Answer:
total amount of sweets=230
Step-by-step explanation:
ratio=8:5:10
total ratio=8+5+10
=23
Adrian=x
Charlie= x+20
Ben=1/2×(x+20)
Charlie's share
10/23×(x+20+x+(1/2×x+20))=x+20
10/23×(x+20+x+(x+20/2))=x+20
10/23×(x+20+x+x+20/2)=x+20
10/23×(2(x+20)+(2×x)+(x+20/2)/2=x+20
10/23×(2x+40+2x+x+20)/2=x+20
10/23×(2x+2x+x+40+20)/2=x+20
10/23×(5x+60)/2=x+20
50x+600/46=x+20
50x+600=46(x+20)
50x+600=46x+920
50x-46x=920-600
4x=320
4x/4=320/4
x=80
Total amount of sweet
x+x+20+1/2(x+20)
80+80+20+1/2(80+20)
180+1/2(100)
180+50
230
What is the intermediate step in the form (x + a)2 = b as a result of completing the
square for the following equation?
5x2 – 168 = -60x + 12
Answer:
5x2 – 168 = -60x + 12
5x*2 – 156 = -60x
-55x*2=156
55x=-78
x=-1.41818181818
also know as 18/7 or 1 4/7
Answer:
[tex](x+6)^{2}[/tex] = 51
Step-by-step explanation:
5x2 – 168 = -60x + 12
5x2 + 60 x – 180 = 0
[tex]x^{2}[/tex] + 12 x – 15 = 0
[tex]x^{2}[/tex] + 12 x = 15
+ 36 + 36
[tex]x^{2}[/tex] + 12 x + 36 = 51
[tex](x+6)^{2}[/tex] = 51
[tex]\sqrt{(x+6)^{2} }[/tex] = [tex]\sqrt{51}[/tex]
x + 6 = [tex]\sqrt{51}[/tex]
x = -6 ± [tex]\sqrt{51}[/tex]
what are the domain and range of the function on the graph?
Answer:
The domain: All real numbers.
The range: y>0
Step-by-step explanation:
Domain means all possible x values, and by looking at the graph it covers all real numbers.
Range means all possible y values, and since the x axis is a horizontal asyntope, the graph will never touch the x axis, which is why the range is y>0.
Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7?
x = –24, x = 16
x = –16, x = 24
x = –1, x = 9
x = 1, x = –9
Answer:
x = - 16, x = 24
Step-by-step explanation:
Given f(x) = 7 then equate f(x) to 7
0.5 | x - 4 | - 3 = 7 ( add 3 to both sides )
0.5 | x - 4 | = 10 ( divide both sides by 0.5 )
| x - 4 | = 20
The expression inside the absolute value bars can be positive or negative, so
x - 4 = 20 ( add 4 to both sides )
x = 24
OR
- (x - 4) = 20
- x + 4 = 20 ( subtract 4 from both sides )
- x = 16 ( multiply both sides by - 1 )
x = - 16
Answer:
The Answer is B
Step-by-step explanation:
Your Welcome
Three siblings are doing their washing and hanging all the items on the washing line.
On each line there is a shirt, a jumper and a towel. Each one has one spotted, one plain and one striped item, BUT none of them has the same item in the same design as their sibling. Sandra’s jumper is the same design as Paul’s towel and Paul’s jumper is the same design as Kerry’s towel. Kerry’s jumper is stripped and Sandra’s shirt is spotted.
a) Who has a striped shirt?
b) What design is Paul’s towel?
c) Who has a spotted jumper?
Answer:
A.) Paul
B.) Plain
C.) Paul
Step-by-step explanation:
Paul: Shirt - Striped; Jumper - Spotted; Towel - Plain
Kerry: Shirt - Plain; Jumper - Striped; Towel - Spotted
Sandra: Shirt - Spotted; Jumper - Plain; Towel - Striped
Hope this helps! Have a nice dayy! :)
Evaluate the expression using the Commutative and Associative properties of numbers.
Name the property used in each step.
13 + 23 + 12 + 7
Given:
The expression is:
[tex]13+23+12+7[/tex]
To find:
The value of the given expression by using Commutative and Associative properties of numbers.
Solution:
We have,
[tex]13+23+12+7[/tex]
Applying parenthesis and brackets, we get
[tex]=[13+(23+12)]+7[/tex]
[tex]=[13+(12+23)]+7[/tex] [Commutative properties of numbers]
[tex]=[(13+12)+23]+7[/tex] [Associative properties of numbers]
[tex]=(25+23)+7[/tex]
Using Associative properties of numbers, we get
[tex]=25+(23+7)[/tex] [Associative properties of numbers]
[tex]=25+30[/tex]
[tex]=55[/tex]
Therefore, the value of the given expression 55.
I need help with this
Answer:
the first option on the screen
c) Make k the subject of the formula t = ak/ 20
Answer:
k=20t/a
Step-by-step explanation:
20t=ak
20t/a=k
k=20t/a
if f(x)=3^x+10x and g(x)=5x-3, find (f-g)(x)
Answer:
[tex]3^x+5x+3[/tex]
Step-by-step explanation:
Given that,
[tex]f(x)=3^x+10x[/tex]
and
[tex]g(x)=5x-3[/tex]
We need to find (f-g)(x).
We know that,
(f-g)(x) = f(x)-g(x)
[tex]=3^x+10x-(5x-3)\\\\=3^x+10x-5x+3\\\\=3^x+5x+3[/tex]
So, the value of (f-g)(x) is [tex]3^x+5x+3[/tex].
Triangles J K L and X Y Z are shown. The length of side J is 3, the length of side K is 6, and the length of side L is 4. The length of side X is 4, the length of side Y is 4, and the length of side Z is 5.
Classify each of the triangles as acute, obtuse, or right.
Triangle JKL is
triangle.
Triangle XYZ is
triangle.
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are acute, scalene, obtuse, equilateral, isosceles and right angled triangle.
For a right angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the square of the remaining two sides.
For an obtuse triangle, the square of the longest side is greater than the sum of the square of the remaining two sides.
For an acute triangle, the square of the longest side is less than the sum of the square of the remaining two sides.
In triangle JKL:
J² + L² = 3² + 4² = 25
K² = 6² = 36 > 25 (J² + L²)
Hence triangle JKL is an obtuse triangle
In triangle XYZ:
X² + Y² = 4² + 4² = 32
Z² = 5² = 25 < 32 (X² + Y²)
Hence triangle XYZ is an acute triangle.
Answer:
obtuse & acute
Step-by-step explanation:
.........................
Answer:
The literals are; a, b, and c
The constants are; c, and 3
The variables are; x, and y
Step-by-step explanation:
The literals (numbers) are letters which represent numbers in an expression or equation, and to which mathematical operations, including, addition, subtraction, division, and multiplication can be applied
The given equation is a·x² + b·x + c - y + 3 = 0
The literals are;
'a', 'b', and 'c'
The constants are the values that remain the same always in an equation and does not change
The constants are;
'c', and '3'
The variables are the values that vary in relation to one another
The variables are;
'x', and 'y'
Elimination method
a-b=3
2a+3b=b
Answer:
a=3/2 b=-1 1/2
Step-by-step explanation:
i 6 = solve plz........
i’m losing my mind over this question :,) help asap would be amazing
find the length of c.
- 12sqrt3
- 16sqrt3
- 12sqrt6
- 16sqrt6
Answer:
I think it's either C or A
PLEASE HELP MEEE I NEED HELP
Answer:
how do I do another question
Answer:
6 seconds
Step-by-step explanation:
Start by assigning x to value you are trying to find - in this case, the number of seconds until Luigi catches up with Mario.
After x seconds, the distance Luigi has traveled will be the same as the distance Mario has traveled plus 90, since Mario is 90 meters ahead of Luigi.
So our equation is 50x = 35x + 90
Subtracting 35x from both sides: 15x = 90
Dividing both sides by 15: x = 6
So Luigi will catch up with Mario in 6 seconds.
Five hundred fifteen billion, eight hundred fifty-seven million, five hundred forty-nine thousand, forty-eight
Answer:
515,857,549,048
Step-by-step explanation:
I guess you are to write in numerals
Five hundred fifteen billion = 515,000,000,000
eight hundred fifty-seven million = 857,000,000
five hundred forty-nine thousand = 549,000
forty-eight = 48
Total = 515,000,000,000 + 857,000,000 + 549,000 + 48
= 515,857,549,048
Therefore,
Five hundred fifteen billion, eight hundred fifty-seven million, five hundred forty-nine thousand, forty-eight = 515,857,549,048
Please help I’ll give brainliest
Write the complement of (90° - a)
Answer:
The complement is ‘a’
Step-by-step explanation:
Mathematically, when two angles are complementary, or said to be a complement of each other, when added, they equal 90 degrees
So, by subtracting the above from 90 degrees, we have its complement
So, we have this as;
90 - (90-a)
= 90 - 90 + a = a
Convert log_8 1=0 into an exponential equation
o 1^0=8
O 0^8=1
o '8^0=1
o '8^=8
Given:
The logarithmic equation is:
[tex]\log_81=0[/tex]
To find:
The exponential equation for the given logarithmic equation.
Solution:
We have,
[tex]\log_81=0[/tex]
It can be rewritten as:
[tex]8^{\log_81}=8^{0}[/tex]
Using [tex]a^{\log_ax}=x[/tex], we get
[tex]1=8^0[/tex]
[tex]8^0=1[/tex]
Therefore, the correct option is C.
In one area, the lowest angle of elevation of the sun in winter is 20 degrees. Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.
Answer:
11.1 feet
Step-by-step explanation:
From the solution triangle attached, the required distance is represented as x ; the value of x can be obtained using trigonometry ;
Cosθ = opposite / Adjacent
Cos 20 = 10.5 / x
x * Cos 20 = 10.5
x = 10.5 / cos 20
x = 11.174 feets
find the lateral area of the prism
Answer:
We know that the lateral area of any prism is the sum of the areas of its side faces. Thus, the lateral area of a triangular prism is the sum of the side faces, that is the three rectangular faces. The formula to find the lateral area of a triangular prism is, (a + b + c) h or Ph.
so
20×6= 120 sq in
Answer:
120 sq in.
Step-by-step explanation:
LA = ah
LA = 20 × 6
A = 120
Please help I’ll give brainliest
Answer:
[tex]3ft^2[/tex]
Step-by-step explanation:
SA = [tex]6a^{2}[/tex]
SA = [tex]6(3)^2[/tex] Solve for the exponent first
SA = 6(9) Multiply
SA = 54 square feet
Frank has $8000 that he plans to split into two investments. He wrote the following two equations to represent the interests he will earn from each of the two investment options.
2000 A+ 6000B=520
400A+400B=480
Determine the interest rates, A and B as percentages
Answer:
Step-by-step explanation:
I still think your equations are wrong...
4000/4000 not 400/400 since the total investment is to be $8000
not $800
Step-by-step explanation:
2000 A+ 6000B=520
4000A+4000B =480
~~~~~~~~~~~~~~~~~~~~~
2000 A+ 6000B=520
-2000A - 2000B =-240
4000B = 280
B=7%
A=5%
The function h is defined by h (x) = 3x2 + 7.
Find h(5x).
h (5x) = ?
Answer:
h(5x) = 75x² + 7
Step-by-step explanation:
h(x) = 3x² + 7
h(5x) = 3(5x)² + 7
h(5x) = 3(25x²) + 7
h(5x) = 75x² + 7
[tex]h(5x) = 75x^2 + 7[/tex]
To find h(5x), you simply need to substitute 5x in place of x in the function [tex]h(x) = 3x^2 + 7[/tex] and then simplify the expression.
[tex]h(x) = 3x^2 + 7[/tex]
Now, replace x with [tex]5x: h(5x) = 3(5x)^2 + 7[/tex]
Simplify: [tex]h(5x) = 3(25x^2) + 7[/tex]
Now, calculate [tex]3 * 25: h(5x) = 75x^2 + 7[/tex]
So, [tex]h(5x) = 75x^2 + 7[/tex]
To know more about substitute:
https://brainly.com/question/29383142
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An investment of 100,000 AED increases at a rate of 16% per year. What is
the value of the investment after 20 years? Give your answer to 2 decimal
places
Answer:
1,946,075.95 AED
Step-by-step explanation:
Firstly, we write the general formula for an exponential increase as follows;
V(t) = A( 1 + r)^t
where V(t) is the value after some number of years t
A is the investment amount which is 100,000 AED
r is the rate of increase which is 16% = 16/100 = 0.16
t is the number of years which is 20
substituting these values;
V(20) = 100,000( 1 + 0.16)^20
V(20) = 100,000(1.16)^20
V(20) = 1,946,075.95 AED
Help plzzz plzzz asappp!!!!
Answer:
α = 27.9794744° ≈ 28.0 m (nearest tenth)
Step-by-step explanation:
Step 1:
Opposite (O) = 42.5 (the side opposite to the reference angle, α)
Adjacent (A) = 80
Hypotenuse (H) = the longest side opposite to the right angle
2. We are given the adjacent (A) and opposite (O) lengths, we would use TOA. Which is:
Tan α = Opp/Adj
Plug in the values
Tan α = 42.5/80
3. Make α stand alone
α = [tex] tan^{-1}(\frac{42.5}{80}) [/tex]
4. α = 27.9794744° ≈ 28.0 m (nearest tenth)
11) Write the explicit formula
for the sequence below and
use it to find the 47th term:
-3, 5, 13, 21,...
Answer:
365
Step-by-step explanation:
tn = t1 + (n - 1)(d)
t(47) = -3 + (47 - 1)(8)
t(47) = -3 + (46)(8)
t(47) = -3 + 368
t(47) = 365
The initial temperature of a solution was 16°C. The temperature dropped 3°C every minute. What was the temperature of the water after 15 minutes in °C?
Answer:
1 degree c
Step-by-step explanation:
can someone help me with this question
Answer:
What does the question mean can u explain me after that I will help u out in question
Which is equivalent to 3V8^1/4x
BROO SM PLS HELP
Answer:
= 24 3/4x
Step-by-step explanation:
3* 8 1/4x
Here 8 1/4 is a mixed fraction.
Convert it to improper fraction
8 1/4 = 33/4
So, 3*33/4 x
99/4 x
= 24 3/4x
That is
Hope this will helpful.
gimmie brainlist :)
Keller performed the work below to express the polynomial in factored form:
r(x) = x4 – 8x2 – 9
r(x) = (x2 + 1)(x2 – 9)
(x) = (x + 1)(x – 1)(x + 3)(x – 3)
Explain the error he made and complete the factorization correctly.
Answer:
He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots.
Step-by-step explanation:
He made the following mistake, he assumed that polynomial [tex](x^{2}+1) = (x^{2}-1)[/tex], having for granted that [tex]x^{2}+1[/tex] has two real roots, instead of two complex roots. The true factorized form of the fourth grade polynomial is:
[tex]r(x) = (x^{2}+1)\cdot (x^{2}-9)[/tex]
[tex]r(x) = (x- i)\cdot (x+i)\cdot (x+3)\cdot (x-3)[/tex]