Factorize
ху
+ 3x +3y
+ 18
Answer:
(x+6)(y+3)
Step-by-step explanation:
xy + 3x + 6y + 18x(y + 3) + 6(y+3)(x+6)(y+3)Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
For the given inequalities, the graph can be plotted as shown below. Now when the coordinates have been plotted the point that will satisfy both the inequalities is (-2,2).
Hence, the correct option is B.
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A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of `pi`.)
The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³
How to find volume?The volume of the air space surrounding the cone inside the cylinder is as follows:
volume of the air space = volume of cylinder - volume of a cone
volume of cylinder = πr²h
volume of cylinder = π16 × 5²
volume of cylinder = 400π
volume of the cone = 1 / 3 πr²h
volume of the cone = 1 / 3 × π × 12 × 4²
volume of the cone = 64π
Therefore,
volume of the air space = 400π - 64π
volume of the air space = 336π
volume of the air space = 1055.04 cm³
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Two taps, *A* and *B* are of different sizes. Tap A fills a container with water in 3 minutes and Tap B fills the same container in 5 minutes. How much time Will it take if both the taps are turned on at the same time.
answer with working
\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }
Solve this ...
this is the question of laws of indices(exponent)
Answer:
5
Step-by-step explanation:
Given expression:
[tex]\dfrac{6^{n+2}-6^n}{6^{n+1}+6^n}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]
[tex]\implies \dfrac{6^n6^2-6^n}{6^n6^1+6^n}[/tex]
Factor:
[tex]\implies \dfrac{6^n(6^2-1)}{6^n(6^1+1)}[/tex]
Cancel [tex]6^n[/tex] :
[tex]\implies \dfrac{(6^2-1)}{(6^1+1)}[/tex]
Simplify:
[tex]\implies \dfrac{36-1}{6+1}[/tex]
[tex]\implies \dfrac{35}{7}[/tex]
[tex]\implies 5[/tex]
What is the missing number below in the solution to 968 divided by 10
Answer: 484/5
Step-by-step explanation:
For this word problem, it seems confusing with the wording but the equation would just be:
968÷10=x
solving for x, we get 484/5.
Select the correct answer.
Which set of coordinates satisfies the system of equations y=x-3 and y=-2x+1?
Y
w
A
N
9
83
B
-1
-2
3
5
C
3
4
O
Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]
Step-by-step explanation:
Setting the equations equal to each other.
[tex]x-3=-2x+1\\\\3x=4\\\\x=\frac{4}{3}\\\\\implies y=\frac{4}{3}-3=-\frac{5}{3}[/tex]
How many hours did theo and kade do separately?
identify if each function is a polynomial function. justify your answer.
Functions which are polynomials are y=[tex]5x^{4} +x^{2} -8[/tex] ,y=[tex]7x^{3}[/tex] and y=[tex]6^{x}[/tex]
Given Functions : 1) y=[tex]-x^{2} +1/1-2x[/tex] 2)y=[tex]5x^{4} +x^{2} -8[/tex]. 3) y=[tex]7x^{3}[/tex]and g(x)=[tex]6^{x}[/tex].
We need to find which functions are polynomials. We know that polynomials is an expression consisting of indeterminates and coefficients that involves only the operations of addition, subtraction, multiplication and non negative integers .
First function is y=[tex]-x^{2} +1/1-2x[/tex]
The above function is not a polynomial because it has not a variable containing power in whole number and it is in fraction form. Two different polynomials can form numerator and denominator in a fraction.
Second function is y=[tex]5x^{4} +x^{2} -8[/tex]
The above function is a polynomial as it has a variable having power and it is not in fraction also.
Third function is y=[tex]7x^{3}[/tex]
The above function is also a polynomial for the same reason.
Fourth function is g(x)=[tex]6^{x}[/tex].
The above function is also a polynomial.
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What is 3m+5m?
>8
>8m
>8m2
HELPPPPP ITS URGENTTTTT
click on the photo
Answer:
x=67.4
Step-by-step explanation:
well sin30:1/2
So y is not 30 since 5/13 doesn’t equal 1/2
So it’s either the the third or fourth option
And x>y
So option 4 is correct
Solve using a proportion.
Mario spends 8 hours each week practicing soccer. How many hours will Mario spend on soccer practice after 21 weeks?
A. 168 hours
B. 186 hours
C. 160 hours
D. 29 hours
The original price of a nail file is $0.60. How much will Emir pay if he buys it during the sale?
after 1 year, 80% of the initial amount of a radioactive substance remains. what is the half-life of the substance? half-life is
If a radioactive substance remains 80% of the initial amount then the half life of the radioactive substance is 2.5 years.
Given 80% of the initial amount of a radioactive substance remains.
If after 1 year the value or weight of the radioactive substance remains 80% means the rate of disappearing is 20% per annum.
If we clearly observe then it is forming a geometric progression and the rate is 80%.
Geometric progression will be if we assume the initial quantity be 100
is:
100,80,64,.........
we have to calculate the value of years in the value of term is 0.
the value of nth term of a geometric progression is [tex]ar^{n-1}[/tex]
so,
r is 0.8
100*[tex]0.8^{n-1}[/tex]=0
[tex]0.8^{n-1}[/tex]=0
if we calculate this we will find n-1=11
n=12
So the full life of radioactive substance is 12 and the half life will be 6 years.
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A small company manufactures picnic tables. The daily fixed cost is 1,200 and the variable cost is $45 per table. How many picnic tables can be produced for a total daily cost of 4,800.
Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:
C(n) = 1200 + 45n.
Now, we have to solve for n when C(n) = 4800, hence:
1200 + 45n = 4800
45n = 3600
n = 3600/45
n = 80.
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Which graph represents the following piecewise defined function?
-2x, x<-2
g(x)= -x², -2
X, X >1
Answer: See Attachment
Step-by-step explanation: I wasn’t sure if you meant -2 < x, but that’s the work I did to get the answer. If you can, send a picture of the question itself in case you didn’t mean -2 < x.
Solve using the factoring method: x2 + 4x - 21 = 0
Answer:
x² + 4x - 21 = 0
x² + 7x - 3x - 21 = 0
x ( x + 7 ) -3 ( x + 7 ) = 0
( x - 3 ) ( x + 7 ) = 0
∴ x - 3 = 0 or x + 7 = 0
x = 0 + 3 x = 0 - 7
x = 3 x = -7
find sizes of unknown angles
Answer:
a=75
b=70
c=110
d=105
e=110
f=105
Step-by-step explanation:
If the domain of the square root function f(x) is , which statement must be true?7 is subtracted from the x-term inside the radical.The radical is multiplied by a negative number.7 is added to the radical term.The x-term inside the radical has a negative coefficient.
The question was incomplete. Below you will find the missing content.
The square root function f(x) is x <= 7
Options are :
A. 7 is subtracted from the x-term inside the radical.
B. The radical is multiplied by a negative number.
C. 7 is added to the radical term.
D. The x-term inside the radical has a negative coefficient.
Option D is correct, which is : The x-term inside the radical has a negative coefficient.
Given, the domain of the square root function f(x) is x <= 7
Consider the function y = √x.
The domain of this function is x ≥ 0 and the range is y ≥ 0.
The expression inside the radical must be greater than or equal to zero.
Now, if x ≤ 7
x - 7 ≤ 0
7 - x ≥ 0
And the function y = √(7-x) will have the domain x ≤ 7.
This implies that the x-term inside the radical has a negative coefficient.
Therefore, the statement that the x-term inside the radical has a negative coefficient must be true.
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Simplify fully 4d2-6d2+5d2
Answer:
3d²
Step-by-step explanation:
Hello!
To simplify, we combine the like terms by adding them.
Like termsLike terms are terms with the same variable and degree. A degree is a power to which the term is raised. Like terms can have numerical coefficients. For example, a coefficient of 4 to x² would mean 4 times x².
We can see that the variable d² is common throughout the three terms, meaning they are like terms. We can simply add and subtract them.
Simplify4d² - 6d² + 5d²-2d² + 5d²3d²The simplified form is 3d².
perimeter =
help me please thank u :)
Answer:
[tex]\fbox {Perimeter = 37.92}[/tex]
Step-by-step explanation:
Finding the missing side :
⇒ Take the tan value of the listed angle
⇒ tan 60° = √3 = 6/x
⇒ x = 6/√3 × √3/√3 = 2√3 = 2(1.73) = 3.46
Solving :
⇒ Perimeter = 10 + 2(6 + 3.46)
⇒ Perimeter = 10 + 2(9.46)
⇒ Perimeter = 19 + 18.92
⇒ Perimeter = 37.92
A 2-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent, total 100 percent. Column 2 has entries 40 dollars, 40 dollars, 40 dollars, 40 dollars, blank total.
Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show. After paying the agent, Daniel takes home $120. Use the diagram to answer the following questions.
Daniel’s agent made
.
Daniel and the agent made a total of
from the show.
Answer:
Amount in Blank total = $160
Amount of money Daniel’s agent made = $40
Amount of money Daniel and the agent made
from the show = $160
Step-by-step explanation:
this question is based on the calculation of percentages
so,
it is is given in the question that -
Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show.
After paying the agent, Daniel takes home = $120
so,
let 'x' is the total amount of money that Daniel earned form the show
it is also given that Daniel promised to give 25 % to his agent from what he earned from the show
so, percentage of money left to the Daniel is
100-25 = 75%
therefore according to the question,
75percent of the x = $120
75/100×(x) = 120
3/4×(x) = 120
3x = 120×4
3x = 480
x = $160
so the total amount of money Daniel earned from the show is $160
Now we know that Daniel’s agent made 25% of the total amount of money earned from the show
therefore
25percent of 160 = Daniel’s agent made
25/100 ×160 = Daniel’s agent made
$40 = Daniel’s agent made
so the amount of money earned by Daniel’s agent made is $40
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Answer: Daniel’s agent made
✔ $40
Daniel and the agent made a total of
✔ $160
from the show.
.
Step-by-step explanation:
Use the numbers below to answer the following
question.
6^1, 3^2, 2^3, 1^7
Which shows the numbers ordered from least to
greatest?
Definition:
[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]
also
[tex]a^1=a\\\\a^0=1[/tex]
[tex]6^1=6\\\\3^2=3\cdot3=9\\\\2^3=2\cdot2\cdot2=8\\\\1^7=1[/tex]
therefore
[tex]\huge\boxed{1^7 < 6^1 < 2^3 < 3^2}[/tex]Three years ago, dedrick's age was a third of francisca's age. in 13 years, francisca's age will be twice dedrick's age. how old are they now?
Answer:
Step-by-step explanation:
According to the first statement, "Three years ago, Dedrick's age was a third of Francisca's age":
D - 3 = (1/3) * (F - 3)
According to the second statement, "In 13 years, Francisca's age will be twice Dedrick's age":
F + 13 = 2 * (D + 13)
Now, we have a system of two equations. We can solve these equations to find their current ages.
Step 1: Solve the first equation for D in terms of F:
D - 3 = (1/3) * (F - 3)
3D - 9 = F - 3
3D = F + 6
D = (F + 6) / 3
Step 2: Substitute the expression for D into the second equation:
F + 13 = 2 * ((F + 6) / 3 + 13)
Step 3: Solve for F:
F + 13 = 2 * ((F + 6) / 3 + 13)
F + 13 = 2 * (F + 6 + 39)
F + 13 = 2 * (F + 45)
F + 13 = 2F + 90
F - 2F = 90 - 13
-F = 77
F = -77
Step 4: Find D using the expression we found earlier:
D = (F + 6) / 3
D = (-77 + 6) / 3
D = -71 / 3
Now, we have found their ages, but we encounter a problem. Both Francisca and Dedrick's ages are coming out as negative, which is not meaningful in this context. It suggests that there might be an error in the initial information provided or in the equations derived from it.
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Use the law of cosines to find each missing side. Round to the nearest tenth
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As per the law of cosine, the measure of angle x can be written as,
[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]
Hence, the value of x is 117.8°. thus, the correct option is A.
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What is the radius for a circle whose equation is +=367
O A 18
OB. 1296
O C. 6
O D. 36
Simplify cubed 5 -10/27
The correct answer for the given expression is 99.22.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
The expression will be solved as:-
E = [tex]({5 -\dfrac{10}{27}})^3[/tex]
E = [tex](\dfrac{135-10}{27})^3[/tex]
E =[tex]\dfrac{125}{27}^3[/tex]
E = 99.22
Therefore the correct answer for the given expression is 99.22.
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Kelly brought a pair of sneakers for 35.00 she also brought a pile of different laces. Each set of laces,l, costs 3.00. Write a variable expression to show how Kelly could calculate her total cost
Answer:
35+3I
Step-by-step explanation:
35+3I
The inverse of the function f(x) = 1/2x + 10is shown.
h(x) = 2x-0
What is the missing value?
Answer:
20
Step-by-step explanation:
the inverse of
y=1/2x + 10
is
x=1/2y+10
from here you just solve for y
x-10 = 1/2y
2(x-10) = y
2x-20 = y
Which system of equations can be used to find the roots of the equation 4x/2=x/3+2x
The system of equation can be used to find the root of the equation is y= x³-4x² +2x and y=0 , y=4x² and y= x³+2x
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
y=-4x²
y= x³+2x
By equating the above equation we have
-4x²=x³+2x
Now, y= x³-4x² +2x
and y=0
By equating the above equation we have
x³-4x² +2x=0
y=4x²
y= -x³-2x
By equating the above equation we have
4x²=-x³-2x
Lastly,
y=4x²
y= x³+2x
By equating the above equation we have
4x²=x³+2x
Hence, the equation can be used is y= x³-4x² +2x and y=0 ,
y=4x² and y= x³+2x
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