Answer:
[tex](C) \dfrac{x+3}{x}[/tex]
Step-by-step explanation:
We want to determine an equivalent expression to:
[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]
Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.
[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]
Step 2: Change the division sign to multiplication
[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]
Step 3: Cancel out common terms and simplify
[tex]= \dfrac{x+3}{x}[/tex]
The correct option is C.
The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]
Given expression is,
[tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]
Use factorization, [tex]x^{2} -9=(x-3)(x+3)[/tex]
Now simplify the given expression.
[tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]
Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]
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Pls answer i will mark as branliest
Answer:
Part A:
x = 80 degrees
Part B:
A => Corresponding Angles (They correspond to each other)
Hope This Helps!
Don't hesitate asking anything regarding this!
Really need help :( struggling
Answer:
B
Step-by-step explanation:
The original amount will be the coefficient of (1 + 0.04)^r which is $728.00.
which words have vertical symmetry for all of the letters in the word?
Answer:
palindromes
Step-by-step explanation:
palindromes are spelled the same forward and backward, thus have vertical symmetry.
Given the function f(x) = –0.5|2x + 2| + 1, for what values of x is f(x) = 6? x = 6, x = –5 x = 5, x = –5 x = 7, x = –6 no solution
Answer:
Step-by-step explanation:
This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:
-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us
-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us
| 2x + 2 | = -10.
Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative is distance, there is no solution to this equation.
Answer:
no solution
Step-by-step explanation:
This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:
-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us
-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us
| 2x + 2 | = -10.
Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative
Antoine has a solid, spherical ball of clay with a radius of 5 cm. If he shapes it into a solid, cone–shaped figure with a radius of 2 cm, what will the height of the cone be?
Answer:
Step-by-step explanation:
We'll call height h.
The equations of a cone and sphere are:
Cones: 1/3 * base area * h
Spheres: 4/3 π * r³
The base area of a cone would be the area of a circle equation:
π * r² = π * 2² = 4π.
Because you're converting from sphere to cone, you would set their equations equal to each other.
1/3 * 4π * h = 4/3 π * 5³
Next, isolate h.
h = (4/3 π * 5³)/(1/3 * 4π)
h = 125
Hope this helps!
Answer:125
Step-by-step explanation:
Work out m and c for the line: y = 8 x
Answer:
m = 8 and c = 0
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 8x ← is in slope- intercept form, that is y = 8x + 0
with m = 8 and c = 0
When you multiply a function by -1 what is the effect on its graph?
Answer:
Step-by-step explanation:
Depends on what you mean by multiplying by - 1. I assume you are not going to multiply the y or f(x) term by - 1.
If that is so, take an example. Suppose you have a graph that is y=x^2
That's a parabola that opens upwards and it has a line going through its focus which is a point on the +y axis.
When you multiply the right hand side by - 1, the graph you get will be y = - x^2.
That opens downward and the focus is on the - y axis.
That means that the effect of the graph is that it flips over the x axis, which I think is the third answer.
Answer:
c
Step-by-step explanation:
ape x
10 people have pink cups. then 5 of those 10 people got red cups and threw the pink cups away. how many people have pink cups?⇒⇒
Answer:
5 people have pink cups
Step-by-step explanation:
10-5=5
:D
Answer:
5
Step-by-step explanation:
10-5=5
^--^
PLZZZZZZZZZ HLPPPPPPPP MEEEEEEEEEEE
which of the following is made up of one base and a vertex not in the same plane as the base? check all that apply
a. cone
b. prism
c. cylinder
d. pyramid
Answer:
a. cone. Since it's the only shape with one base and a vertex not on the same plane
Write -1/19, 7/4, -4/7 from least to greatest
Answer:
-4/7, -1/19, 7/4
Step-by-step explanation:
The fractions converted into decimals would be -0.05, 1.75, -0.57
What is the numerical solution to the equation five less than three times a number equals four more than eight times the numbers?
A. -9/5
B. 1/11
C. -1/5
D. 1/5
Answer:
Option A
Step-by-step explanation:
Let us first consider the equation at hand. We are given that this equation is as follows, five less than three times a number equals four more than eight times the numbers. Convert this into a numerical format;
[tex]3x - 5 = 4 + 8x[/tex]
where x = " the number "
[tex]3x - 5 = 4 + 8x,\\- 5 = 4 + 5x,\\- 9 = 5x,\\\\x = - 9 / 5 \\\\Solution - Option A[/tex]
If you wish, take a look at this verbal explanation. To solve the equation 3x - 5 = 4 + 8x, one would first subtract 3x on either side of the equation, resulting in the simplified equation - 5 = 4 + 5x. Subtracting - 4 from either side, - 5 - 4 = - 9, and so we receive - 9 = 5x. Dividing 5 on either side, x = - 9 / 5, Option A.
The temperature at 3:00pm was 15 degrees. At midnight the temperature was -2 degrees. What is the difference between those two temperatures
Step-by-step explanation:
(-2)-(+15)=(-17)
the difference between those two temperature s is (-17)
The distance between points (1, 2) and (x 1 ,y 1 ) is the square root of (x 1 -1)^ 2 +(y 1 -2)^ 2
Answer:
True
Step-by-step explanation:
The distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].
The given points are (1, 2) and [tex](x_{1} , y_{1})[/tex] .
We to find the distance between the given points.
What is the formula to find the distance between points?The formula to find the distance between points is [tex]\sqrt{(x_{1}-x_{2} )^{2}-(y_{1}-y_{2} )^{2} }[/tex].
Now, [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex]
Therefore, the distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].
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The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3). What are the x- and y-coordinates of point M, which partitions the directed line segment into the ratio 2:5?
Answer:
the answer is -6, 2
Step-by-step explanation:
Answer:
the answer is -6, 2
Step-by-step explanation:
Answer:
ANSWER
x = { - 20}{7}
y={ 4}{7}
Step-by-step explanation:
Given the following number line, what number could be A if XY - ZA?
X
Y Z
-6
A. -5
B. -1
C. 5
D. 6
Answer:
C. 5
Step-by-step explanation:
XY= -1-(-5)= 4
ZA= A-1= 4 ⇒ A=1+4= 5
A=5
A donut shop is experimenting with two new types of cream-filled treats, one with raspberry filling, and the other with peach. A batch of raspberry donuts cooks in 11 minutes while a batch of peach donuts cooks in only 8 minutes. Let x represent the number of raspberry-filled donuts and let y represent the number of peach-filled donuts. Write an inequality to represent how many batches of the new type of donuts can be produced in a 10 hour day. a. c. b. d.
Step-by-step explanation:
X= raspberry
X = 600 ÷ 11 = 54 batches
[ 60 minutes = 1 hour]
[600 minutes = 10 hours]
Y = peach
Y = 600 ÷ 8 = 75 batches
Answer:
its b
Step-by-step explanation:
it just is
The profit ,P dollars, earned by students at a high school selling boxes of chocolates is approximated to be P= -60x^2+600x , where x dollars is the selling price of one box of chocolates. What selling price gives the maximum profit?
Answer:
Selling price of 5 gives the maximum profit
Step-by-step explanation:
What we do here is to find the first derivative, since at maximum points, the profit will be set to zero.
Mathematically, we have;
dp/dx = -120x + 600
We now equate this to zero
0 = -120x + 600
120x = 600
x = 600/120
x = 5
can someone help me?
can you please help ?
Answer:
17
Step-by-step explanation:
Plot in the points for each variable to find the y-intercept.
1=-4(4)+c
1=-16+c
1+16=c
17=c
9=-4(2)+c
9=-8+c
9+8=c
17=c
Answer:
Step-by-step explanation:
Given:
2 Points
(4,1) and
(2,9)
Slope
m = (y2 - y1)/(x2 - x1)
y2 = 9
y1 = 1
x2 = 2
x1 = 4
m = (9 - 1) / (2 - 4)
m = 8 / - 2
m = - 4
y intercept
y = mx + b
y = -4x + b
Use (9, 1) to find the y intercept
1 = - 4*9 + b
1 = - 36 + b
b = 37
Answer
The equation is y = - 4x + 37
3:7 ratio what fraction does he get
Answer:
3/10
Step-by-step explanation:
Josh and Lucy share some money in the ratio 3:7.
3+7=10
The fraction Lucy gets is 7/10
The fraction Josh must get is 3/10.
What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work. y = 2x + 17 y = 1/2x + 8 y = -2x - 7 y = -1/2x + 2
Answer:
y = -1/2x + 2
Step-by-step explanation:
If two lines are perpendicular then the product of their slopes are -1
m1*m2 = -1
where m1 amd m2 is slope of two lines.
_______________________________________
Given line
y = 2x-3\
it is in form of y = mx+c (slope intercept form)
where m is slope and c is y intercept
Thus, slope of line y = 2x-3 is 2
Now we know that product of two lines are -1
let m be slope of other line
then m*2 = -1
m = -1/2
thus, slope of required line is -1/2
let the line be y = mx+c but m = -1/2
thus
y = -1/2 x + c
given that point(-6,5) lies on it
we use -6 in plca of x and 5 in place of y
5 = -1/2 *-6 + c
=>5 = 3 +c
=> c = 5-3 = 2
Thus, equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5) is y = -1/2x + 2
What is ? 5(x+y)-3(x+y)
Answer:
2(x+y)
Step-by-step explanation:
Simple 5-3 with some added variables that don't change.
Using the graphing method, which of the following choices is the
solution of system: 3y = x-9
y = -x + 1
Answer:
y=x_1 is the solution of system
I need help with these two please help me!
Answer:
0.50
Step-by-step explanation:
Simply plug -2 in for x into the equation.
2(2^-2) = 0.50
Answer:
0.50
Step-by-step explanation:
What is the length of segment GH?
Answer:
4√5
Step-by-step explanation:
Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
Coordinates given:
H(8, 1)
G(0, -3)
d = [tex]\sqrt{(8-0)^2 + (1+3)^2}[/tex] = 4√5
Answer:
StartRoot 80 EndRoot
80 square root is the answer
Step-by-step explanation:
|GH|² = (8 - 0)² + (1 - (-3))²
|GH|² = 64 + 16
|GH|² = 80
GH = sqrt(80)
pls mark as brainliest
Order The numbers from least to greatest
0.453, 0.35, 4/5
Answer:
Step-by-step explanation:
0.35
0.453
4/5
the diagram shows a star made by surrounding a regular octagon with triangles, explain why angle a must be 135 degrees
Answer:
From the sum of angles on a straight line, given that the rotation of each triangle attached to the sides of the octagon is 45° as they move round the perimeter of the octagon, the angle a which is supplementary to the angle turned by the triangles must be 135 degrees
Step-by-step explanation:
Given that the triangles are eight in number we have;
1) (To simplify), we consider the five triangles on the left portion of the figure, starting from the bottom-most triangle which is inverted upside down
2) We note that to get to the topmost triangle which is upright , we count four triangles, which is four turns
3) Since the bottom-most triangle is upside down and the topmost triangle, we have made a turn of 180° to go from bottom to top
4) Therefore, the angle of each of the four turns we turned = 180°/4 = 45°
5) When we extend the side of the octagon that bounds the bottom-most triangle to the left to form a straight line, we see the 45° which is the angle formed between the base of the next triangle on the left and the straight line we drew
6) Knowing that the angles on a straight line sum to 180° we get interior angle in between the base of the next triangle on the left referred to above and the base of the bottom-most triangle as 180° - 45° = 135°.
Please help me I've been stuck on this for a bit
Answer:
A=1.5 units²
Step-by-step explanation:
a²+b²=c²
2.5²+1.5²=c²
a²+2.25=6.25
a²=4.00
a=2
A=1/2 x b x h
A=1/2 x 1.5 x 2
A=1.5 units²
Answer:
1.5
Step-by-step explanation:
Use the pythagorean theorem. a^2+b^2=c^2. a and b are the legs, or the shorter sides of the triangle. If you don't know which ones are shorter, just know that c is opposite of the right angle which is 2.5 in this case. So c is 2.5 and a is 1.5. Now you plug the values into the equation
1.5^2+b^2=2.5^2
2.25+b^2= 6.25 .Simplify the equation
b^2= 4 .Subtract 2.25 from both sides.
b= 2. Square root both sides.
Based on the picture, a is the base and b is the height. The area of a triangle is 1/2(bh) .You already know the base and height you you plug it in again
1/2(1.5*2)= 1/2(3)= 1.5
Select the correct answer.
If the factors of quadratic function gare (x-7) and (x + 3), what are the zeros of function g?
O A
-7 and 3
-7 and -3
O C.
3 and 7
OD.
-3 and 7
Answer: -3 and 7
Step-by-step explanation:
x - 7
Add 7 to get 0
x - 7 ( + 7) = 0
x + 3
Subtract 3 to get 0
x + 3 ( - 3) = 0
What is the inverse of the given function?
Answer: -7, -1, 5, -5
Step-by-step explanation:
In order to find the inverse, swap the x's and y's and solve for y.
[tex]y=\dfrac{5x+1}{-x+7}\\\\\\\underline{Swap\ the\ x's\ and\ y's}:\\x=\dfrac{5y+1}{-y+7}\\\\\\\underline{\text{Multiply both sides by -y+1 to clear the denominator}}:\\x(-y+7)=5y+1\\-xy+7x=5y+1\\\\\\\underline{\text{Add xy and subtract 1 from both sides}}:\\7x-1=xy+5y\\\\\\\underline{\text{Factor out the y from the right side}}:\\7x-1=y(x+5)\\\\\\\underline{\text{Divide x+5 from both sides}}:\\\dfrac{7x-1}{x+5}=y[/tex]
Since the boxes you need to fill in show -x in the denominator, multiply the equation by -1/-1:
[tex]y=\dfrac{-1}{-1}\bigg(\dfrac{7x+1}{x+5}\bigg)\\\\\\\large\boxed{f^{-1}(x)=\dfrac{-7x-1}{-x-5}\qquad for\ x \neq -5}[/tex]