a. The expanded and simplified form is: -4a + 16
b. The expanded and simplified form is: 3a^2 + 6a
c. The expanded and simplified form is: 6x - 10
d. The expanded and simplified form is: x^2 - x - 6
e. The expanded and simplified form is: x^2 + 8x + 16
Sure, let's expand and simplify each expression step by step:
a. -4(a - 4)
Step 1: Apply the distributive property (multiply -4 by each term inside the parentheses).
-4(a) + -4(-4)
Step 2: Simplify the terms.
-4a + 16
So, the expanded and simplified form is: -4a + 16
b. 3a(a + 2)
Step 1: Apply the distributive property (multiply 3a by each term inside the parentheses).
3a * a + 3a * 2
Step 2: Simplify the terms.
3a^2 + 6a
So, the expanded and simplified form is: 3a^2 + 6a
c. 4x - 2(5 - x)
Step 1: Apply the distributive property (multiply -2 by each term inside the parentheses).
4x - 2 * 5 + 2 * x
Step 2: Simplify the terms.
4x - 10 + 2x
Step 3: Combine like terms.
6x - 10
So, the expanded and simplified form is: 6x - 10
d. (x - 3)(x + 2)
Step 1: Apply the distributive property (multiply x by each term inside the second parentheses and then multiply -3 by each term inside the second parentheses).
x * x + x * 2 - 3 * x - 3 * 2
Step 2: Simplify the terms.
x^2 + 2x - 3x - 6
Step 3: Combine like terms.
x^2 - x - 6
So, the expanded and simplified form is: x^2 - x - 6
e. (x + 4)^2
Step 1: Apply the square of a binomial formula: (a + b)^2 = a^2 + 2ab + b^2
(x)^2 + 2(x)(4) + (4)^2
Step 2: Simplify the terms.
x^2 + 8x + 16
So, the expanded and simplified form is: x^2 + 8x + 16
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Select all decimals that are equivalent to
(
9
×
100
)
+
(
2
×
10
)
+
(
3
×
1
10
)
+
(
5
×
1
100
)
.
A.
92.35
B.
920.350
C.
902.35
D.
92.350
E.
920.35
F.
920.035 I really need help
Answer:
B, E
Step-by-step explanation:
( 9 × 100 ) + ( 2 × 10 ) + ( 3 × 0.10 ) + ( 5 ×0.01 ) = 920.35
A. 92.35
B. 920.350
C. 902.35
D. 92.350
E. 920.35
F. 920.035
If each month in a year was paired with all the possible numbers of days in the month will the result be a function? Explain
Using the function concept, it is found that the result would not be a function, as for each month, there would be multiple possible number of days.
What is the condition for a relation to represent a function?In a function, one value of the input can be related to only one value of the output.
In this problem, the input is the month and the output is the possible number of days in the month.
Since there is a month with either 28 or 29 days, and the other months have either 30 or 31 days, the are multiple outputs for each input, hence, the result is not a function.
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Pls answer if you only know the correct answer! Thanks! :))
The ratio is (J/W) = 7/6. Or. J= (7/6)• W .
Second line: J= (7/6)• 24. J= 28.
Third line: J= (7/6)• 18. J= 21
A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15, how much is the cost of the pair of pants?
15 divided by two is 7.5 and ten plus 7.5 is 17.5…. It says less than half the cost so I would round down to get $17 for the pain of pants
The cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A certain t-shirt costs $10 less than half the cost of a pair of pants. If the t-shirt costs $15.
Let x be the cost of the pair of pants.
The value of x can be found as follows:
x = 15/2 + 10
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division.
x = $17.5
Thus, the cost of the pair of pants is $17.5 or $17 if the certain t-shirt costs $10 less than half the cost of a pair of pants.
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Can someone plz help me
Answer:
37500
Step-by-step explanation:
pattern is multiplying by -5.
-7,500*-5 = 37,500
Have a nice day! :-)
1. Find x.
Please help ASAP
Answer: 2.31
Step-by-step explanation:
Sabina has a box containing bottles of juice. The three flavors are
orange, mango and apple. The ratio of these flavor’s is 3 : 5 : 4 There are 35
bottles of mango juice. How many bottles are there altogether?
Answer:
[tex]36 + 35 = 71[/tex]
Step-by-step explanation:
[tex]3 + 5 + 4 = 12 \\ \\ 3 \times 3 = 9 \\ 5 \times 3 = 15 \\ 4 \times 3 = 12 \\ 9 + 15 + 12 = 36[/tex]
Answer:71 is correct
Step-by-step explanation:
3+5+4=12
3*3=9
5*3=15
4*3=12
9+5+12=36
36+35=71
Can you tell I suck at math?
Answer:
B). 34.85°
Step-by-step explanation:
From trigonometric ratios:
[tex] \sin(C) = \frac{opposite}{hypotenuse} [/tex]
Opposite = 16
Hypotenuse = 28
[tex] \sin(C) = \frac{16}{28} \\ \\ C = { \sin}^{ - 1} ( \frac{16}{28} ) \\ \\ C = 34.85 \degree[/tex]
Convert 7.5 gallons to quarts using a unit multiplier
Answer:
30 quarts
Step-by-step explanation:
4 quarts = 1 gallon
7.5 gallons * 4 quarts/ 1 gallon = 30 quarts
when x=1,2,3,.... find limit x->infinity
choice
a. 0
b. 1
c. 2
d. 3
f. 4
help me!!!
Let y = √x, so the limit can be rewritten as
[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]
Now,
[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]
so we can rewrite the limit further as
[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]
Combine the rational terms:
[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]
Then in the limit, we get
[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]
20 The nth term of an arithmetic series is Un where un > 0 for all n.
The sum to n terms of the series is Sn
Given that u4 = 6 and that S11 = (u6)2 + 18
Find the value of u20
Answer:
Hi,
[tex]u_{20}=30[/tex]
Step-by-step explanation:
[tex]u_n=u_1+(n-1)*r, \ r= commun\ ratio.\\u_4=u_1+3*r=6\\u_6=u_1+5r\\(u_6)^2=u_1^2+10ru_1+25r^2\\s_n=u_1+u_1+r+u_1+2r+...+u_1+10r=11*u_1+55r\\s_{11}=(u_6)^2+18\ \\\Longrightarrow\ u_1^2+10ru_1+25r^2+18=11u_1+55r\\\Longrightarrow\ 4r^2+2r-12=0\\\Longrightarrow\ 2r^2+r-6=0\\r=\dfrac{3}{2} \ or\ r=-2\ (excluded)\\\\u_1=6-3r=\dfrac{3}{2} \\\\\\\boxed{u_{20}=u_1+19*r=30}\\[/tex]
The value of the 20th term of the arithmetic series will be 30
What is arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Un = u₁+(n-1) x r
u₄ = u₁ +(3 x r)=6
u₆ = u₁ +5r
u₆²=u₁²+10ru₁+25r²+18=11u₁+55r
Sn= u₁+u₁+r+u₁+2r+.............u₁+10r= (11 x u₁) +55 r
4r²+2r-12=0
2r²+r-6=0
r=3/2
u₁=6-3r=3/2
u₂₀=u₁+(19 x r)= 30
Hence the value of the 20th term of the arithmetic series will be 30
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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
1 : 5
Step-by-step explanation:
3 students zoo
15 students aquarium
zoo : not zoo
3: 15
Divide each side by 3
3/3 : 15/3
1 : 5
Can anyone please help?
Answer:
i don't know
( lol )
heheeeee
find the surface area of each figure. Round to the nearest tenth if necessary.
Answer: 318 km²
Let's find the areas of the triangles
Formula: base x height / 2
9 x 6 = 54
54/2 = 27
Multiply by 2 since there are two triangles (I know, we already got the areas from 9 x 6)
27 x 2 = 54
Now let's try to find the areas of all the rectangular sides
Formula: length x width
9 x 11 = 99
8 x 11 = 88
7 x 11 = 77
99 + 88 + 77 = 264
Add up all the areas
264 + 54 = 318
SImplify to standard form (a+bi)
(12-9i)²
Answer:
Hello,
Step-by-step explanation:
Formula used (a+b)^2=a²+2ab+b²
[tex](12-9i)^2=3^2*(4-3i)^2\\\\=9*(16-9-24i)\\\\=9*(7-24i)\\\\=63-216i\\[/tex]
pls help solve for x
Answer:
x=4
Step-by-step explanation:
(x-1+5)×5=(2+x+4)×4
or, 5×(x+4)=4×(x+6)
or, 5x+20=4x+24
or, 5x-4x=24-20
or, x=4
17. ralph is 3 times as old as sarah. in 4 years ralph will only be twice as old as sara will be then. find ralph’s age now.
Answer:
Sara is now 4, will be 8 in 4 years. Ralph is now 12, will be 16 in 4 years.
Simplify [tex]x^{2} - 36[/tex]
Answer:
[tex] {x}^{2} - 36 \\ = (x + 6)(x - 6)[/tex]
Step-by-step explanation:
x^2-36
(x+6) ( x-6)
it's helpful to you
Answer:
[tex](x-6)(x+6)[/tex]
Step-by-step explanation:
In order to simplify this equation, one must use the quadratic factoring patterns. These patterns are as follows:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
This pattern works because, if one is to distribute the terms in the parenthesis by multiplying each term in one of the parenthesis by every term in the other, the result is the original equation:
[tex](a-b)(a+b)\\\\=(a)(a)+(a)(-b)+(a)(b)+(b)(-b)\\\\=a^2-ab+ab-b^2\\\\=a^2-b^2[/tex]
One can apply this pattern to the given equation, remember (6) times itself equals (36). Therefore, one can state the following: ([tex]36=6^2[/tex]), thus one can apply it to the given equation:
[tex]x^2-36\\\\=x^2-6^2\\\\=(x-6)(x+6)[/tex]
30 points please help
Find the volume of the pyramid.
76.34 ft3
458.06 ft3
916.11 ft3
305.37 ft3
Answer:
With the formula of lwh/3 the answer is 305.37
Step-by-step explanation:
l×w×h /3 =305.37
Answer:
916.11 ft³
Step-by-step explanation:
(9×6)×7.83/2×13/3
= 211.41×13/3
= 916.11 ft³
Answered by GAUTHMATH
A girl is 18 years younger than her mother. In 6 years time, the sum of their ages will be 54. How old is the girl now?
Answer:
12 yrs.
Step-by-step explanation:
let present age of girl=x
age of mother=x+18
after 6 yrs
age of girl=x+6
age of mother=x+18+6=x+24
according to the condition of question
(x+6)+(x+24)=54
2x+30=54
2x=54-30=24
x=24/2=12
what is the quotient of 64/-11
Answer:
-5.82
Possible by long devison and the rule that if there is one negitive then the answer is negitive
Three chains, each 14 feet in length, are
linked end to end. Two longer chains of
equal length are added to make a total
length of 100 feet. What is the length of
one of the longer chains?
A. 29 ft
B. 36 ft
C. 42 ft
D. 58 ft
E. 72 ft
Answer:
29 feet
Step-by-step explanation:
14 × 3 = 42
100 - 42 = 58
58 ÷ 2 = 29
One of the longer chains is 29 feet long.
Hope this helps.
HELP! TRIGONOMETRY QUESTION!!
Use the law of cosines, which says
189² = 215² + 123² - 2×215×123 cos(∠P)
==> cos(∠P) = 25,633/52,890
==> ∠P ≈ 61.06°
Below is a histogram representing the test scores from Mrs. Jackson's 2nd period History class. How many students scored a 90 or above?
Answer:
either 5 or 6
Step-by-step explanation:
I can't have a direct answer because you didn't get all of the histogram in there, but from what I can conclude from just this there's definitely either 5 or 6.
What is the solution to the system that is created by the equation y = - x + 6
Answer:
If you draw the graph of y = -x + 6 on the above graph the solution to system will be the coordinates of the point of intersection.
the equation of the line drawn above is y = 0.5x
so you can also find the solution by solving the system
y = 0.5x
y = -x + 6
0.5x = -x + 6
1.5x = 6
x = 6/1.5 = 4
and y = 0.5*4 = 2
The answer is (4, 2) - the third choice.
Step-by-step explanation:
2axy-4a^2xy^2+6a^3x^2
Answer:
2ax(y-2ay^2+3a^2x)
Step-by-step explanation:
2axy-4a^2xy^2+6a^3x^2
Given data
we have the following expression
2axy-4a^2xy^2+6a^3x^2
let us factor this expression
we have
2ax(y-2ay^2+3a^2x)
The common factor is 2ax
And the factorized expression is 2ax(y-2ay^2+3a^2x)
HELP ME PLS!
i need the first 4 examples
Answer:
1) 6а-9b=3(2a-3b)
2)8a-12b=4(2a-3b)
3) 5ab-5ac=5a(b-c)
4) 6ax+6ay=6a(x+y)
How do you simplify 3 times the square root 13?
Answer:
3√13
Step-by-step explanation:
3√13
This expression cannot be simplified because you cannot take any common factor outside the root.
Let f (x) = 3x + 1 and let g(x) = x - 1. Find (fog) (5)
0 0
O 15
O 4
O 7
Answer:
13
Step-by-step explanation:
(fog)=3(x-1)+1
ie puting the function of g in f
so (fog)= 3x-3 + 1= 3x-2
finding fog
(fog)(5)= 3(5)-2
ie sub stitute 5 in x
(fog)(5)=15-2=13
what percentage of 50kg is 65 kg?
Answer:
130
Step-by-step explanation:
65/50*100= 130