Final answer:
To find the unit rate of a 16oz soda bottle that costs $3.49, divide the price by the ounces, resulting in $0.218125 per ounce, which rounds to $0.22 per ounce.
Explanation:
The question is about calculating the unit rate of a 16oz bottle of soda that costs $3.49. To find the unit rate, we divide the total cost by the number of ounces. Thus, the unit rate is $3.49 ÷ 16 oz, which equals approximately $0.218125 per ounce. Rounding to the nearest tenth of a cent, the unit rate is $0.22 per ounce.
find the quotient 16 2/3 ÷ 5 5/7
Answer:
2 11/12
Step-by-step explanation:
(50/3)/(40/7)
=50/3*7/40
=5/3*7/4
=35/12
=2 11/12
let's convert firstly, the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{16\frac{2}{3}}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}}~\hfill \stackrel{mixed}{5\frac{5}{7}}\implies \cfrac{5\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{40}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{50}{3}\div\cfrac{40}{7}\implies \cfrac{\stackrel{5}{\begin{matrix} 50 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{3}\cdot \cfrac{7}{\underset{4}{\begin{matrix} 40 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\implies \cfrac{35}{12}\implies 2\frac{11}{12}[/tex]
If you apply the below transformations to the square root parent function,
F(x) = VX, what is the equation of the new function?
• Shift 12 units right.
• Shift seven units down.
Answer:
We have the following function: [tex]f(x) =\sqrt{x}[/tex]
We know that given a function f(x), the function g(x) = f(x+m) is exactly the same function f(x) but shifted m units to the left.
Therefore, to shift the function 12 units right we should:
[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x-12) =\sqrt{x-12}[/tex]
We know that given a function f(x), the function g(x) = f(x)+m is exactly the same function f(x) but shifted m units up.
Therefore, to shift seven units down we should:
[tex]f(x) =\sqrt{x}[/tex] ⇒ [tex]f(x) =\sqrt{x}-7[/tex]
Factoring Trinomials (
Factor each completely.
1) 3p² – 2p - 5
Answer:
factors (3p - 5) and (p + 1)
Step-by-step explanation:
The quadratic formula always "works" when you're looking to factor a quadratic expression or equation. Here, the coefficients are a = 3, b = -2 and c = -5. The discriminant is thus b²-4ac, which here is (-2)²-4(3)(-5), or 4+60, or 64. Because this discriminant is positive, we know that the quadratic has two real, unequal roots. These roots are:
-(-2)±√64 2 ± 8
p = ------------------- = --------------- = 10/6 and -1, or 5/3 and -1.
2(3) 6
These roots correspond to the factors (3p - 5) and (p + 1).
what is the sum of 12x^2+3x+6 and -7x^2-4x-2
Answer: [tex]5x^2-x+4[/tex]
Step-by-step explanation:
In addition of polynomials, you only have to add the like terms.
Remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Then, given the polynomial [tex]12x^2+3x+6[/tex] and the polynomial [tex]-7x^2-4x-2[/tex], you can find the sum of them by adding the like terms.
Observe the procedure below:
[tex](12x^2+3x+6)+(-7x^2-4x-2)=12x^2+3x+6-7x^2-4x-2=5x^2-x+4[/tex]
Therefore, the sum is:
[tex]5x^2-x+4[/tex]
Martha is training for a duathlon, which includes biking and running. She knows that yesterday she covered a total distance of over 55.5 miles in more than than 4.5 hours of training. Martha runs at a speed of 6 mph and bikes at a rate of 15.5 mph.
Answer:
Distance: 6x + 15.5y > 55.5
Time: x + y > 4.5
Step-by-step explanation:
We are given that Martha is training for a duathlon and she covered a total distance of over 55.5 miles in more than than 4.5 hours of training.
Also, she runs at a speed of 6 mph and bikes at a rate of 15.5 mph.
We are to write inequalities representing the distance she traveled and the total time she spent training.
Distance: 6x + 15.5y > 55.5
(formula for distance = speed x time so speeds for running and biking are multiplied by their number of hours)
Time: x + y > 4.5
(she trained for more than 4.5 hours, x hours for running and y hours for biking.
How can △WXY be mapped to △MNQ?
First, translate vertex w to vertex M. Next, reflect △WXY across the line containing
1) line segment WX
2) line segment WY
3) line segment XY
4) line segment MQ
Answer:
A: Line Segment WX
Step-by-step explanation:
100% on edge 2020
Answer:
WX is correct
Step-by-step explanation:
Got a 100 in edge quiz.
The given graph represents the function f(x) = 2(5)
How will the appearance of the graph change if the a
value in the function is decreased, but rerrains greater
than 0?
The graph will increase at a slower rate.
The graph will show a decreasing, rather than
increasing, function.
The graph will show an initial value that is lower on
the y-axis
The graph will increase at a constant additive rate,
rather than a multiplicative rate.
What’s the awnser
Answer:
It's C on e2020
Step-by-step explanation:
45+45-6+122/5+92-35*9+12-10/2+19-25?
Answer:-568/5
Step-by-step explanation:
Answer:
-568/5 is the answer
The difference of 2 numbers is 21 and the quotient of the equation is 4 then what are the two numbers?
Answer:
The two numbers are 28 and 7.
Step-by-step explanation:
Let the first number be x
Let the second number be y
The difference of x and y is x-y=21
The quotient of two numbers is x/y = 4
x-y =21 (This is equation 1)
x/y=4 (This is equation 2)
By solving equation 2 we will get the value of x.
x/y=4
x=4y (Lets call it equation 3)
Now, put the value of x(equation 3) in (equation 1)
x-y=21
4y-y=21
3y=21
y=21/3
y=7
Now put the value of y in equation 3 to get the value of x
x=4y
x=4(7)
x=28
Solution Set {(x,y)(28,7)}
Answer:
28 and 7
Step-by-step explanation:
What is the other solution?
Answer:
-6
Step-by-step explanation:
m^2 - 36 = 0
Add 36 to each side
m^2 -36+36 = 0+36
m^2 = 36
Take the square root of each side
sqrt( m^2) = ± sqrt(36)
m = ±6
We know one root is 6
The other root is -6
Find the arc length of the partial circle
Answer:
7pi/2
Step-by-step explanation:
If was a full, the circumference or the arc length would be 2pi*r where r in this case is 7 so it would be 14pi.
Now this only a quarter of that, so this arc length is actually 14pi/4.
This can be reduced 14pi/4 =7pi/2
Answer:
3.5pi
Step-by-step explanation:
KA
For f(x) = 2x+1 and g(x)=x^2-7, find (f*g)(x).
Answer:
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Step-by-step explanation:
We have the following functions
[tex]f (x) = 2x+1[/tex]
[tex]g (x) = x^2-7[/tex]
To find [tex](f*g)(x)[/tex] we must multiply the function f (x) with the function g (x)
Then we perform the following operation
[tex](f*g) (x) =(2x+1)(x^2-7)[/tex]
Apply the distributive property
[tex](f*g) (x) =2x^3-14x^2+x^2-7 [/tex]
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Finally we have that:
[tex](f*g) (x) =2x^3-13x^2-7 [/tex]
Sienna has $8 and is saving $3 per week. Jacob has $6 and is saving $4 per week. Which model represents the equatio
that can determine when Sienna will have the same amount of money as Jacob?
Let the amount saving by Sienna and Jacob be x
Sienna has $8 and is saving $3 per week
So the equation will be 3x + 8
Jacob has $6 and is saving $4 per week
So the equation will be 4x + 6
Sienna will have same amount as Jacob, so
3x + 8 = 4x + 6
So the model two will represents the equation that Sienna will have same amount as Jacob.
Answer:
Model B
Step-by-step explanation:
Model B correctly displays sienna's and jacob's equations.
For sienna, the $8 can be represented as 8 unit blocks, which is displayed in model 2. The $3 per week can be represented as 3 x tiles, as shown in the picture, because it represents how many weeks.
For jacob, the model shows 6 unit blocks which represents his 6 dollars. The $4 per week is represented with the 4 x tiles, and we use x tiles because we are calculating how many weeks.
which equation is in quadratic form?
a)4(x-2)^2+3x-2+1=0
b)8x^5+4x^3+1=0
c)10x^8+7x^4+1=0
d)9x^16+6x^4+1=0
The domain of a function is representative of which one of the following
characteristics of the function?
A. all possible outputs of the function
B. all possible F(x) values of the function
c. all possible (x, y) coordinates
D. all possible inputs of the function
Answer:
D. all possible inputs of the function
Step-by-step explanation:
Lets look at the options one by one
A. all possible outputs of the function
This is not the correct option because the possible outputs are range of the function
B. all possible F(x) values of the function
Not correct because the f(x) values are the output of the function.
c. all possible (x, y) coordinates
This is also not correct because domain only consists of all the values of independent variable that make the function produce some output
D. all possible inputs of the function
This is the correct answer because domain is the set of all values of independent variable for which the function is not undefined ..
Based on the graph below, how would you describe the curve?
A. The curve is a 'one-to-one' function
B. The curve is a linear function
c. The curve is not a function
D. The curve is a 'many-to-one" function
D. is the correct answer
Hopes this helps
Mrs. Culland is finding the center of a circle whose equation
is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. Her
work is shown.
x2 + y2 + 6x + 4y – 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (y2 + 4y) = 3
(x2 + 6x + 9) + (x2 + 4y + 4) = 3 + 9 + 4
Answer:
The center of the circle is (-3,-2)
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex]x^{2} +y^{2}+6x+4y-3=0[/tex]
Completing the square
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}+6x) +(y^{2}+4y)=3[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=3+9+4[/tex]
[tex](x^{2}+6x+9) +(y^{2}+4y+4)=16[/tex]
Rewrite as perfect squares
[tex](x+3)^{2} +(y+2)^{2}=16[/tex]
therefore
The center of the circle is (-3,-2)
Answer: ITS D !! ON EDGE
Step-by-step explanation:
(25 points) Can someone please solve this I just need to see how its solved to understand
x = total amount of students in 8th Grade.
we know only one-thrid of the class went, so (1/3)x or x/3 went.
we also know 5 coaches went too, and that the total amount of that is 41.
[tex]\bf \stackrel{\textit{one third of all students}}{\cfrac{1}{3}x}+\stackrel{\textit{coaches}}{5}=\stackrel{\textit{total}}{41}\implies \cfrac{x}{3}+5=41\implies \cfrac{x}{3}=41-5 \\\\\\ \cfrac{x}{3}=36\implies x=3(36)\implies x=108[/tex]
now, to verify, well, what do you get for (108/3) + 5?
Reflection Lines
A reflection line is equidistant from a pre-image point and its image.
Therefore, in segment AA’, point M is the
Answer:
Midpoint
Step-by-step explanation:
Equidistant from the pre = image AA would be the middle
Answer:
Mid Point, thats all there is, its the answer, just that
Step-by-step explanation:
Please answer this question in the picture!
Ignore the writing over it and the answer! It’s probably wrong.
Answer:
c [tex]113\:m[/tex]
Step-by-step explanation:
[tex]113,391 = 4\frac{9}{10}[2\frac{1}{10}]^{2} + 135 \\ \\ 113 ≈ h[/tex]
I am joyous to assist you anytime.
The formula V = πr2h gives the volume of a cylinder with radius r and height h. Solve the formula for r. Show your work.
Answer:
[tex]r = \sqrt{\frac{V}{\pi h}}[/tex]
Step-by-step explanation:
The formula to calculate the volume is:
[tex]V = \pi r^{2} h[/tex]
Where r is the radius and h the height of the cylinder.
We need to isolate r. First step is to move pi and h, they can go to the other side dividing.
[tex]V = \pi r^{2} h\\ \pi r^{2} h = V\\ \pi r^{2} =\frac{V}{h}\\r^{2} =\frac{V}{\pi h}[/tex]
Second step, as radius is with an exponent of two, we can use square root.
[tex]r^{2} =\frac{V}{\pi h}\\\sqrt{r^{2}} = \sqrt{\frac{V}{\pi h}}[/tex]
Finally, we can isolate radius - r
[tex]r = \sqrt{\frac{V}{\pi h}}[/tex]
To the nearest hundredth of a centimeter, what is the length of the hypotenuse?
[1] cm
92.58 cm
Answer:
106.90 cm
Step-by-step explanation:
Given
Angle=30 degrees
Base=92.58 cm
So,
We will have to use the triangular ratios to find the hypotenuse.
The triangular ratio that will be used for this will be cosine because we know the value of angle and base since it involves both cosine will be used.
cosθ=Base/Hypotense
cos30=92.58/Hypotenuse
0.8660=92.58/Hypotenuse
Hypotenuse=92.58/0.8660
=106.90 cm ..
Answer:
Hypotenuse = 107.02
Step-by-step explanation:
Points to remember
If angles of a triangle are 30°, 60° and 90° then the sides are in the ratio
1 : √3 : 2
It is given a right angled triangle with angles 30°, 60°, 90°
and height = 95.58 cm
To find the hypotenuse
From the figure we can write,
Base : Height : Hypotenuse = 1 : √3 : 2 = Base : 92.58 : Hypotenuse
Therefore Hypotenuse = (92.58 * 2)/√3
= 107.02 cm
Find the missing factor.
4b2 + 17b + 15 = (b + 3)(
)
Answer:
(4b + 5)
Step-by-step explanation:
To get 4b^2 you already have b^2 if you put b inside the second set of brackets. But that would mean you don't have 4 anywhere to get 4b^2.
So the first step has to be
(b + 3)(4b
Now look at the 15 for a moment. It is plus 15. The only way you can get a plus 15 is if both signs are plus (after the b terms) or both terms are minus.
The middle term (17b) is plus so both terms after b are plus.
(b + 3)(4b +
Now we need something that multiplies to 15. 3*5 = 15. So the term you want is 5.
(b + 3)(4b + 5)
Does the middle term work?
5*b + 3*4b = 5b + 12b = 17b
Everything looks fine.
The second factor is 17b.
Question 101 points)
Which equation in slope-intercept form represents the line that passes through (5, 1) and
(-4,7)
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================[/tex]
[tex]\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}[/tex]
Paula Pruitt invested $4,334 in the stock market. The investment has declined 7% in value. Determine the worth of the investment now
Answer:
(4334/100)*93 = $ 4,030.62
Step-by-step explanation:
N/A
write the equation of the line that passes through the points (7,-4) and (-1,3), first in point slope form
The given line that passes through the points (7,-4) and (-1,3).
The slope is
[tex]m = \frac{3 - - 4}{ - 1 - 7} = - \frac{7}{8} [/tex]
The point-slope form is obtained using:
[tex]y-y_1= m (x-x_1) [/tex]
When (7,-4) is used the point-slope form is
[tex]y + 4= - \frac{7}{8} (x - 7) [/tex]
We expand now to get;
[tex]y = - \frac{7}{8}x + \frac{49}{8} - 4[/tex]
This implies that,
[tex]y = - \frac{7}{8}x + \frac{17}{8}[/tex]
Let f(x)=x2+4x+12 . What is the vertex form of f(x)? What is the minimum value of f(x)?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2(1)}~~,~~12-\cfrac{4^2}{4(1)} \right)\implies (-2~~,~~12-4)\implies (-2~,~8)[/tex]
well, the quadratic has a leading term with a positive coefficient, meaning is a parabola opening upwards, like a "bowl", comes from above down down down, reaches a U-turn, namely the vertex, and goes back up up up.
so the minimum value is at the vertex of course, and the minumum is well, just the y-coordinate of the vertex, 8.
Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 1/2 yard long. How many pieces of string does Ms. Cole have?
Answer:
8
Step-by-step explanation:
got it right
Answer:
8
Step-by-step explanation:
got it right in Ed
A roller coaster can take 162 passengers around the track in 9
minutes. The roller coaster operates at a constant rate.
How many passengers can the roller coaster take around the track per minute?
Answer: 18 people per minute
Step-by-step explanation: 162 divide by 9 equals 18
To find the answer, divide 162 by 9, since you divide 9 by 9 to get 1 minute.
162/9=18
The roller coaster takes 18 passengers around the track per minute.
Hope this helps!
Yesterday, a factory used 2/3 of a tub of peanut butter. They use 1/6 of a tub of peanut butter for each batch of peanut butter cookies. How many batches of peanut butter cookies did the factory make yesterday?
The number of batches is 4.
What is the unitary method?When a problem arises if 4 is required for 2 of these things then how many things does 20 require?
We use the unitary method to solve the problem where we find how much is required for one thing and then multiply it by the required.
Solving the given problem.1/6 tub of peanut butter is used for one batch of cookies.
2/3 of it was used for the whole day.
So to find the total number of batches we divide the total tub used by the amount of tub used for one batch of cookies hence = 2/3/(1/6) = 4
Hence the answer to the given problem is 4.
Learn more about the Unitary method here
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