The average cost for 16 gallons is $46.272
How to calculate the cost of 16 gallons ?The first step is to calculate the price of one gallon
5= 14.46
1= x
cross multiply
5x= 14.46
x= 14.46/5
x= 2.892
The price of 16 gallons can be calculated as follows
= 16 × 2.892
= 46.272
Hence the price of 16 gallons is $46.272
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6. Imran's father is x² years old while Imran is x years old. In 4x years' time, Imran's father will be twice as old as him.
(i) Form an equation in x and show that it reduces to x² - 6x=0.
(ii) Solve the equation x² - 6x = 0.
(iii) Find the age of Imran's father when Imran was born.
The solution of the quadratic equation is (ii) 0 and 6. (iii) Imran's father was 30 years old when Imran was born.
Quadratic equation in one variable is generally of the form of ax²+bx+c=0 where x is the variable and a, b and c are constants.
The degree of a quadratic polynomial is 2 and there are 2 solutions for a quadratic equations.
The graph of a quadratic equation is parabolic in shape.
Imran's father is x² years when Imran is x years. So after 4x years:
Imran's father's age=x²+4x
Imran's age=x+4x=5x
Now Imran's father is twice as old as Imran
∴2×(5x)=x²+4x
or, 10x=x²+4x
or, x²-6x=0
Hence the equation reduces to a quadratic equation of the form x²-6x=0.
ii) Solving the quadratic equation:x²-6x=0
Breaking into factors we get:
or, x(x-6)=0
either x=0 or x-6=0 or, x=6
Therefore the solution of the equation is 0,6 .
iii) When x=6 i.e, Imran is 6 years old,
age of his father = x²=6²=36 years.
So when Imran was born 6 years ago age of his father=36-6=30 years old.
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Rosemary cut 3 wooden sticks to use as the sides of a triangle. Which list below could be the lengths, in inches, of the sticks Rosemary cut?
The length in inches of the triangle will be (A) 6, 8, 10.
What exactly is Pythagorean Theorem?According to the Pythagorean Theorem, the length of the legs and of a right triangle is related to the length of the hypotenuse h by the following equation:[tex]h^2=l_1^2+l_2^2[/tex]As a result, in item a:
h² = 6² + 8²h² = 100h = 10As a result, it is a right triangle.
Item b:
h² = 2² + 5²h² = 29h = √29 ≠ 100It's not a perfect triangle.
Item c:
h² = 5² + 6²h² = 61h = √61 ≠ 7It's not a perfect triangle.
Item d:
h² = 2² + 3²h² = 13h = √13 ≠ 5Therefore, the length in inches of the triangle will be (A) 6, 8, 10.
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The correct question is given below:
Rosemary is cutting 3 wooden sticks to build part of a kite frame. The part she is building must be a right triangle. Which choice below could be the lengths, in inches, of the sticks rosemary cut?
A. 6, 8, 10.
B. 2, 5, 10.
C. 5, 6, 7.
D. 2, 3, 5.
Simplify the following equation shown in the picture below :
Answer:
D
Step-by-step explanation:
2x - 14x = 12x
3x²
6y + 7y = 13y
3²-12x-13y
Mr. Rell runs 14 miles every 2 hours. How far
can he run in 7 hours?
Answer:
28
Step-by-step explanation:
you have to multiply 14 ×2 =28
simplify: 3/x+1 - 1/x-1 - 2x/x^2+1
The simplified expression of 3/x+1 - 1/x-1 - 2x/x^2+1 is [-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
How to simplify the expression?The expression is given as
3/x+1 - 1/x-1 - 2x/x^2+1
Take the LCM of the first two terms
So, we have
(3x - 3 - x - 1)/(x^2 - 1) - 2x/x^2+1
This gives
2x - 4/(x^2 - 1) - 2x/x^2+1
Take the LCM
[(2x - 4)(x^2 + 1) -2x(2x^2 - 1)]/(x^4 - 1)
Expand
[2x^3 - 4x^2 + 2x - 4 - 4x^3 + 2]/[x^4 - 1]
Evaluate the like terms
[-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
Hence, the simplified expression of 3/x+1 - 1/x-1 - 2x/x^2+1 is [-2x^3 - 4x^2 + 2x - 2]/[x^4 - 1]
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Paul wants to hand out flyers for his new tutoring business. So far he has
handed out 30 flyers. He has 10 more days before his first customers arrive
and would like to hand out a total of 250 flyers. Write and solve an equation
to find how many flyers he would have to hand out each day to meet his
goal.
The equation to find the number of flyers is 10 x + 30 = 250 and the flyers he will hand over each day is 22.
Number of flyers handed out = 30
Total number of flyers = 250
The equation will be:
30 + 10 x = 250
Solving the equation, we get that:
Subtract 30 from both the sides:
10 x = 250 - 30
10 x = 220
Divide both sides by 10:
x = 220 / 10
x = 22
Therefore, the equation to find the number of flyers is 10 x + 30 = 250 and the flyers he will hand over each day is 22.
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The points (–5, 4) and (9, –2) are on a line. Find the intercepts to the nearest tenth.
Answer:
The y-intercept = (0, 13/7).
The x-intercept = (13/3, 0).
To the nearest tenth they are
y-intercept (0, 1.9)
x-intercept (4.3, 0)
Step-by-step explanation:
First find the equation oif the line joining these points:
Slope of line = (4 - (-2)) / (-5-9))
= 6/-14
= -3/7
y - y1 = m(x - x1)
Using m = -3.7 and (x1, y1) = (-5, 4)
y - 4 = -3/7(x - (-5)
y = -3/7x -15/7 + 4
y = -3/7x + 13/7 is the equation of the line.
The y-intercept (when x = 0)
= 0 + 13/7
= (0, 13/7)
The x-intercept:
0 = -3/7x + 13/7
x = -13/7 / -3/7
= 13/3.
x intercept is (13/3, 0)
Please answer this question for me. I’ll mark you as the brainliest.
Find composite numbers that have the following characteristics (options in the photo).
Answer:
I am not so sure but the answer I think is 1st option
2 1/2 divided by 2 5/8
Answer:
20/21
Step-by-step explanation:
2 1/2 divided by 2 5/8
2 1/2 is 5/2
2 5/8 is 21/8
5/2 ÷ 21/8 =
5/2 × 8/21 = 20/21
I converted 600 kcal into units of btu, joules, and kwh. the answers were 0.70, 2380, and 2.51x106; except i forgot which number goes with which units. what is the correct pairing of values and units?
600 kcal, when converted, is equivalent to 2380 BTU, 2.51 x 10^6 joules, and 0.70 kwh.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume, etc. to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
kcal, BTU, joules, and kwh are all units of energy. To convert kcal to these units, we can use the following conversions:
1 kcal = 3.96567 BTU
1 kcal = 4184 joules
1 kcal = 0.00116222 kwh
Converting 600 kcal to BTU, joules and kwh:
1 kcal = 3.96567 BTU
600 kcal = 600(3.96567 BTU)
600 kcal = 2379.4 BTU ≅ 2380 BTU
1 kcal = 4184 joules
600 kcal = 600(4184 joules)
600 kcal = 2.51 x 10^6 joules
1 kcal = 0.00116222 kwh
600 kcal = 600(0.00116222 kwh)
600 kcal = 0.697333 kwh ≅ 0.70 kwh
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
A
Step-by-step explanation:
Really lost on this one :(
Applying the definition of supplementary angles, x = 18; m<PNO = 70°.
What are Supplementary Angles?If two angles lie on a straight line adjacent to each other, both angles are supplementary, thus, their sum is equal to 180 degrees.
Angle MNO and angle PNO are supplementary angles, therefore:
m<MNO + m<PNO = 180 degrees.
m<MNO = 110°
m<PNO = (3x + 16)°
Substitute
110 + 3x + 16 = 180
126 + 3x = 180
126 + 3x - 126 = 180 - 126
3x = 54
x = 18
m<PNO = 3x + 16 = 3(18) + 16
m<PNO = 70°
Therefore, applying the definition of supplementary angles, x = 18; m<PNO = 70°.
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community gym charges a 60$ membership fee and a 70$ monthly fee. workout gym charges a 190$ membership fee and a 60$ monthly fee
For 13 months the membership is done using the equivalent of two given monthly fees for community and workout gym.
Why do you use the word equivalent?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value. By dividing both numbers by the same number, one can convert a division problem into an analogous problem while keeping the ratio between the two numbers constant. The equivalent is defined as something that is almost identical to or equal to another object. Two numbers that are equivalent are (2+2) and 4. These two things are equivalent since 2+2=4. equal to make equivalent.
Let x be the months
then community month= workout month
60+70x=190+60x
⇒70x-60x=190-60
⇒10x=130
⇒x=13 be the months be the working.
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Of the 200200 parking spaces in a parking lot, 6\%6% of the spaces are reserved for handicapped parking. Of those parking spaces NOT reserved for handicapped parking, 2020 are suitable for compact cars only. How many spaces that are NOT reserved for handicapped parking are suitable for non-compact cars?
Using proportions, it is found that 38 spaces are suitable for non-compact cars.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have that:
94% of the spaces are not reserved for handicapped parking, hence this number is of 0.94 x 200 = 188.Of those, 20% are suitable for compact cars, hence 0.2 x 188 = 38.38 spaces are suitable for non-compact cars.
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How can Aaron find the number of days until he posts a new article and a new podcast
on the same day?
Find the GCF of 3 and 5.
Find the LCM of 3 and 5.
PLEASE HELPPPP
The required time can be found by using the least common multiple. The waiting time is 15 days.
What is the minimum time to publish a new article and a new podcast on the same day?
In accordance with this question, Aaron publishes a new article every 3 days and a new podcast every 5 days and we need to determine the minimum period until a new article and a new podcast are published on the same time.
Greatest common factor is the maximum integer that can divided two or more integers such that an integer is found and the least common multiple is the minimum integer greater than two or more numbers are part of it. The required time can be found by using the least common multiple.
The integers 3 and 5 are prime numbers and there is no greatest common factor greater than 1 and their least common multiple is the product of the two numbers, that is, 15.
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name the intersection of line n and AC
A. point B
B. Point C
C. Point A
D. Point D
The correct answer is option B which from the diagram is depicted to be is point C
What is a line?
This is a term science and mathematics that represents the interval between two points. This interval shows the distance the points are from each each other. Line is the basic form of representation of graphics, as it takes to represent what the creative designer assigns it to be.
A line is one dimensional, this means that it represents only a dimension which is usually the length.
what is point of intersection?Points of intersection is a point where two lines meet. This point is of importance when describing the position of another. The angle on a straight line is 180 degrees but when another line intersects the angle between the two lines will vary depending on the point of intersection.
As regards the question. the two line intersected at point C
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9. The volume of a box in cubic feet can be expressed as V(x) = x³ - 3x² - 10x or as the product of three linear factors with integer coefficients. The width of the box is 5-x. What is the length, width, and height of the box in factored form? A. -x(5-x)(x+2) B. X(5-x)(x+2) C. X(5-x)(x-2) D. -x(5-x)(x-2)
The length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
The box is in the shape of a cuboid
The volume of a cuboid = l b h, where l is the length, b is the breath or width and h is the height
Putting the values of width and volume in the formula
x³ - 3x²-10x = l ×(5-x) × h
This becomes a cubic equation
l × h = (x³-3x²-10x)/ 5-x
l × h = -x²-2x
l × h = -x(x+2)
Now, putting the value of l × h in the equation we get
v= -x ( x+ 2) (5-x)
v = -x (x-5)(x +2)
Hence, the length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
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Diane cycled a total distance of 71,808 feet on a bicycle path surrounding a lake she cycled eight laps where each lap was the same length what was the length of each lap around the lake
The length of each lap around the lake is 8976 feet.
We are informed that Diane cycled 8 laps around the lake. Also, Diane covered total distance of 71,808 feet. So, length of 8 laps = total distance covered by Diane. Hence, the length of each lap will be calculated by performing division.
Length of 1 lap = total distance covered by Diane ÷ length of 8 laps
Keep the values in formula to find the length of each lap.
Length of each lap = 71,808 ÷ 8
Performing division to find the length of each lap
Length of each lap = 8976 feet
Thus, the length of each lap around the lake is 8976 feet.
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r² + √s
how do i solve this im stuck?
Answer:
What variable do I solve for?
Step-by-step explanation:
N is an even number
(B) what type of number is n+ 1?
Answer:
Odd
Step-by-step explanation:
If n is even, we can assign it any even number, like 2. after every even comes an odd, so 2+1=3. Just like 4+1=5, the next number after any even is odd.
Jane buys candy that costs $6 per pound. She will buy less than 5 pounds of candy. What are the possible amounts she will spend on candy?
Answer:
Less than $30=========================
GivenCost of candy is $6 per pound,Amount of candy is less than 5 pounds.To findThe possible amounts will be spentSolutionLet the amount of money be x, then, considering she buys more than zero pounds of candy, the total she spends is:
0*6 < x < 5*60 < x < 30Jane will spend between zero and $30.
Answer:
$0 < x < $30
Step-by-step explanation:
To find:-
The possible amounts that Jane will pay for candies .Answer:-
We are here given that , Jane buys candies which are $6 per pound . She buys less than 5 pounds on candies .
Now since she purchased some candies therefore, the amount she spent will be greater than " 0 " .
Now she buys less than 5 pounds of candies . Cost of that would be $6*5 = $30 .
Hence she purchased somewhere between them that is between $0 and $30 .
If we denote the amount spent by Jane on candies by "x" , then ; we can represent this situation as ;
[tex]:\implies \sf \pink{ \$ 0 < x < \$30} \\[/tex]
Hence the required answer is " $0 < x < $30 .
Which expression shows a way to factor 20+12?
2( 11 + 13 )
4( 4 + 3 )
2(10 + 5)
4( 5 + 3 )
Answer:
4(5+3)
Step-by-step explanation:
4x5 is 20
4x3 is 12
each bit in the brackets gets multiplied by 4
please tell me the additive invers of -25, 18, and -4.5!! Thanks!
Answer:
-1/25, 1/18, -2/9
Step-by-step explanation:
The additive inverse of a number is also called the reciprocal. The reciprocal is the number that is multiplied to get 1.
Two tankers contain 850 litres and 680 litres of kerosene oil respectively. find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times
The maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times is 170 Litres.
Amount of kerosene in first tanker = 850 litres
Amount of kerosene in Second tanker = 680 litres
The maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times will be the HCF of amount of kerosene in first tanker and amount of kerosene in second tanker i.e., HCF of 850 litres and 680 litres.
To calculate HCF of 850 and 680 , we can write
850 = 2 × 5 × 5 × 17
680 = 2 × 2 × 2 × 5 × 17
HCF of 850 and 680 = 2 × 5 × 17 = 170
The maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times is 170 Litres.
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Last week, Jaime spent 34, 30,45,30,40,38,
and 28 minutes practicing for football. Find
the ________________
.Round to the
nearest whole number,
Answer:
35 average minutes at practice.
Step-by-step explanation:
Answer:
What do I find?
If it's the mean then the answer is 35.
Step-by-step explanation:
34, 30, 45, 30, 40, 38, 28 ==> 7 numbers
34+30+45+30+40+38+28=245
245/7=35
I WILL GIVE BRAINLIEST
An NFL playing field is a rectangle. The length of the field (excluding end zones) is 40 yards more than twice the width. The perimeter of there playing field is 260 yards. What are the dimensions of the field in yards?
The length of the NFL playing field is 100 yards and the width is 30 yards.
What is perimeter?
The perimeter of an object is the distance round the shape or object.
The perimeter of a shape is obtained by summing length and width of the shape in two places.
P = 2(L + W)
where;
L is the length of the shapeW is the width of the shapeFrom the given question,
L = 2W + 40
260 = 2(L + W)
260 = 2(2W + 40 + W)
260 = 2(3W + 40)
260 = 6W + 80
260 -80 = 6W
180 = 6W
180/6 = W
30 = W
L = 2W + 40
L = 2(30) + 40
L = 100 yards
Thus, the length of the NFL playing field is 100 yards and the width is 30 yards.
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As of 2016, Chicago, Illinois, has a population of approximately 2.7 million people and covers 227 square miles of land. Miami, Florida, has a
population of approximately 440,000 people and covers 36 square miles of land.
Which city has a greater population density? Move the correct city into the first blank, and move numbers into the remaining blanks to justify
the answer.
The city with the greater population density is
because
Step-by-step explanation:
Answer: 12,633.7. Step-by-step explanation: population of Chicago, in 2003 = 2,869,121. The area of Chicago = is 227.1 square miles.
Find the measures of the angles of following triangle. The ratio of the measures of the three angles is 5: 4: 7 .
Answer:
56.25º, 45º and 78.75º respectively
Step-by-step explanation:
I need your help!
In this diagram,
Answer:
15
Step-by-step explanation:
I can't explain lol its 15 tho
The points (10,w) and ( – 6, – 9) fall on a line with a slope of 1. What is the value of w?
i need an answer ASAP
Greetings from Brasil...
We have 2 ways to solve:
1 - through the expression of the slope m (attached figure 1)
2 - determinat (attached figure 2)
1:
m = ΔY/ΔX
as m = 1, as stated in the statement, then
1 = (- 9 - w)/(-6 - 10)
w = 7check attachments
________________________________
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