Each side of equilateral triangle will have the length equals to 42.7 cm.
Quadrilaterals
There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.
You should find the perimeter of the rectangle.
2P=23+23+41+41= 128 cm
The equilateral triangle will have the same perimeter of the rectangle. An equilateral triangle presents the equal three sides, thus,
128= 3L
L=128/3=42.7 cm
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Which of the equations below represents
this ellipse?
a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1
The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
What is the equation of the ellipse represented in the graph?
Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Coordinates of the centera, b - Lengths of the semiaxesPlease notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
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Area=
Help me please!! Thanks so much-needed
First you have to figure out the side length of the triangle.
sin(60)= X/8
Let's call x the side length.
8 sin(60)=X
X=6.93
The multiply it by 4
The area is 27.72
A dairy farmer decides to sell three fifth of her 500 cows. How many cows will she be left with after the deal is complete?
From the diagram below, we can tell that ___.
Answer: b. the two triangles are similar by SAS
Step-by-step explanation:
These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.
Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.
[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]
[tex]\frac{6}{9} = 0.6666[/tex]
THey are similar. This means the triangles can be prooven similar with SAS.
Given that a randomly chosen flight arrives in los angeles (lax), what is the probability that the carrier is american airlines (aa)?
Using concepts of probability, it exists found that there exists a 4.7% probability that it arrives at American airlines (aa).
What is probability?A probability exists given by the number of expected outcomes divided by the number of total outcomes.
Over a large number of trials, a percentage can also define the probability of a single event.
In this question, analyzing the problem on the internet, we have that over a considerable number of flights, of those which came on time, 4.7% of them were in American airlines.
There exists a 4.7% probability that it arrives on American airlines(aa).
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Answer: 2316/16924 = 0.137 = 13.7%
Step-by-step explanation:
Select the correct answer what are the solutions to this quadratic equation 4x^2-10=10-20x
Answer:
x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2
Step-by-step explanation:
HELP HELP PLEASEEE
Theo has 2.5k followers. He knows that if he posts daily, he will gain 1k followers each day.
In this scenario, identify the initial value and rate of change. Then, explain why this is or is not
proportional and/or a linear relationship.
Geometry: complete this proof (ASAP!!! It’s urgent)
Answer:
1. BD bisects <CBE, AE || BD (Given)
2. <EBD ~= <CBD (Definition of < Bisectors)
3. <AEB ~= <EBD (Alternate Interior Angles Theorem)
4. <CAE ~= <CBD (Corresponding Angles Postulate)
5. <CAE ~= <AEB (Transitive Property of Congruence)
6. AB ~= BE (Converse of Isosceles Triangles Theorem)
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation: 4x − 3y = 34
Second equation: 3x + 2y = 17
Answer:
Multiply both sides of the first equation by 2.
Multiply both sides of the second equation by 3.
Step-by-step explanation:
The y terms are
-3y
2y
The LCM of 2 and 3 is 6.
We need the y terms to add to zero.
Multiply both sides of the first equation by 2 to get -6y.
Multiply both sides of the second equation by 3 to get 6y.
Then -6y + 6y = 0 eliminating the y terms after adding the equations.
Perfect pizza has 16 toppings listed on their menu. how many ways could a customer choose a pizza that contains 5 different toppings?
Answer:
4368 ways
Step-by-step explanation:
Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.
what expression is equivalent to 6+3(n-4)-8+2n
Answer:
Step-by-step explanation:
Comment
Begin by removing the brackets.
6+3(n-4)-8+2n
6 + 3n - 12 - 8 + 2n Collect like terms
3n + 2n + 6 - 12 - 8 Combine
5n - 14
Answer
5n - 14
(08.07 HC)
An expression is shown below:
f(x) = 2x²-3x - 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Answer:
Below in bold.
Step-by-step explanation:
Part A
At the x-intercepts f(x) = 0, therefore:
2x^2 - 3x - 5 = 0
(2x - 5)(x + 1) = 0
x = 5/2, -1)
So the x intercepts are (-1, 0) and (5/2, 0).
Part B
The Coefficient of x^2 is positive ( it is 2) So the graph opens upwards and the vertex will be a minimum.
Convert f(x) to vertex form, by completing the square:
f(x) = 2x^2 - 3x - 5
= 2(x^2 - 3/2x) - 5
= 2[(x - 3/4)^2 - 9/16] - 5
= 2(x - 3/4)^2 -18/16 - 80/16
= 2(x - 3/4)^2 - 49/8
So the coordinates of the vertex are
(3/4, -49/8) or
(0.75, -6.125) in decimal form.
Part C
To graph f(x) you would first mark the points on the x axis which we found in Part 1 and the vertex found in Part 2. This vertex will be the bottom of the 'U'.
The graph is a parabola shaped roughly like a U, and will be symmetrical about the line x = 0.75 (which passes through the vertex).
You would also plot 2 more points above the x axis so as to get an accurate graph. 1 would be to the left of the line of symmetry and 1 to its right.
Suggest x = - 2 and calculate f(-2) = 2(-2)^2 - 3(-2) - 5 = 11.
- that is the point (-2,11) and the other would be x = 4, f(x) = 15. (4, 15)
Once you have plotted these points draw a smooth u shaped curve through them.
can someone please help mee ( will give brainliest 20 points!!!)
The piecewise function graphed below is given as follows:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex][tex]f(x) = x + 2, -2 < x \leq 3[/tex][tex]f(x) = -1, 3 < x \leq 5[/tex]What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex]
For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:
[tex]f(x) = x + 2, -2 < x \leq 3[/tex]
For x greater than 3 until 5, the function is constant at -1, hence the definition is:
[tex]f(x) = -1, 3 < x \leq 5[/tex]
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In using the multiple regression method, we can model the effects of the different levels of a qualitative independent variable by using a(n) ____________
For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
According to the statement
we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.
So, For his purpose, we know that the
A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.
And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.
By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.
So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
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Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3 write an equation to determine the area, a, of the patio that will be painted. a = (x 18)(x 35) a = (x 15)(x 25) 30 a = (x 5)(x 22) a = (x 25)(x 15) − 30
The correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
What is Geometrical figure?Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.
According to the given Information:Length of the rectangular patio is (x+25).
Width of the rectangular patio is (x+15).
Length of bench is 5.
Width of the bench is 1.
Area of rectangle:Area of a rectangle is:
A = Length x Width
Area of rectangular patio is:
A[tex]_1[/tex] = (x + 25)(x + 15)
Area of bench is:
A[tex]_2[/tex] = 10 x 3
= 30
The painting area is:
A = A[tex]_1[/tex] - A[tex]_2[/tex]
A = (x + 25)(x + 15) - 30
Therefore, the correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
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A jar contains 5 orange marbles, 3 black marbles, and 6 brown marbles. event a = drawing a brown marble on the first draw event b = drawing an orange marble on the second draw if two marbles are drawn from the jar, one after the other and not replaced, what is p(b|a) expressed in simplest form?
The probability of event A and event B IS 15/91.
What is the probability?
Probability determines the odds that a random event would occur. The odds lie between 0 and 1.
The probability of event A = number of brown marbles / total number of marbles
= 6/14
The probability of event B = number of orange marbles / total number of marbles -1
= 5/13
P(A and B) =6/14 x 5/13
= 30/182
= 15/91
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Answer:
B.) 5/13
Step-by-step explanation:
15/3=5
91/7=13
5/13
BRAINEST IS VERYYYY APPRECATED
PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3
How to determine the graph of f(x) + g(x)?The functions are given as:
f(x) = x + 3
g(x) = x
From the above functions, we can see that the function g(x) is the parent function of a linear function.
When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points
(x, y)= (0, b) and (-b, -b)
Where b is the y-intercept of the other function
i.e b = 3 from f(x) = x + 3
So, we have the following points
(0, 3) and (-3, -3)
Next, we draw the points and we connect the points
When the equation of f(x) + g(x) is calculated, we have
f(x) + g(x) = 2x + 3
See attachment for the graph of the functions
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Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]
[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]
next,
g(f(-5)) represents value of y at x = f(-5) = 1
hence,
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\sf \:g(f( - 5)) = 5[/tex]10. Ali's crystal ball grants two-fifths of one-fifth of
all wishes. This is ?% of all wishes.
(A)
2
(B)
25
(C) 8
(D) 60
Answer:
C
Step-by-step explanation:
2/5 x1/5 = 2/25 If you divide 2 by 25, you get.08. To change a decimal into a percent, you move the decimal two places to the right to get 8%
How many 5-digit numbers can be created
using the digits 2, 3, 5, 7, and 8 without
repeating any digits within that 5-digit
number?
Answer:
120.
Step-by-step explanation:
That would be factorial 5, written 5!.
That is 5*4*3*2*1
= 120.
Answer:
120
Step-by-step explanation:
We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.
Box 1
Box 2
Box 3
Box 4
Box 5
In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...
Box 1 --> 5 choices
Box 2 --> 4 choices
Box 3 --> 3 choices
Box 4 --> 2 choices
Box 5 --> 1 choice
Therefore the amount of 5 digit numbers that can be created is:
[tex]5\times4\times3\times2\times1[/tex] or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:
120 5-digit numbers
Solve the equation in the image (yr 8 maths, 50pts)
Answer: x = 4
Step-by-step explanation:
Given equation
4x - 20 = -x
Add x on both sides
4x - 20 + x = -x + x
5x - 20 = 0
Add 20 on both sides
5x - 20 + 20 = 0 + 20
5x = 20
Divide 5 on both sides
5x / 5 = 20 / 5
[tex]\Large\boxed{x=4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What are angles <3 and <4 ?alternate interior angles
alternate exterior angles
vertical angles
corresponding angles
whats the surface area of the rectangular prism
The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.
What is the area of a rectangle?The area of a rectangle with length and width is
Area = length × width
I.e., A = l × w sq. units
How to calculate the area of the rectangular prism?A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.
So, the areas of each face are as follows:
A(R1) = l × w
A(R2) = l × h
A(R3) = w × h
A(R4) = l × w
A(R5) = l × h
A(R6) = w × h
Thus, the area of the prism = sum of areas of all the faces
⇒ Area of the prism = lw + lh + wh + lw + lh + wh
⇒ A = 2lw + 2lh + 2wh
⇒ A = 2(lw + lh + wh)
Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]h = \frac{2A}{b}[/tex]
Step-by-step explanation:
We are given:
[tex]A = \frac{1}{2} b h[/tex]
To solve for [tex]h[/tex], we have to rearrange the equation to make [tex]h[/tex] the subject:
[tex]A = \frac{1}{2} b h[/tex]
⇒ [tex]2A = bh[/tex] [multiplying both sides by 2]
⇒ [tex]\frac{2A}{b} = h[/tex] [dividing both sides by b]
⇒ [tex]h = \frac{2A}{b}[/tex] [swapping sides]
(b) Expand and simplify (x - 3) (2x + 3)(4x + 5)
Answer:
8x³ - 2x² - 51x - 45
Step-by-step explanation:
(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL
= (x - 3)(8x² + 10x + 12x + 15)
= (x - 3)(8x² + 22x + 15)
multiply each term in the second factor by each term in the first factor.
x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis
= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms
= 8x³ - 2x²- 51x - 45
Expand first 2 bracket first to get:
2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.
2x^2 - 3x - 9 (4x + 5)
2x^2 x 4x = 8x^4
2x^2 x 5 = 10x^2
Repeat for the next two numbers next to the bracket.
You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45
Final simplified answer of:
8x^3 - 2x^2 - 51x - 45
Hope this helps!
A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes? (1 point) 0 x<9.02 or x> 9.48 because lx - 9.251 > 0.23 o x<9.25 or x > 9,48 because ix - 0.231 9.25 > 0 0 x€ 9.02 or x> 9.48 because ix - 0.231 9.25 > 0 o x< 9.25 or x> 9.48 because ix - 9.25| > 0.23
Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
What is the range?In mathematics, the range of a function can refer to one of two notions that are closely related.The function's codomain, the function's visual representation.A binary relation f between two sets X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y.To find the rejected masses:
If each pack of trail mixes is supposed to weigh 9.25 oz and must be within 0.23 oz of that weight to be accepted, then rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
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The correct question is given below:
A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?
Rick runs 5 miles which burns approximately 500 calories. how many miles would rick have to run to burn one pound of adipose tissue?
35miles Rick have to run to burn one pound of adipose tissue.
According to the given question.
Rick runs 5miles to burn 500 calories.
⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.
As we know that
1 pound = 3,500 calories.
So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles
Hence, 35miles Rick have to run to burn one pound of adipose tissue.
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write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-6,6) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of -15
Answer:
[tex]y=-\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
Slope of line with given x and y intercepts
The x-intercept is when y = 0.
Therefore, if the x-intercept is 5 ⇒ (5, 0).
The y-intercept is when x = 0.
Therefore, the y-intercept is -15 ⇒ (0, -15).
Inputting these two points into the slope formula to find the slope of this line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]
Slope of function f(x)
If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.
[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]
Equation of f(x) in point-slope form
Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]
Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:
[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]
[tex]\implies y=-\dfrac{1}{3}x+4[/tex]
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The function f(x) = –Two-sevenths (five-thirds)x is reflected over the y-axis to create g(x). Which points represent ordered pairs on g(x)? Check all that apply.
The values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
Reflection of coordinatesReflection is a transformation technique that changes the position of an object on an xy-plane.
If the function f(x) is reflected over y-axis, the resulting function is y = f(-x). Given the following function;
f(x) = -2/7(5/3)x
This can also be written as;
f(x) = -10/21 x
Replace x as -x
f(-x) = -10/21(-x)
f(-x) = g(x) = 10/21x
Hence the values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
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What two nonnegative real numbers with a sum of have the largest possible product?.
The two non negative real numbers with a sum of 60 that have the largest possible product are 30 and 30.
What are non negative numbers?
Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.
An integer that is either positive or zero is considered a non-negative integer.
Let us assume the two non negative numbers are [tex]x[/tex] and [tex]y[/tex].
According to the question,
Sum of two non negative numbers = 60
⇒ [tex]x+y=60[/tex]
⇒ [tex]y=60-x[/tex]
Their product will be given as,
⇒ [tex]P=xy[/tex]
⇒ [tex]P=x(60-x)[/tex]
⇒ [tex]P=60x-x^2[/tex]
For the product to be largest [tex]P'(x)=0[/tex]
⇒ [tex]P'(x) = 60-2x[/tex]
⇒ [tex]60-2x=0[/tex]
⇒ [tex]2x=60[/tex]
⇒ [tex]x=30[/tex]
Now, for the value of [tex]y[/tex]
⇒ [tex]y=60-x[/tex]
⇒ [tex]y=60-30[/tex]
⇒ [tex]y=30[/tex]
Therefore, the two non negative numbers are 30, 30.
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