1.
[tex]
2\sqrt{4}\cdot3\sqrt{8} \\
2\cdot3\sqrt{4\cdot8} \\
6\sqrt{32} \\
6\sqrt{4^2\cdot2} \\
6\cdot4\sqrt{2} \\
\boxed{24\sqrt{4}} \\
[/tex]
2.
[tex]
2\sqrt{4}+3\sqrt{8} \\
\boxed{4+3\sqrt{8}}
[/tex]
Hope this helps.
r3t40
Find the value of x.
a 25
b40
c45
d60
The graph below is an be example of which type of function
Please help! TRIG! I really need someones help. 6 points!!!
We're looking for a model of the form
[tex]y=a\cos(b(x-c))+d[/tex]
[tex]a[/tex] is the amplitude, equal to half the difference between the maximum and minimum hours of daylight:
[tex]a=\dfrac{15.3-9.1}2=3.1[/tex]
[tex]b[/tex] determines the period of the cosine function. The period itself is [tex]\dfrac{2\pi}b[/tex], which we want equal to 365, so that
[tex]365=\dfrac{2\pi}b\implies b=\dfrac{2\pi}{365}[/tex]
(so that the value in the second box should be 365)
[tex]c[/tex] determines the horizontal shift of the cosine function. We'll come back to this in a moment.
[tex]d[/tex] represents the vertical shift of the function. The standard function is bounded between -1 and 1:
[tex]-1\le\cos x\le1[/tex]
Our new function has an amplitude of 3.1, so that
[tex]-3.1\le3.1\cos x\le3.1[/tex]
We want the range of values to fall between 15.3 and 9.1, so we want to pick [tex]d[/tex] such that
[tex]\begin{cases}-3.1+d=9.1\\3.1+d=15.3\end{cases}\implies d=12.2[/tex]
So the current model is
[tex]y=3.1\cos\left(\dfrac{2\pi}{365}x\right)+12.2[/tex]
[tex]c[/tex] represents the horizontal shift of the function. [tex]x=0[/tex] represents the first day of the year, which according to the current model tells us we should expect [tex]3.1\cos0+12.2=15.3[/tex] hours of daylight on the first day of the year. But this conflicts with the data. We want this maximum to occur on the 172nd day of the year, so we shift the model by this amount, and the model is
[tex]y=\boxed{3.1}\cos\left(\dfrac{2\pi}{\boxed{365}}}(x-\boxed{172})\right)+\boxed{12.2}[/tex]
an airplane is traveling at a constant speed of 600 miles per hour. How many feet does it travel in 10 seconds? Remember that 1 mile is 5280 feet.
The answer is:
The airplane will travel 8800 feet in 10 seconds.
Why?It's a conversion exercise, we need to be careful in order to solve it with no mistakes.
First:
We need to remember that 1 hour is equal to 60 minutes, and 1 minute is equal to 60 seconds, so, to calculate how many seconds are in one hour, we need to perform the following operation:
[tex]Time=1hour*\frac{60minutes}{1hour}*\frac{60seconds}{nminute}=3600seconds[/tex]
Second:
We need to convert from miles to feet, we need to remember that 1 mil is equal to 5280 feet.
So, solving we have:
[tex]Speed=600\frac{miles}{hour}*\frac{1hour}{3600seconds}*\frac{5280ft}{1mile}=880\frac{ft}{seconds}[/tex]
Now, calculating how many feet does it travel in 10 seconds, we have:
[tex]distance=speed*time\\\\distance=880\frac{ft}{seconds}*10seconds=8800ft[/tex]
We have that the airplane will travel 8800 feet in 10 seconds.
Have a nice day!
Which of the following is not a postulate of Euclidean geometry?
Answer:
B just took it.
Step-by-step explanation:
The fact that all right angles can be bisected is not a postulate of Euclidean geometry.
Euclidean geometryEuclidean geometry is the classical form of geometry first described by Euclid in his work Elements. He gathered all the mathematical knowledge known to the Greeks at the time, today his work presents itself as the first known axiomatization in the history of mathematics.
Originally, it was only cultivated on a plane and in three-dimensional space, at the same time linking it with the physical world that it was supposed to describe, thus preventing the possibility of studying other varieties of geometry.
Learn more about Euclidean geometry in https://brainly.com/question/4637858
Match each function formula with the corresponding transformation of the parent function y=-x2-1.
Reflected across the y-axis
Translated right by 1 unit
Translated down by 1 unit
Translated up by 1 unit
Reflected across the x-axis
Translated left by 1 unit
1. y=-x2-1
2. y=-(x - 1)2 - 1
3. y= x2 +1
4. y=-x2
5. y=-(x+ 1)2 - 1
6. y=-x2 - 2
Answer:
Since, when a function f(x) is reflected across x-axis then resultant function is -f(x), and reflected across y-axis then resultant function is f(-x),
Also, In translation of f(x),
If the transformed function is,
g(x) = f(x+a)
If a is positive then function is shifted a unit left,
If a is negative then function is shifted a unit right,
While, if transformed function is,
g(x) = f(x) + a
If a is positive then function is shifted a unit up,
If a is negative then function is shifted a unit right,
Here, the given parent function is,
[tex]y=-x^2-1[/tex]
Hence, by the above explanation we can match the unction formula with the corresponding transformation, shown below,
1. [tex]y=-x^2-1[/tex] : Reflected across the y-axis
2. [tex]y=-(x - 1)^2 - 1[/tex] : Translated right by 1 unit
3. [tex]y= x^2 +1[/tex] : Reflected across the x-axis
4.[tex]y=-x^2[/tex] : Translated up by 1 unit
5. [tex]y=-(x+ 1)^2 - 1[/tex] : Translated left by 1 unit
6. [tex]y=-x2 - 2[/tex] : Translated down by 1 unit
HELP PLEASE ANSWER!!!! (25 POINTS!!!)
What does it mean for an equation to have no solution or infinitely many solutions?
Answer:
An equation to have no solution means that the system of equations do not intersect at all and therefore will not have any solutions. If an equation has indefinite many solutions then the system of equations will have the same line since they are intersecting each other
Step-by-step explanation:
Explain why the equation 6|x| + 25 = 15 has no solution. When one solves, they arrive at a step where |x| is equal to a negative number. Since | x| can never be negative, there is no solution. When one solves, they arrive at a step where x is equal to a negative number. Since x can never be negative inside of the absolute value bars, there is no solution. The statement is false. There is a solution. When one solves, they arrive at a step where |x| is equal to a fraction that may not be represented as an integer. Since | x| must be an integer, there is no solution.
Answer:
Step-by-step explanation:
6|x| + 25 = 15
6|x| = 15 - 25
6|x| = -10
|x| = - [tex]\frac{10}{6}[/tex]
By definition, the absolute value of any number must be positive, hence | x| can never be negative, there is no solution.
-1/4x+5=3/4. I can't get access to the answer to this question! And, my request on "contact us" will not go through!!
For this case we must solve the following linear equation:
[tex]- \frac {1} {4} x + 5 = \frac {3} {4}[/tex]
Subtracting 5 from both sides of the equation we have:
[tex]- \frac {1} {4} x = \frac {3} {4} -5\\- \frac {1} {4} x = \frac {3-20} {4}\\- \frac {1} {4} x = - \frac {17} {4}[/tex]
Multiplying by 4 on both sides of the equation:
[tex]-x = -17[/tex]
Multiplying by -1 on both sides of the equation we have:
[tex]x = 17[/tex]
Answer:
[tex]x = 17[/tex]
Answer: [tex]x=17[/tex]
Step-by-step explanation:
You need to solve for the variable "x":
The first step is to subtract 5 from both side of the equation, then:
[tex]-\frac{1}{4}x+5-5=\frac{3}{4}-5\\\\-\frac{1}{4}x=-\frac{17}{4}[/tex]
The final step is to multiply both sides of the equation by -4.
Therefore, the value of the variable "x" is the following:
[tex](-4)(-\frac{1}{4}x)=(-\frac{17}{4})(-4)\\\\x=17[/tex]
Multiply.
(x^2+ 3x + 2)•(2x^2+ 3x - 1)
Answer:
see explanation
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x²(2x² + 3x - 1) + 3x(2x² + 3x - 1) + 2(2x² + 3x - 1)
Distribute all 3 parenthesis
= 2[tex]x^{4}[/tex] + 3x³ - x² + 6x³ + 9x² - 3x + 4x² + 6x - 2
Collect like terms
= 2[tex]x^{4}[/tex] +9x³ + 12x² + 3x - 2
Answer:
2x^4+9x^3-7x^2-6x-2
Step-by-step explanation:
=2x^4+3x^3-x^2+6x^3+9x^2-3x-x^2-3x-2
Simplify
=2x^4+9x^3-7x^2-6x-2
0 is in quadrant III and cos^2 0=1/4
Answer:
θ = 240
and
cos(θ) = -0.5
Step-by-step explanation:
Theta is in the third quadrant, that meansit goes from 180 to 270 degrees
Then,
cos^2 (θ) =1/4
cos (θ) = ± 1/2
θ = arccos(0.5)
θ = 60
But in the third quadrant
θ = 180 + 60 = 240
θ = 240
and
cos(θ) = -0.5
What is the area of the polygon given below?
Answer:
D.
Step-by-step explanation:
To find this area, we can break it up into two rectangles, one with dimensions of 4x19 and another of 24x11. All we have to do is find the areas of both rectangles and add them together!
Since 4*19=76 and 11*24=264, we get D. 340 square units as our answer.
For this case we have that the area of the figure is given by the sum of the areas of two rectangles. The area of a rectangle is given by:
[tex]A = a * b[/tex]
Where:
a, b: They are the sides of the rectangle
[tex]A_ {1} = 24 * 11\\A_ {1} = 264[/tex]
On the other hand:
[tex]A_{2} = 4 * (4 + 11 + 4) = 4 * 19 = 76[/tex]
Thus, the total area is:
[tex]A_ {t} = 264 + 76\\A_ {t} = 340[/tex]
The total area is 340 square units
Answer:
Option D
which unit of measure would be appropriate for the area of a picture that is 20 centimeters tall and 15 centimeters wide
Answer:300 cm2(in the case of rectangle)
Step-by-step explanation:
The question is ambiguous.Something is missing.what is the shape of the object is not told here.
But if you consider it a "rectangle",the angles will be right angles.
area of a rectangle=length×breadth
=20cm×15cm
=300 centimetre2
Answer: square centimeters
Step-by-step explanation:
Hi, the answer to the question is square centimeters.
The lengths of the picture are in centimeters. So, when you calculate the area of the picture that is a triangle you obtain square centimeters.
Mathematically speaking:
20cm x 15 cm = 300 square centimeters
By multiplying the same unit you obtain the square unit.
Feel free to ask for more if it´s necessary or if you did not understand something.
Determine the output, f(x), if the input to the function box below is 8.
f(x)=3x-1
Answer:
The output is 23
Step-by-step explanation:
we know that
f(x) ----> is the output
x ----> is the input
we have that
f(x)=3x-1
For x=8 (input)
Find the value of f(x) (output)
f(8)=3(8)-1=23
The output is 23
Which quadratic function has Vertex (-1,4) and passes through (4,19)
HELP
Answer:
[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]
Step-by-step explanation:
The equation of a quadratic function in vertex form is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h,k) is the vertex.
It was given in the question that the vertex of the parabola is (-1,4).
When we substitute the vertex into the formula we get:
[tex]f(x)=a(x+1)^2+4[/tex]
The parabola also passes through (4,19) hence it must satisfy its equation.
[tex]19=a(4+1)^2+4[/tex]
[tex]19-4=a(5)^2[/tex]
[tex]15=25a[/tex]
We divide both sides by 25 to get:
[tex]a=\frac{15}{25}= \frac{3}{5}[/tex]
Hence the quadratic function is:
[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]
Please help me!!!!!!!!
Answer:
(2,1)
Step-by-step explanation:
So the first thing you want to do is substitute. You want to plug in the equation for y in for the y value above.
So you would do 3x+4(x-1)=10. As you can see we took the bottom equation and put it in for the top equation. We did this so we only have x s and no y s.
Now you would solve. You would distribute first. You would get 3x+4x-4=10. Now combine like terms. 3+4 is 7 so you would get 7x-4=10.The next thing you want to do is get the 7x by itself so move the 4.You would get 7x=14. Now divided both sides by 7 because you want to get the x by itself.
You would get x=2. Now for the y value just plug it in for an equation above. The easier one would be y=x-1. y=(2)-1 will equal 1. You write your final answer in (x,y) style. Your final answer will then be (2,1)
Answer:
A. (2, 1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+4y=10&(1)\\y=x-1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\3x+4(x-1)=10\qquad\text{use the distributive property}\\3x+4x-4=10\qquad\text{add 4 to both sides}\\7x=14\qquad\text{divide both sides by 7}\\x=2\\\\\text{put the value of x to (2):}\\\\y=2-1\\y=1[/tex]
The graph represents the distribution of the number of questions answered correctly on a 50-question math test.
what is the standard deviation of the data ?
4
8
12
14
Answer:
The answer I believe is 4.
Step-by-step explanation:
Answer: the answer is 4
Step-by-step explanation:
;)
Estimate the solution of the equation x – 8.1 = 5.3 to the nearest whole number.
Answer:
13 is your answer
Step-by-step explanation:
x - 8.1 = 5.3
+8.1 +8.1 Add 8.1 to both sides
x = 13.4
Which if you want the whole number i'd be 13, Because if your rounding the 3, 4 won't bump the 3 up any because 4 isn't greater than 5.
Hope my answer has helped you!
Answer:
x=13
Step-by-step explanation:
A quick rough estimate could be obtained by adding 8 to both sides:
x = 5.3 + 8, or x = 13 (approx.)
The exact solution is x = 8.1 + 5.3 = 13.4 (which rounds down to 13).
Can anyone help me with this GEOMETRY
Answer:
B.) 83.7758
Step-by-step explanation:
Answer:
83.75 cubic inches
Step-by-step explanation:
We are given the diameter of a cone 8 inches, and height 5 inches and we are to find the volume of this cone.
(diameter is 8 inches so radius will be 4 inch)
We know that the volume of a cone is given by:
Volume of cone = [tex] \pi r ^ 2 \frac { h } { 3 } [/tex]
Substituting the given values in the above formula:
Volume of cone = [tex] \pi \times 4 ^ 2 \times \frac { 5 } { 3 } [/tex] = 83.75 cubic inches
(diameter is 8 inches so radius will be 4 inches)
what values of c and d make the equation true?
Answer:
Third option.
Step-by-step explanation:
You need to cube both sides of the equation. Remember the Power of a power property:
[tex](a^m)^n=a^{mn[/tex]
[tex]\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d[/tex]
According to the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)[/tex]
Then. simplifying you get:
[tex]162x^cy^5=162x^6y^{(3+d)}[/tex]
Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6, then the exponent of "x" on the left side must be 6. Therefore:
[tex]c=6[/tex]
You can notice that the exponent of "y" on the left side is 5, then the exponent of "x" on the left side must be 5 too. Therefore "d" is:
[tex]3+d=5\\d=5-3\\d=2[/tex]
M<9= 6x and m<11=120. Find the value of x so that line c is parallel to line d.
Answer:
The value of x is 20°
Step-by-step explanation:
we know that
m∠ 9 and m∠ 11 are corresponding angles
If line c is parallel to line d
then
m∠ 9 = m∠ 11
Substitute
6x=120°
x=20°
Answer:
20
Step-by-step explanation:
:))
please help thank you
Answer:
(-5,-2)
Step-by-step explanation:
because the point is 5 to the left of the origin and 2 down from the origin
Each person in a group of 12 has one pet. Three people have a cat, 2 people have a dog, and the rest have a bird. What is the probability of a person having a cat or a dog?
Answer:
63 % for cats and 37 % for dogs
Step-by-step explanation:
How many solution 6x-4 = x+6 has
Answer:
1 solution
Step-by-step explanation:
This is a linear equation and has one solution
6x - 4 = x + 6 ( subtract x from both sides )
5x - 4 = 6 ( add 4 to both sides )
5x = 10 ( divide both sides by 5 )
x = 10 ← only 1 solution
What is the y-intercept of f(x) = 3^x+2?
A. (9, 0) B. (0, 9) C. (0, -9) D. (9, -9)
Answer:
Step-by-step explanation:
This is not a linear function. This is actually an exponential function.
Answer:
A
Step-by-step explanation:
trust me bro
The simplified formula for calculating monthly lease payment is:
A. MSRP + lease factor
B. depreciation fee + finance fee
C. MSRP - down payment
D. acquisition fee + down payment
The simplified formula for calculating the monthly lease payment for a car is the sum of the depreciation fee and the finance fee. These are calculated based on the car's initial cost, residual value, and the lease factor.
Explanation:In the context of car leasing, the simplified formula used to calculate the monthly lease payment is: depreciation fee + finance fee. The depreciation fee is calculated by subtracting the car's expected residual value at the end of the lease from its initial cost (MSRP) and then dividing this by the number of months in the lease. The finance fee is calculated as the sum of the MSRP and the residual value, multiplied by the lease factor or money factor which is essentially the interest rate.
Learn more about Lease Payment Calculation here:https://brainly.com/question/33942983
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draw a pentagon. Explain how you knew the number of sides and angles to draw.
Answer:
A pentagon is a 5 sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably a math equipment.
Step-by-step explanation:
A pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.
What is the pentagon?A pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape.
In geometry, it is considered as a is a five-sided polygon with five straight sides and five interior angles, which add up to 540°.
A pentagon shape is a plane figure, or a flat (two-dimensional) 5-sided geometric shape.
The measure of each angle of a regular pentagon is given by the below formula. The measure of the central angle a regular pentagon makes a circle, i.e. total measure is 360°.
Hence, a pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.
Learn more about the pentagon here;
https://brainly.com/question/11759904
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which value of c is a solution to the equation c= 2c -4
Answer:
d
Step-by-step explanation:
im very smart (def did not get it wrong and it showed me the answer)
A specific park is rectangular-shaped and has a 3 mile-perimeter. The length is 4 times the width. What are the dimensions of the park?
Answer:
The length of the rectangular park is [tex]1.2\ mi[/tex] and the width of the rectangular park is [tex]0.3\ mi[/tex]
Step-by-step explanation:
Let
x ----> the length of the rectangular park
y ---> the width of the rectangular park
we know that
The perimeter is equal to
[tex]P=2(x+y)[/tex]
[tex]P=3\ mi[/tex]
so
[tex]3=2(x+y)[/tex] -----> equation A
[tex]x=4y[/tex] ----> equation B
substitute equation B in equation A and solve for y
[tex]3=2(4y+y)[/tex]
[tex]3=10y[/tex]
[tex]y=0.3\ mi[/tex]
Find the value of x
[tex]x=4(0.3)=1.2\ mi[/tex]
therefore
The length of the rectangular park is [tex]1.2\ mi[/tex] and the width of the rectangular park is [tex]0.3\ mi[/tex]
Final answer:
To determine the dimensions of a park with a 3-mile perimeter where the length is 4 times the width, we set up the equation 3 = 2l + 2w, substitute l = 4w into it, and solve for width and length. The calculations show the park is 1.2 miles long and 0.3 miles wide.
Explanation:
The student has asked for help to find the dimensions of a rectangular-shaped park with a 3-mile perimeter where the length is 4 times the width. To solve this, we will use the formula for the perimeter of a rectangle P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Since we know the perimeter is 3 miles, we can set up the equation 3 = 2l + 2w. Because the length is 4 times the width, we can also say that l = 4w. Substituting into the first equation, we get 3 = 2(4w) + 2w, which simplifies to 3 = 10w. To find the width, we divide both sides by 10, resulting in w = 0.3 miles. Then, using l = 4w, we find that the length l is 1.2 miles.
Therefore, the dimensions of the park are 1.2 miles long and 0.3 miles wide.
Based on the survey, what is the probability that a person chosen at random is a diabetic patient or an eye patient
First, you must find the total number of people. Add together 32, 54, 78, 112, and 96 to get 372. Next, add the number of diabetic patients with the number of patients with eye problems (54 + 112 = 166).
Your fraction is now 116/372. Simplify this to get your answer, 29/93 or 0.31.