of fuel used.
Then,
Mileage of Car A = [tex]\frac{x^{2} +3x }{x^{2} +4x} =\frac{x(x +3)}{x(x+4)} = \frac{x+3}{x+4}[/tex] miles /gallons
Similarly, the mileage of Car B = distance traveled by car B/gallons of fuel used.
Then,
Mileage of Car B = [tex]\frac{2x+8}{x^{2} +4x} = \frac{2(x+4)}{x(x+4)} =\frac{2}{x}[/tex] miles/gallons
Now, the total mileage of A and B is the average of car A and car B,
Mileage of Car A + Mileage of Car B = [tex]\frac{x^{2} +3x }{x^{2} +4x} + \frac{2x+8}{x^{2} +4x} = \frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
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E Which point is located at (4, -2)? 3 G 다
Answers
The given coordinate tells us that when x = 4, y = - 2
Looking at the graph, the point where x = 4 and y = - 2 is point D
In the quadrilateral below. “Angle WXZ is congruent to Angle YZX." If Ricardo's conjecture is true, which of the following must be true for Quadrilateral WXYZ to be a parallelogram?
Answers
Answer:
∠YXZ ≅ ∠WZX
Explanation:
Given that “Angle WXZ is congruent to Angle YZX."
The angles are shown in the diagram below.
This means that angles WXZ and YZX are alternate angles and thus,
• WX is parallel to ZY.
Consider the diagram below:
Angles YXZ and WZX are congruent by alternate angles, and thus:
• WZ is parallel to XY.
So, we have shown that the opposite sides of the quadrilateral are parallel.
Therefore, in order for quadrilateral WXYZ to be a parallelogram, Angles YXZ and WZX must be congruent.
The first option (∠YXZ ≅ ∠WZX ) is correct.
PLEASE HELP! I WILL GIVE BRAINLIEST The sales tax rate is 50%. How much will it cost to buy a $7.59 panther figureine? (Panther $7.59 plus tax) $11.95$0.57$12.52$11.39
Answers
The sale tax of the product will be:
0.5(7.59)=3.795
then the final price for the panther figurine (with taxes) will be:
7.59+3.795=$11.39
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.2% a.) how much will the interest amount to ?b.) what amount must Miguel pay Julio at the end of 6 months ?
Answers
Given:
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition.
He agreed to pay Julio in 6 months with simple annual interest at 6.2%
So, the interest = r = 6.2% = 0.062
the time = t = 6 months = 6/12 years = 1/2 year
a.) how much will the interest amount to?
The interest is given by the formula:
[tex]I=P\cdot r\cdot t[/tex]Substitute with the given values:
[tex]I=500\cdot0.062\cdot\frac{1}{2}=15.5[/tex]So, the interest = I = $15.5
b.) what amount must Miguel pay Julio at the end of 6 months?
So, Miguel will pay the amount that he borrowed and the interest
so, he will pay:
[tex]P+I=500+15.5=515.5[/tex]So, the answer will be: $515.5
Graph the equationy = 6
Answers
Since the equation has only the variable y and it is a constant value, that means this equation is represented by a horizontal line (the line contains all values of x and always the value of y is 6).
In order to graph this equation, we can graph two points that are on the line (for example, (0, 6) and (1, 6)) and then draw the line that passes through both of them.
So we have:
Determine whether the event below is mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary. Rolling a pair of dice and doubles or a sum of 6 is rolled.Not mutually exclusive.
Answers
The given event is not mutually exclusive.
Remember that mutually exclusive events are those events that can't be both true, that is, if one event is true, then the other is false.
The probability of this event would be
[tex]P=\frac{6+5-1}{36}=\frac{10}{36}=\frac{5}{18}\approx0.28[/tex]Therefore, the probability is 0.28, or 28%, approximately.A changes and8. The graph of y = cos z is transformed to y = a cos (2-c) + d by a vertical expansion by a factor of 2, then translated units right and 2 units up.The new equation is:y=2 cos (x + 5) - 2y= 2 cos (x - 1) +2y= {cos (x - 1) + 2y=2 cos ( - ) - 2
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Option 2 is correct.
what happens to F(x) when x is negative but approaches zero for the function F(x)=1/x whose graph is show below?*PHOTO*
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We have the following function:
[tex]F(x)=\frac{1}{x}[/tex]According to the graph, the function tends to minus infinity when x takes negative values close to zero.
Answer: B. F(x) is a negative number
MATH HELP WILL MARK BRAINLEST
Answers
The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
In the question ,
it is given that ,
the parabola passes through the point (8,6) .
the vertex of the parabola = (6,-6) .
We know that the equation of parabola in the vertex form with vertex (h,k) is
(y - k) = C.(x - h)²
we substitute the vertex and the point passing ,
we get ,
6 - (-6) = C.(8 - 6)²
6 + 6 = C(2)²
12 = 4C
C = 12/4
C = 3
So , the equation is (y - (-6)) = 3.(x - 6)²
y + 6 = 3(x - 6)²
y = 3(x - 6)² - 6
Therefore , The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
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Jupiter's orbital speed is approximately 52 kilometers in 4 seconds. At this rate, how many kilometers will Jupiter travel in 5 seconds?
Answers
Jupiter's orbital speed is approximately 52 kilometers in 4 seconds.
In 4 seconds, she travel = 52km
i.e. in 1 minute she travel = 52/4
In one minutes she travel = 13 km
Distance travel in 5 seconds =
5 x 13 km = 65 km
At this rate Jupitar will travel 65 km in 5 seconds
Answer : Jupitar will travel 65 km in 5 seconds
The main printer in the Ivy Tech library can produce an average of 639copies every hour. For every 36 pages, it costs the college $0.06 forelectricity and supplies. If the library is open from 9AM to 9PM, howmuch money does the college use on printing each day?
Answers
You know that:
- An average of 639 copies per hour can be produced by the main printer.
- The cost for electricity and supplies is $0.06 for every 36 pages produced.
- The library is opened for 12 hours.
Let be "x"the cost (in dollars) for electricity and supplies for 639 copies produced in 1 hour.
You can set up the following proportion:
[tex]\frac{0.06}{36}=\frac{x}{639}[/tex]Solve for "x":
[tex]\begin{gathered} (\frac{0.06}{36})(639)=x \\ \\ x=1.065 \end{gathered}[/tex]Knowing that the cost for electricity and supplies for 639 copies produced in 1 hour is $1.065, youo can multiply it by 12, in order to calculate how much money the college uses on printing each day:
[tex](1.065dollars\text{)}(12)=12.78dollars[/tex]The answer is: The college uses $12.78 on printing each day.
a. If Links printing store will make a 150 copies for the cost of $15.00, then what is theunit rate of price per copy?
Answers
ANSWER
$0.10
EXPLANATION
We have that 150 copies are made for a total cost of $15.00
The unit rate of price per copy is the price of each copy of the printing.
To find the unit rate of price per copy, we have to divide the total price by the total number of copies.
So, we have:
[tex]\frac{15}{150}\text{ = \$0.10}[/tex]This means that the unit rate of price per copy is $0.10
Two farmers John and Harry cultivates twovarieties of rice namely Basmati and Naura.The sale price of these varieties of rice by boththe farmers are as follows:John sells Basmati at $5.00/kg and Naura at$3.50/kg. While Harry sells Basmati at$6.50/kg and Naura at $2.60/kg.Use the matrix to present the prices of rice bytwo farmers.
Answers
Sales price for the rice varieties:
John:
Basmati cost = $5 per kg
Naura cost = $3.5 per kg
Harry:
Basmati cost = $6.5 per kg
Naura cost = $2.6 per kg
Writing in the form matrix:
[tex]\begin{gathered} let\text{ first column represent basmati rice} \\ let\text{ the 2nd column represent Naura rice} \\ In\text{ matrix, x and y can be represented as:} \\ \begin{bmatrix}{x\text{ column}} & {y\text{ column}} \\ {}{{x\text{ column}}} & {{y\text{ column}}}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = Basmati, y = Naura} \\ \\ \begin{bmatrix}{5.00} & {3.50} \\ {6.50} & {2.60}\end{bmatrix}\text{ \lparen option B\rparen} \end{gathered}[/tex]The vertices of ACDE are C(-1, 1), D(3,5), and E(5. - 4). Translate ACDE using vectorr(3. – 1).Enter the correct ordered pair for C', D', and E'. Do NOT use any spaces in your answer.C'D'E
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C (-1,1)
D (3,5)
E (5,-4)
now we are going to translate ACDE using vector r(3,-1)
C'(2,0)
D'(6,4)
E'(8,-5)
use distributive property to fill in the blanks (4×7) - (4×3) = ___ × (7-3)
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Hello! I need help with this questionTriangle DOG was rotated to create triangle D'O'G''. Describe the transformation using details and degrees.
Answers
Answer:
180 degrees rotation about the origin
Explanation:
First, we need to identify the coordinates of DOG and D'O'G' as follows
D(-2, 1) ---> D'(2, -1)
O(-3, 3) ---> O'(3, -3)
G(1, 1) ---> G'(-1, -1)
Therefore, the rule for the transformation is
(x, y) ---> (-x, -y)
This rule is the rule for a 180 degrees rotation about the origin. So, the transformation is a 180 degrees rotation about the origin.
if a pound of almonds cost eight dollars how many ounces can be bought for $3.80
Answers
Proportions
A pound of almonds is said to cost 8 dollars.
But one pound is equivalent to 16 ounces, therefore:
16 ounces cost 8 dollars
Dividing by 8 we get that
2 ounces of almonds cost 1 dollar
Thus, for $3.80 we can buy 2*3.80 = 7.60 ounces of almonds
okay I think your name was Mrs Huggins can you please help me with the rest of this fraction I'm really struggling and I accidentally signed off because of a network error I'm really sad please
Answers
In a previous session we worked on the subtraction of the mixed numbers 2 1/8 and 1 7/8 and reached the following result:
[tex]2\frac{1}{8}-1\frac{7}{8}=\frac{17}{8}-\frac{15}{8}=\frac{2}{8}[/tex]This fraction 2/8 can be simplified. Both values 2 and 8 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator of the fraction by 2:
[tex]\frac{2\div2}{8\div2}=\frac{1}{4}[/tex]If the radius of circle M is 7, and LK = 18, find JK
Answers
Answer:
JK = 24
Explanation:
If the radius of circle M is 7, we can say that MJ = 7 and ML = 7
So, the length of MK will be equal to:
MK = ML + LK
MK = 7 + 18
MK = 25
Now, we have a right triangle JMK, and we know the length of one leg MJ = 7 and the length of the hypotenuse MK = 25. Using the Pythagorean theorem, we can find the length of the other side JK, so
[tex]\begin{gathered} JK=\sqrt[]{MK^2-MJ^2^{}} \\ JK=\sqrt[]{25^2-7^2} \\ JK=\sqrt[]{625-49} \\ JK=\sqrt[]{576} \\ JK=24 \end{gathered}[/tex]Therefore, the value of JK is 24.
The segments shown below could form a triangle.
9
A
C
C
B
4
B
A
15
True or false
Answers
No/False - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
In light of the question -In geometry, a triangle is a closed two-dimensional figure with three sides, three corners, and three vertices.Triangles are considered polygons with the fewest sides. In this article, we will discuss in detail what a triangle is, its types, properties and formulas.Learn more about triangles here. In geometry, a triangle is a type of polygon with three sides and three vertices. A triangle is considered a three-sided polygon.The sum of the three angles of a triangle is 180°. A triangle is contained in a single plane. There are six types of triangles based on their side and angle measurements.A triangle has only three sides joined by corners. Therefore, no matter what kind of triangle it is, it always has three sides.CalculationNo - there is a rule that state that the sum of two sides of a triangle must be greater than the 3rd side.
While 9+15 >4
and 4+15 >9
9+4 is not greater than 15 - so this triangle cannot be made.
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For this assignment, leave all answers as simplified fractions.A bag contains letter tiles that spell the name of the state MISSISSIPPI. Find the theoretical probabilityof drawing one tile at random for each of the following.1. P(M)2. P(S)3. P)4. P(not M)5. P(not S)6. P(not 1)
Answers
ANSWER
[tex]\begin{gathered} 1)\frac{1}{11} \\ 2)\frac{4}{11} \\ 4)\frac{10}{11} \\ 5)\frac{7}{11} \end{gathered}[/tex]EXPLANATION
From the given question;
MISSISSIPPI has 11 words
The number of M is 1
The number of S is 4
Hence;
1.
[tex]P(M)=\frac{1}{11}[/tex]2. P(S);
[tex]P(S)=\frac{4}{11}[/tex]4. P(not M) ;
[tex]\begin{gathered} 1-P(M) \\ =1-\frac{1}{11} \\ =\frac{10}{11} \end{gathered}[/tex]5. P(not S);
[tex]\begin{gathered} P(not\text{ S})=1-P(S) \\ =1-\frac{4}{11} \\ =\frac{7}{11} \end{gathered}[/tex]What percentage of 3436 is 20
Answers
Let x percent of 3436 be 20.
Recall, percentage is expressed in terms of 100. This means that
x/100 * 3436 = 20
34.36x = 20
Dividing both sides of the equation by 34.36, we have
34.36x/34.36 = 20/34.36
x = 0.582%
Thus, 0.582% of 3436 is 20