4 is the correct value from the set {1, 2, 3, 4} which is the solution to the equation 3x + 3 = 15.
What is a solution of an equation?A solution of an equation refers to a value or values that satisfy the given equation. It is the value or values that make the equation true when substituted for the variable(s) in the equation. Equations are mathematical expressions that contain an equals sign and can have one or more variables. A solution is typically represented as a number, but it can also be a set of numbers, a range of values, or an expression. Finding the solutions of an equation is an important part of solving mathematical problems and has many practical applications in fields such as engineering, physics, and finance.
Solution of the given equation 3x + 3 = 15 means when we put a value in x we should get the result as 15, that is left hand side of the equation should be equal to the right hand side of the equation.
Solving the equation we get,
3x + 3 - 3 = 15 - 3
3x = 12
x = 4
Therefore, the value 4 is a solution to the equation.
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PLEASE HELP ME!
Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5
How much more material does Jessica need in order to make the second prism?
Answer:
181.875 cm³
Step-by-step explanation:
You want to know the amount of additional material Jessica needs to make a prism with a volume of 35 cm³ and one that is dilated by a factor of 2.5, given that she has 400 cm³ of material.
Larger volumeThe dilation factor for volume is the cube of the linear dilation factor:
2.5³ = 15.625
so the volume of the scaled-up prism will be ...
(35 cm³) × 15.625 = 546.875 cm³
Total volumeThe total volume of material Jessica needs for the two prisms is ...
35 cm³ + 546.875 cm³ = 581.875 cm³
NeededSince Jessica has 400 cm³ of material, the amount she needs is ...
581.875 cm³ - 400 cm³ = 181.875 cm³
Jessica needs 181.875 cm³ more material to make the second prism.
I need help mad fast
The correct vocab in written as;
DC = semi-circle
<ECD = minor arc
<ECF = point of tangency
CF = chord
How to determine the corresponding termsTo determine the corresponding terms, we need to take note of the following definitions;
Minor arc: It is defined as the shorter arc that connects two endpoints on a circle. It is usually less than 180 degreesMajor arc: It is defined as an arc that measures greater than 180 degrees.Semi- circle: It divides the circle into two equal halves and measures 180 degreesChord: it is defined as a straight line segment with both endpoints found on a circular arc.Learn about circles at: https://brainly.com/question/24375372
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A quadrilateral has vertices P(-5,7), Q(-3,6), and R(-6,0). Which point would make PQRS a rectangle?
~a.) S(-4,-1)
~b.) S(-7,2)
~c.) S(-8,2)
~d.) S(-8,1)
From the given information about the vertices of the quadrilateral, the point at which the PQRS quadrilateral will be made a rectangle is S(17/14, -1/7).
What is a quadrilateral? What are its properties?A quadrilateral is a four-sided polygon, which means it's an unrestricted shape with four straight sides.The parcels of a quadrilateral include Four sides A quadrilateral has four sides.The sum of the angles in a quadrilateral is always 360 degrees.Each type of quadrilateral has its own unique set of parcels and characteristics.Perimeter The border of a quadrilateral is the sum of the lengths of its sides.Area The area of a quadrilateral can be calculated using colorful formulas, depending on the type of quadrilateral and the information given about its sides and angles.What is a rectangle? What are its properties?An example of a quadrilateral with all four angles at right angles (90 degrees) and opposite sides that are parallel and of equal length is a rectangle.The characteristics of a rectangle are as follows: 4 right angles: A rectangle has four angles, and all four of them are right angles, which means they are all 90 degrees.A rectangle's perimeter is determined by adding the lengths of its four sides, which is equal to twice the length plus twice the width.Area: The length times the breadth of a rectangle equals the area of that shape.Perpendicular sides are opposite sides: A rectangle's opposite sides are perpendicular to one another, therefore when they intersect, they do so at a right angle.Parallelograms include rectangles as well: since a rectangleWe need to find the point that would make PQRS a rectangle. We will first determine the fourth vertex S which, when connected to the remaining three vertices, forms a quadrilateral with four right angles.As opposite sides of a rectangle are parallel and equal in length, we can first find the lengths of PQ and RS, which should be equal in a rectangle.From the distance formula, we have:PQ = [tex]\sqrt{6-7)^{2}} +(-3+5)^{2} =\sqrt{[2^{2}+(-2)^{2} } =\sqrt{8}[/tex]RS = [tex]\sqrt{(0 - 6)^2+ (-5 + 3)^2} + \sqrt{[(-6)^2 + (-2)^2] }= \sqrt40}[/tex]The midpoint of PQ is: [tex][(6 - 5)/2, (-3 - 3)/2] = (0, -3)[/tex]The slope of PQ is: [tex](6 - 7)/(-3 + 5) = -1/2[/tex]The equation of the perpendicular bisector of PQ is:[tex]y + 3 = 2(x - 0) or y = 2x - 3[/tex]The midpoint of RS is: [tex][(0 - 6)/2, (-5 - 0)/2] = (-3, -5/2)[/tex]The slope of RS is: [tex](0 - 6)/(-5 + 3) = 3[/tex]The equation of the perpendicular bisector of RS is :[tex]y + 5/2 = (-1/3)(x + 3) or y = (-1/3)x - 1/6[/tex]Now to find the intersection of these two lines, we can set them equal to each other and compute the value for x:[tex]2x - 3 = (-1/3)x - 1/6[/tex][tex]12x - 18 = -2x - 1[/tex]Adding 2x and 18 to both sides gives:[tex]14x = 17x = 17/14[/tex]To find the y-coordinate of the intersection, substitute x into either equation:[tex]y = 2(17/14) - 3 = 1/7[/tex]So, the point that would make PQRS a rectangle is S(17/14, -1/7).To know more about polygons visit:
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The answer is option c.) S(-8,2).
What is quadrilateral?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
For PQRS to be a rectangle, its opposite sides must be parallel and have equal length. We can find the length of PQ and RS using the distance formula:
PQ = √[(Qx - Px)² + (Qy - Py)²]
= √[(-3 - (-5))² + (6 - 7)²]
= √[4 + 1]
= √[5]
RS = √[(Sx - Rx)² + (Sy - Ry)²]
= √[(-8 - (-6))² + (2 - 0)²]
= √[4 + 4]
= √[8]
Since PQ and RS are not equal, we need to find a point S such that PQRS has equal sides. Moreover, the diagonals of a rectangle bisect each other. Hence, we can use the midpoint formula to find a point that bisects PR:
M = [(-5 - 6)/2, (7 + 0)/2]
= (-11/2, 7/2)
Let's consider each option:
a.) S(-4,-1)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-4, -1) cannot be a point of RS.
b.) S(-7,2)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-7 + 6) = -2, so S(-7, 2) cannot be a point of RS.
c.) S(-8,2)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-8, 2) could be a point of RS. Moreover, the distance from S to the midpoint of PR is:
√[(-11/2 - (-8))² + (7/2 - 2)²]
= √[25/4 + 9/4]
= √[34]/2
This is equal to the length of PQ, so PQRS could be a rectangle with S(-8, 2).
d.) S(-8,1)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (1 - 0)/(-8 + 6) = -1, so S(-8, 1) cannot be a point of RS.
Therefore, the answer is option c.) S(-8,2).
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12% of what is 56 inches?
Questions are Below!!!
Answer:
Step-by-step explanation:
Question 1 :
The statement that best describes the solutions of a two-variable equation is (1) The ordered pairs must lie on the graphed equation. This means that any ordered pair (x,y) that satisfies the equation will corresponds to a point on the graph of the equation. In other words, if we plot all the points (x,y) that make the equation true, we will obtain the graph of the equation. Any points that do not lie on the graph is not a solution to the equation. Therefore, when solving a two-variable equation, we need to find the values of x and y that make the equation true and plot those points on the graph to visualize the solutions.
Question 2 :
To use the arithmetic sequence formula, we need to know the first term (a1), the common difference (d), and the desired term (an). In this case, we are given the first term as 4 and the common difference as 3 (since each term is increasing by 3). To find the 10th term, we would replace the variable "n" with 10 in the formula. Therefore, to determine the 10th term of this sequence, we would use the formula:
a10 = a1 + (n-1)d
a10 = 4 + (10-1)*3
a10 = 4 + 27
a10 = 31
Thus, the 10th term of the given sequence is 31.
Question 3 :
The formula an = al + (n-1)d is used to determine the nth term in an arithmetic sequence, where "a" represents the first term in the sequence, "n" represents the term number being solved for, and "d" is the common difference between terms. The formula essentially states that to find any term in an arithmetic sequence, one must add the common difference between terms multiplied by the number of terms-1 to the value of the first term. This formula can be applied to various situations, such as determining the total cost of goods sold in a business with a constant markup percentage, or calculating the number of days it will take to save a given amount of money with a fixed monthly contribution. By understanding the principles behind the formula, individuals can successfully solve problems involving arithmetic sequences in a variety of contexts.
In a circle ABCD, OB = 10 cm. Find the measure of AC.
The measure of AC, in circle ABCD can be found to be 20 cm.
How to find the measure?In Circle ABCD, O is the midpoint of the circle which means that OB is the radius.
As A and C are on opposite sides of the circle, it means that the value of the measure of AC would be the diameter of the circle which can be found if we have the radius.
The diameter which is AC would then be:
= Radius x 2
= OB x 2
= 10 x 2
= 20 cm
In conclusion, the measure of AC is 20 cm.
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help me solve this question fast
Answer:
This is a geometric series with first term 1/4 and common ratio 1/4. So the sum of this series is:
[tex] \frac{ \frac{1}{4} }{1 - \frac{1}{4} } = \frac{1}{4} \div \frac{3}{4} = \frac{1}{4} \times \frac{4}{3} = \frac{1}{3} [/tex]
what is the range of Dan’s car? It’s highway EPA rating is 40mpg and the tank holds 12 gallons
The range at which Dan's car can go is 3.33 miles
What is range of a car?A car's range is the distance it can travel with the current amount of fuel in the tank.
The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.
The range of a car can be measured in the unit of distance.
Therefore the range of a car can be calculated as;
R = distance per gallon/ number of gallon.
Dan's car is 40mpg and has 12 gallons in it's tank.
Therefore it's range = 40/12
= 3.33miles.
therefore the range of Dan's car is 3.33miles
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You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find the probability of p(multiple of 2 or multiple of 3)
The probability of getting a multiple of 2 or a multiple of 3s:
P = 0.67
How to find the probability for the given event?The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes, which in this case are 12.
The multiples of 2 and the multiples of 3 are
{2, 3, 4, 6, 8, 9, 10, 12}
So 8 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:
P = 8/12 = 0.67
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in one day a 20 pound dog eats 3 cups of food. How much would a 50 pound dog eat
what is different about P3(x)=x^4-21x+20x? what interceps would you predict for its graph?
There seems to be an error in the expression for P3(x). It appears to be missing an exponent for the second term.
Assuming that the correct expression is P3(x) = x^4 - 21x^2 + 20x, we can analyze its properties.
The degree of the polynomial P3(x) is 4, which means its graph will have at most 4 x-intercepts and at most 3 turning points.
To find the x-intercepts, we set P3(x) equal to zero and solve for x:
x^4 - 21x^2 + 20x = 0
x(x^3 - 21x + 20) = 0
Using the factor theorem or synthetic division, we can find that x = 0 is a root of the polynomial, so (x-0) is a factor. The remaining cubic factor can be factored as (x-1)(x-4)(x+5).
Therefore, the x-intercepts of the graph of P3(x) are x = 0, x = 1, x = 4, and x = -5.
What intercepts would you predict for its graph?As for the y-intercept, we can find it by setting x = 0:
P3(0) = 0^4 - 21(0)^2 + 20(0) = 0
So the y-intercept is (0,0).
To determine the turning points, we can find the critical points by taking the derivative of P3(x) and setting it equal to zero:
P3'(x) = 4x^3 - 42x + 20
4x^3 - 42x + 20 = 0
Solving this equation yields three critical points: x ≈ -1.23, x ≈ 0.58, and x ≈ 2.65.
We can use the second derivative test to determine the nature of these critical points. The second derivative is:
P3''(x) = 12x^2 - 42
At x ≈ -1.23 and x ≈ 2.65, the second derivative is negative, indicating that these are local maxima. At x ≈ 0.58, the second derivative is positive, indicating that this is a local minimum.
Therefore, the graph of P3(x) has a local maximum at (approximately) (-1.23, P3(-1.23)), a local minimum at (approximately) (0.58, P3(0.58)), and a local maximum at (approximately) (2.65, P3(2.65)).
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What is the polynomial 2m-3m^2+4m^5+21 in standard form??
The standard form of the polynomial 2m-3m²+4m⁵+21 is 4m⁵ - 3m² + 2m + 21.
The standard form of a polynomial is when the polynomial is written with the terms in descending order of degree, with each term having a coefficient and an exponent. To convert the given polynomial 2m-3m²+4m⁵+21 to standard form, we need to rearrange the terms in descending order of degree.
The degree of a term is the exponent of the variable in that term. For example, the degree of the term 4m⁵ is 5, and the degree of the term -3m² is 2.
So, we start by arranging the terms in descending order of degree:
4m⁵ - 3m² + 2m + 21
Next, we can simplify the coefficients of each term if possible. In this case, all of the coefficients are already simplified, so we leave them as they are.
In summary, to convert a polynomial to standard form, we arrange the terms in descending order of degree and simplify the coefficients of each term if possible. This makes it easier to compare and manipulate polynomials, and is often required when solving equations or finding roots of polynomials.
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Natalie saved $9,750 at 5.5%
simple interest per year. After 3
years, what is the earned
interest?
the earned interest after 3 years is $1,608.75.
What is simple interest?
Before delving further into the concept of simple interest, it is worth noting that it is a straightforward method for calculating interest on money, whereby interest is added at a constant rate for each time period and always to the initial principal amount. When we deposit our money into a bank, we can earn interest on our investment. Simple interest is one type of interest that banks may offer.
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal (initial amount)
r = interest rate per year (as a decimal)
t = time (in years)
Substituting the given values, we have:
P = $9,750
r = 0.055 (since the interest rate is 5.5%)
t = 3
I = $9,750 * 0.055 * 3
I = $1,608.75
Therefore, the earned interest after 3 years is $1,608.75.
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Geometry Work
It's due today please help asap
The correct volume of the solid shape given above would be = 3726.1in³.
How to calculate the volume of the solid shape?To calculate the volume of the solid shape, the volume of the cylinder and a cone shoe be subtracted form the Vol of the inner cylinder within the solid shape.
The formula for volume of a cylinder = πr²h
where r = 8in, h = 18in,π= 3.14
vol of cylinder = 3.14× 64×18
= 3617.28in³
volume of cone =⅓πr²h
where hb= 5in
vol = 1/3×3.14×64×5
= 1004.8/3 = 334.9in³
Total volume of shape = 3617.28in³+334.9in³ = 3952.18in³
Vol of inner cylinder = πr²h
where r = 2in
vol = 3.14×4× 18 = 226.08in³
The volume of the shape = 3952.18- 226.08 = 3726.1
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Write the equation of the line in fully simplified slope-intercept form.
Answer:
y=1/2x+4
Step-by-step explanation:
The point of intersection is 4, and it goes up one, right 2 so the rise over run is 1/2
Which quadratic inequality best describes the graph?
Answer: parabolic curve
Step-by-step explanation:
Answer: parabolic curve
Step-by-step explanation:
in a hypothetical study, a pharmaceutical company is interested in finding the dosage of a new medication that best treats panic attacks. ninety people, who are diagnosed with panic attacks, were randomly assigned to three groups: (1) 20 milligrams of the new drug, (2) 30 milligrams of the new drug, and (3) 40 milligrams of the new drug. after 30 days on the medication, each participant records the number of panic attacks they have experienced in the previous seven days. what hypothesis testing technique should the researcher use to analyze the data?
In this scenario, the researcher is interested in comparing the effectiveness of three different doses of a new medication in treating panic attacks. To analyze the data, the researcher can use a hypothesis testing technique called analysis of variance (ANOVA).
ANOVA is a statistical technique used to compare the means of three or more groups to determine if there are significant differences between them. In this case, the means being compared are the number of panic attacks experienced by each group after 30 days on the medication.
The null hypothesis in this study would be that there is no significant difference in the mean number of panic attacks between the three dosage groups, and the alternative hypothesis would be that there is a significant difference in the mean number of panic attacks between at least two of the dosage groups.
The researcher can use a one-way ANOVA test to analyze the data, which will calculate the F-statistic and associated p-value. If the p-value is less than the chosen significance level (usually 0.05), the researcher can reject the null hypothesis and conclude that there is a significant difference in the mean number of panic attacks between at least two of the dosage groups.
If a significant difference is found, post-hoc tests such as Tukey's HSD can be used to determine which specific groups have significantly different means.
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A triangular box of sticky notes is shown. The volume of the box of sticky notes is 54.6 cubic inches. What is the height of the box of sticky notes?
The area of a triangle is equal to half the product of the triangle's base and height. The triangular box has a height of 6 inches.
What is a triangle's area?The area of a right-angle triangle is half of the product of the triangle's base and height.
Area of triangle = [tex]\frac{1}{2} * base * height[/tex]
As stated previously, the lengths of the triangle's altitude and base are 3.5 inches and 5.2 inches, respectively. As a result, the volume of the triangular box is 54.6 cubic inches, and the height of the box must be determined in inches.
The volume of the triangular box =
[tex](\frac{1}{2} * base *height) * Height\\54.6 = (\frac{1}{2} * 5.2 * 3.5) * Height\\Height = \frac{54.6}{2.6 * 3.5} \\Height = 6 inches[/tex]
Therefore the height of the box of sticky notes is 6 inches.
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What is the ¨length of a soccer field¨ unit of measurement
A - Square meters
B - Yards
C - Cubic inches
D - Cubic feet
E - Square centimeters
The unit of measurement "length of a soccer field" is in yards
What is the ¨length of a soccer field¨ unit of measurementThe unit of measurement "length of a soccer field" is typically measured in yards, which is option B.
A standard soccer field is rectangular, with a length ranging from 100 to 130 yards and a width ranging from 50 to 100 yards.
The measurement of the length of a soccer field is based on the distance between the goal lines, which is equivalent to the length of the field.
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Commutative states that the grouping of three terms being added does not affect the result.
Distributive states that the order of two terms being added may be switched which does not affect the result.
Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products.
Which is which because that's what its asking
The first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.
The solution to the aforementioned questionThe first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.
The second statement, "Distributive states that the order of two terms being added may be switched which does not affect the result" is referring to the commutative property of multiplication.
The third statement, "Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products" is referring to the associative property of multiplication.
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A line passes through the point (-4, -3) and has a slope of 5.
Write an equation in slope intercept form for this line.
The equation of the line is y=5x+17.
What is slope intercept form of the equation?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
Here the given the point [tex](x_1,y_1)=(-4,-3)[/tex] and slope m = 5.
Now using equation formula then,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y -(-3)=5(x-(-4))
=> y+3 = 5(x+4)
=> y+3 = 5x+20
=> y = 5x+20-3
=> y = 5x+17
Hence the slope intercept form of the equation is y = 5x+17.
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Sam started the week with a balance of -$10 in his checking account. Then he deposited some money into the account. The ending balance was $70. How much did sam deposit?
Answer:
Sam balance was -10 and the ending balance was $70
=80+(-10)
=$70
Roger can finish his math homework in 6 hours. Trish can finish the
same homework in 5 hours.
What part of the homework will Roger and Trish finish if they
work together for 1 hour?
In linear equation, Roger and Trish can finish 11x/30 of the homework if they work together for x hours.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work. So, working together for one hour, they can finish:
(1/6) + (1/5)
= (5/30) + (6/30)
= 11/30 of the work.
If they work together for x hours, then they will finish:
x × (11/30) = 11x/30
of the work in x hours.
Therefore, Roger and Trish can finish 11x/30 of the homework if they work together for x hours.
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BUNGEE JUMPING Trevor is bungee jumping off of a bridge into a canyon that is 400 feet deep. Trevor's bungee cord is 9 feet more than ten times the distance between Trevor and the bottom of the canyon at the end of his jump. If Trevor is 6 feet tall and the bungee cord is attached to his feet, what will be his height above the bottom of the canyon at the end of his jump? Measure the height from Trevor's head to the bottom of the canyon.
The height above the bottom of the canyon at the end of his jump is 385 feet.
we have,
Canyon depth = 400 feet
Trevor's height= 6 feet
cord length = 9 feet
So, Trevor height to end of jump is
= 400 - (9+6)
= 400 - 15
= 385 feet
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Ted jumped 1,300 times. He did 100 more jumps than Mario. How many jumps did Mario do?
Answer: 1,200
Step-by-step explanation: 1,300 - 100 = 1,200
A scoop from a bin of assorted jelly beans contained a mix of flavors. root beer 5 licorice 22 cinnamon 6 What is the experimental probability that the next jelly bean scooped from the bin will be a cinnamon jelly bean? Write your answer as a fraction or whole number. P(cinnamon)=
Answer: The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials.
In this case, the number of cinnamon jelly beans in the scoop is 6. The total number of jelly beans in the scoop is 5+22+6=33.
Therefore, the experimental probability of scooping a cinnamon jelly bean from the bin is:
P(cinnamon) = number of cinnamon jelly beans / total number of jelly beans
P(cinnamon) = 6 / 33
P(cinnamon) = 2 / 11
So the experimental probability of scooping a cinnamon jelly bean from the bin is 2/11, which can be written as a fraction.
Step-by-step explanation:
5) Danielle goes shopping for yoga pants. The promotion at the
store is if you buy 8 pairs for $98. How much would Danielle pay
if she bought 5 pairs with the same promotion?
find the lemgth of arc PQ
The arc length is D) 3.14 meters.
What is arc length?
In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.
It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.
The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.
[tex]A_L=\frac{\theta}{360\textdegree}2\pi r[/tex]
Here the give circle Radius PR = 3m and θ=60°.
Now using arc length formula then,
=> Arc length [tex]A_L=\frac{\theta}{360\textdegree}2\pi r[/tex]
=> [tex]A_L=\frac{60}{360} \times2\times3.14\times3[/tex]
=> [tex]A_L=\frac{1}{6}\times2\times3.14\times3[/tex]
=> [tex]A_L[/tex] = 3.14 m.
Hence the arc length is D) 3.14 meters.
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Solve for x Trigonometry
Answer:
31.97⁰ to the nearest hundredth.
Step-by-step explanation:
sin x = opposite side / hypotenuse
= 9/17
x = 31.9657
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
-3x^2-298=60x-1
Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.
Define the term "completing the square":A quadratic equation can be made together into perfect square trinomial simply adding or removing elements from both sides, a technique known as "completing the square."
You can use the square's completion as another mathematical tool to solve a variety of problems:
Make algebraic statements simplersolve quadratic problemsTransform expressions between different forms.Quadratic functions' minimum and maximum values should be determined.Given expression:
-3x² - 298 = 60x - 1
isolating the x values:
-3x² - 60x = 298 - 1
-3x² - 60x = 299
Taking -3 common from the left hand side:
-3(x² + 20x) = 299
x² + 20x = - 299/3
This, can be written as:
x² + 2*10x = - 299/3
add both side by 100
x² + 2*10x + 100 = - 299/3 + 100
On simplification:
(x + 10)² = (-299 + 300) /3
(x + 10)² = 1 /3
Comparing obtained expression with the given form: (x+a)²=b
a = 10 and b = 1/3
Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.
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