Question 1
Elena, Lin, and Noah all found the area of Triangle Q to be 14 square units but
reasoned about it differently, as shown in the diagrams. Explain at least one student's
way of thinking and why his or her answer is correct.
Q
Lin
Elena
Q
Noah
Answers
Answer:
For Lin's answer
Step-by-step explanation:
When you have a triangle, you can flip it along a side and join that side with the original triangle, so in this case the triangle has been flipped along the longest side and that longest side is now common in both triangles. Now since these are the same triangle the area remains the same.
Now the two triangles form a quadrilateral, which we can prove is a parallelogram by finding out that the opposite sides of the parallelogram are equal since the two triangles are the same(congruent), and they are also parallel as the alternate interior angles of quadrilateral are the same. So the quadrilaral is a paralllelogram, therefore the area of a parallelogram is bh which id 7 * 4 = 7*2=28 sq units.
Since we already established that the triangles in the parallelogram are the same, therefore their areas are also the same, and that the area of the parallelogram is 28 sq units, we can say that A(Q)+A(Q)=28 sq units, therefore 2A(Q)=28 sq units, therefore A(Q)=14 sq units, where A(Q), is the area of triangle Q.
The reason is while computing the area is found to be 14 square units.
What is area of triangle?The area of Triangle = 1/2* base * height
given:
assumed area to be 14 square units
We will take the case of Elena
In figure the base = 7 units
height = 4 units
Area of triangle
=1/2*base*height
=1/2 * 7 * 4
=7*2
=14 square units
Learn more about area of triangle here:
https://brainly.com/question/22359772
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Related Questions
The radius of a circle measures 8 yd. What is the circumference of the circle? Use 3.14 for pi, and do NOT round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
The answer is
50.24 ydStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius
From the question
r = 8 yd
π = 3.14
Substitute the values into the above formula and solve
Circumference = 2(8)(3.14)
We have the final answer as
50.24 ydHope this helps you
Jackson mows 1/3 of his neighbors lawn in 1/6 of an hour. At this rate, how many lawns of the same size could he mow in one hour?
Answers
3.7m∧5÷3.7m∧2 How do I complete this expression?
Answers
The average ocean depth is 3.7 × 103 m, and the area of the oceans is 3.6 × 1014 m2. What is the total volume of the ocean in liters? (One cubic meter contains 1000 liters. Round your answer to one decimal place.)
Let f(x)
-4x - 6 and g(x) = 3x + 5. Find (fºg)(-3).
Answers
Answer:
Step-by-step explanation:
f(g(-3)
g(-3) = 3(-3) = -9 - 5 = -14
f(-14)= -4(-14) - 6 = 56 - 6 = 50
y=x^2-6x-16 in vertex form
Answers
Answer:
[tex]y=(x-3)^{2} -25[/tex]
Step-by-step explanation:
The standard form of a quadratic equation is [tex]y=ax^{2} +bx+c[/tex]
The vertex form of a quadratic equation is [tex]y=a(x-h)^{2} +k[/tex]
The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.
To find the h-value of the vertex, you use the following equation:
[tex]h=\frac{-b}{2a}[/tex]
In this case, our quadratic equation is [tex]y=x^{2} -6x-16[/tex]. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.
[tex]h=\frac{-b}{2a}[/tex] ⇒ [tex]h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3[/tex]
Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is [tex]y=x^{2} -6x-16[/tex]
[tex]y=x^{2} -6x-16[/tex] ⇒ [tex]y=(3)^{2} -6(3)-16[/tex] ⇒ [tex]y=9-18-16[/tex] ⇒ [tex]y=-25[/tex]
This y-value that we just found is our k-value.
Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: [tex]y=a(x-h)^{2} +k[/tex]
a: 1
h: 3
k: -25
[tex]y=(x-3)^{2} -25[/tex]
Hope this helps!
Introduction to interval notation
Finding Domain and range
Answers
Range will be your y-axis
Solve for v. -8 +5v=-33
Answers
Answer:
v = -5
Step-by-step explanation:
Step 1: Write out equation
-8 + 5v = -33
Step 2: Add 8 on both sides
-8 + 8 + 5v = -33 + 8
5v = -25
Step 3: Divide both sides by 5
5v/5 = -25/5
v = -5
Answer:
Solve
-8 +5v=-33
So 5v=-33+8
(-8 became 8 because we brought it back to the other side to have the v 《5v》 alone and the numbers alone )
5v= -25
So v=-25/5
We simplify -25/5
v=-5
Need help with this question. Will crown brainliest
Answers
g(x)=x+2
f(g(x))=f(x+2)
f(x+2)=1/(x+2)=h(x)
(b - 11) / -29 = -18
Answers
Answer:
b=22
Step-by-step explanation:
1 Remove parentheses.
b-11-29=-18b−11−29=−18
2 Simplify b-11-29b−11−29 to b-40b−40.
b-40=-18b−40=−18
3 Add 4040 to both sides.
b=-18+40b=−18+40
4 Simplify -18+40−18+40 to 2222.
b=22b=22
Question 3.
X and Y are
supplementary angles. Given X=72°, find the value of Y.
Answers
Answer:
Y = 108°Step-by-step explanation:
Since X and Y are supplementary angles it means that the sum of their angles add up to 180°
To find Y , add X and Y and equate it to 180° and solve
That's
X + Y = 180
Y = 180 - X
X = 72°
Y = 180 - 72
We have the final answer as
Y = 108°Hope this helps you
Find the following integral.
Integrate x + 5/x^2 +10x +26 dx
Answers
Answer:
[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsDefinite/Indefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx[/tex]
Step 2: Integrate Pt. 1
Set variables for u-substitution.
Set u: [tex]\displaystyle u = x^2 + 10x + 26[/tex][u] Differentiate [Addition/Subtraction, Basic Power Rule]: [tex]\displaystyle du = 2x + 10 \ dx[/tex]Step 3: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2(x + 5)}{x^2 + 10x + 26}} \, dx[/tex][Integrand] Expand: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{2x + 10}{x^2 + 10x + 26}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][Integral] Logarithmic Integration: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|u| + C[/tex]Back-Substitute: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{1}{2}ln|x^2 + 10x + 26| + C[/tex]Simplify: [tex]\displaystyle \int {\frac{x + 5}{x^2 + 10x + 26}} \, dx = \frac{ln|x^2 + 10x + 26|}{2} + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
a/x + b/x =c, c ne0
i’ll give more points
Answers
Answer:
x = (a +b)/c
Step-by-step explanation:
Perhaps you want to solve for x.
Multiply by x:
a + b = cx
x = (a +b)/c . . . . . divide by c
What is the general form of a conditional statement
Answers
The general form of a conditional statement is written as "if p, then q" in which p is the hypothesis and q is the conclusion.
A rectangle's perimeter is 92 ft. Its length is 5 ft shorter than two times of its width. Use an equation
to find the rectangle's length and width.
Answers
3/4+5/36+7/144+.......+17/5184+19/8100
(a)0.95 (b)1 (c) 0.99 (d)0.98
Answers
Answer:
B) 1
Step-by-step explanation:
All I did was simplify the equation
1509/1600
(Decimal: 0.943125)
HOPE THIS HELPS!!!! :)
<333333333333
Gordon types 3,666 words in 47 minutes. Find the unit rate.
Answers
Answer:
78 Words per minute
Step-by-step explanation:
A unit rate is simply comparable to an average. Given this, we can say the following:
Unit_Rate = 3666 Words / 47 minutes
Unit_Rate = 78 Words per minute
Cheers.
8x-9x = 150/10 helpp
Answers
Answer:
x =-15
Step-by-step explanation:
[tex]8x-9x = \frac{150}{10} \\\\\mathrm{Add\:similar\:elements:}\:8x-9x=-x\\-x=\frac{150}{10}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{150}{10}=15\\-x=15\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{15}{-1}\\\\Simplify\\x=-15[/tex]
I am thinking of a number... 1. The number is greater than 6 x 4.2. The number is even. 3. The number is a multiple of 3. 4. The
difference of the digits is four. 5. What is my number?
Ready? Enter your answer here.
Answers
Answer:
48
Step-by-step explanation:
48 is greater then 6×4.2
It's even
It's a multiple of 3
the difference is 4
help please we can’t figure this out
Answers
Answer:
f(-2) = g(-2)
Step-by-step explanation:
The lines intersect at the point (-2, 4). That means that the solution of the system of equations is (-2, 4). When x = -2, the two functions, f(x) and g(x), have the same value, 4.
That means that f(-2) and g(-2) are equal and are both equal to 4.
Answer: f(-2) = g(-2)
If costheta=4/5 then what is sec^2theta
Answers
Answer:
[tex]\sec^2(\theta)=\frac{25}{16}[/tex]
Step-by-step explanation:
Recall what the relationship between cosine and secant:
[tex]\sec(\theta)=\frac{1}{\cos(\theta)}[/tex]
In other words, secant is the reciprocal of cosine.
So, if we know cosine, we only need to find its reciprocal to find secant.
We are given that cosine is:
[tex]\cos(\theta)=\frac{4}{5}[/tex]
Then secant must be:
[tex]\sec(\theta)=\frac{5}{4}[/tex]
So:
[tex]\sec^2(\theta)=(\frac{5}{4})^2[/tex]
Square:
[tex]\sec^2(\theta)=\frac{25}{16}[/tex]
And we're done!
100 POINTS!! A company has 400 employees. There are 300 female employees. There are 80 employees who are under the age of 25. The probability of randomly selecting an employee who is female or is under the age of 25 is 85%. What is the probability of randomly selecting an employee who is female and under the age of 25?
95%
10%
20%
75%
15%
Answers
Answer:
probability of randomly selecting an employee who is female and under the age of 25= 0.15
In percentage= 15%
Step-by-step explanation:
There are 300 female employees. There are 80 employees who are under the age of 25
Probabilty of choosing a female employees= 300/400
Probabilty of choosing a female employees= 0.75
Probabilty of choosing an employees under the age of 25
= 80/400
Probabilty of choosing an employees under the age of 25
= 0.2
probability of randomly selecting an employee who is female and under the age of 25= 0.2*0.75
probability of randomly selecting an employee who is female and under the age of 25= 0.15
In percentage= 0.15*100
In percentage= 15%
PLEASE ANSWER
The two pentagons seen below are similar figures. What is the scale factor from the
small pentagon on the left to the large pentagon on the right? The pentagons are not
drawn to scale.
Answers
Answer:
The scale factor is 2.2
Step-by-step explanation:
To find the scale factor, you look at the length of any two sides that correspond to each other. For example, in the diagram we can see that the side with the length of 4 on the smaller pentagon corresponds to the side with the length of 8.8 on the larger pentagon.
To find the scale factor, you divide the length of the side of the larger pentagon, by the length of the side of the smaller pentagon.
[tex]\frac{8.8}{4} = 2.2[/tex]
The scale factor is 2.2
Hope this helps!
Find the approximate side length of a square game board with an area of 125in2.
Answers
Answer: 11.18
Step-by-step explanation: To find one side of a square, you need to square root it’s area. The square root of 125 is 11.18.
Summarize the data by filling in the frequency (to the nearest whole number), the relative frequency (3 decimals), and the percent frequency (1 decimal) values below. Class Frequency Relative Frequency Percent Frequency 12-14 ( ) ( ) ( ) 15-7 ( ) ( ) ( ) 18-20 ( ) ( ) ( ) 21-23 ( ) ( ) ( ) 24-26 ( ) ( ) ( ) Total ( ) ( ) ( )
Answers
Answer:
The answer is below
Step-by-step explanation:
The relative frequency is the proportion of a class or interval within a category. It is represented by the formula:
Relative frequency = frequency / total frequency
The percent frequency is the relative frequency expressed in percentage, it is given by the formula:
Percent frequency = Relative frequency × 100%
Using the formulas above, the table is filled:
The total frequency = 39
Class Frequency Relative frequency Percent frequency
12 - 14 2 2/39 = 0.0513 0.0513 × 100% = 5.13%
15 - 17 8 8/39 = 0.2051 0.2051 × 100% = 20.51%
18 - 20 11 11/39 = 0.2821 0.2821 × 100% = 28.21%
21 - 23 9 9/39 = 0.2308 0.2308 × 100% =23.08%
24 - 26 9 9/39 = 0.2308 0.2308 × 100% =23.08%
Class Frequency Relative frequency Percent frequency
12 - 14 2 0.0513 5.13%
15 - 17 8 0.2051 20.51%
18 - 20 11 0.2821 28.21%
21 - 23 9 0.2308 23.08%
24 - 26 9 0.2308 23.08%
Need help on this question anyone please!
Answers
Answer:
f(3)=2
Step-by-step explanation:
To find f(3), we simply need to find the ordered pair at x=3.
From the graph, we can see that the ordered pair at x=3 is (3,2).
Thus, f(3)=2.
And we're done!
Which represents the solution set of the inequality 5x-9321?
O xs"?
23
O x
O x26
O x56
Answers
Any places a dot on a coordinate plane (-3,6) she wants to place another dot across the y axis and it must be 8 points away . Where will any place the other dot
Answers
Answer:
(5,6)
Step-by-step explanation:
move the dot 8 spaces to the right because that is the across the y axis.
use the figure to determine the intersection of planes EAB and EFG
FG
EA
EF
no intersection
Answers
Answer:
Option (3). EF
Step-by-step explanation:
From the figure attached,
Plane defined by EAB can be represented by the face EABF of the square prism also.
Similarly, plane EFG can be represented by the face EFGH of the prism.
Now these sides EABF and EFGH are joining each other at the edge EF of the cuboid.
Therefore, intersection of the given planes is EF.
Option (3) will be the answer.
Field data have indicated that Unit A has a failure rate of 0.0004 failure per hour. Calculate the reliability of the unit for a 150-hour mission.
Answers
Answer:
Reliability= 149.94
Step-by-step explanation:
Field data have indicated that Unit A has a failure rate of 0.0004 failure per hour.
Reliability per hour=1- failure rate
Reliability per hour= 1-0.0004
Reliability per hour= 0.9996
Reliability= rate if reliability * number of hours
Rate of reliability= 0.9996 per hour
Number of hours= 150 hours
Reliability= 0.9996*150
Reliability= 149.94
at an average speed of 3 feet per second. Fuad records the distances and times in a table like the one shown below at this rate, how long will it take the car to travel 21 feet?
Answers
Answer:
7 Sec
Step-by-step explanation:
Answer:
7.0 sec
Step-by-step explanation: