Jenny is making jewelry for an arts and crafts show. She Would like to make at least $100 in sales. She estimates that she will sell at most 50 pieces of jewelry. The bracelets that she is selling cost $2 and the necklaces cost $3
Answers
The Inequalities that represent the above situation are => x + y ≤ 50 and 2x + 3y ≥ 100 and the possible combinations are (20, 30) and (30, 20).
[ Graphs are given below ].
To form the required inequalities, represent the unknown quantities with variables like x, y,..etc.
In the given problem, we don't know the number of items that Jenny will sell so here we represent them with variables 'x' and 'y'.
And obtain expression according to the condition of the given problem. Since we need to represent them in inequalities use signs like less than, greater than, etc.
Here we have
Jenny would like to make at least $100 in sales.
She estimates that she will sell at most 50 pieces of jewelry.
The bracelets that she is selling cost $2 and the necklaces cost $3
Let Jenny sold 'x' bracelets and 'y' necklaces
Number of pieces that Jenny estimated = 50
=> x + y ≤ 50 ----- (1)
Jenny would like to make at least $100 in sales.
=> 2x + 3y ≥ 100 ---- (2)
Let Jenny sell 20 bracelets and 30 necklaces
=> 2(20) + 3(30) ≥ 100
=> 40 + 90 ≥ 100
=> 130 ≥ 100 [ which is true ]
Let Jenny sell 30 bracelets and 20 necklace
=> 2(30) + 3(20) ≥ 100
=> 60 + 60 ≥ 100
=> 120 ≥ 100
∴ The possible combinations are (20, 30) and (30, 20)
Therefore,
The Inequalities that represent the above situation are => x + y ≤ 50 and 2x + 3y ≥ 100 and the possible combinations are (20, 30) and (30, 20).
[ Graphs are given below ].
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Related Questions
Triangles LMN and FGH are shown.
Select the correct button in the table to show whether each statement is true or false.
Answers
The answer to the true and false questions are given below:
1. MN/NL=GH/HF=true2. LM+MN+NL=FG+GH+HF=false3. Triangle LMN is similar to triangle FGH.=trueHow to solve:Coordinates of L = (-1, -3)
M= (1, 3)
N = (1, -3)
Coordinates of F = (2, 6)
G= (3, 9)
H= (3, 6)
To find the distance b/w the points:
\sqrt(x2-x1)^2 + (y2 -y1)^2)
MN/NL =3
GH/HF = 3
Hence, it is true.
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How many times dose 13 go into 26
Answers
Answer:
2
Step-by-step explanation:
26/13=2
Answer:
2
Step-by-step explanation:
26-13=13-13=0
what is the average acce;eration of the particle over the interval 2
Answers
The particle's average acceleration between (1,3) and (3,3) is 0 m/s2.
What is coordinates?The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. The study of algebraic equations on graphs is known as coordinate geometry. Plotting points, lines, and curves on an x and y axis is an example of coordinate geometry. Make corrections. Coordinates are a pair of numbers that are used to locate a point or shape in a two-dimensional plane. A point's position on a 2D plane is defined by two numbers called the x-coordinate and the y-coordinate.
Here,
A= velocity/time
Points: ( 1,3) (3,3)
Velocity: 3-3=0
Time: 3-1=2
0/2= 0 meters/seconds^2
The average acceleration of the particle over the interval (1,3) and (3,3) is 0 m/s^2.
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Complete question:
What is the average acceleration of the particle within the time interval 1 second to 3 seconds? A. -1 meter/second2 B. 0 meters/second2 C. 1 meter/second2 D. 1.5 meters/second2 E. 2 meters/second2
Explain the Fundamental Theorem of Calculus Part 1 (the antiderivative part) and Part 2 (the evaluation part). Then compare each part and specify when one part would be used over the other. Give a real-world example that involves Part 2 of the Fundamental Theorem of Calculus.
I already have an explanation for each separate part but I need help with examples of comparing the two parts, when each part should be used over the other, and a real-world example.
Thanks!
Answers
The Fundamental Theorem of Calculus (FTC) has two parts: Part 1 and Part 2.
What is the parts in calculus?Part 1 (The Antiderivative Part) states that if f is a continuous function on an interval [a, b], then there exists an antiderivative F of f on [a, b], meaning that F'(x) = f(x) for all x in [a, b].
This means that given a function, we can find a new function that when differentiated, returns the original function.
Part 2 (The Evaluation Part) states that if F is an antiderivative of f on [a, b], then the definite integral of f over [a, b] can be calculated as the difference of the values of the antiderivative F evaluated at the endpoints, i.e., ∫_a^bf(x)dx = F(b) - F(a).
This means that we can evaluate the definite integral of a function by finding its antiderivative and evaluating it at the endpoints of the interval.
Part 1 is used to find antiderivatives, while Part 2 is used to evaluate definite integrals. They are complementary and are used in tandem to solve problems involving integration.
A real-world example that involves Part 2 of the FTC is the calculation of the total distance traveled by a moving object. If the velocity of the object is given as a function of time, we can use the FTC to calculate the total distance traveled by finding the definite integral of the velocity function over the time interval and evaluating it at the endpoints. The result is the difference between the final and initial positions of the object.
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if z=1-i then find the argumed of z
Answers
The argument of the complex number z = 1 - i is approximately -0.785 radians.
What is the argument in complex numbers?
In complex numbers, the argument (also called the amplitude or angle) of a complex number is the angle that the complex number makes with the positive x-axis in the complex plane. It is usually expressed in radians and is denoted by arg(z).
Given a complex number z = 1 - i, the argument of z can be found using the inverse tangent function (atan). In this case, we want to find the angle θ such that tan(θ) = (imaginary part of z) / (real part of z):
θ = atan((-1) / 1) = -π/4 radians
Hence, the argument of the complex number z = 1 - i is approximately -0.785 radians.
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the histogram below shows the distances (in meters) of all qualifying throws for the women's javelin event at the 2004 summer olympics.Which of the following terms apply to this histogram? (Select all that apply.)positively skewedsymmetricuniformunimodalbimodalnegatively skewed
Answers
Positively Skewed: A positively skewed distribution is one that has a long tail in the positive direction (to the right).
The mean is usually greater than the median, and the data points are concentrated on the left side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is greater than the median, and the skewness is therefore positive.
Symmetric: A symmetric distribution is one that is perfectly centered around the mean and has equal amounts of data points on either side of the mean. In the histogram, the data points are not perfectly centered around the mean, so this term does not apply.
Uniform: A uniform distribution is one that has all the data points clustered around the same value. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.
Unimodal: A unimodal distribution is one that has a single peak. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.
Bimodal: A bimodal distribution is one that has two peaks. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.
Negatively Skewed: A negatively skewed distribution is one that has a long tail in the negative direction (to the left). The mean is usually less than the median, and the data points are concentrated on the right side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is less than the median, and the skewness is therefore negative.
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I have attached a picture of the question but have typed out the option, i know a little bit about the function and what it would look like but im confuzed on what the plane y=?z=sin(xy)Give reasons for your choices. This function is [zero / linear / parabolic / period] in both x and y, and the function is [the same / not the same]when x is interchanged with y, so its graph is [ symmetric / not symmetric] about the plane y =[ ] . In addition, the function is [zero / linear / parabolic / periodic ] along the x- and y-axes. These conditions are satisfied only by [A / B / C / D / E / F ] and [ I / II / III / IV / V / VI ].
Answers
The function is periodic in both x and y, and the function is the same when x is interchanged with y, so its graph is symmetric about the plane y = 0. In addition, the function is periodic along the x- and y-axes. These conditions are satisfied only by C and IV.
A: The function plane does not have a zero or linear behavior, so this option is not correct.
B: The function does not have a linear behavior, so this option is not correct.
C: The function is periodic in both x and y, so this option is correct.
D: The function does not have a parabolic behavior, so this option is not correct.
E: The function does not have a periodic behavior, so this option is not correct.
F: The function does not have a linear behavior, so this option is not correct.
I: The function is the same when x is interchanged with y, so this option is correct.
II: The function is not symmetric about the plane y = 1, so this option is not correct.
III: The function is not symmetric about the plane y = 2, so this option is not correct.
IV: The function is symmetric about the plane y = 0, so this option is correct.
V: The function is periodic along the x- and y-axes, so this option is correct.
VI: The function is not linear along the x- and y-axes, so this option is not correct.
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One of the top 10 occupations in terms of job growth in the next few years is expected to be registered nurses. The number of people, y, in thousands, employed as registered nurses in a certain country can be estimated by the linear equation
559 x minus 10 y equals negative 27 comma 010
559x−10y=−27,010, where x is the number of years after 2012.
a. Find the slope and the y-intercept of the linear equation.
b. What does the slope mean in this context?
c. What does the y-intercept mean in this context?
Answers
Answer: a. To find the slope and y-intercept of the linear equation, we need to write it in slope-intercept form (y = mx + b). To do this, we can add 10y to both sides and divide both sides by 10 to get:
y = -559x/10 - 2701/10
y = -55.9x - 270.1
The slope of the equation is -55.9, and the y-intercept is -270.1
b. The slope of a linear equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this context, the slope of -55.9 means that for every year after 2012, the number of people employed as registered nurses is expected to decrease by 55.9 thousand.
c. The y-intercept of a linear equation is the point where the line crosses the y-axis. In this context, the y-intercept of -270.1 means that in 2012, there were expected to be 270.1 thousand people employed as registered nurses.
Step-by-step explanation:
Find c round to the nearest tenth c=
Answers
This is the Law of Sines, which is one of the main formulas used in trigonometry to calculate the length of sides and angles of a triangle.
Find c round to the nearest tenth?sin 15° 2 = bc = sin 105° c
2/sin 15° = bc/sin 105°
bc = (2/sin 15°)sin 105°
bc = 2.68 cm
bc ≈ 2.7 cm
It states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.To find the length of side bc, we need to use the Law of Sines and the given information. We know the lengths of sides ac and a, and the angle a. We can plug these into the Law of Sines and solve for b:sin A a/ac = sin B b/bc
sin(15°)2/2 = sin(105°)b/b
b = 2 sin(105°)
b = 2.99 cm
Therefore, side bc is 2.99 cm, rounded to the nearest tenth.To learn more about the Law of Sines refer to:
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Which of the following measurements is the GREATEST in magnitude? Hint: be sure
to convert all the measurements to the same units before comparing them!!!
520 g
52 kg
699 g
O2354 mg
Answers
Answer:
52kg
Step-by-step explanation:
please help i cant figure it out
5(2x-6) + 8 - 2x = x + 2(x-11)
Answers
Answer:
Step-by-step explanation:
10x - 30 + 8 - 2x = x + 2x - 22
8x - 22 = 3x - 22
-3x -3x
5x-22=-22
22 22
5x=0
/5 /5
x=0?
5 integers have a
mean = 6
mode = 5
range = 9.
What could the 5 numbers be?
Answers
Answer:
5, 5, 3, 12, 5
Step-by-step explanation:
This is because the criteria for the numbers are;
*** It must sum up to 30 to get a mean of 6
*** 5 must occur more than once
*** The difference between the largest and smallest number is 9
A company is investigating working conditions throughout its operations and has offered employees the opportunity to complete a questionnaire on this subject.
Select the type of sample that has been formed in each presented situation:
Simple random sample
Stratified random sample
Voluntary response sample
Multistage sample
Answers
Correct answer is :- Voluntary response sample
'What is Voluntary response sample?'
A sample made up of people who have voluntarily decided to take part in the sample group is known as a voluntary response sample.
Those who want to participate in a voluntary response sample typically do so because they are passionate about the topic of the survey. This is why voluntary response samples frequently produce results that are considerably biased, as the majority of participants will have strong opinions on the subject. The ease of joining the survey is another factor in people's participation.
An example would be a TV show host asking his audience to visit his website and participate in an online survey.
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A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p= the true proportion of times the dime would land on heads when spun. Under the assumption that the true proportion is 0,5, 100 simulated proportions for samples of size 25 are shown in the dotplot. Using the dotplot, what do the two dots above 0.70 represent? O There is a 2 in 100 chance that the true proportion of heads is 0.7 O In two simulated samples of 25 spins, the proportion of heads is 0.7. O There is a 2 in 100 chance that the sample proportion of heads is 0.7 O In two simulated samples of 25 spins, the true proportion of heads is 0.7.
Answers
We have an option that says in 2 simulated samples of 25 spins, the proportion of heads is .7 and that would be our best option(d).
A student decides to spin a dim and determine the proportion of times it's lands on heads and the student spins the time 25 times and records that it lands on heads 17 times. So we have a leads on head of 17 out of 25,
So, probability 17/25 =0.68
Let p be the true proportion of times that time would land on heads 1 spun and under this assumption, p is going to be 0.5 simulated proportions for samples of size.
25 are shown to us in a dot plot. So, I'm assuming you can see your dot plot and when you look at the dot plot, you can see that again, each 1 of those dots represents a simulation of sample size, 25 . So basically, almost think of it like 100 different experiments where we did. This 25 times,
so, the question is using the dot plot. What do the 2 dots above .70 represent?
We have an option that says in 2 simulated samples of 25 spins, the proportion of heads is .7 and that would be our best option(d).
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Solve.
How much pure acid is in 780 milliliters of a 14% solution?
The answer is ml.
(Tung an integer or a decimal.)
Answers
The amount of pure acid in the solution is 109.2ml. The solution has been obtained using the concept of proportion.
What is proportion?
When a ratio is expressed as a/b and two ratios are equal, the expression is a proportion. A and B can be any two integers in this case. Understanding many ideas in mathematics and science requires a solid understanding of ratios and proportions.
According to the direct proportion formula, we can state y = kx given a constant k if the quantity y is directly proportional to the quantity x. The direct proportion equation also has a generic form, which is y = kx.
Let 'x' ml be the quantity of pure acid in the solution.
We are given that we have 780 ml of a 14% solution
This means that 780ml is 100%.
So, using proportion:
⇒780/x= 100/14
⇒780*14/100=x
⇒109.2ml = x
Hence, the amount of pure acid in the solution is 109.2ml.
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Shane and Daniel are simplifying the expression 24 ÷ 6 x 2. Daniel says the correct answer is 8, while Shane says the correct answer is 2. Who is correct and why?
Answers
The correct response to the equation 24 ÷ 6 x 2 is 8. As a result, Daniel is right whereas Shane is wrong.
In mathematics, there are certain principles for simplifying various expressions or equations. As a result, 8 is the correct answer since it satisfies to the BODMAS rule. In which case, division comes before multiplication and must come before addition.
In this statement, divide comes first, therefore 24 will be divided by 6, then the result of division will be multiplied by 2 to provide an answer of 8.
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ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left
Answers
She sells 4/19 of the remaining apples in the afternoon, so she sells 17.75 * 4/19 = 2.7 pounds of apples.
She sells 1/4 of the remaining apples in the evening, so she sells (35.5 - 17.75 - 2.7) / 4 = 4.5 pounds of apples.
Ara has 35.5 - 17.75 - 2.7 - 4.5 = 10.5 pounds of apples left
what does this mean on my report card i found it does it mean a good thing or bad thing can you please explain.
Answers
Answer:
It means Progressing
In Progress
Step-by-step explanation:
What is (12^2*5)/4+9-1?
I am giving 15 points away and will give brainiest to the correct answer and who also show there work,
Answers
Answer:
60
Step-by-step explanation:
Calculate the sum or difference
12^2 x 5 / 12
Cancel out the common factor 12
12 x 5
Multiply the numbers
60
Solution:
60
Hope this helps!! <3
Select all the angles of rotation that produce symmetry for this flower.
Flower on polar grid.
A: 45 degrees
B: 90 degrees
C: 135 degrees
D: 180 degrees
E: 225 degrees
F: 270 degrees
Answers
The angles of rotation symmetry for the flower are:
B. 90 degrees
D. 180 degrees
F. 270 degrees
A shape with a rotation symmetry will look the same, after the rotation also.
The order of symmetry is the number of rotations that can be applied to a figure while maintaining its original appearance.
From the image of the flower (image attached at the end of solution), we can see that the lines that pass through the origin of the flower are perpendicular.
The perpendicular lines will form the degrees of 90.
This means that 90 degrees of rotation will produce symmetry for the flower.
Other angles that produce symmetry must be multiples [tex]90^{\circ}[/tex].
These angles are:
[tex]\theta=90^{\circ}, 180^{\circ}, 270^{\circ}, 360^{\circ}[/tex].
Here we have [tex]90^{\circ}, 180^{\circ}, 270^{\circ}[/tex] options
Hence, (B), (D), and (F) are the correct options.
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A rectangular landing strip for an airplane has a perimeter of 8876 feet. If the length is 10 feet longer than 35 times the width, what is the length of the air strip?
Answers
The length of the air strip is 451feet.
What is perimeter?Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthened n sides).
Given in question;
Perimeter= 8876feet
Let the length be x;
and the width be y;
Now, length will be x= 10+35y
Perimeter of rectangle= 2l+2b
8876=2(10+35y)+y
8876=20+700y+y
y=12.6
x=10+35y
x=451;
Hence, the answer by the given perimeter will be 451feet.
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If $8000 is deposited into an account earning simple interest at an annual interest rate of 4% for 10 years, how
much interest was earned? Show you work.
Answers
The interest earned by the investment of $8,000 at an annual simple interest rate of 4% for 10 years is $3,200.
What is the simple interest?The simple interest method is a system that does not accumulate interest on interest.d
The simple interest system is unlike the compound interest system.
The formula for computing the simple interest is principal x rate x time.
Initial deposit = $8,000
Interest rate = 4%
Investment period = 10 years
Interest system = simple interest
Simple interest = P x R x T
= $8,000 x 4% x 10
= $3,200
Thus, the investment will earn a total interest of $3,200.
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H=10.00+0.07x after 20 months
Answers
The numeric value of the function H(x) = 10 + 0.07x when x = 20 is given as follows:
11.4.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function in this problem is defined as follows:
H(x) = 10 + 0.07x.
When x = 20, the numeric value is found replacing the lone instance of x by 20, hence:
H(20) = 10 + 0.07(20)
H(20) = 10 + 1.4
H(20) = 1.4.
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two multiplicative sets s and t yield localizations with the same primes then actually they have the same saturation
Answers
Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.
Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.
Thus, the two sets s and t have the same saturation since they yield the same localization.
If two multiplicative sets s and t yield localizations with the same primes, then the two sets s and t have the same saturation since they yield the same localization.
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TRUE OR FALSE question 8 collaborating with a social scientist to provide insights into human bias and social contexts is an effective way to avoid bias in your data.
Answers
True. Collaborating with a social scientist can help identify and address potential sources of bias in data, allowing for more accurate and meaningful results.
Collaborating with a social scientist to provide insights into human bias and social contexts is an effective way to avoid bias in data. Social scientists can help identify and address potential sources of bias in data, allowing for more accurate and meaningful results. This can be done in several ways. Firstly, they can help identify potential sources of bias, such as demographic variables, cultural norms, and other external factors that may affect the data. Secondly, they can help devise strategies to counter the potential sources of bias. For example, they can suggest methods of incorporating diverse perspectives into the data collection process, or of analyzing data in a way that takes into account the potential effects of bias. Finally, they can provide insights into how social contexts can shape the interpretation of data, and can help ensure that any conclusions drawn from the data take into account the complexity of the social environment. By collaborating with a social scientist, researchers can help ensure that their data is free from bias, allowing for more meaningful and accurate results.
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Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52 B) 84.78 C)127.17 D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88 B) 2.25 C) 1.8 D) 1.5
Answers
The volume of the large container is given as follows:
508.68 in³.
The ratio of the volumes is of:
B) 2.25
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The parameters for the large container are given as follows:
h = 4.5, r = 0.5 x 8 x 1.5 = 6.
(as the diameter is half the radius).
Hence the volume of the large container is obtained as follows:
V = 3.14 x 6² x 4.5 = 508.68 in³.
The ratio is of 2.25, as the radius is squared.
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need help on 12-14. I will be giving brainliest. Thank you
Answers
On solving the provided question, we can say that n this parallelograms (2x+1)+(x+5) =180 => x = 58
What is parallelograms?A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.
here,
in this parallelograms
2x = 1 and x+5
so, (2x+1)+(x+5) =180
3x + 6 = 180
3x = 174
x = 58
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Please help with this ewuation
Answers
Answer: 57°
Step-by-step explanation:
Because the angle has a bisector ON, we should be able to add the angles together to collectively equal 106. This will help us to find c, so then we can solve <LOM.
(10c-23) + (-3c+73) = 106
Now combine like terms of the left side of the equation
7c + 50 = 106
get the variables alone on one side of the equation
7c = 56
c = 8
Now, plug in c to the equation for the degree of <LOM to solve
10(8) -23 = 80 - 23 = 57°
Hope this helps!
if triangles are anions and stars are cations, which of the following situations would lead to the most positive membrane potential?
O Both channel types are open
O only star channels are open
O neither channel type is open
O only triangle channels are open
Answers
A positive cation and a negative anion makes ionic compound. So both the ions i.e cation and anions are open.
Membrane potential is a potential gradient that forces ions to passively move in one direction: positive ions are attracted by the 'negative' side of the membrane and negative ions by the 'positive' one. Generally Voltage gated channels- open and close in response to changes in the voltage or membrane potential; involved in generating action potentials. As stars and triangles represents the cations and anions both channel types are open to lead the most positive membrane potential.
Therefore , both the channel types ( triangle and star ) are open to lead the most positive membrane potential.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answers
The steps that she could use to solve the quadratic equation are determined as:
2(x² + 6x + 9) = 18 + 3(x + 3)² = 21/2What is a Quadratic equation?ax2+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
The solution to the quadratic equation is determined as follows;
2x² + 12x - 3 = 0
2x² + 12x = 3
divide through by 2
x² + 6x = ³/₂
take half of the coefficient of x, square it and add it to both sides of the equation
(x + 3)² = ³/₂ + 3²
x² + 6x + 9 = 9 + ³/₂
2(x² + 6x + 9) = 18 + 3
Thus, the steps that she could use to solve the quadratic equation are determined as 2(x² + 6x + 9) = 18 + 3 and then (x + 3)² = 21/2.
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Complete question:
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.
2(x2 + 6x + 9) = 3 + 182(x2 + 6x) = –32(x2 + =6x) = 3(x + 3)² = 21/22(x2 + 6x + 9) = –3 + 9(x + 3)2 = 6/2