Answer:
third option
Step-by-step explanation:
Given
f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]
The denominator cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
solve x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
The vertical asymptotes are x = 1 and x = - 2
(b) The train is 61 cm long and travels at a speed of 18 cm/s.
It takes 4 seconds for the whole of the train to cross a bridge.
Calculate the length of the bridge.
Answer:
The length of the bridge is 72 cm
Step-by-step explanation:
In order to find the length of bridge, we have to apply distance formula which is D = S × T where S represents speed and T is time :
[tex]d = s \times t[/tex]
[tex]let \: s = 18,t = 4[/tex]
[tex]d = 18 \times 4[/tex]
[tex]d = 72 \: cm[/tex]
The length of the bridge is 11 cm .
What is relationship between distance time and speed ?When an object moves in a straight line at a steady speed, we can calculate its speed if we know how far it travels and how long it takes. This equation shows the relationship between speed, distance traveled and time taken:
Speed is distance divided by the time taken.
For example, a car travels 30 kilometers in 2 hours.
Its speed is 30 ÷ 2 = 15km/hr.
Formula used :
Distance = Speed * Time
Time = Distance / Speed
Speed = Distance / Time
According to the question
Length of train = 61 cm
Speed of train = 18 cm/s
Time taken to cross the bridge = 4 seconds
In this length traveled by train = length of train + Length of bridge
( as time given is to completely cross platform )
Therefore,
length traveled by train = 61 + Length of bridge
formula used
Distance = Speed * Time
61 + Length of bridge = 18 * 4
61 + Length of bridge = 72
Length of bridge = 72 - 61
Length of bridge = 11 cm
Hence, the length of the bridge is 11 cm .
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Which number line represents the solution set for the inequality –negative StartFraction one-half EndFraction x is greater than or equal to 4.x ≥ 4?
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the left.
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the left.
A number line from negative 10 to 10 in increments of 2. A point is at negative 2 and a bold line starts at negative 2 and is pointing to the right.
A number line from negative 10 to 10 in increments of 2. A point is at negative 8 and a bold line starts at negative 8 and is pointing to the right.
Answer:
it's b :)
Step-by-step explanation:
A number line which represents the solution set for the given inequality is: option B.
What is a number line?A number line refers to a type of graph with a graduated straight line which contains numerical values (both positive and negative numbers) that are placed at equal intervals along its length.
Next, we would solve the given inequality:
-½x ≥ 4
-x ≥ 4 × 2
x ≤ -8.
Therefore, a number line which represents the solution set for the given inequality is a number line from -10 to 10 in increments of 2 with a point at -8 and a bold line starts at -8 while pointing to the left.
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PLS HELP. i really need this fast ill give brainliest too
Answer:
24 square units
Step-by-step explanation:
Use the formula for area of a parallelogram to solve. The base is 6 units, and the height is 4 units.
A = bh
A = (6)(4)
A = 24 square units
The area of the parallelogram is 24 square units.
Will Give Brainliest, Answer ASAP m∠O =
m∠N =
Answer:
∠ O = 61°, ∠ N = 119°
Step-by-step explanation:
In a parallelogram
Consecutive angles are supplementary
Opposite angles are congruent, thus
x + 2x - 3 = 180
3x - 3 = 180 ( add 3 to both sides )
3x = 183 ( divide both sides by 3 )
x = 61°
Thus
∠ O = ∠ M = x = 61°
∠ N = ∠ P = 2x - 3 = 2(61) - 3 = 122 - 3 = 119°
Anyone want to help...?
Answer:
-1
Step-by-step explanation:
3/2 * (-22/33)
Simplify by dividing the second fraction by 11
3/2 * (-2/3)
Rewriting
3/3 * (-2/2)
-1/1
Answer:
-1
Step-by-step explanation:
(a/b)(c/d) = (a*c)(
(3/2)(-22/33)
(3*-22)/(2*33) = -66/66 = -1
A classroom floor has an area of
(30x^3 + 8x^2, with a width of 2x feet.
What is the length of the floor?
Answer:
15x² + 4x feet
Step-by-step explanation:
We need to calculate (30x³ + 8x²) / 2x.
(30x³ + 8x²) / 2x
= 30x³ / 2x + 8x² / 2x
= 15x² + 4x
Solve the simultaneous equation
X+3y=13
X-y=5
Answer:
x = 7
y = 2
Step-by-step explanation:
In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y
x + 3y = 13 ........ Equation 1
x - y = 5...........Equation 2
From Equation 2,
x = 5 + y
Substitute 5 + y for x in Equation 1
x + 3y = 13 ........ Equation 1
5 + y + 3y = 13
5 + 4y = 13
4y = 13 - 5
4y = 8
y = 8/4
y = 2
Since y = 2, substitute , 2 for y in Equation 2
x - y = 5...........Equation 2
x - 2 = 5
x = 5 + 2
x = 7
Therefore, x = 7 and y = 2
Write an equation for the line in the graph that passes through the points (0,4) and (12,16).
Answer:
We have,
y-y1=m(x-x1)
or,y-4=-1(x-0)
or,y-4=-x
or,x+y=4 is the required equation
Step-by-step explanation:
it it helps u ...plz mark it as brainliest
Find the slope of the line that passes through the points (-8,-3) and (2, 3)
0
1
3/5
5/3
Answer:
The answer is
[tex] \frac{3}{5} [/tex]Step-by-step explanation:
To find the slope passing through two points we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]Where
m is the slope
( x1 , y1) and ( x2 , y2) are the points
From the question the points are
(-8,-3) and (2, 3)
So the slope is
[tex]m = \frac{3 + 3}{2 + 8} = \frac{6}{10} = \frac{3}{5} [/tex]Hope this helps you
In the first quadrant you start at 5, 6 and move 4 units down. What point will you end up at? Thanks for your help! - Someone who's better at English than math
Answer:
(5, 2)
Step-by-step explanation:
(5, 6) go down 4 units means subtract 4 from the y
(5, 2)
The point to end up will be (5, 2).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
In the first quadrant you start at (5, 6 ) and move 4 units down.
Now,
Since, In the first quadrant you start at 5, 6 and move 4 units down.
Hence, The end up point = (5, 6 - 4)
= (5, 2)
Thus, The point to end up will be (5, 2).
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Each packet of the cooking oil weighs 2/5th of a kilogram and one kilogram of the cooking oil costs $6.5. Sara went to the grocery shop to buy some items to stock her kitchen. If she bought 8 packets of the cooking oil, how much money did she spend? A $19.60 B $18.20 C $20.80 D $23.40
Answer:
C) $20.80
Step-by-step explanation:
1 kg of cooking oil = $6.5
1 packet of cooking oil =2/5 kg
If 1 kg of cooking oil = $6.5
2/5kg of cooking oil = $X
Cross Multiply
1kg × $X = 2/5kg × $6.5
$X = 13/5
$X = 2.6
Hence 2/5kg of oil cost $2.6
Since 1 packet of oil = 2/5kg of oil , 1 packet of oil cost $2.6
The amount she spent if she bought if she bought 8 packets of the cooking oil is calculated as:
1 packet of oil = $2.6
8 packets of oil =
$2.5 × 8
= $20.80
Therefore,if Sara bought 8 packets of oil, the amount she would spend = $20.80
HELP i don’t know how to do this
Answer:
4a
Step-by-step explanation:
4a
the top and right are a-b, but you have to add the b’s back in, so really all sides are a
a+a+a+a=4a
Answer: 4a
Step-by-step explanation: perimeter is the length of all sides added together. Every length is given combine like variables and you will get 4a+2b-2b. 2b-2b is 0 which leaves you with 4a
7 liters of gasoline between their 4 cars. How many liters of gasoline should each car get?
Answer:
1.75 liters for each car.
Step-by-step explanation:
Divide:
*7 / 4 = 1.75.
Check:
*1.75 x 4 = 7.
The base of a triangle is two times its height. If the area of the triangle is 36, then what is the height of the triangle?
We have:
h - height
b = 2h - base
A = 36 - area
so:
[tex]A=\frac{1}{2}\cdot b\cdot h\\\\A=\frac{1}{2}\cdot 2\cdot h \cdot h\\\\A=h^2\\\\36=h^2\quad|\sqrt{(\dots)}\\\\\boxed{h=6}[/tex]
two similar cups are 3 cm and 5 cm deep if the larger cup
s hold 675 cm cube of water what is the volume of the smaller one
Answer:
145.8
Step-by-step explanation:
l.s.f for the two is 3:5
volume scale factor will be 3³:5³ which us 27:125
so 27×675 / 125
= 145.8
Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. 1 point
Answer:
y = - 140
Step-by-step explanation:
The statement
y varies jointly as x & z is written as
y = kxzto find y when x = 7 and z = -5 we must first find the relationship between the variables
when y = - 180
z = 15
x = - 3
- 180 = k(15)(-3)
-180 = - 45k
Divide both sides by - 45
k = 4
The formula for the variation is
y = 4xzwhen
x = 7
z = -5
y = 4(7)(-5)
y = 4(-35)
y = - 140Hope this helps you
Given that p=x^2-y^2/x^2+xy
I. Express p in the simplest form
ii. Find the value of p if x=-4 and y=-6
Answer:
p = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
p = [tex]\frac{x^2-y^2}{x^2+xy}[/tex] ( factorise numerator and denominator )
x² - y² ← is a difference of squares and factors as (x - y)(x + y)
x² + xy ← factor out x from each term
= x(x + y) , thus
p = [tex]\frac{(x-y)(x+y)}{x(x+y)}[/tex] ← cancel (x + y) on numerator/ denominator
= [tex]\frac{x-y}{x}[/tex] ← substitute x = - 4, y = - 6
= [tex]\frac{-4-(-6)}{-4}[/tex]
= [tex]\frac{-4+6}{-4}[/tex]
= [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]
Given f(x) = 2x - 7, complete parts (a) through (c).
A. Solve f(x)=0.
B. What do the answers to parts (a) and (b) tell you about the graph of y=f(x)
Answer:
a) x=7/2
Step-by-step explanation:
a) since f(x) is=0, plug in 0 to → f(x)=2x-7 [this f(x)]. you would get 0=2x-7. solve for x by adding 7 and dividing by 2 which you get x=7/2.
Then value of [tex]x[/tex] is 7/2
What is function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input . Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is the set of values that have the potential of coming out as outputs of a function.
given function:
[tex]f(x)[/tex]= 2[tex]x[/tex] -7
So,[tex]f(x)[/tex]= 0
2[tex]x[/tex] -7=0
2[tex]x[/tex]= 7
[tex]x[/tex]= 7/2
The graph is attached below.
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convert the equation f(x)=1/2x^2+3x-2 to vertex form
Answer:
Step-by-step explanation:
Hello, please consider the following.
The "vertex form" is as below.
[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]
Let's do it!
[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]
Thank you.
how many 6-digit numbers can be created using8, 0, 1, 3, 7, and 5 if each number is used only once?
Answer:
600 numbers
Step-by-step explanation:
For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.
However, 0 cannot be used as the first digit, because it would make a 5-digit number.
Therefore
there are 5 choices for the first digit (exclude 0)
there are 5 choices for the first digit (include 0)
there are 4 choices for the first digit
there are 3 choices for the first digit
there are 2 choices for the first digit
there are 1 choices for the first digit
for a total of 5*5*4*3*2*1 = 600 numbers
If EH = 23, calculate AB.
Youngblood say you want me back in your life...
Answer:
2/4 = 23/AB
1/2 = 23/AB
AB= 46
Hope it helps ^_^
can u help me with this?
Answer: Yes. The sales tax is 5% which equals $4.20 for $84
Step-by-step explanation:
[tex]\dfrac{0.60}{12}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.20}{24}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.80}{36}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{2.40}{48}=0.05\qquad \rightarrow 5\%[/tex]
The sales tax rate is proportional for the values in the table.
$84 x 0.05 = $4.20
The sales tax on a purchase of $84 is $4.20
If a polygon has an area of 10 cm² and is dilated by a factor of 2, what will be the area of the dilated polygon?
Area depends on the product of sides,
so if the sides are shortened by a factor of 2, area will reduce by a factor of 4. (2×2)
new area = 10/4=2.5 cm²
find the lower quartile for the data {47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4}
Answer:
The lower quartile is 23.4
Step-by-step explanation:
The given data are;
47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4
Rearranging the data, we have;
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term
However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile
The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.
Dawn and Jackson have baseball cards in the ratio of 2:3. Together, they have a total of 60 baseball cards. How many baseball cards does each child have?
Answer:
24 and 36
Step-by-step explanation:
2x + 3x = 60
5x = 60
x = 12
Dawn has 2(12) = 24
Jackson has 3(12) = 36
Step-by-step explanation:
To find the number of baseball cards each person received we must first find the total parts
That's
2 + 3 = 5
For Dawn
Dawn's part is 2
We have
2/5 × 60
= 24 baseball cardsFor Jackson
Jackson's part is 3
That's
3/5 × 60
= 36 baseball cardsHope this helps you
PLEASE HELP ME WORTH 20 POINTS It looks like the graph of the parents function f(x)x^2. However:
- It has been reflected (flipped) over the x-axis
-It has been shifted down 4 units.
-It had been shifted left 1 unit
Step 1: Start with the equation f(x) = x2. Write the equation for the graph of g(x) that has been reflected, or flipped, over the x-axis.
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been shifted down 4 units.
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted left 1 unit.
flipped : [tex]-x^2[/tex]
moving down: [tex] -x^2+4[/tex]
shifting left [tex] -(x+1)^2+4[/tex]
expanding it: [tex] -x^2-2x+3[/tex]
Answer:
1. f(x)=x^2
f(x)=-x^2
2. f(x)=-x^2-4
3. f(x)=-(x+1)^2-4
On a coordinate plane, a triangle has points (negative 5, 1), (2, 1), (2, negative 1).
Use the drop downs to answer the following questions about the distance between the points (−5, 1) and (2, −1).
What is the distance of the horizontal leg?
What is the distance of the vertical leg?
Use the Pythagorean theorem. What is the distance between the two points?
Answer:
The answer is below
Step-by-step explanation:
The points of the triangle are (- 5, 1), (2, 1), (2, - 1). The distance between two points is given by:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The horizontal leg is formed by points with the same y axis. Therefore the points that make up the horizontal leg is (- 5, 1), (2, 1). The Distance of the horizontal leg is:
[tex]Horizontal\ leg=\sqrt{(2-(-5))^2+(1-1)^2}=\sqrt{7^2+0}=7\ units[/tex]
The vertical leg is formed by points with the same x axis. Therefore the points that make up the vertical leg is (2 1), (2, 1-). The Distance of the vertical leg is:
[tex]Vertical\ leg=\sqrt{(2-2)^2+(-1-1)^2}=\sqrt{0+(-2)^2}=2\ units[/tex]
The hypotenuse is gotten using Pythagorean theorem. It is gotten by:
Hypotenuse² = (Horizontal leg)² + (Vertical leg)²
Hypotenuse² = 7² + 2²
Hypotenuse² = 49 + 4 = 53
Hypotenuse = √53
Hypotenuse = 7.28 unit
Answer:
The answer are 7, 2 and 53
Step-by-step explanation:
Brian invested his savings in two investment funds. The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit. How much did he invest in Fund B, if both funds together returned a 2% profit?
Answer: Brian invested $16000 in Fund B .
Step-by-step explanation:
Let x be the amount Brian invested in Fund B.
Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.
i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320
Profit on Fund B = 1% of x = 0.01x
Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)
= 0.02(8000+x)
As per question,
Combined profit=Profit on Fund A+Profit on Fund B
[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]
Hence, Brian invested $16000 in Fund B .
how many eighth rests are in a half rest?
[fill in the blank]
In this figure,AB and CD are parallel.
AB is perpendicular to line segment_____. If the length of EF is a units, then the length of GH is_____units.
Answer:
1. GH
2. a
Step-by-step explanation:
Perpendicular: When 2 lines meet at 90 degrees
1. It is line segment GH because AB and GH meet at a 90 degree angle (since there is a box at angle GHF indicating that it is 90 degrees)
2. It has to be a units because it is a rectangle where the top and bottom are congruent and the sides are too
This is a rectangle since AB and CD are parallel and GH can be a transversal line, according to same side interior angles theorem EGH is a also 90 degrees. That means FEG is 90 degrees too because then the quadrilateral will add up to 360 degrees