The domain of the function f(t) is best described as 608 ≤ t ≤ 620
How to determine the domain of the function?From the question, we have the following parameters that can be used in our computation:
Rate = 2.5 kilograms per hour
Mass of the car (including the fuel) = 1550 kg
Mass of the car (not including the fuel) = 1520 kg
Calculate the times using the rate and the masses above
So, we have the following representations
Time 1 = 1550/2.5
Time 1 = 620
Time 2 = 1520/2.5
Time 2 = 608
Express as an interval
608 ≤ t ≤ 620
Hence, the domain is 608 ≤ t ≤ 620
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The price for 7/8 of a pound of almonds is $6.65 . What is the cost of 3 and 1/2 pounds at the same rate?
The cost of 3 and 1/2 pounds of almond at the same rate is $26.60.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In the illustration given as m/n, it should be noted that m is the numerator and n is the denominator.
Since the price for 7/8 of a pound of almonds is $6.65, the fraction per pound will be done by dividing the amount for a pound by 7/8.
= $6.65 ÷ 7/8
= $7.6
The cost of 3 and 1/2 pounds at the same rate is:
= 3 1/2 × $7.6
= $26.60
In conclusion, the cost is $26.60.
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what are steps to solving 30,002-28,596
Answer:
1,406
Step-by-step explanation:
F(x)=(x+2)^2 (x-3) graph the function
The value of the equation f ( x ) is
f ( x ) = x³ + x² - 8x - 12
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( x + 2 )²( x -3 ) be equation (1)
Now , on simplifying the equation , we get
f ( x ) = ( x + 2 )²( x -3 )
f ( x ) = ( x² + 4x + 4 ) ( x - 3 )
Now , multiplying each term with ( x - 3 ) , we get
f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4
f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12
On simplifying the equation ,we get
f ( x ) = x³ + x² - 8x - 12
Now , the value of the equation f ( x ) = x³ + x² - 8x - 12
On graphing the equation , we get
The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below
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A homeowner sections off part of her backyard for a vegetable garden. The width of the garden is 4 ft shorter than the length. The perimeter of the garden is 52 ft. What are the dimensions of the garden?
Answer:
length = 15ft
width = 11ft
Step-by-step explanation:
p = 2L + 2w = 52ft
w = L - 4
Substitute: 2L + 2(L-4) = 52
Simplify and solve:
2L + 2L - 8 = 52
4L - 8 = 52
4L = 60
L = 15
w = 15-4 = 11
Check:
2(15) + 2(11) = 52?
30 + 22 = 52!!!
Are travels 120 miles and one and a half hours what is the average speed for miles per hour
Answer: 80
Step-by-step explanation:
You have 120 miles in one and a half hour
120÷1 1\2 =80 is your speed
In ARST, r = 71 cm, /T=48° and /R=37°. Find the length of t, to the nearest 10th of
a centimeter.
In the given triangle, the length of side t is 87.7 cm
Calculating the length of a side in a triangleFrom the question, we are to determine the length of t.
From the given information,
r = 71 cm
∠T = 48°
∠R = 37°
From the law of sines, we can write that
t / sin T = r / sin R
t / sin 48° = 71/sin 37°
t = (71 × sin 48°)/sin 37°
t = 87.6736
t ≈ 87.7 cm
Hence, the length of t is 87.7 cm
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if f(x)=2x+6 , g(x)= - 5x - 9 what is the product of and g?
Answer:
f(x) * g(x) = -10x2 - 48x - 54
Step-by-step explanation:
(2x+6) * (-5x-9)
-10x2 - 18x - 30x - 54
-10x2 - 48x - 54
Simplify this equation please
48
Answer:
Please look at the attached image, thank you so much! Hope this helps! :D
Step-by-step explanation:
Answer:
6.92820323028, rounded would be 6.92. Even more rounded would be 7.
Step-by-step explanation:
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Marlon buys 9 packs of hot dogs. There are 6 hot dogs in each pack. After the barbecue, 35 hot dogs are left over. How many hot dogs were eaten
Answer: 19
Step-by-step explanation:
9x6= 54
So there’s 54 hot dogs in total
Subtract the amount left
54-35= 19
There are 19 hot dogs left
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Find the equation for the line that passes through the point (−2,0), and that is parallel to the line with the equation y=−12x−72
The linear equation parallel to y = -12x - 72 that passes through (-2, 0) is:
y = -12x - 24
How to find the linear equation?A general linear equation is written as:
y = m*x + b
Where m is the slope, and b is the y-intercept.
And two lines are parallel only if the lines have the same slope and a different y-intercept.
So, if we want to find a line parallel to:
y = -12x - 72
Then the slope of our line must be -12, then our line is something like:
y = -12x + b
Now we know that the line must pass through (-2, 0), replacing that in our line we get:
0 = -12*-2 + b
0 = 24 + b
-24 = b
The linear equation is:
y = -12x - 24
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SOLVE U
2u - 2/3 = - 3/4u+3
U =
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of u is 4/3
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2u - 2/3 = -(3/4)u + 3
Add 2/3 on both sides.
2u = -(3/4)u + 3 + 2/3
Add (3/4)u on both sides.
2u + (3/4)u = 3 + 2/3
(8u + 3u) / 4 = (9 + 2)/3
11u/4 = 11/3
u/4 = 1/3
u = 4/3
Thus,
The value of u is 4/3
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 0.70L to 0.14L
Answer:
5
Step-by-step explanation:
0.7/0.14
7/10×100/14
7×100/10×14
5
5 divided by 1135………
Answer:
227
Step-by-step explanation:
just divide it by how many times it goes into 1135
Answer:
227
Step-by-step explanation:
Patrick is in a grocery store parking lot, 90meters away from his car. If he pushes his shopping cart at a constant velocity of 2meterspersecond toward his car, how much time will it take him to get one-third of the way to his car?
Write your answer as a whole number.
15 seconds of time will it take him to get one-third of the way to his car
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given,
Patrick is in a grocery store parking lot, 90meters away from his car
Patrick pushes his shopping cart at a constant velocity of 2meterspersecond toward his car.
We need to find time will it take him to get one-third of the way to his car
one-third of the way to his car means 1/3 of 90 which is 30 meters.
Speed =Distance/ Time
Time=Distance/speed
=30/2
=15 units.
Hence, 15 seconds of time will it take him to get one-third of the way to his car
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3.A cheetah runs 100 m in 6 seconds. At this rate, how long will it take the cheetah to run 150 m?
Answer: 9 seconds
hope it was helpful (^ = ^)
Step-by-step explanation:
x=number of seconds
100m/6s=150/x
Cross multiply and make x the subject
100m(x)=150m(6s)
x=(150m x 6s)/100m = 9s
therefore it would take the cheetah 9 seconds to run the 150m
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The solution is Option D.
The equation of the line is y = 28x
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the total distance traveled by the car y = 476 miles
Let the total amount of gasoline x = 17 gallons
So , the equation of line is given by
y = mx + c
where m is the slope
Slope m = y /x
Substituting the value for y and x in the equation , we get
Slope m = 476 / 17
= 28
Therefore , the equation of line is y = 28x and the graph is given below
Hence , The equation of the line is y = 28x
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Arturo buys 12 bottles of grapefruit juice at the corner store for a total cost of $8.64. If each bottle costs the same amount, how much is 16 bottles of juice?
Answer:
[tex]\huge\boxed{\sf \$ \ 11.52}[/tex]
Step-by-step explanation:
Given that,12 bottles of juice = $8.64
Using unitary method.Divide 12 to both sides
12/12 bottle of juice = $8.64/12
1 bottle of juice = $0.72
Multiply 16 to both sides
1 × 16 bottles of juice = $0.72 × 16
16 bottles of juice = $11.52[tex]\rule[225]{225}{2}[/tex]
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Answer:
13 years
Step-by-step explanation:
7. Casey bought a 15.4-pound turkey and an 11.6-pound ham for Thanksgiving and paid $38.51. Her
friend Jane bought a 10.2-pound turkey and a 7.3-pound ham from the same store and paid $24.84.
Find the cost per pound of turkey and the cost per pound of ham.
Answer:
t = 1.195pounds.
Step-by-step explanation:
The cost per pound of Turkey and Ham are: 1.195pounds and 1.733pounds respectively.
By observing the question, we must notice this is a word problem and can be written mathematically thus;
For Casey:
15.4t + 11.6h = 38.51
For Jane:
10.2t + 7.3h = 24.84
Therefore, to find the cost per pound of Turkey and Ham, the pair of equations need to be solved simultaneously.
Therefore, we can make t the subject of the formula in equation (2) as follows;
t = (24.84 - 7.3h)/10.2
Therefore, we can substitute the value of t into equation (1) to get;
15.4{(24.84 - 7.3h)/10.2} + 11.6h = 38.51
37.51 - 11.023h + 11.6h = 38.51
0.577h = 1
h = 1.733pounds
Therefore, by substituting the value of h into equation 1, we get the value of t to be;
t = 1.195pounds.
Simplify Oa Ob Oc Od 10x² -32 4
Answer:
Step-by-step explanation:
Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 5x2 + 14x - 3 < 0 The solution set is O A. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) O B. The solution set is the empty set. Which number line below shows the graph of the solution set? O A. В. + -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 7 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4. 7 8 C. + + + + + + + D. + -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 5 7 8 E. F. + + + + -7 -6 -3 -2 -1 1 2 3 6 -8 -7 -6 -5 -4 -3 -2 -1 1 3 5 6 7 8 OG. →O H.
lcd by inspection and division of 1/4, 3/32, 5/48, and 1/8
Part a: the LCD is measured to be 96 utilizing the inspection method.
Part b: By division of prime numbers: 96.
Explain the term LCD of the Fractions?The LCD of above fractions can be calculated using one of two methods. The inspection method is a name for the first technique. With this approach, the denominator's multiples are acquired, and the result is determined by selecting a common multiple from the pool of available multiples.The division by prime numbers is the name of the second approach. To acquire the LCD, find a prime number which divides the following fractions.The given number are-
1/4, 3/32, 5/48, and 1/8
Part a:
Find the multiples of the provided fractions' denominators, which are 4, 32, 48, and 8.
4 = 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88, 92, 96.
32 = 32, 64, 96, 128, 160, 192, 224, 256, 288 ,320.
48 = 48, 96, 144, 192, 240, 288, 336, 384, 432 and 480.
8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
The computation shows that 96, which really is divisible by 4, 32, 48, and 8, is the lowest common multiple.
As a result, the LCD is measured to be 96 utilizing the inspection method.
Part b: By division of prime numbers:
Determine the factors of the given fractions' denominators, 4, 32, 48, and 8.
4 = 2, 2
32 = 2, 2, 2, 2 and 2.
48 = 2, 2, 2, 2 and 3.
8 = 2, 2 and 2.
The generated number, 96, can be divided by the provided fractions' denominators.
As a result, the outcome is 96.
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-4 3/4 = x-1 1/5
Whats the value of x
Answer:3/4 * 1/5 = 3/20 = 0.15
Step-by-step explanation:Multiple: 3/
4 * 1/5 = 3 · 1/4 · 5 = 3/20
Multiply both numerators and denominators. The result fraction keep to the lowest possible denominator GCD(3, 20) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - three quarters multiplied by one-fifth is three twentieths.
How is solving a real-world problem with a system of equations similar to solving a real-world problem with a single equation in one variable? How is the process different?
Answer:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
Step-by-step explanation:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
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The length of a rectangle is 3ft longer than its width.
If the perimeter of the rectangle is,58ft find its length and width.
The length and width of the rectangle is 16 ft and 13 ft respectively.
What is the dimensions of the rectangle?The perimeter of a rectangle = 2(length + width)
Perimeter of the rectangle = 58 ftWidth of the rectangle = w ftLength of the rectangle = (w + 3) ftThe perimeter of a rectangle = 2(length + width)
58 = 2{(w + 3) + w}
58 = 2(w + 3 + w)
58 = 2(3 + 2w)
open parenthesis
58 = 6 + 4w
subtract 6 from both sides
58 - 6 = 4w
52 = 4w
divide both sides by 4
w = 52/4
w = 13
Hence,
Width of the rectangle = w ft
= 13 ft
Length of the rectangle = (w + 3) ft
= 13 + 3
= 16 ft
Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively
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No
0.7
What’s the percentage
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
Given the function f (x)= x2 −5x + 6 , evaluate
Actually 20 is the answer
A student is using colored beads to make a model of magnesium hydroxide, Mg(OH)2. Magnesium atoms are
represented by orange beads, oxygen atoms by green beads, and hydrogen atoms by blue beads.
Model bead color key.
Magnesium orange beads O (orange)
Oxygen green beads O (green)
Hydrogen blue beads O (blue)
What combination of beads should the student use for the model?
The combination of beads that the student will use to make a model of magnesium hydroxide, Mg(OH)₂ is
Magnesium orange beads - 1Oxygen green beads - 2Hydrogen blue beads - 2What is model of molecule?Molecule models depict the positions of the various atoms, roughly to scale, and typically with color coding, as well as how they are joined together.
These models are helpful tools for visualizing the structures and shapes of groupings of atoms, which is vital for understanding the behavior of molecules
Over the course of the development of contemporary atomic theory, models have been employed to represent atom configurations.
The model of magnesium hydroxide, Mg(OH)₂ will require the atoms in the ratio:
Magnesium : Oxygen : Hydrogen = 1 : 2 : 2
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The volume of a cube with side s is s3. Edna bought a cube-shaped jewelry box that has 7-inch sides. What is the volume of the jewelry box?
The volume of the jewelry box will be;
⇒ 343 inch³
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The volume of a cube with side s = s³
And, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Now,
Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Hence, The volume of the jewelry box = 7³
= 7 x 7 x 7
= 343 inch³
Thus, The volume of the jewelry box will be;
⇒ 343 inch³
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Convert 170 gallons into cubic feet. Round
your answer to the nearest tenth.
*Note: you must use these exact conversion factors to
get this question right.
Answer:22.7
Step-by-step explanation: 170/7.481=22.724234728 rounded to the nearest tenth is 22.7
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Answer:
The function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x
Step-by-step explanation:
Transformation techniques
Transformation is the process of changing the position of an object on the xy-plane.Given the parent functionf(x) = 4xIf the function is not reflected over x-axis, the resulting function will be f(x) = -4xIf the resulting function is compressed by a factors of 1/8, hence the final function rule will be;g(x) = 1/8(-4x)g(x) = -1/2xHence the function rule g(x) after the given transformations of the graph of f(x)=4x is g(x) = -1/2x
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