Answer:
The answer is C) 57.46cm2
Step-by-step explanation:
To find the area of a trapezoid you add together the parallel lines and times the answer by the height. Then you divide it by 2.
Answer:
The answer is B, 160 cm2
Step-by-step explanation:
To find the area of a trapezoid we have to use the following equation:
A= 0.5*(b1*b2)*h
a= area
b1: base 1
b2: base 2
h: height
Then,
A= 0.5*(14cm+18cm)*10cm = 160 cm2.
Restrict the domain of the function f(x) = (x-2)^2 so it has an inverse. Then determine its inverse function.
Answer:
Look to the bold answer down
Step-by-step explanation:
* Lets explain how to restrict the domain of the quadratic function
- The quadratic function is two-to-one function
- The inverse of it is one-to-two which is not a function
- So we can not find the inverse of the quadratic function until restrict its
domain
- We restrict the domain at the x-coordinate of the vertex of the function
∵ f(x) = (x - h)² + k is the standard form of the quadratic function, where
(h , k) are the coordinates of its vertex
- To restrict the domain we put x > h for the right part of the parabola
or x < h for the left part of the parabola
* Lets solve the problem
∵ f(x) = (x - 2)²
∵ f(x) = (x - h)² + k is the standard form of the quadratic function
∴ h = 2 and k = 0
∴ The vertex of the parabola is (2 , 0)
- We will restrict the domain at x = 2
∴ The domain of the function f(x) to have inverse is x > 2 or x < 2
* The restriction domain is x > 2 or x < 2
- To find the inverse of the function switch x and y and solve for the
new y
∵ f(x) = (x - 2)²
∵ f(x) = y
∴ y = (x - 2)²
- Switch x and y
∴ x = (y - 2)²
- take square root for both sides
∴ ± √x = y - 2
- Add 2 for both sides
∴ ± √x + 2 = y
∴ [tex]f^{-1}=\sqrt{x}+2=====OR=====f^{-1}=-\sqrt{x}+2[/tex]
* For the domain x > 2 of f(x) the inverse is [tex]f^{-1}(x) = \sqrt{x}+2[/tex]
For the domain x < 2 of f(x) the inverse is [tex]f^{-1}(x)=-\sqrt{x}+2[/tex]
1.) Is f(x)=2x^3 + 2x and odd function
2.) is -5x^3 - 4 and even function ?
3.) 4x-4 an even even function ?
Answer:
yes, no, no
Step-by-step explanation:
For odd functions : −f(x) = f(−x) for all x
For even functions :f(x) = f(−x) for all x
1) -f(x)= -2x^3 -2x
f(-x) = -2x^3-2x
yes
2 ) f(-x) = 5x^3 -4 ≠ f(x)
no
3 ) f(-x) = -4x -4 ≠ f(x)
no
1) [tex]f(-x) = -2x^3-2x[/tex]
The function [tex]f(x)=2x^3 + 2x[/tex] is odd function.
2 ) [tex]f(-x) = 5x^3 -4[/tex] ≠ f(x)
The function [tex]f(x) = -5x^3 - 4[/tex] is not even function.
3 ) f(-x) = -4x - 4 ≠ f(x)
The function f(x) = 4x - 4 is not an even even function.
What are an odd function and an even function?If we obtain an expression that exists equivalent to f(x), we have an even function; if we obtain an expression that stands equivalent to -f(x), we contain an odd function; and if neither occurs, it is neither!
For odd functions :
−f(x) = f(−x) for all x
For even functions :
f(x) = f(−x) for all x
1) [tex]f(-x) = -2x^3-2x[/tex]
Therefore, the function [tex]f(x)=2x^3 + 2x[/tex] is odd function.
2 ) [tex]f(-x) = 5x^3 -4[/tex] ≠ f(x)
Therefore, the function [tex]f(x) = -5x^3 - 4[/tex] is not even function.
3 ) f(-x) = -4x - 4 ≠ f(x)
Therefore, the function f(x) = 4x - 4 is not an even even function.
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The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. what is the maximum height, in feet, the ball will attain?
Answer:
The maximum height is 191.063 ft
Step-by-step explanation:
We can easily solve this question by plotting the graph of the equation below
h(t)=-16t^2+Vt+h
Where
h = initial height = 2ft
V = initial speed = 110 ft/s
t = time in seconds
Please, see attached image below
The maximum height corresponds to
191.063 ft
The maximum height the ball will attain is 115.02 feet.
Explanation:The maximum height can be found by identifying the vertex of the quadratic equation representing the projectile's height.
Given the equation h(t) = -16t^2 + Vt + h, where V is the initial speed of the ball and h is the initial height, we substitute the given values V = 110 and h = 2 into the equation.
The equation becomes h(t) = -16t^2 + 110t + 2.
To find the maximum height, we need to find the vertex of this quadratic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -16 and b = 110. Plugging in these values, we have x = -110 / (2*(-16)) = 110/32 = 3.4375.
Now we can substitute this x-value back into the equation to find the y-coordinate of the vertex. h(3.4375) = -16(3.4375)^2 + 110(3.4375) + 2 = 115.02 feet.
Therefore, the ball will attain a maximum height of 115.02 feet.
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A wise man once said 200 reduced by 3 times my age is 50. What is his age?
He is 50 years old
200-(3*50)=age
200-150= 50
Answer:
50
Step-by-step explanation:
200-(3x)=50
3x=200-50 (Collect like terms)
3x=150
3x/3=150/3 (Divide through by 3)
x=50
Which action describes the first step in both scientific investigation and technological design?
A.researching how solar B.panels work
C.identifying a need for a D.solar panel
communicating to the team that solar panels are easy to install
designing a solution by sketching a prototype for a solar panel
Answer:
The best answer would be D
Step-by-step explanation:
This would be best because if you sketch about an object or thing you are making it can help you better picture what you are making or someone else therefore the answer is D
which money saving option represents ownership
Answer: stocks
^^^^^^^^^^^^^^^^
Which lines are parallel? Check all that apply.
b and f
b and c
c and e
c and d
d and f
e and f
Answer:
b and f
c and e
Step-by-step explanation:
Basically, this question is testing your knowledge on supplementary angles (angles that add up to 180) and corresponding angles (angles that are across from each other that have the same value).
Using the information the diagram has given you, you just need to plug in the correct values for each angle. Once you've completed that, you just match them up. If two of the top right corners are 90.5, then they match! I made a little diagram, though it might be a little confusing :/// I hope I helped a little :)
what is the equation in poiny slope form of the line that is perpendicular to the given line and passes through the point (-4, -3)
Answer:
Step-by-step explanation:
Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].
Ex: 2 --> -½; -2 --> ½
Answer:
Step-by-step explanation:
Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].
Ex: 2 --> -½; -2 --> ½
Help please ..someone
Which of the following relations represents a function?
{(4,2), (4,3), (4, 5), (4,7)}
{(-2, 1), (0,5), (1, -3), (-2, 0)}
{(-1, 3) (-2, 3) (-1, 5) (-2,5)}
{(-3, 1), (1, 4), (-2, 1), (0, 3)}
Answer:
{(-3, 1), (1, 4), (-2, 1), (0, 3)}
Step-by-step explanation:
If a set of ordered pairs represents a function, then there must not be any first coordinate that repeats itself more than once in any of the ordered pairs.
In other words, no x-coordinate should correspond to more than one y-coordinate.
From the given options, the only set of ordered pairs that satisfies the conditions of a function is;
{(-3, 1), (1, 4), (-2, 1), (0, 3)}
The correct answer is the last option.
What is the factorization of the trinomial below?
4x^2+28x + 48
O A. 4(x+3)(x+4)
O B. 4(x+2)(x+4)
O C. (x+2)(x+16)
O D. (x+3)(x + 4)
[tex]4x^2+28x + 48=\\4(x^2+7x+12)=\\4(x^2+3x+4x+12)=\\4(x(x+3)+4(x+3))=\\4(x+3)(x+4)[/tex]
Answer:
A
Step-by-step explanation:
Given
4x² + 28x + 48 ← factor out 4 from each term
= 4(x² + 7x + 12)
To factor the quadratic
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term
The factors are + 4 and + 3, since
4 × 3 = 12 and 4 + 3 = 7, thus
x² + 7x + 12 = (x + 3)(x + 4) and
4x² + 28x + 48 = 4(x + 3)(x + 4) → A
I do not understand how to find Q
Answer:
50
Step-by-step explanation:
You can use that sum of the opposite interior angles is equal to that exterior one.
So (30)+(4x+2)=8+6x
Combine like terms on left
32+4x=8+6x
Subtract 4x on both sides
32=8+2x
Subtract 8 on both sides
24=2x
So x=12
To find Q replace x in 4x+2 with 12 giving you 4(12)+2=48+2=50
just to add to the great reply above
Check the picture below.
Q = 4(12) + 2 = 50.
Explain why the initial value of any function of the form
f(x) = a(b) is equal to a.
Answer:
The answer in the procedure
Step-by-step explanation:
we have
[tex]f(x)=a(b)^{x}[/tex]
This is a exponential function
where
a is the initial value
b is the base
we know that
The initial value of the function is the value of f(x) when the value of x is equal to zero
substitute x=0 in the function
[tex]f(0)=a(b)^{0}[/tex]
Remember that any number to the zero power is one
so
[tex](b)^{0}=1[/tex]
substitute
[tex]f(0)=a*1=a[/tex]
please help
A manager measured the number of goods, y, that his company produced in x hours. The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.
Which equation, in point-slope form, correctly represents the goods produced by the company after x hours?
A.y−45=5(x+9)
B.y−45=5(x−9)
C.y+9=5(x+45)
D.y−9=5(x−45)
Answer:
Option B. [tex]y-45=5(x-9)[/tex]
Step-by-step explanation:
Let
x -----> the number of hours
y ----> the number of goods
we know that
The equation of a line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=5\ \frac{goods}{h}[/tex] ----> the rate is the same that the slope of the linear equation
[tex]point\ (9,45)[/tex] --->(At hour 9, the company had produced 45 goods)
substitute
[tex]y-45=5(x-9)[/tex]
A group of 125 teenagers were asked which of the following activities they would most likely choose to spend their free time doing: reading a book, watching television, playing video games, or listening to music. The results are displayed in the circle graph below.
How many teenagers chose watching television?
35
40
45
50
there is an attachment at the bottom.
From the Circle Graph, We can notice that :
★ 32% of 125 teenagers chose watching Television
[tex]:\implies \mathsf{\left(\dfrac{32}{100} \times 125\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \mathsf{\left(\dfrac{32}{20} \times 25\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \mathsf{\left(\dfrac{8}{5} \times 25\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \mathsf{\left(8 \times 5\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \large\boxed{\mathsf{40}}\;\textsf{teenagers chose watching television}[/tex]
Is 4.00 equivalent to the number 4?
Answer:
Yes, it's the same number.
Answer: Of course, it's just that mathematician geniuses added a point and two zeros after it.
Please help will give brainlist Write the equation of a function whose parent function, f(x) = x + 5, is shifted 3 units to the right.
g(x) = x + 3
g(x) = x + 8
g(x) = x − 8
g(x) = x + 2
The equation of a function whose parent function, f(x) = x + 5, is shifted 3 units to the right will be; g(x) = x + 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that, the parent function f(x) = x + 5 is shifted 3 units to the right
If the function of x is translated horizontally to the right by h units, then the new function will be g(x) = f(x - h)
If the function of x is translated horizontally to the left by h units, then the new function will be g(x) = f(x + h)
Thus, f(x) = x + 5 is shifted 3 units to the right:
The new function is
g(x) = f(x - h)
Here h = 3
f(x) = x + 5
The x in f(x) will change to (x - 3)
= (x - 3) + 5
The new function g(x) = x + 2
Hence, Option D is correct
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Final answer:
The correct equation after shifting the parent function f(x) = x + 5 three units to the right is g(x) = x + 2.
Explanation:
The equation of a function that is shifted 3 units to the right from its parent function, f(x) = x + 5, will incorporate that horizontal shift by subtracting 3 from the variable x before applying the rest of the function. Therefore, the new function, g(x), will have the form g(x) = (x - 3) + 5 which simplifies to g(x) = x + 2. This accounts for the fact that the input to the function is effectively 3 units greater for the same output as the original function.
What number should be added to both sides of the equation to complete the square
Answer:
36
Step-by-step explanation:
You take 1/2 the linear term's coefficient and square it.
The linear term is the term that contains just an x and a number -- in this case 12x
Take 1/2 12 = 6
and square it
6^2 = 36
So when you've done that you should get
x^2 + 12x + 36 = 11 + 36
x^2 + 12x + 36 = 47
A box has a length of 6 inches, a width of 8 inches, and a height of 24 inches. Can a cylinder rod with a length of 63.5 centimeters fit in the box?
Answer:
Yes.
Step-by-step explanation:
The longest diagonal in the box is the line between one of the top corners to the opposite bottom corner.
Calculate the length of the longest diagonal in the box:
The diagonal of the base = √(6^2 + 8^2)
= √100 = 10 inches.
The longest diagonal = √( 24^2 + 10^2)
= √676
= 26 inches
= 26 * 2.54
= 66.04 cms.
Therefore the cylinder (length 63.5 cms) rod can fit in the box.
WILL MARK BRAINLIEST
Answer:
587.18 in^2
Step-by-step explanation:
Given:
Diameter = d = 11 inches
Slant height = l =28.5 inches
Radius will be half of diameter
r = d/2 = 11/2 = 5.5 in
We know that the formula for surface area of cone is:
[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\\SA = (3.14*5.5*28.5)+(3.14 * 5.5 * 5.5 )\\= 492.195+94.985\\=587.18\ in^2[/tex]
Hence, second option is correct ..
Answer: second option.
Step-by-step explanation:
We know that we can calculate the surface area of a cone with this formula:
[tex]SA=\pi rl + \pi r^2[/tex]
Where "r" is the radius and "l" is the slant heigth.
We know that the radius is half the diameter, then the radius of this cone is:
[tex]r=\frac{11in}{2}\\\\r=5.5in[/tex]
Since we know tha radius and the slant height, we can substitute values into the formula, using 3.14 for π.
Therefore, we get:
[tex]SA=(3.14)(5.5in)(28.5in) + (3.14)(5.5in)^2=587.18in^2[/tex]
Which ratios form a proportion?
1. 4/10 and 10/25
2. 4/11 and 6/13
3. 4/9 and 9/4
4. 3/5 and 9/25
the height of a ball can be estimated by the following equation h(t) = 8t^2 4t 125 where t is time, in seconds, after the ball was thrown and h(t) is the corresponding height, in meters. what is the height at t=2.3 seconds
Replace t with 2.3 and solve:
8(2.3)^2 +4(2.3) + 125
Simplify:
8(5.29) + 9.2 + 125
42.32 + 9.2 + 125
51.52 + 125
176.52 meters
Answer:
176.52m
Step-by-step explanation:
Given is the height of a ball as
[tex]h(t) = 8t^2+ 4t +125[/tex]
where t is time, in seconds, after the ball was thrown and h(t) is the corresponding height, in meters
When t=2.3, substitute this for t
h(2.3) = [tex]8(2.3)^2 +4(2.3)+ 125 \\=176.52m[/tex]
Find the measure of angle eight in each triangle round each answer to the nearest 10th
Answer:
# m∠A = 65.3°
# m∠A = 25.8°
# m∠A = 22.7°
Step-by-step explanation:
* Lets revise the trigonometry function to solve the problem
- In any right angle triangle:
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
- For angle A
# sin(A) = opposite/hypotenuse
∵ The opposite to ∠A is BC
∵ The hypotenuse is AC
∴ sin(A) = BC/AC
# cos(A) = adjacent/hypotenuse
∵ The adjacent to ∠A is AB
∵ The hypotenuse is AC
∴ cos(A) = AB/AC
# tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB
* Lets solve the problems
# In Δ ABC
∵ m∠B = 90°
∵ AB = 2.3 ⇒ adjacent to angle A
∵ BC = 5 ⇒ apposite to angle A
- To find m∠A use the tangent function because we have opposite
and adjacent sides
∴ tan A = BC/AB
∴ tan A = 5/2.3 ⇒ use tan^-1 to find m∠A
∴ m∠A = [tex]tan^{-1}\frac{5}{2.3}=65.29756[/tex]
* m∠A = 65.3°
# In Δ ABD
∵ m∠B = 90°
∵ AB = 5.4 ⇒ adjacent to angle A
∵ DA = 6 ⇒ the hypotenuse
- To find m∠A use the cosine function because we have adjacent
and hypotenuse sides
∴ cos A = AB/DA
∴ cos A = 5.4/6 ⇒ use cos^-1 to find m∠A
∴ m∠A = [tex]cos^{-1}\frac{5.4}{6}=25.84193[/tex]
* m∠A = 25.8°
# In Δ ABE
∵ m∠B = 90°
∵ EB = 2.4 ⇒ opposite to angle A
∵ EA = 6.8 ⇒ the hypotenuse
- To find m∠A use the sine function because we have opposite
and hypotenuse sides
∴ sin A = EB/EA
∴ sin A = 2.4/6.8 ⇒ use sin^-1 to find m∠A
∴ m∠A = [tex]sin^{-1}\frac{2.4}{6.8}=22.6673[/tex]
* m∠A = 22.7°
Explain what x^(2/3) means using radicals and integer exponents.
A month ago, Kerry weighed 123 1/4 pounds. Now he weighs 120 1/2 pounds. How many pounds did he lose?
For this case we have to:
Initial weight = [tex]123 \frac {1} {4} = \frac {4 * 123 + 1} {4} = \frac {493} {4} = 123.25 \ pounds[/tex]
Final weight =[tex]120 \frac {1} {2} = \frac {2 * 120 + 1} {2} = \frac {241} {2} = 120.5 \ pounds[/tex]
We subtract to know how many pounds he lost:
[tex]123.25-120.5 = 2.75[/tex]
So, Kerry lost 2.75 pounds.
ANswer:
Kerry lost [tex]2 \frac {3} {4}[/tex] pounds.
Answer:[tex]2.75\ pounds[/tex] or [tex]2\frac{3}{4}\ pounds[/tex]
Step-by-step explanation:
You can convert the mixed numbers to decimal numbers. Divide the numerator by the denominator of the fraction and add it to the whole number part:
[tex]123\ \frac{1}{4}\ pounds=(123+0.25)\ pounds=123.25\ pounds[/tex]
[tex]120\ \frac{1}{2}\ pounds=(120+0.5)\ pounds=120.5\ pounds[/tex]
To calculate how many pounds Kerry lost, you need to subtract his weigth of a month ago and his actual weigth.
Therefore, you get that he lost:
[tex]pounds\ lost=123.25\ pounds-120.5\ pounds[/tex]
[tex]pounds\ lost=2.75\ pounds[/tex] or [tex]2\frac{3}{4}\ pounds[/tex]
Help please thank you!
Answer:
[tex]x_1=-2.9\\x_2=0.2[/tex]
Step-by-step explanation:
The first step is to move the [tex]5x[/tex] to the left side of the equation and then add the like terms:
[tex]4x^2+16x-2=5x\\\\4x^2+16x-2-5x=0\\\\4x^2+11x-2=0[/tex]
Now we can apply the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case we can identify that:
[tex]a=4\\b=11\\c=-2[/tex]
Finally, we must substitute these values into the Quadratic formula. Then we get:
[tex]x=\frac{-11\±\sqrt{(11)^2-4(4)(-2)}}{2(4)}[/tex]
[tex]x_1=-2.9\\x_2=0.2[/tex]
An industrial laser cuts steel plates that are 11.93 meters long. The laser can have an error value of at most 0.02 meters.
The inequality |x − | ≤ can be used to find the range of acceptable lengths for the steel plates.
The range of acceptable lengths for the steel plates is ≤ x ≤
Answer:
| x - 11.93 | ≤ 0.0211.91 ≤ x ≤ 11.95Step-by-step explanation:
Error is the difference from the nominal value, hence the nominal value is what is subtracted from x. We want the magnitude of that difference, | x-11.93 |, to be less than the maximum error value, 0.02, so the inequality is ...
|x -11.93| ≤ 0.02
__
We can solve this by "unfolding" it, then adding 11.93:
-0.02 ≤ x -11.93 ≤ 0.02
11.91 ≤ x ≤ 11.95
The point (4, 5) is translated two units left and eight units down. What is the y-coordinate of the image?
since 5 is the y coordinate, subtract 8. 5-8=-3!
Answer:-3
Step-by-step explanation:
Which phrase matches the expression c^3
A.) c cubed
B.) c increased by 3
C.) the sum of 3 and c
D.) 3 cubed
Answer:A
Step-by-step explanation:
Think about it as a process of elimination.
It can't be "B' for the simple fact that "increased by'' is a term that is often used for addition problems.
It can't be "C" because, as previously stated, sum is a term that is used in addition problems.
It can't be "D" because this is a unit that you are using.
A. "c cubed" matches the expression c^3, which means raising c to the power of 3, not the other options.
The correct phrase that matches the expression c^3 is "A.) c cubed."
In mathematics, when you see an exponent of 3 (as in c^3), it indicates that you should multiply the base, c, by itself three times. This is commonly referred to as "c cubed." It signifies that you should raise c to the power of 3, meaning c * c * c. The other options are not accurate representations of c^3:
B.) "c increased by 3" does not involve exponentiation; it implies adding 3 to c.
C.) "the sum of 3 and c" is simply c + 3 and does not involve cubing.
D.) "3 cubed" represents 3^3, which equals 27, and is different from c^3.
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Which is greater 4 P 3 or 4 C 3?
Answer:
[tex]\large\boxed{_4P_3>_4C_3}[/tex]
Step-by-step explanation:
[tex]\left\begin{array}{ccc}_nP_r=\dfrac{n!}{(n-r)!}\\\\_nC_r=\dfrac{n!}{r!(n-r)!}\end{array}\right\}\Rightarrow\dfrac{n!}{(n-r)!}>\dfrac{n^!}{r!(n-r)!}\Rightarrow_nP_r>_nC_r\\\\\text{because}\\-\text{the nominators are the same}\\-\text{the denominator}\ (n-r)!\ \text{is graeter than the denominator}\ r!(n-r)![/tex]
[tex]\text{Let's check our example:}\\\\n!=1\cdot2\cdot3\cdot4\cdot...\cdot n\\\\_4P_3=\dfrac{4!}{(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1!}=\dfrac{24}{1}=24\\\\_4C_3=\dfrac{4!}{3!(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot3\cdot1!}=\dfrac{24}{6}=4\\\\24>4\Rightarrow_4P_3>_4C_3[/tex]
[tex]nPr = \dfrac{n!}{(n-r)!} \\ \\ nCr = \dfrac{n!}{r!(n-r)!}\\ \\ \Rightarrow nPr > nCr\\ \\ \Rightarrow \boxed{4P3 > 4C3}[/tex]