Given that a 6 ounce package costs $1.92,
the cost per ounce is
= $1.92/6
= $0.32
If a 16 ounce package costs $5.28 ,
the cost per ounce will be
= $5.28/16
= $0.33
Given that aA 22 ounce package costs $6.82
if 75 equals 17 multiplied by 2 divided by 84628277 and you find the square root what is the answer in fraction form
I need help finding b for a line that passes through 0,3 and 4,9 with a slope of 1.5
Given:
The points are
[tex](0,3),(4,9)[/tex]To find:
The value of b.
Explanation:
Using the two-point formula,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]Substituting the values we get,
[tex]\begin{gathered} \frac{y-3}{9-3}=\frac{x-0}{4-0} \\ \frac{y-3}{6}=\frac{x}{4} \\ \frac{y-3}{3}=\frac{x}{2} \\ y-3=\frac{3}{2}x \\ y=\frac{3}{2}x+3 \\ y=1.5x+3 \end{gathered}[/tex]It is of the slope-intercept form,
[tex]y=mx+b[/tex]Comparing we get,
The value of b is 3.
Final answer:
The value of b is 3.
if using the method of completing the square to solve te quadratic equation x squared+4x+3=0, which number would have to be added to complete the square
The quadratic equation is given as,
[tex]x^2+4x+3=0[/tex]Apply the Method of Completing Squares as follows,
[tex]\begin{gathered} (x)^2+2(x)(2)+(2)^2-(2)^2+3=0 \\ (x+2)^2=4-3 \\ (x+2)^2=1 \\ x+2=1\text{ or x+2=-1} \\ x=1-2\text{ or }x=-1-2 \\ x=-1\text{ or }x=-3 \end{gathered}[/tex]Thus, the roots of the given equation are -1 and -3.
can you please help me find the answer to the question?
To determine the distance between the forest ranger and the fire, simply use the trig. ratio
Let the distance between the forest ranger and the fire
we have: angle theta = 18 degree
adjacent=350 and opposite = x
The best trig. ratio to use is:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]undefined[/tex]in your own words how you would explain slope to a struggling student and...
Solution
From the given graph
To find the slope of a given line, we pick two points from the graph and use their x and y coordinates to find the slope as shown below
Where
[tex]\begin{gathered} x=0,y=-4 \\ (x_1,y_1)\Rightarrow(0,-4) \\ x=6,y=5 \\ (x_2,y_2)\Rightarrow(6,5) \end{gathered}[/tex]To find the slope of a line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the coordinates into the formula above
[tex]\begin{gathered} \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \frac{y-(-4)}{x-0}=\frac{5-(-4)}{6-0} \\ \frac{y+4}{x}=\frac{5+4}{6} \\ \frac{y+4}{x}=\frac{3}{2} \end{gathered}[/tex]Crossmultiply
[tex]\begin{gathered} 2(y+4)=3(x) \\ 2y+8=3x \\ 2y=3-8 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=\frac{3x-8}{2} \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]Hence, the equation of the given line in the slope-intercept form is
[tex]y=\frac{3}{2}x-4[/tex]18. If you drop a basketball off a cliff and it travels at an average speed of 15 m/s, if the cliff is 60meters high, how long will it take before the basketball hits the ground?
If you drop a basketball off a cliff and it travels at an average speed of 15 m/s, if the cliff is 60
meters high, how long will it take before the basketball hits the ground?
Remember that
The speed (s) is equal to divide the distance (d) by the time (t)
so
s=d/t
Solve for t
t=d/s
substitute teh given values
t=60/15
t=4 sec
therefore
the answer is 4 secondsA parabola has the equation y = x2 - 10x + 28. What are the coordinates of its vertex?h Enter your answer in the box with parenthesis but no spaces in the form
We have the parabola:
[tex]y=x^2-10x+28[/tex]There is one expression that gives you the x-coordinate of the vertex:
[tex]-\frac{b}{2a}[/tex]We know that the standard form of a quadratic function is: ax^2+bx+c, then:
[tex]-\frac{(-10)}{2(1)}=\frac{10}{2}=5[/tex]Now, having x=5 we can substitute it on the original equation:
[tex]\begin{gathered} y=(5)^2-10(5)+28 \\ y=25-50+28 \\ y=3 \end{gathered}[/tex]The vertex of the parabola is (5, 3)
Part 2Jon wants to make a different array using the same number of dots. Which arrays are possible? Choose Yes or No for each option.an array with 3 rows an array with 4 rows an array with 10 rows
Part 2.
He wants to make a different array with the same nuber of dots (30 dots).
He can make an array with a number of rows that are multiples of 30: 2, 3, 5, 6, 10 and 15.
Then, he can use an array with 3 rows and an array of 10 rows, but he can not use an array with 4 rows.
Then, the solution is:
an array with 3 rows: Yes
an array with 4 rows: No
an array with 10 rows: Yes
Find a formula for the nth term in thisarithmetic sequence:a1 = 9,a2 = 13, a3 = 17, a4 = 21, ...an:?
Given:
[tex]a_1=9,a_2=13,a_3=17,a_4=21[/tex]To find:
The nth term formula.
Explanation:
The nth term formula is,
[tex]a_n=a+(n-1)d[/tex]The first term a = 9.
The common difference is,
[tex]\begin{gathered} d=13-9 \\ =4 \end{gathered}[/tex]So, the nth term formula for the sequence is,
[tex]\begin{gathered} a_n=9+(n-1)(4) \\ =9+4n-4 \\ =5+4n \end{gathered}[/tex]Therefore, the nth term formula is,
[tex]a_n=5+4n[/tex]Final answer:
The nth term formula is,
[tex]a_n=5+4n[/tex]1. Chris makes $48,000 a year. He is paid semi-monthly. What is his gross pay per pay period? 2. John earns $59,800 a year. He is paid bi-weekly. What is his annual pay? 3. If Sondy's gross pay is $750 weekly, what is her annual salary? 4. What is Jackie's monthly salary if her annual gross pay is $65,400?
1. Chris makes $48,000 a year. He is paid semi-monthly. What is his gross pay per pay period?
Semi-monthly means he is being paid 2 times a month.
Since there are 12 months in a year so the total number of periods will be
2×12 = 24
So the pay per period will be
[tex]\frac{\$48,000}{24}=\$2,000[/tex]Therefore, Chris's gross pay per period is $2,000
2. John earns $59,800 a year. He is paid bi-weekly. What is his annual pay?
Bi-weekly means he is being paid 2 times a week.
Since there are 52 weeks in a year so the total number of periods will be
2×52 = 104
So the annual pay is
[tex]\frac{\$59,800}{104}=\$575[/tex]Therefore, John's annual pay is $575
3. If Sondy's gross pay is $750 weekly, what is her annual salary?
Since there are 52 weeks in a year
So the annual salary is
[tex]\$750\times52=\$39,000[/tex]Therefore, Sondy's annual salary is $39,000
4. What is Jackie's monthly salary if her annual gross pay is $65,400?
Since there are 12 months in a year
Monthly salary will be
[tex]\frac{\$65,400}{12}=\$5,450[/tex]Therefore, Jackie's monthly salary is $5,450
In triangle ABC, A is a right angle and mB = 45. Find BC. If your answer is not an integer, leave it in simplest radical form. Not drawn to scale O 20 ft 10 ft 20 2 ft 10 2 ft
as we have a right triangle, we can use a trigonometric function to find the hypotenuse
so
Step 1
a)Let
[tex]\begin{gathered} angle=m\measuredangle B=45 \\ opposite\text{ side=10 ft} \\ hypotenuse=BC \end{gathered}[/tex]so, we need a function that relates those values, it is
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]b) now, replace and solve for hypotenuse
[tex]\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ 45=}\frac{10}{BC} \\ isolate\text{ BC} \\ BC=\frac{10}{sin\text{ 45}} \\ BC=\frac{10}{\frac{\sqrt{2}}{2}}=\frac{20}{\sqrt{2}} \\ BC=\frac{20}{\sqrt{2}} \\ Multiply\text{ by }\frac{\sqrt{2}}{\sqrt{2}} \\ BC=\frac{20}{\sqrt{2}*}\frac{\sqrt{2}}{\sqrt{2}} \\ BC=\frac{20\sqrt{2}}{2}=10\sqrt{2} \\ BC=10\sqrt{2} \end{gathered}[/tex]so, the answer is
[tex]10\sqrt{2}\text{ ft}[/tex]I hope this helps you
Based on the information in the table, how many people can be served by36 spring rolls?
In order to calculate how many people can be served by
36 spring rolls we would have to make the following calculation:
So, we can see that for example for 28 people the number of spring rolls that can be served is 56.
Therefore applying the rule of 3 we would be able to calculate the amount of people that can be served by 36 spring rolls.
So, if 56 spring rolls___________________28 people
36 spring rolls____________________x
x=(36 spring rolls*28 people)/56 spring rolls
x=1008/56
x=18 people
Therefore, the amount of people that can be served by 36 spring rolls would be 18 persons.
For the following problem, the answers is given. Show the calculations that are needed to get to the answer.ProblemSolutionSolve this system of equations:X = 10a) - 4x - 3y = -22y = -6b) 4x - 14y = 124Show your work here:
Solution:
Given the system of equations;
[tex]\begin{gathered} -4x-3y=-22\ldots\ldots\ldots\text{.equation}1 \\ 4x-14y=124\ldots.\ldots\text{.}\mathrm{}\text{equation}2 \end{gathered}[/tex]We would show calculation that lead to the answer by elimination method.
STEP 1: Add equation 1 to equation 2;
[tex]\begin{gathered} -4x+4x-3y+(-14y)=-22+124 \\ -17y=102 \end{gathered}[/tex]STEP 2: Divide both sides by -17;
[tex]\begin{gathered} -\frac{17y}{-17}=\frac{102}{-17} \\ y=-6 \end{gathered}[/tex]STEP 3: Substitute the value of y in equation 1;
[tex]\begin{gathered} -4x-3y=-22 \\ -4x-3(-6)=-22 \\ -4x+18=-22 \\ \end{gathered}[/tex]STEP 4: Subtract 18 from both sides;
[tex]\begin{gathered} -4x+18-18=-22-18 \\ -4x=-40 \end{gathered}[/tex]STEP 5: Divide both sides by -4;
[tex]\begin{gathered} -\frac{4x}{-4}=-\frac{40}{-4} \\ x=10 \end{gathered}[/tex]Thus, the solution of the system of equation is;
[tex]x=10,y=-6[/tex]For each equation, determine whether x and y are directly proportional that is, if the equation shows direct variation)If so, then find the constant of proportionality (the constant of variation),3(a) y 8x+1(b) yХProportionalConstant of proportionality: k []ProportionalConstant of proportionality:Not proportionalNot proportional
Answer:
Explanation:
For direct variation equations, we have the general outlook as:
[tex]a\text{ = }\frac{b}{d}\cdot c[/tex]What this simply means is that we have to multiply every instance of the independent variable (c in this case) with a constant ratio or proportionality ratio (b/d in this case) to get the instance of the dependent variable (a in this case)
a) For the first equation, we do not have a direct variation. The reason for this is that there is no constant term that relates to the terms of the dependent variable. The correct choice here is non-proportional
b) For the second fu
find the coordinates of dilation of (3,-4) by scale factor of 3
find the coordinates of dilation of (3,-4) by scale factor of 3
the rule of teh dilation is
(x,y) -------> (ax,ay)
where a is the scale factor
In this problem
a=3
so
(3,-4) --------> (9,-12)
answer is (9,-12)Ethan transformed quadrilateral ABCD to make quadrilateral A’B’C’D’.Are quadrilaterals ABCD and A’B’C’D’ congruent? Why or why not?
Given that the quadrilateral ABCD was translated to A'B'C'D'
Yes, the quadrilaterals ABCD and A'B'C'D' are congruent because:
1. The quadrilaterals ABCD and A'B'C'D' have the same shape as a trapezium
2. The corresponding sides of ABCD and A'B'C'D' are equal, consequently, the corresponding angles are equal.
78.93 × 32.4 this requires standard algorithm take the long way
For this operation, let's start
After all the single multiplications we must add them in rows, and count the dots after
After each multiplication, let's tab or start writing each row one digit to the left, from top to bottom. adding zeros (in red) .
So the product of 78.93 x 32.4 = 2557.332
PLEASE HELP!!To the nearest square unit, what is the area of the regular heptagon shown below? A.2772 square unitsB.1572 square unitsC.792 square unitsD.5545 square units
We are given an heptagon. NOte that we can divide the heptagon in triangles as follows
(The picture is an approximation).
This triangles are all the same , so to calculate the area of heptagon, we simply calculate the area of one of the triangles and then multiply it by 7.
We have the following triangle
REcall that the area of a triangle of base b and height h is given by the formula
[tex]\frac{b\cdot h}{2}[/tex]By taking b=20.8 and h = 21.6, we get
[tex]\frac{20.8\cdot21.6}{2}=224.64[/tex]So, the whole area would be
[tex]7\cdot224.64\text{ =1572.48}[/tex]which rounded to the nearest square unit is 1572
If A denotes the area of the sector of a circle of radius r formed by the central angle 0, find the missing quantity. Ifnecessary, round the answer to two decimal places.6) r = 8 inches, 0 = 5 radians, A = ?F) 40 in2G) 160 in2H) 20 in2J) 320 in2
In order to find the area A of the sector of the given circle, use the following formula:
A = 1/2·r²θ
where θ is in radians.
In this case, you have r = 8 in and θ = 5 radians. Replace these values into the formula for A:
A = 1/2·(8 in)²(5 rad)
A = 160 in²
Hence, the area of the sector is 160 in²
Help with this question, it is one question with 3 parts.
The given function is ,
[tex]f(x)=\frac{x+12}{x-6}[/tex]The inverse of the function is ,
[tex]\begin{gathered} y=\frac{x+12}{x-6} \\ x=\frac{y+12}{y-6} \\ y=\frac{6(x+2)}{x-1} \\ f^{-1}(x)=\frac{6x+12}{x-1} \end{gathered}[/tex]for x ,
[tex]x<1\text{ and x>1 .}[/tex]if x= 1 the function will be undefined.
thus,
[tex]x\ne1[/tex]If the incandescent 100 - watt light bulb is left on for 168 hours ( a whole week),and it costs $0.12 per kwh ,how much does it cost for this lightbulb?A: $20.20B: $2.02 C:20.16D: $0.16
Suppose that the light bulb consumes 100W per hour, in other words, 0.1kWh. Therefore, in 168 hours, the total energy consumption is
[tex]0.1\text{kWh}\cdot168\text{hrs}=16.8kW=16.8\cdot1000W=16800W[/tex]Thus, the total cost is
[tex]0.12\cdot16.8=2.016\approx2.02[/tex]The answer is, approximately $2.02, option B.
i don’t kno how to do this paper i need help with the answers
Solution:
Given:
The three interior angles of a triangle are;
[tex]6x+1,9x+4,6x-14[/tex]To find the value of x, we use the theorem for the sum of interior angles in a triangle.
The sum of interior angles in a triangle is 180 degrees.
Hence,
[tex]\begin{gathered} (6x+1)+(9x+4)+(6x-14)=180^0 \\ \text{Collecting the like terms,} \\ 6x+9x+6x+1+4-14=180 \\ 21x-9=180 \\ 21x=180+9 \\ 21x=189 \\ \text{Dividing both sides by 21 to get the value of x,} \\ x=\frac{189}{21} \\ x=9 \end{gathered}[/tex]Therefore, the value of x is 9.
The height of a cylinder is 7.8 centimeters.The circumference of the base of the cylinder is 20πcentimeters.Which measurement is closest to the volume of the cylinder in cubic centimeters?
The volume of a cylinder is given by the formula:
[tex]V=\pi r^2h[/tex]Where
r is the radius and h is the height
The height is given as 7.8 cm.
The circumference is 20π cm. Let's find the radius:
[tex]\begin{gathered} C=2\pi r \\ 20\pi=2\pi r \\ r=\frac{20\pi}{2\pi} \\ r=10 \end{gathered}[/tex]We have radius and height. Now, let's substitute these into the formula and find the volume of the cylinder. Shown below:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(10)^2(7.8) \\ V=2450.44\text{ cu. cm.} \end{gathered}[/tex]As the number of years decreases from 3 to 2 in the following graph, does the population increase, decrease, or remain the same?
Statement Problem: As the number of years decreases from 3 to 2 in the following graph, does the population increase, decrease or remain the same?
Solution:
From the graph provided;
As the time (number of years) reduces from 3 to 2, the population increases
Question 9 of 10 Select the angle that correctly completes the law of cosines for this triangle. 52 +132 - 2(5)(13)cos __ = 122 67° 13 23° 90 12 O A. 90° B. 67° O C. 23°
where x is the missing angle,
we can solve the operations and find x
[tex]\begin{gathered} -130\cos x=12^2-13^2-5^2 \\ -130\cos x=-50 \\ \cos x=\frac{-50}{-130} \\ \\ x=\cos ^{-1}(\frac{5}{13}) \\ \\ x=67.38 \end{gathered}[/tex]so the right value is 67, option B
Describe what it means to bisect an arc.
Answer
To bisect any segment of a line, arc or a figure simply means dividing that segment into two.
And to bisect an arc, the image below for bisecting an arc AB will help the explanation.
The first step to bisecting an arc is to place the pin end of the compass on each of the ends of the arc, that is, first at point A and then point B,
Then, an arbitrary arc is then drawn for these two cases.
The points where the two arcs drawn meet are then connected to each other using a straight line.
This straight line then bisects the arc AB.
Hope this Helps!!!
7. A convex polygon has 18sides. Find the sum of theinterior angles.
The formula for the sum of all interior angles is
[tex]\text{Sum}=(n-2)180[/tex]where n represents the number of sides. In our case, n=18. Then, by replacing this value into the last formula, we have
[tex]\begin{gathered} \text{Sum}=(18-2)180 \\ \text{Sum}=(16)180 \end{gathered}[/tex]Therefore, the answer is 2880 degrees
The graph shows the parent function f(x) = x. Describe how the y-intercept changes when the graph is shifted, using the equations listed. (MAFS.912. F.BF.2.3) (MAFS.912.F-IF.3.7a) a. ()=+5 b. ℎ()=― 10
The y-intercept is the value of the function when it cross the y axis. When x is 0
In the parent function the y-intercept is 0
[tex]\begin{gathered} f(x)=x \\ f(0)=0 \end{gathered}[/tex]In g(x)
[tex]\begin{gathered} g(x)=x+5 \\ g(0)=0+5 \\ g(0)=5 \end{gathered}[/tex]the y-intercept is 5. Respect to the parent function, y-intercept is 5 units up (in y-axis)
In h(x)
[tex]\begin{gathered} h(x)=x-10 \\ h(0)=0-10 \\ h(0)=-10 \end{gathered}[/tex]The y-intercept is -10. Respect to the parent function, y-intercpet is 10m units down (in y-axis)
In purple: parent function f(x)
In black: function g(x)
In red: function h(x)
question 8. help me understand better the question and its solution please explain step by step do not skip parts
ANSWER
[tex]\begin{equation*} 0.36\text{ mg} \end{equation*}[/tex]EXPLANATION
The given function is:
[tex]D(h)=6e^{-0.7h}[/tex]To determine the amount of the drug that is in the patient after 4 hours, we have to solve for D when h is equal to 4. That is:
[tex]\begin{gathered} D(4)=6e^{-0.7*4} \\ \\ D(4)=6e^{-2.8} \\ \\ D(4)=6*0.06081 \\ \\ D(4)=0.36\text{ mg} \end{gathered}[/tex]That is the answer to two decimal places.
Jack is putting up new shelves. He is using pieces of wood as shown below. Each piece of wood measures 3 1/5 meters long. Jack has 8 pieces of wood that are the same length. A. Write an equation to show how to find the total length, in meters, of the 8 pieces of wood. Jack said that the total length of the 8 pieces of wood is 24 1/5 meters. Is Jack correct? Why or why not? B. Along with the wood, Jack is also using some nails to build the shelves. One box of nails has a mass of 2 3/4 kilograms (kg). Jack used between 1/2 and 3/4 of the nails in the box. How many kilograms of nails did Jack use to build the shelves? Show your work or explain your answer. Type your answer in the box below. Make sure to label each part with A and B.
A)
3 1/5=3+1/5
[tex]x=8(3+\frac{1}{5})[/tex]Where x is the total length of the 8 pieces of wood.
Then,
[tex]\Rightarrow x=24+\frac{8}{5}=25+\frac{3}{5}[/tex]Jack is not correct; he just multiplied 8*24 rather than 24*(8 1/5)
B)
[tex]\begin{gathered} \frac{1}{2}(2+\frac{3}{4})=1+\frac{3}{8} \\ \text{and} \\ \frac{3}{4}(2+\frac{3}{4})=2+\frac{1}{16} \end{gathered}[/tex]Then, Jack used between 1+3/8 kg and 2+1/16 kg of nails