Answer:
x = - 3, x = 0, x = 2
Step-by-step explanation:
To find the zeros equate f(x) to zero, that is
x³ + x² - 6x = 0 ← factor out x from each term
x(x² + x - 6) = 0
x(x + 3)(x - 2) = 0
Equate each factor to zero and solve for x
x = 0
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
Answer: The zeroes of the given function are -3, 0 and 2.
Step-by-step explanation: We are given to find the zeroes of the following function :
[tex]f(x)=x^3+x^2-6x~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
zeroes of a function y = f(x) are found by solving the following equation :
f(x) = 0.
Therefore, from equation (i), we have
[tex]x^3+x^2-6x=0\\\\\Rightarrow x(x^2+x-6)=0\\\\\Rightarrow x(x^2+3x-2x-6)=0\\\\\Rightarrow x(x(x+3)-2(x+3))=0\\\\\Rightarrow x(x-2)(x+3)=0\\\\\Rightarrow x=0,~~x-2=0,~~x+3=0\\\\\Rightarrow x=0,~2,~-3.[/tex]
Thus, the zeroes of the given function are -3, 0 and 2.
The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2. If x is the tens digit and y is the ones digit, which system of equations represents the word problem?
xy = 14 and x - y = 2
x + y = 14 and x - y = 2
x + y = 14 and y - x = 2
Answer:
B. x + y = 14 and x - y = 2
Step-by-step explanation:
Sum means addition, so the sum of the tens digit (x) and the ones digit (y) is equal to 14 (x + y = 14).
Difference means subtraction, so the difference between the tens digit (x) and the ones digit (y) is 2 (x - y = 2).
I hope this helps =)
Answer:
Option B. will be the answer.
Step-by-step explanation:
If the tens digit is x and ones digit is y, then the number formed will be xy.
Now we fill form the equations as per statements given in the question.
"The difference between tens and unit digits is 2"
x - y = 2 --------(1)
"Sum of the digits of two digit number is 14"
x + y = 14 -------(2)
Therefore, system of equations will be as the given equations 1 and 2.
Option B is the answer.
What’s the right triangle definition of tan theta
Final answer:
In mathematics, the right triangle definition of tan theta is the ratio of the length of the side opposite to theta (y) to the length of the side adjacent to theta (x).
Explanation:
The right triangle definition of tan theta (tan θ) involves the ratio of the lengths of two specific sides of the triangle. According to SOHCAHTOA, a mnemonic used to remember the definitions of the sine, cosine, and tangent functions, tan theta is the ratio of the opposite side (y) to the adjacent side (x) of the right triangle, where theta (θ) is one of the non-right angles. This can be written as tan(θ) = y/x.
In other words, the tangent of an angle θ in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
This can be represented as:
tan(θ) = Opposite side / Adjacent side = y / x
For example, if the opposite side y is 5 units and the adjacent side x is 3 units, then tan(θ) = 5 / 3
The Pythagorean Theorem may be applied in conjunction with the definitions of trigonometric functions to solve various problems involving right triangles, but it specifically relates to the relationship between the sides of a right triangle: a² + b² = c², where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.
When solving problems related to right triangles, it is beneficial to remember that the sum of the angles of a triangle is always equal to two right angles (or 180 degrees).
D is the correct answer right
Answer: the answer is A
Step-by-step explanation:
simplify each product.
1.) -3p^2(5p^2+p-7)
2.) (2n-5)(n-3)
3.) (5x-3)^2
4.) (n+5)^2
5.) (j+9)(j-9)
Answer:
number 1 my fried here justin has been taken
Step-by-step explanation:
What number is an outlier for the given data? 23,34,27,7,30,26,28,31,34. A)7 B)23 C)31 D)34
Answer:
A) 7
Step-by-step explanation:
The outlier of a given data set is one that is significantly larger or smaller than the rest of the data.
In this set, most of the values are within the 25-35 range, more or less. But out of all of those numbers, one of the is too small to make sense, which is 7.
Paul graphed the equation y=6 + x. What is the y-coordinations of the point on the graph that has an x coordinate of 12
Answer:
its 18
Step-by-step explanation:
6+12=18
lol
Answer:
y = 18
Step-by-step explanation:
Just let x = 12
y = 6 + x
y = 6 + 12
y = 18
When x = 12, y = 18.
The graph is included to show you what y = 6 + x looks like and it also shows the point (12,18) = (x,y)
f(x)=4(x-1)^2-9 into standard form
Answer:
y=4(x-1)^2-9
Step-by-step explanation:
Replace f(x) with y to find the properties of the parabola
The answer would be y=4(x-1)^2-9
Use the formula to figure out the area. Calculate your answer to the nearest hundredth
Answer:
you need to add the picture
Step-by-step explanation:
Answer:add the picture
Step-by-step explanation:
Solve for the variable. k/3 16/24
Answer:
k=2
Step-by-step explanation:
[tex]\frac{k}{3} = \frac{16}{24}[/tex] Set up your equation
24k=48 Cross multiply
k=2 Divide 24 from both sides
You answer is k=2
For this case we have the following equation:
[tex]\frac {k} {3} = \frac {16} {24}[/tex]
We must find the value of the variable "k":
Simplifying the right side of the equation we have:
[tex]\frac {k} {3} = \frac {8} {12}\\\frac {k} {3} = \frac {4} {6}\\\frac {k} {3} = \frac {2} {3}[/tex]
We multiply by 3 on both sides of the equation:
[tex]k = \frac {2} {3} * 3\\k = 2[/tex]
Answer:
[tex]k = 2[/tex]
hellodjdjdjdjdjdjdjd
Answer:
can't help you sorry
Step-by-step explanation:
can't help you sorry!
Answer:
yes
Step-by-step explanation:
On a coordinate plane, the endpoints of line segment JK are J (-10, 12) K (8, -12). Point L lies on segment JK and divides it into two segments such that to LK is 5: 1. What are the coordinates of point L?
Answer:
(-7,8)
Step-by-step explanation:
The coordinates of the points dividing the line segment in ratio m:n can be calculated as:
[tex](\frac{mx_{1}+nx_{2}}{m+n} ,\frac{my_{1}+ny_{2}}{m+n} )[/tex]
Here x1, y1 are the coordinates of first point J (-10, 12) and x2, y2 are the coordinates of second point K(8, -12).
In this case m will be 5 and n will be 1 as the ratio is 5:1
Using all these values we can find the coordinates of point L
[tex]( \frac{5(-10)+1(8)}{5+1},\frac{5(12)+1(-12)}{5+1} )\\\\ = (\frac{-42}{6} ,\frac{48}{6} )\\\\ =(-7,8)[/tex]
Thus, the coordinates of point L which divides the line segment JK in 5:1 are (-7,8)
The coordinates of point L, which divides the line segment JK in the ratio 5:1, are (5,-8).
Explanation:To find the coordinates of point L that divides the line segment JK in the ratio 5:1, we use the formula for section formula in coordinate geometry. This formula provides the coordinates of a point that divides a line segment into a specific ratio. The formula is X = (m1*x2 + m2*x1) / (m1+m2), Y = (m1*y2 + m2*y1) / (m1+m2), where m1 and m2 are the ratios.
Here, J(-10,12) is x1,y1 and K(8,-12) is x2,y2. The point L is dividing JK in the ratio 5:1, so m1=5 and m2=1. Substituting these values:
X = (5*8 + 1*-10) / (5 + 1) = 30 / 6 = 5, Y = (5*-12 + 1*12) / (5 + 1) = -48 / 6 = -8.
Therefore, the coordinates of point L are (5,-8).
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Ty had 10 eggs. He made 4 servings of scrambled eggs. He used n eggs for each serving.
create an expression to represent the number of eggs Ty has left.
[tex]10-4n=x[/tex]
Hope this helps.
Brainliest would help me as well.
Final answer:
The number of eggs Ty has left after making 4 servings of scrambled eggs, using n eggs for each serving, is represented by the algebraic expression 10 - 4n.
Explanation:
To determine the number of eggs Ty has left after making scrambled eggs, we need to use a simple algebraic expression. If Ty started with 10 eggs and used n eggs for each of the 4 servings, we can represent the number of eggs used in total as 4n.
To find the number of eggs remaining, we subtract the total number of eggs used from the initial number of eggs:
Number of eggs remaining = Initial number of eggs - Number of eggs used
Number of eggs remaining = 10 - 4n
Consider the following equation. 6 ^ ( -x ) + 4 = 3x -1
Answer:
1.68
Step-by-step explanation:
1. Move all of the terms to the left side and set the problem equal to zero.
2. Set each factor equal to zero.
For this case we have the following equation:
[tex]6 ^ {- x} + 4 = 3x-1[/tex]
We must clear the value of x, we follow the steps below:
We subtract 3x on both sides of the equation:[tex]6 ^ {- x} -3x + 4 = -1[/tex]
Add 1 to both sides of the equation:
[tex]6 ^ {- x} - 3x + 4 + 1 = -1 + 1\\6 ^ {- x} - 3x + 5 = 0[/tex]
Each side of the equation is drawn, then the solution is the x value of the intersection point.
[tex]x = 1.68[/tex]
Answer:
See attached image
[tex]x = 1.68[/tex]
Pls help!!!
So I been needing help for the past week now and my friends dk either cuz they just as dumb as me.
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\implies \stackrel{\textit{8\% of (s)ales}}{\left(\cfrac{8}{100} \right)s}\qquad \qquad \begin{cases} c=commission\\ s=total~sales \end{cases}[/tex]
[tex]\bf \stackrel{\textit{her (c)ommision is 8\% of (s)ales}}{c = \cfrac{8}{100}s\implies c=\cfrac{8s}{100}}\implies \stackrel{\textit{we know she made 2560 in commision}}{2560=\cfrac{8s}{100}\implies 256000=8s} \\\\\\ \cfrac{256000}{8}=s\implies 32000=s[/tex]
An ellipse has a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin. Which is the equation of the ellipse in standard form?
ANSWER
[tex]\frac{ {y}^{2} }{49} + \frac{ {x}^{2} }{ 16 } = 1[/tex]
EXPLANATION
The given ellipse has a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin.
The equation of an ellipse with vertex on the y-axis and center at the origin is given by
[tex]\frac{ {y}^{2} }{a ^{2} } + \frac{ {x}^{2} }{ {b}^{2} } = 1[/tex]
[tex]\frac{ {y}^{2} }{( - 7) ^{2} } + \frac{ {x}^{2} }{ {4}^{2} } = 1[/tex]
[tex]\frac{ {y}^{2} }{49} + \frac{ {x}^{2} }{ 16 } = 1[/tex]
The equation of the ellipse with a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin is x^2/16 + y^2/49 = 1.
Explanation:To find the equation of the ellipse in standard form, we need to identify the lengths of the major and minor axes. The given vertex at (0, -7) indicates that the semi-major axis length, a, is 7 because the distance from the center to a vertex measures the semi-major axis. Similarly, the co-vertex at (4, 0) represents the semi-minor axis length, b, which is 4.
Since the center is at the origin (0, 0), the standard form of the ellipse equation is given by x^2/b^2 + y^2/a^2 = 1. Plugging the values of a and b, we get x^2/4^2 + y^2/7^2 = 1. So, the equation of the ellipse is x^2/16 + y^2/49 = 1.
The total surface area of a cube is 600 sq cm what is the length of one edge of the cube
Answer:
4.64
Step-by-step explanation:
s = 6a^3
600=6a^3
100 = a^3
solve for a which would be 4.64
NEED HELP ASAP!! Worth 15 pts!!
Answer:
p = 1/6
Step-by-step explanation:
5/6 - 1/3 n = p(5-2n)
Multiply each side by 6 so we do not have any fractions
6(5/6 - 1/3 n) = 6*p(5-2n)
5 - 2n = 6p (5-2n)
Divide each side by (5-2n) to isolate 6p
(5-2n)/(5-2n) = 6p (5-2n)/ (5-2n)
1 = 6p
Now divide by 6 to get p alone
1/6 = 6p/6
1/6 = p
y < -2x + 4 what is the solution to the inequality?
Answer:
x<\frac{-y+4}{2}
Step-by-step explanation:
Hope this helps!!!
can i get brainliest plzzz thx
Mr. Abrams conducted a survey of 355 students. 72% of them said that they study for tests. How many students said they study for tests?
Rounded Answer: 256
Exact Answer : 255.6
In the xy-coordinate plane shown below, point P has coordinates (8,-6). Which
of the following is an equation of the line that contains points O and P?
a. y = -x + 4
b. y = -x
c. y = x - 4
d. y=-3X
The answer will be D
The equation of the line passing through points O(0,0) and P(8,-6) is y = -3/4x.
Explanation:To find the equation of a line, we need to determine its slope and y-intercept. The slope can be found using the formula (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are coordinates of two points on the line. In this case, we have the coordinates of points O and P: O(0,0) and P(8,-6).
The slope of the line passing through O and P is (-6 - 0) / (8 - 0) = -6 / 8 = -3 / 4.
Since the line passes through the origin (0,0), its y-intercept is 0. Therefore, the equation of the line is y = -3/4x.
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F(x)=-3x+4 and g(x)=x^2 what is (g ° f)(0)
Answer:
[tex]\left(gof\right)\left(0\right)=16[/tex]
Step-by-step explanation:
Given functions are [tex]f\left(x\right)=-3x+4[/tex] and [tex]g\left(x\right)=x^2[/tex].
Using both functions we need to find about what is the value of [tex]\left(gof\right)\left(0\right)[/tex]. That can be done as shown below:
[tex]\left(gof\right)\left(0\right)[/tex]
[tex]=g\left(f\left(0\right)\right)[/tex]
[tex]=g\left(-3\left(0\right)+4\right)[/tex]
[tex]=g\left(0+4\right)[/tex]
[tex]=g\left(4\right)[/tex]
[tex]=4^2[/tex]
[tex]=16[/tex]
Hence final answer is [tex]\left(gof\right)\left(0\right)=16[/tex].
Which of the following is the solution for 9<=1-4x<21
Answer:
-5 < x <=-2
Step-by-step explanation:
9<=1-4x<21
Subtract 1 from each side
9 -1<=1-1-4x<21-1
8 <= -4x < 20
Divide each side by -4. That means to flip all inequalities
8/-4 >= -4x/-4 >20/-4
-2 >=x > -5
-5 < x <=-2
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5. A farmer found a crop circle in his fields. He rode his tractor around it, and found that its
circumference was 1.884 miles. He rode his tractor directly across the center, and found
that the diameter was 0.6 miles. What is the area of the crop circle?
Answer: 0.283 square miles
Step-by-step explanation:
The area of a circle is:
Diameter:A = (π/4) × D2
or, when you know the Circumference:A = C2 / 4π
the table represent the consumer price index for a basket of goods and services for 3 consecutive years. calculate the inflation rate for 2014.
We'll assume that the CPI is given for the END of the year.
Then 2014's rate is the change in price from 2013 in percent,
r = 180/125 - 1 = 36/25 - 1 = 11/25 = 44 %
Answer: choice c
----------
This is a pretty poor question. The questioner should clarify the exact dates of the given values of the CPI, and use the actual values. 44% is an alarming inflation rate, but fortunately a fictitious one here in the US. US inflation in 2014 was around 0.7% so the number the student was asked to compute was off by more than a factor of sixty.
Answer:
C
Step-by-step explanation:
Isaac is working as a security guard. He earns $8.45 an hour. He earns double time for any overtime over 40 hours. Last week he worked 44 hours. How much did he earn last week? (Hint: double time means 2 times the regular hourly rat.)
your answer would be $405.60
The answer is 709.8 You would do 8.45 times 40 = 338 now since he did overtime you multiply it by 2. 338*2= 676. He also did another 4 hours 8.45*4=33.8 now you add these together 33.8+676 = 709.8
I need to know number six and thank you guys for all the help
Answer:
D
Step-by-step explanation:
First of all, a very easy way is to count all the rectangles and then count the squares that are shaded and have balloons.
You'll get 7 squares that are shaded and have balloons and 16 rectangles in total.
So the fraction will be [tex]\frac{7}{16}[/tex]
Another simple way is to just multiply [tex]\frac{7}{8}[/tex] and [tex]\frac{1}{2}[/tex]
[tex]\frac{7}{8}*\frac{1}{2}=\frac{7}{16}[/tex]
the cost of oranges in a grocery store is directly proportional to the number of oranges purchased. elia paid $2.52 for 6 oranges. if p represents the cost(in dollars) and n represents the number of oranges, find the unit rate
Step-by-step explanation:
6 oranges =$2.52
1 orange=$2.52/6
=$0.42
Answer:
Step-by-step explanation:
The answer is aP=0.42n
To get to that answer all you have to do is 2.52/6=0.42
6 oranges=2.52
1 oranges=0.42
What is the sqaure roots for -196
Answer:
if -196 was positive, it could be 14 or -14, but because it is negative, it is considered infinity or unknown
7|n| = 56
anyone know how to do dis?!?!
Answer:
{-8, 8}
Step-by-step explanation:
Simplify 7· |n| = 56 by dividing both sides by 7:
|n| = 8
Because this is an absolute value equation, there are two separate solutions. One is n = +8 and the other is n = -8.
There are two solutions.
[tex]
7\times\mid n\mid=56\Longrightarrow\mid7n\mid=56 \\
\mid7\times x_1\mid=56\Longrightarrow x_1=\frac{56}{7}=\boxed{8} \\
\mid7\times(-x_1)\mid=56\Longrightarrow-x_2=\frac{56}{7}\Longrightarrow x_2=\boxed{-8}
[/tex]
central school is hosting a "central has talent" show. they will award various prizes for the best acts in the show. first place wins the most money
the answer is b and f
Answer:
b f
Step-by-step explanation: