Distribute
3(x + 2) - 9x + 53x + 6 - 9x + 5Add the numbers
3x + 6 - 9x + 53x + 11 - 9xCombine like terms
3x + 11 -9x-6x + 11Distribute
3(x + 2) - 9x +5
3x + 6 - 9x + 5
Add the numbers
3x + 6 - 9x + 5
3x + 11 - 9x
Combine like terms
3x + 11 - 9x
6x + 11
13. When the cost of fuel rose by 10%, Albert decreased his fuel consumption by 10%. Albert claimed that there was no change in his expenditure on fuel consumption. Explain if Albert is right or wrong.
Answer:
Wrong
Step-by-step explanation:
Let cost of Albert's fuel be x.
When cost of fuel rises by 10% :
x (1 + 10%)x (1 + 0.1)1.1xWhen consumption is reduced by 10% :
1.1x (1 - 10%)1.1x (1 - 0.1)1.1x (0.9)0.99xSo clearly there is a 1% change in expenditure. Hence, Albert's claim is wrong.
Answer:
Albert is wrong -- explanation below
Step-by-step explanation:
Albert's expenditure "C" on fuel at any point in time is the product of the unit price, "p", and the amount of fuel purchased, "n".
In an equation form, [tex]C=pn[/tex].
Looking at some time before the changes, let's denote the unit price, the amount of fuel, and the expenditure with subscripts "1" to denote specific values at time 1, before the changes.
[tex]C_1 = p_1 n_1[/tex]
After the changes, note that p1 increased by 10%, and amount of fuel decreased by 10%.
Understanding changing percentages
For values that stay the same, we would multiply by 100% (or 1.00), since multiplying by 1 doesn't change the value.
For a 10% increase, we need 100%+10% which equals 110% or 1.10
For a 10% decrease, we need 100%-10% which equals 90% or 0.90
So, the new prices and amounts and costs at some later time, time 2, are given by [tex]C_2 = p_2 n_2[/tex], where [tex]p_2 = 1.10p_1[/tex] and [tex]n_2 = 0.90n_1[/tex].
Substituting:
[tex]C_2 = p_2 n_2[/tex]
[tex]C_2 = (1.10p_1) (0.90n_1)[/tex]
[tex]C_2 = 0.99 p_1 n_1[/tex]
But remember that [tex]C_1 = p_1 n_1[/tex], so
[tex]C_2 = 0.99 C_1[/tex]
In other words, the next expenditure is 99% as much as (or 1% less than) the old expenditure.
Thus, Albert is incorrect to state that there was NO change in his expenditure.
if you do all you'll get brainliest
Drive-In movie theatres are outdoor movie venues where people park facing a large screen and watch a movie from their own car. Daisy’s Drive-In charges $14.00 for a vehicle and an additional $4.00 per person in the car. Donald’s Drive-In charges $26.00 for a vehicle and an additional $2.00 per person in the car.
Write two equations that represent the 2 drive-in theatres.
Daisy’s Drive-In:
Donald’s Drive-In:
Graph the system of equations. Label the x and y axis and give the graph a title. Label each line.
What is the point of intersection on your graph? What does this mean in context of the problem? Answer in complete sentences.
Compare and contrast the theatre options. When will Daisy’s be a better deal? When will Donald’s be a better deal? Explain how you know. Answer in complete sentences.
Name the property of equality or congruence that justifies going from the first statement to the second statement.
3x+x+7=23
4x+7=23
Answer:
Reflexive Property
Convert 0.50 sen /g to RM/kg
the conversion is:
0.50 sen /g = 5 RM/kg
How to change the units?
First, we know that
1sen = 0.01RM
Then we can change:
0.50 sen /g = 0.50*(0.01 RM) /g = 0.005 RM/g
Now we use the relation:
1g = 0.001kg
So we can rewrite:
0.005 RM/g = 0.005 RM/(0.001kg) = 5 RM/kg
So the conversion is:
0.50 sen /g = 5 RM/kg
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Which pair of functions are inverses of each other?
f(x) = 10x -5 and g(x) = (x+5)/10 are inverses of each other , Option D is the correct answer.
What is a Function ?A function is a mathematical statement which relates two variables , a dependent and an independent variable.
The inverse of a function is found by replacing every y by x and vice versa , and then solve for y
The equation
f(x) = 4/x - 3
or
y= 4/x -3
Replacing y by x
x = 4/y -3
x +3 = 4/y
y = 4/(x+3)
Which do not correlate with the given inverse
f(x) = 10x -5
y = 10x -5
for finding inverse
10y -5 = x
10y = x+5
y = (x+5)/10
g(x) = (x+5)/10
Therefore , Option D is the correct answer.
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ve questions from this section 18 A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km/hr. At 8.30 am a car left Busia for Nairobi at an average speed of 120km/hr. Given that the distance between Nairobi and Busia is 400km. ve questions from this section 18 A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km
The time that the bus arrived Busia is given as 1.00 pm
How to solve for the time of arrivalThe formula with which to solve for the time is given as
D/s = distance / by the speed.
Distance = 400km
Speed = 80km/hr
Time = 400/80
= 5 hours
Therefore the time of arrival from 8.00 am would be 1.00pm
Complete questionA bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km
Calculate The time the car arrived in Busia
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© On Wednesday, Simran walked from home to the train station.
On Thursday, Simran took the bus from home to the train station.
The distance-time graphs show Simran's journey on Wednesday and Thursday.
How many minutes less was her total journey time on Thursday than on Wednesday? Need answer ASAP!
Simran's Journey was 35 minutes less on Thursday as compared to Wednesday
What is a Distance - Time Graph ?Distance Time graph is the relationship between the distance travelled in the respective time on the x axis.
Two distance time graph is given
The Wednesday graph shows the time taken by Simran is
Total Time = 40 minutes
and
The Thursday graph shows the time taken by Simran is
Total Time = 5 minutes
Therefore Simran's Journey was 40-5 , 35 minutes less on Thursday as compared to Wednesday
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What is the equation for the graph shown below?
Answer: D
Explanation:
Since we don't know the y-value of the vertex, let's do this an easy way: plugging in.
Let's use the y intercept since that would be the easiest. Since x=0, the terms with x cancel, and you will get a leading result of -5
A) results in 2, so eliminate it
B) results in -2, so eliminate it
C) results in 5, so eliminate it
D) results in -5, so keep it
Since D was the only one that worked, that is our correct answer.
Which expression is equivalent to 16³?
2⁷
2¹¹
2¹²
2⁶⁴
Answer:
2^12
Step-by-step explanation:
16^3 can be rewritten as (2^4)^3 which can then be rewritten as 2^12 by multiplying the exponents
Can someone help with this q u e s t i o n p l e a s e
The two-way table of column relative frequencies below summarizes survey data on who a person's role model is and their highest level of education.
Based on the data, which of the following statements must be true of the people surveyed?
A) A person whose role model is a family member is less likely to have an advanced degree than a person whose role model is a friend or acquaintance.
B)
A person whose role model is a stranger is more likely to have high school than some college as their highest level of education.
C) A person whose highest level of education is a bachelor's degree is more likely to have a family member than a stranger as a role model.
D) A person whose highest level of education is less than high school is more likely to have a stranger than a friend or acquaintance as a role model.
Based on the data, the true statement about the people surveyed is: option B.
What is a two-way frequency table?A two-way frequency table is a table that's used to graphically the represent frequencies or relative frequencies that are associated with two categorical variables such as role model and level of education.
By critically observing the data provided in this two-way frequency table, we can infer and logically deduce that a person whose role model is a stranger is more likely to have high school (0.4 or 40&) than some college as their highest level of education.
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Answer:
B
Step-by-step explanation:
14%start color #11accd, 14, percent, end color #11accd of the people whose role model is a family member have an advanced degree, but only \maroonD{12\%}12%start color #ca337c, 12, percent, end color #ca337c of people whose role model is a friend or acquaintance have an advanced degree.
This statement is false.
40%start color #1fab54, 40, percent, end color #1fab54 of people who role model is a stranger have high school as their highest level of education, while only \purpleC{23\%}23%start color #aa87ff, 23, percent, end color #aa87ff have some college as their highest level.
This statement is true.
We only know the column relative frequencies, not the row relative frequencies, so we cannot make this claim.
If there were an equal number of people with family members and strangers as role models, then the statement would be true. However, suppose this data came from a sample where 100100100 people have a family member as a role model and 400400400 people have a stranger as a role model.
Family member: 0.23(100)=230.23(100)=230, point, 23, left parenthesis, 100, right parenthesis, equals, 23 would have a bachelor's degree as their highest level of education
Stranger: 0.14(400)=560.14(400)=560, point, 14, left parenthesis, 400, right parenthesis, equals, 56 would have a bachelor's degree as their highest level of education
Without knowing the total number of people in each group, or the row relative frequencies, we can't say this statement is true.
We only know the column relative frequencies, not the row relative frequencies, so we cannot make this claim.
If there were an equal number of people with friends or acquaintances and strangers as role models, then the statement would be true. However, suppose this data came from a sample where 400400400 people have a friend or acquaintance as a role model and 200200200 people have a stranger as a role model.
Friend or acquaintance: 0.12(400)=480.12(400)=480, point, 12, left parenthesis, 400, right parenthesis, equals, 48 would have finished less than high school
Stranger: 0.19(200)=380.19(200)=380, point, 19, left parenthesis, 200, right parenthesis, equals, 38 would have finished less than high school
Without knowing the total number of people in each group, or the row relative frequencies, we can't say this statement is true.
Based on this data, the statement which must be true is, "A person whose role model is a stranger is more likely to have high school than some college as their highest level of education. "
Which of these correctly explains the solution of the system of equations shown
below?
2x + 3y = 6
x+ 3y = 12
O A The equations have x-intercepts at 3 and 12; therefore, (3, 12) is the
O
B. The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is
the solution.
O
C. The lines representing the equations intersect at x= 1 and y = o; therefore,
(1, 0) is the solution.
The equations have v-intercents at 2 and 4: therefore
the solution
The solution of the system of equations is the point (-6, 6), so the correct option is B.
Which statements are correct about the system of equations?
Here we have the system of equations:
2x + 3y = 6
x + 3y = 12
First, let's write these two lines in the slope-intercept form:
y = (6 - 2x)/3 = 2 - (2/3)*x
y = (12 - x)/3 = 4 - (1/3)*x
Now, because "y" is the represents the same variable in both equations, we can write:
2 - (2/3)*x = y = 4 - (1/3)*x
Now we can solve that for x.
2 - (2/3)*x = 4 - (1/3)*x
2 - 4 = (2/3)*x - (1/3)*x
-2 = (1/3)*x
3*(-2) = x = -6
Now, to get the y-value of the solution we can evaluate any of the two lines in x = -6, evaluating the first we get:
y = 4 - (1/3)*x = 4 - (1/3)*(-6) = 4 + 2 = 6
Then the solution of the system is the point (-6, 6). Then the correct statement is B:
"The values of x= -6 and y= 6 satisfy both the equations; therefore, (-6, 6) is the solution."
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Triangle △ABC is reflected across line n to create △ A'B'C', What is the measure of ∠C?
The measure of ∠C is 54°.
To solve the problem :let us assume that line n is a mirror.
∴ ∠A = ∠A' = 59°
∠B = ∠B' = 67°
∠C = ∠C'
According to property of triangles :
Sum of all angles of a triangle is 180°.
∴ A + B + C = 180°
59 + 67 + C = 180
C = [tex]180 - (59 +67)[/tex]
C = 54°
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Answer:
54 degrees
Step-by-step explanation:
rewrite to solve for y
12y+d=-19y+t
When we say to solve for something
⇒ essentially move everything to one side
⇒ and that 'something' to the other
In this case:
⇒ we need to move the y-variable by itself to one side
⇒ and everything else to the other
Let's apply that principle:
[tex]12y+d=-19y+t\\12y+19y=t-d\\31y=t-d\\y=\frac{t-d}{31}[/tex]
Answer: (t-d) / 31
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Answer:
this right here
Step-by-step explanation:
31y=t-d
Which of the following are solutions to the equation below?
Check all that apply.
4x²-12x+9 = 5
□ A. x = -√5 + ³/2
B. x= √√4-3
C. X= -√√4-3
D. x = √5 + 1/2
3
N|W
□ E. x= -√5 +3
2
□ F. X=
√√5+3
2
The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2
What is sridharacharya formula ?
If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0
Which are the solutions of the equation ?The given equation is, 4x²-12x+9 = 5
So, 4x²-12x+9 = 5
⇒ 4x²-12x+9-5 = 0
⇒ 4x²-12x+4 = 0
Comparing this equation with ax²+bx+c = 0 we get,
a = 4, b = -12, c = 4
Applying sridharacharya formula we get,
x = (-(-12)±√((-12)²-4×4×4))/(2×4)
= (12±√(144-64)/8
= (12±√80)/8
= (3±√5)/2
The values of x are (√5+3)/2 & (-√5+3)/2
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Help please, can someone answer.
Answer:
QA) C = 31.4 cm, A = 78.5 cm^2
QB) 36 cm
Step-by-step explanation:
Question A
Circumference formula: 2πr
2π(5) = 31.4 cm
Area formula: πr^2
π(5)^2 = π(25) = 78.5 cm^2
Question B
If you extend the line of the shape to create a quadrilateral and a triangle, you can use the pythagorean theorem to figure out the last length.
9 - 6 = 3
10 - 6 = 4
The lengths of side a and b are 3 and 4, we need to find the length of the hypotenuse
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
5 = c
Now we can combine this number with the rest of the given lengths
10 + 9 + 6 + 6 + 5 = 36 cm
1. SPORTS Hector wants to buy a new football. He initially thought it would cost $36, but when he went to the sporting goods store it was discounted 20%. What is the sale price of the football? 1. SPORTS Hector wants to buy a new football . He initially thought it would cost $ 36 , but when he went to the sporting goods store it was discounted 20 % . What is the sale price of the football ?
Answer:
It cost Hector $28.8
Step-by-step explanation:
How to find the answer:
36 - 20%
= $28.8
How much money do I need now if I am going to recieve $5000 every 6 months (starting in 6 months) for 10 years if the interest rates are 4%/a compounded semiannually?
He needs to have $205783 amount of money to receive $5000 every 6 months for 10 years.
What is Interest ?Interest is the amount of money received , when a certain lump sum amount is deposited.
It is given that the person is receiving ,
Interest = $5000 ,
after six months , every six month
Time Period = 10 years
Interest Rate = 4%
Compounded Semiannual
Let the principal amount be $x
Compound Interest is given by
Amount = P[ 1 + r/n]ⁿˣ
Here x is the time period
Therefore the Amount = x{ 1 +0.04/2}²⁰
x + 5000 *20 = x{ 1 +0.04/2}²⁰
x + 100000 = 1.486 x
x = $205783
Therefore he needs to have $205783 amount of money to receive $5000 every 6 months for 10 years.
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graph the line of best fit
Answer:
something like this
Step-by-step explanation:
you want the line to go as close to as many dots as possible
You are asked to create a new computer password made up of 4 digits followed
by 3 letters.
Determine how many different computer passwords are possible if digits and
letters cannot be repeated.
Answer:if we start with 26 letters in the English/Latin alphabet: 26*25*24*23*
and modern Arabic numerals 0–9,
10*9 do the math by multiplying all
Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800. 2-digit numbers without repetitions:10*9=90. Number of passwords with 4 letters and 2-digit number without repetitions:
a) if the 2-digit numbers must be in one single position (examples:….XB73DY……..GZ57FE): 358800*90 = 32,292,000.
b) if the 2-digit numbers can be in each of the 5 possible positions (ex.:…73XBDY…X73BDY..XB73DY..XBD73Y..XBDY73…) 5*358800*90=161,460,000.
c) if both digits can be in (C6;2) = 6*5/2= 15 positions (ex.: 7XB3DY…X73BDY…..) 15*358800*90=484,380,000.26*25*24*23*10*9 = 32,292,000
Step-by-step explanation:
On a coordinate plane, a solid straight line has a negative slope and goes through (negative 2, 2) and (2, negative 8). Everything above and to the right of the line is shaded. The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.
Which linear equality will not have a shared solution set with the graphed linear inequality?
y > Two-fifthsx + 2
y < Negative five-halvesx – 7
y > Negative two-fifthsx – 5
y < Five-halvesx + 2
The linear inequality [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality. the correct option is D.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
On a coordinate plane, a solid straight line has a negative slope and goes through (-2, 2) and (2, -8).
m = (-8 -2)/ (2 +2)
m = -10/ 4
m = -5/2
The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.
[tex]y \geq -5/2 (x-3)[/tex]
The linear inequality [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality.
Thus, the correct option is D.
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Answer:
its b the guy above me is wrong
Step-by-step explanation:
If 10% off is 20 what is 23% off?
I have to get this done bc its the last day of school fm. So please help me :)))
Answer: it is the median
Step-by-step explanation:
Answer:
it is the Mode,Median,and Mean.
Step-by-step explanation:
There are ALWAYS three measures of the “center"
Find the product of the given polynomials. (5x + 5 - 2x) (4 + 7x -1)
Answer:
21x2 +44x +15
Step-by-step explanation:
20x + 35x2 - 5x + 20 + 35x - 5 - 8x - 14x2 +2x
35x2-14x2 +20x-5x+35x-8x+2x +15
21x2 +44x +15
X^2 - 10x - 20 = 0, which number would have to be added to "complete the square"?
Answer:
45
Step-by-step explanation:
When you're completing the square you're adding (b/2)^2 which in this case is (-5)^2 or 25. This is because when you rewrite it as a square binomial you write it in the form (x+(b/2))^2 which is going to result in x^2+b+(b/2)^2. Since you need to reach 25 you need to add 45 since the last value is at -20.
Answer:
25 to both sides
Step-by-step explanation:
Group x² and x terms
(x² - 10x ) - 20
complete the square
(x² - 10x +25 ) -20 -25
(x-5)² -45
Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many more marbles does cho have in the beginning
a. 5
b. 9
c. 10
d. 15
Answer:
d. 15
Step-by-step explanation:
Let A and C be the initial number of marbles Ali and Cho have, respectively.
We are told that:
A = 3C [Ali had 3 times as many marbles as cho does]
We then discover that
C-4 = A-18 [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]
How many more marbles does cho have in the beginning?
We have 2 equations and 2 unknowns (A and C). That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.
The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.
Eq. 1: A = 3C
Eq. 2: C-4 = A-18
Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:
Eq. 2: C-4 = A-18
C-4 = (3C)-18 [Replace A with 3C, as promised in E1q. 1]
-2C = -14
C=7
If C = 7, then from Eq. 1, A = 21
In the beginning, Ali has 21 marbles and Cho has 7.
Cho has 15 more marbles than Ali in the beginning.
a. 5
b. 9
c. 10
d. 15
Line segment KL is tangent to circle J at point K.
Circle J is shown. Line segment J K is a radius with length r. Line segment K L is a tangent with length 24 and it intersects the circle at point K. A line is drawn from point L to point J and goes through a point on the circle. The length from point L to the point on the circle is 16. The length from the point on the circle to center point J is r.
What is the length of the radius, r?
8 units
10 units
12 units
16 units
Using the tangent theorem, the length of the radius is: B. 10 units.
What is the Tangent Theorem?According to the tangent theorem, since KL is tangent to the circle, therefore, angle JKL = 90°.
Since the triangle is a right triangle, apply the Pythagorean theorem:
(r+16)² = r² + 24²
r² + 32r + 256 = r² + 576
r² - r² + 32r + 256 = 576
32r + 256 = 576
32r = 576 - 256
32r = 320
r = 320/32
r = 10
The radius is: B. 10 units.
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Answer:
B. 10 Units
Step-by-step explanation:
Which of these numbers are larger 1.201 or 1.2 recurring
Answer:
1.2
Step-by-step explanation:
because recurring means endless repeating.
If a polynomial has three terms, x2 12x 36, which factoring method can be considered?
Answer:
Square of a binomial
Step-by-step explanation:
[tex] {(x + 6)}^{2} = {x}^{2} + 12x + 36[/tex]
Mr Abdul made tuna and curry potato filling for some puffs.3/5 of the filling he made was tuna and the rest was curry potato.
After he used 1/8kg of the tuna filling and made another 3/4
kg of curry potato filling, he then had equal amounts of tuna filling
and curry potato filling left. How much tuna filling did he make at first?
Give your answer as a mixed number in its simplest form
At first, he made [tex]2\frac{5}{8}[/tex] kg of tuna filling.
Mr Abdul made tuna and curry potato filling for some puffs.
3/5 of the filling he made was tuna and the rest was curry potato.
So, amount of curry potato = 1- 3/5 = 2/5
Ratio of tuna & curry potato = tuna : curry potato
= 3/5 : 2/5 = 3 : 2
Let amount of tuna = 3x & amount of curry potato = 2x
After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.
According to the question, he then had equal amounts of tuna filling and curry potato filling left.
So, 3x - 1/8 = 2x + 3/4
Multiplying 8 in both sides we get,
⇒ 24x - 1 = 16x +6
⇒ 24x - 16x = 7
⇒ 8x = 7
⇒ x = 7/8
So, 3x = (3×7/8) = 21/8 kg = [tex]2\frac{5}{8}[/tex] tuna filling at first.
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