Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.
How much of each we should mix?
Let's define the variables:
x = ml of A solution used.y = ml of B solution used.We know that we want to make 200ml, then:
x + y = 200
And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:
x*0.5 + y*0.8 = 200*0.68
(the concentrations are written in decimal form)
Then we have the system of equations:
x + y = 200
x*0.5 + y*0.8 = 200*0.68
To solve it we start by isolating x in the first equation:
x = 200 - y
Replacing that in the other equation we get:
(200 - y)*0.5 + y*0.8 = 200*0.68
Now we can solve this for y, we will get:
100 - y*0.5 + y*0.8 = 136
y*0.3 = 136 - 100 = 36
y = 36/0.3 = 120
So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.
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A triangle has sides with lengths of 6 feet, 16 feet, and 17 feet. Is it a right triangle?
Answer:
No.
Step-by-step explanation:
This is not a right triangle. Use the Pythagorean Theorem, \(a^{2} + b^{2}=c^{2} \\\), but write it as \(c^{2}= a^{2}+b^{2}\). The hypotenuse would be 17 feet, so you can insert 17 as \(c^{2}\). \(a\) and \(b\) could be 6 or 16. It can be written either way. The simplified equation would be:
\(c^{2}=a^{2} +b^{2} \\17^{2} = 6^{2} + 16^{2} \\17^{2} = 36+ 256\\17^{2}= 292\\289\neq 292\)
This isn't a right triangle.
I hope this helped :)
A cylinder has a height of 20 ft and a volume of 64,339 ft³.
What is the radius of the cylinder?
Round your answer to the nearest whole number.
676 ft
338 ft
32 ft
26 ft
Answer:
64,339 = π(r^2)(20)
r^2 = 1,023.987
r = 32 ft
En
• un
juego se reparten 210 puntos de forma
inversamente proporcional al número de fallos cometidos.
Gerardo ha cometido 4 fallos, Rubén 6 y Sara 12. ¿Cuántos
puntos le corresponden a cada uno?
Using the given ratio we will get that:
Sara gets 115 points.Gerardo gets 38Rubén gets 57How many points gets each one?
We know that there are a total of 210 points to be divided.
Gerardo gets 4 fails
Rubén gets 6 fails.
Sara gets 12 fails.
Then we have the ratio 4 : 6 : 12
The total of that is 4 + 6 + 12 = 22 fails.
Then; Gerardo gets (4/22) of the points:
G = (4/22)*210 = 38
Ruben gets (6/22) of the points:
R = (6/22)*210 = 57
Sara gets (12/22) of the points:
S = (12/22)*210 = 115
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it seems reasonable to conjecture that lung function fev changes with age age. the following output from r provides information on the association between fev and age
The association between lung function (FEV) and age can be observed through the analysis of the provided output from R.
The output from R likely includes statistical measures such as correlation coefficients or regression analysis results to determine the relationship between FEV and age. These calculations can help quantify the association between the two variables. For example, a correlation coefficient can indicate the strength and direction of the relationship, where a positive value suggests a positive association between FEV and age.
Based on the provided output from R, it can be concluded that there is an association between lung function (FEV) and age. However, without the actual output or specific statistical measures, it is challenging to provide further details or draw more precise conclusions. It is important to consider that the association between FEV and age may not necessarily imply causation, as other factors such as lifestyle, health conditions, and genetics can also impact lung function. Further analysis and additional data would be necessary to fully understand the nature and significance of this association.
Overall, it is reasonable to conjecture that lung function (FEV) changes with age, but a comprehensive analysis of the provided output and additional research would be required to establish the precise relationship between the two variables.
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On a number line, point a is located at 6, point c is located at 9, and point b lies between points a and c. what is the location of b such that the ratio of ab:bc is 3:1? a 6.75 b 7.66 c 8.25 d 10.50
The location of point b on the number line is 8.25.
To find the location of point b on the number line, we need to determine the value that satisfies the ratio of ab:bc being 3:1.
Let's assume that the location of point b is represented by the variable x.
Given that the ratio of ab:bc is 3:1, we can set up the following equation:
ab/bc = 3/1
To find the length of ab and bc, we subtract the respective coordinates:
ab = x - 6
bc = 9 - x
Now we can substitute these values into the equation:
(x - 6)/(9 - x) = 3/1
To solve this equation, we can cross-multiply:
1 * (x - 6) = 3 * (9 - x)
Simplifying the equation:
x - 6 = 27 - 3x
Combine like terms:
4x = 33
Divide both sides by 4:
x = 33/4 = 8.25
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consider the grid of points shown here. suppose that, starting at the point labeled a, you can go one step up or one step to the right at each move. this procedure is continued until the point labeled b is reached. how many different paths from a to b are possible?
The following is an excerpt from A First Training in Probability by Sheldon Ross. (74) = 35 is the right response.
Total moves required are 7, as follows:
Three steps up as well as four steps right.
Remember that perhaps the number of paths equals the number of arranged 7-tuples with 3 U's and 4 R's. As instance, the word URRURRU indicates to travel up, right, up, right, right, up.
There are 7 ways to arrange these letters, 7 ways to arrange the corresponding Us, and 7 ways to arrange the comparable Rs, for a total of 7!3!4! (74).
For each NxN grid, we may write the following as a generalization of our formula: It should be noted that there's a simpler method of writing this: D = N! / (K! * (N-K))! additionally known as the binomial coefficient.
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We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 102 had kids. Based on this, construct a 95% confidence interval for the proportion p of adult residents who are parents in this county.
Answer:
The answer is "\(0.34 \pm 0.060\)".
Step-by-step explanation:
Point estimate = Sample proportion \(= \frac{102}{300}= 0.34\)
For \(95\%\) confidence, \(z = 1.96\)
Hence,
Margin of error\(= 1.96 \times \sqrt{0.34\times \frac{0.84}{300}}=1.96 \times 0.0308 = 0.060\)
Therefore,
Confidence interval in the tri-equality form:
\(\to 0.34 - 0.060 < p < 0.34 + 0.060\\\\\to 0.28 < p < 0.4\)
Confidence interval using point estimate and margin of error:
\(p = 0.34 \pm 0.060\)
Which is equivalent to 4(x + 7)?
0 4x + 7
0 4x + 28
O 4 + 28
O4 + 7x
where do i put the parentheses in 4+3x2-4÷2
Answer:
4+(3x2)-4/2
Step-by-step explanation:
pemdas
Simplify each expression for x=6 a. 12x^0(x^-4) b. 14(x-2)
After solving the expressions we get the value for each of it as:
a. 1/108
b. 7/18
Given:
a. 12x⁰(x⁻⁴)
Apply the multiplication property of exponents.
when variables multiply, the powers are added.
12x⁰⁻⁴
12x⁻⁴
substitute the value of x = 6 in the above term.
12(6)⁻⁴
12 × 1/6⁴
12 × 1/1296
1/108
b. 14(x⁻²)
The algebraic technique for resolving simultaneous linear equations is called the substitution method. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.
directly substitute the value of the x in the expression.
14(6)⁻²
14 × 1/6²
14 × 1/36
7/18
hence after evaluating expressions we get the values as 1/108 and 7/18.
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Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'. On a coordinate plane, 2 parallelograms are shown. Parallelogram M N P Q has points (2, negative 2), (4, negative 2), (3, negative 3), and (1, negative 3). Parallelogram M prime N prime P prime Q prime has points (5, negative 5), (10, negative 5), (8, negative 7), and (3, negative 7). Which statements are true about the parallelograms?
Answer:
The answer is below
Step-by-step explanation:
Which statements are true about the parallelograms? Check all that apply.
The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5
a) The length of side MN is determined using the formula:
\(|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-2)^2+(-2-(-2))^2}=\sqrt{2^2}=2\\ \\ |MN|=2\)
The first option is correct
b) The length of side M'N' is determined using the formula:
\(|M'N'|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(10-5)^2+(-5-(-5))^2}=\sqrt{5^2}=2\\ \\ |M'N'|=5\)
The second option is correct
c) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q' , hence parallelogram M'N'P'Q' is bigger that parallelogram MNPQ. This means that The image is bigger than the pre-image.
The third option is wrong
d) The slopes are given as:
\(Slope\ of\ MQ=\frac{Change\ in\ y}{Change\ in\ x}=\frac{1-2}{-3-(-2)} =1\\ \\Slope\ of\ M'Q'=\frac{Change\ in\ y}{Change\ in\ x}=\frac{3-5}{-7-(-5)} =1\\\)
Option four is correct
e) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence the scale factor is 5/2
Option 5 is wrong
The length of MN and M'N' is 2 and 5 respectively and parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence parallelogram M'N'P'Q' is bigger than parallelogram MNPQ.
Given :
Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.Points - M(2,-2), N(4,-2), P(3,-3), Q(1,-3)Points - M'(5,-5), N'(10,-5), P'(8,-7), Q'(3,-7)A) First, find the length of MN:
\(\rm |MN| = \sqrt{(4-2)^2+(-2-(-2))^2} =2\)
Therefore, this option is correct.
B) Now, find the length of M'N':
\(\rm |M'N'| = \sqrt{(10-5)^2+(-5-(-5))^2} =5\)
Therefore, this option is correct.
C) Parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence parallelogram M'N'P'Q' is bigger than parallelogram MNPQ. So the image is bigger than the pre-image. Therefore, this option is incorrect.
D) MQ slope is given by:
\(\rm m_1 = \dfrac{1-2}{-3-(-2)}=1\)
M'Q' slope is given by:
\(\rm m_2= \dfrac{3-5}{-7-(-5)}=1\)
So, the sides MQ and M'Q' both have the same slope, 1. Therefore, this option is correct.
E) Parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence parallelogram M'N'P'Q' is bigger than parallelogram MNPQ. Therefore, this option is incorrect.
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.
Four different cellular phone plans are shown below.
• Plan 1 charges $0.35 per minute with no monthly fee.
Plan 2 charges a monthly fee of $10.00 plus $0.25 per minute.
• Plan 3 charges a monthly fee of $59.95 with 200 free minutes.
Plan 4 charges a monthly fee of $15.00 plus $0.20 per minute.
Which plan is the least expensive for 200 minutes of cellular phone use?
.
A. Plan 4
B. Plan 3
C. Plan 1
O
D. Plan 2
if f(x) =2x/X-5
Find f^-1(x).
Step-by-step explanation:
Let f(x)=y
y=2x/X-5
y(x-5)=2x
xy-5y=2x
x(y-2)=5y
x=5y/y-2
Apply x=5y/y-2, on f(x)
f(5y/y-2)=2(5y/y-2)/[(5y/y-2)-5]
=(10y/y-2)/[(5y-5y+10)/y-2]
=10y/10
=y
So f^-1(x)=5y/y-2
Add the rational expression:
1/(x+7) + 3/(x+2)
Answer:
\( \frac{1}{x + 7} + \frac{3}{x + 2} \)
\( = \frac{x + 2}{(x + 7)(x + 2) } + \frac{3(x + 7)}{(x + 2)(x + 7)} \)
\( = \frac{x + 2 + 3x + 21}{ {x}^{2} + 9x + 14} \)
\( = \frac{4x + 23}{ {x}^{2} + 9x + 14 } \)
Relational models view data as part of a table or collection of tables in which all key values must be identified. a. True b. False.
The statement is True. Relational models view data as part of a table or collection of tables in which all key values must be identified is True. Relational models define data as a collection of tables where all key values are identified.
A table comprises of rows and columns. Each column has a distinct heading, and each row corresponds to a single record. In this type of model, each table is identified using a unique key, which is a set of columns that define a unique identity for each record. Relational databases are classified into multiple tables.
These tables relate to one another with the aid of foreign keys, which are unique identifiers for records in a table. The relational model is a simple, simple, and extremely scalable data model. It is also widely employed and supported by most database management systems.
As a result, the relational model is commonly used for online transaction processing (OLTP) systems that involve frequent data modification and retrieval.
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What is the total volume of Mountain Dew in this six pack? Each can is 5 inches tall and has a diameter of 3 inches.
The total volume of Mountain Dew in this six-pack is approximately 212.058 cubic inches.
Assuming that each can in the six-pack of Mountain Dew is cylindrical in shape, we can use the formula for the volume of a cylinder to calculate the volume of each can, and then multiply that by the total number of cans in the pack.
The formula for the volume of a cylinder will be;
V = πr²h
where V is volume, r is radius (half the diameter), and h is height.
The radius of each can is 1.5 inches (half of 3 inches), and the height is 5 inches. So the volume of each can is;
V = π(1.5)²(5) = 35.343 cubic inches
To find the total volume of the six-pack, we need to multiply this by the number of cans;
Total volume = 35.343 cubic inches/can × 6 cans
= 212.058 cubic inches
Therefore, the total volume is 212.058 cubic inches.
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Use the table to determine the location with the greatest amount of rainfall and the location with the least amount of rainfall.
Location Amount of Rainfall
Austin, Texas 0.8687 m
Beaumont, Texas 1.534 m
Galveston, Texas 109.5 cm
El Paso, Texas 246.4 mm
Del Rio, Texas 495.3 mm
South Padre, Texas 65.5 cm
a. Using complete sentences, identify the city with the greatest amount of rainfall and the city with the least amount of rainfall, and express the ratio of their respective rainfalls as a decimal number, rounded to the nearest hundredth.
b. Describe what this ratio tells you.
The location with the greatest amount of rainfall is Beaumont, while the location with the least amount is El Paso.
How to identify the place with the greatest and least amount of rainfall?The first step is to make sure to use the same units. Due to this, let's convert everything to meters.
Austin = 0.8687 mBeaumont = 1.534 mGalveston = 1.095 mEl Paso = 0.2464 mDel Rio = 0.4953 mSouth Padre= 0.655mBased on this, Beaumont has the greatest amount of rainfall and El Paso has the lowest amount of rainfall.
How are the two places related?The ratio for these places are 1.5 to 0.2 or 1.5/ 2 = 0.7. This ratio implies that there is a difference of 0.7 meters in the amount of rainfall in these places.
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The other person is right, I used this and it worked.
PLZ HELP ME GUYS WITH THIS EQUATION: Manuel will choose between two restaurants to purchase pizzas for his party. The first restaurant charges a delivery fee of $2 for the entire purchase and $10 per pizza. The second restaurant charges a delivery fee of $5 for the entire purchase and $9 per pizza. Let x be the number of pizzas purchased.
Answer:
x = 3 pizzas
Step-by-step explanation:
Not sure what the question is asking, but I am assuming that the question is asking how many pizzas needs to be ordered for the restaurant ordered to equal each other.Set up equation: \(10x + 2 = 9x + 5\)Simplify the equation:\(x = 3\)
You are the marketing manager for Coffee Junction. The revenue for the company is given by R(x)=− 32x 3+6x 2+18x+4 where R(x) is revenue in thousands of dollars and x is the amount spent each month on advertisement, in thousands of dollars. 0≤x≤25 a) At what level of advertising spending does diminishing returns start? Explain What this diminishing returns means for this company. b) How much revenue will the company earn at that level of advertising spending? c) What does 0≤x≤25 tell us with respect to this problem?
a) Diminishing returns start at x = 1, where the marginal revenue will be less than the marginal cost
b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.
c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.
a) At what level of advertising spending does diminishing returns start?
Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.
b) How much revenue will the company earn at that level of advertising spending?
At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.
c) What does 0≤x≤25 tell us with respect to this problem?
In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.
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6x−10y=-40 in slope intercept form
the graph to the right represents mario’s mile time in minutes, y, based on the number of hours he spends training in hours , x what conclusion can you make
Answer: it is 13+13=26
Step-by-step explanation:
I don’t care.
19. Let c be the distance between Carlisle and Wellesley, let b be the distance between Carlisle
and Stonebridge, and let a be the distance between Wellesley and Stonebridge.
Stonebridge
If you did a circuit, traveling from Carlisle to Wellesley to
Stonebridge and back to Carlisle, you would travel 73 miles.
The distance from Stonebridge to Carlisle is 12 miles
farther than the distance from Wellesley to Carlisle.
.
If you drove from Stonebridge to Carlisle and back to
Stonebridge, and then continued to Wellesley then back to
Stonebridge, you would travel 102 miles.
A. Write a system of linear equations to represent the situation.
Wellesley
D
Not drawn
to scale
Carlisle
B. Solve the system of equations. Explain the meaning of the solution in the context of the
situation.
Wellesley and Stonebridge, Stonebridge and Carlisle and Carlisle and Welleslay is c = 22 miles.
How to illustrate the equation?Let the three places be denoted by S, C and W respectively.
According to question, a,c,b are the distances between Stonebridge(S) & Carlisle(C), Carlisle(C) & Wellesley (W)and Welleslay(W) & Stonebridge(S) respectively.
Since if we travel C to W to S to C to C then it is equal to 73miles.
So,
c + a + b = 73 .....(1)
Since the distance between S and C is 12 miles father than distance between W and A.
So, b = 12 + c .....(II)
Or c = b - 12 ....(2)
Since if we drove S to C and back to S and than to W and back to S, the total travelling is 102 miles.
So, b + b + a + a = 102
Or 2b + 2a = 102 .....(II)
On dividing both sides by 2, we get
b + a = 51 .....(III)
Or a = 51- b ....(3)
Hence, the equation (I), (II) and(III) are the system of equations that represents the given situation
On Putting the values of c and a from equations (2) and (3) in equation (1), we get
b - 12 + 51- b + b = 73
b +39 = 73
Or b = 73 - 39 = 34 miles ....(4)
On putting b =136 miles in equation(2) and (3) , we get
c = b - 12 = 34 - 12 = 22 miles ...(5)
and
a = 51 - 34 = 17 miles ...(6)
Hence, a = 17 miles, b = 34 miles, c = 22 miles
Here, this solution means that the distance between
Wellesley and Stonebridge is a = 17 miles
Stonebridge and Carlisle is b = 34 miles
Carlisle and Welleslay is c = 22 miles.
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What are the solutions to the following equation?
(x+5)2=36
Question 3 options:
-1 and 11
31 and 41
-41 and -31
-11 and 1
Answer:
We have a problem here, Houston.
Step-by-step explanation:
Is "(x+5)2=36" supposed to be (x+5)^2=36 ?
If so,
x = ± 11
-----------------------
If it is indeed (x+5)2=36
then:
2x + 10 = 36
2x = 26
x = 13
None of the answer options fir either of these two interpretations of the equation provided. Please check the equation.
Answer:
-11 and 1
Step-by-step explanation:
did the test
GIVING BRAINLIEST PLEASE DUE TODAY
A. For babysitting, Nicole charges a flat fee of $3, plus $5 per hour.
Write an equation for the cost, C, after h hours of babysitting.
B. How much money will she make if she babysits for 5 hours?
C. If Nicole earned $48.00, how many hours did she babysit?
20 POINTS! If p(4) = 0 for a polynomial function, what is at least one factor of p(x)?
Answer:
0 I think
Step-by-step explanation:
consider the regular expression a(a | b) * b a. describe the language defined by this expression. b. design a finite-state automaton to accept the language defined by the expression.
The regular expression an (a | b)*ba defines a language that consists of strings that start with the letter "a", followed by zero or more occurrences of either "a" or "b", and ends with the sequence "ba".
a. The language defined by the regular expression a(a|b)*ba:
The given regular expression represents a language that consists of strings that start with an 'a', followed by zero or more occurrences of 'a' or 'b' (denoted by the (a|b)* part), and then ending with the sequence 'ba'. In simpler terms, any string that starts with 'a' and ends with 'ba' and has any combination of 'a's and 'b's in the middle belongs to this language.
b. Design a finite-state automaton to accept the language defined by the expression:
To design a finite-state automaton (FSA) for the given regular expression, follow these steps:
1. Create an initial state (q0) and make it the start state.
2. From the initial state (q0), create a transition with the input 'a' to a new state (q1).
3. Create a loop in state q1 with the input 'a' and another loop with the input 'b'. This represents the (a|b)* part of the expression.
4. From state q1, create a transition with the input 'b' to a new state (q2).
5. From state q2, create a transition with the input 'a' to a new state (q3).
6. Make state q3 the final/accepting state.
The designed FSA will accept the language defined by the regular expression an (a|b)*ba. To design a finite-state automaton to accept this language, we can start with a start state, which is represented by a circle. From this start state, we draw an arrow labelled "a" to a new state, which also is represented by a circle. From this new state, we draw two arrows labelled "a" and "b" back to the same state. This represents the zero or more occurrences of "a" or "b". Finally, from this same state, we draw an arrow labelled "b" to a final state, which is represented by a double circle. This final state represents the end of the sequence "ba". The resulting finite-state automaton accepts the language defined by the regular expression an (a | b)*ba.
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I would appreciate your help!
This is from a mental paper
Answer:
(0,0)
Step-by-step explanation:
(0,0) would lie on the line y = 2x
Answer:
(0,0)
Step-by-step explanation:
the equation is very easy to be done by x intercept and y intercept so
x intercept( 0,0 )
because on the coordinate line of x the value of y is zero so when we insert 0 on the value of y x becomes 0
y intercept ( 0,0 )
because on the coordinate line of y the value of x is zero so when we insert 0 on the value of x , y becomes 0
Determine the measure of the interior angle at vertex C. PLEASE HELP ASAP
Answer:
B. 120°
Step-by-step explanation:
Sum of the measures of the interior angle of a polygon with n sides:
(n - 2)180
We have a pentagon, a 5-sided polygon, so n = 5.
We first find the sum of the measures of the angles of any pentagon.
(5 - 2)180 = 3(180) = 540
From the figure, we add the measures of the 5 angles and set the sum equal to 540°.
3x + 4x + 4x + 4x + 3x = 540°
18x = 540°
Divide both sides by 18.
x = 30°
The angle at vertex C measures 4x.
4x = 4 * 30° = 120°
Answer: B. 120°
4 ice cream cones cost $6. At this rate, how much do 7 ice cream cones cost?
this is a test for middle schoolers but anyone is free to answer
Answer:
$42
Step-by-step explanation:
Equation: y = 6x
x = number of ice cream cones
y = 6(7) = 42
Hi! I believe your answer is $10.50. If it's $6 for 4 ice cream cones, divide 6 by 4 and you'll get 1.5, or $1.50 per ice cream cone. For 7 ice cream cones, multiply the unit rate ($1.50 per ice cream cone) by 7. The total cost is $10.50. I hope this helps you! Good luck and have a great day. ❤️✨
What is the correct order of operations for simplifying the expression 2 - 3x + 5 + 71 - 5x)2+x
Answer:
Your answer would be: square the binomial, distribute 7 inside the parentheses, and then combine like terms
Step-by-step explanation: