Answers
Answer:
See below.
Step-by-step explanation:
[tex]\frac{6z^2-12z}{4z^2-16z+16} +\frac{3z}{z^2-z-2} \\\\[/tex]
First, factor the numerators and the denominators:
[tex]=\frac{6z(z-2)}{4(z^2-4x+4)}+\frac{3z}{z^2-z-2}\\=\frac{6z(z-2)}{4(z-2)^2}+\frac{3z}{(z-2)(z+1)}\\=\frac{3z}{2(z-2)}+\frac{3z}{(z-2)(z+1)}[/tex]
Now, make the two denominators equivalent. To do this, we can multiply the first term by (z+1) and multiply the second term by 2. This will give us:
[tex](\frac{z+1}{z+1} )(\frac{3z}{2(z-2)})+(\frac{2}{2})(\frac{3z}{(z-2)(z+1)})\\=\frac{3z(z+1)}{2(z-2)(z+1)}+\frac{6z}{2(z-2)(z+1)} \\[/tex]
Now, combine them since they have a common denominator:
[tex]=\frac{3z^2+3z+6z}{2(z-2)(z+1)}\\ =\frac{3z^2+9z}{2(z-2)(z+1)} \\=\frac{3z(z+3)}{2(z-2)(z+1)}[/tex]
This cannot be simplified further.
Related Questions
Write a pair of integers whose difference gives. (a) a negative integer. (b) zero. (c) an integer smaller than both the integer. (d) an integer smaller than only one of the integers. (e) an integer greater than both the integers.
Answers
Answer:
(a)5 and 8
(b)5 and 5
(c) 7 and 5
(d)6 and 2
(e)6 and -2
Step-by-step explanation:
(a)a negative integer
We consider the integers 5 and 8
Difference = 5-8 =-3
3 is a negative integer.
(b)Zero
We consider the integers 5 and 5
Difference = 5-5 =0
(c) an integer smaller than both the integer.
We consider the integers 7 and 5
Difference = 7-5 =2
2 is smaller than both integers.
(d) an integer smaller than only one of the integers.
We consider the integers 6 and 2
Difference =6-2=4
4 is smaller than only 6.
(e)an integer greater than both the integers
We consider the integers 6 and -2
Difference =6-(-2)=6+2=8
8 is greater than both 6 and -2.
PLEASE HELP WITH THIS 25POINTSSSS!!!!!!
Answers
Which best explains why these two figures are similar or not similar?
Answers
Hey there! :)
Answer:
These two figures are similar because 5/3 equals 15/9.
Step-by-step explanation:
These figures are similar to each other, which means the side-lengths are proportional. Therefore:
[tex]\frac{5}{9} = \frac{15}{9}[/tex]
Side-lengths 15 and 9 are proportional to 5 and 3 because the two fractions are equivalent; the larger rectangle is just 3 times larger.
What is the greatest common factor of (2^5 x 6^7) and ( 2^3 x 6^8)
Answers
Answer:8 12 and 20
Step-by-step explanation:I googled it
What are the radius and circumference of a circle with diameter of 12 meters
Answers
Answer:
radius =6, circumference=37.7 m
Step-by-step explanation:
radius=12/6, circumference=2*pie*r
2*22/7*6=37.7 m
Answer:
Circumference of a circle = 2πr
where r is the radius
radius = diameter / 2
radius = 12 / 2 = 6 m
radius is 6 meters
Circumference = 2π×6
= 12π
= 37.7 meters
Hope this helps
A pattern is made from 4 congruent squares the sides of the squares are parallel to the axis
Answers
Answer:
Coordinate of C = (22, 20)
The Complete Question related to this found at ELEVISE website is stated below:
A pattern is made from four identical squares. The sides of the squares are parallel to the axes. Point A has the coordinates (6, 7)
Point B has the coordinates (38, 36)
Point C is marked on the diagram.
Work out the coordinates of C.
Step-by-step explanation:
Coordinates (x, y)
Point A has the coordinates (6, 7)
Point B has the coordinates (38, 36)
Find attached the drawing
From the labelled diagram
Change in y = 36-7 = 29
Change in x = 38-6 = 32
Using the horizontal axis:
The length of congruent 4 squares is between 38 and 6 = 32
The length of each congruent 4 squares = 32/4
The length of each congruent 4 squares = 8
Therefore the dimensions of the square is 8 by 8
Coordinate of C (x, y)
For x axis = 38 - length of 2 squares OR 6+ length of 2 squares
38 - length of 2 squares =38 - 2(8)
= 38-16 = 22
For y axis = 36 - length of 2 squares
= 36 - 2(8)
= 36-16 = 20
Coordinate of C = (22, 20)
Please answer this question now in two minutes
Answers
Answer:
c. Not enough information
Subtracting Rational Numbers Simplify –3 – 1.
Answers
Answer:
-4
Explanation:
when subtracting a positive integer from a negative, the answer becomes smaller. If the question were to ask -3-(-1) negative 3 minus negative 1, the subtraction sign becomes a addition sign, and you add 1 to -3.
Answer: -4
Step-by-step explanation: To subtract the integers -1 - 1, I would first change the minus sign to plus a negative.
So we have -1 + -1.
Now let's use a number line to find our answer.
Starting at 0, -3 moves us 3 units to the left, then from there,
-1 moves us 1 more unit to the left and we end up at -4.
So -3 + -1 is -4.
Please help me!!!!!!!!!!!!!!!!!
Answers
Answer:
A is the correct option.
Step-by-step explanation:
1/12 = 0.0833333333
Answer:
Option A
Step-by-step explanation:
=> [tex]\frac{1}{12}[/tex] = 0.8333.........
=> [tex]\frac{7}{8}[/tex] = 0.875
=> [tex]\frac{14}{25}[/tex] = 0.56
=> [tex]\frac{17}{20}[/tex] = 0.85
=> [tex]\frac{6}{10}[/tex] = 0.6
So, 1/12 is the repeating decimal whose digits are periodic and repeats infinitely.
How much metres per second did the cyclist travel from 8 a.m. to 10 a.m? (*TIP: 2 hours = 7200 seconds, 2 km= 2000 m). Give the formula used, show your working and round off your answer to two decimal places. Don't forget the unit!
Answers
Answer:
[tex]Speed = 0.28m/s[/tex]
Step-by-step explanation:
Your question seem incomplete; however, I'll assume the given tips as the usable parameters.
Given
Distance = 2km
Time = 2 hours (8am to 10am)
Required
Calculate speed (in metres per seconds)
Speed is calculated as follows:
[tex]Speed = \frac{Distance}{Time}[/tex]
Substitute 2 km for distance and 2 hours for time.
[tex]Speed = \frac{2km}{2hr}[/tex]
Convert km to metres an hr to seconds.
[tex]Speed = \frac{2000m}{7200s}[/tex]
[tex]Speed = 0.277778 m/s[/tex]
[tex]Speed = 0.28m/s[/tex] (Approximated)
Hence, the cyclist travels at 0.28m/s
this Venn diagram shows was played by 10 students let event A = was the same play basketball like even see it with a student play soccer what is a P(A OR B)
Answers
Answer:
B. 3/5 is correct.
Step-by-step explanation:
P(A or B) is the number of students within either set (circle) divided by the total number of students (10).
There are 6 students (3+1+2) in the sets, so
P(A or B) = 6/10 = 3/5
Answer B. 3/5 is correct.
The value of P(A or B) from the Venn diagram is 2/5.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
Event A = Students that play basketball
Event B = Students that play Soccer
Now,
From the Venn diagram,
P(A) = 3/10
P(B) = 2/10
P(A ∩ B ) = 1/10
Now,
P(A or B) = P(A U B ) = P(A) + P(B) - P (A ∩ B)
So,
P(A U B )
= P(A) + P(B) - P (A ∩ B)
= 3/10 + 2/10 - 1/10
= (3 + 2 - 1) / 10
= 4/10
= 2/5
Thus,
The value of P(A or B) is 2/5.
Learn more about the Venn diagram here:
https://brainly.com/question/1605100
#SPJ7
How many values of x make 6x+8= 54 a true statement?
a) one value
b) no values
c) infinite values
Answers
Answer:
c
[tex]7.6666666666[/tex]
bcz its
Step-by-step explanation:
[tex]6 = 54 - 8 \\ 6x = 46 \\ x = 46 \div 6 \\ x = 23 \div 3 \\ [/tex]
What is 9 + 10 ? I’m so confused. People keep telling me it’s 21 but it doesn’t seem right.
Answers
Answer:
It's 21.
Step-by-step explanation:
The factors of 9 are 3 and 3. (You need to multiply 3x3 to get 9.) The factors of 10 are 5 and 2. But, if you multiply 3 by 5, which gives you 15, and multiply the other 3 by 2, which gives you 6, and then add 6 to 15, you get 21.
perpendicular to 2x-3y+12=0
Answers
Answer:
3x +2y = 0
Step-by-step explanation:
Swapping the x- and y-coefficients and negating one of them will get you a perpendicular line. Since you have not specified a point, we can make it go through the origin:
3x +2y = 0
one container is filled with a mixture that is 30% acid a second container is filled with the mixture that is 50% acid the second container is 50% larger than the first and the two containers are emptied into a third container what percent of acid is in the third container
Answers
Answer:
42%
Step-by-step explanation:
x is for the volume of the container
the amount filled in the first container=0.30x
the volume of the first container + 50% of the second=(x+x*50%)=1.5 x
the amount of acid in the second container= 1.5x * 50%=0.75x
total amount of acid in the third one =0.3x+0.75x=1.05x
total solution : x+1.5x=2.5x
percentage=1.05x/2.5x= 0.42 or 42%
PLEASE ALL YOU NEED TO DO IS MATCH NUMBERS *Drag the tiles to the correct boxes to complete the pairs. Match the algebraic addition of each pair of complex numbers to its sum represented graphically.*
Answers
Answer:
1) A = (3 + 5·i) + (2 - 3·i)
2) A = (-3 + 5·i) + (-2 - 3·i)
3) A = (-3 + 5·i) + (2 + 3·i)
4) A = (3 - 5·i) + (2 + 3·i)
Step-by-step explanation:
1) For the first chart, we have;
To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows
A = (3 + 5·i) + (2 - 3·i)
2) For the second chart, we have;
To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows
A = (-3 + 5·i) + (-2 - 3·i)
3) For the third chart, we have;
To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows
A = (-3 + 5·i) + (2 + 3·i)
4) For the fourth chart, we have;
To go from the start point to get the new line, we add the coordinates of the red line end point to the coordinates of the starting line end point as follows
A = (3 - 5·i) + (2 + 3·i)
Calculate the following without the use of a calculator
6-(-4) - 5
Answers
Answer:
Calculate 6-(-4)-5
6-(-4)-56+4-510-55so : 6-(-4)-5 = 5
The Answer is 5
if you calculate it you get 5
A person is standing \(40\) ft from a light post and can see the top of the light at a \(35^\circ\) angle of elevation. The person’s eye level is \(5\) feet from the ground. What is the height of the lightpost to the nearest foot.
Answers
Answer:
The height of the lightpost is 33.008 feet
Step-by-step explanation:
Refer the attached figure
Distance between lamp post and person = AB = 40 feet
Height of person = BC = 5 feet
The angle of elevation = ∠DCE =35°
Height of light post = AD
AB=CE=40 feet
In ΔDCE
[tex]\frac{Perpendicular}{Base}=Tan \theta \\\frac{DE}{CE}=tan 35^{\circ}\\\frac{DE}{40}=tan 35^{\circ}\\DE=40 \times tan 35^{\circ}\\DE=28.008[/tex]
Height of light post = AD=DE+AE=28.008+5=33.008
Hence the height of the lightpost is 33.008 feet
Fill in the blanks to solve 2{,}000 \times 92,000×92, comma, 000, times, 9. 2{,}000 \times 92,000×92, comma, 000, times, 9 Step 111 {} \times \ 2 \times 9× 2×9times, space, 2, times, 9 Step 222 {}\times \ 18× 18times, space, 18 Step 333
Answers
Answer:
[tex]\boxed{}[/tex] =1,000
Step-by-step explanation:
We want to solve: [tex]2{,}000 \times 9[/tex]
Now, 2000=1000 X 2
We were given the following steps:
[tex]S$tep 1: \boxed{1000} \times \ 2 \times 9\\S$tep 2: =\boxed{1000} \times \ 18\\S$tep 3: =18,000[/tex]
Therefore, the blank space is to be filled with 1000.
[tex]2{,}000 \times 9 =18{,}000[/tex]
Como le explicarian a un compañero como se puede descomponer un numero escribiendo sumas y potencias de 10? Como se puede averiguar el valor relativo de cada cifra de un numero? Busquen ejemplos que den cuenta a esta explicacion
Answers
Answer:
Léase explicación detallada para mayor entendimiento.
Step-by-step explanation:
La metodología a utilizar es la siguiente, un número de base 10 es una combinación de dígitos entre 0 y 9, el dígito a la derecha del observador es el dígito pivote, el orden del dígito aumenta a medida que el observador dirige la mirada hacia su izquierda. Asimismo, el orden del dígito disminuye a medida que el observador dirige la mirada hacia su derecha.
Ejemplo - Ponga en orden descendente el orden de los dígitos de 3605.
Se descubre que el 5 es el dígito pivote (Orden 0), 0 esta un orden por encima del dígito pivote (Orden 1), 6 esta a dos órdenes por encima del dígito pivote (Orden 2) y 3 está tres órdenes por encima del dígito de menor pivote (Orden 3). En consecuencia, la jerarquía de los dígitos en orden descendente es 3 - 6 - 0 - 5.
Ejemplo - Ponga en orden ascendente el orden de los dígitos de 245,471.
Se descubre que el 5 es el dígito pivote (Orden 0), 4 está un orden por encima del dígito pivote (Orden 1) y 2 está dos órdenes por encima del dígito pivote (Orden 2). Asimismo, 4 está un orden por debajo del dígito pivote (Orden -1), 7 está dos órdenes por debajo del dígito pivote (Orden -2) y 1 está tres órdenes por debajo del dígito pivote (Orden -3). En consecuencia, la jerarquía de los dígitos en orden ascendente es 1 - 7 - 4 - 5 - 4 - 2.
Ahora, se puede descomponer un número conforme el número a partir de sumar cada dígito multiplicado por 10 elevado por el orden que le corresponde dentro del número, cuyo procedimiento se explica con un ejemplo:
Ejemplo - Descomponga 1268.153 en sumas y potencias de 10.
El dígito 8 es el dígito pivote, existen tres dígitos cuyo es superior al del dígito pivote y tres dígitos con un orden inferior al dígito pivote, entonces este número real se puede reescribir como sigue en orden descendente:
[tex]1268.153 = 1 \times 10^{3} + 2 \times 10^{2} + 6\times 10^{1} + 8 \times 10^{0} + 1 \times 10^{-1} + 5\times 10^{-2} + 3 \times 10^{-3}[/tex]
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Answers
Step-by-step explanation:
In my opinion the reason 4 is incorrect
Answer:
Step-by-step explanation:
step 4 suppose to be :Step 2: Multiply both sides by 2/3.
(2/3)*(3/2x)=(2/3)*(60)
area of the base pentagonal prism with a volume of 50 cubic centimeters and a height of 7.5 centimeters
Answers
Hey there!
To find the volume of any prism, you multiply the base by the height. However, we want to find the base here. So, we do it backwards and take the volume and divide it by the height, and this will give us our base!
50÷7.5=6 2/3
Therefore, the area of the base of a pentagonal prism with a volume of 50 cubic centimeters and a height of 7.5 centimeters is 6 2/3 square centimeters.
Have a wonderful day! :D
Eva is working out the area of the triangle. The base is 7.8 cm and the length of one side is 6.3 cm. I multiply and then divide by 2. What mistake has Eva made?
Answers
Answer:
1/2✖️7.8✖️6.3.
She needs to multiply 1/2 instead of dividing it by two.
Step-by-step explanation:
Triangle area: 1/2✖️base✖️height
Answer:
Eva multiplied by two, and not 1/2.
Step-by-step explanation:
To find the area of a triangle, you must multiply the base and the height by 1/2.
Height: 6.3cm
Base: 7.8cm
1/2×6.3×7.8= 24.57
help me out please need this
Answers
the answer is ur guy
How many roots does a linear equation have?
Answers
Answer:
1 root
Step-by-step explanation:
A linear equation should only cross the x-axis at one point. That means there would only be 1 root. (Root is when y= 0)
Can someone please explain to me where did he get that 13 from or how to get it?
Answers
Answer:
2/9 * (-4 - 3) + 3
= 2/9 * (-7) + 3
= -14/9 + 3
= -14/9 + 27/9
= 13/9
A recipe needs 23 cup(s) of sugar for every 212 cups of flour. If you plan to use 10 cups of flour, how much sugar will you need?
Answers
Answer: you will need approximately 23 grams
Step-by-step explanation: but thats approximately
HELP urgently please please❤️❤️❤️Please
Answers
Answer:
Step-by-step explanation:
From the graph we can notice that :
g(2)=5g(-2)=2g(3)=0g(5)=1Again we can deduce from the graph that :
g(x)=0 when x= -3g(x)=6 when x= 0The figure à shown on ancient coin which was once used in china.the coin is in the shape of a circle of radius 3cm with a square of sides x cm removed from its center.the area of each face of coin is 7picm2.
(1)from an equatin in x and showw that itvis reduces to 2pi-x2=0.
(2)solve the equation 2pi-x2=0.
(3)find the perimeter of the square
Answers
Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
A telephone company charges a fixed monthly rate plus a rate per minute of usage. The company charges $135 for 100 minutes of usage and $375 for 500 minutes of usage. An equation can be written to show the relationship between the total minutes used (x) and the total monthly charges (y). Which of the following best describes the steps to draw the graph of y against x? (1 point)
Answers
Answer:
Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6
The ordered pairs are: (100, 135) and (500, 375)
The first number is the number of minutes of usage and the second number is the charge of the month.
The slope is: ( 375 -135) / (500 - 100) = 240/400 = 0.6
Step-by-step explanation: