ANSWER
x=3
EXPLANATION
The given equation is:
[tex] {x}^{3} - 27 = 0[/tex]
We add 27 to both sides of the equation to get:
[tex] {x}^{3} = 27[/tex]
We write 27 as number to exponent 3.
[tex]{x}^{3} = {3}^{3} [/tex]
The exponents are the same.
This implies that, the bases are also the same.
Therefore
[tex]x = 3[/tex]
The answer is:
The equation has only one root (zero) and its's equal to 3.
[tex]x=3[/tex]
Why?We are working with a cubic equation, it means that there will be three roots (zeroes) for the equation.
To solve the problem, we need to remember the following exponents and roots property:
[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]
[tex](a^{b})^{c}=a^{b*c}[/tex]
So, we are given the equation:
[tex]x^{3}-27=0[/tex]
Isolating x we have:
[tex]x^{3}=27\\\\\sqrt[3]{x^{3}}=\sqrt[3]{27}\\\\x^{\frac{3}{3} }=\sqrt[3]{(3)^{3} }\\\\x^{\frac{3}{3} }=3^{\frac{3}{3} }\\\\x=3[/tex]
Hence, we have that the equation has only one root (zero) and its's equal to 3.
Have a nice day!
Help me with these 2 problems
Answer:
Part a) The width of parking lot is 87m.
Part b) The length of rectangular pool is 94 m
Step-by-step explanation:
a) The area of parking lot Area= 8439 m^2
Length of Parking Lot = Length = 97 m
Width of Parking Lot = Width= ?
Area of rectangle = Length * Width
Putting the values,and finding width,
8439 = 97 * Width
=> Width = 8439/97
=> Width = 87 m
So, The width of parking lot is 87m.
b) Perimeter of rectangular pool = Perimeter= 344 m
Width of rectangular pool = Width = 78 m
Length of rectangular pool = Length = ?
The formula for perimeter is:
Perimeter = 2*(Length + Width)
Putting values in the formula:
344 = 2*(Length + 78)
344/2 = Length + 78
172 = Length + 78
=> Length = 172 - 78
Length = 94 m
So, the length of rectangular pool is 94 m.
determine if -1, 1, 4, 8 is a geometric sequence
ANSWER
No, because there is no common ratio
EXPLANATION
The given sequence is
-1, 1, 4, 8
If this sequence is geometric, then there should be a common ratio among the consecutive terms.
[tex] \frac{1}{ - 1} \ne \frac{4}{1} \ne \frac{8}{4} [/tex]
Hence the sequence
-1, 1, 4, 8
is not a geometric sequence.
Answer:
The sequence is not a geometric sequence
Step-by-step explanation:
In a geometric sequence you find the following term multiplying the current by a fixed quantity called the common ratio.
To prove if a sequence is geometric we need to check if the ratio is consistent across the sequence. To check for the ratio we use the formula:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
were
[tex]r[/tex] is the ratio
[tex]a_n[/tex] is the current term
[tex]a_{n-1}[/tex] is the previous term
Let's star with 1, so [tex]a_n=1[/tex] and [tex]a_{n-1}=-1[/tex]
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{1}{-1}[/tex]
[tex]r=-1[/tex].
Now let's check 4 and 1, so [tex]a_n=4[/tex] and [tex]a_{n-1}=1[/tex]
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{4}{1}[/tex]
[tex]r=4[/tex]
Since the ratios between two pair of numbers are different, we can conclude that the sequence is not geometric.
what is the y-coordinate of the image of P(3,-4) after a reflection in the x-axis?
Answer:
[tex]\boxed{4}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign.
Thus, the y-coordinate becomes [tex]\boxed{\textbf{4}}[/tex].
create a circle with a centre of (0,0) and a radius of 13
Answer:
The equation would be:
[tex]x^2+y^2=169[/tex]
In the attachment!!!
Hope this helps!!!
[tex]Sofia[/tex]
Help please, thanks.
Answer:
B
Step-by-step explanation:
C = R/1.8 - 273
C + 273 = R/1.8
1.8 * (C + 273) = R
1.8 can also be read as the fraction 9/5.
9/5 * (C + 273) = R
Thus your answer is B. Hope I helped!
So, if you add it all up it would be...
1.8 which could also be in the fraction form of 9/5 and 9/5 would be basically C.
So, even though C has 5/9 in the front that wouldn't be the case. It would be the one in parentheses we would be focusing on. So, the answer all together would be C.
I Hope this helps! c:
I NEED HELP WHAT IS 100,00 X 100,00
10,000
x 10,000
________
100,000,000
Answer:
100,000,000
Step-by-step explanation:
Let F(x) 3x^2+2
The quadratic function g(x) is the function f(x) stretch vertically by a factor of 4
Enter the equation of g(x) in the box
Answer: g(x)=12x^2+8
Step-by-step explanation:
original function f(x)=3x^2+2
Now to stretch function vertically and rename to g(x) we just multiply the function by 4;
g(x)=4(3x^2+2)=12x^2+8
Any questions feel free to ask. Thanks
The equation of the function f(x) after stretching is g(x) = 12x² + 8.
What is a function ?A function is a law that relates a dependent and an independent variable.
The function given is
F(x) = 3x²+2
For when a function is vertically stretched
F'(x) = k .F(x)
k >1
here it is given that k = 4
The equation becomes
g(x) = 4( 3x²+2 )
g(x) = 12x² + 8
Therefore , The equation of the function f(x) after stretching is g(x) = 12x² + 8.
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Find the domain and range of the function.
f(x) = |x – 4| + 3
[tex]f(x) = |x-4|+3 \\ \\ \text{We have no existential conditions: }\\ \Rightarrow D = \mathbb{R}\\ \\ |x-4|\geq 0~~\big|+3 \Rightarrow |x-4|+3 \geq 3 \Rightarrow f(x) \geq 3 \\ \\ \Rightarrow \text{The range of the function is }[3,+\infty)[/tex]
ANSWER
Domain:
All real numbers
Range:
[tex]y \geqslant 3[/tex]
EXPLANATION
The given function is
[tex]f(x) = |x - 4| + 3[/tex]
This is the function obtained by the shifting the base absolute value function to the right by 4 units and up by 3 units.
The vertex of this function is at:
(4,3)
The domain is all real numbers because there is no x-value that will make the function undefined.
The least y-value on this graph is 3.
The graph opens up forever.
The range is [3,∞) or y≥3
Solve the following equation. Then place the correct number in the box provided. x - 5 = 10
Answer: [tex]x=15[/tex]
Step-by-step explanation:
You can observe in the exercise that the equation you need to solve is:
[tex]x-5=10[/tex]
You need to find the value of the variable "x" of this equation. To do this, you need to remember the Addition Property of equality, which states that:
[tex]If\ a=b\ then\ a+c=b+c[/tex]
Knowing this, to solve for the variable "x", you must add 5 to both sides of the equation. Therefore, you get this result:
[tex]x-5+5=10+5\\x=15[/tex]
Two angles of a triangle have the same measure and the third one is 12 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.nah
Answer:
68
Step-by-step explanation:
Let x be the measure of one of the angles of the triangle
Two of the angles have the same measure, so another angle is x
The third is 12 degrees more, x+12
The sum of the three angles of a triangle is 180
x+x+x+12 = 180
Combine like terms
3x+12 = 180
Subtract 12 from each side
3x+12-12 = 180-12
3x = 168
Divide by 3
3x/3 = 168/3
x = 56
x=56
x=56
x+12 = 56+12 = 68
The largest angle is 68
Please help its due tonight.
A bridge crosses a circular lake. The bridge is represented by the function
y −x = 2 and the lake is represented by the function x^2 +y ^2 = 100.
a. What is the radius of the lake?
b. Find the length of the bridge.
Answer:
a) The radius of the lake to be r=10 units.
b) [tex]14\sqrt{5}[/tex] units
Step-by-step explanation:
The lake has equation: [tex]x^2+y^2=100[/tex]
We can rewrite this as [tex]x^2+y^2=10^2[/tex]
Comparing this to [tex]x^2+y^2=r^2[/tex]
We have the radius of the lake to be r=10 units.
b) The bridge is represented by the function y −x = 2
This is the same as y=x+2
We substitute this into the equation of the circle to get:
[tex]x^2+(x+2)^2=100[/tex]
[tex]x^2+x^2+4x+4-100=0[/tex]
[tex]2x^2+4x-96=0[/tex]
[tex]x^2+2x-48=0[/tex]
[tex](x+8)(x-6)=0[/tex]
[tex]x=-8,x=6[/tex]
When x=8, y=2(8)+2=18
When x=-6, y=2(-6)+2=-10
The length of the bridge is the distance between the points (8,18) and (-6,-10)
[tex]=\sqrt{(8--6)^2+(18--10)^2}[/tex]
[tex]=\sqrt{196+784}[/tex]
[tex]=\sqrt{196+784}[/tex]
[tex]=\sqrt{980}[/tex]
[tex]=14\sqrt{5}[/tex]
A survey of pet owners found that on average, they spend $1,225 annually per pet, with a standard deviation of $275. Between which two amounts would you expect 95% of the survey’s respondents to spend annually per pet if the sample is approximately normal and comes from a normally distributed population? $675 and $1,500 $675 and $1,775 $950 and $1,500 $950 and $1,775
Answer:
B.$675 and $1,775
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
e2020 exam
simplify please. i'm failing and grade cost 4 summitives.
|-10|+|5|
A)-15
B)-5
C)5
D)15
Answer:
D = 15
Step-by-step explanation:
|-10|+|5|=10+5=15
|-10|=10
|5|=5
Answer:
D)15
Step-by-step explanation:
| | these cancel out the negative in the ten making it a positive
so it would be 10+5
which is 15
A system of two equations has no solution. One equation is -15x+y=18.
Select the equation that would make this system infinitely many solutions.
A) 3y-45x=54
B)3y+45x=54
C)45x+3y=-54
D)45x-3y=54
A.
If you multiply the original equation by 3 you get -45x+3y=54, which is the exact same as A, therefore they have infinite solutions.
what is the surface area of the right cylinder with a height of 20 and a radius of 5
Answer: The answer is 785.4
Step-by-step explanation: Equation is 2πrh+2πr²
Plug in your numbers and hit enter!
Hope this helps
For this case we have by definition, that the surface area of a cylinder is given by:
[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
Where:
A: It's the radio
h: It's the height
According to the given data we have:
[tex]SA = 2 \pi * (5) * 20 + 2 \pi * (5) ^ 2\\SA = 200 \pi + 50 \pi\\SA = 250 \pi\\SA = 785 \ units ^ 2[/tex]
ANswer:
[tex]785 \ units ^ 2[/tex]
what is the x-coordinate of the solution
Answer:
x=-4
Step-by-step explanation:
how to solve system of equation from a table
Answer:
Look for the same entry in both (all) tables.
Step-by-step explanation:
We assume here that the system of equations consists of two equations in two variables. If there are more equations in more variables, the general approach is the same.
A "solution" to a system of equations is a set of variable values that satisfies all equations of the system simultaneously. A table for one equation will generally list sets of variable values that satisfy that equation. When the same set of values appears in the table for each of the equations, then that set of values is the solution.
__
Example
The attachment shows tables for two equations:
y = 2xy = x+3Highlighted are the table entries that are the same for both equations. This is the solution to the system of equations. (x, y) = (3, 6) satisfies both equations:
6 = 2·36 = 3+3Write -1/14,7/9,-4/5 in order from least to greatest
7/9 is going to be the greatest since it is the only positive number and the. it’s going to be -4/5 and then the least is going to be -1/14.
-1/14 , -4/5 , 7/9
The numbers -1/14, 7/9, -4/5 arranged from least to greatest are -4/5, -1/14, 7/9. This is found by converting fractions to decimals for easier comparison and then arranging them in order.
Explanation:To go about solving this, we first consider each number's location on the number line. The numbers closer to the left are smaller than those on the right. Given the numbers -1/14, 7/9, and -4/5, we can start by converting each fraction to a decimal for easier comparison.
-1/14 equals approximately -0.0714, 7/9 equals approximately 0.7777, and -4/5 equals -0.8. Therefore, from smallest to largest, these numbers can be arranged as -0.8, -0.0714, 0.7777. Converting these back to fractions gives us the desired result: -4/5, -1/14, 7/9.
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Please help will give brainliest
This relation is a function because a function, in fact this is a linear function. We have that:
[tex]\left[\begin{array}{cc}x & y\\2 & 3\\4 & 4\\6 & 5\\8 & 6\end{array}\right][/tex]
As you can see below, all the points have been plotted an this is a linear function. Therefore, with two points we can get the equation, so:
[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-3=\frac{4-3}{4-2}(x-2) \\ \\ \\ y-3=\frac{1}{2}(x-2) \\ \\ y=\frac{1}{2}x-1+3 \\ \\ y=\frac{1}{2}x+2 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(2,3) \\ \\ (x_{2},y_{2})=(4,4)[/tex]
Finally, the equation is:
[tex]\boxed{y=\frac{1}{2}x+2}[/tex]
Answer:
y=0.5x +2
Step-by-step explanation:
Lines
m
and
n
are parallel. The equation of line m is =3+3
y
=
3
x
+
3
. What is the equation of line
n
?
Answer:
y = 3x + bStep-by-step explanation:
Parallel lines have the same slope.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of the line m:
[tex]m:\ y=3x+3\to m=3[/tex]
Therefore the equation of a line n parallel to the line m is:
[tex]y=3x+b[/tex]
where b is any real number
Answer y = 3x + b
Step-by-step explanation:
Write an equation for the following points:
(1, 25) (2, 5) (3, 1)
Answer:
Use desmos.com/calculator. It is a graphing calculator that can do many things
Step-by-step explanation:
say thanks and vote
Name two three dimensional figures that produce a square when sliced horizontally by a plane
Answer:
A rectangular prism and a cube.
Step-by-step explanation:
A rectangular prism when sliced by a plane can have a square facing up, meaning that a square will be produced. A cube has all square faces and when cut horizontally will produce a square.
graph the function f(x) = cos(2x) +1
The graph of the function f(x) = cos(2x) + 1 is added as an attachment
Sketching the graph of the function
From the question, we have the following parameters that can be used in our computation:
f(x) = cos(2x) + 1
The above function is a cosine function that has been transformed as follows
Horizontally stretched by a factor of 1/2Shifted up by 1 unitNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
Select the correct answer. Which inequality is true? A. |-5| > |-7| B. |-8| < |-5| C. |9| < |7| D. |-9| > |8|
To determine which inequality is true, compare the absolute values of the given numbers. The correct answer is B, |-8| < |-5|.
Explanation:To determine which inequality is true, we need to compare the absolute values of the given numbers. Absolute value is the distance of a number from zero on the number line. In this case:
A. |-5| is greater than |-7|, so |-5| > |-7| is true.B. |-8| is less than |-5|, so |-8| < |-5| is true.C. |9| is not less than |7|, so |9| < |7| is false.D. |-9| is greater than |8|, so |-9| > |8| is true.
Therefore, the correct answer is B, |-8| < |-5|.
what is the similarity ratio of the smaller to the larger cones?
Answer:
that the are both have a right angle. And that the are both cones.
Step-by-step explanation:
Answer:
3 : 5
Step-by-step explanation:
The ratio can be determined using the radii or the heights of the 2 cones
radii 6 : 10 = 3 : 5 ← in simplest form
height 9 : 15 = 3 : 5 ← in simplest form
A multiple choice test has 5 possible answers. Find the probability of answering all the questions correctly
The answer is 1/5
Step-by-step explanation:
You have the probability of getting 1/5 correct.
For this case, we have by definition, the calculation of probabilities:
[tex]probability = \frac {number\ of \favorable\ cases} {number\ of\ possible\ cases}[/tex]
We have 5 possible answers, and we have only one favorable case, that is, only one correct option among the 5 possible answers.
So, we have:
[tex]Probability = \frac {1} {5} = 0.2[/tex]
Answer:
0.2
Find the surface area of each pyramid to the nearest whole number.
Your answer would be A = 444.72 Or 445
If
q
(
x
)
is a linear function, where
q
(
−
1
)
=
3
, and
q
(
3
)
=
5
, determine the slope-intercept equation for
q
(
x
)
, then find q(2).
The equation of the line is:
q(2) =
If
t
(
x
)
is a linear function, where
t
(
−
4
)
=
3
, and
t
(
4
)
=
4
, determine the slope-intercept equation for
t
(
x
)
, then find t(0).
The equation of the line is:
t(0) =
Answer:
[tex]\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)[/tex]
[tex]\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}[/tex]
[tex]q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}[/tex]
[tex]t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}[/tex]
A total of 800 pre-sale tickets and tickets at the gate were sold to the football city championship game. if the number of tickets sold at the gate was thirteen less then twice the number of pre-sale tickets, how many pre-sale tickets were sold?
ANSWER
271 pre-sale tickets were sold.
EXPLANATION
Let p represent the number of pre-sale tickets and t represent the number of tickets sold.
According to the question,a total of 800 pre-sale tickets and tickets were sold .
This implies that,
[tex]p + t = 800[/tex]
Also the number of tickets sold is 13 less than twice the number of pre-sale tickets.
This gives another equation:
[tex]t = 2p - 13[/tex]
We substitute, the second equation into the first equation to obtain:
[tex]p + 2p - 13 = 800[/tex]
This implies that;
[tex]3p = 813[/tex]
Divide both sides by 3
[tex]p = \frac{813}{3} = 271[/tex]
Hence 271 pre-sale tickets were sold.
By setting up an algebraic equation and denoting pre-sale tickets as x, we discover that 271 pre-sale tickets were sold for the football city championship game.
To solve the problem of how many pre-sale tickets were sold for the football city championship game, we can set up an algebraic equation. Let's denote the number of pre-sale tickets as x. According to the question, the number of tickets sold at the gate is thirteen less than twice the number of pre-sale tickets, which we can express as 2x - 13. We are given that the total number of tickets sold is 800.
So, we set up the equation:
x + (2x - 13) = 800
Combining like terms, we get:
3x - 13 = 800
Adding 13 to both sides:
3x = 813
Then we divide both sides by 3 to find the value of x:
x = 813 / 3
x = 271
Therefore, 271 pre-sale tickets were sold.
What is the product of 2x + y and 5x – y + 3?
Answer:
The correct answer is 10x² + 3xy + 6x - y² + 3y
Step-by-step explanation:
It is given an expression (2x + y)(5x - y + 3)
To find the product
(2x + y)(5x - y + 3) = 2x * 5x - 2x*y + 2x*3 + y*5x -y² + 3y
= 10x² - 2xy + 6x + 5xy - y² + 3y
= 10x² + 3xy + 6x - y² + 3y
Therefore the correct answer is
10x² + 3xy + 6x - y² + 3y
The product of (2x + y) and (5x – y + 3) is found by using the distributive property of multiplication over addition, which gives us: 10x^2 + 3xy + 6x - y^2 + 3y.
Explanation:To find the product of (2x + y) and (5x – y + 3), we need to use the distributive property of multiplication over addition. This involves multiplying each term within the first parentheses by each term in the second parentheses.
The steps are as follows:
Multiply 2x by each term in the second parentheses: (2x*5x, 2x*-y, 2x*3)Multiply y by each term in the second parentheses: (y*5x, y*-y, y*3)Sum up all the products obtained.The result is 10x^2 -2xy + 6x + 5xy - y^2 + 3y. Simplifying further gives us: 10x^2 + 3xy + 6x - y^2 + 3y.
So, the product of (2x + y) and (5x – y + 3) is 10x^2 + 3xy + 6x - y^2 + 3y.
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