Answer:
THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE TOTAL COST OF GASOLINE PURCHASED.
THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE TOTAL GALLONS OF GASOLINE PURCHASED
The complete problem is:
Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.
Annabella can express her average cost per gallon of gasoline as [tex]y = \frac{(2.25x + 2.15(x+5))}{2x+5}[/tex]
What is the meaning of the parts of this rational expression in the context of the situation?
THE NUMERATOR OF THE RATIONAL EXPRESSION REPRESENTS THE __________.
(select one)
1. total cost of the gasoline purchased
2. total number of gallons of gasoline purchased
3. cost per gallon of gasoline
THE DENOMINATOR OF THE RATIONAL EXPRESSION REPRESENTS THE ________.
1. total cost of the gasoline purchased
2. total number of gallons of gasoline purchased
3. cost per gallon of gasoline
So, in this context and based on the given data, the numerator of the expression is referring to the total cost of gasoline purchased, and the denominator is expressing the total gallons of gasoline purchased.
You can deduct this because, the numerator contains the amounts of costs per gallon, being x gallons. On the other hand, you can see in the denominator that there's no costs multiplying the variable, it's just a quantity which refers to the amount of gasoline, not the cost.
Jax solved an equation and justified his steps as shown below. What reason would justify step 2?
3x + 5 > 2 Step 1: Given
3x > -3 Step 2: ?
x> -1 Step 3: Division Property of Equality
Combine Like Terms
Subtraction Property of Equality
Division Property of Equality
Multiplication Property of Equality
What are the angle measures of the triangle 6 12 6sqrt3?
Answer:
The measure of angle A is 30 degree, measure of angle B is 90 degree and measure of angle C is 60 degree.
Step-by-step explanation:
The measures of given sides are 6, 12, [tex]6\sqrt{3}[/tex].
According to the Law of Cosine:
[tex]\cos A=\frac{b^2+c^2-a^2}{2bc}[/tex]
Using Law of Cosine, we get
[tex]\cos A=\frac{(12)^2+(6\sqrt{3})^2-(6)^2}{2(12)(6\sqrt{3})}[/tex]
[tex]\cos A=\frac{216}{144\sqrt{3}}[/tex]
[tex]\cos A=\frac{3}{2\sqrt{3}}[/tex]
[tex]\cos A=\frac{\sqrt{3}{2}[/tex]
[tex]A=30^{\circ}[/tex]
Similarly,
[tex]\cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]
[tex]\cos B=\frac{(6)^2+(6\sqrt{3})^2-(12)^2}{2(6)(6\sqrt{3})}[/tex]
[tex]\cos B=\frac{0}{36\sqrt{3}}[/tex]
[tex]\cos B=0[/tex]
[tex]B=90^{\circ}[/tex]
Therefore, measure of angle A is 30 degree and measure of angle B is 90 degree.
According to angle sum property, the sum of interior angles of a triangle is 180 degree.
[tex]A+B+C=180^{\circ}[/tex]
[tex]30^{\circ}+90^{\circ}+C=180^{\circ}[/tex]
[tex]C=60^{\circ}[/tex]
Therefore the measure of angle C is 60 degree.
The triangle with sides 6, 12, and 6√3 has angles of 30 degrees, 60 degrees, and 90 degrees.
Given a triangle with sides 6, 12, and 6√3, we can find the angles using the Law of Cosines.
First, we use the formula for the Law of Cosines,
c² = a² + b² - 2ab * cos(C).
Let a = 6, b = 6√3, and c = 12.
We substitute these values into the formula to find angle C,
cos(C) = (6² + (6√3)² - 12²) / (2 * 6 * 6√3)
Compute the values inside the formula:
6² = 36
(6√3)² = 108
12² = 144
cos(C) = (36 + 108 - 144) / 72
cos(C) = 0
Therefore, angle C = 90 degrees.
To find the other angles, we use the Law of Sines,
(sin A / a) = (sin B / b) = (sin C / c).
We already know C = 90°, so (sin C / 12) = 1/12.
For angle A,
sin(A) / 6 = 1/12
sin(A) = 6/12 = 1/2
A = 30 degrees
For angle B:
B = 180° - 90° - 30° = 60 degrees
Therefore, the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees.
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection? (1 point) Select one: a. graph of line going through 1, 2 and 3, 4 b. graph of line going through 1, 1 and 3, 3 c. graph of line going through 1, 4 and 3, 10 d. graph of line going through 1, 2 and 2, 5
option: c. graph of line going through (1, 4) and (3, 10)
Step-by-step explanation:It is given that:
Margo has a coin collection.
She was given 1 coin as a gift, and she adds 3 coins per year.
i.e. she started with a initial of one coin and add 3 coins each year.
That is this situation can be represented with the help of a function:
C(t) which represents the number of coins she has in 't' years.
Now,
C(0)=1
Also,
C(t)=3t+1-------------(A)
Hence, we will check each of the given functions whether at the value of t they passes through that point or not.
a)
it is given that:
Graph passes through (1,2) and (3,4)
i.e. when t=1 C(t)=2
and when t=3 C(t)=4
but on putting the value of t in equation (A) it does not hold true.
same could be done for option (b) and option (d).
But in option (c)
It hold true.
c. graph of line going through 1, 4 and 3, 10Since,
when t=1
C(t)=3×1+1=4
when t=3
C(t)=3×3+1=10
Hence, the correct answer is:
c.) graph of line going through 1, 4 and 3, 10
If BE is parallel to CD, the. The value of x is:
A. 10
B. 6
C. 9
the length of a rectangular prism is 4 feet, and the width is 3 feet. The volume of the prism is 9 cubic feet. In inches, what is the height of the prism?
A) 6 inches
B) 8 inches
C) 9 inches
D) 10 inches
Answer:
C 9 inches
Step-by-step explanation:
What is the relative minimum of the function?
relative minimum is -2 when x is -3
A) –6m + 38
B) –6m + 76
C) –6m + 19
D) –24m + 19
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(
a. Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.
Answer:
125 feet
Step-by-step explanation:
Given :
On a softball field, home plate is 43 feet from the pitcher’s mound.
A ball is hit at an angle of 27° east of the pitcher’s mound.
The ball travels 162 feet before it is caught by an outfielder.
To Find : Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.
Solution:
Law of cosines: [tex]a^2 = b^2 + c^2 -2bc cos A[/tex]
∠A = 27°
b = 43
c = 162
Substitute the given values
[tex]a^2 = 43^2 + 162^2 -2(43)(162) cos 27^{\circ}[/tex]
[tex]a^2 = 15679.497105[/tex]
[tex]a = \sqrt{15679.497105}[/tex]
[tex]a =125.21[/tex]
The outfielder must throw the ball 125 feet to return it to the pitcher.
What is the slope of the line whose function f satisfies f(−2)=1 and f(5)=−10f(−2)=1 and f(5)=−10?
A triangle has an area of 30 cm². The base and height are scaled by a factor of 4.
What is the area of the resulting triangle?
Enter your answer in the box.
Answer:
480cm². Verified by correct test results.
Tell whether x and y show direct variation 5y=x
The total scores on the Medical College Admissions Test (MCAT) in 2013 follow a Normal distribution with mean 25.3 and standard deviation 6.5.
a) what are the median and the first and third quartiles of the MCAT scores? what is the interquartile range?
please i need help!!!
The base of an isosceles triangle is 70 centimeters long. The altitude from the vertex angle to the base is 75 centimeters long. Find, to the nearest whole degree, the measure of the base angles of this triangle.
Write an numerical expression to show the product of the difference of 12 and 4 and the sum of 3 and 2.
Person 1 can do a certain job in fifteen minutes, and person 2 can do the same job in thirty minutes. When completing the job together, which expression would be used to represent the amount of work done by person 1?
A.1/15
B.x/15
C.15
pls asap
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=8700(1.04)^4
Using exponential function concepts, it is found that it represents growth of 4%.
Exponential function:An exponential function is modeled by:
[tex]y(t) = y(0)(1 + r)^t[/tex]
In which:
y(0) is the initial value.r is the rate of change. If it is positive, it represents growth, and if it is negative, it represents decay.In this problem, the equation is:
[tex]y = 8700(1.04)^t[/tex]
Hence:
[tex]1 + r = 1.04[/tex]
[tex]r = 0.04[/tex]
Since r = 0.04 is positive, it represents a growth of 4%.
To learn more about exponential function concepts, you can take a look at https://brainly.com/question/24757163
Final answer:
The function y = 8700(1.04)^4 represents an exponential growth with a rate of increase of 4% per time period over four periods.
Explanation:
The given function is y = 8700(1.04)^4. This represents an exponential growth because the base of the exponent, 1.04, is greater than 1. To determine the percentage rate of increase, we observe that the base, 1.04, when written as a percentage, is 104%. This means that the amount increases by 4% over each time periodperiod. Since the exponent is 4, this growth occurs over four time periods. However, the overall increase is not simply 4% multiplied by 4, as exponential growth compounds wicompoundsth each time period.
Is it possible to place 158 books on three shelves so that the first shelf has 8 fewer books than the second and 5 more books than the third shelf?
plz halp
We are given 158 books to place them on three different shelves like A, B, and C.
It says that shelf A has eight fewer books than shelf B and five more books than shelf C.
Mathematically, it can be written as (A = B - 8) and (A = C + 5).
Or we can write it as (B = A + 8) and (C = A - 5).
If we consider there are 'x' books in shelf A, then shelf B would have 'x+8' books and shelf C would have 'x-5' books.
We know that Total books are 158, so its sum must be equal to total books.
A + B + C = 158
x + (x+8) + (x-5) = 158
3x + 3 = 158
3x + 3 - 3 = 158 - 3
3x = 155
[tex] \frac{3x}{3} =\frac{155}{3} [/tex]
x = 51.667 books
But 'x' must be an integer value because number of books can not be a decimal form.
Hence, this arrangement is "NOT possible" for this question.
Answer:
it is NOT possible
Step-by-step explanation:
40 PTS if u do this correctly!
Algebra 1
Do #'s 4,5,6,7,8,9,10,12,13,14
Solve the inequality.
3 + |t + 4| < 10
A. t > 3 or t < –11
B. –3 < t < 11
C. –11 < t < 3
D. t < 3 and t > 11
Answer:
Just took the test Its C
Sue wakes up at 7:45
a.m. and jogs for 40 minutes. she then spends 45 minutes dressing for school before she catches the bus. at what time does sue get on the bus?
To covert 180 seconds to minutes, which proportion should you use?
Four years ago, Tom’s age was 3/4 of the age he will be in 6 years. How old is he now?
Let d represent the number of degrees in one angle of a regular polygon, and n represent the number of sides of the polygon to tessellate. which equation can be used to determine if the polygon will tessellate? 360° · n = d 360° · d = n 360° ÷ d = n n + d = 360° brainly
Answer:
360°/d = kn.
Step-by-step explanation:
To know if a regular polygon can tessellate, we divide 360 by the interior angle of the polygon and the result needs to be an integer, but not in all cases you get the number of sides of the polygon, you get a multiple of the number of sides. So, none of the options are correct, the correct would be
360/d = kn, where k is an integer.
Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase or decrease per time period.
y=16(7/6)^t
Plz help!
I will make up the BRAINLIEST!!!ls tell me the ......distinguish between expression and equation algebraically by providing an example of an algebraic expression and an example of algebraic equation.pls answer this I beg you !!!!
Javier has 4 juice boxes. Three are grape flavored. Write two equivalent fractions that describe the part of the juice boxes that is grape
Final answer:
Javier has 4 juice boxes, 3 of which are grape flavored. The fraction representing grape juice boxes is 3/4, with equivalent fractions being 6/8 and 9/12.
Explanation:
Javier has 4 juice boxes and three are grape flavored. To describe the part of the juice boxes that is grape in the form of a fraction, we would use the total number of juice boxes as the denominator and the number of grape juice boxes as the numerator. So, the fraction representing the grape juice boxes is 3/4 (three out of four).
To write two equivalent fractions, we can multiply the numerator and the denominator by the same number. If we multiply both by 2, we get 6/8, which is equivalent to 3/4. Similarly, multiplying both by 3 gives us 9/12, which is also equivalent to 3/4.
What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)
What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]
Let us find the value of cos([tex] \frac{3\pi}{4} [/tex]) and [tex] sin(\frac{7\pi}{6} ) [/tex]
[tex] cos(\frac{3\pi}{4} )=cos(\pi -\frac{\pi}{4} ) [/tex]
The angle [tex] \pi -\frac{\pi}{4} [/tex] lies in second quadrant.
So, [tex] cos(\frac{3\pi}{4} )=-cos(\frac{\pi}{4} ) =-\frac{1}{\sqrt{2}} [/tex]
[tex] So, cos(\frac{3\pi}{4} )=-\frac{1}{\sqrt{2}} [/tex]
Now, Let us find the value of [tex] sin(\frac{7\pi}{6} ) [/tex]
[tex] sin(\frac{7\pi}{6} ) =sin(\pi +\frac{\pi}{6} )=-sin(\frac{\pi}{6} ) =\frac{-1}{2} [/tex]
[tex] sin(\frac{7\pi}{6} ) =\frac{-1}{2} [/tex]
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]=2*[tex] \frac{-1}{\sqrt{2}} [/tex]-4*[tex] \frac{-1}{2} [/tex]
=[tex] \frac{-2}{\sqrt{2}} +\frac{4}{2} [/tex]
=[tex] \frac{-2\sqrt{2}}{2} +\frac{4}{2} [/tex]
=[tex] \frac{-1\sqrt{2}}{1} +\frac{2}{1} [/tex]
=[tex] -\sqrt{2} +2 [/tex]
=[tex] 2-\sqrt{2} [/tex]
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6})=2-\sqrt{2} [/tex]
Use the triangle pictured to calculate the following measurements.
Perimeter: p = ___ units Semiperimeter: s = ___units Area: A ≈ ___square
triangle is 8 by 12 by 10
Answer:
Step-by-step explanation:
The formula v =bh means that the volume of a prism is equal to its base area times its height. Solve v= bh for b
Answer:
[tex]b = \frac{v}{h}[/tex]
Step-by-step explanation:
The formula v =bh means that the volume of a prism is equal to its base area times its height.
WE need to solve for b, we need to get 'b' alone
v=bh
to get 'b' alone we need to eliminate 'h'
To eliminate any variable we always do opposite operation.'
bh mean b times h
the opposite of multiplication is division
so to eliminate 'h' we divide by 'h' on both sides
[tex]\frac{v}{h} = \frac{bh}{h}[/tex]
[tex]b = \frac{v}{h}[/tex]
The formula for the base area (b) of a prism is b = v/h.
To solve the formula v = bh for b (the base area), to isolate b on one side of the equation. Follow these steps:
Divide both sides of the equation by h:
v/h = b
The base area (b) is now isolated on one side of the equation.
To know more about area here
https://brainly.com/question/30307509
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PLEASE HELP!!
is it right??