Since the are of the first triangle is 12 cm², the area of the second triangle is 33.33 cm².
To answer the question, we need to know what similar triangles are
What are similar triangles?Similar triangles are triangles in which the ratio of their corresponding sides is constant.
Given that the corresponding sides of the two similar triangles are 3 cm and 5 cm respectively. Also, the area of the first triangle is 12 cm². We need to find the area of the second triangle.
Area of second triangleSince the triangles are similar, we have that
(side of second triangle/side of first triangle)² = Area of second triangle/Area of first triangle
Area of second triangle = (side of second triangle/side of first triangle)² × Area of first triangle
= (5 cm/3 cm)² × 12 cm²
= 25/9 × 12 cm²
= 25/3 × 4 cm²
= 100 cm²/3
= 33.33 cm²
So, the area of the second triangle is 33.33 cm².
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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?
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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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
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.
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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Which of the following quadrilaterals must be a parallelogram according to the minimum criteria?
Answer: All of them are correct I think
Step-by-step explanation:
how to plot and graph y1 = 17,105 + 1.31x
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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How do I solve this equation?
(-4x+12)^1/2 = x
[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]
what is the slope of the line shown below?
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
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?
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.
A copy machine makes 44 copies per minute. How long does it take to make 209 copies
Answer:
5 minutes.
44 x 5 = 220,
since 44 x 4 = 176 < 209
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, ∞).
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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I have no clue on this one either
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.
Find the solution to the equation:
-13 + 5a = 3(a - 3)
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 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.
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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9x10^2 which sentence matches the question assigned
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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A four-sided shape has four congruent angles and sides. Which quadrilateral could it be? A. quadrilateral B. trapezoid C. square D. parallelogram
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.
Which of the following rational functions is graphed below
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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Which of the following is a logical conclusion to the conditional statements
below?
If it is a hamburger, then it is a sandwich.
If it is a sandwich, then it can be held in your hands.
Answer:
If it is a hamburger, it can be held in your hands.
Step-by-step explanation:
ABC Corp. has 2,000 bonds outstanding with a $1,000 face value, an 9 percent coupon, 8 years to maturity, annual interest payments, and sells at $1,105.38. The firm also has 40,000 shares of common stock outstanding at a market price of $85 a share and a beta of 0.67. The risk-free rate is 4 percent, the market return is 15 percent, and the tax rate is 20 percent. What is WACC?
The value of WACC is 6.72%
what is WACC?WACC is calculated by multiplying the cost of each capital source (debt and equity) by its relevant weight by market value, and then adding the products together to determine the total.
WACC=[(Market value of Equity*cost of equity+ Market value of Debt* post tax cost of debt)/(Market value of Equity+ Market value of Debt)]
Market value of Equity= 40,000*$85=$3,400,000
Cost of equity=Risk free return+ Beta equity*market retrun
=4 +0.67*15
=7.35
Market value of Debt
=2000*1105.38
=2,210,760
Post tax rate of debt
=9*80(1-20)
=0.0576= 5.76%
WACC= [$3,400,000* 7.35+ 2,210,760 * 5.76%]\ $3,400,000+2,210,760
=6.72%
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On a coordinate plane, a straight red line with a negative slope, labeled g of x, A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sent.
Answer: Both plans cost the same when 50 texts are sent.
Step-by-step explanation:
When x=50 (meaning 50 texts are sent), the y coordinate (which represents the cost) is the same.
EASY 20 POINTS What is the domain of the exponential function shown below?
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
Answer:
45.98
Step-by-step explanation:
there ya go I did this before so I know the correct answer
-6y+y2+3-4y2-7+1-4y
Please help
p + 46 = 94, what is p?
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!
A rancher raises 5 times as many cows as horses. If he has 132 animals
let x = horses
5x = cows
x + 5x = 132
6x = 132
Divide both sides by 6
X = 22
he has 22 horses and 110 cows
There are 22 horses and 110 cows.
What is an equation?"It is a mathematical statement which consists of equal symbol between two mathematical expressions."
For given question,
Let 'c' represents the number of cows and 'h' represents the number of horses.
A rancher raises 5 times as many cows as horses.
So, we get an equation,
⇒ c = 5 × h .................(i)
There are 132 animals.
So, we get an equation,
⇒ c + h = 132 ..................(ii)
Substitute the value of c = 5h in equation (ii)
⇒ c + h = 132
⇒ 5h + h = 132
⇒ 6h = 132
⇒ h = 22
This means, there are 22 horses.
Substitute the vale of h in equation (i),
⇒ c = 5 × h
⇒ c = 5 × 22
⇒ c = 110
This means, there are 110 cows.
Therefore, there are 22 horses and 110 cows.
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E Homework: 3.1 Homework
Evaluate the function f(z) = 3z-8 at the indicated values.
a) Find f(-4).
1
b) Find f
2
c) Find f(z-7).
a) f(-4)=
(Simplify your answer. Type an integer or a simplified fraction.)
THINGS
Replace z with the number inside the parenthesis:
f(z) = 3z-8
a. 3(-4) - 8 = -12-8 = -20
b. 3(1/2)-8 = 1 1/2 - 8 = -6 1/2
c. 3(z-7) - 8 = 3z-21-8 = 3z-29
Solve for x in the triangle. Round your answer to the nearest tenth.
X
9
64°
Answer:
x = 23.0
Step-by-step explanation:
To solve, you have to make the equation:
[tex]cos(64)=\frac{9}{x}[/tex]
Now multiply x to both sides:
[tex]cos(64)*x=9[/tex]
Next divide both sides by cos(64):
[tex]x=\frac{9}{cos(64)}[/tex]
x = 22.9675486404
Round to the tenth:
x = 23.0
Hope it helps and have a nice day!
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?
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! :)
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?
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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i need help thanks11!1!1!1!1!1
Answer:
A
Step-by-step explanation:
Calculus. Factor the given polynomial.
Answer:
X=-2 or x=-7
Step-by-step explanation:
(x+2)(x+7)=0
X=-2 or x=-7