if the area of a square is 32ft how long is the diagonal?
Answers
A square has the same length all 4 sides, therefore in order to find the length of the sides, you would need to find the square root of 32, which would be 5.66 or 4 radical 2. Then to find the diagonal length you would need to split the square diagonally resulting in 2 triangles. We know the side lengths of the triangles but not the hypotenuse( longest side of triangle), which is the diagonal length. To figure this out we would use the Pythagorean theorem a^2 + b^2 = c^2. We know what a and b are so we substitute, do basic algebra, and find that c is equal to 8
Answer: 8
Step-by-step explanation:
To find the diagonal, we need to use two formulas:
Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)
Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
Since every side of a square is the same:
[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]
Our equation:
[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]
The picture below visually explains the problem
Hope this helps!
Related Questions
Jack is 14 years old. In 2032 to Jack will be twice his age. What year is it
Answers
Answer:
2018 I believe.
Step-by-step explanation:
He'll be two times his age in 2032 which is 28 years old. Subtract 28 from 2032 and you get 2018.
Answer:
2018
Step-by-step explanation:
in 2032 he will be 28 years old because he is 2 times older than 14, 2032-14=2018, because 14 years have passed since he was 14
Which statements describe one of the transformations performed on f(x) = x² to create g(x)=3(x+5)² - 2? Choose all that apply. 1 A. A vertical stretch with a scale factor of 3 B. A translation of 5 units to the left C. A vertical stretch with a scale factor of 3 D. A translation of 2 units to the left
Answers
These following translations happened to transform f(x) into g(x):
A. vertical stretch with a scale factor of 3. B. A translation of 5 units to the left.E. A translation of 2 units down.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are as follows:
f(x) = x².g(x) = 3(x + 5)² - 2.The changes were as follows:
x -> x + 5, hence a shift of 5 units left.Multiplication by 3, hence a vertical stretch with a scale of 3.y -> y - 2, hence shifted 2 units down.More can be learned about translations at https://brainly.com/question/4521517
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The soulution to 6+2x>32 is either x>13 or x<13. Which soulution is correct? Explain how you know - prove it with a number
Answers
Answer:
6+2x >32
2x>32-6
2x>26
divide both sides by 2
therefore, x>13
Step-by-step explanation:
this is because x don't has a negative sign or is on the other side
X
2
3
4
A. (1, 2, 3, 4)
B. (2, 6, 10, 14)
C. (1,2)
D. (1, 2), (2, 6), (3, 10), (4, 14)
y
2
6
10
14
Answers
Answer:
B (2,6,10,14)
Step-by-step explanation:
I think C and D are imposible to be the answer.
A and B are 50% to be the answer.
But I choose B.
2sin² theta = sin theta for - 270° ≤ 0 ≤180°
Answers
Answer:
θ = 0°
θ = 30°
θ = 150°
θ = 180°
Step-by-step explanation:
2sin² θ = sin θ
Then
2sin² θ - sin θ = 0
Then
sin θ (2sin θ - 1) = 0
Then
sin θ = 0 or 2sin θ - 1 = 0
Then
sin θ = 0 or sin θ = 1/2
…………………………………………
We have sin θ = 0 and - 270° ≤ θ ≤180°
Then
θ = 0 or θ = π = 180°
On the other hand,
sin θ = 1/2 and - 270° ≤ θ ≤180°
Then
θ = π÷6 or θ = 5π÷6
π÷6 = 30° and 5π÷6 = 150°
B
ED
E D
B
C
B
m
A
DE
Which rule describes the composition of
transformations that maps figure ABCDE to figure
A"B"CD"E"?
ORC.900 orm
OroRC.900
ORc1800 or
OroRC.1800
Answers
Answer: [tex]R_{C, 180^{\circ}} \circ r_{m}[/tex]
Step-by-step explanation:
The sequence is a reflection over line m followed by a rotation 180 degrees about point C.
Among all the options give the last option that is,
⇒ r m0 Rc180° , is the right answer.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Now, In the given figure ABCDE is transformed to figure A”B”C”D”E.
Hence, When a figure is reflected along a line the reflected image is at the same distance to the line as the original figure was.
The figure ABCDE is first reflected through the line m to get the figure A'B'C'D'E'.
When a figure is rotated by 180 degrees the x and y coordinates change its place and y sign is reversed.
A'B'C'D'E' is rotated by 180 degrees to come to figure A"B"C"D"E".
Hence, Among all the options give the last option that is,
⇒ r m0 Rc180° , is the right answer.
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In order to meet ada requirements, a wheelchair ramp must have an angle of elevation of no more than $4.8\degree$. a builder needs to install a ramp to reach a door that is 1.5 feet off the ground. what angle of elevation will this ramp have ?
Answers
"In order to meet ADA requirements, a wheelchair ramp must have an angle of elevation of no more than" the angle of elevation is mathematically given as
∅=3.434
What angle of elevation will this ramp have?Generally, the equation for the angle is mathematically given as
[tex]\theta=\frac{opp}{adj}\\\\Therefore\\\\tan\theta=\frac{1.5}{25}\\\\tan\theta=\frac{1.5}{25}\\\\\theta=tan^{-1}\frac{1.5}{25}\\\\[/tex]
∅=3.434
In conclusion, the angle of elevation
∅=3.434
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find the value of x in the given right triangle
Answers
Answer: 10.6
Step-by-step explanation:
[tex]\sin 62^{\circ}=\frac{x}{12}\\x=12 \sin 62^{\circ} \approx \boxed{10.6}[/tex]
what is the least common denominator of 4/5ths and 5/7ths
Answers
Answer:
35 is the least common denominator
Step-by-step explanation:
35 is the least (smallest) common (same) multiple of 5 and 7. We use the smallest number that both 5 and 7 go into, because its supposed to be easier to use smaller numbers.
4/5 becomes 28/35 and 5/7 becomes 25/35. And now that they have the same denominator, you could add or subtract them.
what is the probability that a month starting with a vowel is drown
Answers
3 out of the 12 start with a vowel: April, August, and October.
Probability can be calculated by taking
# of desired outcomes/total # of outcomes
So, the chance of randomly selecting a month that starts with a vowel is 3/12, or 1/4, which is 0.25 or 25%.
Determine the value of y, if x is 2
Y=x^2+5
Answers
Answer:
y = 9
Step-by-step explanation:
y = (2)^2 + 5
y = 4 + 5
y = 9
_____ cups rice is equivalent to 1 pound
Answers
Answer:
2.5 cups is equal to 1 pound.
Step-by-step explanation:
___2.5__ cups rice is equivalent to 1 pound
Hope This Helped
Answer:
2.5 cups of rice
I hope this helps
Can someone help me with this? Thanks!
Answers
Part (a)
There are 3 face cards (jack, queen, king) in any given suit. We have 4 suits. That gives 3*4 = 12 face cards total.
12/52 = 3/13 is the probability of getting a face card on any random selection. This probably does not change for any future selection because we put the current card back. In other words, the deck has not changed. Contrast this with part (b) where the probabilities will change since the card counts decrease each time (since we don't put the card back).
The probability of getting 3 face cards in a row, with replacement, is:
(3/13)*(3/13)*(3/13) = 0.012289 approximately
This converts to the percentage 1.2289% after moving the decimal point two spots to the right. This is the same as multiplying by 100.
Lastly, round that to one decimal place to get 1.2%
Answer: 1.2The percent sign is already taken care of, so you'll just input the number only.
=============================================================
Part (b)
Like mentioned earlier, the probability of a face card is 12/52
I won't reduce that fraction, as you'll see why below.
After that first card is not put back, the 12 decreases to 12-1 = 11 and we have 52-1 = 51 cards left over.
11/51 is the probability of getting another face card, where we have no replacement going on.
Then 10/50 is the probability of getting a third face card. Again, with no replacement.
Therefore,
(12/52)*(11/51)*(10/50) = 0.009955
is the approximate probability of getting 3 face cards in a row with no replacement. Notice the count down 12,11,10 in the numerators. There's also the countdown 52, 51, 50 in the denominators. This nice pattern only happens if we don't reduce the reducible fractions. This is why I didn't reduce.
Anyways 0.009955 converts to 0.9955% which rounds to 1.0% or simply 1%
Answer: 1please help me get better at math, i need someone who's actually good at it in order to become good myself.
Answers
Answer:
what subject of math? Anything to do with calc is a tough area but I can try.
Step-by-step explanation:
The product of two irrational numbers is (sometime, always, never) rational.
Answers
sometimes
Step-by-step explanation:
irrational numbers are numbers that cannot be expressed as a quotient of 2 numbers
rational numbers are numbers that can be expressed as a fraction.
for example let's take these examples of iirational numbers:
[tex] \sqrt{2} \times \sqrt{2} = 2[/tex]
[tex]\pi \times \pi = 9.86960....[/tex]
the 1st product (2) can be written as a fraction but the second one cannot be written as a fraction
Translate the shape A three squares right and one square up.
What are the coordinates of the vertices of the image?
Answers
Answer:
(4, 3) , (4, 0) , (6, 0)
Step-by-step explanation:
M (1, 4)
M ' ( 1 + 3, 4 - 1)
namely M ' (4, 3)
N (1, 1)
N ' ( 1 + 3 , 1 - 1) ((x, y) 3 squares right and 1 square down means
namely n" (4, 0) ( x + 3, y - 1))
p (3, 1)
p ' ( 3 + 3 , 1 - 1)
namely p' (6, 0)
Step-by-step explanation:
(3,4) not that sure about the coordinates are right
A rectangle is transformed according to the rule r0, 90º. the image of the rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4). what is the location of q?
Answers
For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
A rectangle is transformed according to the rule 90º.
The rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).
Then the location of q will be
For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).
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Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 100 points
packs of collectible cards claim that 1 out of 3 packs contains a rare card. margie bought 7 packs and only received a rare card in 1 of the packs.
margie runs a simulation of 100 trials. in the simulation, she used a random number generator to select 7 digits from 1 to 3 with 1 representing a pack with a rare card and 2 and 3 representing a pack without a rare card. the frequency of the number of packs with rare cards in each trial of 7 samples in the simulation is represented by this table.
what is the best conclusion for margie to make based on the data?
the claim that 1 out of 3 packs contains a rare card is plausible because the simulation shows that only 1 pack with a rare card out of 7 is likely.
the claim that 1 out of 3 packs contains a rare card is plausible because the simulation shows that only 1 pack with a rare card out of 7 is unlikely.
the claim that 1 out of 3 packs contains a rare card is not plausible because the simulation shows that only 1 pack with a rare card out of 7 is likely.
the claim that 1 out of 3 packs contains a rare card is not plausible because the simulation shows that only 1 pack with a rare card out of 7 is unlikely.
Answers
Answer:
My guess would be b or d
Step-by-step explanation:
If AB is tangent to (circle)C at A, find BC.
Answers
The length of r if AB is tangent to circle C, forming a right triangle is 8 units.
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
From the diagram, using Pythagoras theorem:
BC² = AC² + AB²
17² = 15² + r²
r = 8 units
The length of r if AB is tangent to circle C, forming a right triangle is 8 units.
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Victoria is putting down fertilizer in her garden. For every 25 square feet of garden, she needs one pound of fertilizer.
Let p represent the number of pounds of fertilizer.
Let g represent the area, in square feet, of garden she covers.
Which correctly names the independent and dependent variables?
independent variable: number of pounds of fertilizer; dependent variable: number of square feet of garden covered
independent variable: brand of fertilizer; dependent variable: number of pounds of fertilizer
independent variable: number of square feet of garden; dependent variable: number of pounds of fertilizer
independent variable: number of square feet of garden; dependent variable: number of people it takes to fertilize the garden
Answers
The independent variable: number of pounds of fertilizer; and dependent variable: number of square feet of garden covered.
Let
p = number of pounds of fertilizer.g = area, in square feet, of garden she coversWhat is dependent and independent variable?Dependent variable are variables which takes its value based on other values in an equation.
Independent variable are variables which takes its value outside an equation.
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In complete sentences, explain whether or not it makes sense to say that the density of helium is 0.1785 kilograms per square meter.
Answers
No, it does not make any sense to say that the density of helium is 0.1785 kilograms per square meter.
How to express the density of an element?
No, it does not make any sense to say that the density of helium is 0.1785 kilograms per square meter.
The reason why it doesn't make sense is because density of helium, and all the rest of the chemical elements are calculated as;
Density = mass/volume
where;
mass is measured in kilograms.
volume is measured in cubic meter.
Thus, the density of the helium should be expressed as 0.1785 kilograms per cubic meter.
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Pretest: Unit 8
Question 12 of 13
Which option below provides the best description of the relationship between
a quadratic parent function and a square root parent function?
A. The square root function is the quadratic function reflected across
the y-axis.
B. The square root function is the quadratic function reflected across
the line y = x, with a limited domain.
C. The square root function is the quadratic function reflected across
the x-axis.
Answers
B. The square root function is the quadratic function reflected across
the line y = x, with a limited domain.
graph y=x^2 and y=√x and y=x
graph is attached
gathmath
Given lines l, m,n are parallel and cut by two transversal lines, find the value of x. Round your answer to the nearest tenth if necessary.
Answers
Answer: 50.5
Step-by-step explanation:
[tex]\frac{30}{22}=\frac{x}{37}\\x=(30/22)(37) \approx \boxed{50.5}[/tex]
if yassy got score of 9, what is her rank?
Answers
answer:
4nd rank
Step-by-step explanation:
I'm not sure btw.
Please help me with this
Answers
Answer:
65.9 ft
Step-by-step explanation:
The Law of Sines tells us the relationship between an angle and the opposite side. We are given the angle opposite the given side, but we need the angle opposite the side of interest.
__
third angleThe sum of angles in a triangle is 180°, so the measure of the angle at the balloon is ...
angle C = 180° -75° -60° = 45°
ground distanceThen the distance between Amaya and Rochelle (c) is ...
c/sin(C) = r/sin(R)
c = r×sin(C)/sin(R) = (90 ft)×sin(45°)/sin(75°)
c ≈ 65.8846
Amaya and Rochelle are about 65.9 feet apart.
Calculate the discriminant to determine the number of real roots of the quadratic equation y = x^2 + 3x - 10
Ono real roots
three real roots
two real roots
one real root
Answers
The given quadratic equation [tex]y = x^2 + 3x - 10[/tex] Hence, the correct option is D one real root.
How to use discriminant to find the property of solutions of given quadratic equation?Let the quadratic equation given be of the form ax^2 + bx + c = 0, then
The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.
The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:
Real and distinct if the discriminant is positive
Real and equal if the discriminant is 0
Non-real and distinct roots if the discriminant is negative
The given quadratic equation
[tex]y = x^2 + 3x - 10[/tex]
a = 1
b = 3
c = -10
The discriminant
[tex]b^2 - 4ac[/tex]
= 9 - 4(1)(-10)
= 9- 40
= - 31
Thus, Non-real and distinct roots if the discriminant is negative.
Hence, the correct option is D one real root.
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Kara rollerblades at an average speed of 14 km/h.
How far does she rollerblade in 15 minutes?
Answers
If Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.
How far does Kara rollerblade in 15 minutes?Note that, speed is distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Hence, Distance = Speed × time
Given that;
Speed of Kara = 14km/hrTime elapsed = 15min = (15/60)hr = 0.25hrDistance covered = ?Distance = Speed × time
Distance = 14km/hr × 0.25hr
Distance = 3.5km or (3.5×1000)m
Distance = 3.5km or 3500m
Therefore, if Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.
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Which of these values represents the strongest correlation?
O A -0.8
O B. -0.6
O C. -0.5
O D. -0.7
Answers
Answer:
A. -0.8
Step-by-step explanation:
The closer its absolute value to 1, the stronger the relationship is.
A. |-0.8| = 0.8
B. |-0.6| = 0.6
C. |-0.5| = 0.5
D. |-0.7| = 0.7
0.8 is closest to 1, therefore representing the strongest correlation.
Hope this helped :)
5^(9x)=25^(4x+2) SHOW STEPSSSS
Answers
Answer:
x = 4
Step-by-step explanation:
[tex]5^{9x} =25^{4x+2}[/tex]
First you need to get a common base as your number.
[tex]5^{9x} =5^{2(4x+2)}[/tex]
The second number changed because 5 squared is 25. Changing it to this form gives us the same base number of 5. Now we use the distributive property in the exponent.
[tex]5^{9x} =5^{8x+4}[/tex]
Now we can use this statement:
[tex]A^{m} =A^{n}[/tex] if [tex]m=n[/tex]
Using this we solve:
9x = 8x+4
-8x -8x
x = 4
Hope it helps!
Find the value of each variable. The dot represents the center of the circle.
Answers
Answer:
Step-by-step explanation:
By the inscribed angle theorem, [tex]a=21, b=42[/tex]
So, since angles in a triangle add to 180 degrees, the angle vertical to c is [tex]180-21-42=117[/tex], and thus [tex]c=117[/tex]