Sandra calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it?
A
B
C
D
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Related Questions
what is the square root of negative one hundred.?.
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Some random mathematicians invented an imaginary number, i, which is the result of the square root of -1.
[tex] \sqrt{-100} [/tex] -> [tex] \sqrt{-1} * \sqrt{100} [/tex] -> [tex]i * 10[/tex] 10i
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30
Answers
2l + 2w < 30
the second and fourth option are saying she can make the length longer than twelve and the third option forgets to double the length and width so it is accurate. The first option is the right answer.
Answer: (A) The first option is the right answer.
Step-by-step explanation:
l ≤ 12
2l + 2w < 30
Simplify the expression below.
3 · -8 + 5 - 4 ÷ 2
-11.5
-21
-12.5
-27
Answers
hope this helps!
Answer:
-21 I think
I hope i helped you!
Find the missing terms in the following geometric sequence. -12,__,__, -324
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-324/-12=(ar^4)/(ar^1)
27=r^3
3=r
-12=a(3^1)
-12=3a
-4=a
y=-4(3^n)
y(2)=-36
y(3)=-108
Answer:
The nth term for the geometric sequence is given by:
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
where,
[tex]a_1[/tex] is the first term
r is the common ratio of the terms.
As per the statement:
Given the sequence
-12,__,__, -324
here, [tex]a_1 = -12[/tex] and [tex]a_4 = -324[/tex]
Solve for r:
By definition we have;
[tex]a_4 = a_1 \cdot r^3[/tex]
⇒[tex]-324 = -12 \cdot r^3[/tex]
Divide both sides by -12 we have;
[tex]27 = r^3[/tex]
⇒[tex]r = \sqrt[3]{27} =\sqrt[3]{3^3} = 3[/tex]
We have to find the missing terms [tex]a_2, a_3[/tex]
[tex]a_2=a_1 \cdot r[/tex]
⇒[tex]a_2 = -12 \cdot 3 = -36[/tex]
[tex]a_3=a_1 \cdot r^2[/tex]
⇒[tex]a_2 = -12 \cdot 3^2 = -12 \cdot 9 = -108[/tex]
therefore, the missing terms in the following geometric sequence is,
-12,_-36_,_-108_, -324
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
Answers
y + 1 = -3x + 15
y = -3x + 15 - 1
y = -3x + 14 <== or f(x) = -3x + 14
Y+1= -3(x+5) in order to solve first write down the function, then find the current of the function.
Y+1=-3x-15 then this is the current of the function. Multiply the -3 times the X and the 5.
Y=-3x-14 finally this is the slope. To get the slope I added the 1 to the -15
Final answer= Y=3x+14
Determine the type and number of solutions of 6x^2-7x-4=0
A. One real solution
B. Two real solution
C. Two imaginary solutions
D. One real solution and one imaginary solution
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1 over 111 as a decimal
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NEED HELP!!!!!!!!!!!!!!!!!!!!!
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Here, a=1, b=13, and c=30.
The only option that fills in the values correctly is D
Drive Down is a racing video game. The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. What function represents the amount of virtual money a player has in terms of the number of races won?
The independent quantity is the , and the dependent quantity is the _________ and the dependent quantity is the _________ The function representing the situation is _________
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dependent quantity f(x)...or y is total virtual money
the function is : f(x) = 500x + 5000 or y = 500x + 5000
Answer:
The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. This $5000 is fixed.
Let the races won be x
So, the function that represents the amount of virtual money a player has in terms of the number of races won becomes :
[tex]f(x)=500x+5000[/tex]
The independent quantity (x) is : the number of races won
And the dependent quantity f(x) or y is : the total virtual money earned
Find all values of theta between 0 and 360 that satisfy the equation sin2theta=2sinthetacostheta
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applying the identity Sin2A=2sinAcosA
sin2(theta)=sin2(theta)
Hence all the values of Theta satisfy the equations.
Of a group of students 5/8 of them are boys. The girls are put into groups so that each group has 1/6 of the total number of students. How many groups of girls are there?
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If it takes 2 machines 2 minutes to make 2 widgets, how long would it take 200 machines to make 200 widgets?
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what equation of a line is perpendicular to 6x+4y=3?
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The slope is -3/2. A perpendicular slope would equal the negative reciprocal of -3/2, which is 2/3.
The answer would be any line with a slope of 2/3 (ie y=2/3x-1).
To check, graph the given and derived equation.
what is the sum of the geometric sequence -3, 18, -108,... if there are 7 terms?
Answers
Sn=a(1-r^n)/(1-r)
from our sequence;
a=-3
r=-108/18=-6
n=7
thus the sum of the 7 terms will be:
S7=-3(1-(-6)^7)/(1-(-6))
S7=-3(1+279936)/(1+6)
S7=-3(279937)/7
S7=-119,973
the answer is -119,973
What is a rule that describes the translation ABCD ⇒A' B' C' D'?
A. T <3,-2> (ABCD)
B. T <3,2> (ABCD)
C. T <2,-3> (ABCD)
D. T<-3,2> (ABCD)
A. IS WRONG
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* step 1) move 3 units to the left
* step 2) move 2 units up
The movement in step 1 means x becomes x-3
The movement in step 2 means y becomes y+2
Put this together and (x,y) turns into (x-3, y+2)
That's the same as writing T<-3, 2> as choice D is saying
Answer: Choice D
Final answer:
The question seeks the correct translation rule for the movement of quadrilateral ABCD to A'B'C'D'. Translation in geometry involves moving a shape in a consistent direction and distance. Given option A is incorrect, and considering directionality, T <-3,2> (ABCD) is another possibility for the translation.
Explanation:
The question asks for the rule that describes the translation of quadrilateral ABCD to A'B'C'D'. A translation in geometry is a type of transformation that moves every point of a shape the same distance in the same direction. Since option A, which is T <3,-2> (ABCD), is given as incorrect, let's analyze the remaining options.
To determine the correct rule for translation, we need to look at the relative position of the original points and their corresponding points after the translation. For example, if point A were at (x,y) and A' is at (x+3, y-2), this would correspond to a translation of 3 units to the right and 2 units down, which is described by the vector <3, -2>.
Since option A is incorrect and we know that the transformation corresponds to a translation and not a reflection or rotation, let's consider the other options. Looking at option D, T <-3,2> (ABCD), this would imply that every point of quadrilateral ABCD is moved 3 units to the left (because of -3) and 2 units up (because of 2), which would be the reverse of what is described in option A.
3 on the outside, square root 1/5
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To simplify 1/(5 + √3), multiply both numerator and denominator by the conjugate of the denominator, which is 5 - √3. This results in (5 - √3)/22, which is the simplified form of the expression.
The student has asked to evaluate the expression 1/(5 + √3). To simplify this expression, we can multiply both the numerator and the denominator by the conjugate of the denominator to get rid of the square root in the denominator. The conjugate of 5 + √3 is 5 - √3. So, we multiply the expression by (5 - √3)/(5 - √3).
The resulting expression after multiplication:
Numerator: 1 * (5 - √3) = 5 - √3Denominator: (5 + √3) * (5 - √3) which simplifies to 5² - (√3)² = 25 - 3 = 22
So our final answer after simplification is:
(5 - √3)/22
complete question given below:
Evaluate 1/(5+ square root of 3)
How many corners does a cube have? how many faces does a cube have? how many other cubes would share a given corner atom or face atom if several cubes were stacked side-to-side, front-to-back, and top-to-bottom?
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A cube is a 3-dimensional solid figure made by square faces. It would have 8 corners which connects the faces of the cube.
how many faces does a cube have?
There would be 6 faces in a cube
how many other cubes would share a given corner atom or face atom if several cubes were stacked side-to-side, front-to-back, and top-to-bottom?
If several of these cubes are being stacked side-to-side, front-to-back, and top-to-bottom, each corner would share a total of eight cubes. All of the corners would share a different cube. We have eight corners thus eight cubes.
a basketball coach is purchasing 12 shirts for her team, each with a different number. at the checkout counter the clerk places 5 of the shirts in the first bag. how many different ways can a group of 5 shirts be placed in that first bag
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12 * 5
Answer:
792 ways
Step-by-step explanation:
A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1109.
Find the substances half-life in days. Round your answer to the nearest tenth.
Answers
N(t) = N₀ exp(-kt)
where
N₀ = 45 g, original mass
N(t) = mass after time t, days
k = 0.1109, the decay constant.
At half life, N(t) = (1/2)*N₀. Therefore
1/2 = exp(-0.1109t)
Take natural log of each side.
ln(0.5) = -0.1109t
t = ln(0.5)/(-0.1109) = 6.25 days
Answer: 6.3 days (nearest tenth)
N(t) = N₀ exp(-kt)
where
N₀ = 45 g, original mass
N(t) = mass after time t, days
k = 0.1109, the decay constant.
At half life, N(t) = (1/2)*N₀. Therefore
1/2 = exp(-0.1109t)
Take natural log of each side.
ln(0.5) = -0.1109t
t = ln(0.5)/(-0.1109) = 6.25 days
Answer: 6.3 days (nearest tenth)
In your own words, define each of the following terms. a. Whole number b. Digit c. Place value d. Rounded number e. Equals
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The following terms are defined below:
a. Whole number, b. Digit, c. Place value, d. Rounded number, and e. Equals.
a. Whole Number: A whole number is a positive integer not having any fractional or decimal parts. Whole numbers include the set of natural numbers(non-negative integers) along with zero.
b. Digit: A digit, in mathematics, means any of the numerical symbols used to denote numbers in the decimal numeral system.
c. Place value: Place values are the values of a digit in a number based on its position or place within that number. Based on powers of ten, in the decimal numeral system, each digit's position determines its place value.
d. Rounded number: An approximation of a numerical value having been adjusted or approximated to a certain level of precision or a specific place value is called a "rounded number".
e. Equals: Mathematically, the term "equals" is utilized to represent that two quantities or expressions have the same value. The equals sign (=) is a symbol used to indicate equality between two mathematical expressions.
Thus, the above terms are defined.
Learn more about whole numbers here:
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Final answer:
Whole numbers are counting numbers without fractions or decimals, digits are symbols used to represent numbers, place value is the value of a digit based on its position, a rounded number is simplified for ease of use, and equals shows that two quantities have the same value.
Explanation:
In the field of mathematics, the terms mentioned refer to basic concepts essential for understanding numbers and arithmetic operations.
a. Whole number
Whole numbers are the basic counting numbers starting from 0 and including all positive integers (1, 2, 3, ...). They do not include fractions, decimals, or negative numbers.
b. Digit
A digit is any one of the ten symbols used to write numbers. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
c. Place value
Place value refers to the value of a digit based on its position in a number. For instance, in the number 231.45, the place value of the digit '3' is tens, meaning it represents thirty.
d. Rounded number
A rounded number has been altered to a nearby, often simpler number. Rounding is done to make numbers easier to work with, especially when precision is not crucial.
e. Equals
The term 'equals' is used to signify that two quantities are the same in value, often represented by the symbol '='.
In the diagram, HGF is a straight line. Given EF = 4 cm and HG = GF = 3 cm, find :
(i) tan x
(ii) sin y
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[tex]tan(x)= \frac{4}{6} = \frac{2}{3}=.6666667 [/tex]
Now use the inverse tan button (2nd-->tan) to get
[tex] tan^{-1} (.66667)=33.69[/tex]
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
[tex] \frac{siny}{7.211} = \frac{sin33.69}{5} [/tex]
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.
In winter, the temperature in northern Wisconsin can be quite cold. When Lauren woke up this morning (6:00am) the temperature outside was -18°F. When she got home from school (4:00pm) the tempature outside was 4°F. What was the change in temperature from 6:00 am to 4:00 pm?
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A scatter plot is made with the data shown:
Number of People Mowing a Golf Course
2
3
4
5
6
7
8
9
10
Time Taken to Mow the Golf Course
(hours)
16
13
10
8
7
6
4
3
3
What type of association will the scatter plot for this data represent between the number of people mowing the golf course and the time taken to complete mowing the golf course?
No association
Positive linear association
Negative nonlinear association
Positive nonlinear association
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So our answer is Negative nonlinear association.
Answer:
Negative nonlinear association.
Step-by-step explanation:
The perimeter of the rectangle is 34 cm. The perimeter of the triangle is 30 cm. Find the value of n. a. 10 cm c. 14 cm b. 12 cm d. 16 cm
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The value of [m] = 5 cm and [n] = 12 cm.
What is a expression? What is a mathematical equation? What is Perimeter? What is the perimeter of a rectangle and a triangle?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
The perimeter of a rectangle is : p[r] = 2(x + y).The perimeter of a triangle is : p[r] = a + b + c.The perimeter of a rhombus is : p[r] = 4a.The perimeter of a hexagon is : p[r] = 6a.The perimeter of a Parallelogram is : 2(b + h).We have the perimeter of the rectangle is 34 cm. The perimeter of the triangle is 30 cm.
We can write -
2(m + n) = 34
m + n + (n + 1) = 30
Now -
m + n = 17
2n + m = 29
We can write -
m = 17 - n
then -
2n + 17 - n = 29
n = 29 - 17
n = 12 cm
so -
m = 17 - 12
m = 5 cm
Therefore, we get, the value of [m] = 5 cm and [n] = 12 cm.
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if the apothem is 6.9 mm and a side length is 8 mm what is the area of the hexagon
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draw it and draw lines from each corner to every other corner... you're left with 6 triangles
work out the area of one of these triangles from your question... area of hexagon = 6 x area of a triangle
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
Answers
R(x-axis) is the reflection of the original triangle ABC on the x-axis. The new coordinates are given as A' (2, -5), B' (4, -6), and C' (3, -1)
Part b)
R(y=3) is the reflection of the original triangle ABC on the line with equation y=3.
The new coordinates would be A' (2, 1), B' (4, 0), and C' (3, 5)
Part c)
T(-2, 5) is the translation of the original triangle ABC two units left and five units up. The new coordinates would be A'(0, 10), B' (2, 11), and C'(1, 6)
Part d)
T(3, -6) is the translation of the original triangle ABC three units right and six units down. The new coordinates would be A'(5, -1), B'(7, 0), and C'(6, -5)
Part e)
r(90°, 0) is the rotation of the original triangle ABC on the origin by 90° clockwise. The new coordinates would be A'(5, -2), B'(6, -4) and C'(1 -3)
a)
Reflection over x-axis.
We know that when any point is reflected over the x-axis, then the rule of transformation that is applied is:
(x,y) → (x,-y)
Hence,
A (2,5)→ A'(2,-5)
B (4,6) → B'(4,-6)
and C (3,1) → C'(3,-1)
b)
Reflection about the line y=3
We know that any point after reflection is at a fixed distance from the line as it was before reflection.
Hence,
A (2,5)→ A'(2,1)
B (4,6) → B'(4,0)
and C (3,1) → C'(3,5)
c)
T<-2,5>
The rule that is applied to this translation is:
(x,y) → (x-2,y+5)
Hence,
A (2,5)→ A'(0,10)
B (4,6) → B'(2,11)
and C (3,1) → C'(1,6)
d)
T<3,-6>
The rule that is applied to this translation is:
(x,y) → (x+3,y-6)
Hence,
A (2,5)→ A'(5,-1)
B (4,6) → B'(7,0)
and C (3,1) → C'(6,-5)
e)
r(90◦, o)
It is a rotation of a point 90 degree clockwise about the origin.
Hence, the rule that describes this transformation is:
(x,y) → (y,-x)
Hence,
A (2,5)→ A'(5,-2)
B (4,6) → B'(6,-4)
and C (3,1) → C'(1,-3)
A function is shown in the table.
x g(x)
−2 2
−1 −3
0 2
1 17
Which of the following is a true statement for this function?
a. The function is increasing from x = −2 to x = −1.
b. The function is increasing from x = 0 to x = 1.
c. The function is decreasing from x = −1 to x = 0.
d. The function is decreasing from x = 0 to x = 1.
Answers
Only one statement is correct:
B ) The function is increasing from x = 0 to x = 1
Explanation: g ( 0 ) = 2, g ( 1 ) = 17, 2 < 17.
Someone help me please
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50 x 32 = 1600square feet
area of a square is S^2 so the length of the side of a square would be 1600 =S^2
S=sqrt(1600) = 40 feet long
perimeter of a square is 40 x 4 = 160 feet
Use the diagram to find the indicated measurements
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Determine the slope and y-intercept of the line.
y = 5x + 4
a.
Slope = 4, y-intercept is (0, 5)
c.
Slope = 5, y-intercept is (0, 4)
b.
Slope = -5, y-intercept is (0, 4)
d.
Slope = 4, y-intercept is (0, -5)
Please select the best answer from the choices provided
A
B
Answers
The answer would be C. Slope = 5, y-intercept is (0,4)
Answer:
D
Step-by-step explanation:
Correct on A P E X