7/18 is a rational number. A rational number is one that may be expressed as a fraction or as a component of a whole number.
What is a rational number?
Any number that can be stated as a fraction or as a portion of an entire number is considered rational.
The given number in the problem is;
7/18
The number is in the form of p/q and the denominator value is greater than the numerator in fraction form, so that the given number is a rational number.
Hence,7/18 is a rational number.
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Evaluate the expression using x = –1 and y=3. (6x4y3)
Answer:
6(-3)*4(3)*3
-12 *12 *3
-144*3
-432
Answer: -432
Step-by-step explanation:
12x
+3 = 7
5.
+
answer?
Answer: 6
Step-by-step explanation: 12x+3=75
-3 -3
12x=72
12 12
x=6
Answer:
x=6
Step-by-step explanation:
12x+3=75
12x=75-3
12x=72
x=6
I'm bad at math. a plan for a baseball diamond is drawn in a coordinate plane. the baseball diamond is in a shape of a square.with vertices at approximately (0,64),(64,0),(0,—64), and (—64,0). one unit in the coordinate plane represents 1 ft. what is the approximate area of the baseball diamond? what is the area of the trapezoid shown?
Answer:
Area of diamond=8192
Area of trapezoid =72 square unit
Step-by-step explanation:
Area of diamond:
find the distance between the points:
(0,64), (64,0), (0,-64),(-64,0)
d=√(x2-x1)²+(y2-y1)²
d=√64²+64²
d=64√2=90.51( rounded to the nearest hundredth)
since it is shape of square then all sides are equal
A=length*width
A=64√2*64√2
A=8192 square unit4- Area of trapezoid= ((base a +base b)/2) h
base a=3, base b=6 height=8 ( from graph count the tiles)
Area of trapezoid = ((3*6)/2 )* 8
Area=18/2*8
Area=9*8=72 square unit
The area of a diamond is 8192 square units and the area of a trapezoid is 72 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The area of the diamond will be calculated as below:-
find the distance between the points:
(0,64), (64,0), (0,-64),(-64,0)
d=√(x2-x1)²+(y2-y1)²
d=√64²+64²
d=64√2=90.51( rounded to the nearest hundredth)
Since it is the shape of a square then all sides are equal
A=length x width
A=64√2 x 64√2
A=8192 square unit
The area of the trapezoid will be calculated as below:-
Area of trapezoid= ((base a +base b)/2) h
base a=3, base b=6 height=8 ( from graph count the tiles)
Area of trapezoid = ((3*6)/2 )* 8
Area=( 18/2 ) x 8
Area=9 x 8=72 square unit
Therefore, the area of a diamond is 8192 square units and the area of a trapezoid is 72 square units.
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Un grupo de personas se reúnen para ir de excursión, juntándose un total de 20 entre hombres, mujeres y niños. Contando hombres y mujeres juntos, su número resulta ser el triple del número de niños. Además, si hubiera acudido una mujer más, su número igualaría al de hombres. ¿Cuántos hombres, mujeres y niños han ido de excursión?
Answer:
El número de hombres = 8 hombres
El número de mujeres = 7 mujeres
El número de niños = 5 niños
Step-by-step explanation:
El número total de personas en la excursión = 20
La suma de los hombres y las mujeres = 3 veces el número de hijos
El número de mujeres = 1 menos el número de hombres
Sea el número de hijos = A
Sea el número de mujeres = B
Sea el número de hombres = C
Tenemos;
B + C = 3 × A .................... (1)
B = C - 1 .......................... (2)
A + B + C = 20 .............. (3)
Sustituyendo el valor de A + B en la ecuación (1) en la ecuación (3), tenemos;
A + B + C = 20
A + 3 × A = 20
4 × A = 20
A = 5
Sumando la ecuación (1) a la ecuación (2), obtenemos
B + C + B = 3 × A + C - 1
2 · B + C - C + 1 = 3 · A
2 · B + 1 = 3 · A = 3 × 5 = 15
2 · B + 1 = 15
B = (15 - 1) / 2 = 7
B = 7
De la ecuación (2),
B = C - 1
7 = C - 1
C = 7 + 1 = 8
El número de niños = 5
El número de mujeres = 7
El número de hombres = 8.
who would win? Justice leage or the Teen titans, the Thundercats and the Teenage mutant ninja turtles
Answer:
JUSTICE LEAGUE
Step-by-step explanation:
What would be the total if 25%is 18
Answer:
72
Step-by-step explanation:
You would first change 25% to 0.25
Then divide 18 by 0.25 (18/0.25)
Which equals 72
Answer:
4.5 because its basically 18 divided by 4
Step-by-step explanation:
Word Problem 18.) You are ordering T-shirts from a catalog. Each T-shirt costs $15. The cost of shipping is $6 no matter how many shirts you order. The total cost is $111. How many T-shirts did you order? please i need help!!!
Answer:
7 t-shirts
Step-by-step explanation:
Because you know the cost of shipping ($6) is constant no matter the quantity you order (fixed cost), you can subtract it from the total cost of the order to find the total variable cost. Next you divide the left over cost by the cost per t-shirt to get the quantity ordered.
$111 - 6 = $105
$105 / $15 per shirt = 7 t-shirts
Hope this helps!
-The Business Man
Which expression could be used to calculate the volume of the new can?
Answer:
C.
Step-by-step explanation:
pi(r)^2
pi(2x+1)^2
6x(4pix^2+4pix+1pi)
24pix^3+24pix^2+6pix
Answer:
C
Explanation:
Volume for a cylinder is V= (pi)(r^2)(h)
r being radius, h being height.
The radius is 2x+1, so square that
(2x+1)^2 = 4x^2 + 4x + 1
Then multiply by 6x, the height
(4x^2 + 4x + 1)(6x) = 24x^3 + 24x^2 + 6x
Then multiply each term pi, which would be answer C.
Which of the following is a factor of x^2 -5x-6
Answer:
(x-6)(x+1)
Step-by-step explanation:
Nevaeh had 12 blue pencils and 18 red pencils to give out equally among the maximum number of classmates. How many red pencils will she give to each classmate?
Answer:
The answer to this problem is 3
Step-by-step explanation:
is 6 greater than 0.06 and 0.006
Answer:
Yes, 6 is greater then 0.06 and 0.006
Step-by-step explanation:
6 = 6.00
and both 0.06 and 0.006 are not even a whole number
Answer: Yes it is
Step-by-step explanation:
6>0.06 and 6 >0.006
Priscilla can make 2 bracelets in 12 minutes. At this rate, how many bracelets can she make in 48 minutes?
Answer: Priscilla can make 8 bracelets in 48 minutes.
Step-by-step explanation:
So the givens are that:
2 bracelets in 12 minutes, how many in 48 minutes
So find the ratio of bracelets to minutes:
2/12 simplified is 1/6
So Priscilla can make 1 bracelet per 6 minutes. We just need to find how many in 48 minutes.
1/6 * 8 = 8/48
So Priscilla can make 8 bracelets in 48 minutes.
Hence your answer.
DJ tracks the song request she received on Friday night she noted that the number of request for country songs with two more than 4/3 times a number request for hip-hop songs they're 18 request for country songs if X represents the number of request for K-pop songs which equation represents the situation how many request for hip-hop songs did the DJ receive on Friday night
Answer: DJ receive 12 requests for hip-hop songs on Friday night.
Step-by-step explanation:
As per given , we have
[tex]\text{(Number of request country songs ) = }2+\dfrac{4}{3}\times (\text{Number of request for hip-hop songs})[/tex]
Let X represents the number of request for hip-hop songs which equation represents the situation .
If they're 18 request for country songs, then
[tex]18=2+\dfrac{4}{3}X\\\\\Rightarrow\ 18-2 =\dfrac{4}{3}X\\\\\Rightarrow\ 16 =\dfrac{4}{3}X\\\\\Rightarrow\ X=\dfrac{3}{4}\times16= 3\times4=12\\\\\Rightarrow\ X=12[/tex]
Hence, DJ receive 12 requests for hip-hop songs on Friday night.
If the 11th term of a geometric sequence is 32 times larger than the 6th term, then
what is the common ratio of the sequence
Answer:
r = 2
Step-by-step explanation:
nth term of a geometric sequence = [tex] ar^{n - 1} [/tex].
Where,
a = first term, r = common ratio,
We are given that, the 11th term is 32 times larger than the 6th term of the geometric sequence. Thus:
the 6th term can be expressed as [tex] ar^{n - 1} = ar^{6 - 1} [/tex]
[tex] a_6 = ar^{5} [/tex]
The 11th term is expressed as [tex] a_11 = ar^{10} [/tex]
Since the 11th term is 32 times larger than the 6th term, therefore, the following equation can be derived to find the common ratio, r, of the sequence:
[tex] a_11 = 32*a_6 [/tex]
[tex] a_11 = ar^{10} [/tex]
[tex] a_6 = ar^{5} [/tex], therefore:
[tex] ar^{10} = 32*ar^{5} [/tex]
Divide both sides by ar⁵
[tex] \frac{ar^{10}}{ar^5} = \frac{32*ar^{5}}{ar^5} [/tex]
[tex] r^5 = 32 [/tex]
[tex] r^5 = 2^5 [/tex]
[tex] r = 2 [/tex]
Common ratio = 2
please helppp!!!!!!!!
Evaluate the expression when x = 11-2
10
1.-6x4 +X +20
2. 5x2 - 9x2 + 35
3. -8x + 13x3 -10
4. -9x2 + 10x -15
5. -8x2 + 13x3 +20
6. 8x4 + 13x - 10
7.-9x + 10x4 -15
8.-18x3 + 10x2 +20
9. 7x4 + 13x2-10
10. 6x3 + 13x - 10
11. 3x2 + 13x2 -10
12. 2x4 + 13x - 10
Can someone help me please
I'm confused as to why there's a random "10" but the answer is actually pretty simple. Insert (11-210) into the problems.
Basically substitute (11-210) into the numbers with the x variable.
Write the equation for Chelsea's graph in
slope-intercept form. Make sure the slope is
written in simplest form.
Answer:
[tex]y=-4x+16[/tex].
Step-by-step explanation:
From the given graph it is clear that the y-intercept is 16.
The line passes through (-2,24) and (2,8). So, slope of line is
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope=\dfrac{8-24}{2-(-2)}[/tex]
[tex]Slope=\dfrac{-16}{4}[/tex]
[tex]Slope=-4[/tex]
Slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Substitute m=-4 and b=16 in the above equation.
[tex]y=(-4)x+(16)[/tex]
[tex]y=-4x+16[/tex]
Therefore, the required equation is [tex]y=-4x+16[/tex].
Given the following function: f(x) = 3 – 5x
Evaluate f(-8) + f(-10) = ?
Answer:
96
Step-by-step explanation:
f(x) = 3 – 5x
f(-8) + f(-10) = 3 - 5*(-8) + 3 - 5*(-10) =3 + 40 + 3 + 50 =96f(-8) + f(-10) = 96
f(-8) + f(-10) = 96
Step-by-step explanation:f(-8) = 3 - 5×(-8)
= 3 + 40
= 43
f(-10) = 3 - 5×(-10)
= 3 + 50
= 53
f(-8) + f(-10) = 43 + 53 = 96
1. Smplify the expression. -5(6+9k) *
Answer:
-30-45k
Step-by-step explanation:
-5*6=-30
-5*9k=-45k
Answer:
-30 -45k
Step-by-step explanation:
-5(6+9k)
Distribute
-5*6 -5*9k
-30 -45k
I need help please help
Answer:
2.24
Step-by-step explanation:
Which shape does the intersection of the vertical plane with the prism look like?
Answer:
it looks like an triangle in the option above lol
Find the value of b×6 when b=7
Answer:
42
Step-by-step explanation:
It is basically 7×6 when you replace the b with 7
Answer:
The answer is 13.
Step-by-step explanation:
Find the value of 6 + b:
Replacing b by 7 gives 6 + 7. (example)
Find the slope and y-intercept of y = 2x - 5.
I
m =
b
Step-by-step explanation:
y=2x-5 is in y=mx+b
Where m = slope
[tex]slope = m = 2[/tex]
To find y-intercept :
[tex]y = 2x - 5[/tex]
Let x =0
[tex]y = 2(0) - 5 \\ y = 0 - 5 \\ y = - 5[/tex]
A number increased by 5 is less than or equal to 26
Answer:
Equation: x + 5 ≤ 26
Solved: x ≤ 21
The formula for the area of a triangle is A=1/2 bh, where b is the base of the triangle. what is the length of the base if the area is 32cm squared and the height is 4 cm
Answer:
base =16Step-by-step explanation:
[tex]A = \frac{1}{2} \times b \times h\\A = 32\\b = ?=x\\h = 4\\\\32 = \frac{1}{2} \times x \times 4\\\\32 = \frac{4x}{2} \\\\Cross \: Multiply\\\\64 =4x \\Divde \: both \: sides \: of \: the \:equation \:by \: 4\\\\\frac{4x}{4} = \frac{64}{4} \\\\x = 16[/tex]
7)
The first floor of the Willis Tower is 21 feet high. Each additional floor is 12 feet high.
a
Write an equation for the nth floor of the tower.
b.
Find the height of the 65th floor.
Answer:
Step-by-step explanation:
If the first floor of the Willis Tower is 21 feet high. and each additional floor is 12 feet high, then the floor heights as we move from one floor to another we keep increasing by 12feets and forms an arithmetic progression as shown;
21, (21+12), (21+12+12), ...
21, 33, 45...
a) To write an equation for the nth floor of the tower, we will have to find the nth term of the sequence using the formula for finding the nth term of an arithmetic sequence.
The nth term of an arithmetic sequence is expressed as [tex]T_n = a + (n-1)d[/tex]
a is the first term = 21
d is the common difference = 33-21 = 45-33 = 12
n is the number of terms
Substituting the given parameters into the formula;
[tex]T_n = 21+(n-1)*12\\T_n = 21+12n-12\\T_n = 21-12+12n\\T_n = 9+12n[/tex]
Hence the equation for the nth floor of the tower is expressed as [tex]T_n = 9+12n[/tex]
b) To get the height of the 65th floor, we will substitute n = 65 into the formula arrived at in (a)
[tex]T_n = 9+12n\\T_{65} = 9 + 12(65)\\T_{65} = 9+780\\T_{65} = 789 ft[/tex]
Hence the height of the 65th floor is 789feets.
please i need b, d, e, and f
Answer:
In the pics
Step-by-step explanation:
If you have any questions about the way I solved it correctly, don't hesitate to ask ;)
18. What value of “s” would make x =
6 in the following equation?
S + 3(2 + x) = -36
Answer:
S = 60
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
S + 3(2 + x) = -36
Step 2: Define variables
x = 6
Step 3: Plug in variables
S + 3(2 + 6) = -36
Step 4: Parenthesis
S + 3(8) = -36
Step 5: Multiply
S + 24 = -36
Step 6: Subtract 24 on both sides
S = 60
Question 3
Find the domain and range of the function represented by the graph?
A. Domain: -3
Range: -4<=y<=0
B. Domain: {-3, -2, -1, 0, 1}
Range: {-3, -2, 0, 1}
C. Domain: {-4, -3, 0, 1, 2}
Range: {-4, -3, -2, -1, 0}
D. Domain: -4 <= x<=-3
Range: 0<=y<=1
Answer:
Domain: [tex]-3\leq x\leq 1[/tex]
Range: [tex]-4\leq y\leq 0[/tex]
Step-by-step explanation:
If you find the coordinate of the graph you can get the domain and range
(-3,0), (-2,-4), (-1,-2), (0,0), (1, -4)
Now that we have that find the domain and range
Domain - x coordinate
Range - y coordinate
Domain: (-3, -2, -1, 0, 1)
Range: (-4, -2, 0)
Since the domain ranges from -3 to 1 you can use the inequality [tex]-3\leq x\leq 1[/tex] to represent the domain and [tex]-4\leq y\leq 0[/tex] for the range
.5(x+4)=12 help plssssssssssssssssssssssssss
Answer:
[tex]\frac{-13}{5}[/tex] or -2.6
Step-by-step explanation:
To do this you would first have the equation [tex]5(x+4)=12[/tex] and then you could multiply the x+5 by 5 which is 5x+25 so then your equation would be [tex]5x+25=12[/tex] then you would subtract 25 from both sides to cancel out the 25 so then your equation would look like this [tex]5x=-13[/tex] then you would divide from both sides to just get x so you would get [tex]x=\frac{-13}{5}[/tex] so you could leave it as is or you could turn it into a decimal which is -2.6