Answer:
L = 8
w = 3
Step-by-step explanation:
Givens
w = L - 5
L = x
Area = 24
Formula
Area = L * w
Solution
Area = (x) * (x - 5)
24 = x * (x - 5) Remove the brackets
24 = x^2 - 5x Subtract 24 from both sides
0 = x^2 - 5x - 24 This will factor
0 = (x - 8)(x + 3)
x + 3 is an extraneous root. You cannot have a length of -3 units no matter what the units are.
x - 8 = 0
x = 8
Answer
The length = 8
The width is = 8 - 5 = 3
a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:
As a result, 3.0 x 10¹ litter of gasoline will be used for a 450-kilometer trip.
The correct option is B.
What is conversion factor?In fact, a conversion factor is a number that is utilized to multiply as well as divide one set of units by another.. When converting to an equivalent value, the appropriate conversion factor must be utilized. To convert inches into feet, for example, the suitable conversion value becomes 12 inches equal to 1 foot.
What exactly does unit conversion imply?Unit conversion is indeed a multi-step procedure that includes multiplying or dividing by a numerical factor, determining the appropriate number of important digits, and rounding.
According to the given data:The car gets 35 miles for each gallon of gas.
We need to calculate how many liters of petrol will be required for a 450-kilometer trip.
first converting km into miles:
1 km =0.621371 miles.
So,
450 km = 450 x 0.621371
= 279.61 miles.
Now we know that :
One gallon of gasoline will get you 35 miles.
So for 279.61 miles.
Let x be the number of liters of gasoline required to travel the distance.
So
x = 279.61 / 35
x = 7.98 gallons
Now in litters:
1 gallon = 3.78541litters
So,
7.98 * 3.7854 = 30.24
= 3.0 x 10¹ litter
As a result, 3.0 x 10¹ litter of petrol will be used for a 450-kilometer trip.
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I understand that the question you are looking for is:
A car averages 35 miles per gallon of gasoline. How many liters of gasoline will be needed for a trip of 450 kilometers? Some conversion factors, which may be helpful are the following:
1 qt = 0.946 L.
1 mile = 0.621371 km.
1000 m = 1 km.
4 qt = 1 gallon.
1 ft = 12 inches.
a. 2.5 x 10¹ L
b. 3.0 x 10¹ L
c. 3.5 x 10¹ L
d. 4.0 x 10¹ L
e. 4.5 x 10¹ L
Multiple Choice Question.
Show Work Needed.
First of all, every number in each row is odd, so we can eliminate 392 and 394.
The number of elements in each row forms an arithmetic sequence:
• 1st row : 1 element
• 2nd row : 3 elements - and 3 - 1 = 2
• 3rd row : 5 elements - and 5 - 3 = 2
• 4th row : 7 elements - and 7 - 5 = 2
and so on, so that the [tex]n[/tex]-th row has [tex]1 + 2(n-1) = 2n - 1[/tex] elements.
This means that in [tex]n-1[/tex] complete rows, there is a total of
[tex]\displaystyle \sum_{i=1}^{n-1} (2i-1) = n^2 - 2n + 1[/tex]
elements, so that the first element in the subsequent [tex]n[/tex]-th row is the [tex](n^2-2n+2)[/tex]-th number in the sequence {1, 3, 5, 7, …}, i.e the [tex](n^2-2n+2)[/tex]-th odd positive integer. To compute the sum, I use the following well-known formulas.
[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]
Now, the [tex]n[/tex]-th term of the sequence {1, 3, 5, 7, …} is simply [tex]2n-1[/tex], the [tex]n[/tex]-th odd positive integer. So the first element in the [tex]n[/tex]-th row is
[tex]2(n^2-2n+2) - 1 = 2n^2 - 4n + 3[/tex]
and hence the 1st element of the 15th row is
[tex]2\cdot15^2 - 4\cdot15 + 3 = \boxed{393}[/tex]
I'm very confused about this, please explain this to me.
The angles of the given triangle are 136°,24°, and 20°.
Given that a triangle has angles as 4y°,(y-10)°, and 20° and asked to find out the angles of the given triangle
The sum of the angles of the triangle =180°
⇒4y°+(y-10)° + 20°=180° { adding the given angles and equating it to 180° as the sum of the angles in the triangle is 180°}
⇒5y+10=180°.{added all the given angles and equated it to 180°}
⇒5y=170°
⇒y=34°
⇒4y=136°, (y-10)°=24° and 20°
Therefore the angles of the given triangle are 136°,24°, and 20°.
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Find the 59th term of the arithmetic sequence 29, 37, 45, ...
Answer:
AP = 29,37,45,...
d= t2-t1
=37-29
=8
n=59
t59=?
tn=a+(n-1)d
t59=29+(59-1)8
t59=28+58×8
t59=28 + 464
t59=492
Step-by-step explanation:
please mark it brainliest and thank it please
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Royston is driving to a popular amusement park with his family. Royston’s car had 1515 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and refueled the car with 535 gallons. If the car consumed 1745 gallons of gas during the trip, there are still gallons of gas remaining in the tank. 100 points
Answer: 3 gallons of gas left
Step-by-step explanation: since the car started out with 15 1/5 and then fills up 5 3/5 now there is 20 4/5 in the car then since the car consumed 17 4/5 just subtract the 17 4/5 from 20 4/5 and then you get 3 gallons left since 17 - 20 = 3 and 4/5 - 4/5 = 0/0 or 0 the answer is just 3 gallons left
Answer: it is 3 gallons
Step-by-step explanation:
the life insurance policies of an insurance company are classified by the following:
•Age of Insured:
•Under 25 years,
•Between 25 and 50 years,
•over 50 years old;
•Sex;
•Marital status:
•Single or Married
What is the total number of classications?
Answer:
120
Step-by-step explanation:
lf m/1 = 2x + 3, and m/2 = 3x + 7, which is the value of x?
The value of x is -(11/7).
This problem is related to solving an algebraic equation.
In algebra there are many types of equations such as linear equation in one variable and two variable.
Here we have been given two variables and two equations which means we can solve the equation. To solve an equation in algebra it is important that the number of unknowns is equal to the number of equations given.
Given, m/1=2x+3 i.e., m=2x+3
also m/2=3x+7 i.e., m=6x+14
Now equating both the values of m;
2x+3=6x+14
⇒6x-2x=3-14
⇒4x=-11
∴ x= -(11/4)
Hence, the value of x is -11/4.
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ROUND off the answers using the rules for approximate numbers.
Problems: 97.83 - 4.378 + 5.92
and 1,342.8+ 85.32 + 173.54 + 16
The value of the numbers given will be:
1. 108
2. 1618
How to calculate the values?1. The expression given will be calculated as:
= 97.83 - 4.378 + 5.92
= 98 + 4 + 6
= 108
2. 1,342.8+ 85.32 + 173.54 + 16
= 1343 + 85 + 174 + 16
= 1618
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What is this and give me the step by step
Answer:
(2/x²y³)
Step-by-step explanation:
(2(x^-2)y)/(y^4)
x^-2 can also be written as (1/x²)
(2(1/x²)y)/(y^4)
(2/x²)(y)/(y^4)
(2y/x²)/(y^4)
this can also be written as (2y/x²) × (1/y^4)
= 2y/(x² × y^4)
WHEN THE SAME VARIABLE IS DIVIDED THEIR POWERS ARE SUBTRACTED
= (2/x²y³) (we got y³ by y^1 /y^4 The powers got subtracted)
1. BC
[-1 2] [2 3 5]
[6 0] * [0 4 -1]
Step-by-step explanation:
⎡02413524−6⎦⎥⎥⎤ and B=⎣⎢⎢⎡−10021030−1⎦⎥⎥⎤
∴4A=⎣⎢⎢⎡081641220816−24⎦⎥⎥⎤ and 6B=⎣⎢⎢⎡−600126080−6⎦⎥⎥⎤
⇒4A−6B=⎣⎢⎢⎡0−(−6)8−016−04
in a certain country, the true probability of a baby being a girl is 0.473 . among the next seven randomly selected births in the country, what is the probability that at least one of them is a boy ?
The probability that at least one of them is a boy is 0.9947
How to solve for the probability that at least one is a boyThe probability = (1 - P) none of these 7 is a boy
= 1 - P (all girls)
1 - 0.473^7
1 - 0.00529697
= 0.9947
Hence in a certain country, the true probability of a baby being a girl is 0.473 . among the next seven randomly selected births in the country, the probability that at least one of them is a boy is 0.9947
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If a 20-foot tree casts a 35-foot shadow, how tall is a tree that casts a 63-foot shadow
Answer:
T=48
Step-by-step explanation:
Now since I don’t know the height at the present moment, I’ll just make this ratio (of the tree) be represented as x/36. Which is saying that for every ‘x’ amount of feet, there will be 36 feet of shadow.
so we have 4/3=x/36. If I cross multiply 36 and 4, then divide the product by 3, then ‘x’ will be 48.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
looking at the screenshot! it can be a or b
Step-by-step explanation:
-18 ≤26-8<-8
How do I solve?
I don't think you can solve this, considering the given expression is false. However consult a tutor perhaps and see if they can help you further.
need some help could someone explain this for me please?
Step-by-step explanation:
it all starts with having a good definition for a
a = 3x + 6
for the definition of b we need to transform the second equation
x = 1/3 b - 2 = b/3 - 2
3x = b - 6
3x + 6 = b
remember, if a = c and b = c, then it must be a = b.
that is the whole principle here. the symmetric property.
I am not sure what you must do here. so you select on the left the number of the step in the proof ?
if so, then
statement reason : number 1
a = 3x + 6 and 3x = b - 6 division : number 2
a = 3x + 6 and -b = -3x - 6 subtraction : number 3
a = 3x + 6 and b = 3x + 6 division : number 4
a = b = 3x + 6 symmetric : number 5
always remember, every change needed on one side of an equation we need to do on both sides, otherwise the equation is destroyed.
number 2 is "division" as division is a form of multiplication (and multiplication a form of division). we are multiplying by 3.
number 3 subtracts b and also 3x.
number 4 divides by -1.
and number 5 is the fished proof as mentioned above.
Statistics expert daniel yankelovich believes that ________ give americans a certain amount of self-esteem and a fairly clear idea of who they are.
Statistics expert daniel yankelovich believes that middle-class values give Americans a certain amount of self-esteem and a fairly clear idea of who they are.
Who is a statistician?This is the title that is used to refer to the people that have being trained in such a way that they are able to apply statistical approaches and methods to the real life problems that exists in the environment.
They are known to be able to get the solutions to problems by the use of models of statistics and analyzing them as well.
Hence we can say that Statistics expert daniel yankelovich believes that middle-class values give Americans a certain amount of self-esteem and a fairly clear idea of who they are
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A bike wheel.
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
Answer: BABABAB
Step-by-step explanation:
BHBAHBABAHBABHABHBAHBABHABHBAbhaBHBA
Halle el resultado de:
pls ayuda necesito hacer esta tarea :c
Usando la propiedad exponencial, hay que el resultado es: 125/64.
¿Cómo aplicar la propiedad exponencial?Con el expoente negativo, hay que:
[tex]\left(\frac{a}{b}\right)^{-x} = \left(\frac{b}{a}\right)^{x}[/tex]
Así, la expresion equivalente es dada por:
[tex]\left(\frac{16}{25}\right)^{-\frac{3}{2}} = \left(\frac{25}{16}\right)^{\frac{3}{2}}[/tex]
Hay que 25 = 5² y 16 = 4², así:
[tex]\left(\frac{25}{16}\right)^{\frac{3}{2}} = \left(\frac{5^2}{4^2}\right)^{\frac{3}{2}} = \left(\frac{5}{4}\right)^3 = \frac{125}{64}[/tex]
Así, hay que el resultado es: 125/64.
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A month is chosen at random,
then a standard die is rolled.
What is the probability of getting
February, then a number less
than 5?
The probability of getting February, then a number less than 5 is:
P = 1/18
How to find the probability?First, we need to find the two individual probabilities:
We have a total of 12 months, and we assume that the probability for each of these is the same one, then the probability of getting February will be:
p = 1/12.
Now, the standard die has 6 sides, the numbers that are less than 5 are:
{1, 2, 3, 4}
So 4 out of the 6 outcomes are less than 5, then the probability here is:
q = 4/6 = 2/3.
Then the joint probability is:
P = p*q = (1/12)*(2/3) = 2/36 = 1/18
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there are 9 roses and 7 daisies in a vase. (a) what is the ratio of all flowers in the vase to roses? (b) what is the ratio of all flowers in the vase to daisies?
The ratio of all flowers in the vase to roses is 9:16. The ratio of all flowers in the vase to daisies is 16:7.
What is ratio?An expression known as a ratio in mathematics shows how many times one number is contained in another. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, and that of lemons to oranges is 6:8 (or 3:4). (or 4:7).
A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers are usually limited to positive values in settings.
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Awnser for me quickly pleaseee
Answer:
137 ≤ 15x +
Step-by-step explanation:
A new Community Sports Complex is being built in Del Rio. The perimeter of the rectangular playing field is 528 yards. The length of the field is 6 yards less than quadruple the width. What are the dimensions of
the playing field?
The width is yards.
The length is yards.
Save
The dimensions of the playing field the width is 54 yards and the length is 210 yards.
Given that the perimeter of the rectangular playing field is 528 yards and the length of the field is 6 yards less than quadruple the width.
Let the width of the rectangular playing field is x yards and it is given that the length of the field is 6 yards less than quadruple the width means the length is 4x-6.
As we know that the perimeter of the rectangle is two times the sum of length and breadth so.
P=2(l+w)
As it is given that the perimeter is 528 yards.
So, we will substitute all the values in the formula, we get
528=2(4x-6+x)
528=2(5x-6)
528=10x-12
528+12=10x-12+12
540=10x
540/10=10x/10
54=x
Now, substitute this values in l=4x-6 to find the length, we get
l=4(54)-6
l=216-6
l=210
Hence, the dimension of the playing field when the perimeter of the rectangular playing field is 528 yards is width is 54 yards and length is 210 yards.
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pete seria also offers pizza pies with a choice of any of 4 toppings: pepperoni, mushrooms, green peppers, or sausage. how many different pizzas can you make with anywhere from 0 to 4 toppings (assume each pizza can have at most 1 serving of each topping, e.g. no "double pepperoni" on the pizza)?
There are 256 different pizzas can you make with anywhere from 0 to 4 toppings.
Combinations:
Combinations defines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given,
Pizza pies with a choice of any of 4 toppings: pepperoni, mushrooms, green peppers, or sausage.
Here we need to find how many different pizzas can you make with anywhere from 0 to 4 toppings.
Here we need to assume that each pizza can have at most 1 serving of each topping.
Here we have four level of toppings like no serving, single serving, double serving and triple serving.
Suppose you had one topping, let's say mushrooms. How many different possible pizzas would there be?
If you understand the setup right, there would be 4: no topping, single mushrooms, double mushrooms, or triple mushrooms.
Similarly, imagine that there are two toppings, mushrooms and sausage.
Then, there are 4 x 4 = 16 different combinations with two items.
We could continue this for a long time.
If you have only sausage, mushroom, pepperoni and onion, then for a total of
=> 4 x 4 x 4 x 4 = 256 combinations.
Therefore, there are 256 different pizzas can you make with anywhere from 0 to 4 toppings.
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You roll a die ten times and get a six four of those times What is the experimental probability of rolling a six?
Answer:
So if you roll the die ten times, that means every time you roll it, it is 10%, with that knowledge, if you rolled 6, four times, that means the experimental probability is 40% to get 6.
in triangle abc, angle b is 120∘ . it contains bisectors aa1, bb1 and cc1. prove that the angle a1b1c1 is 90∘
The triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
In triangle ABC, ∠A = 120°.
Let AD, BE, and CF be the respective angle bisectors of A, B, and C.AC in ABD is the exterior angles bisector (as DAC=CAX=60°).BE is the internal angle bisector that meets at E. E is the ex-center of ABCD.As a result, DE is the exterior angle bisector of ABCD.
Then, ADE=EDC, and ADC=2ADE.Similarly, for the ABC, F is ex-center because AB is the exterior angle bisector and CF is the interior angle bisector.
As a result, DF is the exterior angle bisector.
∠ADF = ∠FDB, ∠BDA = 2∠ADFBC is a straight line.
∠BDA+∠ADC=180°2∠ADF+2∠ADE=180°∠ADF+∠ADE=90°So, DEF is the right triangle.
As a result, the triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.
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The correct form of the question is given below:
Prove in any ΔABC, if one angle is 120°, the Δ formed by the feet of the angle bisectors is right-angled.
Keith wants to rent a boat and spend less than $69. The boat costs $7 per hour, and Keith has a discount coupon for $8 off. What are the possible numbers of hours Keith could rent the boat?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answer:
8 hours
Step-by-step explanation:
69 = 7t -8
61 = 7t
t = 8.71428571
in a large population, 54 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated?
The probability that at least one of them has been vaccinated is 0.9552
Probability:
Probability defines the possible occurrence of any particular required event.
Given,
Here we need to find in a large population, 54 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated.
Here we have to know that,
The situation where at least one out of 4 are vaccinated includes all but one possibility, that which none of the 4 are vaccinated.
The sum of all probabilities must equal 1.
Let Q be probability none of the 4 are vaccinated.
Let P be probability that at least 1 is vaccinated.
Then the probability is calculated as,
P = 1 - Q
Now if 54% are vaccinated, then 46% are not vaccinated.
Thus any given person has a probability of 0.46 of not being vaccinated.
=> Q = (0.46)⁴
=> Q = 0.0448
Then apply the value to the formula,
=> P = 1 - 0.0448
=> P = 0.9552
Therefore, the probability that at least one of them has been vaccinated 0.9552.
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what is the product of 2x-5 and 3x+4? A. 5x - 1 B.6x² - 7x- 20 C.6x² - 20 D. 6x² + 7x - 20
Answer:
B. 6x²-7x-20
Step-by-step explanation:
(2x-5)(3x+4)
2x(3x+4)-5(3x+4)
Use distributive property.
6x²+8x-15x-20
Combine like terms.
6x²-7x-20
Hope this helps!
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The data measured on ordinal scale exhibits all the properties of data measured on? nominal scale. nominal and interval scales. interval scale. ratio scale.
The data measured on ordinal scale exhibits all the properties of data measured on nominal scale.
What is nominal scale?A nominal scale can be described as the scale of measurement which is been assign events or objects with respect to a discrete categories.
However in relation with nominal scale, Ordinal scale serves as the 2nd level of measurement which help to give the reports of ranking as well as ordering of the data however the degree of variation is not usually considered, hence data measured on ordinal scale exhibits all the properties of data measured on nominal scale.
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determine whether each first-order differential equation is separable, linear, both, or neither. choose one 1. choose one 2. choose one 3. choose one 4. note: you only have two attempts at this problem.
The first-order differential equation is non-separable and non-linear.
[tex]\frac{dx}{dy} +e^{x} y=x^{2} y^{2}[/tex]
[tex]\frac{1}{y^{2} } \frac{dx}{dy} +e^{x} \frac{1}{y} =x^{2}[/tex]
[tex]\frac{dt}{dx} -e^{x} t = -x^{2}[/tex]
Since, x and y terms separated also linear equation
linear and separable both
[tex]\frac{dy}{dx} = cos y = tan x[/tex]
non-linear and non-separable
What distinguishes a linear equation from a non-linear equation?
Something that is linear is related to a line. A line is built using all of the linear equations. A non-linear equation is one that cannot be represented by a straight line. It has a changeable slope value and resembles a graphed curve.
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