Answer:
√4 * √15.
Step-by-step explanation:
√60
=√(4 * 15)
= √4 * √15
Answer:
our answer is [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form
as [tex]2*\sqrt{15}[/tex]
Step-by-step explanation:
[tex]\sqrt{60}[/tex]
We need to solve the above expression
Factors of 60:
1X60, 2X30, 3X20, 4X15, 5X12, 6X10
We need two factors one of which is perfect square
From the above factors only 4X15 full fills our condition as 4 is a perfect square
[tex]\sqrt{60}\\ =\sqrt{4 * 15}\\ We\,\,know\,\, \sqrt{a*b}= \sqrt{a}*\sqrt{b}\\ =\sqrt{4}*\sqrt{15}\\[/tex]
Solving, we get
[tex]2*\sqrt{15}[/tex]
So, our answer is [tex]\sqrt{4}*\sqrt{15}[/tex] or in simplified form
as [tex]2*\sqrt{15}[/tex]
three less than two times a number is 55. What’s the number ?
Let n be a number
2n - 3 = 55
Add 3 to both sides
2n + (-3 + 3) = 55 + 3
2n = 58
Divide 2 to both sides
2n/2 = 58/2
n = 29
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the solution of the equation below? Round your answer to
two decimal places.
10 times log(4x) = 25
Answer:
x ≅ 79.1
Step-by-step explanation:
10log(4x) = 25
2log(4x) = 5
log((4x)²) = 5
(4x)² = 10⁵
16x² = 100,000
x² = 6,250
x ≅ 79.1
(A) 79.06 is the correct answer!
If f(x) = -3 and g(x) = 3x2 + x - 6, find (f+ g)(x).
Answer:
3x^2+x-9
Step-by-step explanation:
f+g
means you are going to add whatever f equals to what g equals
so you have
(-3)+(3x^2+x-6)
Combine like terms
3x^2+x+(-3+-6)
3x^2+x+-9
or
3x^2+x-9
What is the measure of <B 98 108 118 128
Answer:
Step-by-step explanation:
By observation, you can see that the irregular polygon can be split into 4 triangles (see attached image). We know that the sum of the internal angles of 1 triangle is always 180 degrees. Hence the sum of all the internal angles of the polygon is,
180 degrees x 4 triangles = 720 degrees.
Therefore Angle B,
= sum of internal angles - sum of all other known angles
= 720 - (133 +102+117+90+170)
= 108 degrees.
The measure of angle B is 108 degrees.
What is angle sum property?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
We can divide the given polygon in split into 4 triangles.
Using, angle sum property,
The sum of the internal angles of triangle is always 180 degrees.
Hence the sum of all the internal angles of the polygon is,
=180 x 4 triangles
= 720 degrees.
Now, angle B
= 720 - (133 +102+117+90+170)
=720 -612
= 108 degrees.
Hence, angle B is 108 degrees.
Learn more about angle sum property here:
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What is the vertex of the graph of g(x) = |x – 8| + 6? A (6, 8) B (8, 6) C (6, –8) D (–8, 6)
its (8,6)
to get your x, you set what's in the absolute value to 0
so
x-8=0
then subtract 8 on both sides to get
x=8
then your y is just the number to the right of the absolute value so
y=6
Answer: Option B
(8, 6)
Step-by-step explanation:
By definition, for an absolute value function of the form
[tex]f (x) = | x-h | + k[/tex]
the vertex of f(x) will always be at the point
(h, k)
In this case we have the function of value ansoluto:
[tex]g(x) = |x - 8| + 6[/tex]
Therefore in this case
[tex]h=8\\k=6[/tex]
Finally the vertex of the function g(x) is: (8, 6)
The answer is the option B
Can someone help me plz.
Subtract 5x-6 from 7x-1
Answer:
2x+5
because you are subtracting it is basically multiplying (5x-6) by negative one so you have to distribute it out so you are basically adding (7x-1) and (-5x+6) by adding like terms you get 7x-5x= 2x and -1+6=5
so the answer is 2x+5
If two angels are congruent, then the sides opposite those angles are congruent. True or false.
Answer:
The statement is True
Step-by-step explanation:
The Isosceles Triangle Theorem states that;
If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. The converse of this statement is;
if two angles are congruent, then sides opposite those angles are congruent.
Answer:
True.
Step-by-step explanation:
To start with , remember that congruent angles have the same degree of measurement. For example, in an isosceles triangle, the base angles are congruent angles because they both measure 45°
The base angles theorem states that the sides next to congruent angles are equal.The statement is therefore True.If sides of the triangle are congruent, the opposite angles in the triangle are congruent .
f(-5) if f(x)=|x+1|
Answer:
The answer is 6.
Step-by-step explanation:
Plug in: f(-5)=|-5+1|
Because this an absolute problem -5 is positive within |x|
so therefore f(-5)= |6|
when the following fraction is reduced what will be the exponent on the 27 mn^ 3 / 51 m ^ 6 n
the answer is not 65 and not 4
Question 18(Multiple Choice Worth 5 points)
(09.07 MC)
Given a polynomial f(x), if (x - 1) is a factor, what else must be true?
A. f(0) = 1
b. f(1) = 0
c. f(-1) = 0
d. (0) = -1
Answer: Option b
[tex]f (1) = 0[/tex]
Step-by-step explanation:
For a function of the form
[tex]f (x) = ax ^ n + bx ^ {n-1} + ... + c[/tex]
Where n is the main exponent of the polynomial and a, b c are the coefficients of the variables then this polynomial can be written based on its factors as
[tex]f (x) = a (x-h) (x-k) (x-s)...[/tex]
Where [tex]x = h[/tex], [tex]x = k[/tex], [tex]x = s[/tex], ... are the points where [tex]f(x) = 0[/tex]
Therefore if for this case we know that
[tex](x-1)[/tex] is a factor of a polynomial function [tex]f (x)[/tex] then it is fulfilled that
[tex]f (1) = 0[/tex]
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1, 1/3, 1/9, 1/27, .....
a. -3
b. -1/3
c. 1/3
d. 3
Answer:
c.1/3
Step-by-step explanation:
To check, multiply 1/3 each time to each number. Note that the first number is 27:
27 x 1/3 = 27/3 = 9
9 x 1/3 = 9/3 = 3
3 x 1/3 = 3/3 = 1
1 x 1/3 = 1/3
etc.
This means that the common ratio decreases by the common multiple of 1/3.
~
The answer is C.
Hope this helps.
r3t40
what is the value of x?
Answer:
A. 68°
Step-by-step explanation:
sum of angles inside a triangle = 180°
75 + 37 + x = 180
x = 180 - 75 - 37
= 68°
The sum of angles inside a triangle is 180°. so option is A. 68°.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Given angles are; 75 and 37.
The sum of angles inside a triangle = 180°
75 + 37 + x = 180
x = 180 - 75 - 37
x = 68°
Learn more about the triangles;
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WY+ 4) - Y= 6 is a quadratic equation.
True
False
[tex]\bf (WY+4)-Y=6\implies \stackrel{\textit{nope}}{WY+4-Y=6}[/tex]
recall, a quadratic has a polynomial with a degree of 2.
Please help me! This is is rational function and I don’t know how to/ don’t remember how do this! How would I find and write the equation for it?
An answer is
[tex]\displaystyle f\left(x\right)=\frac{\left(x+1\right)^3}{\left(x+2\right)^2\left(x-1\right)}[/tex]
Explanation:
Template:
[tex]\displaystyle f(x) = a \cdot \frac{(\cdots) \cdots (\cdots)}{( \cdots )\cdots( \cdots )}[/tex]
There is a nonzero horizontal asymptote which is the line y = 1. This means two things: (1) the numerator and degree of the rational function have the same degree, and (2) the ratio of the leading coefficients for the numerator and denominator is 1.
The only x-intercept is at x = -1, and around that x-intercept it looks like a cubic graph, a transformed graph of [tex]y = x^3[/tex]; that is, the zero looks like it has a multiplicty of 3. So we should probably put [tex](x+1)^3[/tex] in the numerator.
We want the constant to be a = 1 because the ratio of the leading coefficients for the numerator and denominator is 1. If a was different than 1, then the horizontal asymptote would not be y = 1.
So right now, the function should look something like
[tex]\displaystyle f(x) = \frac{(x+1)^3}{( \cdots )\cdots( \cdots )}.[/tex]
Observe that there are vertical asymptotes at x = -2 and x = 1. So we need the factors [tex](x+2)(x-1)[/tex] in the denominator. But clearly those two alone is just a degree-2 polynomial.
We want the numerator and denominator to have the same degree. Our numerator already has degree 3; we would therefore want to put an exponent of 2 on one of those factors so that the degree of the denominator is also 3.
A look at how the function behaves near the vertical asympotes gives us a clue.
Observe for x = -2,
as x approaches x = -2 from the left, the function rises up in the positive y-direction, andas x approaches x = -2 from the right, the function rises up.Observe for x = 1,
as x approaches x = 1 from the left, the function goes down into the negative y-direction, andas x approaches x = 1 from the right, the function rises up into the positive y-direction.We should probably put the exponent of 2 on the [tex](x+2)[/tex] factor. This should help preserve the function's sign to the left and right of x = -2 since squaring any real number always results in a positive result.
So now the function looks something like
[tex]\displaystyle f(x) = \frac{(x+1)^3}{(x+2 )^2(x-1)}.[/tex]
If you look at the graph, we see that [tex]f(-3) = 2[/tex]. Sure enough
[tex]\displaystyle f(-3) = \frac{(-3+1)^3}{(-3+2 )^2(-3-1)} = \frac{-8}{(1)(-4)} = 2.[/tex]
And checking the y-intercept, f(0),
[tex]\displaystyle f(0) = \frac{(0+1)^3}{(0+2 )^2(0-1)} = \frac{1}{4(-1)} = -1/4 = -0.25.[/tex]
and checking one more point, f(2),
[tex]\displaystyle f(2) = \frac{(2+1)^3}{(2+2 )^2(2-1)} = \frac{27}{(16)(1)} \approx 1.7[/tex]
So this function does seem to match up with the graph. You could try more test points to verify.
======
If you're extra paranoid, you can test the general sign of the graph. That is, evaluate f at one point inside each of the key intervals; it should match up with where the graph is. The intervals are divided up by the factors:
x < -2. Pick a point in here and see if the value is positive, because the graph shows f is positive for all x in this interval. We've already tested this: f(-3) = 2 is positive.-2 < x < -1. Pick a point in here and see if the value is positive, because the graph shows f is positive for all x in this interval.-1 < x < 1. Pick a point here and see if the value is negative, because the graph shows f is negative for all x in this interval. Already tested since f(0) = -0.25 is negative.x > 1. See if f is positive in this interval. Already tested since f(2) = 27/16 is positive.So we need to see if -2 < x < -1 matches up with the graph. We can pick -1.5 as the test point, then
[tex]\displaystyle f(-1.5) = \frac{\left(-1.5+1\right)^3}{\left(-1.5+2\right)^2\left(-1.5-1\right)} = \frac{(-0.5)^3}{(0.5)^2(-2.5)} \\= (-0.5)^3 \cdot \frac{1}{(0.5)^2} \cdot \frac{1}{-2.5}[/tex]
We don't care about the exact value, just the sign of the result.
Since [tex](-0.5)^3[/tex] is negative, [tex](0.5)^2[/tex] is positive, and [tex](-2.5)[/tex] is negative, we really have a negative times a positive times a negative. Doing the first two multiplications first, (-) * (+) = (-) so we are left with a negative times a negative, which is positive. Therefore, f(-1.5) is positive.
Camille is preparing for her English test by typing up the notes she recorded in the margins of her 98-page workbook. She already started typing her notes, and got through the first 14 pages. If Camille types for x hours at a rate of 21 pages per hour, which equation represents the number of pages she has typed, and how many hours will it take to complete the task?
21x + 98 = 14; x = 4
21x = 14 + 98; x = 5
21x + 14 = 98; x = 4
21x - 14 = 98; x = 5
Reset
Submit
Answer:
The correct answer is: 21x + 14 = 98; x = 4.
Step-by-step explanation:
She needs to type the notes she recorded in her 98-page workbook. If whe types x hours at a rate of 21 pages per hour, and 14 pages are already done. Then the equation is:
21x + 14 = 98;
Now, the number of hours she will take to complete the task can be found by solving for 'x':
21x = 98 - 14
21x = 84
x = 4.
Therefore, the correct option is: 21x + 14 = 98; x = 4.
Answer:
21x + 14 = 98; x = 4
Step-by-step explanation:
Camille has already typed notes from the first 14 pages of her workbook, and she types for x hours at a rate of 21 pages per hour. An expression for the one side of the equation needs to represent the total number of pages she has typed in terms of x. The number of pages Camille has typed after x hours is represented by the expression 21x + 14.
The workbook has a total of 98 pages. Thus, the other side of the equation which represents the number of pages Camille has typed after x hours is 98.
Hence, the equation that represents the number of pages she has typed after x hours is 21x + 14 = 98.
Solve the equation to determine how many hours it will take Camille to complete the task.
So, x = 4. Therefore, it takes Camille 4 hours to complete the task.
Answer question please
Answer:
X=30, Scalene
Step-by-step explanation:
A circle is 360, The triangle is in the circle.
Part A:3x+30+2x+20+5x+10=360
10x+60=360
-60=-60
10x=300
x=30
Part B:Side BA is 3(30)+30=120
Side BC is 2(30)+30=90
Side AC is 5(30)+10=160
All three sides are unequal
Use the distributive property to rewrite the expression -1/2(4x-16y+10z) .
Answer:
-2x + 8y - 5z
Step-by-step explanation:
-1/2*4x = -2x
-1/2 * - 16y = 8y
-1/2 * 10z = - 5z
Combine
-2x + 8y - 5z
If you break the question apart like this, you will never get confused by what the signs do. What is left for signs is what you put in the answer.
there 240 students in the middle school band. The band director is dividing the students into groups of 10. Into how many groups will the band director divide the students?
Answer:
Step-by-step explanation:
1 group = 10 students
x group = 240 students.
1/x = 10/240 Cross multiply
10x = 240 Divide by 10
10x/10=240/10 Do the division
x = 24
A grid shows the positions of a subway stop and your house. The subway stop is located at (-5,2) and your house is located at (-9,9). what is the distance, to the nearest unit, between your house and the subway stop?
Answer:
8
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, 2) and (x₂, y₂ ) = (- 9, 9)
d = [tex]\sqrt{(-9+5)^2+(9-2)^2}[/tex]
= [tex]\sqrt{(-4)^2+7^2}[/tex]
= [tex]\sqrt{16+49}[/tex] = [tex]\sqrt{65}[/tex] ≈ 8 ( nearest unit )
Answer: The required distance between my house and the subway stop is 8 units.
Step-by-step explanation: Given that a grid shows the positions of a subway stop and my house. The subway stop is located at (-5,2) and my house is located at (-9,9).
We are to find the distance, to the nearest unit, between my house and the subway stop.
We will be using the following formula :
Distance formula : The distance between the points (a, b) and (c, d) is given by
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points (-5, 2) and (-9, 9) is given by
[tex]D\\\\=\sqrt{(-9-(-5))^2+(9-2)^2}\\\\=\sqrt{(-9+5)^2+7^2}\\\\=\sqrt{4^2+49}\\\\=\sqrt{16+49}\\\\=\sqrt{65}\\\\=8.06.[/tex]
Rounding to the nearest units, we get
D = 8 units.
Thus, the required distance between my house and the subway stop is 8 units.
A vending machine automatically pours coffee into cups. The amount dispensed is normally distributed with a mean of 7.4 oz and a standard deviation of0.26 oz. Find the probability the machine will overflow an 8-oz cup.
Answer:
16%
Step-by-step explanation:
100% - 68% = 32%
32%/2 = 16%
Use substitution to write an equivalent quadratic equation.
(3x + 2)2 + 7 (3x + 2) – 8 = 0
-
u2 + 74 - 8 = 0, where u = (3x + 2)2
u2 + 7u - 8 = 0, where u = 3x + 2
u2 + 70 - 8 = 0, where u = 7(3x + 2)
lu² +4-8=0
What’s the answer?
For this case we can make a change of variable, to obtain a quadratic equation of the form:
[tex]ax ^ 2 + bx + c = 0[/tex]
Making the change:[tex]u = 3x + 2[/tex]
Substituting the change we have:
[tex]u ^ 2 + 7u-8 = 0[/tex]
Thus, the correct option is:[tex]u ^ 2 + 7u-8 = 0[/tex]where [tex]u = 3x + 2[/tex]
Answer:
Option B
Answer:
second option: [tex]u^{2}+7u-8=0[/tex]
Step-by-step explanation:
We have the equation given:
[tex](3x+2)^{2}+7(3x+2)-8=0[/tex]
We can replace the variable in the quardatic equation.
So,
[tex]Putting\\u=3x+2[/tex]
Putting u in place of 3x+2 will give us:
[tex](u)^{2}+7(u)-8=0[/tex]
So the answer is:
[tex]u^{2}+7u-8=0[/tex]
So, the second option is correct ..
Billy is helping to make pizzas for a school function. He's made 25 pizzas so far. His principal asked him to make at least 30 pizzas but no more than 75. Solve the compound inequality and interpret the solution.
30 ≤ x + 25 ≤ 75
Answer: Number of pizzas would be less than 5 but not more than 50.
Step-by-step explanation:
Since we have given that
Number of pizzas so far = 25
His principal asked him to make at least 30 pizzas but no more than 75.
According to question, we have
30 ≤ x + 25 ≤ 75
First we subtract 25 from both the sides:
[tex]30-25\leq x \leq 75-25\\\\=5\leq x\leq 50[/tex]
Hence, number of pizzas would be less than 5 but not more than 50.
The solution to the compound inequality is 5 x 50.
The compound inequality given is 30 x 25 75, where x represents the number of additional pizzas Billy needs to make to satisfy the principal's request. To solve for x, we need to isolate x in the inequality.
First, we subtract 25 from all parts of the compound inequality to shift the 25 pizzas already made to the other side of the inequality. This gives us:
30 - 25 x + 25 - 25 75 - 25
Simplifying the inequality, we get:
5 x 50
This means that Billy needs to make at least 5 more pizzas to reach the minimum requirement of 30 pizzas (since 25 + 5 = 30) and no more than 50 additional pizzas to not exceed the maximum allowed number of 75 pizzas (since 25 + 50 = 75).
Therefore, the number of additional pizzas Billy should make is any integer value between 5 and 50, inclusive. This ensures that the total number of pizzas made will be within the principal's specified range of 30 to 75 pizzas."
Which polynomial is in standard form?
4xy+ 3x^3 5y - 2xy +4x^7y^9
2x+y^7+7y-8x²y^5– 12xy^2
5x^5 - 9x^2y^2 - 3xy^3 + 6y^5
7x^7y^2+5x^11y^5-3xy^2+2 ASAP PLZ
Answer:
option 3 is the answer
Step-by-step explanation:
A polynomial in two variables is said to be in standard form if exponent of one variable is keep decreasing and another variable keep increasing
only option 3 follows it
As here exponent of x start from 5 and decreases up to 0
and exponent of y start from 0 and keep increasing up to 5
rest of the option do not follow this rule
Answer:
c)5x^5 - 9x^2y^2 - 3xy^3 + 6y^5
Step-by-step explanation:
for a sample size of 140 and a proportion of 0.3 what is the standard deviation of the normal curve that can be used to approximate the binomial probability histogram? Round your answer to three decimal places.
Answer:
The answer is b.
Step-by-step explanation:
Have a great day!!
Which of the following is most likely the next step in the series?
Answer:
A
Step-by-step explanation:
A family travels, by plane, five hundred miles from their city to a beach town. Then they take a taxi from the airport to the hotel at the beach. When they ask the driver how far the airport is from the hotel, he tells them twenty kilometers. What is the approximate total distance, in miles, the family traveled? Recall that 1 kilometer is about 0.62 miles.
Answer:
512.4 miles
Step-by-step explanation:
The distance from city to beach town = 500 miles
Distance from airport to hotel = 20 kilometers
In order to find the total distance we have to convert the kilometers in miles to bring both quantities in same unit
So,
1 kilometer = 0.62 miles
20 kilometers = 20*0.62 =12.4 miles
As both the quantities are in same unit,
The total distance = Distance from city to beach town + distance from airport to hotel
= 500 + 12.4
= 512.4 miles
Hence, total distance covered by them is 512.4 miles ..
Which of the following is a solution for the absolute value inequality |x- 6|<4
[tex]\bf |x-6|<4\implies \begin{array}{llll} +(x-6)<4\\ -(x-6)<4 \end{array}\implies \begin{cases} x-6<4\implies &\boxed{x<10}\\ \cline{1-2} -(x-6)<4\\ \stackrel{notice}{x-6\stackrel{\downarrow }{>}-4}\implies &\boxed{x>2} \end{cases}[/tex]
Which unit of measure would be appropriate for the volume of a sphere with a
radius of 2 meters?
O
A Square meters
B. Cubic meters
O
C. Meters
O
D. Centimeters
units like radius, height, width, length or segments are single units, like meter or feet.
areas are double units, so they'd be in say meter² or feet².
volumes are triple units, namely like meter³ or feet³.
Answer:
The unit of measuring volume of the sphere is cubic meter.
Step-by-step explanation:
Given : Sphere with a radius of 2 meters.
To find : Which unit of measure would be appropriate for the volume of sphere.
Solution : We have given Radius = 2 meter .
Volume = [tex]\frac{4}{3}\pi (radius)^{3}[/tex].
Volume = [tex]\frac{4}{3}\pi (2 meter)^{3}[/tex].
Volume of sphere = [tex]\frac{32}{3}\pi[/tex] meter³ .
Therefore, The unit of measuring volume of the sphere is cubic meter.
f(5)=2, find f^-1(2)
Answer: 5
Step-by-step explanation:
f(5) = 2 means that when x = 5, y = 2 --> (5, 2)
f⁻¹(2) is the inverse (when the x and y are swapped) --> when x = 2, y = 5