Answers
The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.
How to determine the perimeter and the area of a composite figure
In this case we have a composite figure formed by six triangles and two rectangles. The perimeter is the sum of the side lengths and the area is the sum of the areas of the triangles and rectangles. The perimeter of the entire figure is described below:
p = AB + BC + CD + DE + EF + FG + GA
p = 5√2 + √10 + √10 + 5 + √10 + 5 + 2√10
p = 10 + 5√2 + 5√10
p = 10 + 5 · (√2 + √10)
p = 10 + 5√2 · (1 + √5)
p = 5 · [2 + √2 · (1 + √5)]
And the area of the composite figure is determined by the following expression:
A = 0.5 · (3) · (1) + (3) · (4) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)
A = 2 · (3) · (1) + (3) · (4) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)
A = 33.5
The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.
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Related Questions
Find the solution to the equation:
-13 + 5a = 3(a - 3)
Answers
Answer:
a=2
Step-by-step explanation:
-13 + 5a = 3a -9 Distribute 3 through the parentheses
-13 + 5a - 3a = -9 Move the variable to the left hand side and change the sign
2a= -9 + 13 collect like terms
2a=4 Divide both sides by 2
a=2
Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used. Lewis is saving for a down payment of $8,750 on a house. The initial amount of money he has saved is $250, and the amount of money he plans on saving every month is $340. To model the situation, he created this equation, where x represents the number of months and y represents the total amount of savings: y = 250 + 340x.
Answers
The fill up for the 3rd step is y - 250 = 340x.
The fill up of the 5th step is [tex]x = \frac{y-250}{340}[/tex]The fill up of the 6th step is [tex]\frac{8750-250}{340} = 25 = x, \frac{8750-250}{340}= 34 = x[/tex]The justification for the 2nd step is subtraction PE.The justification for the 4th step is division PE.What is the simplification about?Note that:
y-250 = 250 + 340 x - 250
y = 250 + 340x.
Make x the subject of the formula:
y - 250 = 340x.
then y-250/340 = x
Then [tex]x = \frac{y-250}{340}[/tex]
The justification for the second step is subtraction property of equality because it undergoes subtraction and the collection of like terms and then subtracting them from one another as shown below:
y-250 = 250 + 340 x - 250
y= 250 + 340x - 250 + 250
Note that (-250 + 250) = 0
y = 250 + 340x.
Lastly, The fill up of the 6th step is substitution of the amount of money saved and then simplifying it.
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A Each topping costs $1
B With no toppinga a pizza costs $14
C With no toppings a pizza costs $6
D Each topping costs $6
Answers
Which of the following rational functions is graphed below
Answers
The answer should be A. :)
The correct rational function of the graph is,
⇒ f (x) = 1 /(x + 5)²
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph is shown in fgigure.
Now, By graph of function,
The graph is not defined at x = - 5.
Hence, From equation (i);
⇒ f (x) = 1 /(x + 5)²
Clearly, Function is noy defined at x = - 5.
Hence, The correct rational function of the graph is,
⇒ f (x) = 1 /(x + 5)²
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Drag the tiles to the boxes to form correct pairs.
Match the cube roots and square roots with their values.
Drag the tiles to the boxes to form correct pairs.
Match the cube roots and square roots with their values.
Match the cube roots and square roots with their values.
Match the cube roots and square roots with their values.
Match the cube roots and square roots with their values.
Answers
The match up are:
√4 = 2∛27 = 3√64 = 8∛64 = 4√49 = 7∛1000 = 10What is square root?The square root, in mathematics is known to be the factor of a number that, is said to be multiplied only by itself and thus it gives the original number.
For example:
[tex]\sqrt{4}[/tex] will give you 2.
Therefore, The match up are:
√4 = 2∛27 = 3√64 = 8∛64 = 4√49 = 7∛1000 = 10Learn more about cube roots from
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how many red apple are in the jar?
Answers
Answer:
2
Step-by-step explanation:
How do I solve this equation?
(-4x+12)^1/2 = x
Answers
[tex](-4x+12)^{1/2}=x\\\sqrt{-4x+12}=x\\\\D:-4x+12\geq0\wedge x\geq0\\D:4x\leq12\wedge x\geq0\\D:x\leq3\wedge x\geq0\\D:x\in\langle0,3\rangle\\\\\sqrt{-4x+12}=x\\-4x+12=x^2\\x^2+4x-12=0\\x^2-2x+6x-12=0\\x(x-2)+6(x-2)=0\\(x+6)(x-2)=0\\x=-6 \vee x=2\\\\-6\not \in D\\\\\boxed{x=2}[/tex]
Given the function h(x)=-5 √x, which statement is true about h(x)?
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (–∞, 0).
The function is decreasing on the interval (0, ∞).
The function is increasing on the interval (0, ∞).
Answers
The true statement about h(x) is (c) the function is decreasing on the interval (0, ∞)
How to interpret the function?The function is given as:
h(x) = -5√x
Next, we plot the graph of the function h(x)
From the attached graph, we can see that:
As x increases from 0, the function value decreases
Hence, the true statement about h(x) is (c) the function is decreasing on the interval (0, ∞)
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Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram
Answers
The probability of drawing a black ball on the second draw will be 3/5.
How to solve the probability?From the information given, the total number of balls will be:
= 2 + 3 = 5 balls.
When the first ball is black and the second is red. This will be:
= 2/5 × 3/4
= 3/10
When the first is red and the second is black, this will be:
= 3/5 × 2/4
= 3/10
Therefore, the probability of drawing a black ball on the second draw will be:
= 3/10 + 3/10
= 3/5.
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p + 46 = 94, what is p?
Answers
48.
Because 46+48 equals 94.
You can easily find out equations to this by subtracting the 46 from 94 to see what p is equal to.
HAVE A NICE DAY!
Zoe thinks of a number. She multiplies it by 3 and adds 4. She gets the same answer when she adds 5 to the number and then multiplies the result by 2.
a. Write an equation, using n for Zoe's number.
b. Solve your equation to find Zoe's number.
Answers
Answer:
Zoe's number is 6
Step-by-step explanation:
Let the number be 'n'
a) Multiply 'n' by 3 ⇒ n*3 = 3n
Add 4 to '3n' ⇒ 3n + 4
Add 5 to 'n' ⇒ n +5
Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10
3n + 4 = 2n + 10
b) 3n + 4 = 2n + 10
Subtract 4 form both sides
3n = 2n + 10 - 4
3n = 2n + 6
Subtract 2n from both sides
3n - 2n = 6
[tex]\sf \boxed{\bf n = 6}[/tex]
Answer:
21 is probably the best answer
Une fonction polynomiale du second degré possède les caractéristiques
suivantes :
• La fonction est croissante sur l'intervalle [0, 8].
• La fonction est décroissante sur l'intervalle ]-10, 0].
• La courbe passe par le point (-8, 4).
PSST
↓
Voici les symboles dont tu pourrais avoir besoin dans ta réponse. N'hésite pas à
les copier-coller à partir d'ici si tu ne les trouves pas sur ton clavier.
[]%
SAVOIR-FAIRE
INDICE
Représente graphiquement la fonction, puis détermine son codomaine. Utilise la
notation décimale au besoin.
Le codomaine est.
Je n’arrive pas à trouver le co domaine si quelqu’un peut m’aider svp?
Answers
A second-degree polynomial takes the form
[tex]f(x) = ax^2 + bx + c[/tex]
for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.
Differentiating f(x) with respect to x gives
[tex]\dfrac{df}{dx} = 2ax + b[/tex]
We're told that
• f(x) is increasing on [0, 8]
• f(x) is decreasing on ]-10, 0]
and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write
[tex]f(x) = ax^2 + c[/tex]
We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint
[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]
Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so
[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]
This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.
Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,
a = 1, c = -60 ⇒ f(x) = x² - 60 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}
a = 2, c = -124 ⇒ f(x) = 2x² - 124 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}
etc.
what is the slope of the line shown below?
Answers
Answer:
C. 2
Step-by-step explanation:
Gradient = [tex]\frac{change in y}{change in x}[/tex]
Gradient = [tex]\frac{6}{3}[/tex]
Gradient = 2
Formula: (Y2-Y1)/(X2-X1)
(-4-2)/(-1-2)=2
When you are trying to find the mean in a dot plot do you want to use the number of dots of the actual number underneath of the dots?
Answers
The number of dots tells us how many times we need to add the actual number underneath the dots. So you need to use both.
Which number should you use for the mean?
Let's suppose we have the next set:
{2, 2, 2, 4, 5, 5, 6}
If you graphed it in a dot plot, then you will have:
3 dots above the number 2.1 dot above the number 4.2 dots above the number 5.1 dot above the number 6.A total of 7 dots.
To find the mean, we just compute:
[tex]M = \frac{2 + 2 + 2 + 4 + 5 + 5 + 6}{7} = 3.7[/tex]
So the number of dots tells us how many times we need to add the actual number underneath the dots. In conclusion, to find the mean you need to use both, the number of dots and the number underneath.
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A four-sided shape has four congruent angles and sides. Which quadrilateral could it be? A. quadrilateral B. trapezoid C. square D. parallelogram
Answers
Answer:
square
Step-by-step explanation:
Option A is also correct somehow
These things can be possible in three optionsquadrilateral (Off course)ParallelogramSquarebut we are not sure about first 2 if they have equal sides or angles
only square have each angle 90 and all sides equal
So Option C is correct
Answer:
C. square
Step-by-step explanation:
Congruent means "the same" (having the same shape and size).
Any four-sided, 2-dimensional shape with straight sides is called a quadrilateral.
There are 6 special types of quadrilaterals:
Rectangle
Opposite sides are parallel and equal in lengthAll interior angles are 90°Square
All sides are equal in lengthAll interior angles are 90°Rhombus
All sides are equal in lengthOpposite sides are parallelOpposite angles are equalParallelogram
Opposite sides parallel and equal in lengthOpposite angles are equalTrapezoid
One pair of opposite parallel sidesIsosceles Trapezoid
One pair of opposite parallel sidesOne pair of non-parallel sides equal in lengthTwo pairs of equal base anglesKite
Two pairs of adjacent sides equal in lengthThe angles included between the sides of differing lengths are equalConclusion
A four-sided shape that has four congruent angles and sides is a SQUARE.
Calculus. Factor the given polynomial.
Answers
Answer:
X=-2 or x=-7
Step-by-step explanation:
(x+2)(x+7)=0
X=-2 or x=-7
9x10^2 which sentence matches the question assigned
Answers
The computation of the index shows that the value of 9 × 10² will be 900.
How to calculate the indices?From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:
= 9 × 10²
Note that 10² simply means that you've to multiply 10 twice. This will be:
= 10 × 10 = 100
Therefore, 9 × 10² will be:
= 9 × 100
= 900
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I need help with this answer please
Answers
Answer:
y=3x+1
Step-by-step explanation:
From the table when X=0,y=1 thus b=1.
When
The gates of an amusement park are closely monitored to determine whether the number of people in the amusement park ever poses a safety hazard. On a certain day, the rate at which people enter amusement park is modeled by the function e(x)=0.03x^3+2, where the rate is measured in hundreds of people per hour since the gates opened. The rate at which people leave the amusement park is modeled by the function l(x)=0.5x+1, where the rate is measured in hundreds of people per hour since the gates opened. What does (e−l)(4) mean in this situation?
Answers
The meaning of (e−l)(4) in this situation is that there are 92 people in the amusement park 4 hours after the gates open.
How to explain the value?e(x) = 0.03x³ + 2
l (x) = 0.5x + 1
Therefore, ( e - l) = [ .03x^3 + 2 ] - [ .5x + 1 ] will be:
= 0.03x³ - 0.5x + 1
Therefore, (e - l ) (4) = 0.03(4)³ - 0.5(4) + 1 = 92
Therefore, it means that 4 hours after the park opens, the rate that the number of people is changing is 92 people per hour
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-6y+y2+3-4y2-7+1-4y
Please help
Answers
EASY 20 POINTS What is the domain of the exponential function shown below?
Answers
Answer:
It's all real numbers except whatever makes the expression undefined
Step-by-step explanation:
(−∞,∞)
Answer:
All real numbers
Step-by-step explanation: (−∞,∞)
the cost of catering a dinner is $11.95 per person plus a $25 for delivery and setup . which statement is true about the graph of the function the represents the average cost per person
Answers
Answer:
45.98
Step-by-step explanation:
there ya go I did this before so I know the correct answer
an isosceles trapezoid with bases 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the exact area of the trapezoid.
PLS HELP ME OUT FIRST ANSWER GETS BRAINLIEST
Answers
The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.
Height of the trapezoidThe height of the trapezoid is calculated as follows;
From the image, the sum of h1 and h2 is the height of the trapezoid.
Each of the height will be calculated using Pythagoras theorem as follows;
half of b1 = 12/2 = 6half of b2 = 16/2 = 8h1² = r² - (b1/2)²
h1² = 10² - 6²
h1² = 64
h1 = √64
h1 = 8
h2² = r² - (b1/2)²
h2² = 10² - 8²
h2² = 36
h2 = √36
h2 = 6
Total height = 8 + 6 = 14
Area of the trapezoidA = ¹/₂(b₁ + b₂)H
A = ¹/₂(12 + 16) x 14
A = 196 sq units.
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A copy machine makes 44 copies per minute. How long does it take to make 209 copies
Answers
Answer:
5 minutes.
44 x 5 = 220,
since 44 x 4 = 176 < 209
Which of the following quadrilaterals must be a parallelogram according to the minimum criteria?
Answers
Answer: All of them are correct I think
Step-by-step explanation:
Logarithmic to Exponential
A=B⋅LogXC
A = 11
B = 4
C = 190
Substitute the values for A, B, and C into the logarithmic equation and solve for X.
Answers
[tex]A = B \log_x C\\\\\text{Given that,}~~ A = 11, ~B = 4~ C = 190\\\\~~~~~~~~11 = 4 \log_x (190)\\\\\implies \log_x (190) = \dfrac{11}4\\\\\implies x^{\tfrac{11}4} = 190\\\\\implies x = 190^{\tfrac 4{11}}\\\\ \implies x \approx 6.7397[/tex]
how to plot and graph y1 = 17,105 + 1.31x
Answers
The attached graph represents the graph of the equation y1 = 17,105 + 1.31x
How to plot and graph the equation?The equation is given as:
y1 = 17,105 + 1.31x
To plot and graph the equation, we set some values for x and calculate the corresponding y values.
Let x = 0, 1, 2 and 3.
So, we have:
y1 = 17,105 + 1.31 * 0 = 17105
y1 = 17,105 + 1.31 * 1 = 17106.31
y1 = 17,105 + 1.31 * 2 = 17107.62
y1 = 17,105 + 1.31 * 3 = 17108.93
The graph can then be plotted using the above points
See attachment
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7. Look at the number sentence below.
1+2+3+4 +-----------+ 80 = 3240
71 +72+73+ ---------+ 80 = 755
What is the sum of numbers from 1 to 70?
a)3240-10
b) 3240-80
c) 3240 +755
d) 3240-755
Answers
Answer: 3240-755
Step-by-step explanation:
We know that:
[tex](1+2+\cdots+80)-(71+72+\cdots+80)=1+2+\cdots+70[/tex]
Thus, [tex]1+2+\cdots+70=\boxed{3240-755}[/tex]
I have no clue on this one either
Answers
Answer:
Area of the triangle = 210 cm^2 .
Step-by-step explanation:
Perimeter of triangle = 4x + 1 + 3x - 1 + 3x = 70
10x = 70 - 1 + 1 = 70
x = 7.
Area A = 1/2 * base * height
= 1/2 * 3x * (3x - 1)
= 1/2 * 3(7) * (3(7) -1)
= 1/2 * 21 * 20
= 210.
Victoria bought a dress on 40% discount, and saved a massive $60. How much did the dress cost originally? How much did she pay for it?
Answers
Answer:
Answer: Original price = $150 Amount Paid = $90
Step-by-step explanation:
First we make a proportion 60/x = 40/100. When we cross multiply and divided to get x by itself we get $150 dollars. This is the original price of the dress. Now we take $150-$60 and we get $90. This is what Victoria paid for the dress after the 40% discount.
Hope this helps! :)