The height from the ground at which the ladder touched the building is 12feet.
What is a right-angled triangle?A right-angled triangle is a type of triangle that has three sides and one of its three angles as 90°.
Analysis:
The ladder length, height of the ladder from the ground, and the distance of the foot of the ladder from the foot of the building form a right angle triangle.
let x, be the distance from the foot of the building to the foot of the ladder.
x+7 = height of ladder from building to foot of building.
length of ladder = 13 feet
using Pythagoras, we have
[tex](13)^{2}[/tex] = [tex]x^{2}[/tex] + [tex](x+7)^{2}[/tex]
169 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 7x + 7x + 49
169 = 2[tex]x^{2}[/tex] + 14x + 49
2[tex]x^{2}[/tex] + 14x = 169-49
2[tex]x^{2}[/tex] + 14x = 120
divide through by 2
[tex]x^{2}[/tex] + 7x - 60 = 0
[tex]x^{2}[/tex] +12x -5x - 60 = 0
(x+12) -5(x+12) = 0
(x+12)(x-5) = 0
x = -12 or 5
Since measurement cannot be negative, therefore x = 5
Height the ladder touches the building is x+7 = 5+7 = 12 feet
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I NEED HELP IN THIS PLSSS
Answer:
1. A
2. i think c not sure
Step-by-step explanation:
x² + y² = 34
=
y = x+2
Show your working.
Answer:
[tex]\left \{ {{y=5} \atop {x=3}} \right.[/tex] or [tex]\left \{ {{y=-3} \atop {x=-5}} \right.[/tex]
Step-by-step explanation:
Answer:
(- 5, - 3 ) , (3, 5 )
Step-by-step explanation:
x² + y² = 34 → (1)
y = x + 2 → (2)
substitute y = x + 2 into (1)
x² + (x + 2)² = 34
x² + x² + 4x + 4 = 34
2x² + 4x + 4 = 34 ( subtract 34 from both sides )
2x² + 4x - 30 = 0 ( divide through by 2 )
x² + 2x - 15 = 0 ← in standard form
(x + 5)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 3 = 0 ⇒ x = 3
substitute these values into (2) for corresponding values of y
x = - 5 : y = - 5 + 2 = - 3 ⇒ (- 5, - 3 )
x = 3 : y = 3 + 2 = 5 ⇒ (3, 5 )
This is the question picture
Answer:
A = X
B=Z
C=Y
Step-by-step explanation:
As they are congruent, their corresponding angles are also congruent
Answer:
a)
angle a is congruent to angle x
angle b is congruent to angle z
angle c is congruent to angle y
b)
line ab is congruent to line xz
line ac is congruent to line xy
line bc is congruent to line zy
c)
triangle bca is congruent to triangle zyx
What is the ratio of lines b : c if A is 77°
Answer:
3rd option
Step-by-step explanation:
the ratio of b : c is the cos77° , that is
cos77° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{c}[/tex] ≈ 0.224951054.
The volume of this rectangular prism is 51,615 cubic yards. What is the value of v? (will mark brainliest)
Answer:
v = 37 yards
Step-by-step explanation:
Volume of a rectangular prism = width × length × height
Given:
volume = 51,615 yd³width = vlength = 93 ydheight = 15 ydSubstituting the given values into the formula and solving for v:
⇒ 51615 = v × 93 × 15
⇒ 51615 = 1395 v
⇒ v = 51615 ÷ 1395
⇒ v = 37
Answer:
v = 37 yds
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 51,615 yd³l = 93 ydsw = v ydsh = 15 ydsSubstitute the values above and solve for v:
51,615 = 93 × v × 15
51,615 = 1395v
51,615/1395 = 1395v/1395
37 = v
Final answer: 37 yds
Hope this helps!
What is the circumference of the following circle? Diameter=3 Radius=1.5
Answer: 3π in terms of pi or 9.42 if in π or pi= 3.14
Step-by-step explanation:
HELP!!!!!!
This is the only thing i dont understand in my math class
Answer:
{1, 2, 3, 4}
Step-by-step explanation:
Concepts
The domain of a function is all the possible x-values for that function. In other words, it's all the x-coordinates listed in the graph.
Application
In this case, we have to list the domain of the given function. To do this, we have to first label the points, and then list their x-coordinates in increasing order.
Solution
Points:
(1, 4)(2, 3)(3, 2)(4, 1)X-Coordinates:
1, 2, 3, 4Domain:
{1, 2, 3, 4}solve 3y= x+1 and 2y= x
Answer:
(2, 1 )
Step-by-step explanation:
3y = x + 1 → (1)
2y = x → (2)
substitute 2y = x into (1)
3y = 2y + 1 ( subtract 2y from both sides )
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (2)
2(1) = x
2 = x
solution is (2, 1 )
Answer:
{y,x} = {-1,-2}
Step-by-step explanation:
2y = - 2
[2] y = - 1
// Plug this in for variable y in equation [1]
[1] 3•(-1) - x = -1
[1] - x = 2
// Solve equation [1] for the variable x
[1] x = - 2
// By now we know this much :
y = -1
x = -2
{y,x} = {-1,-2}
hope this helps
pls mark brainliest
What is the perimeter of the triangle below?
48.0 units
14.7 units
16.7 units
24.0 units
Which equation is y = 9x2 9x – 1 rewritten in vertex form? y = 9 (x one-half) squared minus thirteen-fourths y = 9 (x one-half) squared minus 1 y = 9 (x one-half) squared five-fourths y = 9 (x one-half) squared minus five-fourths
Answer:
A
Step-by-step explanation:
James is given the diagram below and asked to prove that ZD ZF. What
would be the missing step of the proof?
Given: DE = FE, and Eo forms the angle bisector of ZDEF.
Prove: ZD ZF
E
D
o
Reasons
Given
Statements
1. DEFE, EO forms the angle
bisctor of ZDEF
2.
3. EO EO
4. ADEO AFEO
5. ZD ZF
Definition of an angle bisector
Reflexive Property of Equality
SAS Congruency Theorem
Corresponding parts of congruent
triangles are congruent
O A. ZEDO ZEDO
O B. ZEDO: ZEFO
O C. ZDEO = ZFEO
O D. ZEOF ZEOD
Answer:
C, ∠DEO ≅ ∠FEO
Step-by-step explanation:
The bisector EO bisects the angle ∠DEF, an interior angle of ΔDEF.
This means the angle is divided into 2 equal angles.
⇒ ∠DEO ≅ ∠FEO
Which is the graph of f(x) = x^2 – 2x + 3?
Answer:
The first graph
Step-by-step explanation:
-2x is the key here, when you add a subtraction sign to the x-axis it goes right.
+2x would be the graph on the bottom because it is translated to the left.
So the first graph on your picture is the answer.
Answer+Step-by-step explanation:
x² – 2x + 3 = (x - 1)² + 2
Then
The vertex of the parabola is the point (1 , 2)
then
The graph number 1 (on top) is the one which represents f
Which is the graph of y-3=-2/3(x+6)
Answer:
The first graph.
Type the correct answer in the box. Use numerals instead of words
In circle A. DB has a length 6.47 centimeters. What is m DAB in radians? Round your answer to two decimal places.
2.9 cm B m DAB= radians
I NEED HELP ASAP!
The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.
What is the Length of an Arc?Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.
Given the following:
Length of arc = 6.47 cm
Radius (r) = 2.9 cm
θ = m∠DAB
Plug in the values into the arc length formula:
6.47 = θ × 2.9
6.47/2.9 = θ
θ = 2.23 radians
m∠DAB = 2.23 radians
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Answer:
DAB = 2.23 radians
Hope this helps!
Step-by-step explanation:
Question 3
ceiling fan the blades of a ceiling fan have a length of 26 inches. the tips of the blades follow a circular path. how far does the tip of a
blade travel in 1/5 of a rotation? round to the nearest hundredth of an inch,
________inches
The distance the blades travel in 1/5 of a rotation is 32.67 in
Since the distance the blades of the ceiling fan rotate is the length of an arc, we find this length
What is the length of an arc?The length of an arc is given by
L = Ф/360° × 2πr where
Ф = angle of rotation and r = length of blades of fanSince
Ф = 1/5 of a rotation = 1/5 × 360° = 72° and r = 26 inThe distance the blades travelSo, substituting the values of the variables into the equation, we have
L = Ф/360° × 2πr
L = 72°/360° × 2π × 26 in
L = 1/5 × 52π in
L = 10.4π in
L = 32.67 in
So, the distance the blades travel in 1/5 of a rotation is 32.67 in
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please awnser quickly
Answer:
R' (- 1, 6 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
R (- 1, - 6 ) → R' (- 1, 6 )
Answer:
the answer should be (-1, -6) because remember when you are doing these kind of problems of pluging in the points in a coordinate plane remember the quadraunts to help you know everything you need in case of future problems.
So back remember first is x and then y so when we analyze the point the x is -1 and the y is -6 so the point r represnts= (-1,-6)
so hopefully that is the correct answer and have a great day.
remember first is x and then y
Step-by-step explanation:
Which of the following is a statistical question?
Select one:
How many of Mrs. Malone's students earned an A for the first nine weeks?
How many students missed question #5 on Mrs. Malone's math test yesterday?
How many of Mrs Malone's students turn in their homework each day?
the answer is b
Step-by-step explanation:
hope this helps if not let me know have a blessed day
Answer:
See below for answers and explanation
Step-by-step explanation:
A statistical question has variability in collecting the data, and doesn't have one definitive answer:
Question 1: How many of Mrs. Malone's students earned an A for the first nine weeks? This is not a statistical question because you can narrow down exactly how many.
Question 2: How many students missed question #5 on Mrs. Malone's math test yesterday? This is not a statistical question because you can easily take all the worksheets done on the math test and find an exact number.
Question 3: How many of Mrs Malone's students turn in their homework each day? This is a statistical question because not every student will consistently turn in their homework each day, so there will be variability while collecting that data.
Hence, Question 3 is a statistical question
Helppp!
The net of a solid figure is shown below:
Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side length equal to 3 inches
Which calculation will give the total surface area of the solid figure?
3 ⋅ 6 ⋅ 6 square inches
6 ⋅ 3 ⋅ 3 ⋅ 3 square inches
3 ⋅ 6 ⋅ 6 ⋅ 6 square inches
6 ⋅ 3 ⋅ 3 square inches
Answer:
It's the the 4th one. 6.3.3
A straight line whose equation is 3y-2x=-2 meets the x-axis at R determine the coordinates of R
Answer:
3y-2x=-2
The straight line meets the X-axis when y = 0
Hence, 3(0) - 2(x) = -2
2x = 2
x = 1
Therefore, the coordinates of R is (1,0)
Determine each segment length in right triangle ABC
The length of BC= 7√2 and BD = 7.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given:
AD= 7, AC= 14
In Δ BDC
cos 45 = B/ H
1/√2 = 7/ BC
BC= 7√2
In Δ BDC
sin 45 = P/H
1/√2= BD / 7√2
BD = 7
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Question Number 14 of 20 - Geometry The equation of line kis y = = 1 -X – 2. The equation of line m is -2x + 6y = 18. Lines k and m are - 3 F perpendicular G intersecting but not perpendicular H parallel I the same line
Based on the calculations, the two lines have the same slope but different intercepts and as such are parallel.
The condition for two parallel lines.In Geometry, two lines are considered to be parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
For two perpendicular lines, we have:
m₁m₂ = -1.
From line k, we have this equation:
y = 1/3x - 2
From line m, we have this equation:
-2x + 6y = 18.
6y = 18 + 2x
y = 18/6 + 2/6x
y = 1/3x + 3.
Therefore, we can deduce that the two lines have the same slope (1/3) but different intercepts and as such are parallel.
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A loaf of bread and 4 scones cost £3.30. If the loaf costs 90 pence how much would one scone cost ? .
Answer:
Step-by-step explanation:
Givens
4 scones
1 loaf of bread
Total cost = 3.30
Equation
Let the loaf of bread = b
Let the scones = s
Cost = b + 4s
Solution
Substitute the givens into the equation
b + 4s = Cost
90 + 4s = 3.30 Subtract 90 from both sides
90-90 + 4s = 3.30-90 Combine
4s = 2.40 Divide by 4
4s/4 = 2.40/4
s = 0.6 of a pound
Answer: 1 scone = 60 pence.
I will mark brainliest!!!
What is the slope?
A. 3/2
B. 1/2
C. 3/4
D. 2/3
A box with square base and a height of 8cm has a volume of 1 332 cm3. find the length of the side base
Answer:
12.9 cm
Explanation:
Volume of rectangular box = Length × Width × Height
Given following:
Height = 8 cmConsider one of the base side as xSolve for volume:
L × W × H = Vx × x × 8 = 1332x² = 1332/8x = √166.5 ≈ 12.9 cmYolanda says she can use a sphere to model the surface area of the boulders on this beach. explain whether yolanda is correct. yolanda is . since the boulders have , the best shape to model the surface area is a .
Yolanda is correct since the boulders have a circular shape, the best shape to model the surface area of a sphere.
What is a sphere?
A sphere is a three dimensional object that has all the set of all points equidistant from a single point in space. An example of a sphere is a ball. The boulder in this question has a spherical shape.
Surface area of a sphere = 4πr²
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Answer:
Step-by-step explanation:
Yolanda is correct since the boulders have a circular shape, the best shape to model the surface area of a sphere.
What is a sphere?
A sphere is a three dimensional object that has all the set of all points equidistant from a single point in space. An example of a sphere is a ball. The boulder in this question has a spherical shape.
Surface area of a sphere = 4πr²
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PLEASE HELP!
Before you answer:
-No spam (Will be reported)
-No incorrect answers (Will be reported)
-Correct answers and explanations will be mark as BRAINLIEST
Answer:
For the circle with the diameter of 7cm, the area is about 38.48cm and the circumference is about 22cm
For the circle with the diameter of 5cm, the area is about 19.63cm and the circumference is about 15.7cm
Step-by-step explanation:
The formula to find the area of a circle is pi*r^2
The formula to find the circumference is 2*pi*r
r = radius, which can be determined simply by taking the diameter, and dividing it by 2.
Answer:
See below ~
Step-by-step explanation:
Circle 1 :
Area = πr² = 22/7 x (7/2)² = 11 x 7/2 = 77/2 = 37.5 cm²Circumference = 2πr = 2 x 22/7 x 7/2 = 2 x 11 = 22 cmCircle 2 :
Area = πr² = 22/7 x (5/2)² = 22/7 x 25/4 = 550/28 = 19.64 cm²Circumference = 2πr = 2 x 22/7 x 5/2 = 220/14 = 15.71 cmUse the diagrams to determine which statements are true. Select all statements that are true.
Answer:
I don't see your questions.
Egypt. Africa. America
PLEASE HELP! URGENT! ASAP! WILL GIVE BRAINLEST!
Answer:
0.25π
Step-by-step explanation:
→ Expand the bracket
4 × cos²Ф = 2
→ Divide both sides by 2
cos²Ф = 0.5
→ Square root both sides
cos Ф = [tex]\frac{\sqrt{2} }{2}[/tex]
→ Inverse cosine [tex]\frac{\sqrt{2} }{2}[/tex]
cos⁻¹ ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = 0.25π
Answer:
Answer:
0.25π
Step-by-step explanation:
→ Expand the bracket
4 × cos²Ф = 2
→ Divide both sides by 2
cos²Ф = 0.5
→ Square root both sides
cos Ф =
→ Inverse cosine
cos⁻¹ ( ) = 0.25π
Step-by-step explanation:
Find the area of a circle with a radius of 9. Leave the answer in terms of π.
Answer:
A = 81π units²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius ) , then
A = π × 9² = 81π units²
Compared to if she had bought no items on sale, by what percent was jan’s total grocery bill discounted? round to two decimal places. a. 15.85% b. 16.50% c. 16.65% d. 17.50%
The total percentage by which Jan's groceries were discounted is 16.65% approximately. (Option C). See the attached and the explanation below.
How was the total percentage discount arrived at?Step 1 - Reverse engineer, the figures to get the original prices first.
You can do this by dividing the discounted prices by the result that you get when you remove the decimal version of the discounted percentage from number one. For Chicken that would be 8.47/(1-0.85) = $9.96 (Original price.)Step 2 - Sum up all the discounted prices as well as the Original prices then find the difference.
This comes to 22.47 - 18.72 = $3.75Step 3 - Divide the difference by the original price to get the percentage difference
$3.75/$22.47 = 16.68% (Nearest answer is Option C)
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