The cost per unit ounce is obtained by computing the quotient:
[tex]c=\frac{C}{N}.[/tex]Where:
• c is the cost per unit ounce,
,• C is the cost,
,• N is the number of ounces that you get for C.
In this problem we have:
• C = $5.19,
,• N = 16.8 ounces.
Computing the quotient, we get:
[tex]c=\frac{5.19}{16.8}\cong0.31[/tex]dollars per ounce.
Answer: B. $0.31
L Pretest: Unit 2Question 5 of 21Which of the following represents the factorization of the polynomial functiongraphed below? (Assume it has no constant factor.)55
1) The best way to tackle questions like this is to locate the x-intercepts. Since according to the options the leading coefficient is 1, we just need to locate the zeroes and plug them into the quadratic equation form, in its factored form.
2) So now, let's write out the factored form and plug the zeroes into them:
[tex]\begin{gathered} y=a(x-x_1)(x-x_2) \\ y=1(x-1)(x-3) \\ y=(x-1)(x-3) \end{gathered}[/tex]A gumball machine contains 5 blue gumballs and 4 red gumballs. Two gumballs are purchased, one after the other, without replacement.
Find the probability that the second gumball is red.
===================================================
Work Shown:
5 blue + 4 red = 9 total
A = P(1st is red, 2nd is red)
A = P(1st is red)*P(2nd is red, given 1st is red)
A = (4/9)*(3/8)
A = 12/72
B = P(1st is blue, 2nd is red)
B = P(1st is blue)*P(2nd is red, given 1st is blue)
B = (5/9)*(4/8)
B = 20/72
C = P(2nd is red)
C = A+B
C = 12/72 + 20/72
C = 32/72
C = 4/9
3. Trapezoid JKLM with vertices J(-4, 3), K(-2, 7),L(2,7), and M(3, 3) in the line y = 1.what would the reflection coordinates be
First, we graph the trapezoid and the line
If we reflect the figure across the line y = 1, then we get the following figure
As you can observe in the graph, the vertices would be J'(-4,-1), K'(-2,-5), L'(2,-5), and M'(3,-1).
For which pair of triangles would you use ASA to prove the congruence of the two triangles?
Solution:
Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. According to this, the correct answer is:
C.
diameter = 10.5in.we are learning something about area of circle.
Use the formula for the area of a circle:
[tex]A=\pi\cdot r^2[/tex]First, we need to find the radius r. Since the radius is half the diameter, then:
[tex]\begin{gathered} r=\frac{10.5\text{ in}}{2} \\ \therefore r=5.25in \end{gathered}[/tex]Substitute the value for r in the formula for the area of the circle:
[tex]\begin{gathered} A=\pi\cdot(5.25in)^2 \\ \approx86.6in^2 \end{gathered}[/tex]Therefore, the area of a circle of diameter 10.5 in is approximately 86.6 squared inches.
What is the value of x? Enter your answer in the box. x =
Step-by-step explanation:
it is an equilateral triangle : all 3 sides are if equal length (indicated by the same symbol on each side).
automatically with that comes the conclusion that all 3 angles have the same size.
and since the sum of all angles in a triangle is always 180°, this means every angle is 180/3 = 60°.
therefore,
2x - 4 = 60
2x = 64
x = 32
and FYI
5y = 60
y = 12
2625÷32 long division way
Answer: 82 R1 or decimal form 82.031
Step-by-step explanation:
0082
. --------
-0
26
. - 0
. 262
. -256
65
-64
. 1
What is 175% of 48? Show work.
Let 175% of 48 be y.
This implies that
[tex]\frac{175}{100}\times48=y[/tex]To evaluate y,
[tex]\begin{gathered} \frac{175}{100}\times48=y \\ \Rightarrow\frac{175\times48}{100}=y \\ \frac{8400}{100}=y \\ \Rightarrow y=84 \end{gathered}[/tex]Hence, 175% of 48 is 84.
Write a relation consisting of five ordered pairs that satisfies the following conditions. The relation is a function. Switching the x- and y-coordinates of each ordered pair results in a relation that is not a function.
Answer:
Step-by-step explanation:
If each value of x only has one corresponding value of y, it is a function. You can test this just by eye or by graphing and doing the vertical line test by rolling a pencil or other straight object across to make sure only one point is on the line at a time
Is x = -2 the linear equation that matches this table of ordered pairs?Explain why or why not.Xy-2 7-2 1-2 -5(x, y)(-2,7)(-2, 1)(-2,-5)
Answer:
All the points given (-2,7) (-2,1) (-2,-5) have the x-coordinate of -2, then those points lie in the x=-2, so it matches the table.
A window washer drops a tool from their platform 155ft high. The polynomial -16t^2+155 tells us the height, in feet, of the tool t seconds after it was dropped. Find the height, in feet, after t= 1.5 seconds.
Conner plans to plow a field in one day. Before lunch he plows 15 acres, which is 30% of the field. Howmany acres will he have to plow after lunch in order to finish the field?
Solution:
Let the total field to plow be 100 %
According to the question,
The field plowed before lunch is shown below:
15 acres field = 30%
30 % field = 15 acres
1 % field = 15/30 acres
The field plow after lunch is 70%.
[tex]\begin{gathered} 70\text{ \% of field = }\frac{15}{30}\times70 \\ =35\text{ acres} \end{gathered}[/tex]Final Answer:
Therefore, the field to plow after lunch in order to finish the field is 35 acres.
find the slope of #1 y = 2x - 3#2 (-2,-4) (-1,-2)#3 y = 1/3x - 4# 4 (4,0) (4,1)
1. slope= 2
2. slope=2
3. slope= 1/3
4. slope indefinite, vertical line
Explanation
Step 1
[tex]\begin{gathered} y=\text{ 2x-3} \\ \end{gathered}[/tex]the equation is given in slope(m) - intercept(b)
[tex]\begin{gathered} y=\text{ mx+b} \\ \text{then} \\ mx+b=2x-3 \\ m=2 \\ \text{slope}=2 \end{gathered}[/tex]Step 2
when you have two points of a line, P1 and P2 the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1(-2,-4) P2(-1,-2)
replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-2-(-4)}{-1-(-2)} \\ \text{slope}=\frac{-2+4}{-1+2}=\frac{2}{1}=2 \\ \text{slope}=2 \end{gathered}[/tex]Step 3
[tex]y=\frac{1}{3}x-4[/tex]similar to the #1. ,the equation is given in slope(m) - intercept(b)
[tex]\text{the slope = }\frac{1}{3}[/tex]Step 4
let
[tex]P1(4,0)\text{ and P2(4,1)}[/tex][tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{1-0}{4-4}=\frac{1}{0}=\text{indefined} \\ it\text{ means the line is vertical} \end{gathered}[/tex]x + y = 5 y - 2x = -4
x = 3, y = 2
Explanations:The equations are:
x + y = 5......................(1)
y - 2x = -4...................(2)
Make x the subject of the the formula
x = 5 - y...............(3)
Substitute equation (3) into equation (2)
y - 2(5 - y) = -4
y - 10 + 2y = -4
3y = -4 + 10
3y = 6
y = 6 / 3
y = 2
Substitute the value of y into equation (3)
x = 5 - 2
x = 3
draw a right triangle with a leg that as a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to nearest tenth.
Question:
Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.
Solution:
A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:
In this case, the appropriate trigonometric identity is:
[tex]\sin (55^{\circ})\text{ = }\frac{y}{h}[/tex]where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:
[tex]\sin (55^{\circ})\text{ = }\frac{10}{h}[/tex]and solving for h, we get:
[tex]h\text{ = }\frac{10}{\sin (55^{\circ})}\text{ = 12.207}\approx12.21[/tex]then, the correct answer is:
[tex]h\text{ =}12.21[/tex]Im confused on what you have to do in order to find the answer
Given:
The ship is moved from (-10,9) to (-1,-5) in the coordinate plane.
To find:
The transformation rule
Explanation:
The initial point can be written to obtain the terminal point as follow,
[tex](-10+9,9-14)\rightarrow(-1,-5)[/tex]In general,
We write,
[tex](x,y)\rightarrow(x+9,y-14)[/tex]Final answer: Option C.
[tex](x,y)\operatorname{\rightarrow}(x+9,y-14)[/tex]
Help on math question precalculus ChoicesVertical shift Period DomainRange Phase shift Amplitude
All the x-values that satisfy the function - Domain
Translating the sine or cosine curve up or down - Vertical shift
How long a given function takes to repeat itself - Period.
A horizontal shift of a sine or cosine function- Phase shift
All the y-values that satisfy the function- Range
Distance from the horizontal axis or midline to the maximum and minimum points - Amplitude
a wall in marcus bedroom is 8 2/5 feet high and 16 2/3 feet long. of he paints 1/2 of the wall blue, how many square feet will be blue?140128 2/157064 2/15
Answer:
[tex]70[/tex]Explanation:
What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue
So, we need to simply get the area of the room and divide this by half
Mathematically, the area of a rectangle is the product of its two sides
Thus, we have it that the area of the room is:
[tex]\begin{gathered} 8\frac{2}{5}\times16\frac{2}{3} \\ \frac{42}{5}\times\frac{50}{3}\text{ = 14}\times10=140ft^2 \end{gathered}[/tex]Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2
We have this as:
[tex]140\times\frac{1}{2}=70ft^2[/tex]
Point M is the midpoint of AB. If AM = b² + 5b and
MB = 3b + 35, what is the length of AM?
Step-by-step explanation:
since M is the midpoint, it means that AM = MB.
so,
b² + 5b = 3b + 35
b² + 2b - 35 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case (x is called b, don't get confused, as this is not the factor of x) this gives us
b = (-2 ± sqrt(2² - 4×1×-35))/(2×1) =
= (-2 ± sqrt(4 + 140))/2 = (-2 ± sqrt(144))/2 =
= (-2 ± 12)/2 = -1 ± 6
b1 = -1 + 6 = 5
b2 = -1 - 6 = -7
therefore, we have 2 solutions
b = 5
AM = 5² + 5×5 = 25 + 25 = 50
b = -7
AM = (-7)² + 5×-7 = 49 - 35 = 14
control, as AM = MB
MB = 3×5 + 35 = 15 + 35 = 50
or
MB = 3×-7 + 35 = -21 + 35 = 14
AM = MB in both cases, so, all is correct.
16. Eric is deciding how many trees to plant.
Here are his estimates of the time it will take.
Number of trees
1 tree
2 trees
3 trees
4 trees
5 trees
Time
30 minutes
40 minutes
50 minutes
60 minutes
70 minutes
With each additional tree , the estimated time increases by 10 minutes .
in the question ,
a table with number of trees and time required to plant them is given .
For planting 1 tree 30 minutes is required to plant them .
for planting 2 trees 40 minutes is required to plant them .
increase in number of tree = 2 tree - 1 tree = 1 tree
change in time required = 40 min - 30 min = 10 min
for planting 3 trees , 50 minutes is required to plant them .
increase in number of tree = 3 trees - 2 trees = 1 tree
change in time required = 50 min - 40 min = 10 min
So, we can see that for every additional tree planted the time increases by 10 minutes .
Therefore , with each additional tree , the estimated time increases by 10 minutes .
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I need help for problem number 9. On the right side of the paper.
Constant of variation ( k ):
• y = 2/3
,• x = 1/4
[tex]k=\frac{y}{x}=\frac{\frac{2}{3}}{\frac{1}{4}}=\frac{8}{3}[/tex]k = 8/3
Based on k we can find the value of y when x =3/4 as follows:
[tex]\begin{gathered} k=\frac{y}{x} \\ y=k\cdot x \\ y=\frac{8}{3}\cdot\frac{3}{4}=2 \end{gathered}[/tex]Answer:
• k = 8/3
,• When ,x, = ,3/4,,, y = 2
Draw the angle 0=-pi/2 in standard position find the sin and cos
An angle in standard position has the vertex at the origin and the initial side is on the positive x-axis.
Thus, the initial side of the angle is:
Now, half the circumference measures pi, thus, pi/2 is a quarte of the circumference. As we want to find the angle -pi/2, then we need to rotate the terminal side clockwise:
Find the sine and the cosine.
The sine and the cosine in the unit circle are given by the coordinates as follows:
[tex](\cos\theta,\sin\theta)[/tex]As can be seen in the given unit circle, the terminal side is located at:
[tex](0,-1)[/tex]Thus, the values of cosine and sine are:
[tex]\begin{gathered} \cos\theta=0 \\ \sin\theta=-1 \end{gathered}[/tex]Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40
minutes on reading and math homework. How much longer did Sara spend on her homework than Mia?
Sara spent 15 minutes longer than (the difference is 15 min) Mia in her homework.
According to the question,
We have the following information:
Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40 minutes on reading and math homework.
So, it means that the total time spent by Sara in her homework is:
35+20 minutes
55 minutes
So, the differences between their time spent in her homework (will give us the more time taken by Sara) is:
Time spent by Sara in her homework-time spent by Mia in her homework
(55-40) minutes
15 minutes
Hence, Sara spent 15 more minutes than Mia.
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I got the last question right that was similar so I’m unsure what I’m doing wrong for this one
Solve x:
[tex][/tex]80% of _ = 20?4-4-4-
Let
x -----> the missing number
we know that
80%=80/100=0.80
so
0.80x=20
solve the linear equation for x
Divide by 0.80 both sides
x=20/0.80
x=25
the answer is 25
From the given proportional relationship, which of the following points lie on the same line?
As per given by the question,
There are given that a graph of line.
Now,
h
Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometres she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate. How far can Eliana drive on 22 liters of fuel? What if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km? How many liters of fuel does she need?
Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.
81 km=9 liters
9 km= 1 liter
She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.
By unitary method,
22 liters = 22 × 9 km
= 198 km
Also, given that if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.
We need to find the amount of fuel she would need.
Let 139.4 km = x liters
By unitary method,
x = 139.4 / 9
x = 15.5 liters
Therefore, Eliana can drive 198 km with 22 liters of fuel.
If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel
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Solve 2/3 (6w+12) this equation
Answer:
4w+8
Step-by-step explanation:
If f (x)- VX-3, complete the following statement:x + 219) =
Given that;
[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]To get f(19), let's substitute 19 for x in the function f(x);
[tex]\begin{gathered} f(x)=\frac{3}{x+2}-\sqrt{x-3} \\ f(19)=\frac{3}{19+2}-\sqrt{19-3} \\ f(19)=\frac{3}{21}-\sqrt{16} \\ f(19)=\frac{1}{7}-4 \\ f(19)=-3\frac{6}{7} \end{gathered}[/tex]Therefore, the value of f(19) is;
[tex]f(19)=-3\frac{6}{7}[/tex]you own a pet store that sells fish tank you brought a fish tank for $35 and are going to mark it up 20% what is the selling price going to be on the fish tank
If you're marking the fish tank up by 20%, it means you're looking to sell it at 120% of its original value.
Now, let's use a rule of three to calculate such percentage:
Thereby,
[tex]x=\frac{120\cdot35}{100}\rightarrow x=42[/tex]The selling price would be $42
