The height of the wall is calculated to be approximately 12 feet using the Pythagorean theorem with the given measurements.
Explanation:This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, we have a triangle formed by the wall, the ground and the ladder. Let's say the ladder's length is 'c', the wall's height is 'a' and the base from the person to the wall is 'b'. According to the problem:
The person is 6 feet from the bottom of the ladder, hence one side of the triangle (b) is 9 feet.Since the person's height just touch the ladder, so the ladder's length (c) is the height of the person plus the distance from the person to the wall, hence c = 6 feet + 9 feet = 15 feet.Using the Pythagorean theorem, we get:
a^2 + b^2 = c^2
Where a is the height of the wall. Substituting in the values we get:
a^2 + 9^2 = 15^2
Solving for 'a', we find that the height of the wall is approximately 12 feet.
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Using the Pythagorean theorem, the length of the ladder and subtract the person's height to find the wall's height is 4.82 feet.
Explanation:To find the height of the wall, we can use similar triangles. The person's height and distance from the wall create a right triangle with the ladder. The ladder acts as the hypotenuse of this right triangle. Using the Pythagorean theorem, we can find the length of the ladder. Then, we subtract the person's height from this length to find the height of the wall.
Let's denote the height of the wall as h. The person's height is 6 feet and they are 9 feet from the wall. The foot of the ladder is 6 feet from the person, so it forms a right triangle with legs measuring 6 feet and 9 feet.
Using the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse, we have:
6^2 + 9^2 = c^2
36 + 81 = c^2
117 = c^2
c = sqrt(117) = 10.82 feet (rounded to two decimal places)
Therefore, the height of the wall is 10.82 feet - 6 feet (person's height) = 4.82 feet.
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The sides of the cubes are numbered 1 -6. If they are both tossed, what is the probability that they both will be 3?
Answer:
1/6 * 1/6 = 1/36 or 0.027%
Step-by-step explanation:
This is because there is a 1/6 chance the cubes will land on 3. Sincer there is 2 of them, multiply them by each other. Do not add.
Hope this helps!
solve 9(x + 1)^2 = 144
Answer:
x = 3
x = -5
Step-by-step explanation:
(9)(x+1)(x+1) = 144
(9)(x²+2x+1) = 144
9x²+18x+9 = 144
9x²+18x = 135
x²+2x = 15
x(x+2) = 15
x = 3
x= -5
Answer: [tex]x_1=3\\x_2=-5[/tex]
Step-by-step explanation:
Divide boht sides of the eqeuation by 9:
[tex]\frac{9(x+1)^2}{9}=\frac{144}{9}\\\\(x+1)^2=16[/tex]
Remembert that:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Then, applying this, you get:
[tex]x^2+2(x)(1)+1^2=16\\x^2+2x+1=16[/tex]
Subtract 16 from both sides:
[tex]x^2+2x+1-16=16-16\\x^2+2x-15=0[/tex]
Factor the quadratic equation. Find two numbers whose sum be 2 and whose product be -15, then:
[tex](x-3)(x+5)=0\\x_1=3\\x_2=-5[/tex]
Y=3x-5 y=6x-8 show all steps and write the solution
Step 1: Set the two equations equal to each other and solve for x.
3x -5 = 6x - 8
3x + (-5+5) = 6x -8 + 5
(3x - 6x) = (6x - 6x) - 3
-3x/-3 = -3/-3
x = 1
Step 2: To solve for y take one of the given equation of your choice (for the purpose of this explanation I will only do y = 3x - 5) and replace x with 1, then solve for y
y = 3(1) - 5
y = 3 - 5
y = -2
(1,-2)
Check:
-2 = 3(1) - 5 ---> - 2 = -2
-2 = 6(1) - 8 ---> -2 = -2
Hope this helped!
Answer:
x=1
and y= -2
Step-by-step explanation:
y=3x-5 y=6x-8
On equating the two equations:
3x-5= 6x-8
Taking terms of x on one side and constant terms on the other
6x-3x= 8-5
3x= 3
Dividing both sides by 3, we get
x=1
Now, putting value of x in y=3x-5, we get
y=3-5
= -2
Hence, Solution is:
x=1 and y= -2
2 Points
What is the slope of the line shown below
(3,9)
(1,1)
ANSWER
The slope is 4
EXPLANATION
We want to find the slope of the line goin through (3,9) and (1,1)
We use the slope formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
We substitute the points into the slope formula to get;
[tex]m = \frac{1 - 9}{1 - 3} [/tex]
This simplifies to:
[tex]m = \frac{ - 8}{ - 2} [/tex]
[tex]m = 4[/tex]
Hence the slope of the line is 4.
You can solve the following proportion by cross multiplying what will the equation be after you cross multiply x/7 = 4/14
x in (-oo:+oo)
2/7 = x/14 // - x/14
2/7-(x/14) = 0
2/7-1/14*x = 0 // - 2/7
-1/14*x = -2/7 // : -1/14
x = -2/7/(-1/14)
x = 4
x = 4
i hope this helps
Answer:
x*14 = 7*4
Step-by-step explanation:
Use ΔDEF to complete the statements. Angle E is the included angle between sides . The included angle between sides FE and DF is angle .
Answer:
second choice
third choice
Step-by-step explanation:
righty whighty edg 2020
From the given diagram of triangle DEF:
Included angle E is between sides DE and FE.Included angle F is between sides FE and DF.Triangle DEF is shown in the image attached below/.
Triangle DEF has the following sides:
Side FESide DFSide DEThe triangle also shows that:
Angle E, as an included angle is between side sides DE and FE. Both sides meet at point E.Also,
The angle that lie between side FE and side DF is angle F. Both sides meet at point F.In summary, from the given diagram of triangle DEF:
Included angle E is between sides DE and FE.Included angle F is between sides FE and DF.Learn more here:
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which of the following is most likely the next step in the series ?
Answer:
C.
Step-by-step explanation:
Answer:
The correct answer is C.
Step-by-step explanation:
We have given some pattern in the series.
We need to find the next step which follows and continue the series.
We know that, we have three given patterns in the question. In the first we have given a pattern which is made by the joining of three dots, and in the second pattern made by the joining of five dots and in the third pattern made by the joining of the five dots.
In the following way, we can say that the next step in the series and fourth pattern follows same pattern as given in the above. That's why next pattern made by the joining of seven dots, but in the following given options next to next pattern is given which is joining by nine dots, therefore we choose option which is the next step in the series.
HURRY ANSWER ASAP!
A rectangular prism with a volume of 3 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4
unit cubes does it take to fill the prism?
So, 1 cube equals 1/4 unit.
4 cubes will equal 1 whole unit.
If the volume of the rectangular prism is 3 cubic units, all you have to do is multiply.
4*3=12
So it would take a total of 12 cubes to fill the prism.
Hope this helps.
Lines CB and CA are tangents to circle O at B and A. We can conclude that, for circle O, angle BOA and angle BCA are ___, and angle BOC and angle BCO are ____.
Blank 1 options: equal, complementary, supplementary
Blank 2 options: equal, complementary, supplementary
Answer:
Blank 1 ⇒ supplementary
Blank 2 ⇒ complementary
Step-by-step explanation:
* Lets revise some facts to solve the problem
- The tangent to a circle is a line touch the circle at one point
- The tangent and the radius of a circle are perpendicular to each
other at the point of contact
- If the two angles are supplementary, then the sum of their measure
is 180°
- If the two angles are complementary, then the sum of their measure
is 90°
* Now lets solve the question
∵ CB and CA are two tangents to the circle O at B and A
∵ OB and OA are radii
∴ OB ⊥ BC at point B and OA ⊥ AC at point A
∴ m∠OBC = 90° and m∠OAC = 90°
- In figure CBOA is a quadrilateral
∴ The sum of the measures of its interior angles is 360°
∵ m∠CBO + m∠BOA + m∠OAC + m∠BCA = 360°
∵ m∠CBO = 90° , m∠OAC = 90°
∴ 90° + m∠BOA + 90° + m∠BCA = 360°
∴ 180° + m∠BOA + m∠BCA = 360° ⇒ subtract 180 from both sides
∴ m∠BOA + m∠BCA = 180°
∴ ∠BOA and ∠BCA are supplementary
- In Δ CBO
∵ The sum of the measures of the interior angles of any triangle is 180°
∴ m∠BOC + m∠BCO + m∠CBO = 180°
∵ m∠CBO = 90°
∴ m∠BOC + m∠BCO + 90° = 180° ⇒ subtract 90° from both sides
∴ m∠BOC + m∠BCO = 90°
∴ ∠BOC and ∠BCO are complementary
Answer:
Blank 1: Supplementary
Blank 2:Complementary
Step-by-step explanation: I picked these and got it right
Find the supplement of an angle that measures 89°.
A. 61° B. 1° C. 31° D. 91°
Answer:
D
Step-by-step explanation:
Supplementary angles sum to 180°
Subtract the given angle from 180 for the supplement, that is
180° - 89° = 91° ← the supplementary angle
Final answer:
The supplement of an 89° angle is found by subtracting it from 180°, giving us 91°. Therefore, the correct answer is 91°, which is option D.
Explanation:
To find the supplement of an angle, we need to know that supplementary angles add up to 180 degrees. Given an angle that measures 89°, we can find its supplement by subtracting the given angle from 180°.
So, 180° - 89° = 91°.
The supplement of an angle that measures 89° is 91°, which corresponds to option D.
Specify the domain for the function !!! 10 points - Help needed !
The answer is:
The domain for the function is all the real numbers,
Domain:(-∞,∞)
Why?Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.
We are given the function:
[tex]f(x)=\frac{1}{x^{2}-5x+25 }[/tex]
Where, the denominator is given by the expression:
[tex]x^{2}-5x+25[/tex]
For the given expression (quadratic equation), we have that:
[tex]a=1\\b=-5\\c=25[/tex]
Calculating the discriminat of the quadratic function, in order to know if the denominator of the function has roots (zeroes) at the real numbers, we have:
[tex]Discriminant=b^{2} -4ac[/tex]
[tex]Discriminant=-5^{2} -4(1)(25)[/tex]
[tex]Discriminant=25 -100=-75[/tex]
Now, as we know, if the discriminant of a quadratic function is less than 0, the quadratic function has no roots in the real numbers.
Therefore, since the denominator (quadratic function) has no roots in the real numbers, the domain for the function will be equal to all the real numbers.
Domain:(-∞,∞)
Hence, the answer is the third option, the domain for the function is all the real numbers,
Domain:(-∞,∞)
Have a nice day!
Help with this question
Answer:
-2
Step-by-step explanation:
2x + y = 10 Subtract 2x from both sides.
2x-2x + y = 10 - 2x Combine the left.
y = 10 - 2x
The slope is the number in front of the x -- in this case - 2
The answer is - 2
Which algebraic expression represents the phrase “six less than a number”?
Answer:
x-6
Step-by-step explanation:
Let the number be x
Then the algebraic expression “six less than a number” can be represented as:
x - 6
So, "six less than a number” can be represented as: x - 6
A total of 119 golden tickets were sold for an NBA match. A hundred general tickets and 6 platinum tickets were also sold. The price of a general ticket was three-fourth the cost of the golden ticket. The price of a platinum ticket was twice that of the golden ticket. How much was priced at, if the total collection from-ticket sales was $6,592? a golden ticket
Pls show steps...
Answer:
Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.
119g + 100t + 6p = 6592
t = 3/4g
p = 2g
119g + 100(3/4)g + 6(2g) = 6592
g = 32
t = 3/4(32) = 24
p = 32(2) = 64
A golden ticket costs $32. A regular ticket costs $24. A platinum ticket costs $64. Hope this helps!
Answer:
Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.
119g + 100t + 6p = 6592
t = 3/4g
p = 2g
119g + 100(3/4)g + 6(2g) = 6592
g = 32
t = 3/4(32) = 24
p = 32(2) = 64
Step-by-step explanation:
Which equation could be used to calculate the sum of the geometric series?
1/3 + 2/9 + 4/27 + 8/81 + 16/243
Answer:
The equation is:
[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]
[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]
The sum is:
[tex]S=\frac{211}{243}[/tex]
--------------------------------------------------------------------
If the sequence is infinite, the formula is:
[tex]S = \frac{a_1}{1-r}[/tex]
-------------------------------------------------------------------
Step-by-step explanation:
We must calculate the radius of the geometric series
[tex]r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}[/tex]
The first term of the series is: [tex]a_1=\frac{1}{3}[/tex]
The last term of the series is: [tex]a_n=\frac{16}{243}[/tex]
If the sequence is finite then the formula is:
[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]
[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]
[tex]S=\frac{211}{243}[/tex]
If the sequence is infinite then by definition as the radius are [tex]0 <| r | <1[/tex] then the formula for the sum of the geometric sequence is:
[tex]S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1[/tex]
Answer:
A
Step-by-step explanation:
got it right on edge
A month of the year is chosen at random. What is the probability that the month starts with the letter J or m
5/24
1/6
1/4
5/12
what is the volume of the cylinder below?
Hello There!
To find a cylinder, we use the formula Pi*radius “squared” *height
First, let’s put in our values. Our radius is 5 but in our formula, we have to square 5 so we get a product of 25.
Then we multiply 25 by 9 because you will see in our formula we have to multiply by the height. 25*9 equals 225
Now, we are putting our value in terms of pi so our answer would be 225
Answer “C”
Answer:
175
Step-by-step explanation:
APEXX!!!!
simplify 3 square root of 7 over 5 square root of 7
The simplified form of ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by dividing it.
Given that simplify 3 square root of 7 over 5 square root of 7 that is [tex]3\sqrt7 / 5\sqrt7.[/tex]
To find the ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by dividing it by following steps:
Step 1: Factorize the numerator and denominator.
Numerator [tex]= 3\sqrt7 = 3(\sqrt7)[/tex]
Denominator [tex]= 5\sqrt7 = 5(\sqrt7)[/tex]
Step 2: Divide both numerator and numerator by common factor gives:
Ratio = numerator/denominator
[tex]= \sqrt7(3)/\sqrt7(5)[/tex]
Divide both numerator and numerator by [tex]\sqrt7[/tex] gives:
= 3/5.
Therefore, the simplified form of ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by dividing it.
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The mass of a clownfish is 2.5 x 10 to the negative 1 power kilograms. The mass of a pilot whale is 3 x 10 to the third power kilograms. About how many times as massive is the pilot whale than the clownfish?
Answer:
Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.
Step-by-step explanation:
Mass of clown fish = 2.5 X 10 ^-1 kg
Mass of pilot whale = 3 X 10 ^ 3 kg
Find the ratio of Mass of pilot whale to the ratio of Mass of clown fish
Mass of pilot whale : Mass of clown fish
3 X 10 ^ 3 : 2.5 X 10 ^-1
It can be written as
3 X 10 ^ 3 / 2.5 X 10 ^-1
1.2 x 10^4
So, Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.
what is the axis of symmetry of h(x)= -x^2-2x+8
Answer:
The answer is 2.
Step-by-step explanation:
The equation for finding the axis of symmetry is:
x=-\frac{b}{2a}
Plug the numbers from the equation in:
a=1
b=-2
x=-\frac{-2}{2(1)}
Solve:
x=\frac{2}{1}
x=2
hope this helps :)
Please help ASAP!!! I WILL MAKE BRAINLIEST
Answer: 42.5
Step-by-step explanation:
The answer is 42.5
Answer: 42.5 cm
Step-by-step explanation: Its really simple. You multiply 8.5 cm and 5 cm to get 42.5 cm.
Jack found 11 starfish eat starfish has 5 arms how many arms did the starfish have in all
11 • 55 = 55
The starfish had 55 arms all together.
Hope this helps!
What is the volume of the portion of the aquarium with water in it?
101 cm³
14000 cm³
32,200 cm³
46,200 cm³
I think the answer is 32,2000cm^3
Answer: C
Step-by-step explanation: i got 100% on test
It takes William 45 minutes to weed the garden. It takes his younger sister May 75 minutes to do the same job. If they work together, how long will it take them?
A. 25 minutes
B. 28 minutes
C. 36 minutes
D. 60 minutes
Answer:
B. 28 minutes
Step-by-step explanation:
According to the given statement,
William weeds the whole garden in 45 minutes, then in one minute he will weed 1/45 of the garden
and
similarly, 1/75 of the garden in one minute.
When they both will work together, they will weed (1/45+1/75) of the garden in one minute
Solving the equation:
= [tex]\frac{1}{45}+ \frac{1}{75}\\= \frac{75+45}{3375}\\ =\frac{120}{3375}\\ = 0.036[/tex]
Garden weeded in one minute by both = 0.036
So, number of minutes to weed whole garden = 1/0.036
= 27.77 minutes
Rounding off will give us: 28 minutes
So,
Option B is the correct answer ..
Simplify the expression
3a(3-a)+3(a^2-3)+3a
Answer:
12a−9
Step-by-step explanation:
Distribute:
=(3a)(3)+(3a)(−a)+(3)(a2)+(3)(−3)+3a
=9a+−3a2+3a2+−9+3a
Combine Like Terms:
=9a+−3a2+3a2+−9+3a
=(−3a2+3a2)+(9a+3a)+(−9)
=12a+−9
Answer:
3 (4 a - 3)
Step-by-step explanation:
Simplify the following:
3 a (3 - a) + 3 (a^2 - 3) + 3 a
3 a (3 - a) = 9 a - 3 a^2:
9 a - 3 a^2 + 3 (a^2 - 3) + 3 a
3 (a^2 - 3) = 3 a^2 - 9:
3 a^2 - 9 - 3 a^2 + 9 a + 3 a
Grouping like terms, 3 a^2 - 3 a^2 + 9 a + 3 a - 9 = (9 a + 3 a) - 9 + (-3 a^2 + 3 a^2):
(9 a + 3 a) - 9 + (-3 a^2 + 3 a^2)
9 a + 3 a = 12 a:
12 a - 9 + (-3 a^2 + 3 a^2)
3 a^2 - 3 a^2 = 0:
12 a - 9
Factor 3 out of 12 a - 9:
Answer: 3 (4 a - 3)
36°
The adjacent angles 21 and 22 have measures of:
38, 142
76, 104
28, 152
Answer:
Option "A" might be the correct option
Step-by-step explanation:
By the Angles of Intersecting Chords Theorem, When two chords intersect inside a circle, then the measure of the angle formed is one half the sum of chord's intercepted arcs.
In the diagram : -
⇒ ∠ 1 = 38°
Now, again by the diagram,
∠1 and ∠2 are linear pairs,
⇒ ∠1 + ∠2 = 180°
⇒ 38° + ∠2 = 180°
⇒ ∠2 = 142°
Answer:
38,142.
Step-by-step explanation:
The measure of angle 1 = the sum of the measure of the 2 arcs / 2
= (36 + 40) / 2
= 38 degrees.
A basket contains 6 oranges and 4 tangerines. a sample of 3 is drawn. find the probability that they are all oranges
The probability of drawing 3 oranges from a basket of 6 oranges and 4 tangerines is 1/6 or approximately 0.167.
Explanation:This problem is a probability question in the field of mathematics. It is asking us to find the probability that all three fruits drawn from the basket are oranges. This can be solved using the concept of combinations from probability theory.
The total number of fruits in the basket is 10 (6 oranges and 4 tangerines). We want to draw a sample of 3 fruits. The number of ways to draw 3 fruits from a total of 10 (regardless of type) is given by the combination formula C(n, r), where n is the total number of items and r is the number of items to choose. So we have C(10, 3) = 120 possible ways.
Next, consider the scenario we're interested in--drawing 3 oranges. The total number of ways to draw 3 oranges from a total of 6 oranges is C(6, 3) = 20 possible ways.
So, the probability of drawing 3 oranges is the number of ways to draw 3 oranges divided by the total number of ways to draw 3 fruits. So, the probability is 20/120 = 1/6 or approximately 0.167.
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Final answer:
The probability of drawing 3 oranges from a basket containing 6 oranges and 4 tangerines is found using combinations. The calculation shows that the probability of selecting all oranges in a draw of 3 fruits is 1/6.
Explanation:
The question asks to find the probability that when three fruits are drawn from a basket containing 6 oranges and 4 tangerines, all three are oranges. This is a problem of probability without replacement, which can be solved using combinations.
To find the probability of drawing 3 oranges out of 3 fruits, we calculate the combinations of choosing 3 oranges from 6 and then divide it by the combinations of choosing 3 fruits from the total 10 fruits in the basket.
The number of ways to select 3 oranges out of 6 is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items, and k is the number of items to choose. So, we have:
Ways to pick 3 oranges: C(6, 3)
Total ways to pick 3 fruits: C(10, 3)
Then the probability is calculated by:
P(all oranges) = C(6, 3) / C(10, 3)
Calculating the combinations, we have:
P(all oranges) = (6! / (3! × (6-3)!)) / (10! / (3! × (10-3)!)) = (6 × 5 × 4) / (3 × 2 × 1) divided by (10 × 9 × 8) / (3 × 2 × 1) = 20 / 120 = 1/6.Thus, the probability that all three fruits are oranges is 1/6.
What is the volume of the rectangular solid?
A) 11 cubic centimeters
B) 22 cubic centimeters
C) 30 cubic centimeters
D) 40 cubic centimeters
Answer:
40 cm
Step-by-step explanation:
Multiply the length, the width, and the height. You can multiply them in any order to get the same result. The formula for finding the volume of a rectangular solid is:
Volume = Length * Height * Width,
or V = L * H * W.
what expression is equivalent to ( X 3 ) 4 ?
Answer:
4
Step-by-step explanation:
Final answer:
The expression equivalent to (X^3)^4 is X^12. You calculate this by multiplying the exponents, resulting in X raised to the power of 3 times 4, which equals 12.
Explanation:
The expression (X^3)^4 is equivalent to X^(3*4), which is X^12. This follows the rule that when you raise a power to a power, you multiply the exponents. A number raised to the fourth power, like in this case, means that number is multiplied by itself four times. Generalizing this, for any base 'n' and exponents 'a' and 'b', the expression (n^a)^b is equal to n^(a*b).
For example, similar to (5^3)^4 being 5^(3*4) or 5^12, which is twelve fives multiplied together. Therefore, our given expression simplifies to X multiplied by itself a total of twelve times.
Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. X=2 when y=2
Answer:
see explanation
Step-by-step explanation:
Given that y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition
x = 2 when y = 2
k = yx = 2 × 2 = 4, hence
y = [tex]\frac{4}{x}[/tex] ← equation of variation