Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation 2(3x-3)-5-2(x-3)+ 15 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is (Type an integer or a simplified fraction.) O B. The solution set is {x x is a real number O C. The solution set is ø A chef has 10 brands of hot sauce. In how many ways can the chef pick 3 to mix into a gumbo? | different ways There are In order to start a small business, a student takes out a simple interest loan for $3000.00 for 9 months at a rate of 11.75% a. How much interest must the student pay? b. Find the future value of the loan a. The amount of interest is S (Round to the nearest cent as needed) b. The future value is $ (Round to the nearest cent as needed.) Use an algebraic equation to find the measure of each angle that is represented in terms of x. 2x+30° 2x+40 m & 2x+30° m & 2x+ 40°=
Answers
Answer and Step-by-step explanation:
(i) The solution for equation: 2(3x-3) - 5 = 2(x-3) + 15 is:
2(3x-3) - 5 = 2(x-3) + 15
6x - 6 - 5 = 2x - 6 +15
6x - 2x = - 6 + 15 + 6 + 5
4x = 20
x = 5
The solution x is a real number and equals 5.
(ii) Since the order of hot sauce that goes into the gumbo doesn't matter, use combination:
[tex]C^{10}_{3}[/tex] = [tex]\frac{10!}{3! (10-3)!}[/tex]
[tex]C^{10}_{3}[/tex] = [tex]\frac{10.9.8.7!}{3.2.1.7!}[/tex]
[tex]C^{10}_{3}[/tex] = 120
There are 120 ways of picking 3 sauces out of 10.
(iii) Interest is calculated as:
interest = principal*rate*time
Principal is the value of the loan;
Rate is how much it will increase;
Time is for how long the loan will be taken. In this case, time is 9/12 since it was for months;
Interest = 3000 * [tex]\frac{11.75}{100}*\frac{9}{12}[/tex]
Interest = 264.37
The interest the student will pay will be: $264.37.
Future Value = principal + interest
future value = 3000 + 264.37
future value = 3264.37
The future value for the student is $3264.37.
(iv) As shown in the image in the attachment, the sum of the equations equals 90:
2x + 30 + 2x + 40 = 90
4x = 20
x = 5
2x + 30 = 2.5 + 30 = 402x + 40 = 2.5 + 40 = 50The angles are 40° and 50°
Related Questions
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Arrange the proof of the given statement in correct order to show that R is an equivalence relation. (Prove the given relation is reflexive first, and then symmetric and transitive.)
Answers
Answer:
The given relation R is equivalence relation.
Step-by-step explanation:
Given that:
[tex]((a, b), (c, d))\in R[/tex]
Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.
To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.
1. First of all, let us check reflexive property:
Reflexive property means:
[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]
Here we need to prove:
[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]
As per the given relation:
[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.
[tex]\therefore[/tex] R is reflexive.
2. Now, let us check symmetric property:
Symmetric property means:
[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]
Here we need to prove:
[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]
As per the given relation:
[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]
[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]
Hence true.
[tex]\therefore[/tex] R is symmetric.
3. R to be transitive, we need to prove:
[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]
[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)
[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)
To prove:
To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]
Multiply (1) with (2):
[tex]adcf = bcde\\\Rightarrow fa = be[/tex]
So, R is transitive as well.
Hence proved that R is an equivalence relation.
The relation R is an equivalence if it is reflexive, symmetric and transitive.
The order to options required to show that R is an equivalence relation are;
((a, b), (a, b)) ∈ R since a·b = b·aTherefore, R is reflexiveIf ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ RTherefore, R is symmetricIf ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·cMultiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈RTherefore R is transitiveFrom the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.Reasons:
Prove that the relation R is reflexive
Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)
The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c
By multiplication property of equality; a·b = b·a
Therefore;
((a, b), (a, b)) ∈ R
The relation, R, is reflexive.Prove that the relation, R, is symmetric
Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c
Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R
((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.
Therefore, the relation, R, is symmetric.Prove that R is transitive
Symbolically, transitive property is as follows; If x = y, and y = z, then x = z
From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c
Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e
By multiplication, a·d × c·f = b·c × d·e
a·d·c·f = b·c·d·e
Therefore;
a·f·c·d = b·e·c·d
a·f = b·e
Which gives;
((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.Therefore;
R is an equivalence relation, since R is reflexive, symmetric, and transitive.
Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.
Learn more about equivalent relations here:
https://brainly.com/question/1503196
the tax rate is 3.9%. What is the tax on $42?
Answers
Answer:
$43.64
Step-by-step explanation:
Answer:
1.64
Step-by-step explanation:
To find the tax, multiply the cost by the tax rate
42 * 3.9%
Change to decimal form
42 *.039
1.638
Round to the nearest cent
1.64
Please help me with this question!!!!!! PLEASE.
Answers
Answer:
B. -9, 7
Step-by-step explanation:
For the rational expression to be undefined the denominator has to equal 0.
x² + 2x - 63 = 0
Factor left side.
(x - 7)(x + 9) = 0
Set factors equal to 0.
x - 7 = 0
x = 7
x + 9 = 0
x = -9
x = -9 or x = 7
Answer:
B
Step-by-step explanation:
A rational expression is undefined when the denominator of the expression equals 0 (this is because anything over 0 is undefined). In other words, to find the values for which the given expression is undefined, we simply have to find the zeros of the denominator. We can ignore the numerator. Thus, let:
[tex]0=x^2+2x-63[/tex]
This is now a quadratic. Solve for the quadratic. I will factor but you can do whatever you like (complete the square, quadratic formula, etc.).
We notice that two factors that multiply to -63 and also add to +2 is 9 and -7. Thus:
[tex]0=(x+9)(x-7)[/tex]
[tex]x+9=0 ; x=-9[/tex]
[tex]x-7=0; x=7[/tex]
The zeros are -9 and 7.
The denominator will equal 0 at these values, and the expression will be undefined.
55=2.7[tex]55=2.7\sqrt{x} +14[/tex] what is the value of x
Answers
Answer:
230.59
Step-by-step explanation:
55 = 2.7sqrt(x) + 14
41 = 2.7sqrt(x)
15.185=sqrt(x)
x = 15.185^2
x=230.59
Which answer needs to be true to be able to use the SSS Congruence Postulate to prove △ABC≅△DBC? AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ and ∠ACB≅∠DCB ∠ACB≅∠DCB and ∠A≅∠D AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ or AC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Answers
Answer:
The correct option is;
[tex]\overline{AB}\cong \overline{DB}[/tex] and [tex]\overline{AC}\cong \overline{DC}[/tex]
Step-by-step explanation:
The steps to prove that ΔABC ≅ ΔDBC with the SSS Congruence postulate
We have;
Statement, Reason
BC ≅ BC, Reflexive property
[tex]\overline{AB}\cong \overline{DB}[/tex], Option selected
[tex]\overline{AC}\cong \overline{DC}[/tex], Option selected
ΔABC ≅ ΔDBC, SSS Congruency Postulate
Therefore, whereby all three sides of the triangles ABC and DBC are congruent, then ΔABC is congruent to ΔDBC.
Answer:
AC≅DF
AB≅DE
Step-by-step explanation:
took the test :)
Select the correct answer. Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs. If you assume he takes an equal amount of time to compose each song and graph this relationship with the number of weeks on the x-axis and the number of songs on the y-axis, what is Wayne's unit rate for composing a song?
Answers
Answer:
3 weeks for one song
Step-by-step explanation:
The function would be y = 3x + b
Answer:
it is 1/3 of a song per week for all you people that cant do math
Step-by-step explanation:
What is the area of the trapezoid?
30 square units
60 square units
90 square units
120 square units
Answers
Answer:
not d
Step-by-step explanation:
i tried it hehhe
Answer: 60 square units
Step-by-step explanation:
What is the length Y in this picture ?
Answers
Answer:
5
Step-by-step explanation:
The triangle pictured is a 45-45-90 triangle, meaning both legs are the same length, 5.
An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years
Answers
Answer:
y = 7,595.96(1.02)x
Step-by-step explanation:
y = 7,595.96(1.02)x
a normal linear equation is basically y = x + b
in this case,
y = amount of money in the bank accountx = number of yearsb is not required because there are no new deposits or withdrawals from the accountSince the accounts earns 2% interest per year, then you need to multiply the original amount by 1.02. As more years pass, the account will increase by 1.02, so the account increases by 1.02x. Since the original amount is $7,595.96, that will be our starting point.
Answer:
C y = 7,595.96(1.02)x
Step-by-step explanation:
How many times would you have to cross the Golden Gate Bridge in order to travel the exact distance between Wolverhampton and Birmingham?
Answers
Answer:
Hey!
Well...the distance from Birmingham to Wolverhampton in about 12 miles (19km)
The length of the Golden Gate bridge is 2,737m OR 2.737 km...in miles it's 1.701
So you will have to cross it about 11.2 times (3 sf)
Step-by-step explanation:
19 km / 1.701km = 11.16990005878895
Rounded up to a degree of accuracy = 3 sf
= 11.2
Hope this helps!
the total surface area of a cube is 294cm2. work out the volume of the cube.
Answers
Answer: 343 cm³
Step-by-step explanation:
The surface area of a cube is 6s^2, where s is the side length of a square. Thus, first do 294/6 to get 49. Then take the square root of 49 to get that each side of the cube is 7. The volume of a cube is s^2, so simply do 7*7*7 to get that the volume of the cube is 343cm^3
Hope it helps <3
Answer:
V =343 cm^3
Step-by-step explanation:
The surface area of a cube is given by
SA = 6s^2 where s is the side length
294 = 6s^2
Divide by 6
294 / 6 = s^2
49 = s^2
Take the square root of each side
sqrt(49) = sqrt(s^2)
7 =s
The volume of a cube is
V = s^3
V = 7^3
V =343 cm^3
Factor x2 – 3x – 28. An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Identify the values that should be written to complete the X diagram. On the top: On the bottom: On the sides: Rewrite the expression using the numbers on the sides of the X diagram. Use double grouping to factor the four terms. x2 – 3x – 28 =
Answers
Answer:
(x - 7)(x + 4)
Step-by-step explanation:
Note that 4 times 7 is 28, and that -7x + 4x = -3x.
Therefore, x^2 - 3x - 28 factors into (x - 7)(x + 4)
The factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).
What is a quadratic equation?
It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Writing a number or any mathematical object as the result of several factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
The factorization will be done as below:-
x² – 3x – 28
Split the middle term as 7 and 4.
x² – 7x + 4x – 28 = 0
x ( x - 7 ) + 4 ( x -7 ) = 0
Take x-7 common from the whole equation.
( x - 7 ) ( x + 4 ) = 0
Therefore, the factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ2
6TH GRAD LE MATH PLEASE HELP ME
Answers
Answer: 6
Step-by-step explanation: I think..... this is a division sign, nvm... so 4 divided by 8/12 is basically 4 x 12/8 which is 48/8 simplified is/equals 6!
Answer:
6
Step-by-step explanation:
4 / 8/12 = 4 * 12/8 = 4 * 3/2 = 6
which linear inequality is represented by the graph?
Answers
y < or = 1/2x + 3
Explanation
We know when x = 0, y has to be 3 (y intercept).
Therefore y>= or <= 2x + 4 is wrong since substituting x = 0 gives y=4.
Since you need the shaded part of the graph that’s under the line you need all the y values that are smaller than and equal to the inequality.
If it was greater than or smaller to the area above the line would be shaded.
Suppose that p partners equally share the profits from a sale of $3,600. Which algebraic expression represents this situation?
Answers
Given : p partners equally share the profits from a sale of $3,600
To find : Which algebraic expression represents this situation
Solution:
Number of Partners = p
Total Profit = $ 3600
Profit of Each Partner = Total Profit / number of Partners
=> Profit of Each Partner = 3600 / p
Hence is algebraic expression that represent the Share of each partner
Answer:
D
Step-by-step explanation:
100% on quiz
Help!!!! please!!!!!
Answers
Answer:
60 or 70
Step-by-step explanation:
Answer:
The shape is a trapezium; so use the formula for solving area of a trapezium to solve it. Which is
1/2(a+b)×h
=1/2(10+6)×7
=1/2 × 16 × 7
= 8×7
=56
what's the product of 9 (-8)
Answers
Answer:
-72
Step-by-step explanation:
I googled it.
Answer:
-72
Step-by-step explanation:
You take the 9, multiply by the -8, and boom. You get -72.
And when you multiply two opposite signs together, it equals to a negative number.
Boom bam boom you became a bit smarter
graph e(x) = √x − 10 .
Answers
Answer:
I Believe if so, this is your answer
Step-by-step explanation:
y = e ( x )
OR
y = √ x − 10
Given the following logarithmic equation, think about how you would solve each one. Now,
describe those processes using at least 3 to 4 sentences. Then solve, showing your work.
Equation 1: log2 + logx = log3
Answers
Answer: x = 3/2
Step-by-step explanation:
log (2) + log (x) = log (3) Given
log(2x) = log(3) Condensing log rules
2x = 3 Cancellation log rule
[tex]x=\dfrac{3}{2}[/tex] Division Property
Step 1: Calculate the measures of center for Mrs. Hampton's data in the dot plot (round your answer to the nearest tenths place). Show your work and briefly explain each step. (Measures of Center are the Mean and Median of a data set)
Answers
*dot plot is shown in the attachment below
Answer:
Mean = 6.3
Median = 6
Step-by-step explanation:
Measures of centre, mean and median, can be calculated as follows:
First, bear in mind that each dot represents a value in the data set.
==>Mean:
Mean is the sum of all values in the data set divided by the number of data set we have.
The sum can be calculated as follows:
0 (1) = 0
4 (3) = 12
5(8) = 40
6(3) = 18
7(1) = 7
8(5) = 40
9(2) = 18
10 (3) = 30
Sum = 0+12+40+18+7+40+18+30 = 165
No of data set = 26
Mean = 165/26 = 6.346 ≈ 6.3 (nearest tenth place)
==>Median: this is the middle value in the data set. Since the number of data set is even number (26) , the middle value lies between the 13th and 14th data points. The average of the 13th and 14th data points will give us the median value.
Thus, the 13th and 14th values are both 6.
Therefore, median = (6+6) ÷ 2 = 6
Answer:
The mode is 5, because 5 occurs 8 times, which is more than any other numbers occurring more than once. The median is 6, and this is because when you line up the numbers in order and cross them off to find the middle number, it is 6. I rounded to the mean to about 6.4. I got this by adding all of the numbers up, or by doing 12 + 40 +18 +7, etc, and got the total of 165. Because there is a total of 26 data points, I divided those numbers and got 6.3461, which ends up rounding to 6.4.
Step-by-step explanation:
change wording
In a school the the duration of primary section is 40 min and senior section is hour if the bell rings at 9 am together when will the next bell ring together
Answers
Answer:
11 a.m.
Step-by-step explanation:
Duration of Primary Period = 40 min
Duration of Senior Section =1 hour = 60 min
To find out when the next bell will ring together, we first determine the LCM of 40 and 60.
Multiples of 40 are: 40,80,120,160,...
Multiples of 60 are: 60, 120, 180, 240...
From the above, we observe that the bell will ring together exactly 120 Minutes after 9 a.m.
Therefore:
9+120 Min =9 +2 Hours =11 a.m.
Therefore, the bell of the primary section and senior section will ring together at exactly 11 am.
use
tiles
Algebra
factor for X^2-2x-3
Answers
Answer:
I hope it's correct
Think of 5 positive that have a mode of 4, a median of 8, a mean of 9 and a range of 12
Answers
Explanation:
Mode : 4
Median : 8
Mean : (8.5 + 4 + 8 + 4 + 20.5)/5 = 45/5 = 9
Range : 20.5 - 8.5 = 12
Caroline, Colin & Sarah share some money in the ratio 1 : 9 : 1.
In total, Caroline and Sarah receive £28.
How much does Colin get?
Answers
Answer:
Colin got £126
Step-by-step explanation:
Here we want to know how much Colin got from the sharing.
We can collapse the ratio to mean;
Colin : Caroline + Sarah
= 9:1 + 1 = 9:2
So total ratio is 9 + 2 = 11
If Caroline and Sarah got £28 we need to find the total money shared
Let the total money shared be £x
Thus;
2/11 * x = 28
2x = 11 * 28
x = (11 * 28)/2
x = 11 * 14 = £154
So the amount of money Colin got would be;
£154 - £28 = £126
At the deli, Alberto paid $24.33 for 7.4
pounds of sliced ham. What was the
price of one pound of sliced ham?
Answers
Answer:
About $3.28
Step-by-step explanation:
Divide 24.33 by 7.4
Answer:
3.28783783784...
Step-by-step explanation:
You're description could turn into 24.33 : 7.4.
You turn 7.4 into 1, and divide 7.4 / 1.
(It is 7.4)
Then, you divide 24.33 / 7.4.
It is 3.28783783784.......
or, If you want you're answer close to an natural number, It is 3.
I don't understand???? I'll give the brainliest!!!!!
Answers
Answer:
37Option A is the correct option.
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} - 2ab \: \cos \: c \: = {c}^{2} \\ a = 4 \\ b = 5 \\ c = 2 \\ \\ 2ab \: cos \: c = {a}^{2} + {b}^{2} - {c}^{2} \\ \: \: \: \: \: \: \: \: = {(4)}^{2} + {(5)}^{2} - {(2)}^{2} \\ \: \: \: \: \: \: \: \: = 16 + 25 - 4 \\ \: \: \: \: \: \: = 41 - 4 \\ \: \: \: \: \: \: = 37[/tex]
Hope this helps...
Good luck on your assignment...
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 2 , will he have enough paint to cover the tank with one layer of paint? [take = 3.142]
Answers
Answer:
He will have enough paint to cover the tank with one layer of paint
Step-by-step explanation:
To calculate the area of the surface that has to be painted, we will have to calculate the lateral surface of the cylinder
Lateral surface of the cylinder is given by
A=2πrh
Where,
π=3.142
r=1.1/2m=
h=1.4m
A=2πrh
=2*3.142*1.1/2*1.4
=4.84m^2
He uses 250ml to cover 1m^2
To cover 4.84m^2, he will use
4.84m^2 × 250ml of paint
=1,210ml of paint is needed
He has 2 litres of paint
2litres =2000ml
Tublu has 2000ml of paint but needs 1210ml of paint
Therefore,
He has an excess of 2000-1210
=790ml
The answer is yes, he will have enough paint to cover the tank with one layer of paint.
Mrs. Sing invests $12,876 for her business at an annual interest rate of 7 percent for 3 years. Which number will Mrs. Sing substitute for r in the simple interest formula? I = p r t
Answers
Answer:
she wills substitute r with 7%.
Step-by-step explanation:
Just did it.
Answer:
R = 7%
Principal (P)
Rate (R)
Time (t)
Step-by-step explanation:
The full intrest rate formula is i=prt
You are looking for r
R is the interest rate 7%
So i = 12,876*7%*3years will be the full equation.
Helppp!!!! please!!!
Answers
Answer:
B. 24700
Step-by-step explanation:
Answer:
b. 24700 cm³
Step-by-step explanation:
[tex]\frac{lwh}{3} \\\\65*30*38/3 = 24700 cm^3[/tex]
Hope this helps! :)
F(x)3x+5/x what is f(a+2)
A: 3a+5/a+2
B:3(a+2)+5/a+2
C:3(f(a))+5/f(a)+2