Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 12 inches, and the width QR is labeled as 6 inches. The side LM of the square is labeled as 6 inches
Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
(Sorry for the low quality image)
Answers
Answer:
Sam is incorrect
Step-by-step explanation:
We can calculate the lengths of the diagonals using Pythagoras' identity.
The diagonals divide the rectangle and square into 2 right triangles.
Consider Δ SRQ from the rectangle
SQ² = SR² + RQ² = 12² + 6² = 144 + 36 = 180 ( take square root of both sides )
SQ = [tex]\sqrt{180}[/tex] ≈ 13.4 in ( to 1 dec. place )
Consider Δ ONM from the square
OM² = ON² + NM² = 6² + 6² = 36 + 36 = 72 ( take square root of both sides )
OM = [tex]\sqrt{72}[/tex] ≈ 8.5 in ( to 1 dec. place )
Now 2 × OM = 2 × 8.5 = 17 ≠ 13.4
Then diagonal OM is not twice the length of diagonal SQ
Related Questions
The graph of
y = x3 is transformed as shown in the graph below. Which equation represents the transformed
function?
5
4
3
2
1
3
-1
1
2
5
X
-2
y=x²-4
y =(x-4)
Answers
The x axis at 1
The function f(x) = x³ after translation becomes g(x) = x³ - 4.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the function f(x) = x³ and its transformed graph as shown in the image.
The function f(x) is translated downwards. This is called downward translation. Assume that the function f(x) after the translation becomes g(x). The function f(x) = x³ passes through the origin. After translation, all the {y} - coordinates will be shifted in the downward direction by 4 units. So, we can write the final function as -
g(x) = f(x) - 4
g(x) = x³ - 4
Therefore, the function f(x) = x³ after translation becomes g(x) = x³ - 4.
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Here is some information about a group of 20 children.
Boys
Girls
Left-handed
3
2
Right-handed
9
6
A child is chosen at random from the group.
a)
What is the probability that the chosen child is a girl?
Give your answer as a fraction.
b)
What is the probability that the chosen child is a left-handed girl?
Give your answer as a fraction.
Answers
Answer:
a) 8/20 = 8 is the total of the girls and 20 is the total of the kids
b)2/20 = 2 is the total of girls that are left handed and 20 is the total of the kids
The graph of an equation with a negative discriminant always has which characteristic?
Answers
Answer:
The graph does not intercept the x-axis
Step-by-step explanation:
Hi there!
When the discriminant is positive, it means that in the quadratic equation, you can take the square root of this number and end up with two distinct solutions, one negative and one positive. The graph will intercept the x-axis twice.
When the discriminant is zero, it means that you won't be taking the square root of any number in the quadratic equation and you'll end up with two solutions that are equal, or just one distinct solution. The graph will intercept the x-axis once.
When the discriminant is negative, it means that the quadratic has no real solutions, meaning that it does not intercept the x-axis. It is impossible to take the square root of a negative number.
I hope this helps!
In Sean's class there are 13 boys and 16 girls. Sean will randomly pull one of their names out of a hat to give
a presentation to the class. Which of the following is the probability the student picked will be a girl?
(1) 0.45
(3) 0.62
(2) 0.55
(4) 0.81
Answers
Answer:
0.62
Step-by-step explanation:
it is because the number of girls in the class is larger than the number of boys in the class which means the probability is high
The probability of picking a girl is 0.55.
What is probability?'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'
According to the given problem,
Number of boys = 13
Number of girls = 16
Total number of students = 13 + 16
= 29
Probability = [tex]\frac{Favorable events}{Total number of events}[/tex]
= [tex]\frac{16}{29}[/tex]
= 0.55
Hence, we can conclude, the probability of picking a girl is 0.55.
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PERFORMANCE TASK : “TRANSVERSAL CITY MAP”
This project will help you to demonstrate your knowledge of parallel lines, transversals and the angles that are created by them. You will be designing a city map using the guidelines listed below. Your map must be drawn on construction paper or poster board. Use a ruler to make your streets straight! Have a title for your map, and make it neat and organized! You will be graded on accuracy, creativity and neatness.
Guidelines:
1) There must be a title for your map.
2) Your city must have three streets that are parallel to each other and one street that intersects all three of the parallel streets. You must name all of these streets.
3) Your city has a hospital that is alternate exterior to the school that is in your city. Draw and name the hospital and the school.
4) The school and the drugstore are at corresponding locations. Draw and name the drugstore.
5) The drugstore and the pet shop are at vertical locations. Draw and name the pet shop.
6) The pet shop and the gas station are at alternate interior locations. Draw and name the gas station.
7) The hospital and the park are at same side exterior locations. Draw and name the park.
8) The gas station and the grocery store are at same side interior locations. Draw and name the grocery store.
9) The grocery store and the nail salon are at vertical locations. Draw and name the salon.
10) The nail salon and bank are at corresponding locations. Draw Target.
11) The bank and a fast food restaurant are at same side interior locations. Draw and name the fast food restaurant.
12) Your city has a mall that is in a corresponding location to the bookstore that is in your city. Draw and name the mall and the bookstore. (If you did all of the others correctly, then the bookstore and the mall only have one place to be located)
Answers
In constructing a transversal city map by applying the knowledge of transversal and parallel lines, a map named California City Map has been drawn as shown in the image attached below.
(See attachment).
Recall:
Parallel lines are straight lines that do not meet each other.Transversal line is a that run through two or more straight lines that are parallel.Special angles are formed when transversal intersects parallel lines, which are: corresponding angles, same-side interior angles, same-side exterior angles, alternate exterior and alternate interior angles, and vertical angles.Using the knowledge of all these, an map named, "California City Map" has been drawn as shown in the image attached below.
The details are as follows:
1. Title for the map is:
California City Map.2. The three streets that are parallel are:
Adams BoulevardBeverly DriveCarroll AvenueThe street (transversal) that intersects the three is:
Darlin Way3. St. Michael Hospital is alternate exterior to Baptist Model School
4. Baptist Model School and Living Well Drug Store are in corresponding locations to each other.
5. Living Well Drug Store and Vik Pet Store are at vertical locations.
6. Vik Pet Store and Elite Gas-station are at alternate interior locations.
7. St. Michael Hospital and Livingstone Park are at same-side exterior locations.
8. Elite Gas-station and Richie Grocery Store are at same-side interior locations.
9. Richie Grocery Store and Beautyjay Nail salon are at vertical locations.
10. Beautyjay Nail salon and Retro Bank Plc are at corresponding locations.
11. Retro Bank Plc and Tessy's Fast Food Restaurant are at same-side interior locations.
12. California City Mall and Remis Bookstore are at corresponding locations.
In summary, in constructing a transversal city map by applying the knowledge of transversal and parallel lines, a map named California City Map has been drawn as shown in the image attached below.
(See attachment).
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The graphs below have the same shape. What is the equation of the blue
graph?
F(X) = x2
5
G(X) = ?
5
G(X) =
Answers
Answer:
[tex]g(x) = (x - 2)^2 + 1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
Required
Determine g(x)
f(x) represents the parent function. And from the graph, we have:
[tex]f(x) = x^2[/tex]
f(x) is first shifted 2 units right.
The rule is:
[tex]f'(x) = f(x - 2)[/tex]
So, we have:
[tex]f'(x) = (x - 2)^2[/tex]
Next, f'(x) is shifted 1 unit up to give g(x), the blue graph.
The rule to this is:
[tex]g(x) = f'(x) + 1[/tex]
[tex]g(x) = (x - 2)^2 + 1[/tex]
Using the right triangle below. What is the name for side BC?
A) Hypotenuse
B) Adjacent
C) Opposite
D) None of the above
Answers
Answer:
C) Opposite
Step-by-step explanation:
For angle x, the 2 sides that it lies between are either adjacent or hypotenuse. The one the angle doesn't touch is the opposite.
Ahhh please help I’m having a hard time with this(￣^￣)ゞ
Answers
Answer:
A x+y
B x+0 + (y+0)
Step-by-step explanation:
(x+0) + y+0
Adding 0
x+y
Changing the order of the parentheses
x+0 + (y+0)
is still the same
What is the solution to the system of equations graphed below? Pls Quick
Answers
hope that helps
The point (1,−1) satisfies the inequality 40x−22y≤50.
Answers
Không thảo mãn vì
44.1-22.(-1)=66
No, the point (1,-1) does not the satisfy the inequality 40x-22y<=50.
What is an inequality?
It is a type of equation in which greater than less than or equal to are used instead of only equal to.
How to solve an inequality?
To check whether whether a point satisfies an inequality or not we need to just put it in the inequality. So,
40x-22y<=50
40(1)-22(-1)=40+22=62
62 is not less than and not equal to 50. So it does not satisfies the inequality.
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If the equation of a line is 2y+3x=3, what is the x intercept of the line? HELP MEEE PLEASE
Answers
Answer:
the anwers is b= 3/2 And yeah that's you're anwers
Answer:
(1,0)
Step-by-step explanation:
Hi there!
We're given the equation of the line as 2y+3x=3, and we want to find the x intercept of the line.
The x intercept is the coordinate point at which the line passes through the x axis. Therefore, the value of y at the x intercept will be 0.
So we can substitute 0 as y in 2y+3x=3; we'll only have x left if we do this to solve for the x intercept.
2(0)+3x=3
multiply
3x=3
divide both sides by 3
x=1
so the x intercept is 1; as a point it's (1,0)
Hope this helps! :D
Line p is parallel to line q
Which set of statements about the angles is true ?
Answers
Find the equation of a line that is parallel to y = 5x + 1 and passes through the point (3, -4).
Give your answer in the form y = mx + b.
Answers
Given:
The equation of a line is:
[tex]y=5x+1[/tex]
A line is parallel to the given line and passes through the point (3,-4).
To find:
The equation of the line in the slope intercept form.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept of the line.
We have,
[tex]y=5x+1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=5[/tex]
Slope of the given line is 5.
We know that the slopes of parallel lines are equal. So, the slope of the required line is 5.
The required line passes through the point (3,-4) with slope 5. So, the equation of the required line is:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-4)=5(x-3)[/tex]
[tex]y+4=5(x)+5(-3)[/tex]
[tex]y+4=5x-15[/tex]
Subtracting 4 from both sides, we get
[tex]y+4-4=5x-15-4[/tex]
[tex]y=5x-19[/tex]
Therefore, the equation of the required line is [tex]y=5x-19[/tex].
Each figure shows a triangle with one of its angle bisectors.
12) 22 - 38°. Find mZTRS.
Answers
Answer:
76 degrees
Step-by-step explanation:
this special line is an angle bisected.
that means it splits the angle at its starting point in 2 halves. as these names indicate, both parts are of equal size (half of the general angle).
we know one part (2) of this split angle : 38 degrees.
the other part (1) had to be equally sized : 38 degrees.
so, the total angle at point R is the sum of both split angles:
TRS = 38+38 = 76 degrees.
What is the average rate of change of the function f(x)=2x^2+x+5 over the interval -2<x<2?
A. -4
B. -1
C. 1
D. 4
Answers
Answer:
C
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 2, 2 ] , then
f(b) = f(2) = 2(2)² + 2 + 5 = 8 + 2 + 5 = 15
f(a) = f(- 2) = 2(- 2)² + (- 2) + 5 = 8 - 2 + 5 = 11 , then
average rate of change = [tex]\frac{15-11}{2-(-2)}[/tex] = [tex]\frac{4}{4}[/tex] = 1 → C
Does this graph show a function? Explain how you know.
Answers
Answer:
Option C, functions can only have one y-value at any given x-place
Find angle C!!!!! See the image below! I need this answer fast
Answers
Answer:
55
Angle C is a inscribed angle of the of Arc Ba.
CA is the diameter so that means Arc BA equal 110 becuase
110+70=180.
Angle C is half of Arc BA so Angle C is
[tex]55[/tex]
Which are possible dimensions of the cylinder?
Answers
Answer:
B
Step-by-step explanation:
pls give me brainliest
Answer:
A cylinder is a three-dimensional figure like a prism, but with bases that are circles. A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.
Option is B
Step-by-step explanation:
Solve the equation 5x - 10 = 25
please tell me the working
Answers
Answer:
x = 7
Step-by-step explanation:
5x - 10 = 25
shift -10 to the other side then -10 become plus 10
5x = 25 + 10
now do addition in right hand side
5x = 35
shift 5 to right hand side . 5 divides 35 because in multiplication when u shift number or variables to other side it changes to division)
x = 35/5
x = 7
The solution to the equation 5x - 10 = 25 is x = 7.
To solve the equation 5x - 10 = 25, we want to isolate the variable 'x' on one side of the equation.
First, we can start by getting rid of the constant term on the left side of the equation. We do this by adding 10 to both sides:
5x - 10 + 10 = 25 + 10
This simplifies to:
5x = 35
Next, we want to isolate 'x' by dividing both sides of the equation by the coefficient of 'x', which is 5:
5x/5 = 35/5
This yields:
x = 7
Therefore, the solution to the equation 5x - 10 = 25 is x = 7. We can verify this by substituting x = 7 back into the original equation:
5(7) - 10 = 25
35 - 10 = 25
25 = 25
Since the equation holds true, we can conclude that x = 7 is the solution.
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Can one of you help me pls it's urgent
Answers
Answer:
Hello,
I am pretty sure that is is the last answer. 3√3.
Step-by-step explanation:
I hope this helps!
Answer:
The last answer
Step-by-step explanation:
This is asking you to do 9 divided by 3. After you divide 3 by 9 divided by 3 to get the answer
9 divided by 3 equals 3
3 divided by 3 equals 1
A manager hires labour and rents capital equipment in a very competitive market. Currently the wage rate is GH¢2 per hour and capital is rented at GH¢5 per hour, the unit price of the product is GH¢0.25 and total cost is 1000. Suppose the firm's production function is as follows: � = 14�*.,�*., + 10 i. What is the amount of labour and capital the firm should employ in order to maximize output? [Hint: Maximise the product function subject to the cost constraint] ii. What is the maximum profit?
Answers
Solution :
It is given that the manager hires a labor and he rents the capital equipment [tex]\text{in a very competitive market}[/tex].
Presently the rate of the wage is at $ 10 per hour and the capital is been rented at $ 0.25. If the [tex]\text{marginal product}[/tex] of the labor is 50 units of the output per hour and the marginal.
Therefore, the answer is
14 + 10 = 24
Elizabeth sells popcorn to the students at the annual school dance. She pays $30.00 to rent the popcorn maker and $0.75 in supplies for each bag of popcorn. If Elizabeth buys supplies for p bags of popcorn, which equation expresses her total cost, c, in dollars?
Answers
Answer:
c = $30 + $0.75p
Step-by-step explanation:
total cost = total fixed cost + total variable cost
total fixed cost = $30
Fixed costs are costs that do not vary with output.
total variable cost = variable cost per unit x total unit
p x 0.75
Variable costs are costs that vary with production
Simplify the expression by adding like terms: 5a-3+5b+20-a-2b
I need help with this!!
Answers
Add the like variables
Step-by-step explanation:
4a+3b+17
is your answer
hear is your explanation
through: (-4, 3), slope
4
Answers
Answer:
the equation is y=4x+19
Step-by-step explanation:
Mark as brainllest if correct
from a ship at sea,the angle of elevation of the top and. bottom a vertical lighthouse standing on the edge of a vertical cliff are 31° abd 26°, respectively. if the light house is 25.0m high,calculate the height of the cliff
Answers
[tex]<marquee>Give:/u Name[/tex]
1.5 m
7.1 m
7.1 m
V=
Answers
Answer:
75.615 m^3
Step-by-step explanation:
volume is length x width x height
7.1*7.1*1.5
75.615 m^3
Answer:
POINTS
Step-by-step explanation:
Adam builds model rockets. Where he lives, his backyard is 12 feet below sea level. When he ignites his rocket, it flies a maximum of 350 feet straight up into the air before releasing its parachute. What is the altitude of Adam’s rocket at its highest point, as measured from sea level
Answers
Answer:
338 feet
Step-by-step explanation:
350 - 12 = 338
Solve for x. Leave your answer in simplest radical form.
Answers
There are two Right angled triangles in the given figure, with two missing sides, let's name the other missing side be " y "
According to Pythagoras theorem,
[tex] \boxed{ \large \boxed{h {}^{2} = {b}^{2} + p{}^{2} }}[/tex]
note :
p = perpendicular / opposite sideb = base / adjacent sideh = hypotenuselet's solve for " y² " first ( square of other missing side )
[tex]➢ \: \: {y}^{2} = {8}^{2} + 3 {}^{2} [/tex]
[tex]➢ \: \: {y}^{2} = 64 + 9[/tex]
[tex]➢ \: \: {y}^{2} = 73[/tex]
now let's solve for " x " , by using pythagorous theorem
[tex]➢ \: \: {x}^{2} = {y}^{2} + {6}^{2} [/tex]
[tex]➢ \: \: {x}^{2} = 73 + 36[/tex]
[tex]➢ \: \:x {}^{2} = 109[/tex]
[tex]➢ \: \: x = \sqrt{109} [/tex]
Approximate :
[tex]➢ \: \: 10.44 \: \: units[/tex]
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
Luca works at an appliance store. He recently sold 12 appliances, 6 of which were
dishwashers. What is the experimental probability that the next appliance Luca sells will be a
dishwasher?
Write your answer as a fraction or whole number.
Answers
Answer:
1/2
Step-by-step explanation:
Answer:
0.50
Step-by-step explanation:
6 out of the total 12 appliances sold were dishwashers, so the experimental probability that the next appliance sold will be a dishwasher is 6/12, or 1/2, or 0.50.
Lorenzo bought several pounds of chocolate-covered peanuts and
gave the cashier a $20 bill. Write an expression for the amount of change he will
receive if p represents the cost of the peanuts
Answers
Answer:
20 - p
Step-by-step explanation:
If p represents the cost of the peanuts, it has to be subtracted from 20 to find how much change Lorenzo will receive.
So, set up the expression:
20 - p
The expression to represent how much change he will get is 20 - p