the 4th partial sum of the series is approximately 1.4236.
The general term of the series is given by an = n^(-2), for n >= 1.
Therefore, the first four terms are:
a1 = 1^(-2) = 1
a2 = 2^(-2) = 1/4
a3 = 3^(-2) = 1/9
a4 = 4^(-2) = 1/16
The 4th partial sum, s4, is given by:
s4 = a1 + a2 + a3 + a4 = 1 + 1/4 + 1/9 + 1/16 ≈ 1.4236
what is series?
In mathematics, a series is the sum of the terms of a sequence of numbers. It is the result of adding the terms of a sequence and is written using sigma notation as Σan, where n ranges from 1 to infinity and an is the nth term of the sequence.
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Triangulation is a method of finding the location of an object based on measurements made from two other locations.
Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.
Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.
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What is an example of dilate?
An example of dilation math is a square of side 5 units can be dilated to a square of side 15 units, but the shape of the square remains the same.
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.In mathematics, a dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the spaceTo dilate a figure by a scale factor, multiply both the x-coordinate and the y-coordinate of each point by the scale factor. The new points are (4, -1), (6, -10), and (10, 8)To learn more about dilation refers to:
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What is the pixel size?
Pixel size refers to the physical dimensions of an individual pixel in a digital image. It is typically measured in micrometers (µm) or nanometers (nm).
The pixel size determines the resolution of an image, as a larger pixel size will result in a lower resolution image, and vice versa.
In digital cameras, the pixel size is directly related to the sensor size. A larger sensor will typically have larger pixels, which can result in better low-light performance and less noise in the final image.
However, larger pixels also mean that the sensor will have fewer pixels overall, which can result in a lower resolution image.
In conclusion, Pixel size is one of the factors that affect the resolution of the image. A larger pixel size will result in a lower resolution image but it is beneficial for low-light performance.
It is important to consider the pixel size when choosing a camera or device with a built-in camera. It is also important to consider the sensor size, as a larger sensor typically results in larger pixels.
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The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(at least 2 heads).
13%
25%
50%
80%
Probability of getting at least 2 heads is 50%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given the sample space for tossing a coin 3 times as,
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Total number of outcomes in the sample space = 8
At least 2 heads means, heads can be 2 or more, for which the only possibilities are 2 heads or 3 heads.
Number of outcomes having 2 heads = 3
Number of outcomes having 3 heads = 1
P(at least 2 heads) = P(2 heads) + P(3 heads)
= 3/8 + 1/8
= 4/8
= 1/2
= 0.5 = 50%
Hence there is a 50% chance for getting at least 2 heads.
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Answer:
Probability of getting at least 2 heads is 50%.
Step-by-step explanation:
What is Probability?
Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given the sample space for tossing a coin 3 times as,
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Total number of outcomes in the sample space = 8
At least 2 heads means, heads can be 2 or more, for which the only possibilities are 2 heads or 3 heads.
Number of outcomes having 2 heads = 3
Number of outcomes having 3 heads = 1
P(at least 2 heads) = P(2 heads) + P(3 heads)
= 3/8 + 1/8
= 4/8
= 1/2
= 0.5 = 50%
Hence there is a 50% chance for getting at least 2 heads.
Are triangles ABC and ADC congruent?
No, triangles ABC and ADC are not congruent.
To determine if two triangles are congruent, we must use the Side-Angle-Side (SAS) Congruence Theorem. This theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of a second triangle, then these two triangles are congruent.
In this case, we can see that sides AB and AD are equal, but angles A and D are not equal. Therefore, triangles ABC and ADC are not congruent. To prove this calculationally, we can use the Law of Cosines. First, we can calculate the length of side BC by using the Law of Cosines:
BC^2 = AB^2 + AC^2 - 2AB * AC * cos(A)
BC = √(AB^2 + AC^2 - 2AB * AC * cos(A))
Then, we can calculate the length of side DC by using the Law of Cosines:
DC^2 = AD^2 + AC^2 - 2AD * AC * cos(D)
DC = √(AD^2 + AC^2 - 2AD * AC * cos(D))
Finally, we can compare BC and DC. Since BC ≠ DC, we can conclude that triangles ABC and ADC are not congruent.
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Write an equation that represents the line.
Use exact numbers.l
An equation that represents the line is Y is (-4/3)x+2 is the solution.
How can you determine a line's precise equation?Y = mx+b, where m is the slope and b is the y-intercept, is the formula for a line's slope-intercept (the point on the y-axis where the line crosses it). Replace m with the value you determined for your slope. In our case, the formula might be written as y = 1x+b or y = x+b if the slope value were substituted.
y=(-4/3)
We have two points since x+2 = -1.33x+2:
(3) and (2) are calculated from the graph.
We are aware that the line's equation is
y=mx+b
m=slope
m=(y2-y1)/(x2-x1)
m=(2-(-2))/(0-3)
therefore the slope is what we have
m=4/-3
m=-4/3
-4/3=-1.3333
We must track down "b"
using the example (0,2)
There are
2=m*0+b
2=b
Finally, here is
Y=(-4/3)x+2 is the solution.
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p = 9.7 inches, mm∠Q=93° and mm∠O=82°. Find the length of q, to the nearest 10th of an inch.
Answer:
its 9.7 bc if you insert P into V Is mutiply so it burst inside the mathmatic equation u get 9,7
Step-by-step explanation:
Three grade 8 classes decided to raise money for 2 charities by selling boxes of greeting cards. A box of cards cost $3.80 from the supplier and sold for $6.00. One class sold 150 boxes, the second 175, and the third 225. If the proceeds were divided equally between the 2 charities, how much did each receive?
The amount each charity received is $605
How much did each charity receive?The first step is to determine the total number of boxes sold.
Total boxes sold = 150 + 175 + 225 = 550
The next step is to calculate the profit made from the sales.
Profit = (selling price - cost price) x total boxes sold
Profit = ($6 - $3.80) x 550
Profit = 2.20 x 550 =1210
Amount each charity received = $121/ 2 = $605
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Jonathan needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 3 hours and charged him $141 for parts. The total was $336. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The required equation is x × 3 = 336 - 141. The cost of the labor per hour is $65.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x be the cost of the labor per hour.
We know that
x × 3 = labor cost
141 + x × 3 = total cost
We also know that the total cost is $336
So we can write the equation:
141 + x × 3 = 336
Solving for x:
x × 3 = 336 - 141
x × 3 = 195
x = 195/3
x = 65
Therefore, the cost of the labor per hour is $65.
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Is an R-squared value of 0.8 good?
In some fields, a good R-Squared reading could be required to meet criteria of 0.9 or above. An R-Squared value above 0.7 is typically regarded as indicating a high level of correlation in the financial industry, whilst a value below 0.4 would indicate a low level of correlation.
What Exactly Is Residual Value?
The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.
A good residual value is what?
Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.
A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.
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How do you construct a perpendicular bisector of Class 9?
A perpendicular bisector is a line that intersects a segment of a line at its midpoint, forming two equal segments.
To construct a perpendicular bisector of a line segment in class 9, the following steps should be followed:
1. Draw the line segment and mark the midpoint of the segment.
2. Take a compass and place the point at the midpoint of the line segment.
3. Adjust the width of the compass such that it is slightly greater than half the length of the line segment.
4. Make an arc above and below the line segment.
5. Draw a line through the two points of intersection of the arc and the line segment. This line is the perpendicular bisector of the line segment.
The formula for the perpendicular bisector is (x - x1) / (x2 - x1) = (y - y1) / (y2 - y1), where (x1, y1) and (x2, y2) are the coordinates of points on the line segment.
To calculate the perpendicular bisector of the line segment:
1. Calculate the midpoint of the line segment using the midpoint formula (x1 + x2) / 2 and (y1 + y2) / 2.
2. Substitute the coordinates of the midpoint and the endpoints into the perpendicular bisector formula.
3. Solve the equation to find the equation of the perpendicular bisector.
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For the following data, find the correlation coefficient. Does the line of best fit have positive correlation, negative correlation, or no correlation?
X 4 2 8 3 4 8 5 1 2
y 3 6 7 8 9 1 2 3 5
The correlation coefficient of the given set of data is −0.17 which is negative correlation.
What is correlation coefficient?A correlation coefficient is a metric that expresses a correlation of some kind, or a statistical association between two variables. The variables could be two columns of a specific data set of observations, also known as a sample, or two parts of a multivariate random variable with a well-known distribution.
∑x = 4+2+8+3+4+8+5+1+2
∑x = 37
∑y = 3+6+7+8+9+1+2+3+5
∑y = 44
n = 9
[tex]$ \bar{\text x} = \frac{\Sigma \text x}{n} = \frac{37}{9} = 4.1[/tex]
[tex]$ \bar{\text y} = \frac{\Sigma \text y}{n} = \frac{44}{9} = 4. 8[/tex]
x - [tex]\bar{\text x}[/tex] y - [tex]\bar{\text y}[/tex] [tex](\text x -\bar{\text x} ) ( \text y - \bar{\text y} )[/tex]
−0.1 −1.8 0.18
−2.1 1.2 −2.52
3.9 2.2 8.58
−1.1 3.2 −3.52
−0.1 4.2 −0.42
3.9 −3.8 −14.82
0.9 −2.8 −2.52
−3.1 −1.8 5.58
−2.1 0.2 −0.42
[tex]\Sigma (\text x -\bar{\text x} ) ( \text y - \bar{\text y} )[/tex]
= −9.88
(x - [tex]\bar{\text x}[/tex])² (y - [tex]\bar{\text y}[/tex])²
0.01 3.24
4.41 1.44
15.21 4.84
1.21 10.24
0.01 17.64
15.21 14.44
0.81 7.84
9.61 3.24
4.41 0.04
∑(x - [tex]\bar{\text x}[/tex])² ∑(y - [tex]\bar{\text y}[/tex])²
= 50.89 = 62.96
Coefficient of correlation, r = [tex]$ \frac{\Sigma (\text x -\bar{\text y} ) ( \text y - \bar{\text y} )}{\sqrt{\Sigma(\text x -\bar{\text x} )^2} \sqrt{\Sigma(\text y-\bar{\text y} )^2}}[/tex]
r = [tex]$ \frac{-9.88} {\sqrt{50.89 } \sqrt{62.96}}[/tex]
r = [tex]$ -\frac{247\sqrt{8010086} } {4005043}[/tex]
r = −0.17
Thus, the correlation coefficient of the given set of data is −0.17 which is negative correlation.
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evaluate the expression
Answer:
-6
Step-by-step explanation:
What is 2 with an exponent of 4?
What is the formula for midpoint rule?
The formula for midpoint rule is M =∑ n i = 1 f ( m i ) Δx.
In this equation, I represents the ith rectangle, n the number of rectangles that comprise the area under the curve, f (m I) the function of the curve as defined by the ith rectangle's midpoint, and x the width of each rectangle. In calculus, the midpoint formula may be used to estimate the same area on an x-y plot. It is necessary to give an interval with a lower and upper border where the computed area will begin and stop, as well as the number of units, or subintervals, that the interval will be divided into when computing the area under the curve of a function. More rectangles enhance estimation precision (n).
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Give an equation for a logarithmic function that has the following features.
1. The range of the function is (-∞, ∞).
2. The domain of the function is (2, ∞).
3. The vertical asymptote of the function is = 2.
4. The graph does not cross through the point (3, 0).
Any equation in the variable x that contains a logarithm is called a logarithmic equation.
What are the features logarithmic function?The graphs of all logarithmic functions will have the following characteristics: The graph of logarithmic functions passes through the points (1,0). If the base of a logarithmic function is greater than 1, then the graph increases.Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ayLogarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos)Two kinds of logarithms are often used in chemistry: common (or Briggian) logarithms and natural (or Napierian) logarithms. The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number.To learn more about logarithmic function refers to:
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Please help I need help
Answer: e, a, f, c
Step-by-step explanation:
v evenly cuts through line tv and line VS. you can tell because the single line on each side....... rest should be correct
What should be added to x2 xy y2 to obtain 2x2 3xy class 7?
To obtain the equation 2x² + 3xy from x² xy y², you would need to add 1x² and 2xy to the original equation.
In order to obtain the equation 2x² + 3xy from x² xy y², you must add some terms to the original equation. The equation 2x² + 3xy represents a polynomial of degree 2, with x² and xy as the leading terms.
The original equation, x² xy y², is also a polynomial of degree 2, but it does not have the same leading terms as the desired equation.
By adding terms to the original equation, we can change the coefficients of the leading terms to match those of the desired equation. In this case, we need to add 1x² and 2xy to the original equation.
This can be simplified as x² + xy + y² + x² + 2xy = 2x² + 3xy. The polynomial x² and 2xy should be added to x² xy y² to get 2x² + 3xy.
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The diagram shows a sector of a circle radius 11cm angle of sector 135 degrees, show that the perimeter of the sector is greater than 47.5
the perimeter of the sector is not greater than 47.5.
What is Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given, a sector of a circle radius of 11 cm angle of sector 135 degrees
From the general formula of the Perimeter of the circle:
perimeter = 2 * pi * radius
In our case radius = 11 cm
Thus,
Perimeter = 2 * pi * 11
Primetime = 69.14
Since the arc is 135 degrees
Perimeter of arc = 135/360 * perimeter of whole circle
Perimeter of arc = 135/360 * 69.14
The perimeter of the arc = 25.925cm
Therefore, the perimeter of the sector is not greater than 47.5.
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What is the coefficient of X²Y in the product 7x² 5y X² 3y?
So, on solving the provided question, we can say that coefficient of X²Y in the product 7x² +5y +X²- 3y is 7
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of X²Y in the product 7x² +5y +X²- 3y is 7
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Carter walked for a while at three miles per hour, and then continued his journey on a bus travelling at 15 miles per hour. his time on the bus was twice as long as his time walking. how long did he ride on the bus if the total distance he covered was 66 miles? let t equal the time he walked (hours).
Answer: He rode on the bus for 3 hours
Step-by-step explanation:
1. We add 15 miles and 3 miles to get 18 miles.
2. Then 66/18 is 3.6666
3. Convert to whole number
Then 15x3 is 45
66-45 is 21
21/3=7
so he walked for 7 hours and rode the bus for 3 hours
The equation for line g is y = 14x – 44. Suppose lines g and h are perpendicular, and the point (–2, 1) lies on line h. Write an equation in standard form for line h.
Answer:
Line h is y = -(1/14)x + (8/7)
Step-by-step explanation: A perpendicular line will have a slope that is the negative inverse of the reference line. The reference line in this problem is y=14x-44. The slope of 14 is inverted to 1/14 and multiplied by -1 to yield a new slope of -(1/14) for the perpendicular line. The perpendicular line will have the form of y = -(1/14)x + b.
Any value of b will still result in a line perpendicular to y=14x-44. But we want a line for h that goes through point (-2,1). To find a value of b that moves the line so that it intersects (-2,1), substitute the value (-2,1) for (x,y) in the equation y = -(1/14)x + b, and then solve for b.
y= -(1/14)*(x) + b
1 = -(1/14)*(-2) + b for (-2,1)
1 = (2/14) + b
1- (1/7) = b
b = (6/7)
The equation for line h becomes y = -(1/14)x + (6/7)
See the attached worksheet.
Answer: x+14y=12
Step-by-step explanation: got this off an assignment on mcgrawhill still dont know how to get that tho good luck
Perform the operation and simply answer fully
Answer:
[tex]\frac{5}{24}[/tex]
Step-by-step explanation:
[tex]\frac{5x^3}{6}[/tex] × [tex]\frac{1}{4x^3}[/tex] ( cancel x³ on numerator/ denominator )
= [tex]\frac{5}{6}[/tex] × [tex]\frac{1}{4}[/tex]
= [tex]\frac{5(1)}{6(4)}[/tex]
= [tex]\frac{5}{24}[/tex]
what is the sum of the measure of the exterior angles of a regular dodecahon
Answer:
The measure of each exterior angle of a regular dodecagon will be =360∘12=30∘
Sophie plotted thee point in the coordinate plane: (1, 1), (–5, 1), (–3, 5), (–1, 5). What hape i created when thee vertice are connected?
Sophie plotted the point in the coordinate plane: (1, 1), (–5, 1), (–3, 5), (–1, 5) so, when the vertices are connected the shape formed is a rectangle.
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral.
Thus, when Sophie plotted the point in the coordinate plane: (1, 1), (–5, 1), (–3, 5), (–1, 5), the vertices connected form the shape of a rectangle.
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Find the radius of a circle in which the central angle, 0, is 60° and intercepts an arc of length 77 cm.
The radius is ?cm
The radius of the circle is 73.6 cm
What is length of an arc?Arc length is the distance between two points along a section of a curve or circle.It is the measure of the distance along a curved line. In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference.
The length of an arc is given tetha/360× 2πr
where r is the radius and
tetha is the angle
Therefore 77 = /360 ×2×3.14×r
77 = 1/6× 6.28r
multiply both sides by 6
77×6 = 6.28r
462 = 6.28r
divide both sides by 6.28
r = 462/6.28
r = 73.6cm
Therefore the radius of the circle is 73.6 cm
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Out of a journey of 300km;the firt part of ditance 85km i covered at a peed of 51km/h, the econd part of 90km at a peed of 135km/h and the remaining ditance at a peed of 75km/h. Find:
(1) the ditance covered at a peed of 75km/h. (2) the total time taken. (3) the average peed for the whole journey
125 km are traveled when traveling at a pace of 75 km/h.
The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.
Given that,
The first 85 kilometers are traveled at a 51 km/hr pace.
A pace of 135 km/hr is used to cover the second 90 km stretch.
75 km/hr is used to cover the remaining distance.
Journey distance is 300 kilometers.
Distance traveled at 75 km/hr is equal to 300 - (85 + 90) = 125 kilometers.
The total time required was 300/261 miles per hour, or 1.14 hours.
The distance traveled divided by the time required equals 300/1.14, or 263.15 kilometers per hour, as the average speed for the whole trip.
Thus, 125 km are traveled when traveling at a pace of 75 km/h.
The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.
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3. Which statement describes the
graphs of y = -x + 3 and y = -x + 6?
Answer:
They are parallel
Step-by-step explanation:
Ignore the +3 and the +6 for this problem because both of these graphs have an equal slope!
They both have a leading coefficient of -1, which means their slopes are equal. Because of this, they are parallel.
Here is a fun fact: If two graphs have the same slope (number in front of x) and have different y-intercepts (b values/constants added/subtracted) then they are parallel.
Hope this helps!
please help!
Find the measures of x and y. Explain your process
Using the fact that the sum of the interior angles of a triangle must be 180°, we will see that y = 70°, and x and y are vertical angles, so x = 70°.
How to find the measures of x and y?
First, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write a linear equation to find the value of y.
y° + 60° + 50° = 180°
We can solve that for y, we will get:
y° = 180° - 60° - 50°
y° = 180° - 110°
y° = 70°
Then the measure of angle y is 70 degrees.
Now, notice that angles x and y are vertical angles (have a common vertex but no common sides).
Vertical angles always have the same measure, then the measure of angle x is also 70°.
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Translate the sentence into an algebraic equation. Use x for the variable.
“The sum of a number and 4 is multiplied by 2 and the result is -30.”
Answer:
2(x+4)=-30
Step-by-step explanation: