What is the value of x?
1/3 (Square root of 2) units
1/2 (Square root of 3) units
2 (Square root of 3) units
3 (Square root of 2) units
Answers
x = 3 (Square root of 2) units
Answer:
[tex]3[/tex] (Square root of [tex]2[/tex]) units
Step-by-step explanation:
we know that
The larger triangle is an isosceles right triangle
so
Applying the Pythagoras Theorem
[tex]6^{2} =x^{2} +x^{2} \\ 36=2x^{2} \\18=x^{2}\\x=\sqrt{18}\ units \\x=3\sqrt{2}\ units[/tex]
Related Questions
Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows that it decays at a rate of 25% every hour.
Identify whether this situation represents exponential growth or decay. Then determine the rate of growth or decay, r, and identify the initial amount, A.
Answers
[tex]y=A(1-r)^{x}[/tex]
where
[tex]y[/tex] is the amount after a time [tex]x[/tex]
[tex]A [/tex] is the initial amount
[tex]r[/tex] is the the decay percent in decimal form
The first ting we are going to do is find [tex]r[/tex] by dividing our decay rate of 25% by 100%: [tex]r= \frac{25}{100} =0.25[/tex].
We also know from our problem that [tex]y=64[/tex]. Lets replace [tex]y[/tex] and [tex]r[/tex] in our formula:
[tex]64=A(1-0.25)^{x} [/tex]
[tex]64=A(0.75)^{x} [/tex]
We know now that our decay rate is 0.75, and since 0.75<1, we can conclude that this situation represents exponential decay.
Now, to find the initial amount, we are going to solve our equation for [tex]A[/tex]:
[tex]64=A(0.75)^{x} [/tex]
[tex]A= \frac{64}{0.75 ^{x} } [/tex]
Notice that [tex]A[/tex] will depend on the number of ours [tex]x[/tex].
Answer:
This situation models exponential decay because the substance decays with time.
The radioactive substance decays at the rate of : 25%
r=25/100 =0.25
The initial amount of substance is 64 grams. So, . A=64
Step-by-step explanation:
What is the mean absolute deviation for the data set?
{20, 24, 12, 44, 68}
16.81
17.04
17.52
17.92
Answers
Answer:
17.92
Step-by-step explanation:
I took the test and had the same question, plus the screenshot above
The Mean Absolute Deviation is 17.92.
What is Mean Absolute Deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set. A measure of variance in a data set is the mean absolute deviation.
Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set.
Given:
Data set: {20, 24, 12, 44, 68}
Mean of the data = (20+ 24+ 12+ 44+ 68)/ 5 = 168/5
= 33.6
Mean Absolute Deviation
= {| 20- 33.6| + |24- 33.6| + |12-33.6| + | 44-33.6| + |68-33.36|} / 5
= (13.6+ 9.6 + 21.6+ 10.4 + 34.4 )/ 5
= 89.6/ 5
= 17.92
Hence, the Mean Absolute Deviation is 17.92.
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One gallon of paint covers 200 square feet. How many gallon are needed to paint a rectangular floor that is 60 feet by 40 feet
Answers
1 gallon for 200 sq ft
(2400 sq ft)/(200 sq ft) = 12 gallons of paint
What is the wavelength of an earthquake wave if it has a speed of 7 km/s and a frequency of 3 Hz?
Answers
wavelength = speed / frequency (5000m/s /10Hz)
Answer: Our wavelength will be 2333.3 m.
Step-by-step explanation:
Since we have given that
Wave speed = 7 km/ s
Frequency = 3 Hz
We need to find the wavelength of an earthquake wave:
As we know that :
[tex]Frequency=\dfrac{Wave\ speed}{wavelength}[/tex]
First we convert km/sec to m/sec.
So, 7 km/sec= 7000 m/sec
so, our wavelength becomes
[tex]\dfrac{Wave\ speed}{frequency}\\\\\\=\dfrac{7000\ m/sec}{3\ Hz}\\\\\\=2333.33\ m[/tex]
So, our wavelength will be 2333.3 m.
The attendance of your club increased by 30% from last year. There are 195 people in the club now. How many people were in the club last year?
Answers
1.3n = 195
n=195÷1.3
n=150
Answer
increased by 30% from last year. There are 195 people in the club now.
How many people were in the club last year
Step-by-step explanation:
1.3n = 195
n=195÷1.3
n=150 people where in the club last year.
What side length would you specify if you were required to create a regular hexagonal plate that was composed of 33 cm2 of sheet metal? Sketch the hexagon, dimension the side length on the sketch to 0.1 cm, and indicate your grid spacing. Justify your dimension.
Answers
The side length to create a regular hexagonal plate is 3.6 cm. Using the GeoGebra graph to create the sketch where 1 unit = 0.1cm.
The side length of a regular hexagon.
The side length of a regular hexagon can be calculated by using the formula:
[tex]Area=\dfrac{3\sqrt{3}}{2}\times S^2[/tex]
where; S = side length[tex]S=\sqrt{\dfrac{2 \times Area }{3\sqrt{3}}[/tex]
Given that the area is 33 cm²
[tex]S=\sqrt{\dfrac{2 \times 33 }{3\sqrt{3}}[/tex]
Side length (S) = 3. 56 cm
Therefore, the side length to create a regular hexagonal plate is 3.6 cm. See below for the sketch of the hexagon where 1/2 unit = 0.1cm.
Nita brings $6 to her grandma's house. these dolls represent 20% of Anita's doll collection shown in the diagram. what is the total number of dolls in Anita's doll collection
Answers
You can get this by multiplying the number in 20% by 5, which would get you to 100% and 30.
Please, could anyone help????
please explain it and how to it.......
BRAINLIEST WILL BE GIVEN TO CORRECT
Answers
The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the standard form of the equation for this line?
Answers
.. y -1 = (1/4)(x -12)
.. 4y -4 = x -12 . . . . multiply by 4
.. x -4y = -4 +12 . . . add 12-4y
.. x -4y = 8 . . . . . . . the equation in standard form
Please help me please
Answers
the answer is 81
In an orchard, there are 15 apple trees,27 orange trees,,and a cherry tree.what is the ratio of orange trees?
Answers
The sum of two numbers is 13, the difference is 4. What are the numbers?
Please Help!
Answers
In the rhombus, what are m angle 1, m angle 2, and m angle 3? The diagram is not drawn to scale.
Answers
Angle 2 = 64
Angle 3 = 64
If you'd like an explanation, let me know!
Hope this helps!! :)
Isabela had a taxable income of $82350 and filed her federal income tax return with the single filing status. Using the table below find the amount she has to pay in taxes.
Answers
Answer:
B. $16,778.00.
Step-by-step explanation:
What is the slant height of a square pyramid that has a surface area of 279 square meters and a side length of 9 meters?
Answers
Answer:
l = 11 meters
Step-by-step explanation:
Surface area = s² + 2s*l
Where "l" is the slant height
Given: Surface area = 279 ; side length s = 9
Now plug in these values in the above formula, we get
279 = 9^2 + 2*9*l
279 = 81 + 18*l
18l = 279 - 81
18l = 198
Dividing both sides by 18, we get
l = 198/18
l = 11 meters
Therefore, slant height of the square pyramid = 11 meters
Hope this will helpful.
Thank you.
Which system of equations can you
use to find the roots of the equation
2x3 + 4x2 – x + 5 = –3x2 + 4x + 9?
y = 2x3 + x2 + 3x +5
y =9
y = 2x3 + x2
y = 3x + 14
y = 2x3 + 4x2 – x + 5
y = –3x2 + 4x + 9
Answers
Roots are both: x=-4, x= -1/2 , x= 1
Proof:
Solve for x over the real numbers:
2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9
Subtract -3 x^2 + 4 x + 9 from both sides:
2 x^3 + 7 x^2 - 5 x - 4 = 0
The left hand side factors into a product with three terms:
(x - 1) (x + 4) (2 x + 1) = 0
Split into three equations:
x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0
Add 1 to both sides:
x = 1 or x + 4 = 0 or 2 x + 1 = 0
Subtract 4 from both sides:
x = 1 or x = -4 or 2 x + 1 = 0
Subtract 1 from both sides:
x = 1 or x = -4 or 2 x = -1
Divide both sides by 2:
Answer: x = 1 or x = -4 or x = -1/2
Answer:
c the last one
Step-by-step explanation:
Two squares are drawn. The larger Square has area of 400 in.². The area of the two squares have a ratio of 1 to 4. What is the side length S of the smaller square?
Answers
For this, we use the following relationship:
A1 / A2 = 4/1
Substituting:
400 / A2 = 4/1
From here, we clear A2:
A2 = (1/4) * (400)
A2 = 100 in ^ 2
We now look for the side of the small square, we use the following relationship:
A = S ^ 2
We cleared S:
S = root (A)
S = root (100)
S = 10 in
Answer:
the side length S of the smaller square is:
S = 10 in
Answer: S=10 in
Step-by-step explanation:
The first thing we must do in this case is to find the area of the smallest square.
For this, we use the following relationship:
A1 / A2 = 4/1
Substituting:
400 / A2 = 4/1
From here, we clear A2:
A2 = (1/4) * (400)
A2 = 100 in ^ 2
We now look for the side of the small square, we use the following relationship:
A = S ^ 2
We cleared S:
S = root (A)
S = root (100)
S = 10 in
I copied the guy above me 4 points
What are the equations of the horizontal asymptotes of y = (4e^x+7)/(e^x-1) in the xy plane?
Answers
[tex] \lim_{x \to \infty} f(x) [/tex] = n
where n is a finite number.
in your case you have to caculate separately the two limits:
a) [tex]\lim_{x \to +\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 } [/tex] = [tex] \frac{\infty}{\infty} [/tex]
To solve this, you need to regroup eˣ both on the numerator and on the denominator:
[tex]\lim_{x \to +\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 }[/tex] = [tex]\lim_{x \to +\infty} \frac{4 e^{x} (1 + \frac{7}{ e^{x} } ) }{ e^{x} ( 1 - \frac{1}{ e^{x} } ) }[/tex]
At this point the two eˣ cancel out and the parenthesis tend to 1, therefore
[tex]\lim_{x \to +\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 }[/tex] = 4
Your first horizontal asymptote is y = 4.
b) Let's calcuate now:
[tex]\lim_{x \to -\infty} \frac{4 e^{x} + 7 }{ e^{x} - 1 }[/tex] = [tex] \lim_{x \to -\infty} \frac{0 + 7}{0 - 1} [/tex] = -7
Therefore your second horizontal asymptote is y = -7
Your answer is, hence, y = 4 and y = -7 are horizontal asymptotes of the given function.
Final answer:
The horizontal asymptotes of the function y = (4e^x+7)/(e^x-1) are y = 4 and y = -7, occurring as x approaches positive and negative infinity respectively.
Explanation:
The equations of the horizontal asymptotes of the given function y = (4e^x+7)/(e^x-1) can be found by analyzing the behavior of the function as x approaches positive or negative infinity. In this function, as x approaches infinity, e^x grows much faster than any constant, so the constants can be considered negligible. Thus, the behavior of the numerator and denominator is dominated by the terms involving e^x. As x tends towards infinity, the function approaches the ratio of the coefficients of e^x, which is 4/1, meaning the horizontal asymptote is y = 4. As x tends towards negative infinity, e^x approaches zero, and the function approaches 7/(-1), so there is also an asymptote at y = -7.
It is given that there is a vertical asymptote at x = -1, where the denominator becomes zero and hence "blows up".
Which of the following in equalities matches the graph?
A)-2x+3y>7
B)2x-3y<7
C)-3x+2y >7
D)3x+2y<7
Answers
Two buildings are 200 feet apart. The height of the taller building is 50 ft. The angle of depression from the top of the taller building to the top of the shorter building is 8°. What equation below will correctly determine the height (h) of the shorter building?
Answers
200 times tan 8 = x
28.10816694 = x
28 feet
x is the "missing" part of the shorter building
so now you take 50 feet and subtract it by 28 feet and you will have the height of the shorter building
50 - 28 = 22
the shorter building is 22 ft
How do I answer this equation? -3x+y=12. I'm supposed to find the function for it bt I don't know how. Can you guys help me out please
Answers
You can do this by adding 3x to both sides which would result in y = 3x + 12.
Also, math teachers typically want functions expressed in terms of f(x) instead of y. So, you can replace your y with that to get the final answer of f(x) = 3x + 12.
Answer:
[tex]y=3x+12[/tex]
Step-by-step explanation:
We have been given an equation in standard form [tex]-3x+y=12[/tex]. We are asked to write our given equation as a function.
We know that the function represents a relationship between input and output, where each input gives exactly single output.
To write our given equation as a function we need to convert our given equation into slope-intercept form of equation because in slope-intercept form, there is exactly one y output for each input of x.
[tex]y=mx+b[/tex], where,
m = Slope,
b = The y-intercept.
To convert our given equation into slope-intercept form, we need to get y on left side of our equation.
[tex]-3x+3x+y=3x+12[/tex]
[tex]y=3x+12[/tex]
Now our equation is in form of a function, where each value of x gives exactly one y value.
Graph y = sin(x) on the graphing calculator. Use the graph to determine the height of the barnacle with respect to water level as the boat has traveled the given distance. When the boat has traveled 7 meters, the height of the barnacle is approximately:
Answers
Answer:
The height of the barnacle is approximately is, 0.657 meters.
Step-by-step explanation:
Given the graph below of y =sin(x) ......[1]
Let y be the height of the barnacle and x be the distance the boat has traveled
Given: The boat has traveled 7 meters
i.e, x = 7 meters
to find the height y :
Substitute the value of x =7 meters in [1] we have;
y = sin(7) ≈0.657.
Therefore, the height of the barnacle is approximately is, 0.657 meters.
you can see also in the graph as shown below:
Answer:
1st is C 2nd is B
Step-by-step explanation:
Forty percent of the sheets of construction paper are secondary colors. There are 25 sheets of construction paper. How many of those sheets are secondary colors?
Answers
40% = 0.4
0.4(25) = 10
Total Number of sheets of construction paper= 25
The Percent of the sheets of construction paper that are secondary color = 40%
Percent means out of 100.To find number of secondary color sheet we find 40% of 25.
40%=[tex] \frac{40}{100} [/tex]
Number of sheets which are of secondary color=[tex] \frac{40}{100} of 25 =\frac{1000}{100} =10 [/tex]
Number of secondary color sheets =10.
Which certificate is the lowest level certification that a personal finance manager requires to sell mutual funds, trusts, and variable annuities?
Answers
Which certificate is the lowest level certification that a personal finance manager requires to sell mutual funds, trusts, and variable annuities?
The answer is series 6 certificate.
The series 6 certificate helps an individual to purchase or sell mutual funds, variable life insurance, municipal fund securities, variable annuities and unit investment trusts.
Answer:
The answer is option B - series 6 certificate.
Step-by-step explanation:
If a Play Station was bought for $450 after a 10% discount what was the original price of the Play Station?
Answers
90% = $450
1% = $5
100% = $5 x 100
100% = $500
The original price of the Play Station was $500.
If a Play Station was bought for $450 after a 10% discount. Therefore, The original price of the Play Station was $500.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
It is given that If it was bought after a 10% discount, means it was bought at 90% of the original price:
90% = $450
1% = $5
100% = $5 x 100
100% = $500
Therefore, The original price of the Play Station was $500.
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The radius of a circle is 1 foot. What is the length of a 45 degree arc
Answers
The length of a 45 degree arc on a circle with a radius of 1 foot is π/4 feet.
Explanation:The length of a 45 degree arc can be calculated using the formula for the circumference of a circle. The formula for the circumference is given by C = 2πr, where r is the radius of the circle. In this case, the radius is given as 1 foot. So, we can plug in the values to calculate the circumference as C = 2π(1) = 2π feet.
To find the length of a 45 degree arc, we need to find the fraction of the circumference that corresponds to a 45 degree angle. Since a full circle is 360 degrees, a 45 degree angle is 45/360 = 1/8 of the circumference. Therefore, the length of a 45 degree arc is 1/8 of the circumference, which is (1/8)(2π) feet.
Simplifying this expression, we get the length of a 45 degree arc as (1/8)(2π) = π/4 feet.
A circle has a radius of 12.6 cm.
What is the exact length of an arc formed by a central angle measuring 120°?
Enter your answer in the box. Express your answer using π .
Answers
[the length of a circumference]=2*pi*r
for r=12.6 cm
[the length of a circumference]=2*pi*(12.6)---------> 25.2*pi cm
this is the length for an arc of 360° (full circumference)
now calculate the length for an arc of 120° (applying a rule of three)
if 360°-----------------> 25.2*pi cm
120°---------------> X
X=120*25.2*pi/360----------> 8.4*pi
the answer is 8.4*pi
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
Answers
Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²
if 2π radians (full circumference) has an area of -----> 352.81 cm²
3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²
the answer is 105.84 cm²
Isaac deposits $1,500 in a savings account that earns 5% per year. How much interest will the money have earned at the end of 4 years? $60 $300 $450 $600
Answers
Hope this helps :)
Answer:
The interest earned at the end of 4 years is B) $300.
Step-by-step explanation:
Isaac deposits $1500 in a savings account.
Principle (P) = $1500
Rate of interest (r) = 5% = [tex]\frac{5}{100} = 0.05[/tex]
Time (t) = 4 years
We know that the simple interest formula (i) = P.r.t
Now plug in the given values in the above formula, we get
= 1500 times 0.05 times 4
= 75 times 4
Simple interest = $300
So, the interest earned at the end of 4 years is $300.
Answer is B) $300
WILL GIVE BRAINIEST!! I need your help!
Answers
as in Q#24:
(f o g)(x)= f(g(x)) but [tex] f(x)=(x+2)^{2}[/tex] so in case of f(g(x)) means that we have to eliminate each x in the function f(x) and substitute it with the value of g(x) as the following:
[tex] f(g(x))=(g(x)+2)^{2}[/tex] but [tex]g(x)=\sqrt{x}-2[/tex] so we have to substitute with the value of g(x) in the last equation
[tex] f(g(x))= (\sqrt{x}-2+2)^{2}=(\sqrt{x})^{2}=x[/tex]
by the same way (g o f)(x), it means that g is a function of f where f is a function of x.
so [tex] (g o f)(x)=g(f(x))=\sqrt{f(x)} -2 =\sqrt{(x+2)^2} -2 =x+2-2 =x [/tex]
If you followed the same procedure, u would figure out how to solve the rest urself.