in figure 5.19 to the right PQRS is a rectangle. if PS=5cm and PR=13cm find SR and QS.
Answers
Given:
PQRS is a rectangle.
[tex]PS=5\ cm,\ PR=13\ cm[/tex]
To find:
The length of SR and QS.
Solution:
We know that, all interior angles of a rectangle are right angle. So, [tex]\angle S=90^\circ[/tex].
According to the Pythagoras theorem, in a right angle triangle,
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
Using Pythagoras theorem in triangle PRS, we get
[tex]PR^2=PS^2+SR^2[/tex]
[tex]13^2=5^2+SR^2[/tex]
[tex]169-25=SR^2[/tex]
[tex]144=SR^2[/tex]
Taking square root on both sides.
[tex]\sqrt{144}=SR[/tex]
[tex]12=SR[/tex]
So, the measure of SR is 12 cm.
We know that the diagonals of a rectangle are equal. PR and QS are the diagonals of the rectangle PQRS. So,
[tex]PR=QS[/tex]
[tex]13=QS[/tex]
Therefore, the length of SR is 12 cm and the length of QS is 13 cm.
Related Questions
Halla X
Para una practica de 11 mins q-q
Answers
De nada
Determine if each pair of triangles is congruent. If so, write the congruence
statement and explain how you know the triangles are congruent.
Answers
Answer:
top one, yes. by the SSS theorem
bottom one, no. The bases are not congruent
Step-by-step explanation:
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
Answers
Answer:
9 cm²
Step-by-step explanation:
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
We solve the above question, using the Area of a Triangle
Area = 1/2 × Base × Height
Area = 1/2 × 3 × 6
Area = 9 cm²
Therefore, the total wore that was used was 9cm² of wire
Translate the sentence into an inequality. Ten times the sum of a number and 21 is at most 16. Use the variable y for the unknown number.
Answers
Answer:
10y+ 21 ≥ 16
Step-by-step explanation:
If 10x+6y=7 is a true equation, what would be the value of 6(10x+6y)?
Answers
Answer:
42
Step-by-step explanation:
We know that 10x + 6y = 7, and so
6(10x + 6y) = 6(7) = 42
aurav went to school for 216 days in a full year. If his attendance is 90%, find the number of days on
which the school was open.
Answers
Answer:
The school was open for 240 days
Step-by-step explanation:
216 / x = 90%/100%
216*100= 21,600
21,600/90 = 240
Julius bought F boxes of 24 plastic forks. He already had 39 plastic forks. Now, he has 135 plastic forks. How many boxes of plastic forks did Julius buy in all?
Answers
can someone help me please this is a major grade
Answers
Answer:
$7.63
Step-by-step explanation:
well 6/10 is the same as 0.6 and 3/100 is the same as 0.03
so when you add the 7and 0.6 =7.6 +0.03=7.63
Answer:
7.63
Step-by-step explanation:
7 dollars - 7.00
0.6 dollar - 0.6
0.03 dollar - 0.03
(becoming)
7.00
0.6
0.03
-----------
$7.63
^line up the decimals while adding
Hopefully this helps,
-Rose
In the figure below, m∠ABC = 57 degrees and m∠DAB =116 degrees. What is m∠ABC?
Answers
Answer:
∠ACB = 59°
Step-by-step explanation:
∠BAC = 180 - 116 = 64°
∠ACB = 180 - 64 - 57 = 59°
A door is fixed at the point O. Ben opened it by an angle of 30°. The area swept by the door was {25}{12}\pi\
Answers
Answer:
5 units
Step-by-step explanation:
Area swept by the floor will be the area ofd a sector
Area of a sector = theta/2π * πr²
We are to find the radius r
Given
Area= 25π/12
theta = 30° = π/6
Substitute
25π/12 = 30/360 * πr²
25π/12 = 1/12 * πr²
25/12 = r²/12
r² = 25
r = √25
r = 5
Hence the radius od the part swept by the door is 5 units
A recipe calls for 1/2 of a teaspoon of sugar for every 15 cookies. If you are going to make 75 cookies for a party, how many teaspoon of sugar will you use.
Answers
Answer:
2.5 teaspoons
Step-by-step explanation:
75/15 = 5
1/2 · 5 = 2.5
Answer:
2.5 teaspoons of sugar
Step-by-step explanation:
[tex]\frac{15}{0.5} =\frac{75}{y}[/tex]
Cross multiply.
15 × y = 0.5 × 75
15y = 37.5
15y ÷ 15 = 37.5 ÷ 15
y = 2.5
Factorise using the sum and product method with all the steps!
British curriculum
No links or websites please !
Answers
Answer:
(2x+3)(x-5)
Step-by-step explanation:
Given the expression 2x²-7x-15
Factorize
2x²-10x+3x-15 =0
2x(x-5)+3(x-5)
(2x+3)(x-5)
Hence the factored form of the expression is (2x+3)(x-5)
HI thts way tooo much to answer but ye
The perimeter of a square is 12x - 8. Which of the following is the length of
one side of the square?
Answers
Answer:
3x-2
Step-by-step explanation:
12x-8/4 = 3x-2 is one side length of a square
Just answer the question in the picture. It's just math vocab! DO NOT answer for points OR SPAM LINKS!!! I will REPORT!
Answers
Answer:
A circle is a round shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
The distance from the center to the circumference of a circle
The diameter is the length of the line through the center that touches two points on the edge of the circle.
The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.
In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle.
A line segment that has the endpoints on the circle and passes through the midpoint is called the diameter. The diameter is twice the size of the radius. A line segment that has its endpoints on the circular border but does not pass through the midpoint is called a chord. A circle is the same as 360°.
A line that intersects two or more points on a curve. (From the Latin secare "to cut")
The length of the side opposite the angle divided by the length of the adjacent side.
A line that intersects a circle in exactly one point is called a tangent and the point where the intersection occurs is called the point of tangency. The tangent is always perpendicular to the radius drawn to the point of tangency. A secant is a line that intersects a circle in exactly two points.
Common tangents to two circles may be internal or external. A common internal tangent intersects the line segment connecting the centers of the two circles whereas a common external tangent does not.
Step-by-step explanation:
they are in order! tell me if i made a mistake:)
I NEED HELP Quadratics and Their Solutions
Answers
2nd one is 4th image
3 one is 5th image
4 is 3rd image
5th is 1st image
Solve. 1/2(4x + 2/5) = 4/5
Answers
Answer:
[tex]\frac{1}{2}(4x + \frac{2}{5} ) = \frac{4}{5}\\2x + \frac{1}{5} = \frac{4}{5}\\\frac{10x + 1}{5} = \frac{4}{5}\\10x + 1= 4\\10x = 3\\x = \frac{3}{10}[/tex]
Answer:
x = 3/10
Step-by-step explanation:
Given equation,
→ 1/2(4x + 2/5) = 4/5
Let's solve the problem,
→ 1/2(4x + 2/5) = 4/5
→ 2x + (1/5) = 4/5
→ 2x = (4/5) - (1/5)
→ x = (3/5) × (1/2)
→ [ x = 3/10 ]
Thus, the value is 3/10.
Mrs. Byrne’s class went raspberry picking. The data below show the weights of the cartons of raspberries the students picked.
Answers
Find the Area of the trapezoid.
A. 56
B. 28
C. 49
D. 35
Answers
Answer: b
Step-by-step explanation:
Use PEMDAS to evaluate the expression 7 x 6 + 8 − 16 ÷ 4.
Answers
Answer:
7x^6 + 4
Step-by-step explanation:
whowever answers any 2 I will follow them
Answers
Answer:
1. x = 5 y = 6
2. x = 3 y =5
3. x = 2 y = 4
4. x = 2 y = 1/2
5. x = 6 y = 4
6. x = 2 y = 1
Step-by-step explanation:
i hope it helps u
hii please help i’ll give brainliest:)
Answers
Answer: Caravans
Step-by-step explanation:
wha the MIDPOINT of (-6, 8) and (6, -7)
Answers
hope this helps
Answer:
here you are:
the midpoint for (-6,8) and (6,-7) is (0, 1/2)
Step-by-step explanation:
the midpoint for (-6,8) and (6,-7) is (0, 1/2)
An engineer is designing a fountain that shoots out drops of water. The nozzle from which the water is launched is 3 meters above the ground. It shoots out a drop of water at a vertical velocity of 14 meters per second. Function h models the height in meters, h, of a drop of water t seconds after it is shot out from the nozzle. The function is defined by the equation h(t)=−5t2+14t+3. How many seconds until the drop of water hits the ground?
Answers
Answer:
After 3 seconds
Step-by-step explanation:
Given
[tex]h(t) = -5t^2 + 14t + 3[/tex]
Required
Time the drop will hit the ground
When the drop hits the ground,
[tex]h(t) = 0[/tex]
So, we have:
[tex]0 = -5t^2 + 14t + 3[/tex]
Rewrite as:
[tex]5t^2 - 14t - 3 = 0[/tex]
Expand
[tex]5t^2 + t - 15t - 3 = 0[/tex]
Factorize
[tex]t(5t + 1) -3(5t + 1) = 0[/tex]
Factor out 5t + 1
[tex](t -3)(5t + 1) = 0[/tex]
Split
[tex]t -3 = 0[/tex] or [tex]5t + 1 = 0[/tex]
Solve for t
[tex]t = 3[/tex] or [tex]5t = -1[/tex]
Time cannot be negative.
So:
[tex]t = 3[/tex]
Please help...My answer is close but not close enough..
No links :)
Answers
Answer:
76
Step-by-step explanation:
(5x3)+(5x3)=30
15-6=9
5x9=45
45+30=75
Since 76 is the closest to 75 it's 76
Round the greater number to the tens place. Then calculate the product.
64 x 3
O A. 72
B. 150
C. 180
D. 192
O E. 210
Answers
Answer:
d:192
Step-by-step explanation:
Luke sold 4 times as many books as Maurice. If Maurice had sold 18 more books, he would have tied Luke for first place. How many books did Luke sell?
Answers
Answer:
24
Step-by-step explanation:
I guessed and checked but 24 -18 is 6 and 6 times 4 is 24
M + 18 = 4M
18 = 4M - M
18 = 3M
M = 18/3 = 6
4M = 4(6) = 24 sold by Luke
What is the approximate volume?
Answers
Answer:
B
Step-by-step explanation:
1) find the base area
base area = side^2 = 30^2 = 900 m^2
2) find the Volume
V = (base area x height)/3 = (900 x 21)/3 = 6300 m^3
Answer:
B) 6,300 m³
Step-by-step explanation:
The volume of approximate = L×W×H/3
30×30×21/3=
answer: 6,300
[tex]**************[/tex]
hope it helps...
have a great day!!
Find the surface ara of the square pyramid. Enter your answer in the box
Answers
Answer:
341 cm²
Step-by-step explanation:
The base is 11 x 11 = 121
Then there is 4 side that are triangles, 11 x 10 ÷ 2 = 55 -----> 55 x 4 = 220
220 + 121 = 341
Which function has the same range as
f(x)= -2sqrt (x-3)+8
Answers
Answer:
Answer: : g(x)=-sqrt(x+3)+8
Step-by-step explanation:
The function has the same range is the third one:
g(x)=-sqrt(x+3)+8
The range of this function is:
x+3>=0
sqrt(x+3)>=sqrt(0)
sqrt(x+3)>=0
Multiplying the equation by -1:
-1[ sqrt(x+3)>=0]
- sqrt(x+3)<=0
Adding 8 both sides of the equation:
- sqrt(x+3)+8<=0+8
- sqrt(x+3)+8<=8
g(x)<=8
Then Range g(x)= (-Infinite, 8]
Answer: Third option: g(x)=-sqrt(x+3)+8
factor completely;
3x^2+4x-7
Answers
Answer:
(3x-7) (x+1)
Step-by-step explanation:
3x^2 - 4x - 7
First split the middle term
3x^2 + 3x - 7x - 7
Make into two separate expressions
(3x^2 + 3x) (-7x-7)
Take out what you can
3x (x+1) -7 (x+1)
Now you have your answers
(3x-7) (x+1)