The equation given is a one variable equation, "p".
The question asks to find the value of "p", which is the pounds of peanuts.
So, we need to solve the euqation for "p".
[tex]4.05p+14.40=4.50(p+3)[/tex]First, we need to put all the terms that have "p" in one side. For this, we will have to use the distributive property in the parenthesys first:
[tex]\begin{gathered} 4.05p+14.40=4.50p+4.50\cdot3 \\ 4.05p+14.40=4.50p+13.50 \end{gathered}[/tex]Now, we can substract 4.05p in both sides to get the "p" term of the left to the right:
[tex]\begin{gathered} -4.05p+4.05p+14.40=-4.05p+4.50p+13.50 \\ 14.40=(4.50-4.05)p+13.50 \\ 14.40=0.45p+13.50 \end{gathered}[/tex]Now, we do the same for the 13.50, substract it in both sides:
[tex]\begin{gathered} 14.40-13.50=0.45p+13.50-13.50 \\ 0.9=0.45p \\ 0.45p=0.9 \end{gathered}[/tex]Now, we can divide both sides by 0.45:
[tex]\begin{gathered} \frac{0.45p}{0.45}=\frac{0.9}{0.45} \\ p=2 \end{gathered}[/tex]So, the answer is p = 2, thus, you need 2 pounds of peanuts for the trail mix.
Marked angle 3 different ways
Answer:
where are question I don't understand this question
The graphs shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y. What is the slope of the line?
A: 1/4
B: 8/17
C: 4
D: 6
HELP PLS
Answer: the answer is 6
Step-by-step explanation:
i did it step by step
What is the relationship between the pair of angles ABC and LMN shownin the diagram below?
Solution:
From the given figure
Where
[tex][/tex]A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the interval -2
To check the decay rate, we need to check the variation in y-axis.
Since our interval is
[tex]-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).
[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}[/tex]To compare the decay rates we need to check the variation on the y-axis of both functions.
[tex]\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}[/tex]Now, we calculate their ratio to find how they compare:
[tex]\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}[/tex]This tell us that the exponential function decays at three-fourths the rate of the quadratic function.
And this is the fourth option.
Which of the following is the median of the data set? 15 20 20 25 30 35 40 40 45 50 55(1) 28(2) 30(3) 32(4) 34
Median: The media is the middle number in a list of values. If there is an even number of values (so there is no middle number) then average the middle two values together.
so:
[tex]set\colon\mleft\lbrace15,20,20,25,30,35,40,40,45,50,55\mright\rbrace[/tex]From the data set, we can conclude that the middle number (median) is:
[tex]35[/tex]Let log, 4= 3; log, C = 2; log, D= 5 Ac? Do log What is the value of O A. -11 O B.-15,378 O c. 49 D. 2
Given:
[tex](x+2)^2+(y-3)^2=9[/tex]Circle equation is
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) be the center of the circle and r be the radius.
[tex]\text{Center(-}2,3)\text{ and radius 3}[/tex]Option C is the correct answer.
Match each measurement on the left with an equal measurement on the right. Some answer options on the right will not be used.31/2 yards66 inches2 miles21/2 miles51/2 feet10,560 feet101/2 feet91/2 feet12,300 feet13,200 feet
Solution
Recall
1 yard is 3feet
1 foot is 12inches
1 mile is 5,280 feet
[tex]3\frac{1}{2}\text{yards =10}\frac{1}{2}\text{ ft}[/tex][tex]66\text{inches =5}\frac{1}{2}ft[/tex][tex]\begin{gathered} 1\text{ miles = 5280 ft} \\ 2\text{miles = 10,560ft} \end{gathered}[/tex][tex]\begin{gathered} 1\text{mile = 5280 ft} \\ 2\frac{1}{2}\text{miles =}13,200ft \end{gathered}[/tex]If using the method of completing the square to solve the quadratic equationX2 + 15x + 7 = 0, which number would have to be added to "complete thesquare"?
ANSWER
225/4
EXPLANATION
To complete the square we want to write a part of the equation in the form:
[tex](a+b)^2=a^2+2ab+b^2[/tex]The second term squared is the one we have to add to the equation in order to complete the square.
In this case, the coefficient of x is 15, so b is:
[tex]b=\frac{15}{2}[/tex]And b²:
[tex]b^2=\frac{225}{4}[/tex]If we add 225/4 to both sides of the equation:
[tex]x^2+15x+\frac{225}{4}+7=\frac{225}{4}[/tex]We complete the square:
[tex](x+\frac{15}{2})^2+7=\frac{225}{4}[/tex]Mariana receives a $20 gift card for downloading music and wants to determine how many songs she can purchase.Each downloaded song costs $1.29. If m represents the number of songs downloaded, which inequality represents thegiven situation?20m 2 1.2920m 1.2901.29ms 2001.29m 2 20Mark this and retumSave and ExitNextSubmit
Mariana has a $20 gift card for downloading music → this means that she can spend at most $20 on music, you can symbolize this situation as ≤20
If each song costs $1.29 and she buys "m" number of songs, the total cost of the songs can be expressed as 1.29m
Then the inequality that represents the number of songs she can download is
[tex]1.29m\leq20[/tex]4.The value of x isis order these expressions from least to greatest:χ1- xx-1-1 = x
To answer this question we have to evaluate each expression at the given value of x.
Recall that to evaluate an expression we substitute the variable by the given value.
Evaluating each expression at
[tex]x=-\frac{1}{4}[/tex]we get:
[tex]\begin{gathered} x=-\frac{1}{4}, \\ 1-x=1-(-\frac{1}{4})=1+\frac{1}{4}, \\ x-1=-\frac{1}{4}-1=-(1+\frac{1}{4}), \\ -\frac{1}{-\frac{1}{4}}=\frac{1}{\frac{1}{4}}=4. \end{gathered}[/tex]Therefore, the numbers ordered from least to greatest are:
[tex]x-1,\text{ x, 1-x, -1/x.}[/tex]Answer:
[tex]x-1,\text{ x, 1-x, -1/x.}[/tex]6 Ms. Carson drove 96 miles in 15 hoursWhat was her speed in miles per hour!48 miles per hourB.54 miles per hourС64 miles per hourD. 144 miles per hour
Hello looking for someone to help me out on this question
Answer
The value of x = 14
m∠T = 65°
m∠S = 30°
m∠R = 85°
Explanation
From the given ΔRST,
m∠T + m∠S + m∠R = 180° (Sum of angles in a triangle)
m∠T = (4x + 9)°, m∠S = (2x + 2)° and m∠R = (7x - 13)°
⇒(4x + 9)° + (2x + 2)° + (7x - 13)° = 180°
Grouping the terms, we have
4x + 2x + 7x + 9 + 2 - 13 = 180°
13x - 2 = 180°
13x = 180 + 2
13x = 182
Divide both sides by 13
13x/13 = 182/13
x = 14
Therefore,
m∠T = (4x + 9)° = (4(14) + 9)° = (56 + 9)° = 65°
m∠S = (2x + 2)° = (2(14) + 2)° = (28 + 2)° = 30°
m∠R = (7x - 13)° = (7(14) - 13)° = (98 - 13)° = 85°
Find sum of the pairs of complex numbers.2,8
Given:
Complex numbers are 2 and 8.
Required:
We need to find the sum of the complex numbers.
Explanation:
The given complex can bw\e written as follows.
[tex]2+i(0)\text{ and }8+i(0).[/tex][tex]Add\text{ }2+i(0)\text{ and }8+i(0)[/tex][tex](2+i(0))\text{ + \lparen}8+i(0))=(2+8)+i(0+0)[/tex][tex](2+i(0))\text{ + \lparen}8+i(0))=10+i(0)[/tex]Final answer:
[tex]10[/tex]write the following comparison as a ratio in simplest form using a fraction, a colon and the word to. _ 198 cents to 234 cents is?
Given data:
The expression for the kratio of 198 cents to 234 cents is,
[tex]\begin{gathered} \frac{198}{234}=\frac{18\times11}{18\times13} \\ =\frac{11}{13} \\ =11\colon13 \end{gathered}[/tex]Thus, the correct option is (d).
Please only solve for angle 1 and ignore the question above.
Answer:
[tex]m\angle1\text{ = 115}\degree[/tex]Explanation:
Here, we want to get the value of the angle marked 1
From what we have, the bigger arc measures 236°
Now, we need to get the value of the arc ML
We have that as:
[tex]236-70-60\text{ = 106}\degree[/tex]Finally, we use one of the angle theorems to get the value
In using it, we have to consider the value of the smaller arc JK which is 124°
Now, we have its value as:
[tex]\frac{106\text{ + 124}}{2}\text{ = 115}\degree[/tex]We add the value of the arc ML and the value of the smaller arc JK and divide by 2
Can you show me how to do this problem so I can understand it?
Let's analyze each option to find which transformation generates a hexagon with a greater area:
1)
A translation is a transformation that doesn't change the image shape or size, therefore the area is the same.
2)
A dilation by a scale factor smaller than 1 will reduce the figure, therefore the area will be smaller.
3)
A rotation, just like the translation, doesn't change the image shape or size, therefore the area is the same.
4)
A dilation by a scale factor greater than 1 will make the image bigger, therefore the area will be greater.
So the correct option is the fourth one.
Find the solutions to 2x² - 10x+12= 0.Check all that apply, as there can be more than one awnserA. 2B. 3C. 12D. 4
The given equation is expressed as
2x^2 - 10x + 12 = 0
Dividing each term by 2, it becomes
x^2 - 5x + 6 = 0
This is a quadratic equation. We would solve by applying the method of factorization. The first step is to multiply x^2 with 6. It becomes 6x^2. We would find two terms such that their sum or difference is - 5x and their product is 6x^2. The terms are - 3x and - 2x. By replacing - 5x with - 2x - 3x, we have
x^2 - 2x - 3x + 6 = 0
Factorize by grouping. It becomes
x(x - 2) - 3(x - 2) = 0
(x - 2)(x - 3) = 0
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3
The solutions are
A. 2
B. 3
Find the area of the sector of a circle that has a central angle of \Pi radians and a radius of 0.7 in.Round your answer to the nearest hundredth.The area is ___ in^2
In order to find the area of the sector, let's consider the formula for the area of a circle:
[tex]A=\pi r^2[/tex]The complete circle is equivalent to a sector with central angle 2pi. Knowing this, we can write the following rule of three:
[tex]\begin{gathered} central\text{ }angle\rightarrow area \\ 2\pi\rightarrow\pi r^2 \\ \pi\rightarrow x \end{gathered}[/tex]Now, we can write the following proportion and solve it for x:
[tex]\begin{gathered} \frac{2\pi}{\pi}=\frac{\pi r^2}{x}\\ \\ 2x=\pi r^2\\ \\ x=\frac{\pi r^2}{2}=\frac{\pi\cdot0.7^2}{2}=0.77\text{ in^^b2} \end{gathered}[/tex]Therefore the area is 0.77 in².
the sales tax for the city of Los Angeles is 9.75% how much will you pay for an item that costs $200?
Answer:
$219.5
Explanation
Given
Original cost of an item = $200
Sales tax = 9.75%
Tax = 9.75/100 * 200\
Tax = 9.75 * 2
Tax = $19.5
Amount you will pay = $200 + $19.5
Amount you will pay = $219.5
The bakery you choose cost $1000 per month to rent. The bakery that you almost rented was one fourth for the cost but was too small how much was the other bakery per month PLEASE HELPthis would be for a fifth grader and they have to show how they come up with the answer he would have to use the same scenario on multiple questions like this
The bakery you choose cost $1000 per month.
The bakery that you almost rented was one fourth for the cost: 1/4 of $1000.
When you have a fraction of a quantity you have to multiply the fraction by the value. Doing so, we have:
[tex]\begin{gathered} \frac{1}{4}\cdot1000 \\ \frac{1}{4}\cdot\frac{1000}{1}\text{ (Converting 1000 to a fraction)} \\ \frac{1000}{4}\text{ (Multiplying the numerators and then the denominators)} \\ 250\text{ (Dividing)} \\ \text{The answer is \$250} \end{gathered}[/tex]The function f(t) = -5t to the 2nd power+20t +60 models the approximate height of an object t seconds after it is launched. how many seconds does it take the object to hit the ground?
We know that if we replace t by some number in the equation:
f(t) = -5t² + 20t + 60
the result will be the height of a launched object.
When the object hits the ground its height is 0.
Then
-5t² + 20t + 60 = 0
We want to solve the highlighted equation fot t, the values of t that make it result in 0 will be the seconds when the object is in the ground.
Solving the equation for tIn order to solve the equation
-5t² + 20t + 60 = 0
we want to factor the left side:
Step 1- Common factor
The common factor of -5t², 20t and 60 is -5:
(-5) · 1 = -5
(-5) · (-4) = 20
(-5) · (-12) = 60
Then
-5t² + 20t + 60 = -5(t² -4t - 12)
Then, replacing the equation
-5t² + 20t + 60 = 0
↓
-5(t² -4t - 12) = 0
↓ taking -5 to the right side
(t² -4t - 12) = 0/(-5) = 0
t² - 4t - 12 = 0
Step 2- Factoring a trinomial
We continue the factoring.
We want to factor t² - 4t - 12.
It should look something like:
t² - 4t - 12 = (t + _ )(t + _ )
To complete it we will use two numbers whose:
- product is -12 (third term t² - 4t - 12)
- sum is -4 (second term t² - 4t - 12)
The pair of numbers whose product is -12 are:
(-1) · 12 = -12
1 · (-12) = -12
(-2) · 6 = -12
2 · (-6) = -12
(-3) · 4 = -12
3 · (-4) = -12
We add them, the pairs whose result is -4 is the pair we will use:
-1 + 12 = 11
1 - 12= -11
-2 + 6 = 4
2 - 6 = -4
-3 + 4 = 1
3 - 4 = -1
Then, we will use 2 and -6 (their product is the third term and their sum is the second term):
t² - 4t - 12 = (t + _ )(t + _ )
↓
t² - 4t - 12 = (t + 2)(t - 6)
Then, using the equation we had:
t² - 4t - 12 = 0
↓
(t + 2)(t - 6) = 0
Step 3- finding the possible t values
When a product of two numbers is 0, it means that one of them is 0:
In this case
We have that
(t + 2)(t - 6) = 0
then
t + 2 = 0 or t - 6 = 0
This means that t could have two possible values:
t + 2 = 0 → t = -2
or
t - 6 = 0 → t = 6
Since t means the seconds the object takes to hit the ground, it cannot have a negative value, because it would mean that it happened in the past. so t cannot be -2
Answer: It takes to the object 6 seconds to hit the ground t = 6> Next question Get a similar question You can retry this 8 3 Volume = Surface Area = Lateral Surface Area = Enter an interer or decimal number (more..] Submit Question
From the question, r = 8 cm, h =3 cm
Volume of a cylinder = pi x r^2x h = 22/7 x 8 x8 x 3 = 4224/7 = 603.43 cm^3
surface area of a cylinder= 2 x pi x r x h = 2 x 22/7 x 8 x 3 = 1056/7 =
150.86 cm^2
6. Write a regression equation for the data above. (MD1)Answer of 5. is C.
Looking at the graph of item C in question 5, we can see that it is a straight line, so it is represented by a linear equation of the form:
[tex]y=mx+b[/tex]We can also see that, when the value of x increases, the value of y also increases, which means the slope of the line is positive (m > 0).
With this information and looking at the options, we can conclude that the correct option is B.
Solve for y. d = 5x + 5y 0 y = 5x-d 5 d-5.2 O Y = y = 5(d - 5x) o y Y d-5x 5
Given the equation:
[tex]d=5x+5y[/tex]Solve for y , which mean make y alone on the left side.
So,
[tex]5y=d-5x[/tex]Divide the equation by 5
[tex]y=\frac{d-5x}{5}[/tex]The answer is the last option
The radius of a circle is 2 meters. What is the circle's circumference?r=2 mUse 3.14 for л.meters
To solve this problem, we will use the following formula for the circumference of a circle:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
Substituting
[tex]\begin{gathered} r=\text{ 2 m, } \\ \pi=3.14 \end{gathered}[/tex]in the above formula, we get:
[tex]C=2\times3.14\times2m.[/tex]Simplifying the above result, we get:
[tex]C=12.56m.[/tex]Answer: [tex]\begin{equation*} 12.56m. \end{equation*}[/tex]12-foot-long wooden beam is supported on both ends. When a weight load is placed in the center of the beam,it causes the beam to sag. The sag is called deflection. The graph shows the deflection of the beam,in inches, as a function of the weight load, in pounds, placed in the center of the beam. for every 50-pound increase in the weight load, what will be the change in the deflection?
the change in the deflection with every 100 pounds is,
[tex]=\frac{0.5-0}{100-0}[/tex][tex]=\frac{0.5}{100}[/tex]so for every 50 pounds will be,
[tex]\begin{gathered} =(\frac{\frac{0.5}{100}}{2}) \\ =\frac{0.5}{200} \\ =0.0025 \end{gathered}[/tex]so for every 50 pound increase in the weight, the change in the deflection is 0.25
Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be 90. How old are they now?Patrick is years old, and Pat is ?years old.
Let "x" be the age of Patrick.
Pat is 20 years older than his son Patrick so we can represent this as "x+20".
In two years, the age of patrick will be x+2 and the age of Pat will be x+22.
Since in 2 years, the sum of their ages will be 90, we can write:
[tex]\begin{gathered} x+2+x+22=90 \\ 2x+24=90 \\ 2x=66 \\ x=33 \end{gathered}[/tex]And, the age of Pat is x+20 which is 53.
Therefore, Patrick is 33 years old, and Pat is 53 years old.
9. Find the equation(s) of the line(s) through (2,-2) if the sum of the intercer 10. Find the angle that line l, makes with line l. (a) hirty 10, 4:3x - 2y=5 (b) 1,: 2x + 3y = 6,1 -11. Find the coordinates of the point. (a) equidistant from (4.-) and the origin; as well as on the line 2 (b) equidistant from (3, 8) and (-2,5) on the y-axis (c) J x + 3y = 7 5.1 - 6 = -28 12. Find the equation of the line passing through the point (4.-1) and
Let:
[tex]\begin{gathered} x+3y=7_{\text{ }}(1) \\ 5x-6y=-28_{\text{ }}(2) \end{gathered}[/tex]From (1):
[tex]x=7-3y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 5(7-3y)-6y=-28 \\ 35-15y-6y=-28 \\ 35-21y=-28 \\ -21y=-63 \\ y=\frac{-63}{-21} \\ y=3 \end{gathered}[/tex]Replace the value of y into (3):
[tex]x=7-3(3)=7-9=-2[/tex]Therefore:
x = -2
y = 3
or
(x,y) = (-2,3)
Hi can anybody help me with this?(there is a part two)
ANSWER:
Part A.
D. 6(p - 0.5) = 5.10
Indenting the zeros and state their multiplicities describe the effect on the graph
Answer:
6) The given equation is,
[tex]f(x)=(x+7)^2(2x+1)(x-4)^3[/tex]we know that,
The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity.
we get,
Zero Multiplicity Effect
-7 2 Touches the x axis at x=-7
-1/2 1 Passese through the x axis at x=-1/2
4 3 Passes through the point and the curve bend at x=4