Answer:
Step-by-step explanation:
Even though I have been teaching calculus and precalc for several years now, my mind automatically wants to think in degrees as opposed to radians. So I converted the angle from radians to degrees to get 315. This angle lies in QIV. The reference angle is a 45 degree angle, since 360 - 315 = 45. This is a 45 degree angle, but if you consider direction, measuring clockwise gives you a negative angle. So it could be that the reference angle needs to be identified as -45 degrees. It depends upon what lesson you are dealing with. Regardless, because this is a 45-45-90 right triangle, both the legs measure the same length (because of the Isosceles Triangle Theorem), which is 1. Therefore, if the angle is 45 degrees, then the tangent of it is 1/1 = 1.
NEED HELP WITH A MATH QUESTION
Answer:
[tex]x =18.0[/tex]
Step-by-step explanation:
To solve this problem use the Law of cosine.
The law of cosine says that:
[tex]c^2 = a^2 + b^2 -2abcos(C)[/tex]
In this case we have that:
[tex]c = x\\\\a=30\\\\b=16\\\\C=30\°[/tex]
Therefore
[tex]x^2 = 30^2 + 16^2 -2(30)(16)cos(30\°)[/tex]
[tex]x = \sqrt{30^2 + 16^2 -2(30)(16)cos(30\°)}[/tex]
[tex]x = \sqrt{1156 -831.38}[/tex]
[tex]x = \sqrt{324.62}[/tex]
[tex]x =18.0[/tex]
What conic section is defined by all points in a plane where the difference between the lengths of segments x and y remains constant?
Answer:
hyperbola
Step-by-step explanation:
If the sum is constant, the figure is an ellipse.
If the difference is constant, you get a hyperbola.
If one length is constant, you get a circle.
If the length to a point is the same as the length to a line, you get a parabola.
Answer:
There are four type of conic generated when a double napped cone is cut by a plane
1.Circle
2.Parabola
3.Ellipse
4.Hyperbola
Among these four, Hyperbola is the conic , ,all points in a plane where the difference between the lengths of segments x and y remains constant.
A point on Semi major Axis=(a,0),lying on the Hyperbola.
A point on Semi Minor axis =(0,b),not lying on the Hyperbola.
Take a point D lying on the hyperbola,and two points M and N not lying on the hyperbola.
DM-DN=2a(Length of major axis)
What is magma? a. The molten mixture of rock-forming substances, gases, and water from the mantle.. c. Hardened lava on the surface of the Earth. b. Liquid rock that reaches the surface. d. All of the above Please select the best answer from the choices provided A B C D
Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle
Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.
The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.
the function f(x)=18000(0.7)^x represents the penguin population on an island x years after it was first studied.what was the original population of the penguins on island?
Answer:
1800
Step-by-step explanation:
The original population occurs when time (i.e x) is zero.
hence we substitute x = 0 into the function
Original population, f(0),
= 1800 [tex](0.7)^{0}[/tex] .......... recall anything raised to power of zero is 1
= 1800 (1)
= 1800
The original population of the penguins on island be, 1800.
The correct option is (c)
What is function?A function is defined as a relation between a set of inputs having one output each. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given: f(x)=18000[tex](0.7)^{x}[/tex]
The original population will occurs when time is zero.
So, put x = 0 into the function f(x),
we have,
f(0)= 1800[tex](0.7)^{0}[/tex]
f(0)= 1800*1
f(0)=1800
Hence, the original population of the penguins on island is 1800.
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A group of numbers arranged in a specific order is called a sequence. Create two groups of numbers- one that can be classified as a sequence and another that cannot. Use complete sentences to differentiate between the two groups of numbers. In your final answer, include both groups of numbers and your explanation.
Answer:
1, 3, 6, 7, 9...
1, 4, 8, 7, 11...
Step-by-step explanation:
(1, 3, 6, 7, 9...)
This one is the sequence because it follows a specific pattern, which is 2n-1, or (2 x figure number) - 1. 1x2-1=1. 2x2-1=3. 3x2-1=7. And so on.
(1, 4, 8, 7, 11...)
This one, no matter how you look at it, has no pattern. Its not a proper sequence of numbers.
What is the value of x? A right angle is shown divided into two parts. The measure of one part of the right angle is 30 degrees. The measure of the other part is 4x
Answer:
x=15
Step-by-step explanation:
We know that a right angle is 90 degrees. When we subtract the 30 from 90, we get 60 degrees as the other, smaller angle. Then, we divide 60 by 4 to get 15. This mean x equals 15.
Which function has an inverse that is a function?
A. b(x)=x^2+3
B. d(x)=-9
C. -7x
D. p(x)=lxl
Answer:
C. -7x
Step-by-step explanation:
Only one of the offered choices passes the horizontal line test: at most one point of intersection with any horizontal line.
__
A: a parabola opening upward, so will have two points of intersection with a general horizontal line (only one at the vertex).
B: a horizontal line, so will have an infinite number of points of intersection with a horizontal line.
D. A "V-shaped" graph that will generally have two points of intersection with a horizontal line (only one at the vertex).
Answer:
m(x)=-7x C
Step-by-step explanation:
Edge
1. 112
2. 136
3. 68
4. 158
5. 129
Answer:
4. 158
Step-by-step explanation:
First let's make things a little simpler and put these arcs in terms of x. We know that the degree measure around the outside of a circle, regardless of its size, is 360. So let's say that arc BC is x. That means that arc BDC is 360 - x. This is because arc BC + arc BDC = 360. Substituting in our x's we have:
x + 360 - x = 360 and
360 = 360. (That's just the proof that putting in our x's as we did does in fact work!)
Following the formula then, we have
[tex]22=\frac{1}{2}(360-x-x)[/tex] and
[tex]22=\frac{1}{2}(360-2x)[/tex]
Multiply both sides by 2 to get rid of the fraction and get
44 = 360 - 2x
Subtract 360 rom both sides to get
-316 = -2x
Divide both sides by -2 to get that x = 158
Since we are looking for arc BC and we designated arc BC as our x, that means that arc BC = 158.
Describe the symmetry of the figure. Identify lines of symmetry, if any. Find the angle and the order of any rotational symmetry.
Answer:
(b) line symmetry only
Step-by-step explanation:
This question asks you to identify any applicable form of symmetry the given figure may have.
What is symmetry?For plane figures, three kinds of symmetry are defined:
symmetry about a pointsymmetry about a linerotational symmetryA figure is symmetrical about a point if that point is a midpoint between every point on the figure and a corresponding point on the figure.
A figure is symmetrical about a line if that line is the perpendicular bisector of the segment between any point on the figure and a corresponding point on the figure.
A figure has rotational symmetry if it can be rotated about a center and be congruent to itself. The number of different rotational angles for which this is true is the degree of the rotational symmetry.
Given figureThere is no point within the bounds of the figure that matches the definition of the center of symmetry about a point.
A vertical line through the center of the figure will serve as a line of symmetry. Each point on the left side of the line corresponds to a point on the right side of the line at the same distance. So, the figure has symmetry about a line.
There is no angle other than 360° through which the figure can be rotated to map to itself. It has no rotational symmetry.
I NEED HELP SAVE ME PLEASE!!
Answer:
Option D x=4
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{x-3}+1[/tex]
[tex]g(x)=2\sqrt{x-3}[/tex]
Solve the system by graphing
Remember that the solution of the system of equations (f(x)=g(x)) is the x-coordinate of the intersection point both graphs
The intersection point is (4,2)
therefore
x=4
see the attached figure
Please answer this question correctly for 35 points and brainliest!!
Answer:
11
Step-by-step explanation:
49-5=44
44/4=11
Which circle shows AB that measures 60 degrees?
I say the third circle from the top down. The central angle is the measure of minor arc AB.
The central angle here is 60 degrees, shown by the third circle down from the top. This is the right answer.
The circle that shows chord AB to measure 60 degrees is Option(C).
What is minor chord ?A chord of a circle divides the circle into two regions, which are called the segments of the circle. The minor chord is the shorter arc connecting two endpoints on a circle . The measure of a minor chord is always less than 180° .
How to identify chord AB to measure 60° ?In the four Options given alongside diagram, Option(C) represents a minor chord with its central angle subtended by the minor segment as 60°.
Thus AB is the minor sector of the circle and the angle measures 60° with that chord itself. The other three options do not define the minor chord or segment AB therefore not measuring its central angle.
Therefore, the circle that shows chord AB to measure 60 degrees is Option(C).
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Consider the sequence 130, 143, 156, 169, ... Write an explicit formula to represent the arithmetic sequence and use it to find the 13th term.
A. A(n) = 130 + (n-1)13; 286
B. A(n) = 130 + 13n; 299
C. A(n) = 130 + 13n; 286
D. A(n) = 130 + (n-1)13; 299
please help
Answer:
A(n)=130+13(n-1) ; 86
Step-by-step explanation:
Here is the sequence
130,143,156,169.......
the first term denoted by a is 130 and the common difference denoted by d is second term minus first term
143 - 130 = 13
Hence a=130 and d = 13
Now we have to evaluate to 13th term.
The formula for nth term of any Arithmetic Sequence is
A(n) = a+(n-1)d
Hence substituting the values of a ,and d get
A(n)=130+13(n-1)
To find the 13th term , put n = 13
A(13)=130+13*(13-1)
= 130+13*12
= 130+156
A(13) = 286
The amount that two groups of students spent on snacks in one day is shown in the dot plots below.
Which statements about the measures of center are true? Check all that apply.
The mean for Group A is less than the mean for Group B.
The median for Group A is less than the median for Group B.
The mode for Group A is less than the mode for Group B.
The median for Group A is 2.
The median for Group B is 3.
Answer:
I got B as my answer, hope it helps
The statements that are true about the measures of center are: Option B. The median for Group A is less than the median for Group B and Option C. The mode for Group A is less than the mode for Group B.
What is the median of a data set?The median of a data set is the middle value when the values are arranged in numerical order, or the average of the two middle values if the data set has an even number of elements.
For group A, the median falls between 1 and 2, thus, we can say the median = 1 + 2/2 = 1.5.
For group B, the median falls between 2 and 3, thus, we can say the median = 2 + 3/2 = 2.5.
The mode for group A is 1, while that of group B is 3, therefore, we can conclude that:
B. The median for Group A is less than the median for Group B, and
C. The mode for Group A is less than the mode for Group B.
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The height of the rectangle is multiplied by 4. What is the effect on the area?
Answer:
The new area is 4 times the original area
Step-by-step explanation:
we know that
The area of a rectangle is equal to
[tex]A=bh[/tex]
where
b is the base
h is the height
If the height is multiplied by 4
then
the new area is equal to
[tex]A=(b)(4h)[/tex]
[tex]A=4bh[/tex]
therefore
The new area is 4 times the original area
A deck of cards with four suits; hearts, diamonds, spades, and clubs. you pick one card, put it back and thennpick another card. what is the probability that the first card is a diamond and the second card is not a diamond
1. First, let us find the probability that the first card is a diamond.
Now, since we are given that there are four suits and there are, assumably, an equal number of cards in each suit, we can say that the probability of choosing a diamond card is 1/4. We can also write this out as such, where D = Diamond:
Pr(D) = no. of diamond cards / total number of cards
There are 52 cards in a deck, and 13 cards of each suit, thus:
Pr(D) = 13/52 = 1/4
2. Now we need to calculate the probability of not choosing a diamond as the second card.
In many cases, when given a problem that requires you to find the probability of something not happening, it may be easier to set it out as such:
Pr(A') = 1 - Pr(A)
ie. Pr(A not happening, or not A) = 1 - Pr(A happening, or A)
This works because the total probability is always 1 (100%), and it makes sense that to find the probability of A not happening, we take the total probability and subtract the probability of A actually happening.
Thus, given that we have already calculated that the probability of choosing a Diamond is 1/4, we can now set this out as such:
Pr(D') = 1 - Pr(D)
Pr(D') = 1 - 1/4
Pr(D') = 3/4
3. Now we come to the final step. To find the probability of something and then something else happening, we must multiply the two probabilities together. Thus, given that Pr(D) = 1/4 and Pr(D') = 3/4, we get:
Pr(D)*Pr(D') = (1/4)*(3/4)
= 3/16
Thus, the probability of choosing a diamond as the first card and then not choosing a diamond as the second card is 3/16.
The first card is a diamond and the second card is not a diamond when drawing cards with replacement from a standard deck is 3/16.
The subject of this question is probability, a topic in Mathematics, specifically dealing with the calculation of the likelihood of certain outcomes when drawing cards from a deck. To find the probability that the first card is a diamond and the second card is not a diamond when each card is replaced after being drawn, we must consider two independent events. The probability of drawing a diamond card from a standard deck of 52 cards is 1/4, since there are 13 diamonds out of 52 cards. Because the card is replaced, the probability that the second card is not a diamond remains the same as for any single draw where the desired outcome is not a diamond, which is 39/52 or 3/4. Thus, the combined probability of both events happening in sequence (first drawing a diamond, then drawing a non-diamond) is determined by multiplying the probabilities of individual events: (1/4) × (3/4) = 3/16.
how much larger then 1/4 mile is 9/10 mile please show work
Answer:
13/20 = 0.65 mile
Step-by-step explanation:
Finding the difference of two fractions is usually done by first expressing each of them using a common denominator. Here, both 4 and 10 are factors of 20, so 20 is a suitable common denominator.
9/10 - 1/4 = 18/20 - 5/20 = (18 -5)/20 = 13/20
This can be expressed as a decimal:
13/20 = (13·5)/(20·5) = 65/100 = 0.65
9/10 of a mile is 13/20 of a mile larger than 1/4 of a mile. In decimal, that is 0.65 miles larger.
A vegetable garden and a surrounding path are shaped like a square together are 12 ft wide. The path is 1 feet wide. If one bag of gravel covers 8 square feet, how manu bags are needed to cover the path? Round your answers to the nearest tenth.
Step-by-step answer:
There are two squares, the inner one of which is a garden, surrounded by a path 1 foot wide.
The outer square represents the periphery of the path, as shown in the attached image.
One bag of gravel covers 8 square-feet. Need the number of bags required to cover the path.
Solution:
We first need to find the total area of the path by subtracting the area of garden from the overall area, namely the outer square.
Area of path = 12^2 - 10^2 = 144-100 = 44 sq. ft.
Number of bags required
= area (sq.ft) / area each bag covers
= 44 sq.ft / 8 (sq.ft / bag)
= 5.5 bags
Answer: 6 bags need to be purchased.
in order to come up with a realistic schedule, a manager wants to know how long it usually takes an employee to complete a task. which statistical measurement is the manager most likely to use? A. mean B. median C. mode D. sum
Answer:
A. mean
Step-by-step explanation:
The mean of data is given by the ratio of the sum of all the values to the total number of values. It gives the average value of the set of values.
[tex]\bar{x}=\frac{1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)[/tex]
Here, the manager wants to get an estimate of how much time it takes by each employee to complete a task. The mean will be the sum of time taken by each person to complete a task divided by the number of employees.
Hello, I need help in a compound inequality word problem:
Emily is three years older than twice her sister Mary's age. The sum of their ages is less than 30.
Let x represent Mary's age.
Which inequality represents Mary's possible age?
1. 0
2.0
3.0
4.0
Answer:
3+2x<30
Step-by-step explanation:
3 represents that Emily is 3 years older than 2x
2x represents twice Mary's age
<30 represents that it's always less than 30
Answer:
The compound inequality is [tex]0<x<9[/tex]
Step-by-step explanation:
Consider the provided information.
It is given that Emily is three years older than twice her sister Mary's age.
Let x represent Mary's age.
Then the age of Emily is: 2x+3
The sum of their ages is less than 30.
This can be written as:
[tex]2x+3+x<30[/tex]
[tex]3x+3<30[/tex]
[tex]3x<27[/tex]
[tex]x<9[/tex]
As we know the age can't be a negative number.
Therefore, the age of Mary must be a positive number greater than 0.
Thus, the compound inequality is [tex]0<x<9[/tex]
WILL MARK BRAINLIEST!
Which relation is a function?
Answer:
A
Step-by-step explanation:
A function is not allowed to have two Y values for the same X value. Any table with the same X value appearing more than once is not a function. Only table A qualifies as a function.
Need help with math question
Answer:
1.4%
Step-by-step explanation:
You can only include 7 and 8 in the answer because it didn't include 6 in the question. add the frequency for both of those sizes (14) and divide by the total (1000) to get the probability. multiply by 100 to get answer as a percent. 1.4%
Answer:
1%
Step-by-step explanation:
We are given the results of survey of one thousand families to determine the distribution of families by their size.
We are to find the probability (in percent) that a given family has more than 6 people.
Frequency of people with more than 6 people = 10 + 4 = 14
Total frequency = 1000
P (families with more than 6 people) = (14 / 1000) × 100 = 1.4% ≈ 1%
The area of a parking lot is 805 square meters. A car requires 5 meters and a bus requires 32 square meters of space. There can be at most 80 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how many should be in the lot to maximize income?
Answer:
80 cars will maximize revenue
Step-by-step explanation:
The revenue per square meter for parked cars is ...
$2.00/5 = $0.40
The revenue per square meter for buses is ...
$6.00/32 = $0.1875
Thus the available space should be used to park the maximum number of cars.
80 cars should be in the lot to maximize income.
To maximize income, the parking lot should have 69 cars and 11 buses parked, resulting in a total income of $282.
To maximize income, we need to maximize the revenue generated from parking fees. Let's denote the number of cars as x and the number of buses as y.
Given:
- Area of parking lot: 805 square meters
- Space required for a car: 5 square meters
- Space required for a bus: 32 square meters
- Maximum number of vehicles: 80
We have the following constraints:
1. [tex]\( 5x + 32y \leq 805 \)[/tex] (total area constraint)
2. [tex]\( x + y \leq 80 \)[/tex] (maximum number of vehicles constraint)
The objective function to maximize income is:
Income [tex]\( I = 2x + 6y \)[/tex]
To solve this problem, we'll analyze the feasible region defined by these constraints and find the combination of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that maximizes income.
By solving these constraints, we find that the maximum income occurs at the vertex where [tex]\( x = 69 \) and \( y = 11 \)[/tex].
Therefore, to maximize income, there should be 69 cars and 11 buses parked in the lot.
Anyone know scale factor?
Answer:
B.3
Step-by-step explanation:
If you divide 36 by 12 or 27 by 9 or 21 by 7, you get 3, which means that triangle ABC is 3 times as large as triangle XYZ.
For this case it is observed that the measures of the small triangle are smaller than those of the large triangle, so we have to use a division scale factor. We have to:
[tex]xy = \frac {AB} {3} = \frac {27} {3} = 9\\yz = \frac {BC} {3} = \frac {36} {3} = 12\\xz = \frac {AC} {3} = \frac {21} {3} = 7[/tex]
It is observed that the factor used was [tex]\frac {1} {3}.[/tex]
ANswer:
Option D
Please help, I honestly have no clue if it's each or none.
Answer:
C there is no mode
Step-by-step explanation:
The mode is the number that appears most often. Since there is no number that appears more than once, there is no mode
Which of the following represents the translation of D(−5,4) along vector <6,−8> and its reflection across the y-axis?
Answer:
D (-5 , 4) → D' (1 , -4) → D" (-1 , -4) ⇒ 2nd answer
Step-by-step explanation:
* Lets revise some transformation
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is(x , y - k)
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
* Now lets solve the problem
- The point D is (-5 , 4)
- The vector of the translation is <6 , -8>
∵ 6 is positive number
∴ Point D will translate horizontally 6 units to the right
∵ x-coordinate of D = -5
- Add the x-coordinate of D by 6 to find the x-coordinate of D'
∴ The x-coordinate of D' = -5 + 6 = 1
∴ The x-coordinate of D' = 1
∵ -8 is negative number
∴ Point D will translate vertically 8 units down
∵ y-coordinate of D = 4
- Add the y-coordinate of D by -8 to find the y-coordinate of D'
∴ The y-coordinate of D' = 4 + -8 = -4
∴ The y-coordinate of D' = -4
∴ The coordinates of D' are (1 , -4)
- If point (x , y) reflected across the y-axis then its image is (-x , y)
∵ D' is reflected across the y-axis
∵ D' = (1 , -4)
- Change the sign of its x-coordinate
∴ D" = (-1 , -4)
∴ The coordinates of D" are (-1 , -4)
* D (-5 , 4) → D' (1 , -4) → D" (-1 , -4)
Answer:
D (−5, 4) → D ′(1, −4) → D ″(−1, −4)
Step-by-step explanation:
Use the translation vector <6,−8> to determine the rule for translation of the coordinates: (x,y)→(x+6,y+(−8)).
Apply the rule to translate point D(−5,4).
D(−5,4)→(−5+6,4+(−8))→D'(1,−4).
To apply the reflection across y-axis use the rule for reflection: (x,y)→(−x,y).
Apply the reflection rule to point D'(1,−4).
D'(1,−4)→D''(−1,−4).
Therefore, D(−5,4)→D'(1,−4)→D''(−1,−4) represents the translation of D(−5,4) along vector <6,−8> and its reflection across the y-axis.
Two students from a group of eight boys and 12 girls are sent to represent the school in a parade.If the students are chosen at random, what is the probability that the students chosen are not both girls?a. 12/190b. 33/95c. 62/95d. 178/190
Answer:
The probability that the students chosen are not both girls is 62/95 ⇒ (c)
Step-by-step explanation:
* Lets explain how to find the probability of an event
- The probability of an Event = Number of favorable outcomes ÷ Total
number of possible outcomes
- P(A) = n(E) ÷ n(S) , where
# P(A) means finding the probability of an event A
# n(E) means the number of favorable outcomes of an event
# n(S) means set of all possible outcomes of an event
- Probability of event not happened = 1 - P(A)
- P(A and B) = P(A) . P(B)
* Lets solve the problem
- There is a group of students
- There are 8 boys and 12 girls in the group
∴ There are 8 + 12 = 20 students in the group
- The students are sent to represent the school in a parade
- Two students are chosen at random
∴ P(S) = 20
- The students that chosen are not both girls
∴ The probability of not girls = 1 - P(girls)
∵ The were 20 students in the group
∵ The number of girls in the group was 12
∴ The probability of chosen a first girl = 12/20
∵ One girl was chosen, then the number of girls for the second
choice is less by 1 and the total also less by 1
∴ The were 19 students in the group
∵ The number of girls in the group was 11
∴ The probability of chosen a second girl = 11/19
- The probability of both girls is P(1st girle) . P(2nd girl)
∴ The probability of both girls = (12/20) × (11/19) = 33/95
- To find the probability of both not girls is 1 - P(both girls)
∴ P(not both girls) = 1 - (33/95) = 62/95
* The probability that the students chosen are not both girls is 62/95
what is the exponential form of log5 9 = x?
Step-by-step explanation:
log₅ 9 = x
5^(log₅ 9) = 5^x
9 = 5^x
The total cost to rent a row boat is $14 times the number of hours the boat is used. Write an equation to model this situation if c= total cost and h= number of hours.
Answer:
14h=c
Step-by-step explanation:
14 times total hours boat of used (h) is the total cost of the boat > 14h=c
Complete the equation to show two equivalent expressions.
g2 – 4g – 21 = (g – )(g + )
Answer:
[tex]g^2-4g-21=(g-7)(g+3)[/tex]
Step-by-step explanation:
To complete the left side of the equation, we need to bring it to the form
[tex](g-a)(g+b)[/tex]
expanding this expression we get:
[tex]g^2+bg-ag-ab[/tex]
[tex]g^2+(b-a)g-ab[/tex]
Thus we have
[tex]g^2-4g-21=g^2+(b-a)g-ab[/tex]
from here we see that for both sides of the equation to be equal, it must be that
[tex]b-a=-4[/tex]
[tex]-ab=-21[/tex].
Getting rid of the negative signs we get:
[tex]a-b=4[/tex]
[tex]ab=21[/tex]
At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for [tex]a[/tex] and [tex]b[/tex] systematically.
The solutions to this set are [tex]a=7[/tex] and [tex]b=3[/tex]. (you have to guess on this—it's easier)
Therefore, we have
[tex](g-a)(g+b)=(g-7)(g+3)[/tex]
which completes our equation
[tex]\boxed{ g^2-4g-21=(g-7)(g+3)}[/tex]
Answer: -7 and +3
did the assignment