Answer:
see below (I hope this makes sense!)
Step-by-step explanation:
Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.
Find an equation for the nth term of the arithmetic sequence. 9, 11, 13, 15, ...
Answer:
2n+7
Step-by-step explanation:
First lets find the common difference which is 2, now we can use this formula to find the nth term.
an = a1 + (n - 1 ) d
an= 9+(n-1)2
=9+2n-2
=2n+7
To check let's insert n=5, 2(5)=10+7=17.
15+2=17!
E campsite shop also sells boxes of Pick-Me-Up teabags. The base of each box is a 120 mm square. The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle. Work out the maximum number of boxes that will fit on the shelf.
Answer:
The maximum number of boxes that will fit on the shelf = 189 boxes
Step-by-step explanation:
First, to harmonize the units of the dimensions given, let us convert the unit of the Pick-Me-Up teabags to cm.
1 cm = 10mm
1mm = 0.1cm
∴ 120mm = 0.1 × 120 = 12cm
Therefore, the base of each box is 12cm²
Next, let us calculate the area of the shelf.
Dimension of shelf = 65cm × 35cm
∴ Area of shelf = 65 × 35 = 2275cm²
Therefore, to calculate how many boxes will fit into the shelf, we will divide the area of the shelf by the area of the boxes of Pick-Me-Up teabag. This is shown below.
Area of shelf = 2275cm²
Area of boxes = 12cm²
Number of boxes that will fit on the shelf = Area of shelf ÷ Area of boxes
= 2275 ÷ 12 = 189.58 boxes
since there are no fractional boxes, we will round down to the nearest whole number of boxes.
Hence, the maximum number of boxes that will fit on the shelf = 189 boxes
PLEASE ANSWER QUICKLY ASAP
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope / gradient
c is the y intercept
a).y = 3x + 7
Comparing this equation with the general form above
Gradient of the line = 3
b).2y - 6x = 8
Divide both sides by 2
We have
y - 3x = 8
To make y the subject move 3x to the right side of the equation
That's
y = 3x + 8
Comparing with the general form above that's y = mx + c
The gradient = 3
c).y = 3x + 7
A(2 , y ) , B( x , 4)
Since they lie on the line we can substitute their values into the equation to find the missing points
For A(2 ,y)
We have
y = 3(2) + 7
y = 6 + 7
y = 13For B( x , 4)
4 = 3x + 7
3x = 4 - 7
3x = - 3
Divide both sides by 3
x = - 1Hope this helps you
in the expretion7to the third power-4*3+8 the firstt operation is
Answer:
7³
Step-by-step explanation:
Using PEMDAS, we see that E (which stands for exponents) comes before M (which stands for multiplication) and A (which stands for addition) so the first operation you should do is 7³.
the area of a square poster is 27 in.2. Find the length of one side of the poster to the nearest tenth of an inc
Answer:
5.2 inches
Step-by-step explanation:
Let a be the side of the square poster.
The area of it is:
● A = a^2
● 27 = a^2
● a = √27
● a = √(9×3)
● a = 3√3
● a = 5.19
Round it to the nearest tenth
● a = 5.2 inches
The length of one side of the poster is approximately 5 inches rounded to nearest tenth.
What is rounding of numbers ?We round numbers because they are easy to deal with and they also retain their value to that place they have been rounded.
According to the given question the area of a square poster is 27inch².
We have to determine the length of one side of the poster.
We know area of a square is (side)².
∴ (side)² = 27.
side = [tex]\sqrt{27}[/tex].
We know [tex]\sqrt{25}[/tex] is 5 and [tex]\sqrt{36}[/tex] is 6 so [tex]\sqrt{27}[/tex] will lie between 5 and 8 and much closer to 5.
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plz help ASAP! thank u
Answer: Choice B)
The relation is a function because there are no vertical lines that can be drawn on the graph that pass through more than one point.
This graph passes the vertical line test. Any input (x) leads to one and only one output (y). An example of a graph failing the vertical line test would be a graph that is a sideways parabola.
Which number is closest to O on the number line?
-0.26
0.3
0.275
-0.51
Answer:
-.26
Step-by-step explanation:
If you take the absolute value (indicates how far a number-negative/positive- is from 0) of each number u listed you will find that .26 is the smallest number,thus smallest number.
Answer:
-.26 is closest to 0 on the number line.
Step-by-step explanation:
To find distance we use absolute value to find the smallest absolute value.
The absolute value of each number is as follows
-0.26 (0.26)
0.3 (0.3)
0.275 (0.275)
-0.51 (0.51)
In order from least to greatest we have
.26, .275, .3, .51
Therefore -.26 is closest to 0 on the number line.
Good luck!!
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
SP=2x+3, and LN=5x−14. Find SP.
Answer:
43
Step-by-step explanation:
Using Thales theorem:
● SP/LN = RP /RN
Notice that RN = 2×RP
● SP/LN = RP/2RP
● SP /LN = 1/2
● SP / (5x-14) = 0.5
● (2x+3)/(5x-14) = 0.5
● 2x+3 = 0.5(5x-14)
● 2x+3 = 2.5x -7
Add 7 to both sides
● 2x+3+7 = 2.5x-7+7
● 2x+10 = 2.5x
Sustract 2x brom both sides
● 2x+10-2x = 2.5x-2x
● 10 = 0.5x
Multiply both sides by 2
● 10×2 = 0.5x×2
● 20 = x
Replace x with 20 in Sp expression:
● SP = 2x+3
● SP = 2×20+3
● SP = 43
-3x+2y=6 Find the intercepts. Show your work.
Answer:
The x-intercept is (-2,0)
The y-intercept is (0,3)
Step-by-step explanation:
An x-intercept is the point when the graph crosses the x-axis. In other words, the y-coordinate of the x-intercept is 0 (since it lays on the x-axis). In other words, to solve for the x-intercept(s), plug in 0 for y and solve for x:
[tex]-3x+2y=6\\-3x+2(0)=6\\-3x=6\\x=-2[/tex]
So, the x-intercept is (-2,0).
Likewise, the y-intercept is the point when the graph crosses the y-axis. Because it's on the y-axis, the x-coordinate value would be 0. Thus, to find the y-intercept, plug in 0 for x and solve for y:
[tex]-3x+2y=6\\-3(0)+2y=6\\2y=6\\y=3[/tex]
Thus, the y-intercept is (0,3).
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
24.
What is the slope of a line through (-3, 4) and
(5, 6)?
PLEASE help if you can!!
Answer:
slope = 2 : 8 or 1:4
Step-by-step explanation:
a(-3, 4)
b(5, 6)
slope = rise / run
slope (6-4, 3+5))
slope = 2 : 8 or 1:4
Answer:
Slope =¼
Step-by-step explanation:
[tex](-3, 4) \: (5, 6) \\ x _{1} = - 3 , y_1 = 4 \\ x_2 = 5 \\ y_2 = 6[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{6 - 4}{5 - ( - 3)} \\ m = \frac{2}{8} = \frac{1}{4} [/tex]
plz help me asap!!!!!
What is the equation of the linear function represented by the table?
x
y
–5
14
–2
11
1
8
4
5
y = negative x + 9
y = negative x + 13
y = x + 13
y = x + 9
Answer:
It would be y = -x + 9
Step-by-step explanation:
Answer:
Y=-x+9
Step-by-step explanation:
There were 96 people in a queue to get into a fun fair. There were at least
4 children between any 2 adults.
What was the largest possible number of adults in the queue?
Answer:
32 adulta
Step-by-step explanation:
96÷6 = 16 number of families
now we need to see how many adults there are in 16 families.
and the number is 32 adults.
Answer:
32 adults.
Step-by-step explanation:
At the very least, there are 4 children for every 2 adults. That means that, at the very least, there are 6 people in one group to get into the fun fair.
96 / 6 = 16
So, there are 16 groups trying to get into the fun fair, with 2 adults in each group. 2 * 16 = 32 adults are in the queue.
Hope this helps!
two inches is approximately
Answer:
5.08 cm
Step-by-step explanation: You dont have the choices for answers.
2inches is also 1/6 of a foot, etc
A group of 6 people planned to spend $10.00 each to
rent a boat for an outing. At the last minute, 1 person
could not go on the outing. The others then paid
equally for the boat. How much did each pay?
Answer:
the ansser is $12
Step-by-step explanation:
becases 10 *6 is equal to 60 so if 1 person can not pay then you divide 60 by the remaineing 5 to get 12
A group of 6 people planned to spend $10.00 each to rent a boat for an outing. Each person have to pay 12 dollars.
How to calculate unit price of something?Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
A group of 6 people planned to spend $10.00 each to rent a boat for an outing. At the last minute, 1 person could not go on the outing.
10 x 6 = 60
So if 1 person can not pay then
We will divide 60 by the remaining 5
60/ 5 = 12
Therefore, Each person have to pay 12 dollars.
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In Exercises 22 describe how the change affects
the surface area of the right prism or right cylinder. Thank you!!
Step-by-step explanation:
Total Surface Area of original cylinder
= (2×(22/7)×9)(9+24)
=18×22/7×33
=1,866.8
Total Surface Area of new cylinder
=(2×(22/7)×9/3)(9/3+24/3)
=(2×(22/7)×3)(3+8)
=6×22/7×11
=207.4
Change or Ratio of org. cylinder to new cylinder
=1,866.8/207.4
=9.0009
243 as a power of 3
Answer:
243 as a power of 3
= 3^5
=243
Please does anyone know how to factorize x(x - 1) + 3x
Answer:
=x(x-1) +3x
= x^2-x+3x
=x^2 +2x
=x(x+2)
Step-by-step explanation:
Please answer this in two minutes
Answer:
x = 16
Step-by-step explanation:
The figure shown shows an inscribed angle F and central angle E. Both angles intercept the same arc.
Therefore, angle E is twice the measure of angle F, according to the central angle theorem of a circle.
Thus,
m<E = 2 * m<F
(x + 94)° = 2(55)
We can find the value of x with this equation.
x + 94 = 110
Subtract 94 from both sides
x = 110 - 94
x = 16
What is the divisor of 5.2 and 0.052
Answer:
5.2/0.052 is 100, and 100 is 10^2, so the missing divisor is 10^2
Answer:
100
Step-by-step explanation:
5.2/x = 0.052
Since the decimal place moves 2 places to the left from 5.2 to 0.052, the divisor is 100.
5.2/100 = 0.052
what is square root of the product of the number z and itself
Answer:
[tex]\large\boxed{z}[/tex]
Step-by-step explanation:
What is square root of the product of the number z and itself?
Break down into smaller parts
What is the product of the number z and itself?
Product = multiply
Write an equation multiplying z by itself
z * z
Bring back the full question: What is the square root of the product of the number z and itself?
Now we can just add a [tex]\sqrt{}[/tex] to the front of our equation to solve the problem.
[tex]\sqrt{z * z}[/tex]
Simplify
z * z = [tex]z^{2}[/tex]
[tex]\sqrt{z^{2} }[/tex]
In this case, the square root cancels out the exponent ([tex]z^{2}[/tex]), so [tex]\sqrt{z^{2} }[/tex] can simplify to z.
Hope this helps :)
Which of the following functions has a vertical asymptote at x = 2, a horizontal
asymptote at f(x) = 1, and a root at x = -1?
A.f(x) = 2 + 1
B.f(x) = x 2 + 1
c.f(x) = x 2 - 1
D.f(x) == +1
Answer:
First, an asymptote means that the function "tends to go" to a value, bt actually never reaches it.
The functions here are:
A.f(x) = 2 + 1
B.f(x) = x^2 + 1
c.f(x) = x^2 - 1
D.f(x) == +1
The functions are really poorly written, but i will try to answer this.
first:
"a root at x = -1"
Means that f(-1) = 0,
The only function that is zero when x = -1, is the option c.
f(-1) = (-1)^2 - 1 = 1 - 1 = 0.
Now, if we want to have a vertical asymptote at x = 2, then we should have a function like:
[tex]f(x) = \frac{something}{x - 2}[/tex]
So we want to have a quotient, where the denominator is equal to zero when x = 2, this will lead to a vertical asymptote.
I can not see this in the options provided, so i guess that the functions are just not well written.
For a horizontal asymptote, we have something like:
[tex]f(x) = \frac{something}{x} + 1[/tex]
So as x starts to grow, the first term in the function will start to decrease, until it becomes really close to zero (but is never equal to zero) so in that case we have an horizontal asymptote to f(x) = 1.
Plz help will give brainlist
20 POINTS!! What is the greatest common factor (GCF) of 100^2 - 250xy + 75x?
A. X
B. 25x^2
C. 25x
D. 5x
Answer:
Step-by-step explanation:
25x(4x -10y + 3)
the solution is C. 25x
The function gx) = x^2is transformed to obtain function hr.
h(x) = g(x-3).
Which statement describes how the graph of h is different from the graph of g?
A. The graph of his the graph of g vertically shifted down 3 units.
B. The graph of his the graph of ghorizontally shifted left 3 units.
C. The graph of h is the graph of g vertically shifted up 3 units.
D. The graph of h is the graph of g horizontally shifted right 3 units.
the graph will shift 3 units to the right
What is the image of (4,-7) after a reflection over the line y=x
Answer:
(-4,7)
Step-by-step explanation:
solved by graphing
SIMPLIFY.
6y^3(3 + 4y^2)
Answer:
18y^3 + 24y^5.
Step-by-step explanation:
6y^3(3 + 4y^2)
= 6*3 y^3 + 6*4 y^(3+2)
= 18y^3 + 24y^5.
2. The ratio of
the profit, cost of
materials and labour
in the production of
an article is 5:7:13
respectively. If the
cost of materials is Le
840 more than that of
labour, find the total
cost of producing the
article
Answer:
3500Step-by-step explanation:
Given the ratio of the profit, cost of materials and labour in the production of
an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25
If the cost of labour is x, the cost of material will be 840+x (since the cost of materials is Le 840 more than that of labour) .
Let the total cost of producing the article be y.
Cost of labour = 13/25 * y = x
Cost of labour = 13y/25 = x.................... 1
Cost of material = 7/25*y = 840+x
Cost of material = 7y/25 = 840+x ..................... 2
From 1, 13y = 25x
x = 13y/25 ................... 3
Substituting equation 3 into 2:
7y/25 = 840+x
7y/25 = 840+13y/25
collect the like terms:
7y/25 - 13y/25 = 840
-6y/25 = 840
-6y = 25*840
y = 25*840/6
y = 3,500
Hence the total cost of producing the article is 3500
What is equivalent to 9 3/4?
The answer is supposedly is 3 square root 3, but how is that the answer? can someone tell me the steps?
Step-by-step explanation:
We need to say that [tex]9^{3/4}[/tex] is equivalent to what.
We know that, (3)² = 9
So,
[tex]9^{3/4}=((3)^2)^{3/4}\\\\=3^{3/2}[/tex]
We can write [tex]3^{3/2} =3\times 3^{1/2}[/tex]
And [tex]3^{1/2}=\sqrt{3}[/tex]
So,
[tex]3\times 3^{1/2}=3\sqrt{3}[/tex]
So, [tex]9^{3/4}[/tex] is equivalent to [tex]3\sqrt{3}[/tex].
Hence, this is the required solution.
